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PDFThe Organon
Aristotle
Edited by Roger Bishop Joneswww.rbjones.com
ISBN-10: 1478305622ISBN-13: 978-1478305620
First RBJones.com edition. Revision: 1.12 Date: 2012-09-26 08:53:34
Contents
Contents iii
Preface xiii
Volume 1 CATEGORIES 1Book I The Categories . . . . . . . . . . . . . . . . . . . . . . . 1
Part 1 Equivocally, univocally and derivatively . . . . . . . 1Part 2 Presence and predication . . . . . . . . . . . . . . . . 1Part 3 Subclasses and predicability . . . . . . . . . . . . . . 2Part 4 Expressions . . . . . . . . . . . . . . . . . . . . . . . 2Part 5 Substance . . . . . . . . . . . . . . . . . . . . . . . . . 3Part 6 Quantity . . . . . . . . . . . . . . . . . . . . . . . . . 8Part 7 Relation . . . . . . . . . . . . . . . . . . . . . . . . . . 11Part 8 Quality . . . . . . . . . . . . . . . . . . . . . . . . . . 16Part 9 Action, affection, position, rest, time, place, state . . 20Part 10 Opposite, contrary, privative, positive . . . . . . . . 21Part 11 Contrary . . . . . . . . . . . . . . . . . . . . . . . . . 25Part 12 Prior . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26Part 13 Simultaneous . . . . . . . . . . . . . . . . . . . . . . 27Part 14 Motion . . . . . . . . . . . . . . . . . . . . . . . . . . 28Part 15 To have . . . . . . . . . . . . . . . . . . . . . . . . . . 29
Volume 2 ON INTERPRETATION 31Book I On Interpretation . . . . . . . . . . . . . . . . . . . . . . 31
Part 1 Language, thought, truth; . . . . . . . . . . . . . . . 31Part 2 Nouns . . . . . . . . . . . . . . . . . . . . . . . . . . . 31Part 3 Verbs . . . . . . . . . . . . . . . . . . . . . . . . . . . 32Part 4 Sentences and propositions . . . . . . . . . . . . . . 33Part 5 Simple and composite propositions . . . . . . . . . . 33Part 6 Affirmation, denial, contradictories . . . . . . . . . . 34Part 7 Universal and individual subjects . . . . . . . . . . . 34Part 8 Single affirmations . . . . . . . . . . . . . . . . . . . 36
iv CONTENTS
Part 9 Necessity and contradiction . . . . . . . . . . . . . . 36Part 10 Affirmation or denial requires a noun and a verb . . 39Part 11 Concerning the unity of affirmations . . . . . . . . . 42Part 12 Asserting or denying possibility, contingency, impos-
sibility, necessity . . . . . . . . . . . . . . . . . . . . . 44Part 13 Possibility and contingency . . . . . . . . . . . . . . 46Part 14 Contrary and contradictory . . . . . . . . . . . . . . 50
Volume 3 PRIOR ANALYTICS 53Book I The syllogism defined . . . . . . . . . . . . . . . . . . . 53
Part 1 Perfect and imperfect syllogisms . . . . . . . . . . . 53Part 2 Premisses, their modes and conversions . . . . . . . 54Part 3 Universal and possible premisses . . . . . . . . . . . 55Part 4 The first figure . . . . . . . . . . . . . . . . . . . . . . 56Part 5 The second figure . . . . . . . . . . . . . . . . . . . . 58Part 6 The third figure . . . . . . . . . . . . . . . . . . . . . 60Part 7 The relation between the figures . . . . . . . . . . . . 62Part 8 Necessity, actuality and possibility . . . . . . . . . . 63Part 9 Syllogisms with some necessary premisses . . . . . 64Part 10 The second figure with one necessary premiss . . . 65Part 11 The third figure with one necessary premiss . . . . . 66Part 12 Simple conclusions and necessary conclusions . . . 67Part 13 Proof of or from possibility . . . . . . . . . . . . . . . 68Part 14 Reasoning about possibilities . . . . . . . . . . . . . 69Part 15 Possibility, impossibility . . . . . . . . . . . . . . . . 71Part 16 One premiss necessary, the other problematic . . . . 74Part 17 Second figure, both premisses problematic . . . . . . 76Part 18 One premiss assertoric, the other problematic . . . . 77Part 19 One necessary, other problematic, negative necessary 78Part 20 Both or only one of the premisses is problematic . . 80Part 21 One premiss pure, the other problematic . . . . . . . 81Part 22 One necessary, other problematic, premisses affirma-
tive . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82Part 23 Every syllogism is formed through these figures . . 83Part 24 One premiss must be affirmative, one universal . . . 84Part 25 Every demonstration proceeds through three terms 85Part 26 What sort of problem is difficult to prove . . . . . . 87Part 27 How to reach the principles relative to the problem 88Part 28 To establish something about a whole, look to the
subjects . . . . . . . . . . . . . . . . . . . . . . . . . . 90Part 29 Impossible conclusions and ostensive syllogisms . . 92Part 30 On method, in relation to choice of premisses . . . . 94
CONTENTS v
Part 31 Division into classes is a small part of the method . 94Part 32 Reducing syllogisms to the figures . . . . . . . . . . 96Part 33 On the necessity of syllogistic inference . . . . . . . 97Part 34 Not setting out the terms of the premiss well . . . . 98Part 35 Terms need not be single words . . . . . . . . . . . . 98Part 36 Relations between the terms in a syllogism . . . . . 99Part 37 Predication and categories . . . . . . . . . . . . . . . 100Part 38 Terms repeated in the premisses . . . . . . . . . . . . 100Part 39 Exchanging terms . . . . . . . . . . . . . . . . . . . . 101Part 40 Good and The Good . . . . . . . . . . . . . . . . . . 101Part 41 Transitivity of belonging . . . . . . . . . . . . . . . . 101Part 42 On figures . . . . . . . . . . . . . . . . . . . . . . . . 102Part 43 Proving some part of a definition . . . . . . . . . . . 102Part 44 We must not try to reduce hypothetical syllogisms . 102Part 45 Reduction of syllogisms between figures . . . . . . . 103Part 46 ’not to be this’ and ’to be not-this’ differ in meaning 105
Book II Aspects and properties of the syllogism . . . . . . . . . 108Part 1 The reason common to all syllogisms . . . . . . . . . 108Part 2 Truth and falsity of premiss and conclusion . . . . . 109Part 3 Reaching true conclusions from false premisses . . . 112Part 4 Circular and reciprocal proof . . . . . . . . . . . . . 116Part 5 In the second figure . . . . . . . . . . . . . . . . . . . 118Part 6 In the third figure . . . . . . . . . . . . . . . . . . . . 118Part 7 Conversion of syllogisms . . . . . . . . . . . . . . . . 120Part 8 In the second figure . . . . . . . . . . . . . . . . . . . 121Part 9 In the third figure . . . . . . . . . . . . . . . . . . . . 122Part 10 The syllogism per impossibile . . . . . . . . . . . . . 123Part 11 First figure problems proved per impossibile . . . . 125Part 12 Similarly in the last figure . . . . . . . . . . . . . . . 126Part 13 Demonstration per impossibile differs from ostensive
proof . . . . . . . . . . . . . . . . . . . . . . . . . . . 126Part 14 Drawing a conclusion from opposed premisses . . . 128Part 15 Begging the question . . . . . . . . . . . . . . . . . . 130Part 16 Proof by reductio . . . . . . . . . . . . . . . . . . . . 131Part 17 A false argument depends on its first false statement 133Part 18 Do not allow the same term twice in premisses . . . 133Part 19 When refutation will be possible and when impossible 133Part 20 Deception in the arrangement of the terms . . . . . . 134Part 21 Whenever the extremes are convertible . . . . . . . . 136Part 22 Rhetorical syllogism and induction . . . . . . . . . . 138Part 23 When the major term belongs to the middle . . . . . 138Part 24 Reduction . . . . . . . . . . . . . . . . . . . . . . . . 139
vi CONTENTS
Part 25 Objection . . . . . . . . . . . . . . . . . . . . . . . . . 139Part 26 Probability . . . . . . . . . . . . . . . . . . . . . . . . 141
Volume 4 POSTERIOR ANALYTICS 143Book I Posterior Analytics . . . . . . . . . . . . . . . . . . . . . 143
Part 1 Proceeding from pre-existent knowledge . . . . . . 143Part 2 Unqualified scientific knowledge . . . . . . . . . . . 144Part 3 Terminating regress in indemonstrable premisses . . 146Part 4 Scientific knowledge must rest on essential premisses 148Part 5 Failure of commensurate universality . . . . . . . . 150Part 6 Demonstrative knowledge rests on necessary truths 151Part 7 No demonstration may pass from one genus to an-
other . . . . . . . . . . . . . . . . . . . . . . . . . . . 154Part 8 Commensurately universal premisses yield eternal
conclusions . . . . . . . . . . . . . . . . . . . . . . . . 154Part 9 Attribute demonstration only from ’appropriate’ ba-
sic truths . . . . . . . . . . . . . . . . . . . . . . . . . 155Part 10 Basic truths, peculiar (to a genus), and common (to all) 156Part 11 Existence of forms, contradiction, excluded middle . 158Part 12 There are distinctively scientific questions . . . . . . 159Part 13 Knowledge of the fact differs from knowledge of the
reasoned fact . . . . . . . . . . . . . . . . . . . . . . . 161Part 14 Of all the figures the most scientific is the first . . . . 162Part 15 Atomic connexions and disconnexions . . . . . . . . 163Part 16 Ignorance is error produced by inference . . . . . . 164Part 17 Attributes not atomically connected or disconnected 165Part 18 Demonstration develops from universals, induction
from particulars . . . . . . . . . . . . . . . . . . . . . 167Part 19 Every syllogism is effected by means of three terms 167Part 20 Middle terms cannot be infinite in number . . . . . 169Part 21 That the regress of middles terminates . . . . . . . . 169Part 22 Dialectical considerations . . . . . . . . . . . . . . . 170Part 23 Some corollaries . . . . . . . . . . . . . . . . . . . . . 173Part 24 Universal demonstration is better than particular . . 175Part 25 Affirmative demonstration excels negative . . . . . 178Part 26 Negative demonstration and reductio ad impossibile 179Part 27 Exactness and priority in science . . . . . . . . . . . 180Part 28 A single science is one whose domain is a single genus 180Part 29 One can have several demonstrations of the same
connexion . . . . . . . . . . . . . . . . . . . . . . . . 181Part 30 There is no knowledge by demonstration of chance
conjunctions . . . . . . . . . . . . . . . . . . . . . . . 181
CONTENTS vii
Part 31 Knowledge of things demonstrable cannot be ac-quired by perception . . . . . . . . . . . . . . . . . . 181
Part 32 Basic truths are not limited in number . . . . . . . . 182Part 33 Scientific knowledge differs from opinion . . . . . . 184Part 34 Quick wit is a faculty of hitting upon the middle term
instantaneously . . . . . . . . . . . . . . . . . . . . . 185Book II Posterior Analytics . . . . . . . . . . . . . . . . . . . . . 186
Part 1 Four kinds of question . . . . . . . . . . . . . . . . . 186Part 2 Whether a connexion is a fact . . . . . . . . . . . . . 186Part 3 How essential nature is revealed . . . . . . . . . . . 188Part 4 Whether syllogism is possible . . . . . . . . . . . . . 189Part 5 The method of division a not a process of inference 190Part 6 The definable form must not fall within the syllogism 191Part 7 How then by definition shall we prove essential na-
ture? . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192Part 8 Whether essential nature is demonstrable . . . . . . 193Part 9 There are essential natures which are immediate . . 195Part 10 Defining definition . . . . . . . . . . . . . . . . . . . 195Part 11 We have scientific knowledge when we know the
cause . . . . . . . . . . . . . . . . . . . . . . . . . . . 196Part 12 Middle term as cause . . . . . . . . . . . . . . . . . . 198Part 13 The elements predicated as constituting the definable
form . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200Part 14 The method of selection of analyses and divisions . 204Part 15 Identical and subordinate connexions . . . . . . . . 205Part 16 Whether, when the effect is present the cause also is
present . . . . . . . . . . . . . . . . . . . . . . . . . . 205Part 17 Must identical effects have identical causes? . . . . . 206Part 18 Which of multiple middles is the cause? . . . . . . . 208Part 19 How basic premisses become known. . . . . . . . . 208
Volume 5 TOPICS 211Book I Preliminary considerations . . . . . . . . . . . . . . . . 211
Part 1 What reasoning is . . . . . . . . . . . . . . . . . . . . 211Part 2 For what purposes the treatise is useful . . . . . . . 212Part 3 On the way to proceed . . . . . . . . . . . . . . . . . 213Part 4 Of what parts our inquiry consists . . . . . . . . . . 213Part 5 Definition, property, genus, and accident . . . . . . 214Part 6 Remarks made in criticism of definitions . . . . . . . 215Part 7 Senses borne by the term ’Sameness’ . . . . . . . . . 216Part 8 Confirming the senses of ’definition’ . . . . . . . . . 217Part 9 Categories of predicate . . . . . . . . . . . . . . . . . 217
viii CONTENTS
Part 10 Dialectical propositions and problems . . . . . . . . 218Part 11 Theses . . . . . . . . . . . . . . . . . . . . . . . . . . . 219Part 12 Species of dialectical arguments . . . . . . . . . . . . 220Part 13 Four sources of arguments . . . . . . . . . . . . . . . 221Part 14 Three divisions of propositions and problems . . . . 221Part 15 The number of senses a term bears . . . . . . . . . . 222Part 16 Difference should be examined in same genera . . . 226Part 17 Likeness should be studied in different genera . . . 226Part 18 It is useful to study difference in meaning of a term 227
Book II On various argumentative techniques . . . . . . . . . . 228Part 1 Of problems some are universal, others particular . 228Part 2 Mistaken accidental ascription . . . . . . . . . . . . . 229Part 3 Attributions to terms used in several senses . . . . . 231Part 4 It is well to alter a term into one more familiar . . . 232Part 5 Drawing an opponent into a refutable statement . . 234Part 6 On dichotomies . . . . . . . . . . . . . . . . . . . . . 235Part 7 Contraries and their conjunctions . . . . . . . . . . . 236Part 8 Look for arguments among contradictories . . . . . 238Part 9 Co-ordinates and inflected forms of the terms . . . . 239Part 10 Look at things which are like the subject . . . . . . . 240Part 11 Matters of degree . . . . . . . . . . . . . . . . . . . . 242
Book III Which is the more desirable of two or more things . . . 243Part 1 In themselves . . . . . . . . . . . . . . . . . . . . . . 243Part 2 In their consequences . . . . . . . . . . . . . . . . . . 245Part 3 The particular virtue of species . . . . . . . . . . . . 248Part 4 The more desirable is desirable . . . . . . . . . . . . 249Part 5 Comparative degrees and amounts . . . . . . . . . . 250Part 6 Universals entail particulars . . . . . . . . . . . . . . 250
Book IV The relationship between genus and species . . . . . . 253Part 1 Species are distinguished by essential properties . . 253Part 2 Species falling under more than one genus . . . . . 256Part 3 Species partaking of contratries of the genus . . . . 259Part 4 Things that bear a like relation to one another . . . . 261Part 5 Placing what is a ’state’ inside the genus ’activity’ . 264Part 6 If the term rendered fails to be the genus of anything 267
Book V Whether an attribute is or is not a property . . . . . . . 270Part 1 Essential and Relative Properties . . . . . . . . . . . 270Part 2 Correct rendition of properties . . . . . . . . . . . . 272Part 3 Correct rendition of properties (continued) . . . . . 275Part 4 Whether what is stated is or is not a Property . . . . 278Part 5 Natural properties cannot be essential . . . . . . . . 281Part 6 The point of view of the respective opposites . . . . 284
CONTENTS ix
Part 7 The point of view of things that are in a like relation 287Part 8 The point of view of greater and less degrees . . . . 289
Book VI The discussion of definitions . . . . . . . . . . . . . . . 292Part 1 The five parts of the discussion of definitions . . . . 292Part 2 Obscurity . . . . . . . . . . . . . . . . . . . . . . . . . 293Part 3 Redundancy . . . . . . . . . . . . . . . . . . . . . . . 294Part 4 Intelligibility, priority, circularity . . . . . . . . . . . 296Part 5 When an object in a genus has not been placed in it 299Part 6 Whether the differentiae be those of the genus . . . 300Part 7 Whether application of a term is consistent with its
definition . . . . . . . . . . . . . . . . . . . . . . . . . 305Part 8 Definitions of terms which are relative . . . . . . . . 306Part 9 Definitions of state, of relatives, of contraries . . . . 307Part 10 Like inflexions, ambiguous terms . . . . . . . . . . . 309Part 11 Complex terms, equimembrals . . . . . . . . . . . . 310Part 12 Reality, relatives, imperfection, desirables . . . . . . 312Part 13 Product and sum . . . . . . . . . . . . . . . . . . . . 313Part 14 Definitions as composites or contraries . . . . . . . . 315
Book VII Whether two things are ’the same’ or ’different’ . . . . 317Part 1 Inflections, accidents, categories, degrees... . . . . . 317Part 2 Constraints on definitions apply to sameness . . . . 319Part 3 Reasoning to a thing’s definition . . . . . . . . . . . 319Part 4 The most handy of the commonplace arguments . . 321Part 5 It is more difficult to establish than to overthrow a
definition . . . . . . . . . . . . . . . . . . . . . . . . . 322Book VIII Arrangement and method in posing questions . . . . . 324
Part 1 The premisses which have to be adopted . . . . . . . 324Part 2 Syllogism and demonstration versus induction . . . 328Part 3 Sources of difficulty in discussion . . . . . . . . . . . 330Part 4 The business of a good answerer . . . . . . . . . . . 332Part 5 Premisses generally accepted or rejected without
qualification . . . . . . . . . . . . . . . . . . . . . . . 332Part 6 What the aims of the answerer should be . . . . . . 334Part 7 Terms used obscurely . . . . . . . . . . . . . . . . . . 335Part 8 A premiss relates to a constituent in the reasoning . 335Part 9 Before advancing a position, test it . . . . . . . . . . 336Part 10 Demolish the point on which the fallacy depends . . 336Part 11 Five kinds of criticism of arguments . . . . . . . . . 337Part 12 An argument is called fallacious in four senses . . . 340Part 13 People seem to beg their original question in five ways 341Part 14 Training and practice in arguments . . . . . . . . . . 342
x CONTENTS
Volume 6 ON SOPHISTICAL REFUTATIONS 345Section I Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 345
Part 1 Distinguishing between genuine and sophistical ar-guments . . . . . . . . . . . . . . . . . . . . . . . . . 345
Part 2 Four kinds of arguments used in discussion . . . . . 346Section II Sophistical questions and arguments . . . . . . . . . . 347
Part 3 Five objectives of argument . . . . . . . . . . . . . . 347Part 4 Six sophistical methods involving language . . . . . 347Part 5 Seven fallacies unconnected with language . . . . . 349Part 6 Further discussion of these sophistical refutations . 352Part 7 On the sources of these fallacies . . . . . . . . . . . . 355Part 8 Apparent and sophistical syllogisms . . . . . . . . . 356Part 9 Scientific and dialectical reasoning . . . . . . . . . . 357Part 10 Argument against the word, and against the thought 358Part 11 Dialectical versus contentious and sophistical reason-
ing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 360Part 12 Exposing fallacious and paradoxical sophisms . . . 363Part 13 Making someone babble . . . . . . . . . . . . . . . . 364Part 14 Solecism . . . . . . . . . . . . . . . . . . . . . . . . . 365Part 15 How to ask questions effectively . . . . . . . . . . . 366
Section III Responding to sophistical arguments . . . . . . . . . . 368Part 16 Sophistries must be answered as well as understood 368Part 17 Refutation by fraudulent artifice, equivocation, am-
phiboly . . . . . . . . . . . . . . . . . . . . . . . . . . 369Part 18 Making a distinction versus demolishing a premiss 372Part 19 Equivocal premisses versus equivocal conclusions . 373Part 20 Fallacies involving division and combination of words 374Part 21 Accentuation . . . . . . . . . . . . . . . . . . . . . . . 375Part 22 Identical expressions for distinct things . . . . . . . 375Part 23 Summary on answers for arguments depending on
language . . . . . . . . . . . . . . . . . . . . . . . . . 378Part 24 Dealing with arguments which depend on accident 378Part 25 Arguments depending on expressions not valid abso-
lutely . . . . . . . . . . . . . . . . . . . . . . . . . . . 380Part 26 Comparing the conclusion with its contradictory . . 382Part 27 Begging the question . . . . . . . . . . . . . . . . . . 382Part 28 Refutations reaching their conclusion through the
consequent . . . . . . . . . . . . . . . . . . . . . . . . 383Part 29 Refutations whose reasoning depends on some addi-
tion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 383Part 30 Refutations which make several questions into one . 383Part 31 Those who draw one into repetition . . . . . . . . . 384
CONTENTS xi
Part 32 Refuting solecisms . . . . . . . . . . . . . . . . . . . 385Part 33 Degrees of difficulty in refutation of fallacies . . . . 386
Section IV Epilogue . . . . . . . . . . . . . . . . . . . . . . . . . . . 388Part 34 Review and conclusions . . . . . . . . . . . . . . . . 388
Index 391
Preface
The works of Aristotle on logic have traditionally been referred to collec-tively as “The Organon”. This bare-bones English language edition of thoseworks was prepared for my own use when I sought but failed to find a edi-tion suitable for my purposes, and is now made generally available.
The translations from the original Greek sources were undertaken, dur-ing the first half of the 20th Century, under the general editorship of SirDavid Ross by:
E. M. Edghill (Categories and On Interpretation)A. J. Jenkinson (Prior Analytics)G. R. G. Mure (Posterior Analytics)W. A. Pickard-Cambridge (Topics and On Sophistical Refutations)
The translations were transformed into a form suitable for typesetting (inPalatino 10pt typeface) using LATEX, in the process adding titles for each bookand part (not present in the originals) and an extensive (if unsophisticated)index. Omission of commentary makes it possible to fit the entire Organoninto a single reasonably sized and modestly priced book.
Roger Bishop JonesSeptember 2012
Volume 1 CATEGORIES
Book I The Categories
Part 1 Equivocally, univocally and derivatively
Things are said to be named ‘equivocally’ when, though they have a com-mon name, the definition corresponding with the name differs for each.Thus, a real man and a figure in a picture can both lay claim to the name‘animal’; yet these are equivocally so named, for, though they have a com-mon name, the definition corresponding with the name differs for each. Forshould any one define in what sense each is an animal, his definition in theone case will be appropriate to that case only.
On the other hand, things are said to be named ‘univocally’ which haveboth the name and the definition answering to the name in common. A manand an ox are both ‘animal’, and these are univocally so named, inasmuchas not only the name, but also the definition, is the same in both cases: for ifa man should state in what sense each is an animal, the statement in the onecase would be identical with that in the other.
Things are said to be named ‘derivatively’, which derive their name fromsome other name, but differ from it in termination. Thus the grammarianderives his name from the word ‘grammar’, and the courageous man fromthe word ‘courage’.
Part 2 Presence and predication
Forms of speech are either simple or composite. Examples of the latter aresuch expressions as ‘the man runs’, ‘the man wins’; of the former ‘man’, ‘ox’,‘runs’, ‘wins’.
Of things themselves some are predicable of a subject, and are neverpresent in a subject. Thus ‘man’ is predicable of the individual man, andis never present in a subject.
2 The Categories
By being ‘present in a subject’ I do not mean present as parts are presentin a whole, but being incapable of existence apart from the said subject.
Some things, again, are present in a subject, but are never predicable of asubject. For instance, a certain point of grammatical knowledge is present inthe mind, but is not predicable of any subject; or again, a certain whitenessmay be present in the body (for colour requires a material basis), yet it isnever predicable of anything.
Other things, again, are both predicable of a subject and present in a sub-ject. Thus while knowledge is present in the human mind, it is predicable ofgrammar.
There is, lastly, a class of things which are neither present in a subject norpredicable of a subject, such as the individual man or the individual horse.But, to speak more generally, that which is individual and has the characterof a unit is never predicable of a subject. Yet in some cases there is nothing toprevent such being present in a subject. Thus a certain point of grammaticalknowledge is present in a subject.
Part 3 Subclasses and predicability
When one thing is predicated of another, all that which is predicable of thepredicate will be predicable also of the subject. Thus, ‘man’ is predicated ofthe individual man; but ‘animal’ is predicated of ‘man’; it will, therefore, bepredicable of the individual man also: for the individual man is both ‘man’and ‘animal’.
If genera are different and co-ordinate, their differentiae are themselvesdifferent in kind. Take as an instance the genus ‘animal’ and the genus‘knowledge’. ‘With feet’, ‘two-footed’, ‘winged’, ‘aquatic’, are differentiaeof ‘animal’; the species of knowledge are not distinguished by the same dif-ferentiae. One species of knowledge does not differ from another in being‘two-footed’.
But where one genus is subordinate to another, there is nothing to pre-vent their having the same differentiae: for the greater class is predicated ofthe lesser, so that all the differentiae of the predicate will be differentiae alsoof the subject.
Part 4 Expressions
Expressions which are in no way composite signify substance, quantity,quality, relation, place, time, position, state, action, or affection. To sketchmy meaning roughly, examples of substance are ‘man’ or ‘the horse’, ofquantity, such terms as ‘two cubits long’ or ‘three cubits long’, of quality,
Volume 1 Book I Part 4
Substance 3
such attributes as ‘white’, ‘grammatical’. ‘Double’, ‘half’, ‘greater’, fall un-der the category of relation; ‘in the market place’, ‘in the Lyceum’, underthat of place; ‘yesterday’, ‘last year’, under that of time. ‘Lying’, ‘sitting’,are terms indicating position, ‘shod’, ‘armed’, state; ‘to lance’, ‘to cauterize’,action; ‘to be lanced’, ‘to be cauterized’, affection.
No one of these terms, in and by itself, involves an affirmation; it is bythe combination of such terms that positive or negative statements arise. Forevery assertion must, as is admitted, be either true or false, whereas expres-sions which are not in any way composite such as ‘man’, ‘white’, ‘runs’,‘wins’, cannot be either true or false.
Part 5 Substance
Substance, in the truest and primary and most definite sense of the word,is that which is neither predicable of a subject nor present in a subject; forinstance, the individual man or horse. But in a secondary sense those thingsare called substances within which, as species, the primary substances areincluded; also those which, as genera, include the species. For instance, theindividual man is included in the species ‘man’, and the genus to which thespecies belongs is ‘animal’; these, therefore - that is to say, the species ‘man’and the genus ‘animal’ - are termed secondary substances.
It is plain from what has been said that both the name and the definitionof the predicate must be predicable of the subject. For instance, ‘man’ ispredicted of the individual man. Now in this case the name of the species‘man’ is applied to the individual, for we use the term ‘man’ in describingthe individual; and the definition of ‘man’ will also be predicated of theindividual man, for the individual man is both man and animal. Thus, boththe name and the definition of the species are predicable of the individual.
With regard, on the other hand, to those things which are present in asubject, it is generally the case that neither their name nor their definition ispredicable of that in which they are present. Though, however, the definitionis never predicable, there is nothing in certain cases to prevent the namebeing used. For instance, ‘white’ being present in a body is predicated ofthat in which it is present, for a body is called white: the definition, however,of the colour ‘white’ is never predicable of the body.
Everything except primary substances is either predicable of a primarysubstance or present in a primary substance. This becomes evident by ref-erence to particular instances which occur. ‘Animal’ is predicated of thespecies ‘man’, therefore of the individual man, for if there were no individ-ual man of whom it could be predicated, it could not be predicated of thespecies ‘man’ at all. Again, colour is present in body, therefore in individualbodies, for if there were no individual body in which it was present, it could
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not be present in body at all. Thus everything except primary substances iseither predicated of primary substances, or is present in them, and if theselast did not exist, it would be impossible for anything else to exist.
Of secondary substances, the species is more truly substance than thegenus, being more nearly related to primary substance. For if any oneshould render an account of what a primary substance is, he would render amore instructive account, and one more proper to the subject, by stating thespecies than by stating the genus. Thus, he would give a more instructiveaccount of an individual man by stating that he was man than by stating thathe was animal, for the former description is peculiar to the individual in agreater degree, while the latter is too general. Again, the man who gives anaccount of the nature of an individual tree will give a more instructive ac-count by mentioning the species ‘tree’ than by mentioning the genus ‘plant’.
Moreover, primary substances are most properly called substances invirtue of the fact that they are the entities which underlie everything else,and that everything else is either predicated of them or present in them.Now the same relation which subsists between primary substance and ev-erything else subsists also between the species and the genus: for the speciesis to the genus as subject is to predicate, since the genus is predicated of thespecies, whereas the species cannot be predicated of the genus. Thus wehave a second ground for asserting that the species is more truly substancethan the genus.
Of species themselves, except in the case of such as are genera, no one ismore truly substance than another. We should not give a more appropriateaccount of the individual man by stating the species to which he belonged,than we should of an individual horse by adopting the same method of def-inition. In the same way, of primary substances, no one is more truly sub-stance than another; an individual man is not more truly substance than anindividual ox.
It is, then, with good reason that of all that remains, when we excludeprimary substances, we concede to species and genera alone the name ‘sec-ondary substance’, for these alone of all the predicates convey a knowledgeof primary substance. For it is by stating the species or the genus that weappropriately define any individual man; and we shall make our definitionmore exact by stating the former than by stating the latter. All other thingsthat we state, such as that he is white, that he runs, and so on, are irrele-vant to the definition. Thus it is just that these alone, apart from primarysubstances, should be called substances.
Further, primary substances are most properly so called, because theyunderlie and are the subjects of everything else. Now the same relation thatsubsists between primary substance and everything else subsists also be-tween the species and the genus to which the primary substance belongs,
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on the one hand, and every attribute which is not included within these, onthe other. For these are the subjects of all such. If we call an individual man‘skilled in grammar’, the predicate is applicable also to the species and to thegenus to which he belongs. This law holds good in all cases.
It is a common characteristic of all substance that it is never present in asubject. For primary substance is neither present in a subject nor predicatedof a subject; while, with regard to secondary substances, it is clear from thefollowing arguments (apart from others) that they are not present in a sub-ject. For ‘man’ is predicated of the individual man, but is not present in anysubject: for manhood is not present in the individual man. In the same way,‘animal’ is also predicated of the individual man, but is not present in him.Again, when a thing is present in a subject, though the name may quite wellbe applied to that in which it is present, the definition cannot be applied. Yetof secondary substances, not only the name, but also the definition, appliesto the subject: we should use both the definition of the species and that ofthe genus with reference to the individual man. Thus substance cannot bepresent in a subject.
Yet this is not peculiar to substance, for it is also the case that differen-tiae cannot be present in subjects. The characteristics ‘terrestrial’ and ‘two-footed’ are predicated of the species ‘man’, but not present in it. For they arenot in man. Moreover, the definition of the differentia may be predicated ofthat of which the differentia itself is predicated. For instance, if the charac-teristic ‘terrestrial’ is predicated of the species ‘man’, the definition also ofthat characteristic may be used to form the predicate of the species ‘man’:for ‘man’ is terrestrial.
The fact that the parts of substances appear to be present in the whole,as in a subject, should not make us apprehensive lest we should have toadmit that such parts are not substances: for in explaining the phrase ‘beingpresent in a subject’, we stated that we meant ‘otherwise than as parts in awhole’.
It is the mark of substances and of differentiae that, in all propositions ofwhich they form the predicate, they are predicated univocally. For all suchpropositions have for their subject either the individual or the species. It istrue that, inasmuch as primary substance is not predicable of anything, it cannever form the predicate of any proposition. But of secondary substances,the species is predicated of the individual, the genus both of the species andof the individual. Similarly the differentiae are predicated of the species andof the individuals. Moreover, the definition of the species and that of thegenus are applicable to the primary substance, and that of the genus to thespecies. For all that is predicated of the predicate will be predicated also ofthe subject. Similarly, the definition of the differentiae will be applicable tothe species and to the individuals. But it was stated above that the word
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‘univocal’ was applied to those things which had both name and definitionin common. It is, therefore, established that in every proposition, of whicheither substance or a differentia forms the predicate, these are predicatedunivocally.
All substance appears to signify that which is individual. In the case ofprimary substance this is indisputably true, for the thing is a unit. In the caseof secondary substances, when we speak, for instance, of ‘man’ or ‘animal’,our form of speech gives the impression that we are here also indicating thatwhich is individual, but the impression is not strictly true; for a secondarysubstance is not an individual, but a class with a certain qualification; for itis not one and single as a primary substance is; the words ‘man’, ‘animal’,are predicable of more than one subject.
Yet species and genus do not merely indicate quality, like the term‘white’; ‘white’ indicates quality and nothing further, but species and genusdetermine the quality with reference to a substance: they signify substancequalitatively differentiated. The determinate qualification covers a largerfield in the case of the genus that in that of the species: he who uses theword ‘animal’ is herein using a word of wider extension than he who usesthe word ‘man’.
Another mark of substance is that it has no contrary. What could be thecontrary of any primary substance, such as the individual man or animal? Ithas none. Nor can the species or the genus have a contrary. Yet this char-acteristic is not peculiar to substance, but is true of many other things, suchas quantity. There is nothing that forms the contrary of ‘two cubits long’or of ‘three cubits long’, or of ‘ten’, or of any such term. A man may con-tend that ‘much’ is the contrary of ‘little’, or ‘great’ of ‘small’, but of definitequantitative terms no contrary exists.
Substance, again, does not appear to admit of variation of degree. I donot mean by this that one substance cannot be more or less truly substancethan another, for it has already been stated that this is the case; but that nosingle substance admits of varying degrees within itself. For instance, oneparticular substance, ‘man’, cannot be more or less man either than himselfat some other time or than some other man. One man cannot be more manthan another, as that which is white may be more or less white than someother white object, or as that which is beautiful may be more or less beautifulthan some other beautiful object. The same quality, moreover, is said tosubsist in a thing in varying degrees at different times. A body, being white,is said to be whiter at one time than it was before, or, being warm, is said tobe warmer or less warm than at some other time. But substance is not saidto be more or less that which it is: a man is not more truly a man at one timethan he was before, nor is anything, if it is substance, more or less what it is.Substance, then, does not admit of variation of degree.
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The most distinctive mark of substance appears to be that, while remain-ing numerically one and the same, it is capable of admitting contrary qual-ities. From among things other than substance, we should find ourselvesunable to bring forward any which possessed this mark. Thus, one and thesame colour cannot be white and black. Nor can the same one action be goodand bad: this law holds good with everything that is not substance. But oneand the selfsame substance, while retaining its identity, is yet capable of ad-mitting contrary qualities. The same individual person is at one time white,at another black, at one time warm, at another cold, at one time good, atanother bad. This capacity is found nowhere else, though it might be main-tained that a statement or opinion was an exception to the rule. The samestatement, it is agreed, can be both true and false. For if the statement ‘heis sitting’ is true, yet, when the person in question has risen, the same state-ment will be false. The same applies to opinions. For if any one thinks trulythat a person is sitting, yet, when that person has risen, this same opinion,if still held, will be false. Yet although this exception may be allowed, thereis, nevertheless, a difference in the manner in which the thing takes place.It is by themselves changing that substances admit contrary qualities. It isthus that that which was hot becomes cold, for it has entered into a differentstate. Similarly that which was white becomes black, and that which wasbad good, by a process of change; and in the same way in all other cases itis by changing that substances are capable of admitting contrary qualities.But statements and opinions themselves remain unaltered in all respects: itis by the alteration in the facts of the case that the contrary quality comes tobe theirs. The statement ‘he is sitting’ remains unaltered, but it is at one timetrue, at another false, according to circumstances. What has been said ofstatements applies also to opinions. Thus, in respect of the manner in whichthe thing takes place, it is the peculiar mark of substance that it should becapable of admitting contrary qualities; for it is by itself changing that it doesso.
If, then, a man should make this exception and contend that statementsand opinions are capable of admitting contrary qualities, his contention isunsound. For statements and opinions are said to have this capacity, notbecause they themselves undergo modification, but because this modifica-tion occurs in the case of something else. The truth or falsity of a statementdepends on facts, and not on any power on the part of the statement itselfof admitting contrary qualities. In short, there is nothing which can alter thenature of statements and opinions. As, then, no change takes place in them-selves, these cannot be said to be capable of admitting contrary qualities.
But it is by reason of the modification which takes place within the sub-stance itself that a substance is said to be capable of admitting contrary qual-ities; for a substance admits within itself either disease or health, whiteness
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or blackness. It is in this sense that it is said to be capable of admitting con-trary qualities.
To sum up, it is a distinctive mark of substance, that, while remainingnumerically one and the same, it is capable of admitting contrary qualities,the modification taking place through a change in the substance itself.
Let these remarks suffice on the subject of substance.
Part 6 Quantity
Quantity is either discrete or continuous. Moreover, some quantities aresuch that each part of the whole has a relative position to the other parts:others have within them no such relation of part to part.
Instances of discrete quantities are number and speech; of continuous,lines, surfaces, solids, and, besides these, time and place.
In the case of the parts of a number, there is no common boundary atwhich they join. For example: two fives make ten, but the two fives haveno common boundary, but are separate; the parts three and seven also donot join at any boundary. Nor, to generalize, would it ever be possible in thecase of number that there should be a common boundary among the parts;they are always separate. Number, therefore, is a discrete quantity.
The same is true of speech. That speech is a quantity is evident: forit is measured in long and short syllables. I mean here that speech whichis vocal. Moreover, it is a discrete quantity for its parts have no commonboundary. There is no common boundary at which the syllables join, buteach is separate and distinct from the rest.
A line, on the other hand, is a continuous quantity, for it is possible tofind a common boundary at which its parts join. In the case of the line, thiscommon boundary is the point; in the case of the plane, it is the line: for theparts of the plane have also a common boundary. Similarly you can find acommon boundary in the case of the parts of a solid, namely either a line ora plane.
Space and time also belong to this class of quantities. Time, past, present,and future, forms a continuous whole. Space, likewise, is a continuous quan-tity; for the parts of a solid occupy a certain space, and these have a commonboundary; it follows that the parts of space also, which are occupied by theparts of the solid, have the same common boundary as the parts of the solid.Thus, not only time, but space also, is a continuous quantity, for its partshave a common boundary.
Quantities consist either of parts which bear a relative position each toeach, or of parts which do not. The parts of a line bear a relative position toeach other, for each lies somewhere, and it would be possible to distinguisheach, and to state the position of each on the plane and to explain to what
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sort of part among the rest each was contiguous. Similarly the parts of aplane have position, for it could similarly be stated what was the position ofeach and what sort of parts were contiguous. The same is true with regardto the solid and to space. But it would be impossible to show that the arts ofa number had a relative position each to each, or a particular position, or tostate what parts were contiguous. Nor could this be done in the case of time,for none of the parts of time has an abiding existence, and that which doesnot abide can hardly have position. It would be better to say that such partshad a relative order, in virtue of one being prior to another. Similarly withnumber: in counting, ‘one’ is prior to ‘two’, and ‘two’ to ‘three’, and thus theparts of number may be said to possess a relative order, though it would beimpossible to discover any distinct position for each. This holds good also inthe case of speech. None of its parts has an abiding existence: when once asyllable is pronounced, it is not possible to retain it, so that, naturally, as theparts do not abide, they cannot have position. Thus, some quantities consistof parts which have position, and some of those which have not.
Strictly speaking, only the things which I have mentioned belong to thecategory of quantity: everything else that is called quantitative is a quantityin a secondary sense. It is because we have in mind some one of these quan-tities, properly so called, that we apply quantitative terms to other things.We speak of what is white as large, because the surface over which the whiteextends is large; we speak of an action or a process as lengthy, because thetime covered is long; these things cannot in their own right claim the quan-titative epithet. For instance, should any one explain how long an actionwas, his statement would be made in terms of the time taken, to the effectthat it lasted a year, or something of that sort. In the same way, he wouldexplain the size of a white object in terms of surface, for he would state thearea which it covered. Thus the things already mentioned, and these alone,are in their intrinsic nature quantities; nothing else can claim the name in itsown right, but, if at all, only in a secondary sense.
Quantities have no contraries. In the case of definite quantities this isobvious; thus, there is nothing that is the contrary of ‘two cubits long’ or of‘three cubits long’, or of a surface, or of any such quantities. A man might,indeed, argue that ‘much’ was the contrary of ‘little’, and ‘great’ of ‘small’.But these are not quantitative, but relative; things are not great or small ab-solutely, they are so called rather as the result of an act of comparison. Forinstance, a mountain is called small, a grain large, in virtue of the fact thatthe latter is greater than others of its kind, the former less. Thus there is a ref-erence here to an external standard, for if the terms ‘great’ and ‘small’ wereused absolutely, a mountain would never be called small or a grain large.Again, we say that there are many people in a village, and few in Athens, al-though those in the city are many times as numerous as those in the village:
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or we say that a house has many in it, and a theatre few, though those in thetheatre far outnumber those in the house. The terms ‘two cubits long’, ‘threecubits long’, and so on indicate quantity, the terms ‘great’ and ‘small’ indi-cate relation, for they have reference to an external standard. It is, therefore,plain that these are to be classed as relative.
Again, whether we define them as quantitative or not, they have no con-traries: for how can there be a contrary of an attribute which is not to beapprehended in or by itself, but only by reference to something external?Again, if ‘great’ and ‘small’ are contraries, it will come about that the samesubject can admit contrary qualities at one and the same time, and that thingswill themselves be contrary to themselves. For it happens at times that thesame thing is both small and great. For the same thing may be small in com-parison with one thing, and great in comparison with another, so that thesame thing comes to be both small and great at one and the same time, and isof such a nature as to admit contrary qualities at one and the same moment.Yet it was agreed, when substance was being discussed, that nothing admitscontrary qualities at one and the same moment. For though substance is ca-pable of admitting contrary qualities, yet no one is at the same time both sickand healthy, nothing is at the same time both white and black. Nor is thereanything which is qualified in contrary ways at one and the same time.
Moreover, if these were contraries, they would themselves be contraryto themselves. For if ‘great’ is the contrary of ‘small’, and the same thing isboth great and small at the same time, then ‘small’ or ‘great’ is the contraryof itself. But this is impossible. The term ‘great’, therefore, is not the contraryof the term ‘small’, nor ‘much’ of ‘little’. And even though a man should callthese terms not relative but quantitative, they would not have contraries.
It is in the case of space that quantity most plausibly appears to admit ofa contrary. For men define the term ‘above’ as the contrary of ‘below’, whenit is the region at the centre they mean by ‘below’; and this is so, becausenothing is farther from the extremities of the universe than the region at thecentre. Indeed, it seems that in defining contraries of every kind men haverecourse to a spatial metaphor, for they say that those things are contrarieswhich, within the same class, are separated by the greatest possible distance.
Quantity does not, it appears, admit of variation of degree. One thingcannot be two cubits long in a greater degree than another. Similarly withregard to number: what is ‘three’ is not more truly three than what is ‘five’is five; nor is one set of three more truly three than another set. Again, oneperiod of time is not said to be more truly time than another. Nor is there anyother kind of quantity, of all that have been mentioned, with regard to whichvariation of degree can be predicated. The category of quantity, therefore,does not admit of variation of degree.
The most distinctive mark of quantity is that equality and inequality are
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predicated of it. Each of the aforesaid quantities is said to be equal or un-equal. For instance, one solid is said to be equal or unequal to another; num-ber, too, and time can have these terms applied to them, indeed can all thosekinds of quantity that have been mentioned.
That which is not a quantity can by no means, it would seem, be termedequal or unequal to anything else. One particular disposition or one partic-ular quality, such as whiteness, is by no means compared with another interms of equality and inequality but rather in terms of similarity. Thus it isthe distinctive mark of quantity that it can be called equal and unequal.
Part 7 Relation
Those things are called relative, which, being either said to be of somethingelse or related to something else, are explained by reference to that otherthing. For instance, the word ‘superior’ is explained by reference to some-thing else, for it is superiority over something else that is meant. Similarly,the expression ‘double’ has this external reference, for it is the double ofsomething else that is meant. So it is with everything else of this kind. Thereare, moreover, other relatives, e.g. habit, disposition, perception, knowl-edge, and attitude. The significance of all these is explained by a referenceto something else and in no other way. Thus, a habit is a habit of something,knowledge is knowledge of something, attitude is the attitude of something.So it is with all other relatives that have been mentioned. Those terms, then,are called relative, the nature of which is explained by reference to some-thing else, the preposition ‘of’ or some other preposition being used to in-dicate the relation. Thus, one mountain is called great in comparison withson with another; for the mountain claims this attribute by comparison withsomething. Again, that which is called similar must be similar to somethingelse, and all other such attributes have this external reference. It is to benoted that lying and standing and sitting are particular attitudes, but atti-tude is itself a relative term. To lie, to stand, to be seated, are not themselvesattitudes, but take their name from the aforesaid attitudes.
It is possible for relatives to have contraries. Thus virtue has a contrary,vice, these both being relatives; knowledge, too, has a contrary, ignorance.But this is not the mark of all relatives; ‘double’ and ‘triple’ have no contrary,nor indeed has any such term.
It also appears that relatives can admit of variation of degree. For ‘like’and ‘unlike’, ‘equal’ and ‘unequal’, have the modifications ‘more’ and ‘less’applied to them, and each of these is relative in character: for the terms ‘like’and ‘unequal’ bear ‘unequal’ bear a reference to something external. Yet,again, it is not every relative term that admits of variation of degree. No termsuch as ‘double’ admits of this modification. All relatives have correlatives:
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by the term ‘slave’ we mean the slave of a master, by the term ‘master’, themaster of a slave; by ‘double’, the double of its hall; by ‘half’, the half of itsdouble; by ‘greater’, greater than that which is less; by ‘less,’ less than thatwhich is greater.
So it is with every other relative term; but the case we use to express thecorrelation differs in some instances. Thus, by knowledge we mean knowl-edge the knowable; by the knowable, that which is to be apprehended byknowledge; by perception, perception of the perceptible; by the perceptible,that which is apprehended by perception.
Sometimes, however, reciprocity of correlation does not appear to exist.This comes about when a blunder is made, and that to which the relativeis related is not accurately stated. If a man states that a wing is necessarilyrelative to a bird, the connexion between these two will not be reciprocal, forit will not be possible to say that a bird is a bird by reason of its wings. Thereason is that the original statement was inaccurate, for the wing is not saidto be relative to the bird qua bird, since many creatures besides birds havewings, but qua winged creature. If, then, the statement is made accurate, theconnexion will be reciprocal, for we can speak of a wing, having referencenecessarily to a winged creature, and of a winged creature as being suchbecause of its wings.
Occasionally, perhaps, it is necessary to coin words, if no word exists bywhich a correlation can adequately be explained. If we define a rudder asnecessarily having reference to a boat, our definition will not be appropriate,for the rudder does not have this reference to a boat qua boat, as there areboats which have no rudders. Thus we cannot use the terms reciprocally, forthe word ‘boat’ cannot be said to find its explanation in the word ‘rudder’.As there is no existing word, our definition would perhaps be more accurateif we coined some word like ‘ruddered’ as the correlative of ‘rudder’. Ifwe express ourselves thus accurately, at any rate the terms are reciprocallyconnected, for the ‘ruddered’ thing is ‘ruddered’ in virtue of its rudder. So itis in all other cases. A head will be more accurately defined as the correlativeof that which is ‘headed’, than as that of an animal, for the animal does nothave a head qua animal, since many animals have no head.
Thus we may perhaps most easily comprehend that to which a thing isrelated, when a name does not exist, if, from that which has a name, wederive a new name, and apply it to that with which the first is reciprocallyconnected, as in the aforesaid instances, when we derived the word ‘winged’from ‘wing’ and from ‘rudder’.
All relatives, then, if properly defined, have a correlative. I add this con-dition because, if that to which they are related is stated as haphazard andnot accurately, the two are not found to be interdependent. Let me state whatI mean more clearly. Even in the case of acknowledged correlatives, and
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where names exist for each, there will be no interdependence if one of thetwo is denoted, not by that name which expresses the correlative notion, butby one of irrelevant significance. The term ‘slave,’ if defined as related, notto a master, but to a man, or a biped, or anything of that sort, is not recipro-cally connected with that in relation to which it is defined, for the statementis not exact. Further, if one thing is said to be correlative with another, andthe terminology used is correct, then, though all irrelevant attributes shouldbe removed, and only that one attribute left in virtue of which it was cor-rectly stated to be correlative with that other, the stated correlation will stillexist. If the correlative of ‘the slave’ is said to be ‘the master’, then, thoughall irrelevant attributes of the said ‘master’, such as ‘biped’, ‘receptive ofknowledge’, ‘human’, should be removed, and the attribute ‘master’ aloneleft, the stated correlation existing between him and the slave will remainthe same, for it is of a master that a slave is said to be the slave. On the otherhand, if, of two correlatives, one is not correctly termed, then, when all otherattributes are removed and that alone is left in virtue of which it was statedto be correlative, the stated correlation will be found to have disappeared.
For suppose the correlative of ‘the slave’ should be said to be ‘the man’,or the correlative of ‘the wing’ ‘the bird’; if the attribute ‘master’ be with-drawn from ‘the man’, the correlation between ‘the man’ and ‘the slave’ willcease to exist, for if the man is not a master, the slave is not a slave. Simi-larly, if the attribute ‘winged’ be withdrawn from ‘the bird’, ‘the wing’ willno longer be relative; for if the so-called correlative is not winged, it followsthat ‘the wing’ has no correlative.
Thus it is essential that the correlated terms should be exactly designated;if there is a name existing, the statement will be easy; if not, it is doubtlessour duty to construct names. When the terminology is thus correct, it isevident that all correlatives are interdependent.
Correlatives are thought to come into existence simultaneously. This isfor the most part true, as in the case of the double and the half. The existenceof the half necessitates the existence of that of which it is a half. Similarlythe existence of a master necessitates the existence of a slave, and that of aslave implies that of a master; these are merely instances of a general rule.Moreover, they cancel one another; for if there is no double it follows thatthere is no half, and vice versa; this rule also applies to all such correlatives.Yet it does not appear to be true in all cases that correlatives come into exis-tence simultaneously. The object of knowledge would appear to exist beforeknowledge itself, for it is usually the case that we acquire knowledge of ob-jects already existing; it would be difficult, if not impossible, to find a branchof knowledge the beginning of the existence of which was contemporaneouswith that of its object.
Again, while the object of knowledge, if it ceases to exist, cancels at the
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same time the knowledge which was its correlative, the converse of this isnot true. It is true that if the object of knowledge does not exist there canbe no knowledge: for there will no longer be anything to know. Yet it isequally true that, if knowledge of a certain object does not exist, the objectmay nevertheless quite well exist. Thus, in the case of the squaring of thecircle, if indeed that process is an object of knowledge, though it itself existsas an object of knowledge, yet the knowledge of it has not yet come intoexistence. Again, if all animals ceased to exist, there would be no knowledge,but there might yet be many objects of knowledge.
This is likewise the case with regard to perception: for the object of per-ception is, it appears, prior to the act of perception. If the perceptible is anni-hilated, perception also will cease to exist; but the annihilation of perceptiondoes not cancel the existence of the perceptible. For perception implies abody perceived and a body in which perception takes place. Now if thatwhich is perceptible is annihilated, it follows that the body is annihilated,for the body is a perceptible thing; and if the body does not exist, it followsthat perception also ceases to exist. Thus the annihilation of the perceptibleinvolves that of perception.
But the annihilation of perception does not involve that of the percepti-ble. For if the animal is annihilated, it follows that perception also is annihi-lated, but perceptibles such as body, heat, sweetness, bitterness, and so on,will remain.
Again, perception is generated at the same time as the perceiving subject,for it comes into existence at the same time as the animal. But the perceptiblesurely exists before perception; for fire and water and such elements, out ofwhich the animal is itself composed, exist before the animal is an animal atall, and before perception. Thus it would seem that the perceptible existsbefore perception.
It may be questioned whether it is true that no substance is relative, asseems to be the case, or whether exception is to be made in the case of cer-tain secondary substances. With regard to primary substances, it is quitetrue that there is no such possibility, for neither wholes nor parts of primarysubstances are relative. The individual man or ox is not defined with refer-ence to something external. Similarly with the parts: a particular hand orhead is not defined as a particular hand or head of a particular person, butas the hand or head of a particular person. It is true also, for the most part atleast, in the case of secondary substances; the species ‘man’ and the species‘ox’ are not defined with reference to anything outside themselves. Wood,again, is only relative in so far as it is some one’s property, not in so far asit is wood. It is plain, then, that in the cases mentioned substance is not rel-ative. But with regard to some secondary substances there is a difference ofopinion; thus, such terms as ‘head’ and ‘hand’ are defined with reference to
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that of which the things indicated are a part, and so it comes about that theseappear to have a relative character. Indeed, if our definition of that which isrelative was complete, it is very difficult, if not impossible, to prove that nosubstance is relative. If, however, our definition was not complete, if thosethings only are properly called relative in the case of which relation to an ex-ternal object is a necessary condition of existence, perhaps some explanationof the dilemma may be found.
The former definition does indeed apply to all relatives, but the fact thata thing is explained with reference to something else does not make it essen-tially relative.
From this it is plain that, if a man definitely apprehends a relative thing,he will also definitely apprehend that to which it is relative. Indeed this isself-evident: for if a man knows that some particular thing is relative, assum-ing that we call that a relative in the case of which relation to something isa necessary condition of existence, he knows that also to which it is related.For if he does not know at all that to which it is related, he will not knowwhether or not it is relative. This is clear, moreover, in particular instances.If a man knows definitely that such and such a thing is ‘double’, he will alsoforthwith know definitely that of which it is the double. For if there is noth-ing definite of which he knows it to be the double, he does not know at allthat it is double. Again, if he knows that a thing is more beautiful, it followsnecessarily that he will forthwith definitely know that also than which it ismore beautiful. He will not merely know indefinitely that it is more beau-tiful than something which is less beautiful, for this would be supposition,not knowledge. For if he does not know definitely that than which it is morebeautiful, he can no longer claim to know definitely that it is more beautifulthan something else which is less beautiful: for it might be that nothing wasless beautiful. It is, therefore, evident that if a man apprehends some rela-tive thing definitely, he necessarily knows that also definitely to which it isrelated.
Now the head, the hand, and such things are substances, and it is pos-sible to know their essential character definitely, but it does not necessarilyfollow that we should know that to which they are related. It is not possibleto know forthwith whose head or hand is meant. Thus these are not rela-tives, and, this being the case, it would be true to say that no substance isrelative in character. It is perhaps a difficult matter, in such cases, to make apositive statement without more exhaustive examination, but to have raisedquestions with regard to details is not without advantage.
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Part 8 Quality
By ‘quality’ I mean that in virtue of which people are said to be such andsuch.
Quality is a term that is used in many senses. One sort of quality letus call ‘habit’ or ‘disposition’. Habit differs from disposition in being morelasting and more firmly established. The various kinds of knowledge andof virtue are habits, for knowledge, even when acquired only in a moderatedegree, is, it is agreed, abiding in its character and difficult to displace, un-less some great mental upheaval takes place, through disease or any suchcause. The virtues, also, such as justice, self-restraint, and so on, are noteasily dislodged or dismissed, so as to give place to vice.
By a disposition, on the other hand, we mean a condition that is easilychanged and quickly gives place to its opposite. Thus, heat, cold, disease,health, and so on are dispositions. For a man is disposed in one way oranother with reference to these, but quickly changes, becoming cold insteadof warm, ill instead of well. So it is with all other dispositions also, unlessthrough lapse of time a disposition has itself become inveterate and almostimpossible to dislodge: in which case we should perhaps go so far as to callit a habit.
It is evident that men incline to call those conditions habits which are ofa more or less permanent type and difficult to displace; for those who arenot retentive of knowledge, but volatile, are not said to have such and sucha ‘habit’ as regards knowledge, yet they are disposed, we may say, eitherbetter or worse, towards knowledge. Thus habit differs from disposition inthis, that while the latter in ephemeral, the former is permanent and difficultto alter.
Habits are at the same time dispositions, but dispositions are not neces-sarily habits. For those who have some specific habit may be said also, invirtue of that habit, to be thus or thus disposed; but those who are disposedin some specific way have not in all cases the corresponding habit.
Another sort of quality is that in virtue of which, for example, we callmen good boxers or runners, or healthy or sickly: in fact it includes all thoseterms which refer to inborn capacity or incapacity. Such things are not pred-icated of a person in virtue of his disposition, but in virtue of his inborncapacity or incapacity to do something with ease or to avoid defeat of anykind. Persons are called good boxers or good runners, not in virtue of suchand such a disposition, but in virtue of an inborn capacity to accomplishsomething with ease. Men are called healthy in virtue of the inborn capacityof easy resistance to those unhealthy influences that may ordinarily arise;unhealthy, in virtue of the lack of this capacity. Similarly with regard tosoftness and hardness. Hardness is predicated of a thing because it has that
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capacity of resistance which enables it to withstand disintegration; softness,again, is predicated of a thing by reason of the lack of that capacity.
A third class within this category is that of affective qualities and affec-tions. Sweetness, bitterness, sourness, are examples of this sort of quality,together with all that is akin to these; heat, moreover, and cold, whiteness,and blackness are affective qualities. It is evident that these are qualities, forthose things that possess them are themselves said to be such and such byreason of their presence. Honey is called sweet because it contains sweet-ness; the body is called white because it contains whiteness; and so in allother cases.
The term ‘affective quality’ is not used as indicating that those thingswhich admit these qualities are affected in any way. Honey is not calledsweet because it is affected in a specific way, nor is this what is meant inany other instance. Similarly heat and cold are called affective qualities, notbecause those things which admit them are affected. What is meant is thatthese said qualities are capable of producing an ‘affection’ in the way of per-ception. For sweetness has the power of affecting the sense of taste; heat,that of touch; and so it is with the rest of these qualities.
Whiteness and blackness, however, and the other colours, are not saidto be affective qualities in this sense, but - because they themselves are theresults of an affection. It is plain that many changes of colour take place be-cause of affections. When a man is ashamed, he blushes; when he is afraid,he becomes pale, and so on. So true is this, that when a man is by natureliable to such affections, arising from some concomitance of elements in hisconstitution, it is a probable inference that he has the corresponding com-plexion of skin. For the same disposition of bodily elements, which in theformer instance was momentarily present in the case of an access of shame,might be a result of a man’s natural temperament, so as to produce the corre-sponding colouring also as a natural characteristic. All conditions, therefore,of this kind, if caused by certain permanent and lasting affections, are calledaffective qualities. For pallor and duskiness of complexion are called qual-ities, inasmuch as we are said to be such and such in virtue of them, notonly if they originate in natural constitution, but also if they come aboutthrough long disease or sunburn, and are difficult to remove, or indeed re-main throughout life. For in the same way we are said to be such and suchbecause of these.
Those conditions, however, which arise from causes which may easilybe rendered ineffective or speedily removed, are called, not qualities, butaffections: for we are not said to be such virtue of them. The man whoblushes through shame is not said to be a constitutional blusher, nor is theman who becomes pale through fear said to be constitutionally pale. He issaid rather to have been affected.
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Thus such conditions are called affections, not qualities.In like manner there are affective qualities and affections of the soul. That
temper with which a man is born and which has its origin in certain deep-seated affections is called a quality. I mean such conditions as insanity, iras-cibility, and so on: for people are said to be mad or irascible in virtue of these.Similarly those abnormal psychic states which are not inborn, but arise fromthe concomitance of certain other elements, and are difficult to remove, oraltogether permanent, are called qualities, for in virtue of them men are saidto be such and such.
Those, however, which arise from causes easily rendered ineffective arecalled affections, not qualities. Suppose that a man is irritable when vexed:he is not even spoken of as a bad-tempered man, when in such circumstanceshe loses his temper somewhat, but rather is said to be affected. Such condi-tions are therefore termed, not qualities, but affections.
The fourth sort of quality is figure and the shape that belongs to a thing;and besides this, straightness and curvedness and any other qualities of thistype; each of these defines a thing as being such and such. Because it istriangular or quadrangular a thing is said to have a specific character, oragain because it is straight or curved; in fact a thing’s shape in every casegives rise to a qualification of it.
Rarity and density, roughness and smoothness, seem to be terms indi-cating quality: yet these, it would appear, really belong to a class differentfrom that of quality. For it is rather a certain relative position of the partscomposing the thing thus qualified which, it appears, is indicated by eachof these terms. A thing is dense, owing to the fact that its parts are closelycombined with one another; rare, because there are interstices between theparts; smooth, because its parts lie, so to speak, evenly; rough, because someparts project beyond others.
There may be other sorts of quality, but those that are most properly socalled have, we may safely say, been enumerated.
These, then, are qualities, and the things that take their name from themas derivatives, or are in some other way dependent on them, are said to bequalified in some specific way. In most, indeed in almost all cases, the nameof that which is qualified is derived from that of the quality. Thus the terms‘whiteness’, ‘grammar’, ‘justice’, give us the adjectives ‘white’, ‘grammati-cal’, ‘just’, and so on.
There are some cases, however, in which, as the quality under consider-ation has no name, it is impossible that those possessed of it should have aname that is derivative. For instance, the name given to the runner or boxer,who is so called in virtue of an inborn capacity, is not derived from that ofany quality; for lob those capacities have no name assigned to them. In this,the inborn capacity is distinct from the science, with reference to which men
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are called, e.g. boxers or wrestlers. Such a science is classed as a disposition;it has a name, and is called ‘boxing’ or ‘wrestling’ as the case may be, and thename given to those disposed in this way is derived from that of the science.Sometimes, even though a name exists for the quality, that which takes itscharacter from the quality has a name that is not a derivative. For instance,the upright man takes his character from the possession of the quality of in-tegrity, but the name given him is not derived from the word ‘integrity’. Yetthis does not occur often.
We may therefore state that those things are said to be possessed of somespecific quality which have a name derived from that of the aforesaid qual-ity, or which are in some other way dependent on it.
One quality may be the contrary of another; thus justice is the contrary ofinjustice, whiteness of blackness, and so on. The things, also, which are saidto be such and such in virtue of these qualities, may be contrary the one tothe other; for that which is unjust is contrary to that which is just, that whichis white to that which is black. This, however, is not always the case. Red,yellow, and such colours, though qualities, have no contraries.
If one of two contraries is a quality, the other will also be a quality. Thiswill be evident from particular instances, if we apply the names used to de-note the other categories; for instance, granted that justice is the contraryof injustice and justice is a quality, injustice will also be a quality: neitherquantity, nor relation, nor place, nor indeed any other category but that ofquality, will be applicable properly to injustice. So it is with all other con-traries falling under the category of quality.
Qualities admit of variation of degree. Whiteness is predicated of onething in a greater or less degree than of another. This is also the case withreference to justice. Moreover, one and the same thing may exhibit a qualityin a greater degree than it did before: if a thing is white, it may becomewhiter.
Though this is generally the case, there are exceptions. For if we shouldsay that justice admitted of variation of degree, difficulties might ensue, andthis is true with regard to all those qualities which are dispositions. Thereare some, indeed, who dispute the possibility of variation here. They main-tain that justice and health cannot very well admit of variation of degreethemselves, but that people vary in the degree in which they possess thesequalities, and that this is the case with grammatical learning and all thosequalities which are classed as dispositions. However that may be, it is an in-controvertible fact that the things which in virtue of these qualities are saidto be what they are vary in the degree in which they possess them; for oneman is said to be better versed in grammar, or more healthy or just, thananother, and so on.
The qualities expressed by the terms ‘triangular’ and ‘quadrangular’ do
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not appear to admit of variation of degree, nor indeed do any that haveto do with figure. For those things to which the definition of the triangleor circle is applicable are all equally triangular or circular. Those, on theother hand, to which the same definition is not applicable, cannot be saidto differ from one another in degree; the square is no more a circle than therectangle, for to neither is the definition of the circle appropriate. In short,if the definition of the term proposed is not applicable to both objects, theycannot be compared. Thus it is not all qualities which admit of variation ofdegree.
Whereas none of the characteristics I have mentioned are peculiar toquality, the fact that likeness and unlikeness can be predicated with refer-ence to quality only, gives to that category its distinctive feature. One thingis like another only with reference to that in virtue of which it is such andsuch; thus this forms the peculiar mark of quality.
We must not be disturbed because it may be argued that, though propos-ing to discuss the category of quality, we have included in it many relativeterms. We did say that habits and dispositions were relative. In practicallyall such cases the genus is relative, the individual not. Thus knowledge, as agenus, is explained by reference to something else, for we mean a knowledgeof something. But particular branches of knowledge are not thus explained.The knowledge of grammar is not relative to anything external, nor is theknowledge of music, but these, if relative at all, are relative only in virtue oftheir genera; thus grammar is said be the knowledge of something, not thegrammar of something; similarly music is the knowledge of something, notthe music of something.
Thus individual branches of knowledge are not relative. And it is be-cause we possess these individual branches of knowledge that we are saidto be such and such. It is these that we actually possess: we are called expertsbecause we possess knowledge in some particular branch. Those particularbranches, therefore, of knowledge, in virtue of which we are sometimes saidto be such and such, are themselves qualities, and are not relative. Further, ifanything should happen to fall within both the category of quality and thatof relation, there would be nothing extraordinary in classing it under boththese heads.
Part 9 Action, affection, position, rest, time, place, state
Action and affection both admit of contraries and also of variation of degree.Heating is the contrary of cooling, being heated of being cooled, being gladof being vexed. Thus they admit of contraries. They also admit of variationof degree: for it is possible to heat in a greater or less degree; also to beheated in a greater or less degree. Thus action and affection also admit of
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variation of degree. So much, then, is stated with regard to these categories.We spoke, moreover, of the category of position when we were dealing
with that of relation, and stated that such terms derived their names fromthose of the corresponding attitudes.
As for the rest, time, place, state, since they are easily intelligible, I say nomore about them than was said at the beginning, that in the category of stateare included such states as ‘shod’, ‘armed’, in that of place ‘in the Lyceum’and so on, as was explained before.
Part 10 Opposite, contrary, privative, positive
The proposed categories have, then, been adequately dealt with.We must next explain the various senses in which the term ‘opposite’ is
used. Things are said to be opposed in four senses:(i) as correlatives to one another,(ii) as contraries to one another,(iii) as privatives to positives,(iv) as affirmatives to negatives.Let me sketch my meaning in outline. An instance of the use of the word
‘opposite’ with reference to correlatives is afforded by the expressions ‘dou-ble’ and ‘half’; with reference to contraries by ‘bad’ and ‘good’. Oppositesin the sense of ‘privatives’ and ‘positives’ are ‘blindness’ and ‘sight’; in thesense of affirmatives and negatives, the propositions ‘he sits’, ‘he does notsit’.
(i) Pairs of opposites which fall under the category of relation are ex-plained by a reference of the one to the other, the reference being indicatedby the preposition ‘of’ or by some other preposition. Thus, double is a rela-tive term, for that which is double is explained as the double of something.Knowledge, again, is the opposite of the thing known, in the same sense; andthe thing known also is explained by its relation to its opposite, knowledge.For the thing known is explained as that which is known by something, thatis, by knowledge. Such things, then, as are opposite the one to the other inthe sense of being correlatives are explained by a reference of the one to theother.
(ii) Pairs of opposites which are contraries are not in any way interde-pendent, but are contrary the one to the other. The good is not spoken of asthe good of the bad, but as the contrary of the bad, nor is white spoken ofas the white of the black, but as the contrary of the black. These two typesof opposition are therefore distinct. Those contraries which are such that thesubjects in which they are naturally present, or of which they are predicated,must necessarily contain either the one or the other of them, have no inter-mediate, but those in the case of which no such necessity obtains, always
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have an intermediate. Thus disease and health are naturally present in thebody of an animal, and it is necessary that either the one or the other shouldbe present in the body of an animal. Odd and even, again, are predicatedof number, and it is necessary that the one or the other should be present innumbers. Now there is no intermediate between the terms of either of thesetwo pairs. On the other hand, in those contraries with regard to which nosuch necessity obtains, we find an intermediate. Blackness and whitenessare naturally present in the body, but it is not necessary that either the oneor the other should be present in the body, inasmuch as it is not true to saythat everybody must be white or black. Badness and goodness, again, arepredicated of man, and of many other things, but it is not necessary thateither the one quality or the other should be present in that of which theyare predicated: it is not true to say that everything that may be good or badmust be either good or bad. These pairs of contraries have intermediates:the intermediates between white and black are grey, sallow, and all the othercolours that come between; the intermediate between good and bad is thatwhich is neither the one nor the other.
Some intermediate qualities have names, such as grey and sallow and allthe other colours that come between white and black; in other cases, how-ever, it is not easy to name the intermediate, but we must define it as thatwhich is not either extreme, as in the case of that which is neither good norbad, neither just nor unjust.
(iii) ‘privatives’ and ‘Positives’ have reference to the same subject. Thus,sight and blindness have reference to the eye. It is a universal rule that eachof a pair of opposites of this type has reference to that to which the particular‘positive’ is natural. We say that that is capable of some particular faculty orpossession has suffered privation when the faculty or possession in questionis in no way present in that in which, and at the time at which, it shouldnaturally be present. We do not call that toothless which has not teeth, orthat blind which has not sight, but rather that which has not teeth or sight atthe time when by nature it should. For there are some creatures which frombirth are without sight, or without teeth, but these are not called toothless orblind.
To be without some faculty or to possess it is not the same as the corre-sponding ‘privative’ or ‘positive’. ‘Sight’ is a ‘positive’, ‘blindness’ a ‘pri-vative’, but ‘to possess sight’ is not equivalent to ‘sight’, ‘to be blind’ is notequivalent to ‘blindness’. Blindness is a ‘privative’, to be blind is to be ina state of privation, but is not a ‘privative’. Moreover, if ‘blindness’ wereequivalent to ‘being blind’, both would be predicated of the same subject;but though a man is said to be blind, he is by no means said to be blindness.
To be in a state of ‘possession’ is, it appears, the opposite of being in astate of ‘privation’, just as ‘positives’ and ‘privatives’ themselves are oppo-
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site. There is the same type of antithesis in both cases; for just as blindnessis opposed to sight, so is being blind opposed to having sight.
That which is affirmed or denied is not itself affirmation or denial. By ‘af-firmation’ we mean an affirmative proposition, by ‘denial’ a negative. Now,those facts which form the matter of the affirmation or denial are not propo-sitions; yet these two are said to be opposed in the same sense as the affirma-tion and denial, for in this case also the type of antithesis is the same. For asthe affirmation is opposed to the denial, as in the two propositions ‘he sits’,‘he does not sit’, so also the fact which constitutes the matter of the propo-sition in one case is opposed to that in the other, his sitting, that is to say, tohis not sitting.
It is evident that ‘positives’ and ‘privatives’ are not opposed each to eachin the same sense as relatives. The one is not explained by reference to theother; sight is not sight of blindness, nor is any other preposition used toindicate the relation. Similarly blindness is not said to be blindness of sight,but rather, privation of sight. Relatives, moreover, reciprocate; if blindness,therefore, were a relative, there would be a reciprocity of relation between itand that with which it was correlative. But this is not the case. Sight is notcalled the sight of blindness.
That those terms which fall under the heads of ‘positives’ and ‘privatives’are not opposed each to each as contraries, either, is plain from the followingfacts: Of a pair of contraries such that they have no intermediate, one or theother must needs be present in the subject in which they naturally subsist,or of which they are predicated; for it is those, as we proved,’ in the case ofwhich this necessity obtains, that have no intermediate. Moreover, we citedhealth and disease, odd and even, as instances. But those contraries whichhave an intermediate are not subject to any such necessity. It is not neces-sary that every substance, receptive of such qualities, should be either blackor white, cold or hot, for something intermediate between these contrariesmay very well be present in the subject. We proved, moreover, that thosecontraries have an intermediate in the case of which the said necessity doesnot obtain. Yet when one of the two contraries is a constitutive property ofthe subject, as it is a constitutive property of fire to be hot, of snow to bewhite, it is necessary determinately that one of the two contraries, not oneor the other, should be present in the subject; for fire cannot be cold, or snowblack. Thus, it is not the case here that one of the two must needs be presentin every subject receptive of these qualities, but only in that subject of whichthe one forms a constitutive property. Moreover, in such cases it is one mem-ber of the pair determinately, and not either the one or the other, which mustbe present.
In the case of ‘positives’ and ‘privatives’, on the other hand, neither ofthe aforesaid statements holds good. For it is not necessary that a subject
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receptive of the qualities should always have either the one or the other; thatwhich has not yet advanced to the state when sight is natural is not saideither to be blind or to see. Thus ‘positives’ and ‘privatives’ do not belong tothat class of contraries which consists of those which have no intermediate.On the other hand, they do not belong either to that class which consistsof contraries which have an intermediate. For under certain conditions it isnecessary that either the one or the other should form part of the constitutionof every appropriate subject. For when a thing has reached the stage whenit is by nature capable of sight, it will be said either to see or to be blind, andthat in an indeterminate sense, signifying that the capacity may be eitherpresent or absent; for it is not necessary either that it should see or that itshould be blind, but that it should be either in the one state or in the other.Yet in the case of those contraries which have an intermediate we found thatit was never necessary that either the one or the other should be present inevery appropriate subject, but only that in certain subjects one of the pairshould be present, and that in a determinate sense. It is, therefore, plainthat ‘positives’ and ‘privatives’ are not opposed each to each in either of thesenses in which contraries are opposed.
Again, in the case of contraries, it is possible that there should be changesfrom either into the other, while the subject retains its identity, unless indeedone of the contraries is a constitutive property of that subject, as heat is offire. For it is possible that that that which is healthy should become diseased,that which is white, black, that which is cold, hot, that which is good, bad,that which is bad, good. The bad man, if he is being brought into a betterway of life and thought, may make some advance, however slight, and if heshould once improve, even ever so little, it is plain that he might change com-pletely, or at any rate make very great progress; for a man becomes more andmore easily moved to virtue, however small the improvement was at first. Itis, therefore, natural to suppose that he will make yet greater progress thanhe has made in the past; and as this process goes on, it will change him com-pletely and establish him in the contrary state, provided he is not hinderedby lack of time. In the case of ‘positives’ and ‘privatives’, however, change inboth directions is impossible. There may be a change from possession to pri-vation, but not from privation to possession. The man who has become blinddoes not regain his sight; the man who has become bald does not regain hishair; the man who has lost his teeth does not grow his grow a new set. (iv)Statements opposed as affirmation and negation belong manifestly to a classwhich is distinct, for in this case, and in this case only, it is necessary for theone opposite to be true and the other false.
Neither in the case of contraries, nor in the case of correlatives, nor in thecase of ‘positives’ and ‘privatives’, is it necessary for one to be true and theother false. Health and disease are contraries: neither of them is true or false.
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‘Double’ and ‘half’ are opposed to each other as correlatives: neither of themis true or false. The case is the same, of course, with regard to ‘positives’ and‘privatives’ such as ‘sight’ and ‘blindness’. In short, where there is no sort ofcombination of words, truth and falsity have no place, and all the oppositeswe have mentioned so far consist of simple words.
At the same time, when the words which enter into opposed statementsare contraries, these, more than any other set of opposites, would seem toclaim this characteristic. ‘Socrates is ill’ is the contrary of ‘Socrates is well’,but not even of such composite expressions is it true to say that one of thepair must always be true and the other false. For if Socrates exists, one willbe true and the other false, but if he does not exist, both will be false; forneither ‘Socrates is ill’ nor ‘Socrates is well’ is true, if Socrates does not existat all.
In the case of ‘positives’ and ‘privatives’, if the subject does not exist at all,neither proposition is true, but even if the subject exists, it is not always thefact that one is true and the other false. For ‘Socrates has sight’ is the oppositeof ‘Socrates is blind’ in the sense of the word ‘opposite’ which applies topossession and privation. Now if Socrates exists, it is not necessary that oneshould be true and the other false, for when he is not yet able to acquire thepower of vision, both are false, as also if Socrates is altogether non-existent.
But in the case of affirmation and negation, whether the subject exists ornot, one is always false and the other true. For manifestly, if Socrates exists,one of the two propositions ‘Socrates is ill’, ‘Socrates is not ill’, is true, andthe other false. This is likewise the case if he does not exist; for if he does notexist, to say that he is ill is false, to say that he is not ill is true. Thus it is inthe case of those opposites only, which are opposite in the sense in which theterm is used with reference to affirmation and negation, that the rule holdsgood, that one of the pair must be true and the other false.
Part 11 Contrary
That the contrary of a good is an evil is shown by induction: the contraryof health is disease, of courage, cowardice, and so on. But the contrary ofan evil is sometimes a good, sometimes an evil. For defect, which is an evil,has excess for its contrary, this also being an evil, and the mean. which is agood, is equally the contrary of the one and of the other. It is only in a fewcases, however, that we see instances of this: in most, the contrary of an evilis a good.
In the case of contraries, it is not always necessary that if one exists theother should also exist: for if all become healthy there will be health andno disease, and again, if everything turns white, there will be white, but noblack. Again, since the fact that Socrates is ill is the contrary of the fact that
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Socrates is well, and two contrary conditions cannot both obtain in one andthe same individual at the same time, both these contraries could not exist atonce: for if that Socrates was well was a fact, then that Socrates was ill couldnot possibly be one.
It is plain that contrary attributes must needs be present in subjects whichbelong to the same species or genus. Disease and health require as their sub-ject the body of an animal; white and black require a body, without furtherqualification; justice and injustice require as their subject the human soul.
Moreover, it is necessary that pairs of contraries should in all cases eitherbelong to the same genus or belong to contrary genera or be themselves gen-era. White and black belong to the same genus, colour; justice and injustice,to contrary genera, virtue and vice; while good and evil do not belong togenera, but are themselves actual genera, with terms under them.
Part 12 Prior
There are four senses in which one thing can be said to be ‘prior’ to another.Primarily and most properly the term has reference to time: in this sense theword is used to indicate that one thing is older or more ancient than another,for the expressions ‘older’ and ‘more ancient’ imply greater length of time.
Secondly, one thing is said to be ‘prior’ to another when the sequence oftheir being cannot be reversed. In this sense ‘one’ is ‘prior’ to ‘two’. For if‘two’ exists, it follows directly that ‘one’ must exist, but if ‘one’ exists, it doesnot follow necessarily that ‘two’ exists: thus the sequence subsisting cannotbe reversed. It is agreed, then, that when the sequence of two things cannotbe reversed, then that one on which the other depends is called ‘prior’ to thatother.
In the third place, the term ‘prior’ is used with reference to any order,as in the case of science and of oratory. For in sciences which use demon-stration there is that which is prior and that which is posterior in order; ingeometry, the elements are prior to the propositions; in reading and writing,the letters of the alphabet are prior to the syllables. Similarly, in the case ofspeeches, the exordium is prior in order to the narrative.
Besides these senses of the word, there is a fourth. That which is betterand more honourable is said to have a natural priority. In common parlancemen speak of those whom they honour and love as ‘coming first’ with them.This sense of the word is perhaps the most far-fetched.
Such, then, are the different senses in which the term ‘prior’ is used.Yet it would seem that besides those mentioned there is yet another. For
in those things, the being of each of which implies that of the other, thatwhich is in any way the cause may reasonably be said to be by nature ‘prior’to the effect. It is plain that there are instances of this. The fact of the be-
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Simultaneous 27
ing of a man carries with it the truth of the proposition that he is, and theimplication is reciprocal: for if a man is, the proposition wherein we allegethat he is true, and conversely, if the proposition wherein we allege that heis true, then he is. The true proposition, however, is in no way the cause ofthe being of the man, but the fact of the man’s being does seem somehowto be the cause of the truth of the proposition, for the truth or falsity of theproposition depends on the fact of the man’s being or not being.
Thus the word ‘prior’ may be used in five senses.
Part 13 Simultaneous
The term ‘simultaneous’ is primarily and most appropriately applied tothose things the genesis of the one of which is simultaneous with that ofthe other; for in such cases neither is prior or posterior to the other. Suchthings are said to be simultaneous in point of time. Those things, again, are‘simultaneous’ in point of nature, the being of each of which involves thatof the other, while at the same time neither is the cause of the other’s being.This is the case with regard to the double and the half, for these are recipro-cally dependent, since, if there is a double, there is also a half, and if there isa half, there is also a double, while at the same time neither is the cause ofthe being of the other.
Again, those species which are distinguished one from another and op-posed one to another within the same genus are said to be ‘simultaneous’ innature. I mean those species which are distinguished each from each by oneand the same method of division. Thus the ‘winged’ species is simultaneouswith the ‘terrestrial’ and the ‘water’ species. These are distinguished withinthe same genus, and are opposed each to each, for the genus ‘animal’ hasthe ‘winged’, the ‘terrestrial’, and the ‘water’ species, and no one of theseis prior or posterior to another; on the contrary, all such things appear tobe ‘simultaneous’ in nature. Each of these also, the terrestrial, the winged,and the water species, can be divided again into subspecies. Those species,then, also will be ‘simultaneous’ point of nature, which, belonging to thesame genus, are distinguished each from each by one and the same methodof differentiation.
But genera are prior to species, for the sequence of their being cannotbe reversed. If there is the species ‘water-animal’, there will be the genus‘animal’, but granted the being of the genus ‘animal’, it does not follow nec-essarily that there will be the species ‘water-animal’.
Those things, therefore, are said to be ‘simultaneous’ in nature, the beingof each of which involves that of the other, while at the same time neitheris in any way the cause of the other’s being; those species, also, which aredistinguished each from each and opposed within the same genus. Those
CATEGORIES
28 The Categories
things, moreover, are ‘simultaneous’ in the unqualified sense of the wordwhich come into being at the same time.
Part 14 Motion
There are six sorts of movement: generation, destruction, increase, diminu-tion, alteration, and change of place.
It is evident in all but one case that all these sorts of movement are dis-tinct each from each. Generation is distinct from destruction, increase andchange of place from diminution, and so on. But in the case of alteration itmay be argued that the process necessarily implies one or other of the otherfive sorts of motion. This is not true, for we may say that all affections, ornearly all, produce in us an alteration which is distinct from all other sorts ofmotion, for that which is affected need not suffer either increase or diminu-tion or any of the other sorts of motion. Thus alteration is a distinct sort ofmotion; for, if it were not, the thing altered would not only be altered, butwould forthwith necessarily suffer increase or diminution or some one of theother sorts of motion in addition; which as a matter of fact is not the case.Similarly that which was undergoing the process of increase or was subjectto some other sort of motion would, if alteration were not a distinct form ofmotion, necessarily be subject to alteration also. But there are some thingswhich undergo increase but yet not alteration. The square, for instance, ifa gnomon is applied to it, undergoes increase but not alteration, and so itis with all other figures of this sort. Alteration and increase, therefore, aredistinct.
Speaking generally, rest is the contrary of motion. But the different formsof motion have their own contraries in other forms; thus destruction is thecontrary of generation, diminution of increase, rest in a place, of change ofplace. As for this last, change in the reverse direction would seem to be mosttruly its contrary; thus motion upwards is the contrary of motion down-wards and vice versa.
In the case of that sort of motion which yet remains, of those that havebeen enumerated, it is not easy to state what is its contrary. It appears tohave no contrary, unless one should define the contrary here also either as‘rest in its quality’ or as ‘change in the direction of the contrary quality’, justas we defined the contrary of change of place either as rest in a place or aschange in the reverse direction. For a thing is altered when change of qualitytakes place; therefore either rest in its quality or change in the direction of thecontrary may be called the contrary of this qualitative form of motion. In thisway becoming white is the contrary of becoming black; there is alteration inthe contrary direction, since a change of a qualitative nature takes place.
Volume 1 Book I Part 15
To have 29
Part 15 To have
The term ‘to have’ is used in various senses. In the first place it is used withreference to habit or disposition or any other quality, for we are said to ‘have’a piece of knowledge or a virtue. Then, again, it has reference to quantity,as, for instance, in the case of a man’s height; for he is said to ‘have’ a heightof three or four cubits. It is used, moreover, with regard to apparel, a manbeing said to ‘have’ a coat or tunic; or in respect of something which /wehave on a part of ourselves, as a ring on the hand: or in respect of somethingwhich is a part of us, as hand or foot. The term refers also to content, as inthe case of a vessel and wheat, or of a jar and wine; a jar is said to ‘have’wine, and a corn-measure wheat. The expression in such cases has referenceto content. Or it refers to that which has been acquired; we are said to ‘have’a house or a field. A man is also said to ‘have’ a wife, and a wife a husband,and this appears to be the most remote meaning of the term, for by the useof it we mean simply that the husband lives with the wife.
Other senses of the word might perhaps be found, but the most ordinaryones have all been enumerated.
CATEGORIES
Volume 2 ON INTERPRETATION
Book I On Interpretation
Part 1 Language, thought, truth;
First we must define the terms ‘noun’ and ‘verb’, then the terms ‘denial’ and‘affirmation’, then ‘proposition’ and ‘sentence.’
Spoken words are the symbols of mental experience and written wordsare the symbols of spoken words. Just as all men have not the same writing,so all men have not the same speech sounds, but the mental experiences,which these directly symbolize, are the same for all, as also are those thingsof which our experiences are the images. This matter has, however, beendiscussed in my treatise about the soul, for it belongs to an investigationdistinct from that which lies before us.
As there are in the mind thoughts which do not involve truth or falsity,and also those which must be either true or false, so it is in speech. Fortruth and falsity imply combination and separation. Nouns and verbs, pro-vided nothing is added, are like thoughts without combination or separa-tion; ‘man’ and ‘white’, as isolated terms, are not yet either true or false. Inproof of this, consider the word ‘goat-stag.’ It has significance, but there isno truth or falsity about it, unless ‘is’ or ‘is not’ is added, either in the presentor in some other tense.
Part 2 Nouns
By a noun we mean a sound significant by convention, which has no refer-ence to time, and of which no part is significant apart from the rest. In thenoun ‘Fairsteed,’ the part ‘steed’ has no significance in and by itself, as inthe phrase ‘fair steed.’ Yet there is a difference between simple and compos-ite nouns; for in the former the part is in no way significant, in the latter itcontributes to the meaning of the whole, although it has not an independent
32 On Interpretation
meaning. Thus in the word ‘pirate-boat’ the word ‘boat’ has no meaningexcept as part of the whole word.
The limitation ‘by convention’ was introduced because nothing is by na-ture a noun or name - it is only so when it becomes a symbol; inarticulatesounds, such as those which brutes produce, are significant, yet none ofthese constitutes a noun.
The expression ‘not-man’ is not a noun. There is indeed no recognizedterm by which we may denote such an expression, for it is not a sentence ora denial. Let it then be called an indefinite noun.
The expressions ‘of Philo’, ‘to Philo’, and so on, constitute not nouns, butcases of a noun. The definition of these cases of a noun is in other respectsthe same as that of the noun proper, but, when coupled with ‘is’, ‘was’, or‘will be’, they do not, as they are, form a proposition either true or false, andthis the noun proper always does, under these conditions. Take the words‘of Philo is’ or ‘of Philo is not’; these words do not, as they stand, form eithera true or a false proposition.
Part 3 Verbs
A verb is that which, in addition to its proper meaning, carries with it thenotion of time. No part of it has any independent meaning, and it is a signof something said of something else.
I will explain what I mean by saying that it carries with it the notion oftime. ‘Health’ is a noun, but ‘is healthy’ is a verb; for besides its propermeaning it indicates the present existence of the state in question.
Moreover, a verb is always a sign of something said of something else,i.e. of something either predicable of or present in some other thing.
Such expressions as ‘is not-healthy’, ‘is not, ill’, I do not describe as verbs;for though they carry the additional note of time, and always form a pred-icate, there is no specified name for this variety; but let them be called in-definite verbs, since they apply equally well to that which exists and to thatwhich does not.
Similarly ‘he was healthy’, ‘he will be healthy’, are not verbs, but tensesof a verb; the difference lies in the fact that the verb indicates presenttime, while the tenses of the verb indicate those times which lie outside thepresent.
Verbs in and by themselves are substantival and have significance, for hewho uses such expressions arrests the hearer’s mind, and fixes his attention;but they do not, as they stand, express any judgement, either positive or neg-ative. For neither are ‘to be’ and ‘not to be’ the participle ‘being’ significantof any fact, unless something is added; for they do not themselves indicate
Volume 2 Book I Part 4
Sentences and propositions 33
anything, but imply a copulation, of which we cannot form a conceptionapart from the things coupled.
Part 4 Sentences and propositions
A sentence is a significant portion of speech, some parts of which have anindependent meaning, that is to say, as an utterance, though not as the ex-pression of any positive judgement. Let me explain. The word ‘human’ hasmeaning, but does not constitute a proposition, either positive or negative.It is only when other words are added that the whole will form an affirma-tion or denial. But if we separate one syllable of the word ‘human’ from theother, it has no meaning; similarly in the word ‘mouse’, the part ‘ouse’ hasno meaning in itself, but is merely a sound. In composite words, indeed, theparts contribute to the meaning of the whole; yet, as has been pointed out,they have not an independent meaning.
Every sentence has meaning, not as being the natural means by which aphysical faculty is realized, but, as we have said, by convention. Yet everysentence is not a proposition; only such are propositions as have in themeither truth or falsity. Thus a prayer is a sentence, but is neither true norfalse.
Let us therefore dismiss all other types of sentence but the proposition,for this last concerns our present inquiry, whereas the investigation of theothers belongs rather to the study of rhetoric or of poetry.
Part 5 Simple and composite propositions
The first class of simple propositions is the simple affirmation, the next, thesimple denial; all others are only one by conjunction.
Every proposition must contain a verb or the tense of a verb. The phrasewhich defines the species ‘man’, if no verb in present, past, or future time beadded, is not a proposition. It may be asked how the expression ‘a footedanimal with two feet’ can be called single; for it is not the circumstance thatthe words follow in unbroken succession that effects the unity. This inquiry,however, finds its place in an investigation foreign to that before us.
We call those propositions single which indicate a single fact, or the con-junction of the parts of which results in unity: those propositions, on theother hand, are separate and many in number, which indicate many facts, orwhose parts have no conjunction.
Let us, moreover, consent to call a noun or a verb an expression only, andnot a proposition, since it is not possible for a man to speak in this way whenhe is expressing something, in such a way as to make a statement, whetherhis utterance is an answer to a question or an act of his own initiation.
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34 On Interpretation
To return: of propositions one kind is simple, i.e. that which asserts ordenies something of something, the other composite, i.e. that which is com-pounded of simple propositions. A simple proposition is a statement, withmeaning, as to the presence of something in a subject or its absence, in thepresent, past, or future, according to the divisions of time.
Part 6 Affirmation, denial, contradictories
An affirmation is a positive assertion of something about something, a deniala negative assertion.
Now it is possible both to affirm and to deny the presence of somethingwhich is present or of something which is not, and since these same affir-mations and denials are possible with reference to those times which lie out-side the present, it would be possible to contradict any affirmation or denial.Thus it is plain that every affirmation has an opposite denial, and similarlyevery denial an opposite affirmation.
We will call such a pair of propositions a pair of contradictories. Thosepositive and negative propositions are said to be contradictory which havethe same subject and predicate. The identity of subject and of predicate mustnot be ‘equivocal’. Indeed there are definitive qualifications besides this,which we make to meet the casuistries of sophists.
Part 7 Universal and individual subjects
Some things are universal, others individual. By the term ‘universal’ I meanthat which is of such a nature as to be predicated of many subjects, by ‘indi-vidual’ that which is not thus predicated. Thus ‘man’ is a universal, ‘Callias’an individual.
Our propositions necessarily sometimes concern a universal subject,sometimes an individual.
If, then, a man states a positive and a negative proposition of univer-sal character with regard to a universal, these two propositions are ‘con-trary’. By the expression ‘a proposition of universal character with regardto a universal’, such propositions as ‘every man is white’, ‘no man is white’are meant. When, on the other hand, the positive and negative propositions,though they have regard to a universal, are yet not of universal character,they will not be contrary, albeit the meaning intended is sometimes con-trary. As instances of propositions made with regard to a universal, but notof universal character, we may take the propositions ‘man is white’, ‘manis not white’. ‘Man’ is a universal, but the proposition is not made as ofuniversal character; for the word ‘every’ does not make the subject a uni-versal, but rather gives the proposition a universal character. If, however,
Volume 2 Book I Part 7
Universal and individual subjects 35
both predicate and subject are distributed, the proposition thus constitutedis contrary to truth; no affirmation will, under such circumstances, be true.The proposition ‘every man is every animal’ is an example of this type.
An affirmation is opposed to a denial in the sense which I denote by theterm ‘contradictory’, when, while the subject remains the same, the affirma-tion is of universal character and the denial is not. The affirmation ‘everyman is white’ is the contradictory of the denial ‘not every man is white’, oragain, the proposition ‘no man is white’ is the contradictory of the proposi-tion ‘some men are white’. But propositions are opposed as contraries whenboth the affirmation and the denial are universal, as in the sentences ‘everyman is white’, ‘no man is white’, ‘every man is just’, ‘no man is just’.
We see that in a pair of this sort both propositions cannot be true, butthe contradictories of a pair of contraries can sometimes both be true withreference to the same subject; for instance ‘not every man is white’ and ‘somemen are white’ are both true. Of such corresponding positive and negativepropositions as refer to universals and have a universal character, one mustbe true and the other false. This is the case also when the reference is toindividuals, as in the propositions ‘Socrates is white’, ‘Socrates is not white’.
When, on the other hand, the reference is to universals, but the proposi-tions are not universal, it is not always the case that one is true and the otherfalse, for it is possible to state truly that man is white and that man is notwhite and that man is beautiful and that man is not beautiful; for if a manis deformed he is the reverse of beautiful, also if he is progressing towardsbeauty he is not yet beautiful.
This statement might seem at first sight to carry with it a contradiction,owing to the fact that the proposition ‘man is not white’ appears to be equiv-alent to the proposition ‘no man is white’. This, however, is not the case, norare they necessarily at the same time true or false.
It is evident also that the denial corresponding to a single affirmation isitself single; for the denial must deny just that which the affirmation affirmsconcerning the same subject, and must correspond with the affirmation bothin the universal or particular character of the subject and in the distributedor undistributed sense in which it is understood.
For instance, the affirmation ‘Socrates is white’ has its proper denial inthe proposition ‘Socrates is not white’. If anything else be negatively pred-icated of the subject or if anything else be the subject though the predicateremain the same, the denial will not be the denial proper to that affirmation,but on that is distinct.
The denial proper to the affirmation ‘every man is white’ is ‘not everyman is white’; that proper to the affirmation ‘some men are white’ is ‘noman is white’, while that proper to the affirmation ‘man is white’ is ‘man isnot white’.
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36 On Interpretation
We have shown further that a single denial is contradictorily opposite toa single affirmation and we have explained which these are; we have alsostated that contrary are distinct from contradictory propositions and whichthe contrary are; also that with regard to a pair of opposite propositions it isnot always the case that one is true and the other false. We have pointed out,moreover, what the reason of this is and under what circumstances the truthof the one involves the falsity of the other.
Part 8 Single affirmations
An affirmation or denial is single, if it indicates some one fact about someone subject; it matters not whether the subject is universal and whether thestatement has a universal character, or whether this is not so. Such singlepropositions are: ‘every man is white’, ‘not every man is white’;‘man iswhite’,‘man is not white’; ‘no man is white’, ‘some men are white’; providedthe word ‘white’ has one meaning. If, on the other hand, one word has twomeanings which do not combine to form one, the affirmation is not single.For instance, if a man should establish the symbol ‘garment’ as significantboth of a horse and of a man, the proposition ‘garment is white’ would notbe a single affirmation, nor its opposite a single denial. For it is equivalentto the proposition ‘horse and man are white’, which, again, is equivalentto the two propositions ‘horse is white’, ‘man is white’. If, then, these twopropositions have more than a single significance, and do not form a singleproposition, it is plain that the first proposition either has more than onesignificance or else has none; for a particular man is not a horse.
This, then, is another instance of those propositions of which both thepositive and the negative forms may be true or false simultaneously.
Part 9 Necessity and contradiction
In the case of that which is or which has taken place, propositions, whetherpositive or negative, must be true or false. Again, in the case of a pair ofcontradictories, either when the subject is universal and the propositionsare of a universal character, or when it is individual, as has been said, oneof the two must be true and the other false; whereas when the subject isuniversal, but the propositions are not of a universal character, there is nosuch necessity. We have discussed this type also in a previous chapter.
When the subject, however, is individual, and that which is predicatedof it relates to the future, the case is altered. For if all propositions whetherpositive or negative are either true or false, then any given predicate musteither belong to the subject or not, so that if one man affirms that an eventof a given character will take place and another denies it, it is plain that the
Volume 2 Book I Part 9
Necessity and contradiction 37
statement of the one will correspond with reality and that of the other willnot. For the predicate cannot both belong and not belong to the subject atone and the same time with regard to the future.
Thus, if it is true to say that a thing is white, it must necessarily be white;if the reverse proposition is true, it will of necessity not be white. Again, if itis white, the proposition stating that it is white was true; if it is not white, theproposition to the opposite effect was true. And if it is not white, the manwho states that it is making a false statement; and if the man who states thatit is white is making a false statement, it follows that it is not white. It maytherefore be argued that it is necessary that affirmations or denials must beeither true or false.
Now if this be so, nothing is or takes place fortuitously, either in thepresent or in the future, and there are no real alternatives; everything takesplace of necessity and is fixed. For either he that affirms that it will takeplace or he that denies this is in correspondence with fact, whereas if thingsdid not take place of necessity, an event might just as easily not happen ashappen; for the meaning of the word ‘fortuitous’ with regard to present orfuture events is that reality is so constituted that it may issue in either of twoopposite directions. Again, if a thing is white now, it was true before to saythat it would be white, so that of anything that has taken place it was alwaystrue to say ‘it is’ or ‘it will be’. But if it was always true to say that a thing isor will be, it is not possible that it should not be or not be about to be, andwhen a thing cannot not come to be, it is impossible that it should not cometo be, and when it is impossible that it should not come to be, it must cometo be. All, then, that is about to be must of necessity take place. It resultsfrom this that nothing is uncertain or fortuitous, for if it were fortuitous itwould not be necessary.
Again, to say that neither the affirmation nor the denial is true, maintain-ing, let us say, that an event neither will take place nor will not take place,is to take up a position impossible to defend. In the first place, though factsshould prove the one proposition false, the opposite would still be untrue.Secondly, if it was true to say that a thing was both white and large, boththese qualities must necessarily belong to it; and if they will belong to it thenext day, they must necessarily belong to it the next day. But if an eventis neither to take place nor not to take place the next day, the element ofchance will be eliminated. For example, it would be necessary that a sea-fight should neither take place nor fail to take place on the next day.
These awkward results and others of the same kind follow, if it is anirrefragable law that of every pair of contradictory propositions, whetherthey have regard to universals and are stated as universally applicable, orwhether they have regard to individuals, one must be true and the otherfalse, and that there are no real alternatives, but that all that is or takes place
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38 On Interpretation
is the outcome of necessity. There would be no need to deliberate or to taketrouble, on the supposition that if we should adopt a certain course, a certainresult would follow, while, if we did not, the result would not follow. For aman may predict an event ten thousand years beforehand, and another maypredict the reverse; that which was truly predicted at the moment in the pastwill of necessity take place in the fullness of time.
Further, it makes no difference whether people have or have not actuallymade the contradictory statements. For it is manifest that the circumstancesare not influenced by the fact of an affirmation or denial on the part of any-one. For events will not take place or fail to take place because it was statedthat they would or would not take place, nor is this any more the case ifthe prediction dates back ten thousand years or any other space of time.Wherefore, if through all time the nature of things was so constituted that aprediction about an event was true, then through all time it was necessarythat that should find fulfillment; and with regard to all events, circumstanceshave always been such that their occurrence is a matter of necessity. For thatof which someone has said truly that it will be, cannot fail to take place; andof that which takes place, it was always true to say that it would be.
Yet this view leads to an impossible conclusion; for we see that bothdeliberation and action are causative with regard to the future, and that,to speak more generally, in those things which are not continuously actualthere is potentiality in either direction. Such things may either be or not be;events also therefore may either take place or not take place. There are manyobvious instances of this. It is possible that this coat may be cut in half, andyet it may not be cut in half, but wear out first. In the same way, it is possiblethat it should not be cut in half; unless this were so, it would not be possiblethat it should wear out first. So it is therefore with all other events whichpossess this kind of potentiality. It is therefore plain that it is not of neces-sity that everything is or takes place; but in some instances there are realalternatives, in which case the affirmation is no more true and no more falsethan the denial; while some exhibit a predisposition and general tendencyin one direction or the other, and yet can issue in the opposite direction byexception.
Now that which is must needs be when it is, and that which is not mustneeds not be when it is not. Yet it cannot be said without qualification thatall existence and non-existence is the outcome of necessity. For there is adifference between saying that that which is, when it is, must needs be, andsimply saying that all that is must needs be, and similarly in the case of thatwhich is not. In the case, also, of two contradictory propositions this holdsgood. Everything must either be or not be, whether in the present or in thefuture, but it is not always possible to distinguish and state determinatelywhich of these alternatives must necessarily come about.
Volume 2 Book I Part 9
Affirmation or denial requires a noun and a verb 39
Let me illustrate. A sea-fight must either take place to-morrow or not,but it is not necessary that it should take place to-morrow, neither is it nec-essary that it should not take place, yet it is necessary that it either should orshould not take place to-morrow. Since propositions correspond with facts,it is evident that when in future events there is a real alternative, and a po-tentiality in contrary directions, the corresponding affirmation and denialhave the same character.
This is the case with regard to that which is not always existent or notalways nonexistent. One of the two propositions in such instances must betrue and the other false, but we cannot say determinately that this or thatis false, but must leave the alternative undecided. One may indeed be morelikely to be true than the other, but it cannot be either actually true or actuallyfalse. It is therefore plain that it is not necessary that of an affirmation and adenial one should be true and the other false. For in the case of that whichexists potentially, but not actually, the rule which applies to that which existsactually does not hold good. The case is rather as we have indicated.
Part 10 Affirmation or denial requires a noun and a verb
An affirmation is the statement of a fact with regard to a subject, and thissubject is either a noun or that which has no name; the subject and predicatein an affirmation must each denote a single thing. I have already explainedwhat is meant by a noun and by that which has no name; for I stated thatthe expression ‘not-man’ was not a noun, in the proper sense of the word,but an indefinite noun, denoting as it does in a certain sense a single thing.Similarly the expression ‘does not enjoy health’ is not a verb proper, but anindefinite verb. Every affirmation, then, and every denial, will consist of anoun and a verb, either definite or indefinite.
There can be no affirmation or denial without a verb; for the expressions‘is’, ‘will be’, ‘was’, ‘is coming to be’, and the like are verbs according toour definition, since besides their specific meaning they convey the notionof time. Thus the primary affirmation and denial are as follows: ‘man is’,‘man is not’. Next to these, there are the propositions: ‘not-man is’, ‘not-manis not’. Again we have the propositions: ‘every man is’, ‘every man is not’,‘all that is not-man is’, ‘all that is not-man is not’. The same classificationholds good with regard to such periods of time as lie outside the present.
When the verb ‘is’ is used as a third element in the sentence, there can bepositive and negative propositions of two sorts. Thus in the sentence ‘manis just’ the verb ‘is’ is used as a third element, call it verb or noun, whichyou will. Four propositions, therefore, instead of two can be formed withthese materials. Two of the four, as regards their affirmation and denial,correspond in their logical sequence with the propositions which deal with
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40 On Interpretation
a condition of privation; the other two do not correspond with these.I mean that the verb ‘is’ is added either to the term ‘just’ or to the term
‘not-just’, and two negative propositions are formed in the same way. Thuswe have the four propositions. Reference to the subjoined table will makematters clear:
A. Affirmation B. DenialMan is just Man is not just
×D. Denial C. Affirmation
Man is not not-just Man is not-just
Here ‘is’ and ‘is not’ are added either to ‘just’ or to ‘not-just’. This then isthe proper scheme for these propositions, as has been said in the Analytics.The same rule holds good, if the subject is distributed. Thus we have thetable:
A’. Affirmation B’. DenialEvery man is just Not every man is just
×D’. Denial C’. Affirmation
Not every man is not-just Every man is not-just
Yet here it is not possible, in the same way as in the former case, thatthe propositions joined in the table by a diagonal line should both be true;though under certain circumstances this is the case.
We have thus set out two pairs of opposite propositions; there are more-over two other pairs, if a term be conjoined with ‘not-man’, the latter forminga kind of subject. Thus:
A". Affirmation B". DenialNot-man is just Not-man is not just
×D". Denial C". Affirmation
Not-man is not not-just Not-man is not-just
This is an exhaustive enumeration of all the pairs of opposite proposi-tions that can possibly be framed. This last group should remain distinctfrom those which preceded it, since it employs as its subject the expression‘not-man’.
When the verb ‘is’ does not fit the structure of the sentence (for instance,when the verbs ‘walks’, ‘enjoys health’ are used), that scheme applies, which
Volume 2 Book I Part 10
Affirmation or denial requires a noun and a verb 41
applied when the word ‘is’ was added.Thus we have the propositions: ‘every man enjoys health’, ‘every man
does-not-enjoy-health’, ‘all that is not-man enjoys health’, ‘all that is not-mandoes-not-enjoy-health’. We must not in these propositions use the expression‘not every man’. The negative must be attached to the word ‘man’, for theword ‘every’ does not give to the subject a universal significance, but impliesthat, as a subject, it is distributed. This is plain from the following pairs:‘man enjoys health’, ‘man does not enjoy health’; ‘not-man enjoys health’,‘not man does not enjoy health’. These propositions differ from the formerin being indefinite and not universal in character. Thus the adjectives ‘every’and no additional significance except that the subject, whether in a positiveor in a negative sentence, is distributed. The rest of the sentence, therefore,will in each case be the same.
Since the contrary of the proposition ‘every animal is just’ is ‘no animalis just’, it is plain that these two propositions will never both be true at thesame time or with reference to the same subject. Sometimes, however, thecontradictories of these contraries will both be true, as in the instance beforeus: the propositions ‘not every animal is just’ and ‘some animals are just’ areboth true.
Further, the proposition ‘no man is just’ follows from the proposition‘every man is not just’ and the proposition ‘not every man is not just’, whichis the opposite of ‘every man is not-just’, follows from the proposition ‘somemen are just’; for if this be true, there must be some just men.
It is evident, also, that when the subject is individual, if a question isasked and the negative answer is the true one, a certain positive propositionis also true. Thus, if the question were asked ‘Is Socrates wise?’ and thenegative answer were the true one, the positive inference ‘Then Socrates isunwise’ is correct. But no such inference is correct in the case of universals,but rather a negative proposition. For instance, if to the question ‘Is everyman wise?’ the answer is ‘no’, the inference ‘Then every man is unwise’ isfalse. But under these circumstances the inference ‘Not every man is wise’is correct. This last is the contradictory, the former the contrary. Negativeexpressions, which consist of an indefinite noun or predicate, such as ‘not-man’ or ‘not-just’, may seem to be denials containing neither noun nor verbin the proper sense of the words. But they are not. For a denial must alwaysbe either true or false, and he that uses the expression ‘not man’, if nothingmore be added, is not nearer but rather further from making a true or a falsestatement than he who uses the expression ‘man’.
The propositions ‘everything that is not man is just’, and the contradic-tory of this, are not equivalent to any of the other propositions; on the otherhand, the proposition ‘everything that is not man is not just’ is equivalent tothe proposition ‘nothing that is not man is just’.
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The conversion of the position of subject and predicate in a sentence in-volves no difference in its meaning. Thus we say ‘man is white’ and ‘whiteis man’. If these were not equivalent, there would be more than one contra-dictory to the same proposition, whereas it has been demonstrated that eachproposition has one proper contradictory and one only. For of the proposi-tion ‘man is white’ the appropriate contradictory is ‘man is not white’, and ofthe proposition ‘white is man’, if its meaning be different, the contradictorywill either be ‘white is not not-man’ or ’white is not man’. Now the former ofthese is the contradictory of the proposition ‘white is not-man’, and the latterof these is the contradictory of the proposition ‘man is white’; thus there willbe two contradictories to one proposition.
It is evident, therefore, that the inversion of the relative position of subjectand predicate does not affect the sense of affirmations and denials.
Part 11 Concerning the unity of affirmations
There is no unity about an affirmation or denial which, either positively ornegatively, predicates one thing of many subjects, or many things of thesame subject, unless that which is indicated by the many is really some onething. do not apply this word ‘one’ to those things which, though they havea single recognized name, yet do not combine to form a unity. Thus, manmay be an animal, and biped, and domesticated, but these three predicatescombine to form a unity. On the other hand, the predicates ‘white’, ‘man’,and ‘walking’ do not thus combine. Neither, therefore, if these three formthe subject of an affirmation, nor if they form its predicate, is there any unityabout that affirmation. In both cases the unity is linguistic, but not real.
If therefore the dialectical question is a request for an answer, i.e. eitherfor the admission of a premiss or for the admission of one of two contra-dictories - and the premiss is itself always one of two contradictories - theanswer to such a question as contains the above predicates cannot be a sin-gle proposition. For as I have explained in the Topics, question is not a singleone, even if the answer asked for is true.
At the same time it is plain that a question of the form ‘what is it?’ isnot a dialectical question, for a dialectical questioner must by the form ofhis question give his opponent the chance of announcing one of two alterna-tives, whichever he wishes. He must therefore put the question into a moredefinite form, and inquire, e.g.. whether man has such and such a character-istic or not.
Some combinations of predicates are such that the separate predicatesunite to form a single predicate. Let us consider under what conditions thisis and is not possible. We may either state in two separate propositions thatman is an animal and that man is a biped, or we may combine the two, and
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Concerning the unity of affirmations 43
state that man is an animal with two feet. Similarly we may use ‘man’ and‘white’ as separate predicates, or unite them into one. Yet if a man is a shoe-maker and is also good, we cannot construct a composite proposition andsay that he is a good shoemaker. For if, whenever two separate predicatestruly belong to a subject, it follows that the predicate resulting from theircombination also truly belongs to the subject, many absurd results ensue.For instance, a man is man and white. Therefore, if predicates may alwaysbe combined, he is a white man. Again, if the predicate ‘white’ belongs tohim, then the combination of that predicate with the former composite pred-icate will be permissible. Thus it will be right to say that he is a white man soon indefinitely. Or, again, we may combine the predicates ‘musical’, ‘white’,and ‘walking’, and these may be combined many times. Similarly we maysay that Socrates is Socrates and a man, and that therefore he is the manSocrates, or that Socrates is a man and a biped, and that therefore he is atwo-footed man. Thus it is manifest that if man states unconditionally thatpredicates can always be combined, many absurd consequences ensue.
We will now explain what ought to be laid down.Those predicates, and terms forming the subject of predication, which
are accidental either to the same subject or to one another, do not combine toform a unity. Take the proposition ‘man is white of complexion and musical’.Whiteness and being musical do not coalesce to form a unity, for they belongonly accidentally to the same subject. Nor yet, if it were true to say thatthat which is white is musical, would the terms ‘musical’ and ‘white’ forma unity, for it is only incidentally that that which is musical is white; thecombination of the two will, therefore, not form a unity.
Thus, again, whereas, if a man is both good and a shoemaker, we cannotcombine the two propositions and say simply that he is a good shoemaker,we are, at the same time, able to combine the predicates ‘animal’ and ‘biped’and say that a man is an animal with two feet, for these predicates are notaccidental.
Those predicates, again, cannot form a unity, of which the one is im-plicit in the other: thus we cannot combine the predicate ‘white’ again andagain with that which already contains the notion ‘white’, nor is it right tocall a man an animal-man or a two-footed man; for the notions ‘animal’ and‘biped’ are implicit in the word ‘man’. On the other hand, it is possible topredicate a term simply of any one instance, and to say that some one par-ticular man is a man or that some one white man is a white man.
Yet this is not always possible: indeed, when in the adjunct there is someopposite which involves a contradiction, the predication of the simple termis impossible. Thus it is not right to call a dead man a man. When, however,this is not the case, it is not impossible.
Yet the facts of the case might rather be stated thus: when some such op-
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posite elements are present, resolution is never possible, but when they arenot present, resolution is nevertheless not always possible. Take the proposi-tion ‘Homer is so-and-so’, say ‘a poet’; does it follow that Homer is, or doesit not? The verb ‘is’ is here used of Homer only incidentally, the propositionbeing that Homer is a poet, not that he is, in the independent sense of theword.
Thus, in the case of those predications which have within them no con-tradiction when the nouns are expanded into definitions, and wherein thepredicates belong to the subject in their own proper sense and not in anyindirect way, the individual may be the subject of the simple propositions aswell as of the composite. But in the case of that which is not, it is not true tosay that because it is the object of opinion, it is; for the opinion held about itis that it is not, not that it is.
Part 12 Asserting or denying possibility, contingency,impossibility, necessity
As these distinctions have been made, we must consider the mutual relationof those affirmations and denials which assert or deny possibility or contin-gency, impossibility or necessity: for the subject is not without difficulty.
We admit that of composite expressions those are contradictory each toeach which have the verb ‘to be’ its positive and negative form respectively.Thus the contradictory of the proposition ‘man is’ is ‘man is not’, not ‘not-man is’, and the contradictory of ‘man is white’ is ‘man is not white’, not‘man is not-white’. For otherwise, since either the positive or the negativeproposition is true of any subject, it will turn out true to say that a piece ofwood is a man that is not white.
Now if this is the case, in those propositions which do not contain theverb ‘to be’ the verb which takes its place will exercise the same function.Thus the contradictory of ‘man walks’ is ‘man does not walk’, not ‘not-manwalks’; for to say ‘man walks’ merely equivalent to saying ‘man is walking’.
If then this rule is universal, the contradictory of ‘it may be’ is ‘may notbe’, not ‘it cannot be’.
Now it appears that the same thing both may and may not be; for in-stance, everything that may be cut or may walk may also escape cutting andrefrain from walking; and the reason is that those things that have potential-ity in this sense are not always actual. In such cases, both the positive andthe negative propositions will be true; for that which is capable of walkingor of being seen has also a potentiality in the opposite direction.
But since it is impossible that contradictory propositions should both betrue of the same subject, it follows that ‘it may not be’ is not the contradictoryof ‘it may be’. For it is a logical consequence of what we have said, either
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Asserting or denying possibility, contingency, impossibility, necessity 45
that the same predicate can be both applicable and inapplicable to one andthe same subject at the same time, or that it is not by the addition of theverbs ‘be’ and ‘not be’, respectively, that positive and negative propositionsare formed. If the former of these alternatives must be rejected, we mustchoose the latter.
The contradictory, then, of ‘it may be’ is ‘it cannot be’. The same rule ap-plies to the proposition ‘it is contingent that it should be’; the contradictoryof this is ‘it is not contingent that it should be’. The similar propositions, suchas ‘it is necessary’ and ‘it is impossible’, may be dealt with in the same man-ner. For it comes about that just as in the former instances the verbs ‘is’ and‘is not’ were added to the subject-matter of the sentence ‘white’ and ‘man’, sohere ‘that it should be’ and ‘that it should not be’ are the subject-matter and‘is possible’, ‘is contingent’, are added. These indicate that a certain thingis or is not possible, just as in the former instances ‘is’ and ‘is not’ indicatedthat certain things were or were not the case.
The contradictory, then, of ‘it may not be’ is not ‘it cannot be’, but ‘itcannot not be’, and the contradictory of ‘it may be’ is not ‘it may not be’, but‘cannot be’. Thus the propositions ‘it may be’ and ‘it may not be’ appear eachto imply the other: for, since these two propositions are not contradictory,the same thing both may and may not be. But the propositions ‘it may be’and ‘it cannot be’ can never be true of the same subject at the same time,for they are contradictory. Nor can the propositions ‘it may not be’ and ‘itcannot not be’ be at once true of the same subject.
The propositions which have to do with necessity are governed by thesame principle. The contradictory of ‘it is necessary that it should be’, is not‘it is necessary that it should not be,’ but ‘it is not necessary that it shouldbe’, and the contradictory of ‘it is necessary that it should not be’ is ‘it is notnecessary that it should not be’.
Again, the contradictory of ‘it is impossible that it should be’ is not ‘it isimpossible that it should not be’ but ‘it is not impossible that it should be’,and the contradictory of ‘it is impossible that it should not be’ is ‘it is notimpossible that it should not be’.
To generalize, we must, as has been stated, define the clauses ‘that itshould be’ and ‘that it should not be’ as the subject-matter of the propo-sitions, and in making these terms into affirmations and denials we mustcombine them with ‘that it should be’ and ‘that it should not be’ respectively.
We must consider the following pairs as contradictory propositions:
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It may be. It cannot be.It is contingent. It is not contingent.It is impossible. It is not impossible.It is necessary. It is not necessary.It is true. It is not true.
Part 13 Possibility and contingency
Logical sequences follow in due course when we have arranged the propo-sitions thus. From the proposition ‘it may be’ it follows that it is contingent,and the relation is reciprocal. It follows also that it is not impossible and notnecessary.
From the proposition ‘it may not be’ or ‘it is contingent that it should notbe’ it follows that it is not necessary that it should not be and that it is notimpossible that it should not be. From the proposition ‘it cannot be’ or ‘it isnot contingent’ it follows that it is necessary that it should not be and that itis impossible that it should be. From the proposition ‘it cannot not be’ or ‘itis not contingent that it should not be’ it follows that it is necessary that itshould be and that it is impossible that it should not be.
Let us consider these statements by the help of a table:
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Possibility and contingency 47
A. B.
It may be. It cannot be.
It is contingent. It is not contingent.
It is not impossible thatit should be.
It is impossible thatit should be.
It is not necessary thatit should be.
It is necessary thatit should not be.
C. D.
It may not be. It cannot not be.
It is contingent thatit should not be.
It is not contingent thatit should not be.
It is not impossible thatit should not be.
It is impossible thatit should not be.
It is not necessary thatit should not be.
It is necessary thatit should be.
Now the propositions ‘it is impossible that it should be’ and ‘it is not im-possible that it should be’ are consequent upon the propositions ‘it may be’,‘it is contingent’, and ‘it cannot be’, ‘it is not contingent’, the contradictoriesupon the contradictories. But there is inversion. The negative of the propo-sition ‘it is impossible’ is consequent upon the proposition ‘it may be’ andthe corresponding positive in the first case upon the negative in the second.For ‘it is impossible’ is a positive proposition and ‘it is not impossible’ isnegative.
We must investigate the relation subsisting between these propositionsand those which predicate necessity. That there is a distinction is clear.In this case, contrary propositions follow respectively from contradictorypropositions, and the contradictory propositions belong to separate se-quences. For the proposition ‘it is not necessary that it should be’ is not thenegative of ‘it is necessary that it should not be’, for both these propositionsmay be true of the same subject; for when it is necessary that a thing should
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not be, it is not necessary that it should be. The reason why the propositionspredicating necessity do not follow in the same kind of sequence as the rest,lies in the fact that the proposition ‘it is impossible’ is equivalent, when usedwith a contrary subject, to the proposition ‘it is necessary’. For when it isimpossible that a thing should be, it is necessary, not that it should be, butthat it should not be, and when it is impossible that a thing should not be,it is necessary that it should be. Thus, if the propositions predicating im-possibility or non-impossibility follow without change of subject from thosepredicating possibility or non-possibility, those predicating necessity mustfollow with the contrary subject; for the propositions ‘it is impossible’ and‘it is necessary’ are not equivalent, but, as has been said, inversely connected.
Yet perhaps it is impossible that the contradictory propositions predicat-ing necessity should be thus arranged. For when it is necessary that a thingshould be, it is possible that it should be. (For if not, the opposite follows,since one or the other must follow; so, if it is not possible, it is impossible,and it is thus impossible that a thing should be, which must necessarily be;which is absurd.)
Yet from the proposition ‘it may be’ it follows that it is not impossible,and from that it follows that it is not necessary; it comes about thereforethat the thing which must necessarily be need not be; which is absurd. Butagain, the proposition ‘it is necessary that it should be’ does not follow fromthe proposition ‘it may be’, nor does the proposition ‘it is necessary that itshould not be’. For the proposition ‘it may be’ implies a twofold possibility,while, if either of the two former propositions is true, the twofold possibilityvanishes. For if a thing may be, it may also not be, but if it is necessarythat it should be or that it should not be, one of the two alternatives will beexcluded. It remains, therefore, that the proposition ‘it is not necessary thatit should not be’ follows from the proposition ‘it may be’. For this is true alsoof that which must necessarily be.
Moreover the proposition ‘it is not necessary that it should not be’ is thecontradictory of that which follows from the proposition ‘it cannot be’; for ‘itcannot be’ is followed by ‘it is impossible that it should be’ and by ‘it is nec-essary that it should not be’, and the contradictory of this is the proposition‘it is not necessary that it should not be’. Thus in this case also contradic-tory propositions follow contradictory in the way indicated, and no logicalimpossibilities occur when they are thus arranged.
It may be questioned whether the proposition ‘it may be’ follows fromthe proposition ‘it is necessary that it should be’. If not, the contradictorymust follow, namely that it cannot be, or, if a man should maintain that thisis not the contradictory, then the proposition ‘it may not be’.
Now both of these are false of that which necessarily is. At the sametime, it is thought that if a thing may be cut it may also not be cut, if a thing
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Possibility and contingency 49
may be it may also not be, and thus it would follow that a thing which mustnecessarily be may possibly not be; which is false. It is evident, then, thatit is not always the case that that which may be or may walk possesses alsoa potentiality in the other direction. There are exceptions. In the first placewe must except those things which possess a potentiality not in accordancewith a rational principle, as fire possesses the potentiality of giving out heat,that is, an irrational capacity. Those potentialities which involve a rationalprinciple are potentialities of more than one result, that is, of contrary results;those that are irrational are not always thus constituted. As I have said, firecannot both heat and not heat, neither has anything that is always actualany twofold potentiality. Yet some even of those potentialities which areirrational admit of opposite results. However, thus much has been said toemphasize the truth that it is not every potentiality which admits of oppositeresults, even where the word is used always in the same sense.
But in some cases the word is used equivocally. For the term ‘possible’ isambiguous, being used in the one case with reference to facts, to that whichis actualized, as when a man is said to find walking possible because he isactually walking, and generally when a capacity is predicated because it isactually realized; in the other case, with reference to a state in which real-ization is conditionally practicable, as when a man is said to find walkingpossible because under certain conditions he would walk. This last sort ofpotentiality belongs only to that which can be in motion, the former can existalso in the case of that which has not this power. Both of that which is walk-ing and is actual, and of that which has the capacity though not necessarilyrealized, it is true to say that it is not impossible that it should walk (or, inthe other case, that it should be), but while we cannot predicate this latterkind of potentiality of that which is necessary in the unqualified sense of theword, we can predicate the former.
Our conclusion, then, is this: that since the universal is consequent uponthe particular, that which is necessary is also possible, though not in everysense in which the word may be used.
We may perhaps state that necessity and its absence are the initial prin-ciples of existence and non-existence, and that all else must be regarded asposterior to these.
It is plain from what has been said that that which is of necessity is actual.Thus, if that which is eternal is prior, actuality also is prior to potentiality.Some things are actualities without potentiality, namely, the primary sub-stances; a second class consists of those things which are actual but also po-tential, whose actuality is in nature prior to their potentiality, though poste-rior in time; a third class comprises those things which are never actualized,but are pure potentialities.
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Part 14 Contrary and contradictory
The question arises whether an affirmation finds its contrary in a denial orin another affirmation; whether the proposition ‘every man is just’ finds itscontrary in the proposition ‘no man is just’, or in the proposition ‘every manis unjust’. Take the propositions ‘Callias is just’, ‘Callias is not just’, ‘Calliasis unjust’; we have to discover which of these form contraries.
Now if the spoken word corresponds with the judgement of the mind,and if, in thought, that judgement is the contrary of another, which pro-nounces a contrary fact, in the way, for instance, in which the judgement‘every man is just’ pronounces a contrary to that pronounced by the judge-ment ‘every man is unjust’, the same must needs hold good with regard tospoken affirmations.
But if, in thought, it is not the judgement which pronounces a contraryfact that is the contrary of another, then one affirmation will not find its con-trary in another, but rather in the corresponding denial. We must thereforeconsider which true judgement is the contrary of the false, that which formsthe denial of the false judgement or that which affirms the contrary fact.
Let me illustrate. There is a true judgement concerning that which isgood, that it is good; another, a false judgement, that it is not good; and athird, which is distinct, that it is bad. Which of these two is contrary to thetrue? And if they are one and the same, which mode of expression forms thecontrary?
It is an error to suppose that judgements are to be defined as contraryin virtue of the fact that they have contrary subjects; for the judgement con-cerning a good thing, that it is good, and that concerning a bad thing, that itis bad, may be one and the same, and whether they are so or not, they bothrepresent the truth. Yet the subjects here are contrary. But judgements arenot contrary because they have contrary subjects, but because they are to thecontrary effect.
Now if we take the judgement that that which is good is good, and an-other that it is not good, and if there are at the same time other attributes,which do not and cannot belong to the good, we must nevertheless refuseto treat as the contraries of the true judgement those which opine that someother attribute subsists which does not subsist, as also those that opine thatsome other attribute does not subsist which does subsist, for both theseclasses of judgement are of unlimited content.
Those judgements must rather be termed contrary to the true judge-ments, in which error is present. Now these judgements are those whichare concerned with the starting points of generation, and generation is thepassing from one extreme to its opposite; therefore error is a like transition.
Now that which is good is both good and not bad. The first quality is part
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Contrary and contradictory 51
of its essence, the second accidental; for it is by accident that it is not bad. Butif that true judgement is most really true, which concerns the subject’s intrin-sic nature, then that false judgement likewise is most really false, which con-cerns its intrinsic nature. Now the judgement that that is good is not good isa false judgement concerning its intrinsic nature, the judgement that it is badis one concerning that which is accidental. Thus the judgement which deniesthe true judgement is more really false than that which positively asserts thepresence of the contrary quality. But it is the man who forms that judgementwhich is contrary to the true who is most thoroughly deceived, for contrariesare among the things which differ most widely within the same class. If thenof the two judgements one is contrary to the true judgement, but that whichis contradictory is the more truly contrary, then the latter, it seems, is thereal contrary. The judgement that that which is good is bad is composite.For presumably the man who forms that judgement must at the same timeunderstand that that which is good is not good.
Further, the contradictory is either always the contrary or never; there-fore, if it must necessarily be so in all other cases, our conclusion in the casejust dealt with would seem to be correct. Now where terms have no con-trary, that judgement is false, which forms the negative of the true; for in-stance, he who thinks a man is not a man forms a false judgement. If then inthese cases the negative is the contrary, then the principle is universal in itsapplication.
Again, the judgement that that which is not good is not good is parallelwith the judgement that that which is good is good. Besides these there is thejudgement that that which is good is not good, parallel with the judgementthat that that is not good is good. Let us consider, therefore, what wouldform the contrary of the true judgement that that which is not good is notgood. The judgement that it is bad would, of course, fail to meet the case,since two true judgements are never contrary and this judgement might betrue at the same time as that with which it is connected. For since somethings which are not good are bad, both judgements may be true. Nor is thejudgement that it is not bad the contrary, for this too might be true, sinceboth qualities might be predicated of the same subject. It remains, therefore,that of the judgement concerning that which is not good, that it is not good,the contrary judgement is that it is good; for this is false. In the same way,moreover, the judgement concerning that which is good, that it is not good,is the contrary of the judgement that it is good.
It is evident that it will make no difference if we universalize the positivejudgement, for the universal negative judgement will form the contrary. Forinstance, the contrary of the judgement that everything that is good is goodis that nothing that is good is good. For the judgement that that which isgood is good, if the subject be understood in a universal sense, is equivalent
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to the judgement that whatever is good is good, and this is identical with thejudgement that everything that is good is good. We may deal similarly withjudgements concerning that which is not good.
If therefore this is the rule with judgements, and if spoken affirmationsand denials are judgements expressed in words, it is plain that the universaldenial is the contrary of the affirmation about the same subject. Thus thepropositions ‘everything good is good’, ‘every man is good’, have for theircontraries the propositions ‘nothing good is good’, ‘no man is good’. Thecontradictory propositions, on the other hand, are ‘not everything good isgood’, ‘not every man is good’.
It is evident, also, that neither true judgements nor true propositions canbe contrary the one to the other. For whereas, when two propositions aretrue, a man may state both at the same time without inconsistency, contrarypropositions are those which state contrary conditions, and contrary condi-tions cannot subsist at one and
Volume 2 Book Part 0
Volume 3 PRIOR ANALYTICS
Book I The syllogism defined
Part 1 Perfect and imperfect syllogisms
We must first state the subject of our inquiry and the faculty to which it be-longs: its subject is demonstration and the faculty that carries it out demon-strative science. We must next define a premiss, a term, and a syllogism,and the nature of a perfect and of an imperfect syllogism; and after that, theinclusion or noninclusion of one term in another as in a whole, and what wemean by predicating one term of all, or none, of another.
A premiss then is a sentence affirming or denying one thing of another.This is either universal or particular or indefinite. By universal I mean thestatement that something belongs to all or none of something else; by partic-ular that it belongs to some or not to some or not to all; by indefinite that itdoes or does not belong, without any mark to show whether it is universalor particular, e.g. ‘contraries are subjects of the same science’, or ‘pleasure isnot good’. The demonstrative premiss differs from the dialectical, becausethe demonstrative premiss is the assertion of one of two contradictory state-ments (the demonstrator does not ask for his premiss, but lays it down),whereas the dialectical premiss depends on the adversary’s choice betweentwo contradictories. But this will make no difference to the production of asyllogism in either case; for both the demonstrator and the dialectician arguesyllogistically after stating that something does or does not belong to some-thing else. Therefore a syllogistic premiss without qualification will be anaffirmation or denial of something concerning something else in the way wehave described; it will be demonstrative, if it is true and obtained throughthe first principles of its science; while a dialectical premiss is the giving ofa choice between two contradictories, when a man is proceeding by ques-tion, but when he is syllogizing it is the assertion of that which is apparentand generally admitted, as has been said in the Topics. The nature then ofa premiss and the difference between syllogistic, demonstrative, and dialec-
54 The syllogism defined
tical premisses, may be taken as sufficiently defined by us in relation to ourpresent need, but will be stated accurately in the sequel.
I call that a term into which the premiss is resolved, i.e. both the predi-cate and that of which it is predicated, ‘being’ being added and ‘not being’removed, or vice versa.
A syllogism is discourse in which, certain things being stated, somethingother than what is stated follows of necessity from their being so. I meanby the last phrase that they produce the consequence, and by this, that nofurther term is required from without in order to make the consequence nec-essary.
I call that a perfect syllogism which needs nothing other than what hasbeen stated to make plain what necessarily follows; a syllogism is imperfect,if it needs either one or more propositions, which are indeed the necessaryconsequences of the terms set down, but have not been expressly stated aspremisses.
That one term should be included in another as in a whole is the sameas for the other to be predicated of all of the first. And we say that one termis predicated of all of another, whenever no instance of the subject can befound of which the other term cannot be asserted: ‘to be predicated of none’must be understood in the same way.
Part 2 Premisses, their modes and conversions
Every premiss states that something either is or must be or may be the at-tribute of something else; of premisses of these three kinds some are affir-mative, others negative, in respect of each of the three modes of attribution;again some affirmative and negative premisses are universal, others partic-ular, others indefinite. It is necessary then that in universal attribution theterms of the negative premiss should be convertible, e.g. if no pleasure isgood, then no good will be pleasure; the terms of the affirmative must beconvertible, not however, universally, but in part, e.g. if every pleasure,isgood, some good must be pleasure; the particular affirmative must convertin part (for if some pleasure is good, then some good will be pleasure); butthe particular negative need not convert, for if some animal is not man, itdoes not follow that some man is not animal.
First then take a universal negative with the terms A and B. If no B is A,neither can any A be B. For if some A (say C) were B, it would not be truethat no B is A; for C is a B. But if every B is A then some A is B. For if no Awere B, then no B could be A. But we assumed that every B is A. Similarlytoo, if the premiss is particular. For if some B is A, then some of the As mustbe B. For if none were, then no B would be A. But if some B is not A, there isno necessity that some of the As should not be B; e.g. let B stand for animal
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and A for man. Not every animal is a man; but every man is an animal.
Part 3 Universal and possible premisses
The same manner of conversion will hold good also in respect of necessarypremisses. The universal negative converts universally; each of the affirma-tives converts into a particular. If it is necessary that no B is A, it is necessaryalso that no A is B. For if it is possible that some A is B, it would be possiblealso that some B is A. If all or some B is A of necessity, it is necessary alsothat some A is B: for if there were no necessity, neither would some of the Bsbe A necessarily. But the particular negative does not convert, for the samereason which we have already stated.
In respect of possible premisses, since possibility is used in several senses(for we say that what is necessary and what is not necessary and what is po-tential is possible), affirmative statements will all convert in a manner similarto those described. For if it is possible that all or some B is A, it will be pos-sible that some A is B. For if that were not possible, then no B could possiblybe A. This has been already proved. But in negative statements the case isdifferent. Whatever is said to be possible, either because B necessarily is A,or because B is not necessarily A, admits of conversion like other negativestatements, e.g. if one should say, it is possible that man is not horse, or thatno garment is white. For in the former case the one term necessarily doesnot belong to the other; in the latter there is no necessity that it should: andthe premiss converts like other negative statements. For if it is possible forno man to be a horse, it is also admissible for no horse to be a man; and ifit is admissible for no garment to be white, it is also admissible for noth-ing white to be a garment. For if any white thing must be a garment, thensome garment will necessarily be white. This has been already proved. Theparticular negative also must be treated like those dealt with above. But ifanything is said to be possible because it is the general rule and natural (andit is in this way we define the possible), the negative premisses can no longerbe converted like the simple negatives; the universal negative premiss doesnot convert, and the particular does. This will be plain when we speak aboutthe possible. At present we may take this much as clear in addition to whathas been said: the statement that it is possible that no B is A or some B is notA is affirmative in form: for the expression ‘is possible’ ranks along with ‘is’,and ‘is’ makes an affirmation always and in every case, whatever the termsto which it is added, in predication, e.g. ‘it is not-good’ or ‘it is not-white’ orin a word ‘it is not-this’. But this also will be proved in the sequel. In con-version these premisses will behave like the other affirmative propositions.
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Part 4 The first figure
After these distinctions we now state by what means, when, and how everysyllogism is produced; subsequently we must speak of demonstration. Syl-logism should be discussed before demonstration because syllogism is thegeneral: the demonstration is a sort of syllogism, but not every syllogism isa demonstration.
Whenever three terms are so related to one another that the last is con-tained in the middle as in a whole, and the middle is either contained in, orexcluded from, the first as in or from a whole, the extremes must be relatedby a perfect syllogism. I call that term middle which is itself contained in an-other and contains another in itself: in position also this comes in the middle.By extremes I mean both that term which is itself contained in another andthat in which another is contained. If A is predicated of all B, and B of all C,A must be predicated of all C: we have already explained what we mean by‘predicated of all’. Similarly also, if A is predicated of no B, and B of all C, itis necessary that no C will be A.
But if the first term belongs to all the middle, but the middle to noneof the last term, there will be no syllogism in respect of the extremes; fornothing necessary follows from the terms being so related; for it is possiblethat the first should belong either to all or to none of the last, so that neither aparticular nor a universal conclusion is necessary. But if there is no necessaryconsequence, there cannot be a syllogism by means of these premisses. Asan example of a universal affirmative relation between the extremes we maytake the terms animal, man, horse; of a universal negative relation, the termsanimal, man, stone. Nor again can syllogism be formed when neither thefirst term belongs to any of the middle, nor the middle to any of the last.As an example of a positive relation between the extremes take the termsscience, line, medicine: of a negative relation science, line, unit.
If then the terms are universally related, it is clear in this figure when asyllogism will be possible and when not, and that if a syllogism is possiblethe terms must be related as described, and if they are so related there willbe a syllogism.
But if one term is related universally, the other in part only, to its subject,there must be a perfect syllogism whenever universality is posited with ref-erence to the major term either affirmatively or negatively, and particularitywith reference to the minor term affirmatively: but whenever the universal-ity is posited in relation to the minor term, or the terms are related in anyother way, a syllogism is impossible. I call that term the major in which themiddle is contained and that term the minor which comes under the middle.Let all B be A and some C be B. Then if ‘predicated of all’ means what wassaid above, it is necessary that some C is A. And if no B is A but some C is B,
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it is necessary that some C is not A. The meaning of ‘predicated of none’ hasalso been defined. So there will be a perfect syllogism. This holds good alsoif the premiss BC should be indefinite, provided that it is affirmative: for weshall have the same syllogism whether the premiss is indefinite or particular.
But if the universality is posited with respect to the minor term either af-firmatively or negatively, a syllogism will not be possible, whether the majorpremiss is positive or negative, indefinite or particular: e.g. if some B is oris not A, and all C is B. As an example of a positive relation between theextremes take the terms good, state, wisdom: of a negative relation, good,state, ignorance. Again if no C is B, but some B is or is not A or not ev-ery B is A, there cannot be a syllogism. Take the terms white, horse, swan:white, horse, raven. The same terms may be taken also if the premiss BA isindefinite.
Nor when the major premiss is universal, whether affirmative or nega-tive, and the minor premiss is negative and particular, can there be a syllo-gism, whether the minor premiss be indefinite or particular: e.g. if all B is Aand some C is not B, or if not all C is B. For the major term may be predica-ble both of all and of none of the minor, to some of which the middle termcannot be attributed. Suppose the terms are animal, man, white: next takesome of the white things of which man is not predicated - swan and snow:animal is predicated of all of the one, but of none of the other. Consequentlythere cannot be a syllogism. Again let no B be A, but let some C not be B.Take the terms inanimate, man, white: then take some white things of whichman is not predicated - swan and snow: the term inanimate is predicated ofall of the one, of none of the other.
Further since it is indefinite to say some C is not B, and it is true that someC is not B, whether no C is B, or not all C is B, and since if terms are assumedsuch that no C is B, no syllogism follows (this has already been stated) it isclear that this arrangement of terms will not afford a syllogism: otherwiseone would have been possible with a universal negative minor premiss. Asimilar proof may also be given if the universal premiss is negative.
Nor can there in any way be a syllogism if both the relations of subjectand predicate are particular, either positively or negatively, or the one neg-ative and the other affirmative, or one indefinite and the other definite, orboth indefinite. Terms common to all the above are animal, white, horse:animal, white, stone.
It is clear then from what has been said that if there is a syllogism in thisfigure with a particular conclusion, the terms must be related as we havestated: if they are related otherwise, no syllogism is possible anyhow. It isevident also that all the syllogisms in this figure are perfect (for they are allcompleted by means of the premisses originally taken) and that all conclu-sions are proved by this figure, viz. universal and particular, affirmative and
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negative. Such a figure I call the first.
Part 5 The second figure
Whenever the same thing belongs to all of one subject, and to none of an-other, or to all of each subject or to none of either, I call such a figure the sec-ond; by middle term in it I mean that which is predicated of both subjects,by extremes the terms of which this is said, by major extreme that which liesnear the middle, by minor that which is further away from the middle. Themiddle term stands outside the extremes, and is first in position. A syllo-gism cannot be perfect anyhow in this figure, but it may be valid whetherthe terms are related universally or not.
If then the terms are related universally a syllogism will be possible,whenever the middle belongs to all of one subject and to none of another(it does not matter which has the negative relation), but in no other way. LetM be predicated of no N, but of all O. Since, then, the negative relation isconvertible, N will belong to no M: but M was assumed to belong to all O:consequently N will belong to no O. This has already been proved. Again ifM belongs to all N, but to no O, then N will belong to no O. For if M belongsto no O, O belongs to no M: but M (as was said) belongs to all N: O thenwill belong to no N: for the first figure has again been formed. But since thenegative relation is convertible, N will belong to no O. Thus it will be thesame syllogism that proves both conclusions.
It is possible to prove these results also by reductio ad impossibile.It is clear then that a syllogism is formed when the terms are so related,
but not a perfect syllogism; for necessity is not perfectly established merelyfrom the original premisses; others also are needed.
But if M is predicated of every N and O, there cannot be a syllogism.Terms to illustrate a positive relation between the extremes are substance,animal, man; a negative relation, substance, animal, number - substance be-ing the middle term.
Nor is a syllogism possible when M is predicated neither of any N nor ofany O. Terms to illustrate a positive relation are line, animal, man: a negativerelation, line, animal, stone.
It is clear then that if a syllogism is formed when the terms are universallyrelated, the terms must be related as we stated at the outset: for if they areotherwise related no necessary consequence follows.
If the middle term is related universally to one of the extremes, a par-ticular negative syllogism must result whenever the middle term is relateduniversally to the major whether positively or negatively, and particularlyto the minor and in a manner opposite to that of the universal statement:by ‘an opposite manner’ I mean, if the universal statement is negative, the
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particular is affirmative: if the universal is affirmative, the particular is neg-ative. For if M belongs to no N, but to some O, it is necessary that N doesnot belong to some O. For since the negative statement is convertible, N willbelong to no M: but M was admitted to belong to some O: therefore N willnot belong to some O: for the result is reached by means of the first figure.Again if M belongs to all N, but not to some O, it is necessary that N does notbelong to some O: for if N belongs to all O, and M is predicated also of allN, M must belong to all O: but we assumed that M does not belong to someO. And if M belongs to all N but not to all O, we shall conclude that N doesnot belong to all O: the proof is the same as the above. But if M is predicatedof all O, but not of all N, there will be no syllogism. Take the terms animal,substance, raven; animal, white, raven. Nor will there be a conclusion whenM is predicated of no O, but of some N. Terms to illustrate a positive rela-tion between the extremes are animal, substance, unit: a negative relation,animal, substance, science.
If then the universal statement is opposed to the particular, we havestated when a syllogism will be possible and when not: but if the premissesare similar in form, I mean both negative or both affirmative, a syllogismwill not be possible anyhow. First let them be negative, and let the majorpremiss be universal, e.g. let M belong to no N, and not to some O. It is pos-sible then for N to belong either to all O or to no O. Terms to illustrate thenegative relation are black, snow, animal. But it is not possible to find termsof which the extremes are related positively and universally, if M belongs tosome O, and does not belong to some O. For if N belonged to all O, but Mto no N, then M would belong to no O: but we assumed that it belongs tosome O. In this way then it is not admissible to take terms: our point must beproved from the indefinite nature of the particular statement. For since it istrue that M does not belong to some O, even if it belongs to no O, and sinceif it belongs to no O a syllogism is (as we have seen) not possible, clearly itwill not be possible now either.
Again let the premisses be affirmative, and let the major premiss as be-fore be universal, e.g. let M belong to all N and to some O. It is possible thenfor N to belong to all O or to no O. Terms to illustrate the negative relationare white, swan, stone. But it is not possible to take terms to illustrate theuniversal affirmative relation, for the reason already stated: the point mustbe proved from the indefinite nature of the particular statement. But if theminor premiss is universal, and M belongs to no O, and not to some N, it ispossible for N to belong either to all O or to no O. Terms for the positive rela-tion are white, animal, raven: for the negative relation, white, stone, raven.If the premisses are affirmative, terms for the negative relation are white,animal, snow; for the positive relation, white, animal, swan. Evidently then,whenever the premisses are similar in form, and one is universal, the other
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particular, a syllogism can, not be formed anyhow. Nor is one possible if themiddle term belongs to some of each of the extremes, or does not belong tosome of either, or belongs to some of the one, not to some of the other, orbelongs to neither universally, or is related to them indefinitely. Commonterms for all the above are white, animal, man: white, animal, inanimate.It is clear then from what has been said that if the terms are related to oneanother in the way stated, a syllogism results of necessity; and if there is asyllogism, the terms must be so related. But it is evident also that all thesyllogisms in this figure are imperfect: for all are made perfect by certainsupplementary statements, which either are contained in the terms of neces-sity or are assumed as hypotheses, i.e. when we prove per impossibile. Andit is evident that an affirmative conclusion is not attained by means of thisfigure, but all are negative, whether universal or particular.
Part 6 The third figure
But if one term belongs to all, and another to none, of a third, or if both be-long to all, or to none, of it, I call such a figure the third; by middle term in itI mean that of which both the predicates are predicated, by extremes I meanthe predicates, by the major extreme that which is further from the middle,by the minor that which is nearer to it. The middle term stands outside theextremes, and is last in position. A syllogism cannot be perfect in this figureeither, but it may be valid whether the terms are related universally or notto the middle term.
If they are universal, whenever both P and R belong to S, it follows thatP will necessarily belong to some R. For, since the affirmative statement isconvertible, S will belong to some R: consequently since P belongs to all S,and S to some R, P must belong to some R: for a syllogism in the first figureis produced. It is possible to demonstrate this also per impossibile and byexposition. For if both P and R belong to all S, should one of the Ss, e.g. N,be taken, both P and R will belong to this, and thus P will belong to some R.
If R belongs to all S, and P to no S, there will be a syllogism to prove thatP will necessarily not belong to some R. This may be demonstrated in thesame way as before by converting the premiss RS. It might be proved alsoper impossibile, as in the former cases. But if R belongs to no S, P to all S,there will be no syllogism. Terms for the positive relation are animal, horse,man: for the negative relation animal, inanimate, man.
Nor can there be a syllogism when both terms are asserted of no S. Termsfor the positive relation are animal, horse, inanimate; for the negative rela-tion man, horse, inanimate - inanimate being the middle term.
It is clear then in this figure also when a syllogism will be possible andwhen not, if the terms are related universally. For whenever both the terms
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are affirmative, there will be a syllogism to prove that one extreme belongsto some of the other; but when they are negative, no syllogism will be possi-ble. But when one is negative, the other affirmative, if the major is negative,the minor affirmative, there will be a syllogism to prove that the one extremedoes not belong to some of the other: but if the relation is reversed, no syl-logism will be possible. If one term is related universally to the middle, theother in part only, when both are affirmative there must be a syllogism, nomatter which of the premisses is universal. For if R belongs to all S, P tosome S, P must belong to some R. For since the affirmative statement is con-vertible S will belong to some P: consequently since R belongs to all S, and Sto some P, R must also belong to some P: therefore P must belong to some R.
Again if R belongs to some S, and P to all S, P must belong to some R.This may be demonstrated in the same way as the preceding. And it is possi-ble to demonstrate it also per impossibile and by exposition, as in the formercases. But if one term is affirmative, the other negative, and if the affirma-tive is universal, a syllogism will be possible whenever the minor term isaffirmative. For if R belongs to all S, but P does not belong to some S, it isnecessary that P does not belong to some R. For if P belongs to all R, and Rbelongs to all S, then P will belong to all S: but we assumed that it did not.Proof is possible also without reduction ad impossibile, if one of the Ss betaken to which P does not belong.
But whenever the major is affirmative, no syllogism will be possible, e.g.if P belongs to all S and R does not belong to some S. Terms for the universalaffirmative relation are animate, man, animal. For the universal negativerelation it is not possible to get terms, if R belongs to some S, and does notbelong to some S. For if P belongs to all S, and R to some S, then P will belongto some R: but we assumed that it belongs to no R. We must put the matteras before. Since the expression ‘it does not belong to some’ is indefinite, itmay be used truly of that also which belongs to none. But if R belongs tono S, no syllogism is possible, as has been shown. Clearly then no syllogismwill be possible here.
But if the negative term is universal, whenever the major is negative andthe minor affirmative there will be a syllogism. For if P belongs to no S, andR belongs to some S, P will not belong to some R: for we shall have the firstfigure again, if the premiss RS is converted.
But when the minor is negative, there will be no syllogism. Terms forthe positive relation are animal, man, wild: for the negative relation, animal,science, wild - the middle in both being the term wild.
Nor is a syllogism possible when both are stated in the negative, but oneis universal, the other particular. When the minor is related universally tothe middle, take the terms animal, science, wild; animal, man, wild. Whenthe major is related universally to the middle, take as terms for a negative
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relation raven, snow, white. For a positive relation terms cannot be found, ifR belongs to some S, and does not belong to some S. For if P belongs to all R,and R to some S, then P belongs to some S: but we assumed that it belongsto no S. Our point, then, must be proved from the indefinite nature of theparticular statement.
Nor is a syllogism possible anyhow, if each of the extremes belongs tosome of the middle or does not belong, or one belongs and the other doesnot to some of the middle, or one belongs to some of the middle, the othernot to all, or if the premisses are indefinite. Common terms for all are animal,man, white: animal, inanimate, white.
It is clear then in this figure also when a syllogism will be possible, andwhen not; and that if the terms are as stated, a syllogism results of neces-sity, and if there is a syllogism, the terms must be so related. It is clear alsothat all the syllogisms in this figure are imperfect (for all are made perfectby certain supplementary assumptions), and that it will not be possible toreach a universal conclusion by means of this figure, whether negative oraffirmative.
Part 7 The relation between the figures
It is evident also that in all the figures, whenever a proper syllogism does notresult, if both the terms are affirmative or negative nothing necessary followsat all, but if one is affirmative, the other negative, and if the negative is stateduniversally, a syllogism always results relating the minor to the major term,e.g. if A belongs to all or some B, and B belongs to no C: for if the premissesare converted it is necessary that C does not belong to some A. Similarly alsoin the other figures: a syllogism always results by means of conversion. It isevident also that the substitution of an indefinite for a particular affirmativewill effect the same syllogism in all the figures.
It is clear too that all the imperfect syllogisms are made perfect by meansof the first figure. For all are brought to a conclusion either ostensively or perimpossibile. In both ways the first figure is formed: if they are made perfectostensively, because (as we saw) all are brought to a conclusion by means ofconversion, and conversion produces the first figure: if they are proved perimpossibile, because on the assumption of the false statement the syllogismcomes about by means of the first figure, e.g. in the last figure, if A and Bbelong to all C, it follows that A belongs to some B: for if A belonged to no B,and B belongs to all C, A would belong to no C: but (as we stated) it belongsto all C. Similarly also with the rest.
It is possible also to reduce all syllogisms to the universal syllogisms inthe first figure. Those in the second figure are clearly made perfect by these,though not all in the same way; the universal syllogisms are made perfect by
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converting the negative premiss, each of the particular syllogisms by reduc-tio ad impossibile. In the first figure particular syllogisms are indeed madeperfect by themselves, but it is possible also to prove them by means of thesecond figure, reducing them ad impossibile, e.g. if A belongs to all B, andB to some C, it follows that A belongs to some C. For if it belonged to no C,and belongs to all B, then B will belong to no C: this we know by means ofthe second figure. Similarly also demonstration will be possible in the caseof the negative. For if A belongs to no B, and B belongs to some C, A willnot belong to some C: for if it belonged to all C, and belongs to no B, then Bwill belong to no C: and this (as we saw) is the middle figure. Consequently,since all syllogisms in the middle figure can be reduced to universal syllo-gisms in the first figure, and since particular syllogisms in the first figurecan be reduced to syllogisms in the middle figure, it is clear that particularsyllogisms can be reduced to universal syllogisms in the first figure. Syllo-gisms in the third figure, if the terms are universal, are directly made perfectby means of those syllogisms; but, when one of the premisses is particular,by means of the particular syllogisms in the first figure: and these (we haveseen) may be reduced to the universal syllogisms in the first figure: conse-quently also the particular syllogisms in the third figure may be so reduced.It is clear then that all syllogisms may be reduced to the universal syllogismsin the first figure.
We have stated then how syllogisms which prove that something belongsor does not belong to something else are constituted, both how syllogismsof the same figure are constituted in themselves, and how syllogisms of dif-ferent figures are related to one another.
Part 8 Necessity, actuality and possibility
Since there is a difference according as something belongs, necessarily be-longs, or may belong to something else (for many things belong indeed, butnot necessarily, others neither necessarily nor indeed at all, but it is possiblefor them to belong), it is clear that there will be different syllogisms to proveeach of these relations, and syllogisms with differently related terms, onesyllogism concluding from what is necessary, another from what is, a thirdfrom what is possible.
There is hardly any difference between syllogisms from necessary pre-misses and syllogisms from premisses which merely assert. When the termsare put in the same way, then, whether something belongs or necessarilybelongs (or does not belong) to something else, a syllogism will or will notresult alike in both cases, the only difference being the addition of the expres-sion ‘necessarily’ to the terms. For the negative statement is convertible alikein both cases, and we should give the same account of the expressions ‘to be
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contained in something as in a whole’ and ‘to be predicated of all of some-thing’. With the exceptions to be made below, the conclusion will be provedto be necessary by means of conversion, in the same manner as in the case ofsimple predication. But in the middle figure when the universal statement isaffirmative, and the particular negative, and again in the third figure whenthe universal is affirmative and the particular negative, the demonstrationwill not take the same form, but it is necessary by the ‘exposition’ of a partof the subject of the particular negative proposition, to which the predicatedoes not belong, to make the syllogism in reference to this: with terms sochosen the conclusion will necessarily follow. But if the relation is necessaryin respect of the part taken, it must hold of some of that term in which thispart is included: for the part taken is just some of that. And each of theresulting syllogisms is in the appropriate figure.
Part 9 Syllogisms with some necessary premisses
It happens sometimes also that when one premiss is necessary the conclu-sion is necessary, not however when either premiss is necessary, but onlywhen the major is, e.g. if A is taken as necessarily belonging or not belong-ing to B, but B is taken as simply belonging to C: for if the premisses aretaken in this way, A will necessarily belong or not belong to C. For since nec-essarily belongs, or does not belong, to every B, and since C is one of the Bs,it is clear that for C also the positive or the negative relation to A will holdnecessarily. But if the major premiss is not necessary, but the minor is neces-sary, the conclusion will not be necessary. For if it were, it would result boththrough the first figure and through the third that A belongs necessarily tosome B. But this is false; for B may be such that it is possible that A shouldbelong to none of it. Further, an example also makes it clear that the conclu-sion not be necessary, e.g. if A were movement, B animal, C man: man is ananimal necessarily, but an animal does not move necessarily, nor does man.Similarly also if the major premiss is negative; for the proof is the same.
In particular syllogisms, if the universal premiss is necessary, then theconclusion will be necessary; but if the particular, the conclusion will notbe necessary, whether the universal premiss is negative or affirmative. Firstlet the universal be necessary, and let A belong to all B necessarily, but letB simply belong to some C: it is necessary then that A belongs to some Cnecessarily: for C falls under B, and A was assumed to belong necessarily toall B. Similarly also if the syllogism should be negative: for the proof will bethe same. But if the particular premiss is necessary, the conclusion will notbe necessary: for from the denial of such a conclusion nothing impossibleresults, just as it does not in the universal syllogisms. The same is true ofnegative syllogisms. Try the terms movement, animal, white.
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Part 10 The second figure with one necessary premiss
In the second figure, if the negative premiss is necessary, then the conclusionwill be necessary, but if the affirmative, not necessary. First let the negativebe necessary; let A be possible of no B, and simply belong to C. Since thenthe negative statement is convertible, B is possible of no A. But A belongs toall C; consequently B is possible of no C. For C falls under A. The same resultwould be obtained if the minor premiss were negative: for if A is possiblebe of no C, C is possible of no A: but A belongs to all B, consequently Cis possible of none of the Bs: for again we have obtained the first figure.Neither then is B possible of C: for conversion is possible without modifyingthe relation.
But if the affirmative premiss is necessary, the conclusion will not be nec-essary. Let A belong to all B necessarily, but to no C simply. If then the neg-ative premiss is converted, the first figure results. But it has been proved inthe case of the first figure that if the negative major premiss is not necessarythe conclusion will not be necessary either. Therefore the same result willobtain here. Further, if the conclusion is necessary, it follows that C neces-sarily does not belong to some A. For if B necessarily belongs to no C, C willnecessarily belong to no B. But B at any rate must belong to some A, if it istrue (as was assumed) that A necessarily belongs to all B. Consequently it isnecessary that C does not belong to some A. But nothing prevents such an Abeing taken that it is possible for C to belong to all of it. Further one mightshow by an exposition of terms that the conclusion is not necessary withoutqualification, though it is a necessary conclusion from the premisses. For ex-ample let A be animal, B man, C white, and let the premisses be assumed tocorrespond to what we had before: it is possible that animal should belongto nothing white. Man then will not belong to anything white, but not nec-essarily: for it is possible for man to be born white, not however so long asanimal belongs to nothing white. Consequently under these conditions theconclusion will be necessary, but it is not necessary without qualification.
Similar results will obtain also in particular syllogisms. For whenever thenegative premiss is both universal and necessary, then the conclusion will benecessary: but whenever the affirmative premiss is universal, the negativeparticular, the conclusion will not be necessary. First then let the negativepremiss be both universal and necessary: let it be possible for no B that Ashould belong to it, and let A simply belong to some C. Since the negativestatement is convertible, it will be possible for no A that B should belongto it: but A belongs to some C; consequently B necessarily does not belongto some of the Cs. Again let the affirmative premiss be both universal andnecessary, and let the major premiss be affirmative. If then A necessarily be-longs to all B, but does not belong to some C, it is clear that B will not belong
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to some C, but not necessarily. For the same terms can be used to demon-strate the point, which were used in the universal syllogisms. Nor again,if the negative statement is necessary but particular, will the conclusion benecessary. The point can be demonstrated by means of the same terms.
Part 11 The third figure with one necessary premiss
In the last figure when the terms are related universally to the middle, andboth premisses are affirmative, if one of the two is necessary, then the conclu-sion will be necessary. But if one is negative, the other affirmative, wheneverthe negative is necessary the conclusion also will be necessary, but when-ever the affirmative is necessary the conclusion will not be necessary. Firstlet both the premisses be affirmative, and let A and B belong to all C, and letAC be necessary. Since then B belongs to all C, C also will belong to someB, because the universal is convertible into the particular: consequently ifA belongs necessarily to all C, and C belongs to some B, it is necessary thatA should belong to some B also. For B is under C. The first figure then isformed. A similar proof will be given also if BC is necessary. For C is con-vertible with some A: consequently if B belongs necessarily to all C, it willbelong necessarily also to some A.
Again let AC be negative, BC affirmative, and let the negative premissbe necessary. Since then C is convertible with some B, but A necessarilybelongs to no C, A will necessarily not belong to some B either: for B is underC. But if the affirmative is necessary, the conclusion will not be necessary.For suppose BC is affirmative and necessary, while AC is negative and notnecessary. Since then the affirmative is convertible, C also will belong tosome B necessarily: consequently if A belongs to none of the Cs, while Cbelongs to some of the Bs, A will not belong to some of the Bs - but not ofnecessity; for it has been proved, in the case of the first figure, that if thenegative premiss is not necessary, neither will the conclusion be necessary.Further, the point may be made clear by considering the terms. Let the termA be ‘good’, let that which B signifies be ‘animal’, let the term C be ‘horse’.It is possible then that the term good should belong to no horse, and it isnecessary that the term animal should belong to every horse: but it is notnecessary that some animal should not be good, since it is possible for everyanimal to be good. Or if that is not possible, take as the term ‘awake’ or‘asleep’: for every animal can accept these.
If, then, the premisses are universal, we have stated when the conclusionwill be necessary. But if one premiss is universal, the other particular, and ifboth are affirmative, whenever the universal is necessary the conclusion alsomust be necessary. The demonstration is the same as before; for the particu-lar affirmative also is convertible. If then it is necessary that B should belong
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to all C, and A falls under C, it is necessary that B should belong to some A.But if B must belong to some A, then A must belong to some B: for conver-sion is possible. Similarly also if AC should be necessary and universal: forB falls under C. But if the particular premiss is necessary, the conclusion willnot be necessary. Let the premiss BC be both particular and necessary, andlet A belong to all C, not however necessarily. If the proposition BC is con-verted the first figure is formed, and the universal premiss is not necessary,but the particular is necessary. But when the premisses were thus, the con-clusion (as we proved was not necessary: consequently it is not here either.Further, the point is clear if we look at the terms. Let A be waking, B biped,and C animal. It is necessary that B should belong to some C, but it is possi-ble for A to belong to C, and that A should belong to B is not necessary. Forthere is no necessity that some biped should be asleep or awake. Similarlyand by means of the same terms proof can be made, should the propositionAC be both particular and necessary.
But if one premiss is affirmative, the other negative, whenever the uni-versal is both negative and necessary the conclusion also will be necessary.For if it is not possible that A should belong to any C, but B belongs to someC, it is necessary that A should not belong to some B. But whenever the af-firmative proposition is necessary, whether universal or particular, or thenegative is particular, the conclusion will not be necessary. The proof of thisby reduction will be the same as before; but if terms are wanted, when theuniversal affirmative is necessary, take the terms ‘waking’ - ‘animal’ - ‘man’,‘man’ being middle, and when the affirmative is particular and necessary,take the terms ‘waking’ - ‘animal’ - ‘white’: for it is necessary that animalshould belong to some white thing, but it is possible that waking should be-long to none, and it is not necessary that waking should not belong to someanimal. But when the negative proposition being particular is necessary,take the terms ‘biped’, ‘moving’, ‘animal’, ‘animal’ being middle.
Part 12 Simple conclusions and necessary conclusions
It is clear then that a simple conclusion is not reached unless both premissesare simple assertions, but a necessary conclusion is possible although oneonly of the premisses is necessary. But in both cases, whether the syllogismsare affirmative or negative, it is necessary that one premiss should be similarto the conclusion. I mean by ‘similar’, if the conclusion is a simple assertion,the premiss must be simple; if the conclusion is necessary, the premiss mustbe necessary. Consequently this also is clear, that the conclusion will be nei-ther necessary nor simple unless a necessary or simple premiss is assumed.
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Part 13 Proof of or from possibility
Perhaps enough has been said about the proof of necessity, how it comesabout and how it differs from the proof of a simple statement. We proceedto discuss that which is possible, when and how and by what means it canbe proved. I use the terms ‘to be possible’ and ‘the possible’ of that which isnot necessary but, being assumed, results in nothing impossible. We say in-deed ambiguously of the necessary that it is possible. But that my definitionof the possible is correct is clear from the phrases by which we deny or onthe contrary affirm possibility. For the expressions ‘it is not possible to be-long’, ‘it is impossible to belong’, and ‘it is necessary not to belong’ are eitheridentical or follow from one another; consequently their opposites also, ‘it ispossible to belong’, ‘it is not impossible to belong’, and ‘it is not necessarynot to belong’, will either be identical or follow from one another. For ofeverything the affirmation or the denial holds good. That which is possiblethen will be not necessary and that which is not necessary will be possible. Itresults that all premisses in the mode of possibility are convertible into oneanother. I mean not that the affirmative are convertible into the negative, butthat those which are affirmative in form admit of conversion by opposition,e.g. ‘it is possible to belong’ may be converted into ‘it is possible not to be-long’, and ‘it is possible for A to belong to all B’ into ‘it is possible for A tobelong to no B’ or ‘not to all B’, and ‘it is possible for A to belong to someB’ into ‘it is possible for A not to belong to some B’. And similarly the otherpropositions in this mode can be converted. For since that which is possibleis not necessary, and that which is not necessary may possibly not belong, itis clear that if it is possible that A should belong to B, it is possible also thatit should not belong to B: and if it is possible that it should belong to all, itis also possible that it should not belong to all. The same holds good in thecase of particular affirmations: for the proof is identical. And such premissesare affirmative and not negative; for ‘to be possible’ is in the same rank as‘to be’, as was said above.
Having made these distinctions we next point out that the expression‘to be possible’ is used in two ways. In one it means to happen generallyand fall short of necessity, e.g. man’s turning grey or growing or decaying,or generally what naturally belongs to a thing (for this has not its necessityunbroken, since man’s existence is not continuous for ever, although if a mandoes exist, it comes about either necessarily or generally). In another sensethe expression means the indefinite, which can be both thus and not thus,e.g. an animal‘s walking or an earthquake’s taking place while it is walking,or generally what happens by chance: for none of these inclines by nature inthe one way more than in the opposite.
That which is possible in each of its two senses is convertible into its
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opposite, not however in the same way: but what is natural is convertiblebecause it does not necessarily belong (for in this sense it is possible that aman should not grow grey) and what is indefinite is convertible because itinclines this way no more than that. Science and demonstrative syllogismare not concerned with things which are indefinite, because the middle termis uncertain; but they are concerned with things that are natural, and as arule arguments and inquiries are made about things which are possible inthis sense. Syllogisms indeed can be made about the former, but it is unusualat any rate to inquire about them.
These matters will be treated more definitely in the sequel; our businessat present is to state the moods and nature of the syllogism made from pos-sible premisses. The expression ‘it is possible for this to belong to that’ maybe understood in two senses: ‘that’ may mean either that to which ‘that’ be-longs or that to which it may belong; for the expression ‘A is possible of thesubject of B’ means that it is possible either of that of which B is stated orof that of which B may possibly be stated. It makes no difference whetherwe say, A is possible of the subject of B, or all B admits of A. It is clear thenthat the expression ‘A may possibly belong to all B’ might be used in twosenses. First then we must state the nature and characteristics of the syllo-gism which arises if B is possible of the subject of C, and A is possible of thesubject of B. For thus both premisses are assumed in the mode of possibil-ity; but whenever A is possible of that of which B is true, one premiss is asimple assertion, the other a problematic. Consequently we must start frompremisses which are similar in form, as in the other cases.
Part 14 Reasoning about possibilities
Whenever A may possibly belong to all B, and B to all C, there will be aperfect syllogism to prove that A may possibly belong to all C. This is clearfrom the definition: for it was in this way that we explained ‘to be possiblefor one term to belong to all of another’. Similarly if it is possible for A tobelong no B, and for B to belong to all C, then it is possible for A to belongto no C. For the statement that it is possible for A not to belong to that ofwhich B may be true means (as we saw) that none of those things which canpossibly fall under the term B is left out of account. But whenever A maybelong to all B, and B may belong to no C, then indeed no syllogism resultsfrom the premisses assumed, but if the premiss BC is converted after themanner of problematic propositions, the same syllogism results as before.For since it is possible that B should belong to no C, it is possible also thatit should belong to all C. This has been stated above. Consequently if B ispossible for all C, and A is possible for all B, the same syllogism again results.Similarly if in both the premisses the negative is joined with ’it is possible’:
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e.g. if A may belong to none of the Bs, and B to none of the Cs. No syllogismresults from the assumed premisses, but if they are converted we shall havethe same syllogism as before. It is clear then that if the minor premiss isnegative, or if both premisses are negative, either no syllogism results, or ifone it is not perfect. For the necessity results from the conversion.
But if one of the premisses is universal, the other particular, when themajor premiss is universal there will be a perfect syllogism. For if A is pos-sible for all B, and B for some C, then A is possible for some C. This is clearfrom the definition of being possible. Again if A may belong to no B, andB may belong to some of the Cs, it is necessary that A may possibly notbelong to some of the Cs. The proof is the same as above. But if the par-ticular premiss is negative, and the universal is affirmative, the major stillbeing universal and the minor particular, e.g. A is possible for all B, B maypossibly not belong to some C, then a clear syllogism does not result fromthe assumed premisses, but if the particular premiss is converted and it islaid down that B possibly may belong to some C, we shall have the sameconclusion as before, as in the cases given at the beginning.
But if the major premiss is the minor universal, whether both are affirma-tive, or negative, or different in quality, or if both are indefinite or particular,in no way will a syllogism be possible. For nothing prevents B from reachingbeyond A, so that as predicates cover unequal areas. Let C be that by whichB extends beyond A. To C it is not possible that A should belong - eitherto all or to none or to some or not to some, since premisses in the mode ofpossibility are convertible and it is possible for B to belong to more thingsthan A can. Further, this is obvious if we take terms; for if the premisses areas assumed, the major term is both possible for none of the minor and mustbelong to all of it. Take as terms common to all the cases under consideration‘animal’ - ‘white’ - ‘man’, where the major belongs necessarily to the minor;‘animal’ - ‘white’ - ‘garment’, where it is not possible that the major shouldbelong to the minor. It is clear then that if the terms are related in this man-ner, no syllogism results. For every syllogism proves that something belongseither simply or necessarily or possibly. It is clear that there is no proof ofthe first or of the second. For the affirmative is destroyed by the negative,and the negative by the affirmative. There remains the proof of possibility.But this is impossible. For it has been proved that if the terms are related inthis manner it is both necessary that the major should belong to all the minorand not possible that it should belong to any. Consequently there cannot bea syllogism to prove the possibility; for the necessary (as we stated) is notpossible.
It is clear that if the terms are universal in possible premisses a syllogismalways results in the first figure, whether they are affirmative or negative,only a perfect syllogism results in the first case, an imperfect in the second.
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But possibility must be understood according to the definition laid down,not as covering necessity. This is sometimes forgotten.
Part 15 Possibility, impossibility
If one premiss is a simple proposition, the other a problematic, wheneverthe major premiss indicates possibility all the syllogisms will be perfect andestablish possibility in the sense defined; but whenever the minor premissindicates possibility all the syllogisms will be imperfect, and those whichare negative will establish not possibility according to the definition, butthat the major does not necessarily belong to any, or to all, of the minor. Forif this is so, we say it is possible that it should belong to none or not to all.Let A be possible for all B, and let B belong to all C. Since C falls under B,and A is possible for all B, clearly it is possible for all C also. So a perfectsyllogism results. Likewise if the premiss AB is negative, and the premissBC is affirmative, the former stating possible, the latter simple attribution, aperfect syllogism results proving that A possibly belongs to no C.
It is clear that perfect syllogisms result if the minor premiss states simplebelonging: but that syllogisms will result if the modality of the premisses isreversed, must be proved per impossibile. At the same time it will be evi-dent that they are imperfect: for the proof proceeds not from the premissesassumed. First we must state that if B‘s being follows necessarily from A’sbeing, B’s possibility will follow necessarily from A’s possibility. Suppose,the terms being so related, that A is possible, and B is impossible. If thenthat which is possible, when it is possible for it to be, might happen, andif that which is impossible, when it is impossible, could not happen, and ifat the same time A is possible and B impossible, it would be possible forA to happen without B, and if to happen, then to be. For that which hashappened, when it has happened, is. But we must take the impossible andthe possible not only in the sphere of becoming, but also in the spheres oftruth and predicability, and the various other spheres in which we speakof the possible: for it will be alike in all. Further we must understand thestatement that B‘s being depends on A’s being, not as meaning that if somesingle thing A is, B will be: for nothing follows of necessity from the beingof some one thing, but from two at least, i.e. when the premisses are relatedin the manner stated to be that of the syllogism. For if C is predicated ofD, and D of F, then C is necessarily predicated of F. And if each is possible,the conclusion also is possible. If then, for example, one should indicate thepremisses by A, and the conclusion by B, it would not only result that if A isnecessary B is necessary, but also that if A is possible, B is possible.
Since this is proved it is evident that if a false and not impossible assump-tion is made, the consequence of the assumption will also be false and not
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impossible: e.g. if A is false, but not impossible, and if B is the consequenceof A, B also will be false but not impossible. For since it has been proved thatif B’s being is the consequence of A‘s being, then B’s possibility will followfrom A’s possibility (and A is assumed to be possible), consequently B willbe possible: for if it were impossible, the same thing would at the same timebe possible and impossible.
Since we have defined these points, let A belong to all B, and B be pos-sible for all C: it is necessary then that should be a possible attribute for allC. Suppose that it is not possible, but assume that B belongs to all C: this isfalse but not impossible. If then A is not possible for C but B belongs to all C,then A is not possible for all B: for a syllogism is formed in the third degree.But it was assumed that A is a possible attribute for all B. It is necessary thenthat A is possible for all C. For though the assumption we made is false andnot impossible, the conclusion is impossible. It is possible also in the firstfigure to bring about the impossibility, by assuming that B belongs to C. Forif B belongs to all C, and A is possible for all B, then A would be possible forall C. But the assumption was made that A is not possible for all C.
We must understand ‘that which belongs to all’ with no limitation in re-spect of time, e.g. to the present or to a particular period, but simply withoutqualification. For it is by the help of such premisses that we make syllogisms,since if the premiss is understood with reference to the present moment,there cannot be a syllogism. For nothing perhaps prevents ‘man’ belongingat a particular time to everything that is moving, i.e. if nothing else weremoving: but ‘moving’ is possible for every horse; yet ‘man’ is possible forno horse. Further let the major term be ‘animal’, the middle ‘moving’, thethe minor ‘man’. The premisses then will be as before, but the conclusionnecessary, not possible. For man is necessarily animal. It is clear then thatthe universal must be understood simply, without limitation in respect oftime.
Again let the premiss AB be universal and negative, and assume that Abelongs to no B, but B possibly belongs to all C. These propositions beinglaid down, it is necessary that A possibly belongs to no C. Suppose that itcannot belong, and that B belongs to C, as above. It is necessary then thatA belongs to some B: for we have a syllogism in the third figure: but thisis impossible. Thus it will be possible for A to belong to no C; for if at issupposed false, the consequence is an impossible one. This syllogism thendoes not establish that which is possible according to the definition, but thatwhich does not necessarily belong to any part of the subject (for this is thecontradictory of the assumption which was made: for it was supposed thatA necessarily belongs to some C, but the syllogism per impossibile estab-lishes the contradictory which is opposed to this). Further, it is clear alsofrom an example that the conclusion will not establish possibility. Let A be
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‘raven’, B ‘intelligent’, and C ‘man’. A then belongs to no B: for no intelligentthing is a raven. But B is possible for all C: for every man may possibly beintelligent. But A necessarily belongs to no C: so the conclusion does notestablish possibility. But neither is it always necessary. Let A be ‘moving’,B ‘science’, C ‘man’. A then will belong to no B; but B is possible for all C.And the conclusion will not be necessary. For it is not necessary that no manshould move; rather it is not necessary that any man should move. Clearlythen the conclusion establishes that one term does not necessarily belong toany instance of another term. But we must take our terms better.
If the minor premiss is negative and indicates possibility, from the actualpremisses taken there can be no syllogism, but if the problematic premissis converted, a syllogism will be possible, as before. Let A belong to all B,and let B possibly belong to no C. If the terms are arranged thus, nothingnecessarily follows: but if the proposition BC is converted and it is assumedthat B is possible for all C, a syllogism results as before: for the terms arein the same relative positions. Likewise if both the relations are negative,if the major premiss states that A does not belong to B, and the minor pre-miss indicates that B may possibly belong to no C. Through the premissesactually taken nothing necessary results in any way; but if the problematicpremiss is converted, we shall have a syllogism. Suppose that A belongsto no B, and B may possibly belong to no C. Through these comes nothingnecessary. But if B is assumed to be possible for all C (and this is true) and ifthe premiss AB remains as before, we shall again have the same syllogism.But if it be assumed that B does not belong to any C, instead of possibly notbelonging, there cannot be a syllogism anyhow, whether the premiss AB isnegative or affirmative. As common instances of a necessary and positiverelation we may take the terms white-animal-snow: of a necessary and neg-ative relation, white-animal-pitch. Clearly then if the terms are universal,and one of the premisses is assertoric, the other problematic, whenever theminor premiss is problematic a syllogism always results, only sometimes itresults from the premisses that are taken, sometimes it requires the conver-sion of one premiss. We have stated when each of these happens and thereason why. But if one of the relations is universal, the other particular, thenwhenever the major premiss is universal and problematic, whether affirma-tive or negative, and the particular is affirmative and assertoric, there willbe a perfect syllogism, just as when the terms are universal. The demon-stration is the same as before. But whenever the major premiss is universal,but assertoric, not problematic, and the minor is particular and problem-atic, whether both premisses are negative or affirmative, or one is negative,the other affirmative, in all cases there will be an imperfect syllogism. Onlysome of them will be proved per impossibile, others by the conversion ofthe problematic premiss, as has been shown above. And a syllogism will be
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possible by means of conversion when the major premiss is universal andassertoric, whether positive or negative, and the minor particular, negative,and problematic, e.g. if A belongs to all B or to no B, and B may possibly notbelong to some C. For if the premiss BC is converted in respect of possibility,a syllogism results. But whenever the particular premiss is assertoric andnegative, there cannot be a syllogism. As instances of the positive relationwe may take the terms white-animal-snow; of the negative, white-animal-pitch. For the demonstration must be made through the indefinite nature ofthe particular premiss. But if the minor premiss is universal, and the majorparticular, whether either premiss is negative or affirmative, problematic orassertoric, nohow is a syllogism possible. Nor is a syllogism possible whenthe premisses are particular or indefinite, whether problematic or assertoric,or the one problematic, the other assertoric. The demonstration is the sameas above. As instances of the necessary and positive relation we may takethe terms animal-white-man; of the necessary and negative relation, animal-white-garment. It is evident then that if the major premiss is universal, asyllogism always results, but if the minor is universal nothing at all can everbe proved.
Part 16 One premiss necessary, the other problematic
Whenever one premiss is necessary, the other problematic, there will be asyllogism when the terms are related as before; and a perfect syllogism whenthe minor premiss is necessary. If the premisses are affirmative the conclu-sion will be problematic, not assertoric, whether the premisses are universalor not: but if one is affirmative, the other negative, when the affirmativeis necessary the conclusion will be problematic, not negative assertoric; butwhen the negative is necessary the conclusion will be problematic negative,and assertoric negative, whether the premisses are universal or not. Possi-bility in the conclusion must be understood in the same manner as before.There cannot be an inference to the necessary negative proposition: for ‘notnecessarily to belong’ is different from ‘necessarily not to belong’.
If the premisses are affirmative, clearly the conclusion which follows isnot necessary. Suppose A necessarily belongs to all B, and let B be possiblefor all C. We shall have an imperfect syllogism to prove that A may belongto all C. That it is imperfect is clear from the proof: for it will be provedin the same manner as above. Again, let A be possible for all B, and let Bnecessarily belong to all C. We shall then have a syllogism to prove that Amay belong to all C, not that A does belong to all C: and it is perfect, notimperfect: for it is completed directly through the original premisses.
But if the premisses are not similar in quality, suppose first that the neg-ative premiss is necessary, and let necessarily A not be possible for any B,
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but let B be possible for all C. It is necessary then that A belongs to no C. Forsuppose A to belong to all C or to some C. Now we assumed that A is notpossible for any B. Since then the negative proposition is convertible, B is notpossible for any A. But A is supposed to belong to all C or to some C. Con-sequently B will not be possible for any C or for all C. But it was originallylaid down that B is possible for all C. And it is clear that the possibility of be-longing can be inferred, since the fact of not belonging is inferred. Again, letthe affirmative premiss be necessary, and let A possibly not belong to anyB, and let B necessarily belong to all C. The syllogism will be perfect, butit will establish a problematic negative, not an assertoric negative. For themajor premiss was problematic, and further it is not possible to prove theassertoric conclusion per impossibile. For if it were supposed that A belongsto some C, and it is laid down that A possibly does not belong to any B, noimpossible relation between B and C follows from these premisses. But if theminor premiss is negative, when it is problematic a syllogism is possible byconversion, as above; but when it is necessary no syllogism can be formed.Nor again when both premisses are negative, and the minor is necessary.The same terms as before serve both for the positive relation-white-animal-snow, and for the negative relation-white-animal-pitch.
The same relation will obtain in particular syllogisms. Whenever the neg-ative proposition is necessary, the conclusion will be negative assertoric: e.g.if it is not possible that A should belong to any B, but B may belong to someof the Cs, it is necessary that A should not belong to some of the Cs. For if Abelongs to all C, but cannot belong to any B, neither can B belong to any A.So if A belongs to all C, to none of the Cs can B belong. But it was laid downthat B may belong to some C. But when the particular affirmative in the neg-ative syllogism, e.g. BC the minor premiss, or the universal proposition inthe affirmative syllogism, e.g. AB the major premiss, is necessary, there willnot be an assertoric conclusion. The demonstration is the same as before.But if the minor premiss is universal, and problematic, whether affirmativeor negative, and the major premiss is particular and necessary, there cannotbe a syllogism. Premisses of this kind are possible both where the relationis positive and necessary, e.g. animal-white-man, and where it is necessaryand negative, e.g. animal-white-garment. But when the universal is nec-essary, the particular problematic, if the universal is negative we may takethe terms animal-white-raven to illustrate the positive relation, or animal-white-pitch to illustrate the negative; and if the universal is affirmative wemay take the terms animal-white-swan to illustrate the positive relation, andanimal-white-snow to illustrate the negative and necessary relation. Noragain is a syllogism possible when the premisses are indefinite, or both par-ticular. Terms applicable in either case to illustrate the positive relation areanimal-white-man: to illustrate the negative, animal-white-inanimate. For
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the relation of animal to some white, and of white to some inanimate, is bothnecessary and positive and necessary and negative. Similarly if the relationis problematic: so the terms may be used for all cases.
Clearly then from what has been said a syllogism results or not fromsimilar relations of the terms whether we are dealing with simple existenceor necessity, with this exception, that if the negative premiss is assertoricthe conclusion is problematic, but if the negative premiss is necessary theconclusion is both problematic and negative assertoric. [It is clear also thatall the syllogisms are imperfect and are perfected by means of the figuresabove mentioned.]
Part 17 Second figure, both premisses problematic
In the second figure whenever both premisses are problematic, no syllogismis possible, whether the premisses are affirmative or negative, universal orparticular. But when one premiss is assertoric, the other problematic, if theaffirmative is assertoric no syllogism is possible, but if the universal negativeis assertoric a conclusion can always be drawn. Similarly when one premissis necessary, the other problematic. Here also we must understand the term‘possible’ in the conclusion, in the same sense as before.
First we must point out that the negative problematic proposition is notconvertible, e.g. if A may belong to no B, it does not follow that B may belongto no A. For suppose it to follow and assume that B may belong to no A. Sincethen problematic affirmations are convertible with negations, whether theyare contraries or contradictories, and since B may belong to no A, it is clearthat B may belong to all A. But this is false: for if all this can be that, it doesnot follow that all that can be this: consequently the negative propositionis not convertible. Further, these propositions are not incompatible, ‘A maybelong to no B’, ‘B necessarily does not belong to some of the As’; e.g. it ispossible that no man should be white (for it is also possible that every manshould be white), but it is not true to say that it is possible that no whitething should be a man: for many white things are necessarily not men, andthe necessary (as we saw) other than the possible.
Moreover it is not possible to prove the convertibility of these proposi-tions by a reductio ad absurdum, i.e. by claiming assent to the followingargument: ‘since it is false that B may belong to no A, it is true that it cannotbelong to no A, for the one statement is the contradictory of the other. But ifthis is so, it is true that B necessarily belongs to some of the As: consequentlyA necessarily belongs to some of the Bs. But this is impossible.’ The argu-ment cannot be admitted, for it does not follow that some A is necessarily B,if it is not possible that no A should be B. For the latter expression is used intwo senses, one if A some is necessarily B, another if some A is necessarily
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not B. For it is not true to say that that which necessarily does not belong tosome of the As may possibly not belong to any A, just as it is not true to saythat what necessarily belongs to some A may possibly belong to all A. If anyone then should claim that because it is not possible for C to belong to all D,it necessarily does not belong to some D, he would make a false assumption:for it does belong to all D, but because in some cases it belongs necessarily,therefore we say that it is not possible for it to belong to all. Hence both thepropositions ‘A necessarily belongs to some B’ and ‘A necessarily does notbelong to some B’ are opposed to the proposition ‘A belongs to all B’. Sim-ilarly also they are opposed to the proposition ‘A may belong to no B’. It isclear then that in relation to what is possible and not possible, in the senseoriginally defined, we must assume, not that A necessarily belongs to someB, but that A necessarily does not belong to some B. But if this is assumed,no absurdity results: consequently no syllogism. It is clear from what hasbeen said that the negative proposition is not convertible.
This being proved, suppose it possible that A may belong to no B andto all C. By means of conversion no syllogism will result: for the major pre-miss, as has been said, is not convertible. Nor can a proof be obtained by areductio ad absurdum: for if it is assumed that B can belong to all C, no falseconsequence results: for A may belong both to all C and to no C. In general, ifthere is a syllogism, it is clear that its conclusion will be problematic becauseneither of the premisses is assertoric; and this must be either affirmative ornegative. But neither is possible. Suppose the conclusion is affirmative: itwill be proved by an example that the predicate cannot belong to the subject.Suppose the conclusion is negative: it will be proved that it is not problem-atic but necessary. Let A be white, B man, C horse. It is possible then for Ato belong to all of the one and to none of the other. But it is not possible forB to belong nor not to belong to C. That it is not possible for it to belong, isclear. For no horse is a man. Neither is it possible for it not to belong. For itis necessary that no horse should be a man, but the necessary we found to bedifferent from the possible. No syllogism then results. A similar proof canbe given if the major premiss is negative, the minor affirmative, or if bothare affirmative or negative. The demonstration can be made by means of thesame terms. And whenever one premiss is universal, the other particular, orboth are particular or indefinite, or in whatever other way the premisses canbe altered, the proof will always proceed through the same terms. Clearlythen, if both the premisses are problematic, no syllogism results.
Part 18 One premiss assertoric, the other problematic
But if one premiss is assertoric, the other problematic, if the affirmative is as-sertoric and the negative problematic no syllogism will be possible, whether
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the premisses are universal or particular. The proof is the same as above,and by means of the same terms. But when the affirmative premiss is prob-lematic, and the negative assertoric, we shall have a syllogism. Suppose Abelongs to no B, but can belong to all C. If the negative proposition is con-verted, B will belong to no A. But ex hypothesi can belong to all C: so asyllogism is made, proving by means of the first figure that B may belong tono C. Similarly also if the minor premiss is negative. But if both premissesare negative, one being assertoric, the other problematic, nothing followsnecessarily from these premisses as they stand, but if the problematic pre-miss is converted into its complementary affirmative a syllogism is formedto prove that B may belong to no C, as before: for we shall again have thefirst figure. But if both premisses are affirmative, no syllogism will be possi-ble. This arrangement of terms is possible both when the relation is positive,e.g. health, animal, man, and when it is negative, e.g. health, horse, man.
The same will hold good if the syllogisms are particular. Whenever theaffirmative proposition is assertoric, whether universal or particular, no syl-logism is possible (this is proved similarly and by the same examples asabove), but when the negative proposition is assertoric, a conclusion can bedrawn by means of conversion, as before. Again if both the relations arenegative, and the assertoric proposition is universal, although no conclusionfollows from the actual premisses, a syllogism can be obtained by convert-ing the problematic premiss into its complementary affirmative as before.But if the negative proposition is assertoric, but particular, no syllogism ispossible, whether the other premiss is affirmative or negative. Nor can aconclusion be drawn when both premisses are indefinite, whether affirma-tive or negative, or particular. The proof is the same and by the same terms.
Part 19 One necessary, other problematic, negativenecessary
If one of the premisses is necessary, the other problematic, then if the nega-tive is necessary a syllogistic conclusion can be drawn, not merely a negativeproblematic but also a negative assertoric conclusion; but if the affirmativepremiss is necessary, no conclusion is possible. Suppose that A necessarilybelongs to no B, but may belong to all C. If the negative premiss is convertedB will belong to no A: but A ex hypothesi is capable of belonging to all C: soonce more a conclusion is drawn by the first figure that B may belong to noC. But at the same time it is clear that B will not belong to any C. For assumethat it does: then if A cannot belong to any B, and B belongs to some of theCs, A cannot belong to some of the Cs: but ex hypothesi it may belong to all.A similar proof can be given if the minor premiss is negative. Again let theaffirmative proposition be necessary, and the other problematic; i.e. suppose
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that A may belong to no B, but necessarily belongs to all C. When the termsare arranged in this way, no syllogism is possible.
For (1) it sometimes turns out that B necessarily does not belong to C.Let A be white, B man, C swan. White then necessarily belongs to swan,but may belong to no man; and man necessarily belongs to no swan; Clearlythen we cannot draw a problematic conclusion; for that which is necessaryis admittedly distinct from that which is possible.
(2) Nor again can we draw a necessary conclusion: for that presupposesthat both premisses are necessary, or at any rate the negative premiss.
(3) Further it is possible also, when the terms are so arranged, that Bshould belong to C: for nothing prevents C falling under B, A being possiblefor all B, and necessarily belonging to C; e.g. if C stands for ‘awake’, B for‘animal’, A for ‘motion’. For motion necessarily belongs to what is awake,and is possible for every animal: and everything that is awake is animal.Clearly then the conclusion cannot be the negative assertion, if the relationmust be positive when the terms are related as above. Nor can the oppositeaffirmations be established: consequently no syllogism is possible. A similarproof is possible if the major premiss is affirmative.
But if the premisses are similar in quality, when they are negative a syl-logism can always be formed by converting the problematic premiss into itscomplementary affirmative as before. Suppose A necessarily does not be-long to B, and possibly may not belong to C: if the premisses are convertedB belongs to no A, and A may possibly belong to all C: thus we have thefirst figure. Similarly if the minor premiss is negative. But if the premissesare affirmative there cannot be a syllogism. Clearly the conclusion cannot bea negative assertoric or a negative necessary proposition because no nega-tive premiss has been laid down either in the assertoric or in the necessarymode. Nor can the conclusion be a problematic negative proposition. Forif the terms are so related, there are cases in which B necessarily will notbelong to C; e.g. suppose that A is white, B swan, C man. Nor can the op-posite affirmations be established, since we have shown a case in which Bnecessarily does not belong to C. A syllogism then is not possible at all.
Similar relations will obtain in particular syllogisms. For whenever thenegative proposition is universal and necessary, a syllogism will always bepossible to prove both a problematic and a negative assertoric proposition(the proof proceeds by conversion); but when the affirmative proposition isuniversal and necessary, no syllogistic conclusion can be drawn. This canbe proved in the same way as for universal propositions, and by the sameterms. Nor is a syllogistic conclusion possible when both premisses are affir-mative: this also may be proved as above. But when both premisses are neg-ative, and the premiss that definitely disconnects two terms is universal andnecessary, though nothing follows necessarily from the premisses as they
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are stated, a conclusion can be drawn as above if the problematic premiss isconverted into its complementary affirmative. But if both are indefinite orparticular, no syllogism can be formed. The same proof will serve, and thesame terms.
It is clear then from what has been said that if the universal and negativepremiss is necessary, a syllogism is always possible, proving not merely anegative problematic, but also a negative assertoric proposition; but if theaffirmative premiss is necessary no conclusion can be drawn. It is clear toothat a syllogism is possible or not under the same conditions whether themode of the premisses is assertoric or necessary. And it is clear that all thesyllogisms are imperfect, and are completed by means of the figures men-tioned.
Part 20 Both or only one of the premisses is problematic
In the last figure a syllogism is possible whether both or only one of the pre-misses is problematic. When the premisses are problematic the conclusionwill be problematic; and also when one premiss is problematic, the otherassertoric. But when the other premiss is necessary, if it is affirmative theconclusion will be neither necessary or assertoric; but if it is negative the syl-logism will result in a negative assertoric proposition, as above. In these alsowe must understand the expression ‘possible’ in the conclusion in the sameway as before.
First let the premisses be problematic and suppose that both A and B maypossibly belong to every C. Since then the affirmative proposition is convert-ible into a particular, and B may possibly belong to every C, it follows thatC may possibly belong to some B. So, if A is possible for every C, and C ispossible for some of the Bs, then A is possible for some of the Bs. For wehave got the first figure. And A if may possibly belong to no C, but B maypossibly belong to all C, it follows that A may possibly not belong to some B:for we shall have the first figure again by conversion. But if both premissesshould be negative no necessary consequence will follow from them as theyare stated, but if the premisses are converted into their corresponding affir-matives there will be a syllogism as before. For if A and B may possibly notbelong to C, if ‘may possibly belong’ is substituted we shall again have thefirst figure by means of conversion. But if one of the premisses is universal,the other particular, a syllogism will be possible, or not, under the arrange-ment of the terms as in the case of assertoric propositions. Suppose that Amay possibly belong to all C, and B to some C. We shall have the first figureagain if the particular premiss is converted. For if A is possible for all C, andC for some of the Bs, then A is possible for some of the Bs. Similarly if theproposition BC is universal. Likewise also if the proposition AC is negative,
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and the proposition BC affirmative: for we shall again have the first figureby conversion. But if both premisses should be negative - the one universaland the other particular - although no syllogistic conclusion will follow fromthe premisses as they are put, it will follow if they are converted, as above.But when both premisses are indefinite or particular, no syllogism can beformed: for A must belong sometimes to all B and sometimes to no B. Toillustrate the affirmative relation take the terms animal-man-white; to illus-trate the negative, take the terms horse-man-white- - white being the middleterm.
Part 21 One premiss pure, the other problematic
If one premiss is pure, the other problematic, the conclusion will be problem-atic, not pure; and a syllogism will be possible under the same arrangementof the terms as before. First let the premisses be affirmative: suppose that Abelongs to all C, and B may possibly belong to all C. If the proposition BCis converted, we shall have the first figure, and the conclusion that A maypossibly belong to some of the Bs. For when one of the premisses in the firstfigure is problematic, the conclusion also (as we saw) is problematic. Sim-ilarly if the proposition BC is pure, AC problematic; or if AC is negative,BC affirmative, no matter which of the two is pure; in both cases the con-clusion will be problematic: for the first figure is obtained once more, andit has been proved that if one premiss is problematic in that figure the con-clusion also will be problematic. But if the minor premiss BC is negative, orif both premisses are negative, no syllogistic conclusion can be drawn fromthe premisses as they stand, but if they are converted a syllogism is obtainedas before.
If one of the premisses is universal, the other particular, then when bothare affirmative, or when the universal is negative, the particular affirmative,we shall have the same sort of syllogisms: for all are completed by means ofthe first figure. So it is clear that we shall have not a pure but a problematicsyllogistic conclusion. But if the affirmative premiss is universal, the nega-tive particular, the proof will proceed by a reductio ad impossibile. Supposethat B belongs to all C, and A may possibly not belong to some C: it followsthat may possibly not belong to some B. For if A necessarily belongs to allB, and B (as has been assumed) belongs to all C, A will necessarily belong toall C: for this has been proved before. But it was assumed at the outset thatA may possibly not belong to some C.
Whenever both premisses are indefinite or particular, no syllogism willbe possible. The demonstration is the same as was given in the case of uni-versal premisses, and proceeds by means of the same terms.
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Part 22 One necessary, other problematic, premissesaffirmative
If one of the premisses is necessary, the other problematic, when the pre-misses are affirmative a problematic affirmative conclusion can always bedrawn; when one proposition is affirmative, the other negative, if the affir-mative is necessary a problematic negative can be inferred; but if the nega-tive proposition is necessary both a problematic and a pure negative conclu-sion are possible. But a necessary negative conclusion will not be possible,any more than in the other figures. Suppose first that the premisses are af-firmative, i.e. that A necessarily belongs to all C, and B may possibly belongto all C. Since then A must belong to all C, and C may belong to some B,it follows that A may (not does) belong to some B: for so it resulted in thefirst figure. A similar proof may be given if the proposition BC is necessary,and AC is problematic. Again suppose one proposition is affirmative, theother negative, the affirmative being necessary: i.e. suppose A may possiblybelong to no C, but B necessarily belongs to all C. We shall have the firstfigure once more: and - since the negative premiss is problematic - it is clearthat the conclusion will be problematic: for when the premisses stand thusin the first figure, the conclusion (as we found) is problematic. But if thenegative premiss is necessary, the conclusion will be not only that A maypossibly not belong to some B but also that it does not belong to some B.For suppose that A necessarily does not belong to C, but B may belong toall C. If the affirmative proposition BC is converted, we shall have the firstfigure, and the negative premiss is necessary. But when the premisses stoodthus, it resulted that A might possibly not belong to some C, and that it didnot belong to some C; consequently here it follows that A does not belong tosome B. But when the minor premiss is negative, if it is problematic we shallhave a syllogism by altering the premiss into its complementary affirmative,as before; but if it is necessary no syllogism can be formed. For A sometimesnecessarily belongs to all B, and sometimes cannot possibly belong to anyB. To illustrate the former take the terms sleep - sleeping horse - man; toillustrate the latter take the terms sleep - waking horse - man.
Similar results will obtain if one of the terms is related universally to themiddle, the other in part. If both premisses are affirmative, the conclusionwill be problematic, not pure; and also when one premiss is negative, theother affirmative, the latter being necessary. But when the negative premissis necessary, the conclusion also will be a pure negative proposition; for thesame kind of proof can be given whether the terms are universal or not. Forthe syllogisms must be made perfect by means of the first figure, so that aresult which follows in the first figure follows also in the third. But when theminor premiss is negative and universal, if it is problematic a syllogism can
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be formed by means of conversion; but if it is necessary a syllogism is notpossible. The proof will follow the same course as where the premisses areuniversal; and the same terms may be used.
It is clear then in this figure also when and how a syllogism can beformed, and when the conclusion is problematic, and when it is pure. Itis evident also that all syllogisms in this figure are imperfect, and that theyare made perfect by means of the first figure.
Part 23 Every syllogism is formed through these figures
It is clear from what has been said that the syllogisms in these figures aremade perfect by means of universal syllogisms in the first figure and are re-duced to them. That every syllogism without qualification can be so treated,will be clear presently, when it has been proved that every syllogism isformed through one or other of these figures.
It is necessary that every demonstration and every syllogism shouldprove either that something belongs or that it does not, and this either uni-versally or in part, and further either ostensively or hypothetically. One sortof hypothetical proof is the reductio ad impossibile. Let us speak first ofostensive syllogisms: for after these have been pointed out the truth of ourcontention will be clear with regard to those which are proved per impossi-bile, and in general hypothetically.
If then one wants to prove syllogistically A of B, either as an attribute ofit or as not an attribute of it, one must assert something of something else.If now A should be asserted of B, the proposition originally in question willhave been assumed. But if A should be asserted of C, but C should not beasserted of anything, nor anything of it, nor anything else of A, no syllogismwill be possible. For nothing necessarily follows from the assertion of someone thing concerning some other single thing. Thus we must take anotherpremiss as well. If then A be asserted of something else, or something else ofA, or something different of C, nothing prevents a syllogism being formed,but it will not be in relation to B through the premisses taken. Nor when Cbelongs to something else, and that to something else and so on, no connex-ion however being made with B, will a syllogism be possible concerning Ain its relation to B. For in general we stated that no syllogism can establishthe attribution of one thing to another, unless some middle term is taken,which is somehow related to each by way of predication. For the syllogismin general is made out of premisses, and a syllogism referring to this outof premisses with the same reference, and a syllogism relating this to thatproceeds through premisses which relate this to that. But it is impossible totake a premiss in reference to B, if we neither affirm nor deny anything of it;or again to take a premiss relating A to B, if we take nothing common, but
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affirm or deny peculiar attributes of each. So we must take something mid-way between the two, which will connect the predications, if we are to havea syllogism relating this to that. If then we must take something commonin relation to both, and this is possible in three ways (either by predicatingA of C, and C of B, or C of both, or both of C), and these are the figures ofwhich we have spoken, it is clear that every syllogism must be made in oneor other of these figures. The argument is the same if several middle termsshould be necessary to establish the relation to B; for the figure will be thesame whether there is one middle term or many.
It is clear then that the ostensive syllogisms are effected by means of theaforesaid figures; these considerations will show that reductiones ad alsoare effected in the same way. For all who effect an argument per impossi-bile infer syllogistically what is false, and prove the original conclusion hy-pothetically when something impossible results from the assumption of itscontradictory; e.g. that the diagonal of the square is incommensurate withthe side, because odd numbers are equal to evens if it is supposed to be com-mensurate. One infers syllogistically that odd numbers come out equal toevens, and one proves hypothetically the incommensurability of the diago-nal, since a falsehood results through contradicting this. For this we found tobe reasoning per impossibile, viz. proving something impossible by meansof an hypothesis conceded at the beginning. Consequently, since the false-hood is established in reductions ad impossibile by an ostensive syllogism,and the original conclusion is proved hypothetically, and we have alreadystated that ostensive syllogisms are effected by means of these figures, it isevident that syllogisms per impossibile also will be made through these fig-ures. Likewise all the other hypothetical syllogisms: for in every case the syl-logism leads up to the proposition that is substituted for the original thesis;but the original thesis is reached by means of a concession or some other hy-pothesis. But if this is true, every demonstration and every syllogism mustbe formed by means of the three figures mentioned above. But when thishas been shown it is clear that every syllogism is perfected by means of thefirst figure and is reducible to the universal syllogisms in this figure.
Part 24 One premiss must be affirmative, one universal
Further in every syllogism one of the premisses must be affirmative, anduniversality must be present: unless one of the premisses is universal eithera syllogism will not be possible, or it will not refer to the subject proposed,or the original position will be begged. Suppose we have to prove that plea-sure in music is good. If one should claim as a premiss that pleasure is goodwithout adding ‘all’, no syllogism will be possible; if one should claim thatsome pleasure is good, then if it is different from pleasure in music, it is not
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relevant to the subject proposed; if it is this very pleasure, one is assumingthat which was proposed at the outset to be proved. This is more obvious ingeometrical proofs, e.g. that the angles at the base of an isosceles triangle areequal. Suppose the lines A and B have been drawn to the centre. If then oneshould assume that the angle AC is equal to the angle BD, without claim-ing generally that angles of semicircles are equal; and again if one shouldassume that the angle C is equal to the angle D, without the additional as-sumption that every angle of a segment is equal to every other angle of thesame segment; and further if one should assume that when equal angles aretaken from the whole angles, which are themselves equal, the remainders Eand F are equal, he will beg the thing to be proved, unless he also states thatwhen equals are taken from equals the remainders are equal.
It is clear then that in every syllogism there must be a universal premiss,and that a universal statement is proved only when all the premisses areuniversal, while a particular statement is proved both from two universalpremisses and from one only: consequently if the conclusion is universal,the premisses also must be universal, but if the premisses are universal itis possible that the conclusion may not be universal. And it is clear alsothat in every syllogism either both or one of the premisses must be like theconclusion. I mean not only in being affirmative or negative, but also inbeing necessary, pure, problematic. We must consider also the other formsof predication.
It is clear also when a syllogism in general can be made and when itcannot; and when a valid, when a perfect syllogism can be formed; and thatif a syllogism is formed the terms must be arranged in one of the ways thathave been mentioned.
Part 25 Every demonstration proceeds through three terms
It is clear too that every demonstration will proceed through three termsand no more, unless the same conclusion is established by different pairs ofpropositions; e.g. the conclusion E may be established through the proposi-tions A and B, and through the propositions C and D, or through the propo-sitions A and B, or A and C, or B and C. For nothing prevents there beingseveral middles for the same terms. But in that case there is not one but sev-eral syllogisms. Or again when each of the propositions A and B is obtainedby syllogistic inference, e.g. by means of D and E, and again B by means ofF and G. Or one may be obtained by syllogistic, the other by inductive infer-ence. But thus also the syllogisms are many; for the conclusions are many,e.g. A and B and C. But if this can be called one syllogism, not many, thesame conclusion may be reached by more than three terms in this way, but itcannot be reached as C is established by means of A and B. Suppose that the
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proposition E is inferred from the premisses A, B, C, and D. It is necessarythen that of these one should be related to another as whole to part: for ithas already been proved that if a syllogism is formed some of its terms mustbe related in this way. Suppose then that A stands in this relation to B. Someconclusion then follows from them. It must either be E or one or other of Cand D, or something other than these.
(1) If it is E the syllogism will have A and B for its sole premisses. Butif C and D are so related that one is whole, the other part, some conclusionwill follow from them also; and it must be either E, or one or other of thepropositions A and B, or something other than these. And if it is (i) E, or (ii)A or B, either (i) the syllogisms will be more than one, or (ii) the same thinghappens to be inferred by means of several terms only in the sense whichwe saw to be possible. But if (iii) the conclusion is other than E or A or B,the syllogisms will be many, and unconnected with one another. But if C isnot so related to D as to make a syllogism, the propositions will have beenassumed to no purpose, unless for the sake of induction or of obscuring theargument or something of the sort.
(2) But if from the propositions A and B there follows not E but someother conclusion, and if from C and D either A or B follows or somethingelse, then there are several syllogisms, and they do not establish the con-clusion proposed: for we assumed that the syllogism proved E. And if noconclusion follows from C and D, it turns out that these propositions havebeen assumed to no purpose, and the syllogism does not prove the originalproposition.
So it is clear that every demonstration and every syllogism will proceedthrough three terms only.
This being evident, it is clear that a syllogistic conclusion follows fromtwo premisses and not from more than two. For the three terms make twopremisses, unless a new premiss is assumed, as was said at the beginning, toperfect the syllogisms. It is clear therefore that in whatever syllogistic argu-ment the premisses through which the main conclusion follows (for some ofthe preceding conclusions must be premisses) are not even in number, thisargument either has not been drawn syllogistically or it has assumed morethan was necessary to establish its thesis.
If then syllogisms are taken with respect to their main premisses, everysyllogism will consist of an even number of premisses and an odd number ofterms (for the terms exceed the premisses by one), and the conclusions willbe half the number of the premisses. But whenever a conclusion is reachedby means of prosyllogisms or by means of several continuous middle terms,e.g. the proposition AB by means of the middle terms C and D, the numberof the terms will similarly exceed that of the premisses by one (for the extraterm must either be added outside or inserted: but in either case it follows
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that the relations of predication are one fewer than the terms related), andthe premisses will be equal in number to the relations of predication. Thepremisses however will not always be even, the terms odd; but they willalternate - when the premisses are even, the terms must be odd; when theterms are even, the premisses must be odd: for along with one term one pre-miss is added, if a term is added from any quarter. Consequently since thepremisses were (as we saw) even, and the terms odd, we must make themalternately even and odd at each addition. But the conclusions will not fol-low the same arrangement either in respect to the terms or to the premisses.For if one term is added, conclusions will be added less by one than the pre-existing terms: for the conclusion is drawn not in relation to the single termlast added, but in relation to all the rest, e.g. if to ABC the term D is added,two conclusions are thereby added, one in relation to A, the other in relationto B. Similarly with any further additions. And similarly too if the term isinserted in the middle: for in relation to one term only, a syllogism will notbe constructed. Consequently the conclusions will be much more numerousthan the terms or the premisses.
Part 26 What sort of problem is difficult to prove
Since we understand the subjects with which syllogisms are concerned, whatsort of conclusion is established in each figure, and in how many moods thisis done, it is evident to us both what sort of problem is difficult and what sortis easy to prove. For that which is concluded in many figures and throughmany moods is easier; that which is concluded in few figures and throughfew moods is more difficult to attempt. The universal affirmative is provedby means of the first figure only and by this in only one mood; the univer-sal negative is proved both through the first figure and through the second,through the first in one mood, through the second in two. The particular af-firmative is proved through the first and through the last figure, in one moodthrough the first, in three moods through the last. The particular negative isproved in all the figures, but once in the first, in two moods in the second,in three moods in the third. It is clear then that the universal affirmative ismost difficult to establish, most easy to overthrow. In general, universals areeasier game for the destroyer than particulars: for whether the predicate be-longs to none or not to some, they are destroyed: and the particular negativeis proved in all the figures, the universal negative in two. Similarly with uni-versal negatives: the original statement is destroyed, whether the predicatebelongs to all or to some: and this we found possible in two figures. Butparticular statements can be refuted in one way only - by proving that thepredicate belongs either to all or to none. But particular statements are easierto establish: for proof is possible in more figures and through more moods.
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And in general we must not forget that it is possible to refute statements bymeans of one another, I mean, universal statements by means of particular,and particular statements by means of universal: but it is not possible to es-tablish universal statements by means of particular, though it is possible toestablish particular statements by means of universal. At the same time it isevident that it is easier to refute than to establish.
The manner in which every syllogism is produced, the number of theterms and premisses through which it proceeds, the relation of the premissesto one another, the character of the problem proved in each figure, and thenumber of the figures appropriate to each problem, all these matters are clearfrom what has been said.
Part 27 How to reach the principles relative to the problem
We must now state how we may ourselves always have a supply of syl-logisms in reference to the problem proposed and by what road we mayreach the principles relative to the problem: for perhaps we ought not onlyto investigate the construction of syllogisms, but also to have the power ofmaking them.
Of all the things which exist some are such that they cannot be predicatedof anything else truly and universally, e.g. Cleon and Callias, i.e. the indi-vidual and sensible, but other things may be predicated of them (for each ofthese is both man and animal); and some things are themselves predicatedof others, but nothing prior is predicated of them; and some are predicatedof others, and yet others of them, e.g. man of Callias and animal of man.It is clear then that some things are naturally not stated of anything: for asa rule each sensible thing is such that it cannot be predicated of anything,save incidentally: for we sometimes say that that white object is Socrates, orthat that which approaches is Callias. We shall explain in another place thatthere is an upward limit also to the process of predicating: for the present wemust assume this. Of these ultimate predicates it is not possible to demon-strate another predicate, save as a matter of opinion, but these may be pred-icated of other things. Neither can individuals be predicated of other things,though other things can be predicated of them. Whatever lies between theselimits can be spoken of in both ways: they may be stated of others, and oth-ers stated of them. And as a rule arguments and inquiries are concernedwith these things. We must select the premisses suitable to each problem inthis manner: first we must lay down the subject and the definitions and theproperties of the thing; next we must lay down those attributes which followthe thing, and again those which the thing follows, and those which cannotbelong to it. But those to which it cannot belong need not be selected, be-cause the negative statement implied above is convertible. Of the attributes
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which follow we must distinguish those which fall within the definition,those which are predicated as properties, and those which are predicatedas accidents, and of the latter those which apparently and those which re-ally belong. The larger the supply a man has of these, the more quickly willhe reach a conclusion; and in proportion as he apprehends those which aretruer, the more cogently will he demonstrate. But he must select not thosewhich follow some particular but those which follow the thing as a whole,e.g. not what follows a particular man but what follows every man: for thesyllogism proceeds through universal premisses. If the statement is indefi-nite, it is uncertain whether the premiss is universal, but if the statement isdefinite, the matter is clear. Similarly one must select those attributes whichthe subject follows as wholes, for the reason given. But that which followsone must not suppose to follow as a whole, e.g. that every animal followsman or every science music, but only that it follows, without qualification,and indeed we state it in a proposition: for the other statement is uselessand impossible, e.g. that every man is every animal or justice is all good.But that which something follows receives the mark ‘every’. Whenever thesubject, for which we must obtain the attributes that follow, is contained bysomething else, what follows or does not follow the highest term univer-sally must not be selected in dealing with the subordinate term (for theseattributes have been taken in dealing with the superior term; for what fol-lows animal also follows man, and what does not belong to animal does notbelong to man); but we must choose those attributes which are peculiar toeach subject. For some things are peculiar to the species as distinct from thegenus; for species being distinct there must be attributes peculiar to each.Nor must we take as things which the superior term follows, those thingswhich the inferior term follows, e.g. take as subjects of the predicate ‘ani-mal’ what are really subjects of the predicate ‘man’. It is necessary indeed,if animal follows man, that it should follow all these also. But these belongmore properly to the choice of what concerns man. One must apprehendalso normal consequents and normal antecedents -, for propositions whichobtain normally are established syllogistically from premisses which obtainnormally, some if not all of them having this character of normality. For theconclusion of each syllogism resembles its principles. We must not howeverchoose attributes which are consequent upon all the terms: for no syllogismcan be made out of such premisses. The reason why this is so will be clear inthe sequel.
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Part 28 To establish something about a whole, look to thesubjects
If men wish to establish something about some whole, they must look tothe subjects of that which is being established (the subjects of which it hap-pens to be asserted), and the attributes which follow that of which it is to bepredicated. For if any of these subjects is the same as any of these attributes,the attribute originally in question must belong to the subject originally inquestion. But if the purpose is to establish not a universal but a particularproposition, they must look for the terms of which the terms in question arepredicable: for if any of these are identical, the attribute in question mustbelong to some of the subject in question. Whenever the one term has tobelong to none of the other, one must look to the consequents of the subject,and to those attributes which cannot possibly be present in the predicate inquestion: or conversely to the attributes which cannot possibly be present inthe subject, and to the consequents of the predicate. If any members of thesegroups are identical, one of the terms in question cannot possibly belong toany of the other. For sometimes a syllogism in the first figure results, some-times a syllogism in the second. But if the object is to establish a particularnegative proposition, we must find antecedents of the subject in questionand attributes which cannot possibly belong to the predicate in question. Ifany members of these two groups are identical, it follows that one of theterms in question does not belong to some of the other. Perhaps each ofthese statements will become clearer in the following way. Suppose the con-sequents of A are designated by B, the antecedents of A by C, attributeswhich cannot possibly belong to A by D. Suppose again that the attributesof E are designated by F, the antecedents of E by G, and attributes whichcannot belong to E by H. If then one of the Cs should be identical with oneof the Fs, A must belong to all E: for F belongs to all E, and A to all C, conse-quently A belongs to all E. If C and G are identical, A must belong to someof the Es: for A follows C, and E follows all G. If F and D are identical, A willbelong to none of the Es by a prosyllogism: for since the negative proposi-tion is convertible, and F is identical with D, A will belong to none of the Fs,but F belongs to all E. Again, if B and H are identical, A will belong to noneof the Es: for B will belong to all A, but to no E: for it was assumed to beidentical with H, and H belonged to none of the Es. If D and G are identical,A will not belong to some of the Es: for it will not belong to G, because itdoes not belong to D: but G falls under E: consequently A will not belong tosome of the Es. If B is identical with G, there will be a converted syllogism:for E will belong to all A since B belongs to A and E to B (for B was foundto be identical with G): but that A should belong to all E is not necessary,but it must belong to some E because it is possible to convert the universal
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statement into a particular.It is clear then that in every proposition which requires proof we must
look to the aforesaid relations of the subject and predicate in question: forall syllogisms proceed through these. But if we are seeking consequents andantecedents we must look for those which are primary and most universal,e.g. in reference to E we must look to KF rather than to F alone, and inreference to A we must look to KC rather than to C alone. For if A belongs toKF, it belongs both to F and to E: but if it does not follow KF, it may yet followF. Similarly we must consider the antecedents of A itself: for if a term followsthe primary antecedents, it will follow those also which are subordinate, butif it does not follow the former, it may yet follow the latter.
It is clear too that the inquiry proceeds through the three terms and thetwo premisses, and that all the syllogisms proceed through the aforesaidfigures. For it is proved that A belongs to all E, whenever an identical termis found among the Cs and Fs. This will be the middle term; A and E willbe the extremes. So the first figure is formed. And A will belong to some E,whenever C and G are apprehended to be the same. This is the last figure:for G becomes the middle term. And A will belong to no E, when D and Fare identical. Thus we have both the first figure and the middle figure; thefirst, because A belongs to no F, since the negative statement is convertible,and F belongs to all E: the middle figure because D belongs to no A, and toall E. And A will not belong to some E, whenever D and G are identical. Thisis the last figure: for A will belong to no G, and E will belong to all G. Clearlythen all syllogisms proceed through the aforesaid figures, and we must notselect consequents of all the terms, because no syllogism is produced fromthem. For (as we saw) it is not possible at all to establish a proposition fromconsequents, and it is not possible to refute by means of a consequent of boththe terms in question: for the middle term must belong to the one, and notbelong to the other.
It is clear too that other methods of inquiry by selection of middle termsare useless to produce a syllogism, e.g. if the consequents of the terms inquestion are identical, or if the antecedents of A are identical with those at-tributes which cannot possibly belong to E, or if those attributes are identicalwhich cannot belong to either term: for no syllogism is produced by meansof these. For if the consequents are identical, e.g. B and F, we have the middlefigure with both premisses affirmative: if the antecedents of A are identicalwith attributes which cannot belong to E, e.g. C with H, we have the firstfigure with its minor premiss negative. If attributes which cannot belong toeither term are identical, e.g. C and H, both premisses are negative, either inthe first or in the middle figure. But no syllogism is possible in this way.
It is evident too that we must find out which terms in this inquiry areidentical, not which are different or contrary, first because the object of our
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investigation is the middle term, and the middle term must be not diversebut identical. Secondly, wherever it happens that a syllogism results fromtaking contraries or terms which cannot belong to the same thing, all argu-ments can be reduced to the aforesaid moods, e.g. if B and F are contrariesor cannot belong to the same thing. For if these are taken, a syllogism willbe formed to prove that A belongs to none of the Es, not however from thepremisses taken but in the aforesaid mood. For B will belong to all A and tono E. Consequently B must be identical with one of the Hs. Again, if B and Gcannot belong to the same thing, it follows that A will not belong to some ofthe Es: for then too we shall have the middle figure: for B will belong to allA and to no G. Consequently B must be identical with some of the Hs. Forthe fact that B and G cannot belong to the same thing differs in no way fromthe fact that B is identical with some of the Hs: for that includes everythingwhich cannot belong to E.
It is clear then that from the inquiries taken by themselves no syllogismresults; but if B and F are contraries B must be identical with one of the Hs,and the syllogism results through these terms. It turns out then that thosewho inquire in this manner are looking gratuitously for some other way thanthe necessary way because they have failed to observe the identity of the Bswith the Hs.
Part 29 Impossible conclusions and ostensive syllogisms
Syllogisms which lead to impossible conclusions are similar to ostensive syl-logisms; they also are formed by means of the consequents and antecedentsof the terms in question. In both cases the same inquiry is involved. Forwhat is proved ostensively may also be concluded syllogistically per impos-sibile by means of the same terms; and what is proved per impossibile mayalso be proved ostensively, e.g. that A belongs to none of the Es. For sup-pose A to belong to some E: then since B belongs to all A and A to some ofthe Es, B will belong to some of the Es: but it was assumed that it belongs tonone. Again we may prove that A belongs to some E: for if A belonged tonone of the Es, and E belongs to all G, A will belong to none of the Gs: but itwas assumed to belong to all. Similarly with the other propositions requir-ing proof. The proof per impossibile will always and in all cases be from theconsequents and antecedents of the terms in question. Whatever the prob-lem the same inquiry is necessary whether one wishes to use an ostensivesyllogism or a reduction to impossibility. For both the demonstrations startfrom the same terms, e.g. suppose it has been proved that A belongs to noE, because it turns out that otherwise B belongs to some of the Es and thisis impossible - if now it is assumed that B belongs to no E and to all A, it isclear that A will belong to no E. Again if it has been proved by an ostensive
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syllogism that A belongs to no E, assume that A belongs to some E and itwill be proved per impossibile to belong to no E. Similarly with the rest. Inall cases it is necessary to find some common term other than the subjectsof inquiry, to which the syllogism establishing the false conclusion may re-late, so that if this premiss is converted, and the other remains as it is, thesyllogism will be ostensive by means of the same terms. For the ostensivesyllogism differs from the reductio ad impossibile in this: in the ostensivesyllogism both remisses are laid down in accordance with the truth, in thereductio ad impossibile one of the premisses is assumed falsely.
These points will be made clearer by the sequel, when we discuss the re-duction to impossibility: at present this much must be clear, that we mustlook to terms of the kinds mentioned whether we wish to use an ostensivesyllogism or a reduction to impossibility. In the other hypothetical syllo-gisms, I mean those which proceed by substitution, or by positing a certainquality, the inquiry will be directed to the terms of the problem to be proved- not the terms of the original problem, but the new terms introduced; andthe method of the inquiry will be the same as before. But we must considerand determine in how many ways hypothetical syllogisms are possible.
Each of the problems then can be proved in the manner described; but itis possible to establish some of them syllogistically in another way, e.g. uni-versal problems by the inquiry which leads up to a particular conclusion,with the addition of an hypothesis. For if the Cs and the Gs should be iden-tical, but E should be assumed to belong to the Gs only, then A would belongto every E: and again if the Ds and the Gs should be identical, but E shouldbe predicated of the Gs only, it follows that A will belong to none of the Es.Clearly then we must consider the matter in this way also. The method isthe same whether the relation is necessary or possible. For the inquiry willbe the same, and the syllogism will proceed through terms arranged in thesame order whether a possible or a pure proposition is proved. We must findin the case of possible relations, as well as terms that belong, terms which canbelong though they actually do not: for we have proved that the syllogismwhich establishes a possible relation proceeds through these terms as well.Similarly also with the other modes of predication.
It is clear then from what has been said not only that all syllogisms canbe formed in this way, but also that they cannot be formed in any other. Forevery syllogism has been proved to be formed through one of the aforemen-tioned figures, and these cannot be composed through other terms than theconsequents and antecedents of the terms in question: for from these weobtain the premisses and find the middle term. Consequently a syllogismcannot be formed by means of other terms.
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Part 30 On method, in relation to choice of premisses
The method is the same in all cases, in philosophy, in any art or study. Wemust look for the attributes and the subjects of both our terms, and we mustsupply ourselves with as many of these as possible, and consider them bymeans of the three terms, refuting statements in one way, confirming them inanother, in the pursuit of truth starting from premisses in which the arrange-ment of the terms is in accordance with truth, while if we look for dialecticalsyllogisms we must start from probable premisses. The principles of syllo-gisms have been stated in general terms, both how they are characterizedand how we must hunt for them, so as not to look to everything that is saidabout the terms of the problem or to the same points whether we are con-firming or refuting, or again whether we are confirming of all or of some, andwhether we are refuting of all or some. we must look to fewer points andthey must be definite. We have also stated how we must select with referenceto everything that is, e.g. about good or knowledge. But in each science theprinciples which are peculiar are the most numerous. Consequently it is thebusiness of experience to give the principles which belong to each subject. Imean for example that astronomical experience supplies the principles of as-tronomical science: for once the phenomena were adequately apprehended,the demonstrations of astronomy were discovered. Similarly with any otherart or science. Consequently, if the attributes of the thing are apprehended,our business will then be to exhibit readily the demonstrations. For if noneof the true attributes of things had been omitted in the historical survey,we should be able to discover the proof and demonstrate everything whichadmitted of proof, and to make that clear, whose nature does not admit ofproof.
In general then we have explained fairly well how we must select pre-misses: we have discussed the matter accurately in the treatise concerningdialectic.
Part 31 Division into classes is a small part of the method
It is easy to see that division into classes is a small part of the method wehave described: for division is, so to speak, a weak syllogism; for what itought to prove, it begs, and it always establishes something more generalthan the attribute in question. First, this very point had escaped all thosewho used the method of division; and they attempted to persuade men thatit was possible to make a demonstration of substance and essence. Conse-quently they did not understand what it is possible to prove syllogisticallyby division, nor did they understand that it was possible to prove syllogis-tically in the manner we have described. In demonstrations, when there is
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a need to prove a positive statement, the middle term through which thesyllogism is formed must always be inferior to and not comprehend the firstof the extremes. But division has a contrary intention: for it takes the uni-versal as middle. Let animal be the term signified by A, mortal by B, andimmortal by C, and let man, whose definition is to be got, be signified by D.The man who divides assumes that every animal is either mortal or immor-tal: i.e. whatever is A is all either B or C. Again, always dividing, he lays itdown that man is an animal, so he assumes A of D as belonging to it. Nowthe true conclusion is that every D is either B or C, consequently man mustbe either mortal or immortal, but it is not necessary that man should be amortal animal - this is begged: and this is what ought to have been provedsyllogistically. And again, taking A as mortal animal, B as footed, C as foot-less, and D as man, he assumes in the same way that A inheres either in B orin C (for every mortal animal is either footed or footless), and he assumes Aof D (for he assumed man, as we saw, to be a mortal animal); consequently itis necessary that man should be either a footed or a footless animal; but it isnot necessary that man should be footed: this he assumes: and it is just thisagain which he ought to have demonstrated. Always dividing then in thisway it turns out that these logicians assume as middle the universal term,and as extremes that which ought to have been the subject of demonstrationand the differentiae. In conclusion, they do not make it clear, and show itto be necessary, that this is man or whatever the subject of inquiry may be:for they pursue the other method altogether, never even suspecting the pres-ence of the rich supply of evidence which might be used. It is clear that it isneither possible to refute a statement by this method of division, nor to drawa conclusion about an accident or property of a thing, nor about its genus,nor in cases in which it is unknown whether it is thus or thus, e.g. whetherthe diagonal is incommensurate. For if he assumes that every length is ei-ther commensurate or incommensurate, and the diagonal is a length, he hasproved that the diagonal is either incommensurate or commensurate. Butif he should assume that it is incommensurate, he will have assumed whathe ought to have proved. He cannot then prove it: for this is his method,but proof is not possible by this method. Let A stand for ‘incommensurateor commensurate’, B for ‘length’, C for ‘diagonal’. It is clear then that thismethod of investigation is not suitable for every inquiry, nor is it useful inthose cases in which it is thought to be most suitable.
From what has been said it is clear from what elements demonstrationsare formed and in what manner, and to what points we must look in eachproblem.
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Part 32 Reducing syllogisms to the figures
Our next business is to state how we can reduce syllogisms to the afore-mentioned figures: for this part of the inquiry still remains. If we shouldinvestigate the production of the syllogisms and had the power of discover-ing them, and further if we could resolve the syllogisms produced into theaforementioned figures, our original problem would be brought to a conclu-sion. It will happen at the same time that what has been already said will beconfirmed and its truth made clearer by what we are about to say. For every-thing that is true must in every respect agree with itself First then we mustattempt to select the two premisses of the syllogism (for it is easier to di-vide into large parts than into small, and the composite parts are larger thanthe elements out of which they are made); next we must inquire which areuniversal and which particular, and if both premisses have not been stated,we must ourselves assume the one which is missing. For sometimes menput forward the universal premiss, but do not posit the premiss which iscontained in it, either in writing or in discussion: or men put forward thepremisses of the principal syllogism, but omit those through which they areinferred, and invite the concession of others to no purpose. We must inquirethen whether anything unnecessary has been assumed, or anything neces-sary has been omitted, and we must posit the one and take away the other,until we have reached the two premisses: for unless we have these, we can-not reduce arguments put forward in the way described. In some argumentsit is easy to see what is wanting, but some escape us, and appear to be syllo-gisms, because something necessary results from what has been laid down,e.g. if the assumptions were made that substance is not annihilated by theannihilation of what is not substance, and that if the elements out of whicha thing is made are annihilated, then that which is made out of them is de-stroyed: these propositions being laid down, it is necessary that any part ofsubstance is substance; this has not however been drawn by syllogism fromthe propositions assumed, but premisses are wanting. Again if it is neces-sary that animal should exist, if man does, and that substance should exist,if animal does, it is necessary that substance should exist if man does: butas yet the conclusion has not been drawn syllogistically: for the premissesare not in the shape we required. We are deceived in such cases becausesomething necessary results from what is assumed, since the syllogism alsois necessary. But that which is necessary is wider than the syllogism: forevery syllogism is necessary, but not everything which is necessary is a syl-logism. Consequently, though something results when certain propositionsare assumed, we must not try to reduce it directly, but must first state thetwo premisses, then divide them into their terms. We must take that termas middle which is stated in both the remisses: for it is necessary that the
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middle should be found in both premisses in all the figures.
If then the middle term is a predicate and a subject of predication, or ifit is a predicate, and something else is denied of it, we shall have the firstfigure: if it both is a predicate and is denied of something, the middle figure:if other things are predicated of it, or one is denied, the other predicated, thelast figure. For it was thus that we found the middle term placed in eachfigure. It is placed similarly too if the premisses are not universal: for themiddle term is determined in the same way. Clearly then, if the same term isnot stated more than once in the course of an argument, a syllogism cannotbe made: for a middle term has not been taken. Since we know what sort ofthesis is established in each figure, and in which the universal, in what sortthe particular is described, clearly we must not look for all the figures, butfor that which is appropriate to the thesis in hand. If the thesis is establishedin more figures than one, we shall recognize the figure by the position of themiddle term.
Part 33 On the necessity of syllogistic inference
Men are frequently deceived about syllogisms because the inference is nec-essary, as has been said above; sometimes they are deceived by the similarityin the positing of the terms; and this ought not to escape our notice. E.g. if Ais stated of B, and B of C: it would seem that a syllogism is possible since theterms stand thus: but nothing necessary results, nor does a syllogism. Let Arepresent the term ‘being eternal’, B ‘Aristomenes as an object of thought’,C ‘Aristomenes’. It is true then that A belongs to B. For Aristomenes asan object of thought is eternal. But B also belongs to C: for Aristomenes isAristomenes as an object of thought. But A does not belong to C: for Aris-tomenes is perishable. For no syllogism was made although the terms stoodthus: that required that the premiss AB should be stated universally. Butthis is false, that every Aristomenes who is an object of thought is eternal,since Aristomenes is perishable. Again let C stand for ‘Miccalus’, B for ‘mu-sical Miccalus’, A for ‘perishing to-morrow’. It is true to predicate B of C:for Miccalus is musical Miccalus. Also A can be predicated of B: for musicalMiccalus might perish to-morrow. But to state A of C is false at any rate.This argument then is identical with the former; for it is not true universallythat musical Miccalus perishes to-morrow: but unless this is assumed, nosyllogism (as we have shown) is possible.
This deception then arises through ignoring a small distinction. For if weaccept the conclusion as though it made no difference whether we said ‘Thisbelong to that’ or ‘This belongs to all of that’.
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Part 34 Not setting out the terms of the premiss well
Men will frequently fall into fallacies through not setting out the terms of thepremiss well, e.g. suppose A to be health, B disease, C man. It is true to saythat A cannot belong to any B (for health belongs to no disease) and againthat B belongs to every C (for every man is capable of disease). It would seemto follow that health cannot belong to any man. The reason for this is thatthe terms are not set out well in the statement, since if the things which arein the conditions are substituted, no syllogism can be made, e.g. if ‘healthy’is substituted for ‘health’ and ‘diseased’ for ‘disease’. For it is not true tosay that being healthy cannot belong to one who is diseased. But unless thisis assumed no conclusion results, save in respect of possibility: but such aconclusion is not impossible: for it is possible that health should belong tono man. Again the fallacy may occur in a similar way in the middle figure:‘it is not possible that health should belong to any disease, but it is possiblethat health should belong to every man, consequently it is not possible thatdisease should belong to any man’. In the third figure the fallacy results inreference to possibility. For health and diseae and knowledge and ignorance,and in general contraries, may possibly belong to the same thing, but cannotbelong to one another. This is not in agreement with what was said before:for we stated that when several things could belong to the same thing, theycould belong to one another.
It is evident then that in all these cases the fallacy arises from the settingout of the terms: for if the things that are in the conditions are substituted,no fallacy arises. It is clear then that in such premisses what possesses thecondition ought always to be substituted for the condition and taken as theterm.
Part 35 Terms need not be single words
We must not always seek to set out the terms a single word: for we shalloften have complexes of words to which a single name is not given. Henceit is difficult to reduce syllogisms with such terms. Sometimes too fallacieswill result from such a search, e.g. the belief that syllogism can establishthat which has no mean. Let A stand for two right angles, B for triangle,C for isosceles triangle. A then belongs to C because of B: but A belongsto B without the mediation of another term: for the triangle in virtue of itsown nature contains two right angles, consequently there will be no mid-dle term for the proposition AB, although it is demonstrable. For it is clearthat the middle must not always be assumed to be an individual thing, butsometimes a complex of words, as happens in the case mentioned.
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Part 36 Relations between the terms in a syllogism
That the first term belongs to the middle, and the middle to the extreme,must not be understood in the sense that they can always be predicated ofone another or that the first term will be predicated of the middle in thesame way as the middle is predicated of the last term. The same holds if thepremisses are negative. But we must suppose the verb ‘to belong’ to have asmany meanings as the senses in which the verb ‘to be’ is used, and in whichthe assertion that a thing ‘is’ may be said to be true. Take for example thestatement that there is a single science of contraries. Let A stand for ‘therebeing a single science’, and B for things which are contrary to one another.Then A belongs to B, not in the sense that contraries are the fact of therebeing a single science of them, but in the sense that it is true to say of thecontraries that there is a single science of them.
It happens sometimes that the first term is stated of the middle, but themiddle is not stated of the third term, e.g. if wisdom is knowledge, andwisdom is of the good, the conclusion is that there is knowledge of the good.The good then is not knowledge, though wisdom is knowledge. Sometimesthe middle term is stated of the third, but the first is not stated of the middle,e.g. if there is a science of everything that has a quality, or is a contrary, andthe good both is a contrary and has a quality, the conclusion is that there isa science of the good, but the good is not science, nor is that which has aquality or is a contrary, though the good is both of these. Sometimes neitherthe first term is stated of the middle, nor the middle of the third, while thefirst is sometimes stated of the third, and sometimes not: e.g. if there is agenus of that of which there is a science, and if there is a science of the good,we conclude that there is a genus of the good. But nothing is predicated ofanything. And if that of which there is a science is a genus, and if there isa science of the good, we conclude that the good is a genus. The first termthen is predicated of the extreme, but in the premisses one thing is not statedof another.
The same holds good where the relation is negative. For ‘that does notbelong to this’ does not always mean that ‘this is not that’, but sometimesthat ‘this is not of that’ or ‘for that’, e.g. ‘there is not a motion of a motion ora becoming of a becoming, but there is a becoming of pleasure: so pleasureis not a becoming.’ Or again it may be said that there is a sign of laughter,but there is not a sign of a sign, consequently laughter is not a sign. Thisholds in the other cases too, in which the thesis is refuted because the genusis asserted in a particular way, in relation to the terms of the thesis. Againtake the inference ‘opportunity is not the right time: for opportunity belongsto God, but the right time does not, since nothing is useful to God’. We musttake as terms opportunity - right time - God: but the premiss must be un-
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derstood according to the case of the noun. For we state this universallywithout qualification, that the terms ought always to be stated in the nom-inative, e.g. man, good, contraries, not in oblique cases, e.g. of man, of agood, of contraries, but the premisses ought to be understood with referenceto the cases of each term - either the dative, e.g. ‘equal to this’, or the gen-itive, e.g. ‘double of this’, or the accusative, e.g. ‘that which strikes or seesthis’, or the nominative, e.g. ‘man is an animal’, or in whatever other waythe word falls in the premiss.
Part 37 Predication and categories
The expressions ‘this belongs to that’ and ‘this holds true of that’ must beunderstood in as many ways as there are different categories, and these cat-egories must be taken either with or without qualification, and further assimple or compound: the same holds good of the corresponding negativeexpressions. We must consider these points and define them better.
Part 38 Terms repeated in the premisses
A term which is repeated in the premisses ought to be joined to the first ex-treme, not to the middle. I mean for example that if a syllogism should bemade proving that there is knowledge of justice, that it is good, the expres-sion ‘that it is good’ (or ‘qua good’) should be joined to the first term. Let Astand for ‘knowledge that it is good’, B for good, C for justice. It is true topredicate A of B. For of the good there is knowledge that it is good. Also itis true to predicate B of C. For justice is identical with a good. In this wayan analysis of the argument can be made. But if the expression ‘that it isgood’ were added to B, the conclusion will not follow: for A will be trueof B, but B will not be true of C. For to predicate of justice the term ‘goodthat it is good’ is false and not intelligible. Similarly if it should be provedthat the healthy is an object of knowledge qua good, of goat-stag an objectof knowledge qua not existing, or man perishable qua an object of sense: inevery case in which an addition is made to the predicate, the addition mustbe joined to the extreme.
The position of the terms is not the same when something is establishedwithout qualification and when it is qualified by some attribute or condition,e.g. when the good is proved to be an object of knowledge and when it isproved to be an object of knowledge that it is good. If it has been provedto be an object of knowledge without qualification, we must put as middleterm ‘that which is’, but if we add the qualification ‘that it is good’, the mid-dle term must be ‘that which is something’. Let A stand for ‘knowledge thatit is something’, B stand for ‘something’, and C stand for ‘good’. It is true to
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predicate A of B: for ex hypothesi there is a science of that which is some-thing, that it is something. B too is true of C: for that which C representsis something. Consequently A is true of C: there will then be knowledge ofthe good, that it is good: for ex hypothesi the term ‘something’ indicates thething’s special nature. But if ‘being’ were taken as middle and ‘being’ simplywere joined to the extreme, not ‘being something’, we should not have hada syllogism proving that there is knowledge of the good, that it is good, butthat it is; e.g. let A stand for knowledge that it is, B for being, C for good.Clearly then in syllogisms which are thus limited we must take the terms inthe way stated.
Part 39 Exchanging terms
We ought also to exchange terms which have the same value, word for word,and phrase for phrase, and word and phrase, and always take a word in pref-erence to a phrase: for thus the setting out of the terms will be easier. Forexample if it makes no difference whether we say that the supposable is notthe genus of the opinable or that the opinable is not identical with a particu-lar kind of supposable (for what is meant is the same in both statements), itis better to take as the terms the supposable and the opinable in preferenceto the phrase suggested.
Part 40 Good and The Good
Since the expressions ‘pleasure is good’ and ‘pleasure is the good’ are notidentical, we must not set out the terms in the same way; but if the syllogismis to prove that pleasure is the good, the term must be ‘the good’, but if theobject is to prove that pleasure is good, the term will be ‘good’. Similarly inall other cases.
Part 41 Transitivity of belonging
It is not the same, either in fact or in speech, that A belongs to all of that towhich B belongs, and that A belongs to all of that to all of which B belongs:for nothing prevents B from belonging to C, though not to all C: e.g. let Bstand for beautiful, and C for white. If beauty belongs to something white,it is true to say that beauty belongs to that which is white; but not perhapsto everything that is white. If then A belongs to B, but not to everything ofwhich B is predicated, then whether B belongs to all C or merely belongs toC, it is not necessary that A should belong, I do not say to all C, but evento C at all. But if A belongs to everything of which B is truly stated, it willfollow that A can be said of all of that of all of which B is said. If however A
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is said of that of all of which B may be said, nothing prevents B belonging toC, and yet A not belonging to all C or to any C at all. If then we take threeterms it is clear that the expression ‘A is said of all of which B is said’ meansthis, ‘A is said of all the things of which B is said’. And if B is said of all of athird term, so also is A: but if B is not said of all of the third term, there is nonecessity that A should be said of all of it.
We must not suppose that something absurd results through setting outthe terms: for we do not use the existence of this particular thing, but imitatethe geometrician who says that ‘this line a foot long’ or ‘this straight line’ or‘this line without breadth’ exists although it does not, but does not use thediagrams in the sense that he reasons from them. For in general, if two thingsare not related as whole to part and part to whole, the prover does not provefrom them, and so no syllogism a is formed. We (I mean the learner) usethe process of setting out terms like perception by sense, not as though itwere impossible to demonstrate without these illustrative terms, as it is todemonstrate without the premisses of the syllogism.
Part 42 On figures
We should not forget that in the same syllogism not all conclusions arereached through one figure, but one through one figure, another throughanother. Clearly then we must analyse arguments in accordance with this.Since not every problem is proved in every figure, but certain problemsin each figure, it is clear from the conclusion in what figure the premissesshould be sought.
Part 43 Proving some part of a definition
In reference to those arguments aiming at a definition which have been di-rected to prove some part of the definition, we must take as a term the pointto which the argument has been directed, not the whole definition: for so weshall be less likely to be disturbed by the length of the term: e.g. if a manproves that water is a drinkable liquid, we must take as terms drinkable andwater.
Part 44 We must not try to reduce hypothetical syllogisms
Further we must not try to reduce hypothetical syllogisms; for with the givenpremisses it is not possible to reduce them. For they have not been provedby syllogism, but assented to by agreement. For instance if a man shouldsuppose that unless there is one faculty of contraries, there cannot be onescience, and should then argue that not every faculty is of contraries, e.g. of
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what is healthy and what is sickly: for the same thing will then be at thesame time healthy and sickly. He has shown that there is not one faculty ofall contraries, but he has not proved that there is not a science. And yet onemust agree. But the agreement does not come from a syllogism, but from anhypothesis. This argument cannot be reduced: but the proof that there is nota single faculty can. The latter argument perhaps was a syllogism: but theformer was an hypothesis.
The same holds good of arguments which are brought to a conclusionper impossibile. These cannot be analysed either; but the reduction to whatis impossible can be analysed since it is proved by syllogism, though therest of the argument cannot, because the conclusion is reached from an hy-pothesis. But these differ from the previous arguments: for in the former apreliminary agreement must be reached if one is to accept the conclusion;e.g. an agreement that if there is proved to be one faculty of contraries, thencontraries fall under the same science; whereas in the latter, even if no pre-liminary agreement has been made, men still accept the reasoning, becausethe falsity is patent, e.g. the falsity of what follows from the assumptionthat the diagonal is commensurate, viz. that then odd numbers are equal toevens.
Many other arguments are brought to a conclusion by the help of an hy-pothesis; these we ought to consider and mark out clearly. We shall describein the sequel their differences, and the various ways in which hypotheticalarguments are formed: but at present this much must be clear, that it is notpossible to resolve such arguments into the figures. And we have explainedthe reason.
Part 45 Reduction of syllogisms between figures
Whatever problems are proved in more than one figure, if they have beenestablished in one figure by syllogism, can be reduced to another figure, e.g.a negative syllogism in the first figure can be reduced to the second, and asyllogism in the middle figure to the first, not all however but some only.The point will be clear in the sequel. If A belongs to no B, and B to all C,then A belongs to no C. Thus the first figure; but if the negative statement isconverted, we shall have the middle figure. For B belongs to no A, and to allC. Similarly if the syllogism is not universal but particular, e.g. if A belongsto no B, and B to some C. Convert the negative statement and you will havethe middle figure.
The universal syllogisms in the second figure can be reduced to the first,but only one of the two particular syllogisms. Let A belong to no B and to allC. Convert the negative statement, and you will have the first figure. For Bwill belong to no A and A to all C. But if the affirmative statement concerns
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B, and the negative C, C must be made first term. For C belongs to no A,and A to all B: therefore C belongs to no B. B then belongs to no C: for thenegative statement is convertible.
But if the syllogism is particular, whenever the negative statement con-cerns the major extreme, reduction to the first figure will be possible, e.g. ifA belongs to no B and to some C: convert the negative statement and youwill have the first figure. For B will belong to no A and A to some C. Butwhen the affirmative statement concerns the major extreme, no resolutionwill be possible, e.g. if A belongs to all B, but not to all C: for the statementAB does not admit of conversion, nor would there be a syllogism if it did.
Again syllogisms in the third figure cannot all be resolved into the first,though all syllogisms in the first figure can be resolved into the third. LetA belong to all B and B to some C. Since the particular affirmative is con-vertible, C will belong to some B: but A belonged to all B: so that the thirdfigure is formed. Similarly if the syllogism is negative: for the particularaffirmative is convertible: therefore A will belong to no B, and to some C.
Of the syllogisms in the last figure one only cannot be resolved into thefirst, viz. when the negative statement is not universal: all the rest can beresolved. Let A and B be affirmed of all C: then C can be converted partiallywith either A or B: C then belongs to some B. Consequently we shall getthe first figure, if A belongs to all C, and C to some of the Bs. If A belongsto all C and B to some C, the argument is the same: for B is convertible inreference to C. But if B belongs to all C and A to some C, the first term mustbe B: for B belongs to all C, and C to some A, therefore B belongs to some A.But since the particular statement is convertible, A will belong to some B. Ifthe syllogism is negative, when the terms are universal we must take themin a similar way. Let B belong to all C, and A to no C: then C will belongto some B, and A to no C; and so C will be middle term. Similarly if thenegative statement is universal, the affirmative particular: for A will belongto no C, and C to some of the Bs. But if the negative statement is particular,no resolution will be possible, e.g. if B belongs to all C, and A not belong tosome C: convert the statement BC and both premisses will be particular.
It is clear that in order to resolve the figures into one another the premisswhich concerns the minor extreme must be converted in both the figures: forwhen this premiss is altered, the transition to the other figure is made.
One of the syllogisms in the middle figure can, the other cannot, be re-solved into the third figure. Whenever the universal statement is negative,resolution is possible. For if A belongs to no B and to some C, both B and Calike are convertible in relation to A, so that B belongs to no A and C to someA. A therefore is middle term. But when A belongs to all B, and not to someC, resolution will not be possible: for neither of the premisses is universalafter conversion.
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Syllogisms in the third figure can be resolved into the middle figure,whenever the negative statement is universal, e.g. if A belongs to no C,and B to some or all C. For C then will belong to no A and to some B. Butif the negative statement is particular, no resolution will be possible: for theparticular negative does not admit of conversion.
It is clear then that the same syllogisms cannot be resolved in these fig-ures which could not be resolved into the first figure, and that when syllo-gisms are reduced to the first figure these alone are confirmed by reductionto what is impossible.
It is clear from what we have said how we ought to reduce syllogisms,and that the figures may be resolved into one another.
Part 46 ’not to be this’ and ’to be not-this’ differ in meaning
In establishing or refuting, it makes some difference whether we supposethe expressions ‘not to be this’ and ‘to be not-this’ are identical or differentin meaning, e.g. ‘not to be white’ and ‘to be not-white’. For they do not meanthe same thing, nor is ‘to be not-white’ the negation of ‘to be white’, but ‘notto be white’. The reason for this is as follows. The relation of ‘he can walk’ to‘he can not-walk’ is similar to the relation of ‘it is white’ to ‘it is not-white’; sois that of ‘he knows what is good’ to ‘he knows what is not-good’. For thereis no difference between the expressions ‘he knows what is good’ and ‘he isknowing what is good’, or ‘he can walk’ and ‘he is able to walk’: thereforethere is no difference between their contraries ‘he cannot walk’ - ‘he is notable to walk’. If then ‘he is not able to walk’ means the same as ‘he is ablenot to walk’, capacity to walk and incapacity to walk will belong at the sametime to the same person (for the same man can both walk and not-walk, andis possessed of knowledge of what is good and of what is not-good), but anaffirmation and a denial which are opposed to one another do not belong atthe same time to the same thing. As then ‘not to know what is good’ is notthe same as ‘to know what is not good’, so ‘to be not-good’ is not the same as‘not to be good’. For when two pairs correspond, if the one pair are differentfrom one another, the other pair also must be different. Nor is ‘to be not-equal’ the same as ‘not to be equal’: for there is something underlying theone, viz. that which is not-equal, and this is the unequal, but there is nothingunderlying the other. Wherefore not everything is either equal or unequal,but everything is equal or is not equal. Further the expressions ‘it is a not-white log’ and ‘it is not a white log’ do not imply one another’s truth. For if‘it is a not-white log’, it must be a log: but that which is not a white log neednot be a log at all. Therefore it is clear that ‘it is not-good’ is not the denialof ‘it is good’. If then every single statement may truly be said to be eitheran affirmation or a negation, if it is not a negation clearly it must in a sense
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be an affirmation. But every affirmation has a corresponding negation. Thenegation then of ‘it is not-good’ is ‘it is not not-good’. The relation of thesestatements to one another is as follows. Let A stand for ‘to be good’, B for‘not to be good’, let C stand for ‘to be not-good’ and be placed under B, andlet D stand for ‘not to be not-good’ and be placed under A. Then either Aor B will belong to everything, but they will never belong to the same thing;and either C or D will belong to everything, but they will never belong tothe same thing. And B must belong to everything to which C belongs. For ifit is true to say ‘it is a not-white’, it is true also to say ‘it is not white’: for it isimpossible that a thing should simultaneously be white and be not-white, orbe a not-white log and be a white log; consequently if the affirmation doesnot belong, the denial must belong. But C does not always belong to B: forwhat is not a log at all, cannot be a not-white log either. On the other handD belongs to everything to which A belongs. For either C or D belongs toeverything to which A belongs. But since a thing cannot be simultaneouslynot-white and white, D must belong to everything to which A belongs. Forof that which is white it is true to say that it is not not-white. But A is nottrue of all D. For of that which is not a log at all it is not true to say A, viz.that it is a white log. Consequently D is true, but A is not true, i.e. that it isa white log. It is clear also that A and C cannot together belong to the samething, and that B and D may possibly belong to the same thing.
Privative terms are similarly related positive ter terms respect of this ar-rangement. Let A stand for ‘equal’, B for ‘not equal’, C for ‘unequal’, D for‘not unequal’.
In many things also, to some of which something belongs which doesnot belong to others, the negation may be true in a similar way, viz. that allare not white or that each is not white, while that each is not-white or allare not-white is false. Similarly also ‘every animal is not-white’ is not thenegation of ‘every animal is white’ (for both are false): the proper negationis ‘every animal is not white’. Since it is clear that ‘it is not-white’ and ‘itis not white’ mean different things, and one is an affirmation, the other adenial, it is evident that the method of proving each cannot be the same,e.g. that whatever is an animal is not white or may not be white, and thatit is true to call it not-white; for this means that it is not-white. But we mayprove that it is true to call it white or not-white in the same way for both areproved constructively by means of the first figure. For the expression ‘it istrue’ stands on a similar footing to ‘it is’. For the negation of ‘it is true tocall it white’ is not ‘it is true to call it not-white’ but ‘it is not true to call itwhite’. If then it is to be true to say that whatever is a man is musical or isnot-musical, we must assume that whatever is an animal either is musical oris not-musical; and the proof has been made. That whatever is a man is notmusical is proved destructively in the three ways mentioned.
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In general whenever A and B are such that they cannot belong at the sametime to the same thing, and one of the two necessarily belongs to everything,and again C and D are related in the same way, and A follows C but therelation cannot be reversed, then D must follow B and the relation cannot bereversed. And A and D may belong to the same thing, but B and C cannot.First it is clear from the following consideration that D follows B. For sinceeither C or D necessarily belongs to everything; and since C cannot belongto that to which B belongs, because it carries A along with it and A and Bcannot belong to the same thing; it is clear that D must follow B. Again sinceC does not reciprocate with but A, but C or D belongs to everything, it ispossible that A and D should belong to the same thing. But B and C cannotbelong to the same thing, because A follows C; and so something impossibleresults. It is clear then that B does not reciprocate with D either, since it ispossible that D and A should belong at the same time to the same thing.
It results sometimes even in such an arrangement of terms that one is de-ceived through not apprehending the opposites rightly, one of which mustbelong to everything, e.g. we may reason that ’if A and B cannot belong atthe same time to the same thing, but it is necessary that one of them shouldbelong to whatever the other does not belong to: and again C and D arerelated in the same way, and follows everything which C follows: it will re-sult that B belongs necessarily to everything to which D belongs’: but thisis false. ’Assume that F stands for the negation of A and B, and again thatH stands for the negation of C and D. It is necessary then that either A orF should belong to everything: for either the affirmation or the denial mustbelong. And again either C or H must belong to everything: for they arerelated as affirmation and denial. And ex hypothesi A belongs to everythingever thing to which C belongs. Therefore H belongs to everything to whichF belongs. Again since either F or B belongs to everything, and similarlyeither H or D, and since H follows F, B must follow D: for we know this. Ifthen A follows C, B must follow D’. But this is false: for as we proved thesequence is reversed in terms so constituted. The fallacy arises because per-haps it is not necessary that A or F should belong to everything, or that For B should belong to everything: for F is not the denial of A. For not goodis the negation of good: and not-good is not identical with ‘neither goodnor not-good’. Similarly also with C and D. For two negations have beenassumed in respect to one term.
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Book II Aspects and properties of thesyllogism
Part 1 The reason common to all syllogisms
We have already explained the number of the figures, the character andnumber of the premisses, when and how a syllogism is formed; further whatwe must look for when refuting and establishing propositions, and how weshould investigate a given problem in any branch of inquiry, also by whatmeans we shall obtain principles appropriate to each subject. Since somesyllogisms are universal, others particular, all the universal syllogisms givemore than one result, and of particular syllogisms the affirmative yield morethan one, the negative yield only the stated conclusion. For all propositionsare convertible save only the particular negative: and the conclusion statesone definite thing about another definite thing. Consequently all syllogismssave the particular negative yield more than one conclusion, e.g. if A hasbeen proved to to all or to some B, then B must belong to some A: and if Ahas been proved to belong to no B, then B belongs to no A. This is a differentconclusion from the former. But if A does not belong to some B, it is notnecessary that B should not belong to some A: for it may possibly belong toall A.
This then is the reason common to all syllogisms whether universal orparticular. But it is possible to give another reason concerning those whichare universal. For all the things that are subordinate to the middle term or tothe conclusion may be proved by the same syllogism, if the former are placedin the middle, the latter in the conclusion; e.g. if the conclusion AB is provedthrough C, whatever is subordinate to B or C must accept the predicate A:for if D is included in B as in a whole, and B is included in A, then D will beincluded in A. Again if E is included in C as in a whole, and C is includedin A, then E will be included in A. Similarly if the syllogism is negative. Inthe second figure it will be possible to infer only that which is subordinateto the conclusion, e.g. if A belongs to no B and to all C; we conclude that Bbelongs to no C. If then D is subordinate to C, clearly B does not belong to it.But that B does not belong to what is subordinate to A is not clear by meansof the syllogism. And yet B does not belong to E, if E is subordinate to A.But while it has been proved through the syllogism that B belongs to no C, ithas been assumed without proof that B does not belong to A, consequentlyit does not result through the syllogism that B does not belong to E.
But in particular syllogisms there will be no necessity of inferring whatis subordinate to the conclusion (for a syllogism does not result when this
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premiss is particular), but whatever is subordinate to the middle term maybe inferred, not however through the syllogism, e.g. if A belongs to all Band B to some C. Nothing can be inferred about that which is subordinate toC; something can be inferred about that which is subordinate to B, but notthrough the preceding syllogism. Similarly in the other figures. That whichis subordinate to the conclusion cannot be proved; the other subordinate canbe proved, only not through the syllogism, just as in the universal syllogismswhat is subordinate to the middle term is proved (as we saw) from a premisswhich is not demonstrated: consequently either a conclusion is not possiblein the case of universal syllogisms or else it is possible also in the case ofparticular syllogisms.
Part 2 Truth and falsity of premiss and conclusion
It is possible for the premisses of the syllogism to be true, or to be false,or to be the one true, the other false. The conclusion is either true or falsenecessarily. From true premisses it is not possible to draw a false conclusion,but a true conclusion may be drawn from false premisses, true however onlyin respect to the fact, not to the reason. The reason cannot be establishedfrom false premisses: why this is so will be explained in the sequel.
First then that it is not possible to draw a false conclusion from true pre-misses, is made clear by this consideration. If it is necessary that B shouldbe when A is, it is necessary that A should not be when B is not. If then Ais true, B must be true: otherwise it will turn out that the same thing both isand is not at the same time. But this is impossible. Let it not, because A islaid down as a single term, be supposed that it is possible, when a single factis given, that something should necessarily result. For that is not possible.For what results necessarily is the conclusion, and the means by which thiscomes about are at the least three terms, and two relations of subject andpredicate or premisses. If then it is true that A belongs to all that to whichB belongs, and that B belongs to all that to which C belongs, it is necessarythat A should belong to all that to which C belongs, and this cannot be false:for then the same thing will belong and not belong at the same time. So Ais posited as one thing, being two premisses taken together. The same holdsgood of negative syllogisms: it is not possible to prove a false conclusionfrom true premisses.
But from what is false a true conclusion may be drawn, whether boththe premisses are false or only one, provided that this is not either of thepremisses indifferently, if it is taken as wholly false: but if the premiss is nottaken as wholly false, it does not matter which of the two is false.
(1) Let A belong to the whole of C, but to none of the Bs, neither let Bbelong to C. This is possible, e.g. animal belongs to no stone, nor stone to any
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man. If then A is taken to belong to all B and B to all C, A will belong to allC; consequently though both the premisses are false the conclusion is true:for every man is an animal. Similarly with the negative. For it is possiblethat neither A nor B should belong to any C, although A belongs to all B, e.g.if the same terms are taken and man is put as middle: for neither animal norman belongs to any stone, but animal belongs to every man. Consequentlyif one term is taken to belong to none of that to which it does belong, andthe other term is taken to belong to all of that to which it does not belong,though both the premisses are false the conclusion will be true.
(2) A similar proof may be given if each premiss is partially false.(3) But if one only of the premisses is false, when the first premiss is
wholly false, e.g. AB, the conclusion will not be true, but if the premissBC is wholly false, a true conclusion will be possible. I mean by ‘whollyfalse’ the contrary of the truth, e.g. if what belongs to none is assumed tobelong to all, or if what belongs to all is assumed to belong to none. LetA belong to no B, and B to all C. If then the premiss BC which I take istrue, and the premiss AB is wholly false, viz. that A belongs to all B, it isimpossible that the conclusion should be true: for A belonged to none of theCs, since A belonged to nothing to which B belonged, and B belonged to allC. Similarly there cannot be a true conclusion if A belongs to all B, and Bto all C, but while the true premiss BC is assumed, the wholly false premissAB is also assumed, viz. that A belongs to nothing to which B belongs: herethe conclusion must be false. For A will belong to all C, since A belongs toeverything to which B belongs, and B to all C. It is clear then that when thefirst premiss is wholly false, whether affirmative or negative, and the otherpremiss is true, the conclusion cannot be true.
(4) But if the premiss is not wholly false, a true conclusion is possible.For if A belongs to all C and to some B, and if B belongs to all C, e.g. animalto every swan and to some white thing, and white to every swan, then if wetake as premisses that A belongs to all B, and B to all C, A will belong to all Ctruly: for every swan is an animal. Similarly if the statement AB is negative.For it is possible that A should belong to some B and to no C, and that Bshould belong to all C, e.g. animal to some white thing, but to no snow, andwhite to all snow. If then one should assume that A belongs to no B, and Bto all C, then will belong to no C.
(5) But if the premiss AB, which is assumed, is wholly true, and the pre-miss BC is wholly false, a true syllogism will be possible: for nothing pre-vents A belonging to all B and to all C, though B belongs to no C, e.g. thesebeing species of the same genus which are not subordinate one to the other:for animal belongs both to horse and to man, but horse to no man. If thenit is assumed that A belongs to all B and B to all C, the conclusion will betrue, although the premiss BC is wholly false. Similarly if the premiss AB is
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negative. For it is possible that A should belong neither to any B nor to anyC, and that B should not belong to any C, e.g. a genus to species of anothergenus: for animal belongs neither to music nor to the art of healing, nor doesmusic belong to the art of healing. If then it is assumed that A belongs to noB, and B to all C, the conclusion will be true.
(6) And if the premiss BC is not wholly false but in part only, even so theconclusion may be true. For nothing prevents A belonging to the whole of Band of C, while B belongs to some C, e.g. a genus to its species and difference:for animal belongs to every man and to every footed thing, and man to somefooted things though not to all. If then it is assumed that A belongs to all B,and B to all C, A will belong to all C: and this ex hypothesi is true. Similarly ifthe premiss AB is negative. For it is possible that A should neither belong toany B nor to any C, though B belongs to some C, e.g. a genus to the species ofanother genus and its difference: for animal neither belongs to any wisdomnor to any instance of ‘speculative’, but wisdom belongs to some instance of‘speculative’. If then it should be assumed that A belongs to no B, and B toall C, will belong to no C: and this ex hypothesi is true.
In particular syllogisms it is possible when the first premiss is whollyfalse, and the other true, that the conclusion should be true; also when thefirst premiss is false in part, and the other true; and when the first is true,and the particular is false; and when both are false.
(7) For nothing prevents A belonging to no B, but to some C, and B tosome C, e.g. animal belongs to no snow, but to some white thing, and snowto some white thing. If then snow is taken as middle, and animal as firstterm, and it is assumed that A belongs to the whole of B, and B to some C,then the premiss BC is wholly false, the premiss BC true, and the conclusiontrue. Similarly if the premiss AB is negative: for it is possible that A shouldbelong to the whole of B, but not to some C, although B belongs to some C,e.g. animal belongs to every man, but does not follow some white, but manbelongs to some white; consequently if man be taken as middle term and it isassumed that A belongs to no B but B belongs to some C, the conclusion willbe true although the premiss AB is wholly false. (If the premiss AB is false inpart, the conclusion may be true. For nothing prevents A belonging both toB and to some C, and B belonging to some C, e.g. animal to something beau-tiful and to something great, and beautiful belonging to something great. Ifthen A is assumed to belong to all B, and B to some C, the a premiss AB willbe partially false, the premiss BC will be true, and the conclusion true. Simi-larly if the premiss AB is negative. For the same terms will serve, and in thesame positions, to prove the point.
(9) Again if the premiss AB is true, and the premiss BC is false, the con-clusion may be true. For nothing prevents A belonging to the whole of Band to some C, while B belongs to no C, e.g. animal to every swan and to
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some black things, though swan belongs to no black thing. Consequently ifit should be assumed that A belongs to all B, and B to some C, the conclusionwill be true, although the statement BC is false. Similarly if the premiss ABis negative. For it is possible that A should belong to no B, and not to someC, while B belongs to no C, e.g. a genus to the species of another genus andto the accident of its own species: for animal belongs to no number and notto some white things, and number belongs to nothing white. If then numberis taken as middle, and it is assumed that A belongs to no B, and B to someC, then A will not belong to some C, which ex hypothesi is true. And thepremiss AB is true, the premiss BC false.
(10) Also if the premiss AB is partially false, and the premiss BC is falsetoo, the conclusion may be true. For nothing prevents A belonging to someB and to some C, though B belongs to no C, e.g. if B is the contrary of C,and both are accidents of the same genus: for animal belongs to some whitethings and to some black things, but white belongs to no black thing. If thenit is assumed that A belongs to all B, and B to some C, the conclusion will betrue. Similarly if the premiss AB is negative: for the same terms arranged inthe same way will serve for the proof.
(11) Also though both premisses are false the conclusion may be true.For it is possible that A may belong to no B and to some C, while B belongsto no C, e.g. a genus in relation to the species of another genus, and to theaccident of its own species: for animal belongs to no number, but to somewhite things, and number to nothing white. If then it is assumed that Abelongs to all B and B to some C, the conclusion will be true, though bothpremisses are false. Similarly also if the premiss AB is negative. For nothingprevents A belonging to the whole of B, and not to some C, while B belongsto no C, e.g. animal belongs to every swan, and not to some black things,and swan belongs to nothing black. Consequently if it is assumed that Abelongs to no B, and B to some C, then A does not belong to some C. Theconclusion then is true, but the premisses arc false.
Part 3 Reaching true conclusions from false premisses
In the middle figure it is possible in every way to reach a true conclusionthrough false premisses, whether the syllogisms are universal or particular,viz. when both premisses are wholly false; when each is partially false; whenone is true, the other wholly false (it does not matter which of the two pre-misses is false); if both premisses are partially false; if one is quite true, theother partially false; if one is wholly false, the other partially true. For
(1) if A belongs to no B and to all C, e.g. animal to no stone and to everyhorse, then if the premisses are stated contrariwise and it is assumed that Abelongs to all B and to no C, though the premisses are wholly false they will
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yield a true conclusion. Similarly if A belongs to all B and to no C: for weshall have the same syllogism.
(2) Again if one premiss is wholly false, the other wholly true: for nothingprevents A belonging to all B and to all C, though B belongs to no C, e.g. agenus to its co-ordinate species. For animal belongs to every horse and man,and no man is a horse. If then it is assumed that animal belongs to all of theone, and none of the other, the one premiss will be wholly false, the otherwholly true, and the conclusion will be true whichever term the negativestatement concerns.
(3) Also if one premiss is partially false, the other wholly true. For it ispossible that A should belong to some B and to all C, though B belongs tono C, e.g. animal to some white things and to every raven, though whitebelongs to no raven. If then it is assumed that A belongs to no B, but to thewhole of C, the premiss AB is partially false, the premiss AC wholly true,and the conclusion true. Similarly if the negative statement is transposed:the proof can be made by means of the same terms. Also if the affirmativepremiss is partially false, the negative wholly true, a true conclusion is pos-sible. For nothing prevents A belonging to some B, but not to C as a whole,while B belongs to no C, e.g. animal belongs to some white things, but to nopitch, and white belongs to no pitch. Consequently if it is assumed that Abelongs to the whole of B, but to no C, the premiss AB is partially false, thepremiss AC is wholly true, and the conclusion is true.
(4) And if both the premisses are partially false, the conclusion may betrue. For it is possible that A should belong to some B and to some C, and Bto no C, e.g. animal to some white things and to some black things, thoughwhite belongs to nothing black. If then it is assumed that A belongs to allB and to no C, both premisses are partially false, but the conclusion is true.Similarly, if the negative premiss is transposed, the proof can be made bymeans of the same terms.
It is clear also that our thesis holds in particular syllogisms. For(5) nothing prevents A belonging to all B and to some C, though B does
not belong to some C, e.g. animal to every man and to some white things,though man will not belong to some white things. If then it is stated thatA belongs to no B and to some C, the universal premiss is wholly false, theparticular premiss is true, and the conclusion is true. Similarly if the premissAB is affirmative: for it is possible that A should belong to no B, and notto some C, though B does not belong to some C, e.g. animal belongs tonothing lifeless, and does not belong to some white things, and lifeless willnot belong to some white things. If then it is stated that A belongs to allB and not to some C, the premiss AB which is universal is wholly false,the premiss AC is true, and the conclusion is true. Also a true conclusionis possible when the universal premiss is true, and the particular is false.
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For nothing prevents A following neither B nor C at all, while B does notbelong to some C, e.g. animal belongs to no number nor to anything lifeless,and number does not follow some lifeless things. If then it is stated that Abelongs to no B and to some C, the conclusion will be true, and the universalpremiss true, but the particular false. Similarly if the premiss which is stateduniversally is affirmative. For it is possible that should A belong both to Band to C as wholes, though B does not follow some C, e.g. a genus in relationto its species and difference: for animal follows every man and footed thingsas a whole, but man does not follow every footed thing. Consequently if itis assumed that A belongs to the whole of B, but does not belong to some C,the universal premiss is true, the particular false, and the conclusion true.
(6) It is clear too that though both premisses are false they may yield atrue conclusion, since it is possible that A should belong both to B and to Cas wholes, though B does not follow some C. For if it is assumed that A be-longs to no B and to some C, the premisses are both false, but the conclusionis true. Similarly if the universal premiss is affirmative and the particularnegative. For it is possible that A should follow no B and all C, though Bdoes not belong to some C, e.g. animal follows no science but every man,though science does not follow every man. If then A is assumed to belongto the whole of B, and not to follow some C, the premisses are false but theconclusion is true.
In the last figure a true conclusion may come through what is false, alikewhen both premisses are wholly false, when each is partly false, when onepremiss is wholly true, the other false, when one premiss is partly false, theother wholly true, and vice versa, and in every other way in which it ispossible to alter the premisses.
For (1) nothing prevents neither A nor B from belonging to any C, whileA belongs to some B, e.g. neither man nor footed follows anything lifeless,though man belongs to some footed things. If then it is assumed that A andB belong to all C, the premisses will be wholly false, but the conclusion true.Similarly if one premiss is negative, the other affirmative. For it is possiblethat B should belong to no C, but A to all C, and that should not belong tosome B, e.g. black belongs to no swan, animal to every swan, and animalnot to everything black. Consequently if it is assumed that B belongs to allC, and A to no C, A will not belong to some B: and the conclusion is true,though the premisses are false.
(2) Also if each premiss is partly false, the conclusion may be true. Fornothing prevents both A and B from belonging to some C while A belongs tosome B, e.g. white and beautiful belong to some animals, and white to somebeautiful things. If then it is stated that A and B belong to all C, the premissesare partially false, but the conclusion is true. Similarly if the premiss AC isstated as negative. For nothing prevents A from not belonging, and B from
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belonging, to some C, while A does not belong to all B, e.g. white doesnot belong to some animals, beautiful belongs to some animals, and whitedoes not belong to everything beautiful. Consequently if it is assumed thatA belongs to no C, and B to all C, both premisses are partly false, but theconclusion is true.
(3) Similarly if one of the premisses assumed is wholly false, the otherwholly true. For it is possible that both A and B should follow all C, thoughA does not belong to some B, e.g. animal and white follow every swan,though animal does not belong to everything white. Taking these then asterms, if one assumes that B belongs to the whole of C, but A does not belongto C at all, the premiss BC will be wholly true, the premiss AC wholly false,and the conclusion true. Similarly if the statement BC is false, the statementAC true, the conclusion may be true. The same terms will serve for the proof.Also if both the premisses assumed are affirmative, the conclusion may betrue. For nothing prevents B from following all C, and A from not belongingto C at all, though A belongs to some B, e.g. animal belongs to every swan,black to no swan, and black to some animals. Consequently if it is assumedthat A and B belong to every C, the premiss BC is wholly true, the premissAC is wholly false, and the conclusion is true. Similarly if the premiss ACwhich is assumed is true: the proof can be made through the same terms.
(4) Again if one premiss is wholly true, the other partly false, the conclu-sion may be true. For it is possible that B should belong to all C, and A tosome C, while A belongs to some B, e.g. biped belongs to every man, beauti-ful not to every man, and beautiful to some bipeds. If then it is assumed thatboth A and B belong to the whole of C, the premiss BC is wholly true, thepremiss AC partly false, the conclusion true. Similarly if of the premisses as-sumed AC is true and BC partly false, a true conclusion is possible: this canbe proved, if the same terms as before are transposed. Also the conclusionmay be true if one premiss is negative, the other affirmative. For since it ispossible that B should belong to the whole of C, and A to some C, and, whenthey are so, that A should not belong to all B, therefore it is assumed that Bbelongs to the whole of C, and A to no C, the negative premiss is partly false,the other premiss wholly true, and the conclusion is true. Again since it hasbeen proved that if A belongs to no C and B to some C, it is possible that Ashould not belong to some C, it is clear that if the premiss AC is wholly true,and the premiss BC partly false, it is possible that the conclusion should betrue. For if it is assumed that A belongs to no C, and B to all C, the premissAC is wholly true, and the premiss BC is partly false.
(5) It is clear also in the case of particular syllogisms that a true conclusionmay come through what is false, in every possible way. For the same termsmust be taken as have been taken when the premisses are universal, positiveterms in positive syllogisms, negative terms in negative. For it makes no
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difference to the setting out of the terms, whether one assumes that whatbelongs to none belongs to all or that what belongs to some belongs to all.The same applies to negative statements.
It is clear then that if the conclusion is false, the premisses of the argu-ment must be false, either all or some of them; but when the conclusion istrue, it is not necessary that the premisses should be true, either one or all,yet it is possible, though no part of the syllogism is true, that the conclusionmay none the less be true; but it is not necessitated. The reason is that whentwo things are so related to one another, that if the one is, the other neces-sarily is, then if the latter is not, the former will not be either, but if the latteris, it is not necessary that the former should be. But it is impossible that thesame thing should be necessitated by the being and by the not-being of thesame thing. I mean, for example, that it is impossible that B should neces-sarily be great since A is white and that B should necessarily be great sinceA is not white. For whenever since this, A, is white it is necessary that that,B, should be great, and since B is great that C should not be white, then it isnecessary if is white that C should not be white. And whenever it is neces-sary, since one of two things is, that the other should be, it is necessary, ifthe latter is not, that the former (viz. A) should not be. If then B is not greatA cannot be white. But if, when A is not white, it is necessary that B shouldbe great, it necessarily results that if B is not great, B itself is great. (But thisis impossible.) For if B is not great, A will necessarily not be white. If thenwhen this is not white B must be great, it results that if B is not great, it isgreat, just as if it were proved through three terms.
Part 4 Circular and reciprocal proof
Circular and reciprocal proof means proof by means of the conclusion, i.e.by converting one of the premisses simply and inferring the premiss whichwas assumed in the original syllogism: e.g. suppose it has been necessaryto prove that A belongs to all C, and it has been proved through B; supposethat A should now be proved to belong to B by assuming that A belongs toC, and C to B - so A belongs to B: but in the first syllogism the converse wasassumed, viz. that B belongs to C. Or suppose it is necessary to prove thatB belongs to C, and A is assumed to belong to C, which was the conclusionof the first syllogism, and B to belong to A but the converse was assumed inthe earlier syllogism, viz. that A belongs to B. In no other way is reciprocalproof possible. If another term is taken as middle, the proof is not circular:for neither of the propositions assumed is the same as before: if one of theaccepted terms is taken as middle, only one of the premisses of the first syl-logism can be assumed in the second: for if both of them are taken the sameconclusion as before will result: but it must be different. If the terms are not
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convertible, one of the premisses from which the syllogism results must beundemonstrated: for it is not possible to demonstrate through these termsthat the third belongs to the middle or the middle to the first. If the termsare convertible, it is possible to demonstrate everything reciprocally, e.g. if Aand B and C are convertible with one another. Suppose the proposition AChas been demonstrated through B as middle term, and again the propositionAB through the conclusion and the premiss BC converted, and similarly theproposition BC through the conclusion and the premiss AB converted. But itis necessary to prove both the premiss CB, and the premiss BA: for we haveused these alone without demonstrating them. If then it is assumed that Bbelongs to all C, and C to all A, we shall have a syllogism relating B to A.Again if it is assumed that C belongs to all A, and A to all B, C must belongto all B. In both these syllogisms the premiss CA has been assumed with-out being demonstrated: the other premisses had ex hypothesi been proved.Consequently if we succeed in demonstrating this premiss, all the premisseswill have been proved reciprocally. If then it is assumed that C belongs to allB, and B to all A, both the premisses assumed have been proved, and C mustbelong to A. It is clear then that only if the terms are convertible is circularand reciprocal demonstration possible (if the terms are not convertible, thematter stands as we said above). But it turns out in these also that we usefor the demonstration the very thing that is being proved: for C is proved ofB, and B of by assuming that C is said of and C is proved of A through thesepremisses, so that we use the conclusion for the demonstration.
In negative syllogisms reciprocal proof is as follows. Let B belong to allC, and A to none of the Bs: we conclude that A belongs to none of the Cs.If again it is necessary to prove that A belongs to none of the Bs (whichwas previously assumed) A must belong to no C, and C to all B: thus theprevious premiss is reversed. If it is necessary to prove that B belongs to C,the proposition AB must no longer be converted as before: for the premiss‘B belongs to no A’ is identical with the premiss ‘A belongs to no B’. Butwe must assume that B belongs to all of that to none of which longs. Let Abelong to none of the Cs (which was the previous conclusion) and assumethat B belongs to all of that to none of which A belongs. It is necessary thenthat B should belong to all C. Consequently each of the three propositionshas been made a conclusion, and this is circular demonstration, to assumethe conclusion and the converse of one of the premisses, and deduce theremaining premiss.
In particular syllogisms it is not possible to demonstrate the universalpremiss through the other propositions, but the particular premiss can bedemonstrated. Clearly it is impossible to demonstrate the universal pre-miss: for what is universal is proved through propositions which are uni-versal, but the conclusion is not universal, and the proof must start from the
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conclusion and the other premiss. Further a syllogism cannot be made atall if the other premiss is converted: for the result is that both premisses areparticular. But the particular premiss may be proved. Suppose that A hasbeen proved of some C through B. If then it is assumed that B belongs to allA and the conclusion is retained, B will belong to some C: for we obtain thefirst figure and A is middle. But if the syllogism is negative, it is not possibleto prove the universal premiss, for the reason given above. But it is possibleto prove the particular premiss, if the proposition AB is converted as in theuniversal syllogism, i.e ‘B belongs to some of that to some of which A doesnot belong’: otherwise no syllogism results because the particular premiss isnegative.
Part 5 In the second figure
In the second figure it is not possible to prove an affirmative proposition inthis way, but a negative proposition may be proved. An affirmative propo-sition is not proved because both premisses of the new syllogism are notaffirmative (for the conclusion is negative) but an affirmative proposition is(as we saw) proved from premisses which are both affirmative. The negativeis proved as follows. Let A belong to all B, and to no C: we conclude that Bbelongs to no C. If then it is assumed that B belongs to all A, it is necessarythat A should belong to no C: for we get the second figure, with B as middle.But if the premiss AB was negative, and the other affirmative, we shall havethe first figure. For C belongs to all A and B to no C, consequently B belongsto no A: neither then does A belong to B. Through the conclusion, therefore,and one premiss, we get no syllogism, but if another premiss is assumed inaddition, a syllogism will be possible. But if the syllogism not universal, theuniversal premiss cannot be proved, for the same reason as we gave above,but the particular premiss can be proved whenever the universal statementis affirmative. Let A belong to all B, and not to all C: the conclusion is BC.If then it is assumed that B belongs to all A, but not to all C, A will not be-long to some C, B being middle. But if the universal premiss is negative, thepremiss AC will not be demonstrated by the conversion of AB: for it turnsout that either both or one of the premisses is negative; consequently a syl-logism will not be possible. But the proof will proceed as in the universalsyllogisms, if it is assumed that A belongs to some of that to some of whichB does not belong.
Part 6 In the third figure
In the third figure, when both premisses are taken universally, it is not possi-ble to prove them reciprocally: for that which is universal is proved through
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statements which are universal, but the conclusion in this figure is alwaysparticular, so that it is clear that it is not possible at all to prove through thisfigure the universal premiss. But if one premiss is universal, the other par-ticular, proof of the latter will sometimes be possible, sometimes not. Whenboth the premisses assumed are affirmative, and the universal concerns theminor extreme, proof will be possible, but when it concerns the other ex-treme, impossible. Let A belong to all C and B to some C: the conclusion isthe statement AB. If then it is assumed that C belongs to all A, it has beenproved that C belongs to some B, but that B belongs to some C has not beenproved. And yet it is necessary, if C belongs to some B, that B should be-long to some C. But it is not the same that this should belong to that, andthat to this: but we must assume besides that if this belongs to some of that,that belongs to some of this. But if this is assumed the syllogism no longerresults from the conclusion and the other premiss. But if B belongs to all C,and A to some C, it will be possible to prove the proposition AC, when itis assumed that C belongs to all B, and A to some B. For if C belongs to allB and A to some B, it is necessary that A should belong to some C, B beingmiddle. And whenever one premiss is affirmative the other negative, andthe affirmative is universal, the other premiss can be proved. Let B belongto all C, and A not to some C: the conclusion is that A does not belong tosome B. If then it is assumed further that C belongs to all B, it is necessarythat A should not belong to some C, B being middle. But when the negativepremiss is universal, the other premiss is not except as before, viz. if it isassumed that that belongs to some of that, to some of which this does notbelong, e.g. if A belongs to no C, and B to some C: the conclusion is that Adoes not belong to some B. If then it is assumed that C belongs to some ofthat to some of which does not belong, it is necessary that C should belongto some of the Bs. In no other way is it possible by converting the universalpremiss to prove the other: for in no other way can a syllogism be formed.
It is clear then that in the first figure reciprocal proof is made boththrough the third and through the first figure - if the conclusion is affirma-tive through the first; if the conclusion is negative through the last. For it isassumed that that belongs to all of that to none of which this belongs. In themiddle figure, when the syllogism is universal, proof is possible through thesecond figure and through the first, but when particular through the secondand the last. In the third figure all proofs are made through itself. It is clearalso that in the third figure and in the middle figure those syllogisms whichare not made through those figures themselves either are not of the natureof circular proof or are imperfect.
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Part 7 Conversion of syllogisms
To convert a syllogism means to alter the conclusion and make another syllo-gism to prove that either the extreme cannot belong to the middle or the mid-dle to the last term. For it is necessary, if the conclusion has been changedinto its opposite and one of the premisses stands, that the other premissshould be destroyed. For if it should stand, the conclusion also must stand.It makes a difference whether the conclusion is converted into its contradic-tory or into its contrary. For the same syllogism does not result whicheverform the conversion takes. This will be made clear by the sequel. By contra-dictory opposition I mean the opposition of ‘to all’ to ‘not to all’, and of ‘tosome’ to ‘to none’; by contrary opposition I mean the opposition of ‘to all’ to‘to none’, and of ‘to some’ to ‘not to some’. Suppose that A been proved ofC, through B as middle term. If then it should be assumed that A belongs tono C, but to all B, B will belong to no C. And if A belongs to no C, and B toall C, A will belong, not to no B at all, but not to all B. For (as we saw) theuniversal is not proved through the last figure. In a word it is not possibleto refute universally by conversion the premiss which concerns the majorextreme: for the refutation always proceeds through the third since it is nec-essary to take both premisses in reference to the minor extreme. Similarly ifthe syllogism is negative. Suppose it has been proved that A belongs to noC through B. Then if it is assumed that A belongs to all C, and to no B, B willbelong to none of the Cs. And if A and B belong to all C, A will belong tosome B: but in the original premiss it belonged to no B.
If the conclusion is converted into its contradictory, the syllogisms willbe contradictory and not universal. For one premiss is particular, so that theconclusion also will be particular. Let the syllogism be affirmative, and letit be converted as stated. Then if A belongs not to all C, but to all B, B willbelong not to all C. And if A belongs not to all C, but B belongs to all C, Awill belong not to all B. Similarly if the syllogism is negative. For if A belongsto some C, and to no B, B will belong, not to no C at all, but - not to someC. And if A belongs to some C, and B to all C, as was originally assumed, Awill belong to some B.
In particular syllogisms when the conclusion is converted into its con-tradictory, both premisses may be refuted, but when it is converted into itscontrary, neither. For the result is no longer, as in the universal syllogisms,refutation in which the conclusion reached by O, conversion lacks univer-sality, but no refutation at all. Suppose that A has been proved of some C. Ifthen it is assumed that A belongs to no C, and B to some C, A will not belongto some B: and if A belongs to no C, but to all B, B will belong to no C. Thusboth premisses are refuted. But neither can be refuted if the conclusion isconverted into its contrary. For if A does not belong to some C, but to all B,
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then B will not belong to some C. But the original premiss is not yet refuted:for it is possible that B should belong to some C, and should not belong tosome C. The universal premiss AB cannot be affected by a syllogism at all:for if A does not belong to some of the Cs, but B belongs to some of the Cs,neither of the premisses is universal. Similarly if the syllogism is negative:for if it should be assumed that A belongs to all C, both premisses are re-futed: but if the assumption is that A belongs to some C, neither premiss isrefuted. The proof is the same as before.
Part 8 In the second figure
In the second figure it is not possible to refute the premiss which concernsthe major extreme by establishing something contrary to it, whichever formthe conversion of the conclusion may take. For the conclusion of the refuta-tion will always be in the third figure, and in this figure (as we saw) there isno universal syllogism. The other premiss can be refuted in a manner similarto the conversion: I mean, if the conclusion of the first syllogism is convertedinto its contrary, the conclusion of the refutation will be the contrary of theminor premiss of the first, if into its contradictory, the contradictory. Let Abelong to all B and to no C: conclusion BC. If then it is assumed that B be-longs to all C, and the proposition AB stands, A will belong to all C, since thefirst figure is produced. If B belongs to all C, and A to no C, then A belongsnot to all B: the figure is the last. But if the conclusion BC is converted intoits contradictory, the premiss AB will be refuted as before, the premiss, ACby its contradictory. For if B belongs to some C, and A to no C, then A willnot belong to some B. Again if B belongs to some C, and A to all B, A willbelong to some C, so that the syllogism results in the contradictory of theminor premiss. A similar proof can be given if the premisses are transposedin respect of their quality.
If the syllogism is particular, when the conclusion is converted into itscontrary neither premiss can be refuted, as also happened in the first figure,if the conclusion is converted into its contradictory, both premisses can berefuted. Suppose that A belongs to no B, and to some C: the conclusionis BC. If then it is assumed that B belongs to some C, and the statementAB stands, the conclusion will be that A does not belong to some C. Butthe original statement has not been refuted: for it is possible that A shouldbelong to some C and also not to some C. Again if B belongs to some Cand A to some C, no syllogism will be possible: for neither of the premissestaken is universal. Consequently the proposition AB is not refuted. Butif the conclusion is converted into its contradictory, both premisses can berefuted. For if B belongs to all C, and A to no B, A will belong to no C: but itwas assumed to belong to some C. Again if B belongs to all C and A to some
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C, A will belong to some B. The same proof can be given if the universalstatement is affirmative.
Part 9 In the third figure
In the third figure when the conclusion is converted into its contrary, neitherof the premisses can be refuted in any of the syllogisms, but when the con-clusion is converted into its contradictory, both premisses may be refutedand in all the moods. Suppose it has been proved that A belongs to some B,C being taken as middle, and the premisses being universal. If then it is as-sumed that A does not belong to some B, but B belongs to all C, no syllogismis formed about A and C. Nor if A does not belong to some B, but belongsto all C, will a syllogism be possible about B and C. A similar proof can begiven if the premisses are not universal. For either both premisses arrivedat by the conversion must be particular, or the universal premiss must referto the minor extreme. But we found that no syllogism is possible thus eitherin the first or in the middle figure. But if the conclusion is converted into itscontradictory, both the premisses can be refuted. For if A belongs to no B,and B to all C, then A belongs to no C: again if A belongs to no B, and to allC, B belongs to no C. And similarly if one of the premisses is not universal.For if A belongs to no B, and B to some C, A will not belong to some C: if Abelongs to no B, and to C, B will belong to no C.
Similarly if the original syllogism is negative. Suppose it has been provedthat A does not belong to some B, BC being affirmative, AC being negative:for it was thus that, as we saw, a syllogism could be made. Whenever thenthe contrary of the conclusion is assumed a syllogism will not be possible.For if A belongs to some B, and B to all C, no syllogism is possible (as we saw)about A and C. Nor, if A belongs to some B, and to no C, was a syllogismpossible concerning B and C. Therefore the premisses are not refuted. Butwhen the contradictory of the conclusion is assumed, they are refuted. Forif A belongs to all B, and B to C, A belongs to all C: but A was supposedoriginally to belong to no C. Again if A belongs to all B, and to no C, thenB belongs to no C: but it was supposed to belong to all C. A similar proof ispossible if the premisses are not universal. For AC becomes universal andnegative, the other premiss particular and affirmative. If then A belongsto all B, and B to some C, it results that A belongs to some C: but it wassupposed to belong to no C. Again if A belongs to all B, and to no C, thenB belongs to no C: but it was assumed to belong to some C. If A belongs tosome B and B to some C, no syllogism results: nor yet if A belongs to someB, and to no C. Thus in one way the premisses are refuted, in the other waythey are not.
From what has been said it is clear how a syllogism results in each fig-
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ure when the conclusion is converted; when a result contrary to the premiss,and when a result contradictory to the premiss, is obtained. It is clear thatin the first figure the syllogisms are formed through the middle and the lastfigures, and the premiss which concerns the minor extreme is alway refutedthrough the middle figure, the premiss which concerns the major throughthe last figure. In the second figure syllogisms proceed through the first andthe last figures, and the premiss which concerns the minor extreme is al-ways refuted through the first figure, the premiss which concerns the majorextreme through the last. In the third figure the refutation proceeds throughthe first and the middle figures; the premiss which concerns the major is al-ways refuted through the first figure, the premiss which concerns the minorthrough the middle figure.
Part 10 The syllogism per impossibile
It is clear then what conversion is, how it is effected in each figure, and whatsyllogism results. The syllogism per impossibile is proved when the contra-dictory of the conclusion stated and another premiss is assumed; it can bemade in all the figures. For it resembles conversion, differing only in this:conversion takes place after a syllogism has been formed and both the pre-misses have been taken, but a reduction to the impossible takes place notbecause the contradictory has been agreed to already, but because it is clearthat it is true. The terms are alike in both, and the premisses of both are takenin the same way. For example if A belongs to all B, C being middle, then ifit is supposed that A does not belong to all B or belongs to no B, but to allC (which was admitted to be true), it follows that C belongs to no B or notto all B. But this is impossible: consequently the supposition is false: its con-tradictory then is true. Similarly in the other figures: for whatever moodsadmit of conversion admit also of the reduction per impossibile.
All the problems can be proved per impossibile in all the figures, ex-cepting the universal affirmative, which is proved in the middle and thirdfigures, but not in the first. Suppose that A belongs not to all B, or to no B,and take besides another premiss concerning either of the terms, viz. that Cbelongs to all A, or that B belongs to all D; thus we get the first figure. If thenit is supposed that A does not belong to all B, no syllogism results whicheverterm the assumed premiss concerns; but if it is supposed that A belongs tono B, when the premiss BD is assumed as well we shall prove syllogisticallywhat is false, but not the problem proposed. For if A belongs to no B, andB belongs to all D, A belongs to no D. Let this be impossible: it is false thenA belongs to no B. But the universal affirmative is not necessarily true if theuniversal negative is false. But if the premiss CA is assumed as well, nosyllogism results, nor does it do so when it is supposed that A does not be-
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long to all B. Consequently it is clear that the universal affirmative cannot beproved in the first figure per impossibile.
But the particular affirmative and the universal and particular negativescan all be proved. Suppose that A belongs to no B, and let it have beenassumed that B belongs to all or to some C. Then it is necessary that A shouldbelong to no C or not to all C. But this is impossible (for let it be true andclear that A belongs to all C): consequently if this is false, it is necessarythat A should belong to some B. But if the other premiss assumed relates toA, no syllogism will be possible. Nor can a conclusion be drawn when thecontrary of the conclusion is supposed, e.g. that A does not belong to someB. Clearly then we must suppose the contradictory.
Again suppose that A belongs to some B, and let it have been assumedthat C belongs to all A. It is necessary then that C should belong to some B.But let this be impossible, so that the supposition is false: in that case it istrue that A belongs to no B. We may proceed in the same way if the propo-sition CA has been taken as negative. But if the premiss assumed concernsB, no syllogism will be possible. If the contrary is supposed, we shall havea syllogism and an impossible conclusion, but the problem in hand is notproved. Suppose that A belongs to all B, and let it have been assumed thatC belongs to all A. It is necessary then that C should belong to all B. Butthis is impossible, so that it is false that A belongs to all B. But we have notyet shown it to be necessary that A belongs to no B, if it does not belong toall B. Similarly if the other premiss taken concerns B; we shall have a syllo-gism and a conclusion which is impossible, but the hypothesis is not refuted.Therefore it is the contradictory that we must suppose.
To prove that A does not belong to all B, we must suppose that it belongsto all B: for if A belongs to all B, and C to all A, then C belongs to all B; so thatif this is impossible, the hypothesis is false. Similarly if the other premissassumed concerns B. The same results if the original proposition CA wasnegative: for thus also we get a syllogism. But if the negative propositionconcerns B, nothing is proved. If the hypothesis is that A belongs not toall but to some B, it is not proved that A belongs not to all B, but that itbelongs to no B. For if A belongs to some B, and C to all A, then C willbelong to some B. If then this is impossible, it is false that A belongs to someB; consequently it is true that A belongs to no B. But if this is proved, thetruth is refuted as well; for the original conclusion was that A belongs tosome B, and does not belong to some B. Further the impossible does notresult from the hypothesis: for then the hypothesis would be false, since itis impossible to draw a false conclusion from true premisses: but in fact itis true: for A belongs to some B. Consequently we must not suppose thatA belongs to some B, but that it belongs to all B. Similarly if we should beproving that A does not belong to some B: for if ‘not to belong to some’ and
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‘to belong not to all’ have the same meaning, the demonstration of both willbe identical.
It is clear then that not the contrary but the contradictory ought to besupposed in all the syllogisms. For thus we shall have necessity of inference,and the claim we make is one that will be generally accepted. For if of every-thing one or other of two contradictory statements holds good, then if it isproved that the negation does not hold, the affirmation must be true. Againif it is not admitted that the affirmation is true, the claim that the negation istrue will be generally accepted. But in neither way does it suit to maintainthe contrary: for it is not necessary that if the universal negative is false, theuniversal affirmative should be true, nor is it generally accepted that if theone is false the other is true.
Part 11 First figure problems proved per impossibile
It is clear then that in the first figure all problems except the universal af-firmative are proved per impossibile. But in the middle and the last figuresthis also is proved. Suppose that A does not belong to all B, and let it havebeen assumed that A belongs to all C. If then A belongs not to all B, but toall C, C will not belong to all B. But this is impossible (for suppose it to beclear that C belongs to all B): consequently the hypothesis is false. It is truethen that A belongs to all B. But if the contrary is supposed, we shall have asyllogism and a result which is impossible: but the problem in hand is notproved. For if A belongs to no B, and to all C, C will belong to no B. This isimpossible; so that it is false that A belongs to no B. But though this is false,it does not follow that it is true that A belongs to all B.
When A belongs to some B, suppose that A belongs to no B, and let Abelong to all C. It is necessary then that C should belong to no B. Conse-quently, if this is impossible, A must belong to some B. But if it is supposedthat A does not belong to some B, we shall have the same results as in thefirst figure.
Again suppose that A belongs to some B, and let A belong to no C. It isnecessary then that C should not belong to some B. But originally it belongedto all B, consequently the hypothesis is false: A then will belong to no B.
When A does not belong to an B, suppose it does belong to all B, and tono C. It is necessary then that C should belong to no B. But this is impossible:so that it is true that A does not belong to all B. It is clear then that all thesyllogisms can be formed in the middle figure.
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Part 12 Similarly in the last figure
Similarly they can all be formed in the last figure. Suppose that A does notbelong to some B, but C belongs to all B: then A does not belong to some C.If then this is impossible, it is false that A does not belong to some B; so thatit is true that A belongs to all B. But if it is supposed that A belongs to noB, we shall have a syllogism and a conclusion which is impossible: but theproblem in hand is not proved: for if the contrary is supposed, we shall havethe same results as before.
But to prove that A belongs to some B, this hypothesis must be made. IfA belongs to no B, and C to some B, A will belong not to all C. If then this isfalse, it is true that A belongs to some B.
When A belongs to no B, suppose A belongs to some B, and let it havebeen assumed that C belongs to all B. Then it is necessary that A shouldbelong to some C. But ex hypothesi it belongs to no C, so that it is false thatA belongs to some B. But if it is supposed that A belongs to all B, the problemis not proved.
But this hypothesis must be made if we are prove that A belongs not toall B. For if A belongs to all B and C to some B, then A belongs to some C.But this we assumed not to be so, so it is false that A belongs to all B. But inthat case it is true that A belongs not to all B. If however it is assumed that Abelongs to some B, we shall have the same result as before.
It is clear then that in all the syllogisms which proceed per impossibilethe contradictory must be assumed. And it is plain that in the middle figurean affirmative conclusion, and in the last figure a universal conclusion, areproved in a way.
Part 13 Demonstration per impossibile differs fromostensive proof
Demonstration per impossibile differs from ostensive proof in that it positswhat it wishes to refute by reduction to a statement admitted to be false;whereas ostensive proof starts from admitted positions. Both, indeed, taketwo premisses that are admitted, but the latter takes the premisses fromwhich the syllogism starts, the former takes one of these, along with thecontradictory of the original conclusion. Also in the ostensive proof it is notnecessary that the conclusion should be known, nor that one should sup-pose beforehand that it is true or not: in the other it is necessary to supposebeforehand that it is not true. It makes no difference whether the conclu-sion is affirmative or negative; the method is the same in both cases. Ev-erything which is concluded ostensively can be proved per impossibile, andthat which is proved per impossibile can be proved ostensively, through the
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same terms. Whenever the syllogism is formed in the first figure, the truthwill be found in the middle or the last figure, if negative in the middle, if af-firmative in the last. Whenever the syllogism is formed in the middle figure,the truth will be found in the first, whatever the problem may be. Wheneverthe syllogism is formed in the last figure, the truth will be found in the firstand middle figures, if affirmative in first, if negative in the middle. Supposethat A has been proved to belong to no B, or not to all B, through the first fig-ure. Then the hypothesis must have been that A belongs to some B, and theoriginal premisses that C belongs to all A and to no B. For thus the syllogismwas made and the impossible conclusion reached. But this is the middle fig-ure, if C belongs to all A and to no B. And it is clear from these premissesthat A belongs to no B. Similarly if has been proved not to belong to all B. Forthe hypothesis is that A belongs to all B; and the original premisses are thatC belongs to all A but not to all B. Similarly too, if the premiss CA shouldbe negative: for thus also we have the middle figure. Again suppose it hasbeen proved that A belongs to some B. The hypothesis here is that is that Abelongs to no B; and the original premisses that B belongs to all C, and Aeither to all or to some C: for in this way we shall get what is impossible.But if A and B belong to all C, we have the last figure. And it is clear fromthese premisses that A must belong to some B. Similarly if B or A should beassumed to belong to some C.
Again suppose it has been proved in the middle figure that A belongs toall B. Then the hypothesis must have been that A belongs not to all B, andthe original premisses that A belongs to all C, and C to all B: for thus weshall get what is impossible. But if A belongs to all C, and C to all B, wehave the first figure. Similarly if it has been proved that A belongs to someB: for the hypothesis then must have been that A belongs to no B, and theoriginal premisses that A belongs to all C, and C to some B. If the syllogismis negative, the hypothesis must have been that A belongs to some B, andthe original premisses that A belongs to no C, and C to all B, so that the firstfigure results. If the syllogism is not universal, but proof has been given thatA does not belong to some B, we may infer in the same way. The hypothesisis that A belongs to all B, the original premisses that A belongs to no C, andC belongs to some B: for thus we get the first figure.
Again suppose it has been proved in the third figure that A belongs to allB. Then the hypothesis must have been that A belongs not to all B, and theoriginal premisses that C belongs to all B, and A belongs to all C; for thuswe shall get what is impossible. And the original premisses form the firstfigure. Similarly if the demonstration establishes a particular proposition:the hypothesis then must have been that A belongs to no B, and the origi-nal premisses that C belongs to some B, and A to all C. If the syllogism isnegative, the hypothesis must have been that A belongs to some B, and the
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original premisses that C belongs to no A and to all B, and this is the middlefigure. Similarly if the demonstration is not universal. The hypothesis willthen be that A belongs to all B, the premisses that C belongs to no A and tosome B: and this is the middle figure.
It is clear then that it is possible through the same terms to prove eachof the problems ostensively as well. Similarly it will be possible if the syllo-gisms are ostensive to reduce them ad impossibile in the terms which havebeen taken, whenever the contradictory of the conclusion of the ostensivesyllogism is taken as a premiss. For the syllogisms become identical withthose which are obtained by means of conversion, so that we obtain imme-diately the figures through which each problem will be solved. It is clearthen that every thesis can be proved in both ways, i.e. per impossibile andostensively, and it is not possible to separate one method from the other.
Part 14 Drawing a conclusion from opposed premisses
In what figure it is possible to draw a conclusion from premisses which areopposed, and in what figure this is not possible, will be made clear in thisway. Verbally four kinds of opposition are possible, viz. universal affirma-tive to universal negative, universal affirmative to particular negative, par-ticular affirmative to universal negative, and particular affirmative to partic-ular negative: but really there are only three: for the particular affirmative isonly verbally opposed to the particular negative. Of the genuine oppositesI call those which are universal contraries, the universal affirmative and theuniversal negative, e.g. ‘every science is good’, ‘no science is good’; the oth-ers I call contradictories.
In the first figure no syllogism whether affirmative or negative can bemade out of opposed premisses: no affirmative syllogism is possible becauseboth premisses must be affirmative, but opposites are, the one affirmative,the other negative: no negative syllogism is possible because opposites af-firm and deny the same predicate of the same subject, and the middle term inthe first figure is not predicated of both extremes, but one thing is denied ofit, and it is affirmed of something else: but such premisses are not opposed.
In the middle figure a syllogism can be made both oLcontradictories andof contraries. Let A stand for good, let B and C stand for science. If then oneassumes that every science is good, and no science is good, A belongs to all Band to no C, so that B belongs to no C: no science then is a science. Similarlyif after taking ‘every science is good’ one took ‘the science of medicine isnot good’; for A belongs to all B but to no C, so that a particular sciencewill not be a science. Again, a particular science will not be a science if Abelongs to all C but to no B, and B is science, C medicine, and A supposition:for after taking ‘no science is supposition’, one has assumed that a particular
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science is supposition. This syllogism differs from the preceding because therelations between the terms are reversed: before, the affirmative statementconcerned B, now it concerns C. Similarly if one premiss is not universal: forthe middle term is always that which is stated negatively of one extreme, andaffirmatively of the other. Consequently it is possible that contradictoriesmay lead to a conclusion, though not always or in every mood, but only ifthe terms subordinate to the middle are such that they are either identical orrelated as whole to part. Otherwise it is impossible: for the premisses cannotanyhow be either contraries or contradictories.
In the third figure an affirmative syllogism can never be made out ofopposite premisses, for the reason given in reference to the first figure; buta negative syllogism is possible whether the terms are universal or not. LetB and C stand for science, A for medicine. If then one should assume thatall medicine is science and that no medicine is science, he has assumed thatB belongs to all A and C to no A, so that a particular science will not bea science. Similarly if the premiss BA is not assumed universally. For ifsome medicine is science and again no medicine is science, it results thatsome science is not science, The premisses are contrary if the terms are takenuniversally; if one is particular, they are contradictory.
We must recognize that it is possible to take opposites in the way wesaid, viz. ‘all science is good’ and ‘no science is good’ or ‘some science isnot good’. This does not usually escape notice. But it is possible to establishone part of a contradiction through other premisses, or to assume it in theway suggested in the Topics. Since there are three oppositions to affirmativestatements, it follows that opposite statements may be assumed as premissesin six ways; we may have either universal affirmative and negative, or uni-versal affirmative and particular negative, or particular affirmative and uni-versal negative, and the relations between the terms may be reversed; e.g.A may belong to all B and to no C, or to all C and to no B, or to all of theone, not to all of the other; here too the relation between the terms may bereversed. Similarly in the third figure. So it is clear in how many ways andin what figures a syllogism can be made by means of premisses which areopposed.
It is clear too that from false premisses it is possible to draw a true con-clusion, as has been said before, but it is not possible if the premisses areopposed. For the syllogism is always contrary to the fact, e.g. if a thing isgood, it is proved that it is not good, if an animal, that it is not an animalbecause the syllogism springs out of a contradiction and the terms presup-posed are either identical or related as whole and part. It is evident also thatin fallacious reasonings nothing prevents a contradiction to the hypothesisfrom resulting, e.g. if something is odd, it is not odd. For the syllogismowed its contrariety to its contradictory premisses; if we assume such pre-
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misses we shall get a result that contradicts our hypothesis. But we mustrecognize that contraries cannot be inferred from a single syllogism in sucha way that we conclude that what is not good is good, or anything of thatsort unless a self-contradictory premiss is at once assumed, e.g. ‘every ani-mal is white and not white’, and we proceed ‘man is an animal’. Either wemust introduce the contradiction by an additional assumption, assuming,e.g., that every science is supposition, and then assuming ‘Medicine is a sci-ence, but none of it is supposition’ (which is the mode in which refutationsare made), or we must argue from two syllogisms. In no other way than this,as was said before, is it possible that the premisses should be really contrary.
Part 15 Begging the question
To beg and assume the original question is a species of failure to demonstratethe problem proposed; but this happens in many ways. A man may notreason syllogistically at all, or he may argue from premisses which are lessknown or equally unknown, or he may establish the antecedent by means ofits consequents; for demonstration proceeds from what is more certain and isprior. Now begging the question is none of these: but since we get to knowsome things naturally through themselves, and other things by means ofsomething else (the first principles through themselves, what is subordinateto them through something else), whenever a man tries to prove what isnot self-evident by means of itself, then he begs the original question. Thismay be done by assuming what is in question at once; it is also possible tomake a transition to other things which would naturally be proved throughthe thesis proposed, and demonstrate it through them, e.g. if A should beproved through B, and B through C, though it was natural that C should beproved through A: for it turns out that those who reason thus are proving Aby means of itself. This is what those persons do who suppose that they areconstructing parallel straight lines: for they fail to see that they are assumingfacts which it is impossible to demonstrate unless the parallels exist. So itturns out that those who reason thus merely say a particular thing is, if it is:in this way everything will be self-evident. But that is impossible.
If then it is uncertain whether A belongs to C, and also whether A be-longs to B, and if one should assume that A does belong to B, it is not yetclear whether he begs the original question, but it is evident that he is notdemonstrating: for what is as uncertain as the question to be answered can-not be a principle of a demonstration. If however B is so related to C thatthey are identical, or if they are plainly convertible, or the one belongs to theother, the original question is begged. For one might equally well prove thatA belongs to B through those terms if they are convertible. But if they are notconvertible, it is the fact that they are not that prevents such a demonstration,
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not the method of demonstrating. But if one were to make the conversion,then he would be doing what we have described and effecting a reciprocalproof with three propositions.
Similarly if he should assume that B belongs to C, this being as uncertainas the question whether A belongs to C, the question is not yet begged, butno demonstration is made. If however A and B are identical either becausethey are convertible or because A follows B, then the question is begged forthe same reason as before. For we have explained the meaning of beggingthe question, viz. proving that which is not self-evident by means of itself.
If then begging the question is proving what is not self-evident by meansof itself, in other words failing to prove when the failure is due to the the-sis to be proved and the premiss through which it is proved being equallyuncertain, either because predicates which are identical belong to the samesubject, or because the same predicate belongs to subjects which are iden-tical, the question may be begged in the middle and third figures in bothways, though, if the syllogism is affirmative, only in the third and first fig-ures. If the syllogism is negative, the question is begged when identicalpredicates are denied of the same subject; and both premisses do not beg thequestion indifferently (in a similar way the question may be begged in themiddle figure), because the terms in negative syllogisms are not convertible.In scientific demonstrations the question is begged when the terms are re-ally related in the manner described, in dialectical arguments when they areaccording to common opinion so related.
Part 16 Proof by reductio
The objection that ‘this is not the reason why the result is false’, which wefrequently make in argument, is made primarily in the case of a reductioad impossibile, to rebut the proposition which was being proved by the re-duction. For unless a man has contradicted this proposition he will not say,‘False cause’, but urge that something false has been assumed in the earlierparts of the argument; nor will he use the formula in the case of an ostensiveproof; for here what one denies is not assumed as a premiss. Further whenanything is refuted ostensively by the terms ABC, it cannot be objected thatthe syllogism does not depend on the assumption laid down. For we use theexpression ‘false cause’, when the syllogism is concluded in spite of the refu-tation of this position; but that is not possible in ostensive proofs: since if anassumption is refuted, a syllogism can no longer be drawn in reference to it.It is clear then that the expression ‘false cause’ can only be used in the case ofa reductio ad impossibile, and when the original hypothesis is so related tothe impossible conclusion, that the conclusion results indifferently whetherthe hypothesis is made or not. The most obvious case of the irrelevance of an
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assumption to a conclusion which is false is when a syllogism drawn frommiddle terms to an impossible conclusion is independent of the hypothesis,as we have explained in the Topics. For to put that which is not the causeas the cause, is just this: e.g. if a man, wishing to prove that the diagonal ofthe square is incommensurate with the side, should try to prove Zeno’s the-orem that motion is impossible, and so establish a reductio ad impossibile:for Zeno’s false theorem has no connexion at all with the original assump-tion. Another case is where the impossible conclusion is connected with thehypothesis, but does not result from it. This may happen whether one tracesthe connexion upwards or downwards, e.g. if it is laid down that A belongsto B, B to C, and C to D, and it should be false that B belongs to D: for ifwe eliminated A and assumed all the same that B belongs to C and C to D,the false conclusion would not depend on the original hypothesis. Or againtrace the connexion upwards; e.g. suppose that A belongs to B, E to A and Fto E, it being false that F belongs to A. In this way too the impossible conclu-sion would result, though the original hypothesis were eliminated. But theimpossible conclusion ought to be connected with the original terms: in thisway it will depend on the hypothesis, e.g. when one traces the connexiondownwards, the impossible conclusion must be connected with that termwhich is predicate in the hypothesis: for if it is impossible that A shouldbelong to D, the false conclusion will no longer result after A has been elimi-nated. If one traces the connexion upwards, the impossible conclusion mustbe connected with that term which is subject in the hypothesis: for if it is im-possible that F should belong to B, the impossible conclusion will disappearif B is eliminated. Similarly when the syllogisms are negative.
It is clear then that when the impossibility is not related to the originalterms, the false conclusion does not result on account of the assumption. Orperhaps even so it may sometimes be independent. For if it were laid downthat A belongs not to B but to K, and that K belongs to C and C to D, the im-possible conclusion would still stand. Similarly if one takes the terms in anascending series. Consequently since the impossibility results whether thefirst assumption is suppressed or not, it would appear to be independent ofthat assumption. Or perhaps we ought not to understand the statement thatthe false conclusion results independently of the assumption, in the sensethat if something else were supposed the impossibility would result; butrather we mean that when the first assumption is eliminated, the same im-possibility results through the remaining premisses; since it is not perhapsabsurd that the same false result should follow from several hypotheses, e.g.that parallels meet, both on the assumption that the interior angle is greaterthan the exterior and on the assumption that a triangle contains more thantwo right angles.
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Part 17 A false argument depends on its first false statement
A false argument depends on the first false statement in it. Every syllogismis made out of two or more premisses. If then the false conclusion is drawnfrom two premisses, one or both of them must be false: for (as we proved) afalse syllogism cannot be drawn from two premisses. But if the premisses aremore than two, e.g. if C is established through A and B, and these throughD, E, F, and G, one of these higher propositions must be false, and on thisthe argument depends: for A and B are inferred by means of D, E, F, and G.Therefore the conclusion and the error results from one of them.
Part 18 Do not allow the same term twice in premisses
In order to avoid having a syllogism drawn against us we must take care,whenever an opponent asks us to admit the reason without the conclusions,not to grant him the same term twice over in his premisses, since we knowthat a syllogism cannot be drawn without a middle term, and that termwhich is stated more than once is the middle. How we ought to watch themiddle in reference to each conclusion, is evident from our knowing whatkind of thesis is proved in each figure. This will not escape us since we knowhow we are maintaining the argument.
That which we urge men to beware of in their admissions, they oughtin attack to try to conceal. This will be possible first, if, instead of drawingthe conclusions of preliminary syllogisms, they take the necessary premissesand leave the conclusions in the dark; secondly if instead of inviting assentto propositions which are closely connected they take as far as possible thosethat are not connected by middle terms. For example suppose that A is to beinferred to be true of F, B, C, D, and E being middle terms. One ought thento ask whether A belongs to B, and next whether D belongs to E, instead ofasking whether B belongs to C; after that he may ask whether B belongs toC, and so on. If the syllogism is drawn through one middle term, he oughtto begin with that: in this way he will most likely deceive his opponent.
Part 19 When refutation will be possible and whenimpossible
Since we know when a syllogism can be formed and how its terms must berelated, it is clear when refutation will be possible and when impossible. Arefutation is possible whether everything is conceded, or the answers alter-nate (one, I mean, being affirmative, the other negative). For as has beenshown a syllogism is possible whether the terms are related in affirmativepropositions or one proposition is affirmative, the other negative: conse-
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quently, if what is laid down is contrary to the conclusion, a refutation musttake place: for a refutation is a syllogism which establishes the contradictory.But if nothing is conceded, a refutation is impossible: for no syllogism is pos-sible (as we saw) when all the terms are negative: therefore no refutation ispossible. For if a refutation were possible, a syllogism must be possible;although if a syllogism is possible it does not follow that a refutation is pos-sible. Similarly refutation is not possible if nothing is conceded universally:since the fields of refutation and syllogism are defined in the same way.
Part 20 Deception in the arrangement of the terms
It sometimes happens that just as we are deceived in the arrangement of theterms, so error may arise in our thought about them, e.g. if it is possible thatthe same predicate should belong to more than one subject immediately,but although knowing the one, a man may forget the other and think theopposite true. Suppose that A belongs to B and to C in virtue of their nature,and that B and C belong to all D in the same way. If then a man thinks that Abelongs to all B, and B to D, but A to no C, and C to all D, he will both knowand not know the same thing in respect of the same thing. Again if a manwere to make a mistake about the members of a single series; e.g. supposeA belongs to B, B to C, and C to D, but some one thinks that A belongs toall B, but to no C: he will both know that A belongs to D, and think that itdoes not. Does he then maintain after this simply that what he knows, hedoes not think? For he knows in a way that A belongs to C through B, sincethe part is included in the whole; so that what he knows in a way, this hemaintains he does not think at all: but that is impossible.
In the former case, where the middle term does not belong to the sameseries, it is not possible to think both the premisses with reference to each ofthe two middle terms: e.g. that A belongs to all B, but to no C, and both B andC belong to all D. For it turns out that the first premiss of the one syllogismis either wholly or partially contrary to the first premiss of the other. For ifhe thinks that A belongs to everything to which B belongs, and he knowsthat B belongs to D, then he knows that A belongs to D. Consequently ifagain he thinks that A belongs to nothing to which C belongs, he thinks thatA does not belong to some of that to which B belongs; but if he thinks thatA belongs to everything to which B belongs, and again thinks that A doesnot belong to some of that to which B belongs, these beliefs are wholly orpartially contrary. In this way then it is not possible to think; but nothingprevents a man thinking one premiss of each syllogism of both premisses ofone of the two syllogisms: e.g. A belongs to all B, and B to D, and againA belongs to no C. An error of this kind is similar to the error into whichwe fall concerning particulars: e.g. if A belongs to all B, and B to all C,
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A will belong to all C. If then a man knows that A belongs to everythingto which B belongs, he knows that A belongs to C. But nothing preventshis being ignorant that C exists; e.g. let A stand for two right angles, B fortriangle, C for a particular diagram of a triangle. A man might think that Cdid not exist, though he knew that every triangle contains two right angles;consequently he will know and not know the same thing at the same time.For the expression ‘to know that every triangle has its angles equal to tworight angles’ is ambiguous, meaning to have the knowledge either of theuniversal or of the particulars. Thus then he knows that C contains tworight angles with a knowledge of the universal, but not with a knowledgeof the particulars; consequently his knowledge will not be contrary to hisignorance. The argument in the Meno that learning is recollection may becriticized in a similar way. For it never happens that a man starts with aforeknowledge of the particular, but along with the process of being led tosee the general principle he receives a knowledge of the particulars, by an act(as it were) of recognition. For we know some things directly; e.g. that theangles are equal to two right angles, if we know that the figure is a triangle.Similarly in all other cases.
By a knowledge of the universal then we see the particulars, but we donot know them by the kind of knowledge which is proper to them; conse-quently it is possible that we may make mistakes about them, but not thatwe should have the knowledge and error that are contrary to one another:rather we have the knowledge of the universal but make a mistake in appre-hending the particular. Similarly in the cases stated above. The error in re-spect of the middle term is not contrary to the knowledge obtained throughthe syllogism, nor is the thought in respect of one middle term contrary tothat in respect of the other. Nothing prevents a man who knows both thatA belongs to the whole of B, and that B again belongs to C, thinking that Adoes not belong to C, e.g. knowing that every mule is sterile and that thisis a mule, and thinking that this animal is with foal: for he does not knowthat A belongs to C, unless he considers the two propositions together. So itis evident that if he knows the one and does not know the other, he will fallinto error. And this is the relation of knowledge of the universal to knowl-edge of the particular. For we know no sensible thing, once it has passedbeyond the range of our senses, even if we happen to have perceived it, ex-cept by means of the universal and the possession of the knowledge whichis proper to the particular, but without the actual exercise of that knowledge.For to know is used in three senses: it may mean either to have knowledgeof the universal or to have knowledge proper to the matter in hand or toexercise such knowledge: consequently three kinds of error also are possi-ble. Nothing then prevents a man both knowing and being mistaken aboutthe same thing, provided that his knowledge and his error are not contrary.
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And this happens also to the man whose knowledge is limited to each of thepremisses and who has not previously considered the particular question.For when he thinks that the mule is with foal he has not the knowledge inthe sense of its actual exercise, nor on the other hand has his thought causedan error contrary to his knowledge: for the error contrary to the knowledgeof the universal would be a syllogism.
But he who thinks the essence of good is the essence of bad will think thesame thing to be the essence of good and the essence of bad. Let A standfor the essence of good and B for the essence of bad, and again C for theessence of good. Since then he thinks B and C identical, he will think that Cis B, and similarly that B is A, consequently that C is A. For just as we sawthat if B is true of all of which C is true, and A is true of all of which B istrue, A is true of C, similarly with the word ‘think’. Similarly also with theword ‘is’; for we saw that if C is the same as B, and B as A, C is the same asA. Similarly therefore with ‘opine’. Perhaps then this is necessary if a manwill grant the first point. But presumably that is false, that any one couldsuppose the essence of good to be the essence of bad, save incidentally. Forit is possible to think this in many different ways. But we must consider thismatter better.
Part 21 Whenever the extremes are convertible
Whenever the extremes are convertible it is necessary that the middle shouldbe convertible with both. For if A belongs to C through B, then if A and Care convertible and C belongs everything to which A belongs, B is convert-ible with A, and B belongs to everything to which A belongs, through C asmiddle, and C is convertible with B through A as middle. Similarly if theconclusion is negative, e.g. if B belongs to C, but A does not belong to B, nei-ther will A belong to C. If then B is convertible with A, C will be convertiblewith A. Suppose B does not belong to A; neither then will C: for ex hypothesiB belonged to all C. And if C is convertible with B, B is convertible also withA, for C is said of that of all of which B is said. And if C is convertible in rela-tion to A and to B, B also is convertible in relation to A. For C belongs to thatto which B belongs: but C does not belong to that to which A belongs. Andthis alone starts from the conclusion; the preceding moods do not do so as inthe affirmative syllogism. Again if A and B are convertible, and similarly Cand D, and if A or C must belong to anything whatever, then B and D will besuch that one or other belongs to anything whatever. For since B belongs tothat to which A belongs, and D belongs to that to which C belongs, and sinceA or C belongs to everything, but not together, it is clear that B or D belongsto everything, but not together. For example if that which is uncreated is in-corruptible and that which is incorruptible is uncreated, it is necessary that
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what is created should be corruptible and what is corruptible should havebeen created. For two syllogisms have been put together. Again if A or Bbelongs to everything and if C or D belongs to everything, but they cannotbelong together, then when A and C are convertible B and D are convertible.For if B does not belong to something to which D belongs, it is clear that Abelongs to it. But if A then C: for they are convertible. Therefore C and Dbelong together. But this is impossible. When A belongs to the whole of Band to C and is affirmed of nothing else, and B also belongs to all C, it isnecessary that A and B should be convertible: for since A is said of B and Conly, and B is affirmed both of itself and of C, it is clear that B will be said ofeverything of which A is said, except A itself. Again when A and B belongto the whole of C, and C is convertible with B, it is necessary that A shouldbelong to all B: for since A belongs to all C, and C to B by conversion, A willbelong to all B.
When, of two opposites A and B, A is preferable to B, and similarly D ispreferable to C, then if A and C together are preferable to B and D together,A must be preferable to D. For A is an object of desire to the same extent asB is an object of aversion, since they are opposites: and C is similarly relatedto D, since they also are opposites. If then A is an object of desire to thesame extent as D, B is an object of aversion to the same extent as C (sinceeach is to the same extent as each - the one an object of aversion, the otheran object of desire). Therefore both A and C together, and B and D together,will be equally objects of desire or aversion. But since A and C are preferableto B and D, A cannot be equally desirable with D; for then B along with Dwould be equally desirable with A along with C. But if D is preferable toA, then B must be less an object of aversion than C: for the less is opposedto the less. But the greater good and lesser evil are preferable to the lessergood and greater evil: the whole BD then is preferable to the whole AC. Butex hypothesi this is not so. A then is preferable to D, and C consequentlyis less an object of aversion than B. If then every lover in virtue of his lovewould prefer A, viz. that the beloved should be such as to grant a favour,and yet should not grant it (for which C stands), to the beloved’s grantingthe favour (represented by D) without being such as to grant it (representedby B), it is clear that A (being of such a nature) is preferable to granting thefavour. To receive affection then is preferable in love to sexual intercourse.Love then is more dependent on friendship than on intercourse. And if it ismost dependent on receiving affection, then this is its end. Intercourse theneither is not an end at all or is an end relative to the further end, the receivingof affection. And indeed the same is true of the other desires and arts.
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Part 22 Rhetorical syllogism and induction
It is clear then how the terms are related in conversion, and in respect ofbeing in a higher degree objects of aversion or of desire. We must now statethat not only dialectical and demonstrative syllogisms are formed by meansof the aforesaid figures, but also rhetorical syllogisms and in general anyform of persuasion, however it may be presented. For every belief comeseither through syllogism or from induction.
Now induction, or rather the syllogism which springs out of induction,consists in establishing syllogistically a relation between one extreme andthe middle by means of the other extreme, e.g. if B is the middle term be-tween A and C, it consists in proving through C that A belongs to B. Forthis is the manner in which we make inductions. For example let A standfor long-lived, B for bileless, and C for the particular long-lived animals, e.g.man, horse, mule. A then belongs to the whole of C: for whatever is bilelessis long-lived. But B also (‘not possessing bile’) belongs to all C. If then C isconvertible with B, and the middle term is not wider in extension, it is nec-essary that A should belong to B. For it has already been proved that if twothings belong to the same thing, and the extreme is convertible with one ofthem, then the other predicate will belong to the predicate that is converted.But we must apprehend C as made up of all the particulars. For inductionproceeds through an enumeration of all the cases.
Such is the syllogism which establishes the first and immediate premiss:for where there is a middle term the syllogism proceeds through the middleterm; when there is no middle term, through induction. And in a way induc-tion is opposed to syllogism: for the latter proves the major term to belongto the third term by means of the middle, the former proves the major tobelong to the middle by means of the third. In the order of nature, syllogismthrough the middle term is prior and better known, but syllogism throughinduction is clearer to us.
Part 23 When the major term belongs to the middle
We have an ‘example’ when the major term is proved to belong to the mid-dle by means of a term which resembles the third. It ought to be knownboth that the middle belongs to the third term, and that the first belongs tothat which resembles the third. For example let A be evil, B making waragainst neighbours, C Athenians against Thebans, D Thebans against Pho-cians. If then we wish to prove that to fight with the Thebans is an evil, wemust assume that to fight against neighbours is an evil. Evidence of this isobtained from similar cases, e.g. that the war against the Phocians was anevil to the Thebans. Since then to fight against neighbours is an evil, and
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to fight against the Thebans is to fight against neighbours, it is clear that tofight against the Thebans is an evil. Now it is clear that B belongs to C andto D (for both are cases of making war upon one’s neighbours) and that Abelongs to D (for the war against the Phocians did not turn out well for theThebans): but that A belongs to B will be proved through D. Similarly if thebelief in the relation of the middle term to the extreme should be producedby several similar cases. Clearly then to argue by example is neither likereasoning from part to whole, nor like reasoning from whole to part, butrather reasoning from part to part, when both particulars are subordinate tothe same term, and one of them is known. It differs from induction, becauseinduction starting from all the particular cases proves (as we saw) that themajor term belongs to the middle, and does not apply the syllogistic con-clusion to the minor term, whereas argument by example does make thisapplication and does not draw its proof from all the particular cases.
Part 24 Reduction
By reduction we mean an argument in which the first term clearly belongsto the middle, but the relation of the middle to the last term is uncertainthough equally or more probable than the conclusion; or again an argumentin which the terms intermediate between the last term and the middle arefew. For in any of these cases it turns out that we approach more nearly toknowledge. For example let A stand for what can be taught, B for knowl-edge, C for justice. Now it is clear that knowledge can be taught: but it isuncertain whether virtue is knowledge. If now the statement BC is equallyor more probable than AC, we have a reduction: for we are nearer to knowl-edge, since we have taken a new term, being so far without knowledge thatA belongs to C. Or again suppose that the terms intermediate between B andC are few: for thus too we are nearer knowledge. For example let D stand forsquaring, E for rectilinear figure, F for circle. If there were only one term in-termediate between E and F (viz. that the circle is made equal to a rectilinearfigure by the help of lunules), we should be near to knowledge. But whenBC is not more probable than AC, and the intermediate terms are not few, Ido not call this reduction: nor again when the statement BC is immediate:for such a statement is knowledge.
Part 25 Objection
An objection is a premiss contrary to a premiss. It differs from a premiss,because it may be particular, but a premiss either cannot be particular at allor not in universal syllogisms. An objection is brought in two ways andthrough two figures; in two ways because every objection is either universal
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or particular, by two figures because objections are brought in opposition tothe premiss, and opposites can be proved only in the first and third figures.If a man maintains a universal affirmative, we reply with a universal or aparticular negative; the former is proved from the first figure, the latter fromthe third. For example let stand for there being a single science, B for con-traries. If a man premises that contraries are subjects of a single science, theobjection may be either that opposites are never subjects of a single science,and contraries are opposites, so that we get the first figure, or that the know-able and the unknowable are not subjects of a single science: this proof is inthe third figure: for it is true of C (the knowable and the unknowable) thatthey are contraries, and it is false that they are the subjects of a single science.
Similarly if the premiss objected to is negative. For if a man maintainsthat contraries are not subjects of a single science, we reply either that allopposites or that certain contraries, e.g. what is healthy and what is sickly,are subjects of the same science: the former argument issues from the first,the latter from the third figure.
In general if a man urges a universal objection he must frame his contra-diction with reference to the universal of the terms taken by his opponent,e.g. if a man maintains that contraries are not subjects of the same science,his opponent must reply that there is a single science of all opposites. Thuswe must have the first figure: for the term which embraces the original sub-ject becomes the middle term.
If the objection is particular, the objector must frame his contradictionwith reference to a term relatively to which the subject of his opponent’s pre-miss is universal, e.g. he will point out that the knowable and the unknow-able are not subjects of the same science: ‘contraries’ is universal relativelyto these. And we have the third figure: for the particular term assumed ismiddle, e.g. the knowable and the unknowable. Premisses from which it ispossible to draw the contrary conclusion are what we start from when we tryto make objections. Consequently we bring objections in these figures only:for in them only are opposite syllogisms possible, since the second figurecannot produce an affirmative conclusion.
Besides, an objection in the middle figure would require a fuller argu-ment, e.g. if it should not be granted that A belongs to B, because C does notfollow B. This can be made clear only by other premisses. But an objectionought not to turn off into other things, but have its new premiss quite clearimmediately. For this reason also this is the only figure from which proof bysigns cannot be obtained.
We must consider later the other kinds of objection, namely the objec-tion from contraries, from similars, and from common opinion, and inquirewhether a particular objection cannot be elicited from the first figure or anegative objection from the second.
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Part 26 Probability
A probability and a sign are not identical, but a probability is a generallyapproved proposition: what men know to happen or not to happen, to be ornot to be, for the most part thus and thus, is a probability, e.g. ‘the envioushate’, ‘the beloved show affection’. A sign means a demonstrative propo-sition necessary or generally approved: for anything such that when it isanother thing is, or when it has come into being the other has come into be-ing before or after, is a sign of the other’s being or having come into being.Now an enthymeme is a syllogism starting from probabilities or signs, and asign may be taken in three ways, corresponding to the position of the middleterm in the figures. For it may be taken as in the first figure or the second orthe third. For example the proof that a woman is with child because she hasmilk is in the first figure: for to have milk is the middle term. Let A repre-sent to be with child, B to have milk, C woman. The proof that wise men aregood, since Pittacus is good, comes through the last figure. Let A stand forgood, B for wise men, C for Pittacus. It is true then to affirm both A and B ofC: only men do not say the latter, because they know it, though they state theformer. The proof that a woman is with child because she is pale is meantto come through the middle figure: for since paleness follows women withchild and is a concomitant of this woman, people suppose it has been provedthat she is with child. Let A stand for paleness, B for being with child, C forwoman. Now if the one proposition is stated, we have only a sign, but ifthe other is stated as well, a syllogism, e.g. ‘Pittacus is generous, since ambi-tious men are generous and Pittacus is ambitious.’ Or again ‘Wise men aregood, since Pittacus is not only good but wise.’ In this way then syllogismsare formed, only that which proceeds through the first figure is irrefutable ifit is true (for it is universal), that which proceeds through the last figure isrefutable even if the conclusion is true, since the syllogism is not universalnor correlative to the matter in question: for though Pittacus is good, it isnot therefore necessary that all other wise men should be good. But the syl-logism which proceeds through the middle figure is always refutable in anycase: for a syllogism can never be formed when the terms are related in thisway: for though a woman with child is pale, and this woman also is pale, itis not necessary that she should be with child. Truth then may be found insigns whatever their kind, but they have the differences we have stated.
We must either divide signs in the way stated, and among them desig-nate the middle term as the index (for people call that the index which makesus know, and the middle term above all has this character), or else we mustcall the arguments derived from the extremes signs, that derived from themiddle term the index: for that which is proved through the first figure ismost generally accepted and most true.
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It is possible to infer character from features, if it is granted that the bodyand the soul are changed together by the natural affections: I say ‘natural’,for though perhaps by learning music a man has made some change in hissoul, this is not one of those affections which are natural to us; rather I referto passions and desires when I speak of natural emotions. If then this weregranted and also that for each change there is a corresponding sign, and wecould state the affection and sign proper to each kind of animal, we shallbe able to infer character from features. For if there is an affection whichbelongs properly to an individual kind, e.g. courage to lions, it is necessarythat there should be a sign of it: for ex hypothesi body and soul are affectedtogether. Suppose this sign is the possession of large extremities: this maybelong to other kinds also though not universally. For the sign is proper inthe sense stated, because the affection is proper to the whole kind, thoughnot proper to it alone, according to our usual manner of speaking. The samething then will be found in another kind, and man may be brave, and someother kinds of animal as well. They will then have the sign: for ex hypothesithere is one sign corresponding to each affection. If then this is so, and wecan collect signs of this sort in these animals which have only one affectionproper to them - but each affection has its sign, since it is necessary thatit should have a single sign - we shall then be able to infer character fromfeatures. But if the kind as a whole has two properties, e.g. if the lion isboth brave and generous, how shall we know which of the signs which areits proper concomitants is the sign of a particular affection? Perhaps if bothbelong to some other kind though not to the whole of it, and if, in thosekinds in which each is found though not in the whole of their members,some members possess one of the affections and not the other: e.g. if a manis brave but not generous, but possesses, of the two signs, large extremities, itis clear that this is the sign of courage in the lion also. To judge character fromfeatures, then, is possible in the first figure if the middle term is convertiblewith the first extreme, but is wider than the third term and not convertiblewith it: e.g. let A stand for courage, B for large extremities, and C for lion.B then belongs to everything to which C belongs, but also to others. ButA belongs to everything to which B belongs, and to nothing besides, but isconvertible with B: otherwise, there would not be a single sign correlativewith each affection.
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Volume 4 POSTERIOR ANALYTICS
Book I Posterior Analytics
Part 1 Proceeding from pre-existent knowledge
All instruction given or received by way of argument proceeds from pre-existent knowledge. This becomes evident upon a survey of all the speciesof such instruction. The mathematical sciences and all other speculative dis-ciplines are acquired in this way, and so are the two forms of dialecticalreasoning, syllogistic and inductive; for each of these latter make use of oldknowledge to impart new, the syllogism assuming an audience that acceptsits premisses, induction exhibiting the universal as implicit in the clearlyknown particular. Again, the persuasion exerted by rhetorical arguments isin principle the same, since they use either example, a kind of induction, orenthymeme, a form of syllogism.
The pre-existent knowledge required is of two kinds. In some cases ad-mission of the fact must be assumed, in others comprehension of the mean-ing of the term used, and sometimes both assumptions are essential. Thus,we assume that every predicate can be either truly affirmed or truly deniedof any subject, and that ‘triangle’ means so and so; as regards ‘unit’ we haveto make the double assumption of the meaning of the word and the exis-tence of the thing. The reason is that these several objects are not equally ob-vious to us. Recognition of a truth may in some cases contain as factors bothprevious knowledge and also knowledge acquired simultaneously with thatrecognition - knowledge, this latter, of the particulars actually falling underthe universal and therein already virtually known. For example, the studentknew beforehand that the angles of every triangle are equal to two right an-gles; but it was only at the actual moment at which he was being led on torecognize this as true in the instance before him that he came to know ‘thisfigure inscribed in the semicircle’ to be a triangle. For some things (viz. thesingulars finally reached which are not predicable of anything else as sub-ject) are only learnt in this way, i.e. there is here no recognition through a
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middle of a minor term as subject to a major. Before he was led on to recog-nition or before he actually drew a conclusion, we should perhaps say thatin a manner he knew, in a manner not.
If he did not in an unqualified sense of the term know the existence ofthis triangle, how could he know without qualification that its angles wereequal to two right angles? No: clearly he knows not without qualificationbut only in the sense that he knows universally. If this distinction is notdrawn, we are faced with the dilemma in the Meno: either a man will learnnothing or what he already knows; for we cannot accept the solution whichsome people offer. A man is asked, ‘Do you, or do you not, know that everypair is even?’ He says he does know it. The questioner then produces aparticular pair, of the existence, and so a fortiori of the evenness, of whichhe was unaware. The solution which some people offer is to assert that theydo not know that every pair is even, but only that everything which theyknow to be a pair is even: yet what they know to be even is that of whichthey have demonstrated evenness, i.e. what they made the subject of theirpremiss, viz. not merely every triangle or number which they know to besuch, but any and every number or triangle without reservation. For nopremiss is ever couched in the form ‘every number which you know to besuch’, or ‘every rectilinear figure which you know to be such’: the predicateis always construed as applicable to any and every instance of the thing. Onthe other hand, I imagine there is nothing to prevent a man in one senseknowing what he is learning, in another not knowing it. The strange thingwould be, not if in some sense he knew what he was learning, but if he wereto know it in that precise sense and manner in which he was learning it.
Part 2 Unqualified scientific knowledge
We suppose ourselves to possess unqualified scientific knowledge of a thing,as opposed to knowing it in the accidental way in which the sophist knows,when we think that we know the cause on which the fact depends, as thecause of that fact and of no other, and, further, that the fact could not beother than it is. Now that scientific knowing is something of this sort isevident - witness both those who falsely claim it and those who actuallypossess it, since the former merely imagine themselves to be, while the latterare also actually, in the condition described. Consequently the proper objectof unqualified scientific knowledge is something which cannot be other thanit is.
There may be another manner of knowing as well - that will be discussedlater. What I now assert is that at all events we do know by demonstration.By demonstration I mean a syllogism productive of scientific knowledge, asyllogism, that is, the grasp of which is eo ipso such knowledge. Assuming
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then that my thesis as to the nature of scientific knowing is correct, the pre-misses of demonstrated knowledge must be true, primary, immediate, betterknown than and prior to the conclusion, which is further related to them aseffect to cause. Unless these conditions are satisfied, the basic truths willnot be ‘appropriate’ to the conclusion. Syllogism there may indeed be with-out these conditions, but such syllogism, not being productive of scientificknowledge, will not be demonstration. The premisses must be true: for thatwhich is non-existent cannot be known - we cannot know, e.g. that the diag-onal of a square is commensurate with its side. The premisses must be pri-mary and indemonstrable; otherwise they will require demonstration in or-der to be known, since to have knowledge, if it be not accidental knowledge,of things which are demonstrable, means precisely to have a demonstrationof them. The premisses must be the causes of the conclusion, better knownthan it, and prior to it; its causes, since we possess scientific knowledge of athing only when we know its cause; prior, in order to be causes; antecedentlyknown, this antecedent knowledge being not our mere understanding of themeaning, but knowledge of the fact as well. Now ‘prior’ and ‘better known’are ambiguous terms, for there is a difference between what is prior andbetter known in the order of being and what is prior and better known toman. I mean that objects nearer to sense are prior and better known to man;objects without qualification prior and better known are those further fromsense. Now the most universal causes are furthest from sense and partic-ular causes are nearest to sense, and they are thus exactly opposed to oneanother. In saying that the premisses of demonstrated knowledge must beprimary, I mean that they must be the ‘appropriate’ basic truths, for I iden-tify primary premiss and basic truth. A ‘basic truth’ in a demonstration isan immediate proposition. An immediate proposition is one which has noother proposition prior to it. A proposition is either part of an enunciation,i.e. it predicates a single attribute of a single subject. If a proposition is di-alectical, it assumes either part indifferently; if it is demonstrative, it laysdown one part to the definite exclusion of the other because that part is true.The term ‘enunciation’ denotes either part of a contradiction indifferently. Acontradiction is an opposition which of its own nature excludes a middle.The part of a contradiction which conjoins a predicate with a subject is anaffirmation; the part disjoining them is a negation. I call an immediate basictruth of syllogism a ‘thesis’ when, though it is not susceptible of proof bythe teacher, yet ignorance of it does not constitute a total bar to progress onthe part of the pupil: one which the pupil must know if he is to learn any-thing whatever is an axiom. I call it an axiom because there are such truthsand we give them the name of axioms par excellence. If a thesis assumesone part or the other of an enunciation, i.e. asserts either the existence orthe non-existence of a subject, it is a hypothesis; if it does not so assert, it is
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a definition. Definition is a ‘thesis’ or a ‘laying something down’, since thearithmetician lays it down that to be a unit is to be quantitatively indivisible;but it is not a hypothesis, for to define what a unit is is not the same as toaffirm its existence.
Now since the required ground of our knowledge - i.e. of our conviction- of a fact is the possession of such a syllogism as we call demonstration, andthe ground of the syllogism is the facts constituting its premisses, we mustnot only know the primary premisses - some if not all of them - beforehand,but know them better than the conclusion: for the cause of an attribute’s in-herence in a subject always itself inheres in the subject more firmly than thatattribute; e.g. the cause of our loving anything is dearer to us than the objectof our love. So since the primary premisses are the cause of our knowledge- i.e. of our conviction - it follows that we know them better - that is, aremore convinced of them - than their consequences, precisely because of ourknowledge of the latter is the effect of our knowledge of the premisses. Nowa man cannot believe in anything more than in the things he knows, unlesshe has either actual knowledge of it or something better than actual knowl-edge. But we are faced with this paradox if a student whose belief rests ondemonstration has not prior knowledge; a man must believe in some, if notin all, of the basic truths more than in the conclusion. Moreover, if a man setsout to acquire the scientific knowledge that comes through demonstration,he must not only have a better knowledge of the basic truths and a firmerconviction of them than of the connexion which is being demonstrated: morethan this, nothing must be more certain or better known to him than thesebasic truths in their character as contradicting the fundamental premisseswhich lead to the opposed and erroneous conclusion. For indeed the con-viction of pure science must be unshakable.
Part 3 Terminating regress in indemonstrable premisses
Some hold that, owing to the necessity of knowing the primary premisses,there is no scientific knowledge. Others think there is, but that all truths aredemonstrable. Neither doctrine is either true or a necessary deduction fromthe premisses. The first school, assuming that there is no way of knowingother than by demonstration, maintain that an infinite regress is involved, onthe ground that if behind the prior stands no primary, we could not knowthe posterior through the prior (wherein they are right, for one cannot tra-verse an infinite series): if on the other hand - they say - the series terminatesand there are primary premisses, yet these are unknowable because inca-pable of demonstration, which according to them is the only form of knowl-edge. And since thus one cannot know the primary premisses, knowledge ofthe conclusions which follow from them is not pure scientific knowledge nor
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properly knowing at all, but rests on the mere supposition that the premissesare true. The other party agree with them as regards knowing, holding thatit is only possible by demonstration, but they see no difficulty in holdingthat all truths are demonstrated, on the ground that demonstration may becircular and reciprocal.
Our own doctrine is that not all knowledge is demonstrative: on the con-trary, knowledge of the immediate premisses is independent of demonstra-tion. (The necessity of this is obvious; for since we must know the prior pre-misses from which the demonstration is drawn, and since the regress mustend in immediate truths, those truths must be indemonstrable.) Such, then,is our doctrine, and in addition we maintain that besides scientific knowl-edge there is its originative source which enables us to recognize the defini-tions.
Now demonstration must be based on premisses prior to and betterknown than the conclusion; and the same things cannot simultaneously beboth prior and posterior to one another: so circular demonstration is clearlynot possible in the unqualified sense of ‘demonstration’, but only possibleif ‘demonstration’ be extended to include that other method of argumentwhich rests on a distinction between truths prior to us and truths withoutqualification prior, i.e. the method by which induction produces knowl-edge. But if we accept this extension of its meaning, our definition of un-qualified knowledge will prove faulty; for there seem to be two kinds of it.Perhaps, however, the second form of demonstration, that which proceedsfrom truths better known to us, is not demonstration in the unqualified senseof the term.
The advocates of circular demonstration are not only faced with the diffi-culty we have just stated: in addition their theory reduces to the mere state-ment that if a thing exists, then it does exist - an easy way of proving any-thing. That this is so can be clearly shown by taking three terms, for toconstitute the circle it makes no difference whether many terms or few oreven only two are taken. Thus by direct proof, if A is, B must be; if B is, Cmust be; therefore if A is, C must be. Since then - by the circular proof - if Ais, B must be, and if B is, A must be, A may be substituted for C above. Then‘if B is, A must be’=‘if B is, C must be’, which above gave the conclusion ‘ifA is, C must be’: but C and A have been identified. Consequently the up-holders of circular demonstration are in the position of saying that if A is, Amust be - a simple way of proving anything. Moreover, even such circulardemonstration is impossible except in the case of attributes that imply oneanother, viz. ‘peculiar’ properties.
Now, it has been shown that the positing of one thing - be it one termor one premiss - never involves a necessary consequent: two premisses con-stitute the first and smallest foundation for drawing a conclusion at all and
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therefore a fortiori for the demonstrative syllogism of science. If, then, A isimplied in B and C, and B and C are reciprocally implied in one another andin A, it is possible, as has been shown in my writings on the syllogism, toprove all the assumptions on which the original conclusion rested, by circu-lar demonstration in the first figure. But it has also been shown that in theother figures either no conclusion is possible, or at least none which provesboth the original premisses. Propositions the terms of which are not con-vertible cannot be circularly demonstrated at all, and since convertible termsoccur rarely in actual demonstrations, it is clearly frivolous and impossibleto say that demonstration is reciprocal and that therefore everything can bedemonstrated.
Part 4 Scientific knowledge must rest on essentialpremisses
Since the object of pure scientific knowledge cannot be other than it is, thetruth obtained by demonstrative knowledge will be necessary. And sincedemonstrative knowledge is only present when we have a demonstration, itfollows that demonstration is an inference from necessary premisses. So wemust consider what are the premisses of demonstration - i.e. what is theircharacter: and as a preliminary, let us define what we mean by an attribute‘true in every instance of its subject’, an ‘essential’ attribute, and a ‘commen-surate and universal’ attribute. I call ‘true in every instance’ what is trulypredicable of all instances - not of one to the exclusion of others - and at alltimes, not at this or that time only; e.g. if animal is truly predicable of everyinstance of man, then if it be true to say ‘this is a man’, ‘this is an animal’ isalso true, and if the one be true now the other is true now. A correspondingaccount holds if point is in every instance predicable as contained in line.There is evidence for this in the fact that the objection we raise against aproposition put to us as true in every instance is either an instance in which,or an occasion on which, it is not true. Essential attributes are (1) such asbelong to their subject as elements in its essential nature (e.g. line thus be-longs to triangle, point to line; for the very being or ‘substance’ of triangleand line is composed of these elements, which are contained in the formulaedefining triangle and line): (2) such that, while they belong to certain sub-jects, the subjects to which they belong are contained in the attribute’s owndefining formula. Thus straight and curved belong to line, odd and even,prime and compound, square and oblong, to number; and also the formuladefining any one of these attributes contains its subject - e.g. line or numberas the case may be.
Extending this classification to all other attributes, I distinguish thosethat answer the above description as belonging essentially to their respec-
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tive subjects; whereas attributes related in neither of these two ways to theirsubjects I call accidents or ‘coincidents’; e.g. musical or white is a ‘coinci-dent’ of animal.
Further (a) that is essential which is not predicated of a subject otherthan itself: e.g. ‘the walking [thing]’ walks and is white in virtue of beingsomething else besides; whereas substance, in the sense of whatever signifiesa ‘this somewhat’, is not what it is in virtue of being something else besides.Things, then, not predicated of a subject I call essential; things predicated ofa subject I call accidental or ‘coincidental’.
In another sense again (b) a thing consequentially connected with any-thing is essential; one not so connected is ‘coincidental’. An example of thelatter is ‘While he was walking it lightened’: the lightning was not due to hiswalking; it was, we should say, a coincidence. If, on the other hand, thereis a consequential connexion, the predication is essential; e.g. if a beast dieswhen its throat is being cut, then its death is also essentially connected withthe cutting, because the cutting was the cause of death, not death a ‘coinci-dent’ of the cutting.
So far then as concerns the sphere of connexions scientifically known inthe unqualified sense of that term, all attributes which (within that sphere)are essential either in the sense that their subjects are contained in them, orin the sense that they are contained in their subjects, are necessary as wellas consequentially connected with their subjects. For it is impossible forthem not to inhere in their subjects either simply or in the qualified sensethat one or other of a pair of opposites must inhere in the subject; e.g. inline must be either straightness or curvature, in number either oddness orevenness. For within a single identical genus the contrary of a given attributeis either its privative or its contradictory; e.g. within number what is not oddis even, inasmuch as within this sphere even is a necessary consequent of not- odd. So, since any given predicate must be either affirmed or denied of anysubject, essential attributes must inhere in their subjects of necessity.
Thus, then, we have established the distinction between the attributewhich is ‘true in every instance’ and the ‘essential’ attribute.
I term ‘commensurately universal’ an attribute which belongs to everyinstance of its subject, and to every instance essentially and as such; fromwhich it clearly follows that all commensurate universals inhere necessarilyin their subjects. The essential attribute, and the attribute that belongs toits subject as such, are identical. E.g. point and straight belong to line es-sentially, for they belong to line as such; and triangle as such has two rightangles, for it is essentially equal to two right angles.
An attribute belongs commensurately and universally to a subject whenit can be shown to belong to any random instance of that subject and whenthe subject is the first thing to which it can be shown to belong. Thus, e.g.
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(1) the equality of its angles to two right angles is not a commensurately uni-versal attribute of figure. For though it is possible to show that a figure hasits angles equal to two right angles, this attribute cannot be demonstratedof any figure selected at haphazard, nor in demonstrating does one take afigure at random - a square is a figure but its angles are not equal to tworight angles. On the other hand, any isosceles triangle has its angles equalto two right angles, yet isosceles triangle is not the primary subject of thisattribute but triangle is prior. So whatever can be shown to have its anglesequal to two right angles, or to possess any other attribute, in any random in-stance of itself and primarily - that is the first subject to which the predicatein question belongs commensurately and universally, and the demonstra-tion, in the essential sense, of any predicate is the proof of it as belongingto this first subject commensurately and universally: while the proof of itas belonging to the other subjects to which it attaches is demonstration onlyin a secondary and unessential sense. Nor again (2) is equality to two rightangles a commensurately universal attribute of isosceles; it is of wider ap-plication.
Part 5 Failure of commensurate universality
We must not fail to observe that we often fall into error because our con-clusion is not in fact primary and commensurately universal in the sense inwhich we think we prove it so. We make this mistake (1) when the subject isan individual or individuals above which there is no universal to be found:(2) when the subjects belong to different species and there is a higher univer-sal, but it has no name: (3) when the subject which the demonstrator takesas a whole is really only a part of a larger whole; for then the demonstra-tion will be true of the individual instances within the part and will holdin every instance of it, yet the demonstration will not be true of this subjectprimarily and commensurately and universally. When a demonstration istrue of a subject primarily and commensurately and universally, that is to betaken to mean that it is true of a given subject primarily and as such. Case(3) may be thus exemplified. If a proof were given that perpendiculars to thesame line are parallel, it might be supposed that lines thus perpendicularwere the proper subject of the demonstration because being parallel is trueof every instance of them. But it is not so, for the parallelism depends noton these angles being equal to one another because each is a right angle, butsimply on their being equal to one another. An example of (1) would be asfollows: if isosceles were the only triangle, it would be thought to have itsangles equal to two right angles qua isosceles. An instance of (2) would bethe law that proportionals alternate. Alternation used to be demonstratedseparately of numbers, lines, solids, and durations, though it could have
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been proved of them all by a single demonstration. Because there was nosingle name to denote that in which numbers, lengths, durations, and solidsare identical, and because they differed specifically from one another, thisproperty was proved of each of them separately. To-day, however, the proofis commensurately universal, for they do not possess this attribute qua linesor qua numbers, but qua manifesting this generic character which they arepostulated as possessing universally. Hence, even if one prove of each kindof triangle that its angles are equal to two right angles, whether by meansof the same or different proofs; still, as long as one treats separately equi-lateral, scalene, and isosceles, one does not yet know, except sophistically,that triangle has its angles equal to two right angles, nor does one yet knowthat triangle has this property commensurately and universally, even if thereis no other species of triangle but these. For one does not know that trian-gle as such has this property, nor even that ‘all’ triangles have it - unless ‘all’means ‘each taken singly’: if ‘all’ means ‘as a whole class’, then, though therebe none in which one does not recognize this property, one does not knowit of ‘all triangles’.
When, then, does our knowledge fail of commensurate universality, andwhen it is unqualified knowledge? If triangle be identical in essence withequilateral, i.e. with each or all equilaterals, then clearly we have unqual-ified knowledge: if on the other hand it be not, and the attribute belongsto equilateral qua triangle; then our knowledge fails of commensurate uni-versality. ‘But’, it will be asked, ‘does this attribute belong to the subject ofwhich it has been demonstrated qua triangle or qua isosceles? What is thepoint at which the subject. to which it belongs is primary? (i.e. to what sub-ject can it be demonstrated as belonging commensurately and universally?)’Clearly this point is the first term in which it is found to inhere as the elimi-nation of inferior differentiae proceeds. Thus the angles of a brazen isoscelestriangle are equal to two right angles: but eliminate brazen and isosceles andthe attribute remains. ‘But’ - you may say - ‘eliminate figure or limit, and theattribute vanishes.’ True, but figure and limit are not the first differentiaewhose elimination destroys the attribute. ‘Then what is the first?’ If it is tri-angle, it will be in virtue of triangle that the attribute belongs to all the othersubjects of which it is predicable, and triangle is the subject to which it canbe demonstrated as belonging commensurately and universally.
Part 6 Demonstrative knowledge rests on necessary truths
Demonstrative knowledge must rest on necessary basic truths; for the ob-ject of scientific knowledge cannot be other than it is. Now attributes at-taching essentially to their subjects attach necessarily to them: for essentialattributes are either elements in the essential nature of their subjects, or con-
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tain their subjects as elements in their own essential nature. (The pairs ofopposites which the latter class includes are necessary because one mem-ber or the other necessarily inheres.) It follows from this that premisses ofthe demonstrative syllogism must be connexions essential in the sense ex-plained: for all attributes must inhere essentially or else be accidental, andaccidental attributes are not necessary to their subjects.
We must either state the case thus, or else premise that the conclusion ofdemonstration is necessary and that a demonstrated conclusion cannot beother than it is, and then infer that the conclusion must be developed fromnecessary premisses. For though you may reason from true premisses with-out demonstrating, yet if your premisses are necessary you will assuredlydemonstrate - in such necessity you have at once a distinctive character ofdemonstration. That demonstration proceeds from necessary premisses isalso indicated by the fact that the objection we raise against a professeddemonstration is that a premiss of it is not a necessary truth - whether wethink it altogether devoid of necessity, or at any rate so far as our opponent’sprevious argument goes. This shows how naive it is to suppose one’s basictruths rightly chosen if one starts with a proposition which is (1) popularlyaccepted and (2) true, such as the sophists’ assumption that to know is thesame as to possess knowledge. For (1) popular acceptance or rejection is nocriterion of a basic truth, which can only be the primary law of the genusconstituting the subject matter of the demonstration; and (2) not all truth is‘appropriate’.
A further proof that the conclusion must be the development of neces-sary premisses is as follows. Where demonstration is possible, one who cangive no account which includes the cause has no scientific knowledge. If,then, we suppose a syllogism in which, though A necessarily inheres in C,yet B, the middle term of the demonstration, is not necessarily connectedwith A and C, then the man who argues thus has no reasoned knowledgeof the conclusion, since this conclusion does not owe its necessity to themiddle term; for though the conclusion is necessary, the mediating link isa contingent fact. Or again, if a man is without knowledge now, thoughhe still retains the steps of the argument, though there is no change in him-self or in the fact and no lapse of memory on his part; then neither had heknowledge previously. But the mediating link, not being necessary, mayhave perished in the interval; and if so, though there be no change in himnor in the fact, and though he will still retain the steps of the argument, yethe has not knowledge, and therefore had not knowledge before. Even if thelink has not actually perished but is liable to perish, this situation is possibleand might occur. But such a condition cannot be knowledge.
When the conclusion is necessary, the middle through which it wasproved may yet quite easily be non-necessary. You can in fact infer the nec-
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essary even from a non-necessary premiss, just as you can infer the true fromthe not true. On the other hand, when the middle is necessary the conclu-sion must be necessary; just as true premisses always give a true conclusion.Thus, if A is necessarily predicated of B and B of C, then A is necessarilypredicated of C. But when the conclusion is nonnecessary the middle can-not be necessary either. Thus: let A be predicated non-necessarily of C butnecessarily of B, and let B be a necessary predicate of C; then A too will be anecessary predicate of C, which by hypothesis it is not.
To sum up, then: demonstrative knowledge must be knowledge of a nec-essary nexus, and therefore must clearly be obtained through a necessarymiddle term; otherwise its possessor will know neither the cause nor thefact that his conclusion is a necessary connexion. Either he will mistake thenon-necessary for the necessary and believe the necessity of the conclusionwithout knowing it, or else he will not even believe it - in which case he willbe equally ignorant, whether he actually infers the mere fact through middleterms or the reasoned fact and from immediate premisses.
Of accidents that are not essential according to our definition of essentialthere is no demonstrative knowledge; for since an accident, in the sense inwhich I here speak of it, may also not inhere, it is impossible to prove itsinherence as a necessary conclusion. A difficulty, however, might be raisedas to why in dialectic, if the conclusion is not a necessary connexion, suchand such determinate premisses should be proposed in order to deal withsuch and such determinate problems. Would not the result be the same ifone asked any questions whatever and then merely stated one’s conclusion?The solution is that determinate questions have to be put, not because thereplies to them affirm facts which necessitate facts affirmed by the conclu-sion, but because these answers are propositions which if the answerer af-firm, he must affirm the conclusion and affirm it with truth if they are true.
Since it is just those attributes within every genus which are essentialand possessed by their respective subjects as such that are necessary it isclear that both the conclusions and the premisses of demonstrations whichproduce scientific knowledge are essential. For accidents are not necessary:and, further, since accidents are not necessary one does not necessarily havereasoned knowledge of a conclusion drawn from them (this is so even if theaccidental premisses are invariable but not essential, as in proofs throughsigns; for though the conclusion be actually essential, one will not knowit as essential nor know its reason); but to have reasoned knowledge of aconclusion is to know it through its cause. We may conclude that the middlemust be consequentially connected with the minor, and the major with themiddle.
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Part 7 No demonstration may pass from one genus toanother
It follows that we cannot in demonstrating pass from one genus to another.We cannot, for instance, prove geometrical truths by arithmetic. For thereare three elements in demonstration: (1) what is proved, the conclusion - anattribute inhering essentially in a genus; (2) the axioms, i.e. axioms whichare premisses of demonstration; (3) the subject-genus whose attributes, i.e.essential properties, are revealed by the demonstration. The axioms whichare premisses of demonstration may be identical in two or more sciences: butin the case of two different genera such as arithmetic and geometry you can-not apply arithmetical demonstration to the properties of magnitudes unlessthe magnitudes in question are numbers. How in certain cases transferenceis possible I will explain later.
Arithmetical demonstration and the other sciences likewise possess, eachof them, their own genera; so that if the demonstration is to pass from onesphere to another, the genus must be either absolutely or to some extent thesame. If this is not so, transference is clearly impossible, because the extremeand the middle terms must be drawn from the same genus: otherwise, aspredicated, they will not be essential and will thus be accidents. That is whyit cannot be proved by geometry that opposites fall under one science, noreven that the product of two cubes is a cube. Nor can the theorem of any onescience be demonstrated by means of another science, unless these theoremsare related as subordinate to superior (e.g. as optical theorems to geometryor harmonic theorems to arithmetic). Geometry again cannot prove of linesany property which they do not possess qua lines, i.e. in virtue of the fun-damental truths of their peculiar genus: it cannot show, for example, thatthe straight line is the most beautiful of lines or the contrary of the circle; forthese qualities do not belong to lines in virtue of their peculiar genus, butthrough some property which it shares with other genera.
Part 8 Commensurately universal premisses yield eternalconclusions
It is also clear that if the premisses from which the syllogism proceeds arecommensurately universal, the conclusion of such i.e. in the unqualifiedsense - must also be eternal. Therefore no attribute can be demonstratednor known by strictly scientific knowledge to inhere in perishable things.The proof can only be accidental, because the attribute’s connexion with itsperishable subject is not commensurately universal but temporary and spe-cial. If such a demonstration is made, one premiss must be perishable andnot commensurately universal (perishable because only if it is perishable
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will the conclusion be perishable; not commensurately universal, becausethe predicate will be predicable of some instances of the subject and not ofothers); so that the conclusion can only be that a fact is true at the moment -not commensurately and universally. The same is true of definitions, since adefinition is either a primary premiss or a conclusion of a demonstration, orelse only differs from a demonstration in the order of its terms. Demonstra-tion and science of merely frequent occurrences - e.g. of eclipse as happen-ing to the moon - are, as such, clearly eternal: whereas so far as they are noteternal they are not fully commensurate. Other subjects too have propertiesattaching to them in the same way as eclipse attaches to the moon.
Part 9 Attribute demonstration only from ’appropriate’basic truths
It is clear that if the conclusion is to show an attribute inhering as such, noth-ing can be demonstrated except from its ‘appropriate’ basic truths. Conse-quently a proof even from true, indemonstrable, and immediate premissesdoes not constitute knowledge. Such proofs are like Bryson’s method ofsquaring the circle; for they operate by taking as their middle a commoncharacter - a character, therefore, which the subject may share with another- and consequently they apply equally to subjects different in kind. Theytherefore afford knowledge of an attribute only as inhering accidentally, notas belonging to its subject as such: otherwise they would not have been ap-plicable to another genus.
Our knowledge of any attribute‘s connexion with a subject is accidentalunless we know that connexion through the middle term in virtue of whichit inheres, and as an inference from basic premisses essential and ’appropri-ate‘ to the subject - unless we know, e.g. the property of possessing anglesequal to two right angles as belonging to that subject in which it inheres es-sentially, and as inferred from basic premisses essential and ’appropriate’ tothat subject: so that if that middle term also belongs essentially to the mi-nor, the middle must belong to the same kind as the major and minor terms.The only exceptions to this rule are such cases as theorems in harmonicswhich are demonstrable by arithmetic. Such theorems are proved by thesame middle terms as arithmetical properties, but with a qualification - thefact falls under a separate science (for the subject genus is separate), but thereasoned fact concerns the superior science, to which the attributes essen-tially belong. Thus, even these apparent exceptions show that no attribute isstrictly demonstrable except from its ‘appropriate’ basic truths, which, how-ever, in the case of these sciences have the requisite identity of character.
It is no less evident that the peculiar basic truths of each inhering at-tribute are indemonstrable; for basic truths from which they might be de-
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duced would be basic truths of all that is, and the science to which theybelonged would possess universal sovereignty. This is so because he knowsbetter whose knowledge is deduced from higher causes, for his knowledgeis from prior premisses when it derives from causes themselves uncaused:hence, if he knows better than others or best of all, his knowledge wouldbe science in a higher or the highest degree. But, as things are, demonstra-tion is not transferable to another genus, with such exceptions as we havementioned of the application of geometrical demonstrations to theorems inmechanics or optics, or of arithmetical demonstrations to those of harmon-ics.
It is hard to be sure whether one knows or not; for it is hard to be surewhether one’s knowledge is based on the basic truths appropriate to eachattribute - the differentia of true knowledge. We think we have scientificknowledge if we have reasoned from true and primary premisses. But thatis not so: the conclusion must be homogeneous with the basic facts of thescience.
Part 10 Basic truths, peculiar (to a genus), and common (toall)
I call the basic truths of every genus those clements in it the existence ofwhich cannot be proved. As regards both these primary truths and the at-tributes dependent on them the meaning of the name is assumed. The factof their existence as regards the primary truths must be assumed; but it hasto be proved of the remainder, the attributes. Thus we assume the meaningalike of unity, straight, and triangular; but while as regards unity and mag-nitude we assume also the fact of their existence, in the case of the remainderproof is required.
Of the basic truths used in the demonstrative sciences some are peculiarto each science, and some are common, but common only in the sense ofanalogous, being of use only in so far as they fall within the genus constitut-ing the province of the science in question.
Peculiar truths are, e.g. the definitions of line and straight; commontruths are such as ‘take equals from equals and equals remain’. Only somuch of these common truths is required as falls within the genus in ques-tion: for a truth of this kind will have the same force even if not used gener-ally but applied by the geometer only to magnitudes, or by the arithmeticianonly to numbers. Also peculiar to a science are the subjects the existenceas well as the meaning of which it assumes, and the essential attributesof which it investigates, e.g. in arithmetic units, in geometry points andlines. Both the existence and the meaning of the subjects are assumed bythese sciences; but of their essential attributes only the meaning is assumed.
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For example arithmetic assumes the meaning of odd and even, square andcube, geometry that of incommensurable, or of deflection or verging of lines,whereas the existence of these attributes is demonstrated by means of the ax-ioms and from previous conclusions as premisses. Astronomy too proceedsin the same way. For indeed every demonstrative science has three elements:(1) that which it posits, the subject genus whose essential attributes it exam-ines; (2) the so-called axioms, which are primary premisses of its demonstra-tion; (3) the attributes, the meaning of which it assumes. Yet some sciencesmay very well pass over some of these elements; e.g. we might not expresslyposit the existence of the genus if its existence were obvious (for instance, theexistence of hot and cold is more evident than that of number); or we mightomit to assume expressly the meaning of the attributes if it were well under-stood. In the way the meaning of axioms, such as ‘Take equals from equalsand equals remain’, is well known and so not expressly assumed. Never-theless in the nature of the case the essential elements of demonstration arethree: the subject, the attributes, and the basic premisses.
That which expresses necessary self-grounded fact, and which we mustnecessarily believe, is distinct both from the hypotheses of a science andfrom illegitimate postulate - I say ‘must believe’, because all syllogism, andtherefore a fortiori demonstration, is addressed not to the spoken word, butto the discourse within the soul, and though we can always raise objectionsto the spoken word, to the inward discourse we cannot always object. Thatwhich is capable of proof but assumed by the teacher without proof is, ifthe pupil believes and accepts it, hypothesis, though only in a limited sensehypothesis - that is, relatively to the pupil; if the pupil has no opinion ora contrary opinion on the matter, the same assumption is an illegitimatepostulate. Therein lies the distinction between hypothesis and illegitimatepostulate: the latter is the contrary of the pupil’s opinion, demonstrable, butassumed and used without demonstration.
The definition - viz. those which are not expressed as statements thatanything is or is not - are not hypotheses: but it is in the premisses of ascience that its hypotheses are contained. Definitions require only to be un-derstood, and this is not hypothesis - unless it be contended that the pupil’shearing is also an hypothesis required by the teacher. Hypotheses, on thecontrary, postulate facts on the being of which depends the being of the factinferred. Nor are the geometer’s hypotheses false, as some have held, urg-ing that one must not employ falsehood and that the geometer is utteringfalsehood in stating that the line which he draws is a foot long or straight,when it is actually neither. The truth is that the geometer does not drawany conclusion from the being of the particular line of which he speaks, butfrom what his diagrams symbolize. A further distinction is that all hypothe-ses and illegitimate postulates are either universal or particular, whereas a
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definition is neither.
Part 11 Existence of forms, contradiction, excluded middle
So demonstration does not necessarily imply the being of Forms nor a Onebeside a Many, but it does necessarily imply the possibility of truly predicat-ing one of many; since without this possibility we cannot save the universal,and if the universal goes, the middle term goes witb. it, and so demonstra-tion becomes impossible. We conclude, then, that there must be a singleidentical term unequivocally predicable of a number of individuals.
The law that it is impossible to affirm and deny simultaneously the samepredicate of the same subject is not expressly posited by any demonstrationexcept when the conclusion also has to be expressed in that form; in whichcase the proof lays down as its major premiss that the major is truly affirmedof the middle but falsely denied. It makes no difference, however, if we addto the middle, or again to the minor term, the corresponding negative. Forgrant a minor term of which it is true to predicate man - even if it be also trueto predicate not-man of it - still grant simply that man is animal and not not-animal, and the conclusion follows: for it will still be true to say that Callias- even if it be also true to say that not-Callias - is animal and not not-animal.The reason is that the major term is predicable not only of the middle, butof something other than the middle as well, being of wider application; sothat the conclusion is not affected even if the middle is extended to cover theoriginal middle term and also what is not the original middle term.
The law that every predicate can be either truly affirmed or truly de-nied of every subject is posited by such demonstration as uses reductio adimpossibile, and then not always universally, but so far as it is requisite;within the limits, that is, of the genus - the genus, I mean (as I have al-ready explained), to which the man of science applies his demonstrations.In virtue of the common elements of demonstration - I mean the commonaxioms which are used as premisses of demonstration, not the subjects northe attributes demonstrated as belonging to them - all the sciences have com-munion with one another, and in communion with them all is dialectic andany science which might attempt a universal proof of axioms such as the lawof excluded middle, the law that the subtraction of equals from equals leavesequal remainders, or other axioms of the same kind. Dialectic has no defi-nite sphere of this kind, not being confined to a single genus. Otherwise itsmethod would not be interrogative; for the interrogative method is barredto the demonstrator, who cannot use the opposite facts to prove the samenexus. This was shown in my work on the syllogism.
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Part 12 There are distinctively scientific questions
If a syllogistic question is equivalent to a proposition embodying one of thetwo sides of a contradiction, and if each science has its peculiar propositionsfrom which its peculiar conclusion is developed, then there is such a thing asa distinctively scientific question, and it is the interrogative form of the pre-misses from which the ‘appropriate’ conclusion of each science is developed.Hence it is clear that not every question will be relevant to geometry, nor tomedicine, nor to any other science: only those questions will be geometricalwhich form premisses for the proof of the theorems of geometry or of anyother science, such as optics, which uses the same basic truths as geome-try. Of the other sciences the like is true. Of these questions the geometer isbound to give his account, using the basic truths of geometry in conjunctionwith his previous conclusions; of the basic truths the geometer, as such, isnot bound to give any account. The like is true of the other sciences. There isa limit, then, to the questions which we may put to each man of science; noris each man of science bound to answer all inquiries on each several subject,but only such as fall within the defined field of his own science. If, then, incontroversy with a geometer qua geometer the disputant confines himself togeometry and proves anything from geometrical premisses, he is clearly tobe applauded; if he goes outside these he will be at fault, and obviously can-not even refute the geometer except accidentally. One should therefore notdiscuss geometry among those who are not geometers, for in such a com-pany an unsound argument will pass unnoticed. This is correspondinglytrue in the other sciences.
Since there are ‘geometrical’ questions, does it follow that there are alsodistinctively ‘ungeometrical’ questions? Further, in each special science -geometry for instance - what kind of error is it that may vitiate questions,and yet not exclude them from that science? Again, is the erroneous con-clusion one constructed from premisses opposite to the true premisses, oris it formal fallacy though drawn from geometrical premisses? Or, perhaps,the erroneous conclusion is due to the drawing of premisses from anotherscience; e.g. in a geometrical controversy a musical question is distinctivelyungeometrical, whereas the notion that parallels meet is in one sense geo-metrical, being ungeometrical in a different fashion: the reason being that‘ungeometrical’, like ‘unrhythmical’, is equivocal, meaning in the one casenot geometry at all, in the other bad geometry? It is this error, i.e. error basedon premisses of this kind - ‘of’ the science but false - that is the contrary ofscience. In mathematics the formal fallacy is not so common, because it isthe middle term in which the ambiguity lies, since the major is predicatedof the whole of the middle and the middle of the whole of the minor (thepredicate of course never has the prefix ‘all’); and in mathematics one can,
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so to speak, see these middle terms with an intellectual vision, while in di-alectic the ambiguity may escape detection. E.g. ‘Is every circle a figure?’ Adiagram shows that this is so, but the minor premiss ‘Are epics circles?’ isshown by the diagram to be false.
If a proof has an inductive minor premiss, one should not bring an ‘ob-jection’ against it. For since every premiss must be applicable to a number ofcases (otherwise it will not be true in every instance, which, since the syllo-gism proceeds from universals, it must be), then assuredly the same is true ofan ‘objection’; since premisses and ‘objections’ are so far the same that any-thing which can be validly advanced as an ‘objection’ must be such that itcould take the form of a premiss, either demonstrative or dialectical. On theother hand, arguments formally illogical do sometimes occur through tak-ing as middles mere attributes of the major and minor terms. An instance ofthis is Caeneus’ proof that fire increases in geometrical proportion: ‘Fire’, heargues, ‘increases rapidly, and so does geometrical proportion’. There is nosyllogism so, but there is a syllogism if the most rapidly increasing propor-tion is geometrical and the most rapidly increasing proportion is attributableto fire in its motion. Sometimes, no doubt, it is impossible to reason frompremisses predicating mere attributes: but sometimes it is possible, thoughthe possibility is overlooked. If false premisses could never give true con-clusions ‘resolution’ would be easy, for premisses and conclusion would inthat case inevitably reciprocate. I might then argue thus: let A be an existingfact; let the existence of A imply such and such facts actually known to meto exist, which we may call B. I can now, since they reciprocate, infer A fromB.
Reciprocation of premisses and conclusion is more frequent in mathe-matics, because mathematics takes definitions, but never an accident, for itspremisses - a second characteristic distinguishing mathematical reasoningfrom dialectical disputations.
A science expands not by the interposition of fresh middle terms, but bythe apposition of fresh extreme terms. E.g. A is predicated of B, B of C, Cof D, and so indefinitely. Or the expansion may be lateral: e.g. one majorA, may be proved of two minors, C and E. Thus let A represent number -a number or number taken indeterminately; B determinate odd number; Cany particular odd number. We can then predicate A of C. Next let D repre-sent determinate even number, and E even number. Then A is predicable ofE.
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Part 13 Knowledge of the fact differs from knowledge ofthe reasoned fact
Knowledge of the fact differs from knowledge of the reasoned fact. To be-gin with, they differ within the same science and in two ways: (1) when thepremisses of the syllogism are not immediate (for then the proximate causeis not contained in them - a necessary condition of knowledge of the rea-soned fact): (2) when the premisses are immediate, but instead of the causethe better known of the two reciprocals is taken as the middle; for of two re-ciprocally predicable terms the one which is not the cause may quite easilybe the better known and so become the middle term of the demonstration.Thus (2) (a) you might prove as follows that the planets are near becausethey do not twinkle: let C be the planets, B not twinkling, A proximity. ThenB is predicable of C; for the planets do not twinkle. But A is also predica-ble of B, since that which does not twinkle is near - we must take this truthas having been reached by induction or sense-perception. Therefore A is anecessary predicate of C; so that we have demonstrated that the planets arenear. This syllogism, then, proves not the reasoned fact but only the fact;since they are not near because they do not twinkle, but, because they arenear, do not twinkle. The major and middle of the proof, however, may bereversed, and then the demonstration will be of the reasoned fact. Thus: letC be the planets, B proximity, A not twinkling. Then B is an attribute of C,and A - not twinkling - of B. Consequently A is predicable of C, and the syllo-gism proves the reasoned fact, since its middle term is the proximate cause.Another example is the inference that the moon is spherical from its man-ner of waxing. Thus: since that which so waxes is spherical, and since themoon so waxes, clearly the moon is spherical. Put in this form, the syllogismturns out to be proof of the fact, but if the middle and major be reversed it isproof of the reasoned fact; since the moon is not spherical because it waxesin a certain manner, but waxes in such a manner because it is spherical. (LetC be the moon, B spherical, and A waxing.) Again (b), in cases where thecause and the effect are not reciprocal and the effect is the better known, thefact is demonstrated but not the reasoned fact. This also occurs (1) when themiddle falls outside the major and minor, for here too the strict cause is notgiven, and so the demonstration is of the fact, not of the reasoned fact. Forexample, the question ‘Why does not a wall breathe?’ might be answered,‘Because it is not an animal’; but that answer would not give the strict cause,because if not being an animal causes the absence of respiration, then beingan animal should be the cause of respiration, according to the rule that ifthe negation of causes the non-inherence of y, the affirmation of x causes theinherence of y; e.g. if the disproportion of the hot and cold elements is thecause of ill health, their proportion is the cause of health; and conversely, if
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the assertion of x causes the inherence of y, the negation of x must cause y’snon-inherence. But in the case given this consequence does not result; fornot every animal breathes. A syllogism with this kind of cause takes placein the second figure. Thus: let A be animal, B respiration, C wall. Then Ais predicable of all B (for all that breathes is animal), but of no C; and con-sequently B is predicable of no C; that is, the wall does not breathe. Suchcauses are like far-fetched explanations, which precisely consist in makingthe cause too remote, as in Anacharsis’ account of why the Scythians haveno flute-players; namely because they have no vines.
Thus, then, do the syllogism of the fact and the syllogism of the reasonedfact differ within one science and according to the position of the middleterms. But there is another way too in which the fact and the reasoned factdiffer, and that is when they are investigated respectively by different sci-ences. This occurs in the case of problems related to one another as subordi-nate and superior, as when optical problems are subordinated to geometry,mechanical problems to stereometry, harmonic problems to arithmetic, thedata of observation to astronomy. (Some of these sciences bear almost thesame name; e.g. mathematical and nautical astronomy, mathematical andacoustical harmonics.) Here it is the business of the empirical observers toknow the fact, of the mathematicians to know the reasoned fact; for the lat-ter are in possession of the demonstrations giving the causes, and are oftenignorant of the fact: just as we have often a clear insight into a universal, butthrough lack of observation are ignorant of some of its particular instances.These connexions have a perceptible existence though they are manifesta-tions of forms. For the mathematical sciences concern forms: they do notdemonstrate properties of a substratum, since, even though the geometricalsubjects are predicable as properties of a perceptible substratum, it is not asthus predicable that the mathematician demonstrates properties of them. Asoptics is related to geometry, so another science is related to optics, namelythe theory of the rainbow. Here knowledge of the fact is within the provinceof the natural philosopher, knowledge of the reasoned fact within that of theoptician, either qua optician or qua mathematical optician. Many sciencesnot standing in this mutual relation enter into it at points; e.g. medicine andgeometry: it is the physician’s business to know that circular wounds healmore slowly, the geometer’s to know the reason why.
Part 14 Of all the figures the most scientific is the first
Of all the figures the most scientific is the first. Thus, it is the vehicle of thedemonstrations of all the mathematical sciences, such as arithmetic, geome-try, and optics, and practically all of all sciences that investigate causes: forthe syllogism of the reasoned fact is either exclusively or generally speak-
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ing and in most cases in this figure - a second proof that this figure is themost scientific; for grasp of a reasoned conclusion is the primary conditionof knowledge. Thirdly, the first is the only figure which enables us to pur-sue knowledge of the essence of a thing. In the second figure no affirmativeconclusion is possible, and knowledge of a thing’s essence must be affirma-tive; while in the third figure the conclusion can be affirmative, but cannotbe universal, and essence must have a universal character: e.g. man is nottwo-footed animal in any qualified sense, but universally. Finally, the firstfigure has no need of the others, while it is by means of the first that theother two figures are developed, and have their intervals closepacked untilimmediate premisses are reached.
Clearly, therefore, the first figure is the primary condition of knowledge.
Part 15 Atomic connexions and disconnexions
Just as an attribute A may (as we saw) be atomically connected with a subjectB, so its disconnexion may be atomic. I call ‘atomic’ connexions or discon-nexions which involve no intermediate term; since in that case the connex-ion or disconnexion will not be mediated by something other than the termsthemselves. It follows that if either A or B, or both A and B, have a genus,their disconnexion cannot be primary. Thus: let C be the genus of A. Then, ifC is not the genus of B - for A may well have a genus which is not the genusof B - there will be a syllogism proving A’s disconnexion from B thus:
all A is C,no B is C,therefore no B is A.Or if it is B which has a genus D, we haveall B is D,no D is A,therefore no B is A, by syllogism;and the proof will be similar if both A and B have a genus. That the genus
of A need not be the genus of B and vice versa, is shown by the existence ofmutually exclusive coordinate series of predication. If no term in the seriesACD...is predicable of any term in the series BEF...,and if G - a term in theformer series - is the genus of A, clearly G will not be the genus of B; since, ifit were, the series would not be mutually exclusive. So also if B has a genus,it will not be the genus of A. If, on the other hand, neither A nor B has agenus and A does not inhere in B, this disconnexion must be atomic. If therebe a middle term, one or other of them is bound to have a genus, for thesyllogism will be either in the first or the second figure. If it is in the first,B will have a genus - for the premiss containing it must be affirmative: if in
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the second, either A or B indifferently, since syllogism is possible if either iscontained in a negative premiss, but not if both premisses are negative.
Hence it is clear that one thing may be atomically disconnected from an-other, and we have stated when and how this is possible.
Part 16 Ignorance is error produced by inference
Ignorance - defined not as the negation of knowledge but as a positive stateof mind - is error produced by inference.
(1) Let us first consider propositions asserting a predicate’s immediateconnexion with or disconnexion from a subject. Here, it is true, positive errormay befall one in alternative ways; for it may arise where one directly be-lieves a connexion or disconnexion as well as where one’s belief is acquiredby inference. The error, however, that consists in a direct belief is withoutcomplication; but the error resulting from inference - which here concernsus - takes many forms. Thus, let A be atomically disconnected from all B:then the conclusion inferred through a middle term C, that all B is A, will bea case of error produced by syllogism. Now, two cases are possible. Either(a) both premisses, or (b) one premiss only, may be false. (a) If neither A is anattribute of any C nor C of any B, whereas the contrary was posited in bothcases, both premisses will be false. (C may quite well be so related to A andB that C is neither subordinate to A nor a universal attribute of B: for B, sinceA was said to be primarily disconnected from B, cannot have a genus, andA need not necessarily be a universal attribute of all things. Consequentlyboth premisses may be false.) On the other hand, (b) one of the premissesmay be true, though not either indifferently but only the major A-C since,B having no genus, the premiss C-B will always be false, while A-C may betrue. This is the case if, for example, A is related atomically to both C and B;because when the same term is related atomically to more terms than one,neither of those terms will belong to the other. It is, of course, equally thecase if A-C is not atomic.
Error of attribution, then, occurs through these causes and in this formonly - for we found that no syllogism of universal attribution was possiblein any figure but the first. On the other hand, an error of non-attributionmay occur either in the first or in the second figure. Let us therefore firstexplain the various forms it takes in the first figure and the character of thepremisses in each case.
(c) It may occur when both premisses are false; e.g. supposing A atomi-cally connected with both C and B, if it be then assumed that no C is and allB is C, both premisses are false.
(d) It is also possible when one is false. This may be either premiss indif-ferently. A-C may be true, C-B false - A-C true because A is not an attribute
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of all things, C-B false because C, which never has the attribute A, cannot bean attribute of B; for if C-B were true, the premiss A-C would no longer betrue, and besides if both premisses were true, the conclusion would be true.Or again, C-B may be true and A-C false; e.g. if both C and A contain B asgenera, one of them must be subordinate to the other, so that if the premisstakes the form No C is A, it will be false. This makes it clear that whethereither or both premisses are false, the conclusion will equally be false.
In the second figure the premisses cannot both be wholly false; for if all Bis A, no middle term can be with truth universally affirmed of one extremeand universally denied of the other: but premisses in which the middle isaffirmed of one extreme and denied of the other are the necessary conditionif one is to get a valid inference at all. Therefore if, taken in this way, theyare wholly false, their contraries conversely should be wholly true. But thisis impossible. On the other hand, there is nothing to prevent both premissesbeing partially false; e.g. if actually some A is C and some B is C, then if it ispremised that all A is C and no B is C, both premisses are false, yet partially,not wholly, false. The same is true if the major is made negative instead ofthe minor. Or one premiss may be wholly false, and it may be either of them.Thus, supposing that actually an attribute of all A must also be an attributeof all B, then if C is yet taken to be a universal attribute of all but universallynon-attributable to B, C-A will be true but C-B false. Again, actually thatwhich is an attribute of no B will not be an attribute of all A either; for if itbe an attribute of all A, it will also be an attribute of all B, which is contraryto supposition; but if C be nevertheless assumed to be a universal attributeof A, but an attribute of no B, then the premiss C-B is true but the major isfalse. The case is similar if the major is made the negative premiss. For infact what is an attribute of no A will not be an attribute of any B either; and ifit be yet assumed that C is universally non-attributable to A, but a universalattribute of B, the premiss C-A is true but the minor wholly false. Again, infact it is false to assume that that which is an attribute of all B is an attributeof no A, for if it be an attribute of all B, it must be an attribute of some A. Ifthen C is nevertheless assumed to be an attribute of all B but of no A, C-Bwill be true but C-A false.
It is thus clear that in the case of atomic propositions erroneous inferencewill be possible not only when both premisses are false but also when onlyone is false.
Part 17 Attributes not atomically connected or disconnected
In the case of attributes not atomically connected with or disconnected fromtheir subjects, (a) (i) as long as the false conclusion is inferred through the‘appropriate’ middle, only the major and not both premisses can be false. By
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‘appropriate middle’ I mean the middle term through which the contradic-tory - i.e. the true-conclusion is inferrible. Thus, let A be attributable to Bthrough a middle term C: then, since to produce a conclusion the premissC-B must be taken affirmatively, it is clear that this premiss must always betrue, for its quality is not changed. But the major A-C is false, for it is by achange in the quality of A-C that the conclusion becomes its contradictory- i.e. true. Similarly (ii) if the middle is taken from another series of pred-ication; e.g. suppose D to be not only contained within A as a part withinits whole but also predicable of all B. Then the premiss D-B must remainunchanged, but the quality of A-D must be changed; so that D-B is alwaystrue, A-D always false. Such error is practically identical with that whichis inferred through the ‘appropriate’ middle. On the other hand, (b) if theconclusion is not inferred through the ‘appropriate’ middle - (i) when themiddle is subordinate to A but is predicable of no B, both premisses must befalse, because if there is to be a conclusion both must be posited as assertingthe contrary of what is actually the fact, and so posited both become false:e.g. suppose that actually all D is A but no B is D; then if these premisses arechanged in quality, a conclusion will follow and both of the new premisseswill be false. When, however, (ii) the middle D is not subordinate to A, A-Dwill be true, D-B false - A-D true because A was not subordinate to D, D-Bfalse because if it had been true, the conclusion too would have been true;but it is ex hypothesi false.
When the erroneous inference is in the second figure, both premisses can-not be entirely false; since if B is subordinate to A, there can be no middlepredicable of all of one extreme and of none of the other, as was stated be-fore. One premiss, however, may be false, and it may be either of them.Thus, if C is actually an attribute of both A and B, but is assumed to be anattribute of A only and not of B, C-A will be true, C-B false: or again if C beassumed to be attributable to B but to no A, C-B will be true, C-A false.
We have stated when and through what kinds of premisses error will re-sult in cases where the erroneous conclusion is negative. If the conclusion isaffirmative, (a) (i) it may be inferred through the ‘appropriate’ middle term.In this case both premisses cannot be false since, as we said before, C-B mustremain unchanged if there is to be a conclusion, and consequently A-C, thequality of which is changed, will always be false. This is equally true if (ii)the middle is taken from another series of predication, as was stated to bethe case also with regard to negative error; for D-B must remain unchanged,while the quality of A-D must be converted, and the type of error is the sameas before.
(b) The middle may be inappropriate. Then (i) if D is subordinate toA, A-D will be true, but D-B false; since A may quite well be predicable ofseveral terms no one of which can be subordinated to another. If, however,
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(ii) D is not subordinate to A, obviously A-D, since it is affirmed, will alwaysbe false, while D-B may be either true or false; for A may very well be anattribute of no D, whereas all B is D, e.g. no science is animal, all musicis science. Equally well A may be an attribute of no D, and D of no B. Itemerges, then, that if the middle term is not subordinate to the major, notonly both premisses but either singly may be false.
Thus we have made it clear how many varieties of erroneous inferenceare liable to happen and through what kinds of premisses they occur, in thecase both of immediate and of demonstrable truths.
Part 18 Demonstration develops from universals, inductionfrom particulars
It is also clear that the loss of any one of the senses entails the loss of acorresponding portion of knowledge, and that, since we learn either byinduction or by demonstration, this knowledge cannot be acquired. Thusdemonstration develops from universals, induction from particulars; butsince it is possible to familiarize the pupil with even the so-called mathe-matical abstractions only through induction - i.e. only because each subjectgenus possesses, in virtue of a determinate mathematical character, certainproperties which can be treated as separate even though they do not ex-ist in isolation - it is consequently impossible to come to grasp universalsexcept through induction. But induction is impossible for those who havenot sense-perception. For it is sense-perception alone which is adequate forgrasping the particulars: they cannot be objects of scientific knowledge, be-cause neither can universals give us knowledge of them without induction,nor can we get it through induction without sense-perception.
Part 19 Every syllogism is effected by means of three terms
Every syllogism is effected by means of three terms. One kind of syllogismserves to prove that A inheres in C by showing that A inheres in B and B inC; the other is negative and one of its premisses asserts one term of another,while the other denies one term of another. It is clear, then, that these are thefundamentals and so-called hypotheses of syllogism. Assume them as theyhave been stated, and proof is bound to follow - proof that A inheres in Cthrough B, and again that A inheres in B through some other middle term,and similarly that B inheres in C. If our reasoning aims at gaining credenceand so is merely dialectical, it is obvious that we have only to see that ourinference is based on premisses as credible as possible: so that if a middleterm between A and B is credible though not real, one can reason throughit and complete a dialectical syllogism. If, however, one is aiming at truth,
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one must be guided by the real connexions of subjects and attributes. Thus:since there are attributes which are predicated of a subject essentially or nat-urally and not coincidentally - not, that is, in the sense in which we say ‘Thatwhite (thing) is a man’, which is not the same mode of predication as whenwe say ‘The man is white’: the man is white not because he is something elsebut because he is man, but the white is man because ‘being white’ coincideswith ‘humanity’ within one substratum - therefore there are terms such asare naturally subjects of predicates. Suppose, then, C such a term not itselfattributable to anything else as to a subject, but the proximate subject of theattribute B - i.e. so that B-C is immediate; suppose further E related immedi-ately to F, and F to B. The first question is, must this series terminate, or canit proceed to infinity? The second question is as follows: Suppose nothingis essentially predicated of A, but A is predicated primarily of H and of nointermediate prior term, and suppose H similarly related to G and G to B;then must this series also terminate, or can it too proceed to infinity? There isthis much difference between the questions: the first is, is it possible to startfrom that which is not itself attributable to anything else but is the subjectof attributes, and ascend to infinity? The second is the problem whether onecan start from that which is a predicate but not itself a subject of predicates,and descend to infinity? A third question is, if the extreme terms are fixed,can there be an infinity of middles? I mean this: suppose for example thatA inheres in C and B is intermediate between them, but between B and Athere are other middles, and between these again fresh middles; can theseproceed to infinity or can they not? This is the equivalent of inquiring, dodemonstrations proceed to infinity, i.e. is everything demonstrable? Or doultimate subject and primary attribute limit one another?
I hold that the same questions arise with regard to negative conclusionsand premisses: viz. if A is attributable to no B, then either this predicationwill be primary, or there will be an intermediate term prior to B to which a isnot attributable - G, let us say, which is attributable to all B - and there maystill be another term H prior to G, which is attributable to all G. The samequestions arise, I say, because in these cases too either the series of priorterms to which a is not attributable is infinite or it terminates.
One cannot ask the same questions in the case of reciprocating terms,since when subject and predicate are convertible there is neither primarynor ultimate subject, seeing that all the reciprocals qua subjects stand in thesame relation to one another, whether we say that the subject has an infinityof attributes or that both subjects and attributes - and we raised the ques-tion in both cases - are infinite in number. These questions then cannot beasked - unless, indeed, the terms can reciprocate by two different modes, byaccidental predication in one relation and natural predication in the other.
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Part 20 Middle terms cannot be infinite in number
Now, it is clear that if the predications terminate in both the upward and thedownward direction (by ‘upward’ I mean the ascent to the more universal,by ‘downward’ the descent to the more particular), the middle terms cannotbe infinite in number. For suppose that A is predicated of F, and that the in-termediates - call them BB’B"... - are infinite, then clearly you might descendfrom and find one term predicated of another ad infinitum, since you havean infinity of terms between you and F; and equally, if you ascend from F,there are infinite terms between you and A. It follows that if these processesare impossible there cannot be an infinity of intermediates between A andF. Nor is it of any effect to urge that some terms of the series AB...F are con-tiguous so as to exclude intermediates, while others cannot be taken into theargument at all: whichever terms of the series B...I take, the number of inter-mediates in the direction either of A or of F must be finite or infinite: wherethe infinite series starts, whether from the first term or from a later one, is ofno moment, for the succeeding terms in any case are infinite in number.
Part 21 That the regress of middles terminates
Further, if in affirmative demonstration the series terminates in both direc-tions, clearly it will terminate too in negative demonstration. Let us assumethat we cannot proceed to infinity either by ascending from the ultimate term(by ‘ultimate term’ I mean a term such as was, not itself attributable to a sub-ject but itself the subject of attributes), or by descending towards an ultimatefrom the primary term (by ‘primary term’ I mean a term predicable of a sub-ject but not itself a subject). If this assumption is justified, the series will alsoterminate in the case of negation. For a negative conclusion can be provedin all three figures. In the first figure it is proved thus: no B is A, all C isB. In packing the interval B-C we must reach immediate propositions - as isalways the case with the minor premiss - since B-C is affirmative. As regardsthe other premiss it is plain that if the major term is denied of a term D priorto B, D will have to be predicable of all B, and if the major is denied of yetanother term prior to D, this term must be predicable of all D. Consequently,since the ascending series is finite, the descent will also terminate and therewill be a subject of which A is primarily non-predicable. In the second figurethe syllogism is, all A is B, no C is B,..no C is A. If proof of this is required,plainly it may be shown either in the first figure as above, in the second ashere, or in the third. The first figure has been discussed, and we will proceedto display the second, proof by which will be as follows: all B is D, no C isD..., since it is required that B should be a subject of which a predicate is af-firmed. Next, since D is to be proved not to belong to C, then D has a further
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predicate which is denied of C. Therefore, since the succession of predicatesaffirmed of an ever higher universal terminates, the succession of predicatesdenied terminates too.
The third figure shows it as follows: all B is A, some B is not C. Thereforesome A is not C. This premiss, i.e. C-B, will be proved either in the samefigure or in one of the two figures discussed above. In the first and secondfigures the series terminates. If we use the third figure, we shall take as pre-misses, all E is B, some E is not C, and this premiss again will be proved bya similar prosyllogism. But since it is assumed that the series of descendingsubjects also terminates, plainly the series of more universal non-predicableswill terminate also. Even supposing that the proof is not confined to onemethod, but employs them all and is now in the first figure, now in the sec-ond or third - even so the regress will terminate, for the methods are finitein number, and if finite things are combined in a finite number of ways, theresult must be finite.
Thus it is plain that the regress of middles terminates in the case of nega-tive demonstration, if it does so also in the case of affirmative demonstration.That in fact the regress terminates in both these cases may be made clear bythe following dialectical considerations.
Part 22 Dialectical considerations
In the case of predicates constituting the essential nature of a thing, it clearlyterminates, seeing that if definition is possible, or in other words, if essentialform is knowable, and an infinite series cannot be traversed, predicates con-stituting a thing’s essential nature must be finite in number. But as regardspredicates generally we have the following prefatory remarks to make. (1)We can affirm without falsehood ‘the white (thing) is walking’, and ‘that big(thing) is a log’; or again, ‘the log is big’, and ‘the man walks’. But the af-firmation differs in the two cases. When I affirm ‘the white is a log’, I meanthat something which happens to be white is a log - not that white is thesubstratum in which log inheres, for it was not qua white or qua a species ofwhite that the white (thing) came to be a log, and the white (thing) is conse-quently not a log except incidentally. On the other hand, when I affirm ‘thelog is white’, I do not mean that something else, which happens also to be alog, is white (as I should if I said ‘the musician is white,’ which would mean‘the man who happens also to be a musician is white’);on the contrary, log ishere the substratum - the substratum which actually came to be white, anddid so qua wood or qua a species of wood and qua nothing else.
If we must lay down a rule, let us entitle the latter kind of statementpredication, and the former not predication at all, or not strict but accidentalpredication. ‘White’ and ‘log’ will thus serve as types respectively of predi-
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cate and subject.We shall assume, then, that the predicate is invariably predicated strictly
and not accidentally of the subject, for on such predication demonstrationsdepend for their force. It follows from this that when a single attribute ispredicated of a single subject, the predicate must affirm of the subject ei-ther some element constituting its essential nature, or that it is in some wayqualified, quantified, essentially related, active, passive, placed, or dated.
(2) Predicates which signify substance signify that the subject is identicalwith the predicate or with a species of the predicate. Predicates not signify-ing substance which are predicated of a subject not identical with themselvesor with a species of themselves are accidental or coincidental; e.g. white isa coincident of man, seeing that man is not identical with white or a speciesof white, but rather with animal, since man is identical with a species of an-imal. These predicates which do not signify substance must be predicates ofsome other subject, and nothing can be white which is not also other thanwhite. The Forms we can dispense with, for they are mere sound withoutsense; and even if there are such things, they are not relevant to our discus-sion, since demonstrations are concerned with predicates such as we havedefined.
(3) If A is a quality of B, B cannot be a quality of A - a quality of a quality.Therefore A and B cannot be predicated reciprocally of one another in strictpredication: they can be affirmed without falsehood of one another, but notgenuinely predicated of each other. For one alternative is that they shouldbe substantially predicated of one another, i.e. B would become the genus ordifferentia of A - the predicate now become subject. But it has been shownthat in these substantial predications neither the ascending predicates northe descending subjects form an infinite series; e.g. neither the series, manis biped, biped is animal, &c., nor the series predicating animal of man, manof Callias, Callias of a further. subject as an element of its essential nature,is infinite. For all such substance is definable, and an infinite series cannotbe traversed in thought: consequently neither the ascent nor the descent isinfinite, since a substance whose predicates were infinite would not be de-finable. Hence they will not be predicated each as the genus of the other;for this would equate a genus with one of its own species. Nor (the otheralternative) can a quale be reciprocally predicated of a quale, nor any termbelonging to an adjectival category of another such term, except by acciden-tal predication; for all such predicates are coincidents and are predicated ofsubstances. On the other hand - in proof of the impossibility of an infinite as-cending series - every predication displays the subject as somehow qualifiedor quantified or as characterized under one of the other adjectival categories,or else is an element in its substantial nature: these latter are limited in num-ber, and the number of the widest kinds under which predications fall is
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also limited, for every predication must exhibit its subject as somehow qual-ified, quantified, essentially related, acting or suffering, or in some place orat some time.
I assume first that predication implies a single subject and a single at-tribute, and secondly that predicates which are not substantial are not pred-icated of one another. We assume this because such predicates are all co-incidents, and though some are essential coincidents, others of a differenttype, yet we maintain that all of them alike are predicated of some substra-tum and that a coincident is never a substratum - since we do not class as acoincident anything which does not owe its designation to its being some-thing other than itself, but always hold that any coincident is predicated ofsome substratum other than itself, and that another group of coincidentsmay have a different substratum. Subject to these assumptions then, neitherthe ascending nor the descending series of predication in which a single at-tribute is predicated of a single subject is infinite. For the subjects of whichcoincidents are predicated are as many as the constitutive elements of eachindividual substance, and these we have seen are not infinite in number,while in the ascending series are contained those constitutive elements withtheir coincidents - both of which are finite. We conclude that there is a givensubject (D) of which some attribute (C) is primarily predicable; that theremust be an attribute (B) primarily predicable of the first attribute, and thatthe series must end with a term (A) not predicable of any term prior to thelast subject of which it was predicated (B), and of which no term prior to itis predicable.
The argument we have given is one of the so-called proofs; an alter-native proof follows. Predicates so related to their subjects that there areother predicates prior to them predicable of those subjects are demonstrable;but of demonstrable propositions one cannot have something better thanknowledge, nor can one know them without demonstration. Secondly, ifa consequent is only known through an antecedent (viz. premisses priorto it) and we neither know this antecedent nor have something better thanknowledge of it, then we shall not have scientific knowledge of the conse-quent. Therefore, if it is possible through demonstration to know anythingwithout qualification and not merely as dependent on the acceptance of cer-tain premisses - i.e. hypothetically - the series of intermediate predicationsmust terminate. If it does not terminate, and beyond any predicate taken ashigher than another there remains another still higher, then every predicateis demonstrable. Consequently, since these demonstrable predicates are in-finite in number and therefore cannot be traversed, we shall not know themby demonstration. If, therefore, we have not something better than knowl-edge of them, we cannot through demonstration have unqualified but onlyhypothetical science of anything.
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As dialectical proofs of our contention these may carry conviction, butan analytic process will show more briefly that neither the ascent nor the de-scent of predication can be infinite in the demonstrative sciences which arethe object of our investigation. Demonstration proves the inherence of es-sential attributes in things. Now attributes may be essential for two reasons:either because they are elements in the essential nature of their subjects, orbecause their subjects are elements in their essential nature. An example ofthe latter is odd as an attribute of number - though it is number’s attribute,yet number itself is an element in the definition of odd; of the former, mul-tiplicity or the indivisible, which are elements in the definition of number.In neither kind of attribution can the terms be infinite. They are not infinitewhere each is related to the term below it as odd is to number, for this wouldmean the inherence in odd of another attribute of odd in whose nature oddwas an essential element: but then number will be an ultimate subject ofthe whole infinite chain of attributes, and be an element in the definition ofeach of them. Hence, since an infinity of attributes such as contain their sub-ject in their definition cannot inhere in a single thing, the ascending series isequally finite. Note, moreover, that all such attributes must so inhere in theultimate subject - e.g. its attributes in number and number in them - as tobe commensurate with the subject and not of wider extent. Attributes whichare essential elements in the nature of their subjects are equally finite: other-wise definition would be impossible. Hence, if all the attributes predicatedare essential and these cannot be infinite, the ascending series will terminate,and consequently the descending series too.
If this is so, it follows that the intermediates between any two terms arealso always limited in number. An immediately obvious consequence ofthis is that demonstrations necessarily involve basic truths, and that the con-tention of some - referred to at the outset - that all truths are demonstrableis mistaken. For if there are basic truths, (a) not all truths are demonstrable,and (b) an infinite regress is impossible; since if either (a) or (b) were not afact, it would mean that no interval was immediate and indivisible, but thatall intervals were divisible. This is true because a conclusion is demonstratedby the interposition, not the apposition, of a fresh term. If such interposi-tion could continue to infinity there might be an infinite number of termsbetween any two terms; but this is impossible if both the ascending and de-scending series of predication terminate; and of this fact, which before wasshown dialectically, analytic proof has now been given.
Part 23 Some corollaries
It is an evident corollary of these conclusions that if the same attribute A in-heres in two terms C and D predicable either not at all, or not of all instances,
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of one another, it does not always belong to them in virtue of a common mid-dle term. Isosceles and scalene possess the attribute of having their anglesequal to two right angles in virtue of a common middle; for they possess itin so far as they are both a certain kind of figure, and not in so far as theydiffer from one another. But this is not always the case: for, were it so, ifwe take B as the common middle in virtue of which A inheres in C and D,clearly B would inhere in C and D through a second common middle, andthis in turn would inhere in C and D through a third, so that between twoterms an infinity of intermediates would fall - an impossibility. Thus it neednot always be in virtue of a common middle term that a single attribute in-heres in several subjects, since there must be immediate intervals. Yet if theattribute to be proved common to two subjects is to be one of their essentialattributes, the middle terms involved must be within one subject genus andbe derived from the same group of immediate premisses; for we have seenthat processes of proof cannot pass from one genus to another.
It is also clear that when A inheres in B, this can be demonstrated if thereis a middle term. Further, the ‘elements’ of such a conclusion are the pre-misses containing the middle in question, and they are identical in numberwith the middle terms, seeing that the immediate propositions - or at leastsuch immediate propositions as are universal - are the ‘elements’. If, on theother hand, there is no middle term, demonstration ceases to be possible: weare on the way to the basic truths. Similarly if A does not inhere in B, thiscan be demonstrated if there is a middle term or a term prior to B in whichA does not inhere: otherwise there is no demonstration and a basic truth isreached. There are, moreover, as many ‘elements’ of the demonstrated con-clusion as there are middle terms, since it is propositions containing thesemiddle terms that are the basic premisses on which the demonstration rests;and as there are some indemonstrable basic truths asserting that ‘this is that’or that ‘this inheres in that’, so there are others denying that ‘this is that’ orthat ‘this inheres in that’ - in fact some basic truths will affirm and some willdeny being.
When we are to prove a conclusion, we must take a primary essentialpredicate - suppose it C - of the subject B, and then suppose A similarlypredicable of C. If we proceed in this manner, no proposition or attributewhich falls beyond A is admitted in the proof: the interval is constantlycondensed until subject and predicate become indivisible, i.e. one. We haveour unit when the premiss becomes immediate, since the immediate premissalone is a single premiss in the unqualified sense of ‘single’. And as in otherspheres the basic element is simple but not identical in all - in a system ofweight it is the mina, in music the quarter-tone, and so on - so in syllogismthe unit is an immediate premiss, and in the knowledge that demonstrationgives it is an intuition. In syllogisms, then, which prove the inherence of
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an attribute, nothing falls outside the major term. In the case of negativesyllogisms on the other hand, (1) in the first figure nothing falls outside themajor term whose inherence is in question; e.g. to prove through a middle Cthat A does not inhere in B the premisses required are, all B is C, no C is A.Then if it has to be proved that no C is A, a middle must be found betweenand C; and this procedure will never vary.
(2) If we have to show that E is not D by means of the premisses, all D isC; no E, or not all E, is C; then the middle will never fall beyond E, and E isthe subject of which D is to be denied in the conclusion.
(3) In the third figure the middle will never fall beyond the limits of thesubject and the attribute denied of it.
Part 24 Universal demonstration is better than particular
Since demonstrations may be either commensurately universal or particu-lar, and either affirmative or negative; the question arises, which form is thebetter? And the same question may be put in regard to so-called ‘direct’demonstration and reductio ad impossibile. Let us first examine the com-mensurately universal and the particular forms, and when we have clearedup this problem proceed to discuss ‘direct’ demonstration and reductio adimpossibile.
The following considerations might lead some minds to prefer particulardemonstration.
(1) The superior demonstration is the demonstration which gives usgreater knowledge (for this is the ideal of demonstration), and we havegreater knowledge of a particular individual when we know it in itself thanwhen we know it through something else; e.g. we know Coriscus the musi-cian better when we know that Coriscus is musical than when we know onlythat man is musical, and a like argument holds in all other cases. But com-mensurately universal demonstration, instead of proving that the subject it-self actually is x, proves only that something else is x - e.g. in attemptingto prove that isosceles is x, it proves not that isosceles but only that trian-gle is x - whereas particular demonstration proves that the subject itself isx. The demonstration, then, that a subject, as such, possesses an attribute issuperior. If this is so, and if the particular rather than the commensuratelyuniversal forms demonstrates, particular demonstration is superior.
(2) The universal has not a separate being over against groups of sin-gulars. Demonstration nevertheless creates the opinion that its function isconditioned by something like this - some separate entity belonging to thereal world; that, for instance, of triangle or of figure or number, over againstparticular triangles, figures, and numbers. But demonstration which touchesthe real and will not mislead is superior to that which moves among unre-
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alities and is delusory. Now commensurately universal demonstration is ofthe latter kind: if we engage in it we find ourselves reasoning after a fashionwell illustrated by the argument that the proportionate is what answers tothe definition of some entity which is neither line, number, solid, nor plane,but a proportionate apart from all these. Since, then, such a proof is charac-teristically commensurate and universal, and less touches reality than doesparticular demonstration, and creates a false opinion, it will follow that com-mensurate and universal is inferior to particular demonstration.
We may retort thus. (1) The first argument applies no more to commen-surate and universal than to particular demonstration. If equality to tworight angles is attributable to its subject not qua isosceles but qua triangle,he who knows that isosceles possesses that attribute knows the subject asqua itself possessing the attribute, to a less degree than he who knows thattriangle has that attribute. To sum up the whole matter: if a subject is provedto possess qua triangle an attribute which it does not in fact possess qua tri-angle, that is not demonstration: but if it does possess it qua triangle therule applies that the greater knowledge is his who knows the subject as pos-sessing its attribute qua that in virtue of which it actually does possess it.Since, then, triangle is the wider term, and there is one identical definitionof triangle - i.e. the term is not equivocal - and since equality to two rightangles belongs to all triangles, it is isosceles qua triangle and not trianglequa isosceles which has its angles so related. It follows that he who knows aconnexion universally has greater knowledge of it as it in fact is than he whoknows the particular; and the inference is that commensurate and universalis superior to particular demonstration.
(2) If there is a single identical definition i.e. if the commensurate univer-sal is unequivocal - then the universal will possess being not less but morethan some of the particulars, inasmuch as it is universals which comprisethe imperishable, particulars that tend to perish.
(3) Because the universal has a single meaning, we are not therefore com-pelled to suppose that in these examples it has being as a substance apartfrom its particulars - any more than we need make a similar supposition inthe other cases of unequivocal universal predication, viz. where the pred-icate signifies not substance but quality, essential relatedness, or action. Ifsuch a supposition is entertained, the blame rests not with the demonstra-tion but with the hearer.
(4) Demonstration is syllogism that proves the cause, i.e. the reasonedfact, and it is rather the commensurate universal than the particular which iscausative (as may be shown thus: that which possesses an attribute throughits own essential nature is itself the cause of the inherence, and the commen-surate universal is primary; hence the commensurate universal is the cause).Consequently commensurately universal demonstration is superior as more
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especially proving the cause, that is the reasoned fact.(5) Our search for the reason ceases, and we think that we know, when
the coming to be or existence of the fact before us is not due to the coming tobe or existence of some other fact, for the last step of a search thus conductedis eo ipso the end and limit of the problem. Thus: ‘Why did he come?’ ‘Toget the money - wherewith to pay a debt - that he might thereby do whatwas right.’ When in this regress we can no longer find an efficient or finalcause, we regard the last step of it as the end of the coming - or being orcoming to be - and we regard ourselves as then only having full knowledgeof the reason why he came.
If, then, all causes and reasons are alike in this respect, and if this is themeans to full knowledge in the case of final causes such as we have exempli-fied, it follows that in the case of the other causes also full knowledge is at-tained when an attribute no longer inheres because of something else. Thus,when we learn that exterior angles are equal to four right angles becausethey are the exterior angles of an isosceles, there still remains the question‘Why has isosceles this attribute?’ and its answer ‘Because it is a triangle,and a triangle has it because a triangle is a rectilinear figure.’ If rectilinearfigure possesses the property for no further reason, at this point we have fullknowledge - but at this point our knowledge has become commensuratelyuniversal, and so we conclude that commensurately universal demonstra-tion is superior.
(6) The more demonstration becomes particular the more it sinks into anindeterminate manifold, while universal demonstration tends to the simpleand determinate. But objects so far as they are an indeterminate manifold areunintelligible, so far as they are determinate, intelligible: they are thereforeintelligible rather in so far as they are universal than in so far as they are par-ticular. From this it follows that universals are more demonstrable: but sincerelative and correlative increase concomitantly, of the more demonstrablethere will be fuller demonstration. Hence the commensurate and universalform, being more truly demonstration, is the superior.
(7) Demonstration which teaches two things is preferable to demonstra-tion which teaches only one. He who possesses commensurately universaldemonstration knows the particular as well, but he who possesses particu-lar demonstration does not know the universal. So that this is an additionalreason for preferring commensurately universal demonstration. And thereis yet this further argument:
(8) Proof becomes more and more proof of the commensurate universalas its middle term approaches nearer to the basic truth, and nothing is sonear as the immediate premiss which is itself the basic truth. If, then, prooffrom the basic truth is more accurate than proof not so derived, demonstra-tion which depends more closely on it is more accurate than demonstration
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which is less closely dependent. But commensurately universal demonstra-tion is characterized by this closer dependence, and is therefore superior.Thus, if A had to be proved to inhere in D, and the middles were B and C,B being the higher term would render the demonstration which it mediatedthe more universal.
Some of these arguments, however, are dialectical. The clearest indica-tion of the precedence of commensurately universal demonstration is as fol-lows: if of two propositions, a prior and a posterior, we have a grasp of theprior, we have a kind of knowledge - a potential grasp - of the posterior aswell. For example, if one knows that the angles of all triangles are equal totwo right angles, one knows in a sense - potentially - that the isosceles anglesalso are equal to two right angles, even if one does not know that the isosce-les is a triangle; but to grasp this posterior proposition is by no means toknow the commensurate universal either potentially or actually. Moreover,commensurately universal demonstration is through and through intelligi-ble; particular demonstration issues in sense-perception.
Part 25 Affirmative demonstration excels negative
The preceding arguments constitute our defence of the superiority of com-mensurately universal to particular demonstration. That affirmative demon-stration excels negative may be shown as follows.
(1) We may assume the superiority ceteris paribus of the demonstrationwhich derives from fewer postulates or hypotheses - in short from fewerpremisses; for, given that all these are equally well known, where they arefewer knowledge will be more speedily acquired, and that is a desideratum.The argument implied in our contention that demonstration from fewer as-sumptions is superior may be set out in universal form as follows. Assumingthat in both cases alike the middle terms are known, and that middles whichare prior are better known than such as are posterior, we may suppose twodemonstrations of the inherence of A in E, the one proving it through themiddles B, C and D, the other through F and G. Then A-D is known to thesame degree as A-E (in the second proof), but A-D is better known than andprior to A-E (in the first proof); since A-E is proved through A-D, and theground is more certain than the conclusion.
Hence demonstration by fewer premisses is ceteris paribus superior.Now both affirmative and negative demonstration operate through threeterms and two premisses, but whereas the former assumes only that some-thing is, the latter assumes both that something is and that something else isnot, and thus operating through more kinds of premiss is inferior.
(2) It has been proved that no conclusion follows if both premisses arenegative, but that one must be negative, the other affirmative. So we are
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compelled to lay down the following additional rule: as the demonstrationexpands, the affirmative premisses must increase in number, but there can-not be more than one negative premiss in each complete proof. Thus, sup-pose no B is A, and all C is B. Then if both the premisses are to be againexpanded, a middle must be interposed. Let us interpose D between A andB, and E between B and C. Then clearly E is affirmatively related to B andC, while D is affirmatively related to B but negatively to A; for all B is D,but there must be no D which is A. Thus there proves to be a single nega-tive premiss, A-D. In the further prosyllogisms too it is the same, because inthe terms of an affirmative syllogism the middle is always related affirma-tively to both extremes; in a negative syllogism it must be negatively relatedonly to one of them, and so this negation comes to be a single negative pre-miss, the other premisses being affirmative. If, then, that through which atruth is proved is a better known and more certain truth, and if the negativeproposition is proved through the affirmative and not vice versa, affirma-tive demonstration, being prior and better known and more certain, will besuperior.
(3) The basic truth of demonstrative syllogism is the universal immediatepremiss, and the universal premiss asserts in affirmative demonstration andin negative denies: and the affirmative proposition is prior to and betterknown than the negative (since affirmation explains denial and is prior todenial, just as being is prior to not-being). It follows that the basic premissof affirmative demonstration is superior to that of negative demonstration,and the demonstration which uses superior basic premisses is superior.
(4) Affirmative demonstration is more of the nature of a basic form ofproof, because it is a sine qua non of negative demonstration.
Part 26 Negative demonstration and reductio adimpossibile
Since affirmative demonstration is superior to negative, it is clearly superioralso to reductio ad impossibile. We must first make certain what is the dif-ference between negative demonstration and reductio ad impossibile. Letus suppose that no B is A, and that all C is B: the conclusion necessarily fol-lows that no C is A. If these premisses are assumed, therefore, the negativedemonstration that no C is A is direct. Reductio ad impossibile, on the otherhand, proceeds as follows. Supposing we are to prove that does not inherein B, we have to assume that it does inhere, and further that B inheres in C,with the resulting inference that A inheres in C. This we have to suppose aknown and admitted impossibility; and we then infer that A cannot inherein B. Thus if the inherence of B in C is not questioned, A’s inherence in B isimpossible.
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The order of the terms is the same in both proofs: they differ according towhich of the negative propositions is the better known, the one denying A ofB or the one denying A of C. When the falsity of the conclusion is the betterknown, we use reductio ad impossible; when the major premiss of the syl-logism is the more obvious, we use direct demonstration. All the same theproposition denying A of B is, in the order of being, prior to that denyingA of C; for premisses are prior to the conclusion which follows from them,and ‘no C is A’ is the conclusion, ‘no B is A’ one of its premisses. For thedestructive result of reductio ad impossibile is not a proper conclusion, norare its antecedents proper premisses. On the contrary: the constituents ofsyllogism are premisses related to one another as whole to part or part towhole, whereas the premisses A-C and A-B are not thus related to one an-other. Now the superior demonstration is that which proceeds from betterknown and prior premisses, and while both these forms depend for credenceon the not-being of something, yet the source of the one is prior to that of theother. Therefore negative demonstration will have an unqualified superior-ity to reductio ad impossibile, and affirmative demonstration, being superiorto negative, will consequently be superior also to reductio ad impossibile.
Part 27 Exactness and priority in science
The science which is knowledge at once of the fact and of the reasoned fact,not of the fact by itself without the reasoned fact, is the more exact and theprior science.
A science such as arithmetic, which is not a science of properties qua in-hering in a substratum, is more exact than and prior to a science like harmon-ics, which is a science of pr,operties inhering in a substratum; and similarly ascience like arithmetic, which is constituted of fewer basic elements, is moreexact than and prior to geometry, which requires additional elements. WhatI mean by ‘additional elements’ is this: a unit is substance without position,while a point is substance with position; the latter contains an additionalelement.
Part 28 A single science is one whose domain is a singlegenus
A single science is one whose domain is a single genus, viz. all the subjectsconstituted out of the primary entities of the genus - i.e. the parts of this totalsubject - and their essential properties.
One science differs from another when their basic truths have neither acommon source nor are derived those of the one science from those the other.This is verified when we reach the indemonstrable premisses of a science, for
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they must be within one genus with its conclusions: and this again is verifiedif the conclusions proved by means of them fall within one genus - i.e. arehomogeneous.
Part 29 One can have several demonstrations of the sameconnexion
One can have several demonstrations of the same connexion not only bytaking from the same series of predication middles which are other than theimmediately cohering term e.g. by taking C, D, and F severally to prove A-B- but also by taking a middle from another series. Thus let A be change, Dalteration of a property, B feeling pleasure, and G relaxation. We can thenwithout falsehood predicate D of B and A of D, for he who is pleased suffersalteration of a property, and that which alters a property changes. Again, wecan predicate A of G without falsehood, and G of B; for to feel pleasure is torelax, and to relax is to change. So the conclusion can be drawn through mid-dles which are different, i.e. not in the same series - yet not so that neither ofthese middles is predicable of the other, for they must both be attributable tosome one subject.
A further point worth investigating is how many ways of proving thesame conclusion can be obtained by varying the figure.
Part 30 There is no knowledge by demonstration of chanceconjunctions
There is no knowledge by demonstration of chance conjunctions; for chanceconjunctions exist neither by necessity nor as general connexions but com-prise what comes to be as something distinct from these. Now demonstra-tion is concerned only with one or other of these two; for all reasoning pro-ceeds from necessary or general premisses, the conclusion being necessaryif the premisses are necessary and general if the premisses are general. Con-sequently, if chance conjunctions are neither general nor necessary, they arenot demonstrable.
Part 31 Knowledge of things demonstrable cannot beacquired by perception
Scientific knowledge is not possible through the act of perception. Even ifperception as a faculty is of ‘the such’ and not merely of a ‘this somewhat’,yet one must at any rate actually perceive a ‘this somewhat’, and at a defi-nite present place and time: but that which is commensurately universal andtrue in all cases one cannot perceive, since it is not ‘this’ and it is not ‘now’;
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if it were, it would not be commensurately universal - the term we apply towhat is always and everywhere. Seeing, therefore, that demonstrations arecommensurately universal and universals imperceptible, we clearly cannotobtain scientific knowledge by the act of perception: nay, it is obvious thateven if it were possible to perceive that a triangle has its angles equal to tworight angles, we should still be looking for a demonstration - we should not(as some say) possess knowledge of it; for perception must be of a particular,whereas scientific knowledge involves the recognition of the commensurateuniversal. So if we were on the moon, and saw the earth shutting out thesun’s light, we should not know the cause of the eclipse: we should per-ceive the present fact of the eclipse, but not the reasoned fact at all, since theact of perception is not of the commensurate universal. I do not, of course,deny that by watching the frequent recurrence of this event we might, af-ter tracking the commensurate universal, possess a demonstration, for thecommensurate universal is elicited from the several groups of singulars.
The commensurate universal is precious because it makes clear the cause;so that in the case of facts like these which have a cause other than them-selves universal knowledge is more precious than sense-perceptions andthan intuition. (As regards primary truths there is of course a different ac-count to be given.) Hence it is clear that knowledge of things demonstrablecannot be acquired by perception, unless the term perception is applied tothe possession of scientific knowledge through demonstration. Neverthelesscertain points do arise with regard to connexions to be proved which are re-ferred for their explanation to a failure in sense-perception: there are caseswhen an act of vision would terminate our inquiry, not because in seeing weshould be knowing, but because we should have elicited the universal fromseeing; if, for example, we saw the pores in the glass and the light passingthrough, the reason of the kindling would be clear to us because we shouldat the same time see it in each instance and intuit that it must be so in allinstances.
Part 32 Basic truths are not limited in number
All syllogisms cannot have the same basic truths. This may be shown first ofall by the following dialectical considerations. (1) Some syllogisms are trueand some false: for though a true inference is possible from false premisses,yet this occurs once only - I mean if A for instance, is truly predicable ofC, but B, the middle, is false, both A-B and B-C being false; nevertheless, ifmiddles are taken to prove these premisses, they will be false because everyconclusion which is a falsehood has false premisses, while true conclusionshave true premisses, and false and true differ in kind. Then again, (2) false-hoods are not all derived from a single identical set of principles: there are
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falsehoods which are the contraries of one another and cannot coexist, e.g.‘justice is injustice’, and ‘justice is cowardice’; ‘man is horse’, and ‘man isox’; ‘the equal is greater’, and ‘the equal is less.’ From established principleswe may argue the case as follows, confining ourselves therefore to true con-clusions. Not even all these are inferred from the same basic truths; many ofthem in fact have basic truths which differ generically and are not transfer-able; units, for instance, which are without position, cannot take the place ofpoints, which have position. The transferred terms could only fit in as mid-dle terms or as major or minor terms, or else have some of the other termsbetween them, others outside them.
Nor can any of the common axioms - such, I mean, as the law of excludedmiddle - serve as premisses for the proof of all conclusions. For the kinds ofbeing are different, and some attributes attach to quanta and some to qualiaonly; and proof is achieved by means of the common axioms taken in con-junction with these several kinds and their attributes.
Again, it is not true that the basic truths are much fewer than the conclu-sions, for the basic truths are the premisses, and the premisses are formedby the apposition of a fresh extreme term or the interposition of a fresh mid-dle. Moreover, the number of conclusions is indefinite, though the numberof middle terms is finite; and lastly some of the basic truths are necessary,others variable.
Looking at it in this way we see that, since the number of conclusions isindefinite, the basic truths cannot be identical or limited in number. If, on theother hand, identity is used in another sense, and it is said, e.g. ‘these andno other are the fundamental truths of geometry, these the fundamentals ofcalculation, these again of medicine’; would the statement mean anythingexcept that the sciences have basic truths? To call them identical becausethey are self-identical is absurd, since everything can be identified with ev-erything in that sense of identity. Nor again can the contention that all con-clusions have the same basic truths mean that from the mass of all possiblepremisses any conclusion may be drawn. That would be exceedingly naive,for it is not the case in the clearly evident mathematical sciences, nor is itpossible in analysis, since it is the immediate premisses which are the ba-sic truths, and a fresh conclusion is only formed by the addition of a newimmediate premiss: but if it be admitted that it is these primary immedi-ate premisses which are basic truths, each subject-genus will provide onebasic truth. If, however, it is not argued that from the mass of all possiblepremisses any conclusion may be proved, nor yet admitted that basic truthsdiffer so as to be generically different for each science, it remains to considerthe possibility that, while the basic truths of all knowledge are within onegenus, special premisses are required to prove special conclusions. But thatthis cannot be the case has been shown by our proof that the basic truths of
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things generically different themselves differ generically. For fundamentaltruths are of two kinds, those which are premisses of demonstration and thesubject-genus; and though the former are common, the latter - number, forinstance, and magnitude - are peculiar.
Part 33 Scientific knowledge differs from opinion
Scientific knowledge and its object differ from opinion and the object of opin-ion in that scientific knowledge is commensurately universal and proceedsby necessary connexions, and that which is necessary cannot be otherwise.So though there are things which are true and real and yet can be other-wise, scientific knowledge clearly does not concern them: if it did, thingswhich can be otherwise would be incapable of being otherwise. Nor arethey any concern of rational intuition - by rational intuition I mean an orig-inative source of scientific knowledge - nor of indemonstrable knowledge,which is the grasping of the immediate premiss. Since then rational intu-ition, science, and opinion, and what is revealed by these terms, are the onlythings that can be ‘true’, it follows that it is opinion that is concerned withthat which may be true or false, and can be otherwise: opinion in fact is thegrasp of a premiss which is immediate but not necessary. This view also fitsthe observed facts, for opinion is unstable, and so is the kind of being wehave described as its object. Besides, when a man thinks a truth incapableof being otherwise he always thinks that he knows it, never that he opinesit. He thinks that he opines when he thinks that a connexion, though actu-ally so, may quite easily be otherwise; for he believes that such is the properobject of opinion, while the necessary is the object of knowledge.
In what sense, then, can the same thing be the object of both opinion andknowledge? And if any one chooses to maintain that all that he knows hecan also opine, why should not opinion be knowledge? For he that knowsand he that opines will follow the same train of thought through the samemiddle terms until the immediate premisses are reached; because it is pos-sible to opine not only the fact but also the reasoned fact, and the reason isthe middle term; so that, since the former knows, he that opines also hasknowledge.
The truth perhaps is that if a man grasp truths that cannot be otherthan they are, in the way in which he grasps the definitions through whichdemonstrations take place, he will have not opinion but knowledge: if onthe other hand he apprehends these attributes as inhering in their subjects,but not in virtue of the subjects’ substance and essential nature possessesopinion and not genuine knowledge; and his opinion, if obtained throughimmediate premisses, will be both of the fact and of the reasoned fact; if notso obtained, of the fact alone. The object of opinion and knowledge is not
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quite identical; it is only in a sense identical, just as the object of true andfalse opinion is in a sense identical. The sense in which some maintain thattrue and false opinion can have the same object leads them to embrace manystrange doctrines, particularly the doctrine that what a man opines falselyhe does not opine at all. There are really many senses of ‘identical’, and inone sense the object of true and false opinion can be the same, in another itcannot. Thus, to have a true opinion that the diagonal is commensurate withthe side would be absurd: but because the diagonal with which they are bothconcerned is the same, the two opinions have objects so far the same: on theother hand, as regards their essential definable nature these objects differ.The identity of the objects of knowledge and opinion is similar. Knowledgeis the apprehension of, e.g. the attribute ‘animal’ as incapable of being oth-erwise, opinion the apprehension of ‘animal’ as capable of being otherwise- e.g. the apprehension that animal is an element in the essential nature ofman is knowledge; the apprehension of animal as predicable of man but notas an element in man’s essential nature is opinion: man is the subject in bothjudgements, but the mode of inherence differs.
This also shows that one cannot opine and know the same thing simulta-neously; for then one would apprehend the same thing as both capable andincapable of being otherwise - an impossibility. Knowledge and opinion ofthe same thing can co-exist in two different people in the sense we have ex-plained, but not simultaneously in the same person. That would involve aman’s simultaneously apprehending, e.g. (1) that man is essentially animal -i.e. cannot be other than animal - and (2) that man is not essentially animal,that is, we may assume, may be other than animal.
Further consideration of modes of thinking and their distribution underthe heads of discursive thought, intuition, science, art, practical wisdom,and metaphysical thinking, belongs rather partly to natural science, partlyto moral philosophy.
Part 34 Quick wit is a faculty of hitting upon the middleterm instantaneously
Quick wit is a faculty of hitting upon the middle term instantaneously. Itwould be exemplified by a man who saw that the moon has her brightside always turned towards the sun, and quickly grasped the cause of this,namely that she borrows her light from him; or observed somebody in con-versation with a man of wealth and divined that he was borrowing money,or that the friendship of these people sprang from a common enmity. In allthese instances he has seen the major and minor terms and then grasped thecauses, the middle terms.
Let A represent ‘bright side turned sunward’, B ‘lighted from the sun’, C
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the moon. Then B, ‘lighted from the sun’ is predicable of C, the moon, andA, ‘having her bright side towards the source of her light’, is predicable of B.So A is predicable of C through B.
Book II Posterior Analytics
Part 1 Four kinds of question
The kinds of question we ask are as many as the kinds of things which weknow. They are in fact four: - (1) whether the connexion of an attribute witha thing is a fact, (2) what is the reason of the connexion, (3) whether a thingexists, (4) What is the nature of the thing. Thus, when our question concernsa complex of thing and attribute and we ask whether the thing is thus orotherwise qualified - whether, e.g. the sun suffers eclipse or not - then weare asking as to the fact of a connexion. That our inquiry ceases with thediscovery that the sun does suffer eclipse is an indication of this; and if weknow from the start that the sun suffers eclipse, we do not inquire whetherit does so or not. On the other hand, when we know the fact we ask thereason; as, for example, when we know that the sun is being eclipsed andthat an earthquake is in progress, it is the reason of eclipse or earthquakeinto which we inquire.
Where a complex is concerned, then, those are the two questions we ask;but for some objects of inquiry we have a different kind of question to ask,such as whether there is or is not a centaur or a God. (By ‘is or is not’ I mean‘is or is not, without further qualification’; as opposed to ‘is or is not [e.g.]white’.) On the other hand, when we have ascertained the thing’s existence,we inquire as to its nature, asking, for instance, ‘what, then, is God?’ or‘what is man?’.
Part 2 Whether a connexion is a fact
These, then, are the four kinds of question we ask, and it is in the answers tothese questions that our knowledge consists.
Now when we ask whether a connexion is a fact, or whether a thing with-out qualification is, we are really asking whether the connexion or the thinghas a ‘middle’; and when we have ascertained either that the connexion is afact or that the thing is - i.e. ascertained either the partial or the unqualifiedbeing of the thing - and are proceeding to ask the reason of the connexion orthe nature of the thing, then we are asking what the ‘middle’ is.
(By distinguishing the fact of the connexion and the existence of the thingas respectively the partial and the unqualified being of the thing, I mean
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that if we ask ‘does the moon suffer eclipse?’, or ‘does the moon wax?’, thequestion concerns a part of the thing’s being; for what we are asking in suchquestions is whether a thing is this or that, i.e. has or has not this or thatattribute: whereas, if we ask whether the moon or night exists, the questionconcerns the unqualified being of a thing.)
We conclude that in all our inquiries we are asking either whether there isa ‘middle’ or what the ‘middle’ is: for the ‘middle’ here is precisely the cause,and it is the cause that we seek in all our inquiries. Thus, ‘Does the moon suf-fer eclipse?’ means ‘Is there or is there not a cause producing eclipse of themoon?’, and when we have learnt that there is, our next question is, ‘What,then, is this cause?’ for the cause through which a thing is - not is this orthat, i.e. has this or that attribute, but without qualification is - and the causethrough which it is-not is without qualification, but is this or that as havingsome essential attribute or some accident - are both alike the middle. By thatwhich is without qualification I mean the subject, e.g. moon or earth or sunor triangle; by that which a subject is (in the partial sense) I mean a property,e.g. eclipse, equality or inequality, interposition or non-interposition. For inall these examples it is clear that the nature of the thing and the reason of thefact are identical: the question ‘What is eclipse?’ and its answer ‘The priva-tion of the moon’s light by the interposition of the earth’ are identical withthe question ‘What is the reason of eclipse?’ or ‘Why does the moon suffereclipse?’ and the reply ‘Because of the failure of light through the earth’sshutting it out’. Again, for ‘What is a concord? A commensurate numericalratio of a high and a low note’, we may substitute ‘What ratio makes a highand a low note concordant? Their relation according to a commensurate nu-merical ratio.’ ‘Are the high and the low note concordant?’ is equivalent to‘Is their ratio commensurate?’; and when we find that it is commensurate,we ask ‘What, then, is their ratio?’.
Cases in which the ‘middle’ is sensible show that the object of our in-quiry is always the ‘middle’: we inquire, because we have not perceived it,whether there is or is not a ‘middle’ causing, e.g. an eclipse. On the otherhand, if we were on the moon we should not be inquiring either as to the factor the reason, but both fact and reason would be obvious simultaneously.For the act of perception would have enabled us to know the universal too;since, the present fact of an eclipse being evident, perception would then atthe same time give us the present fact of the earth‘s screening the sun’s light,and from this would arise the universal.
Thus, as we maintain, to know a thing’s nature is to know the reasonwhy it is; and this is equally true of things in so far as they are said withoutqualification to he as opposed to being possessed of some attribute, and inso far as they are said to be possessed of some attribute such as equal to rightangles, or greater or less.
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Part 3 How essential nature is revealed
It is clear, then, that all questions are a search for a ‘middle’. Let us nowstate how essential nature is revealed and in what way it can be reduced todemonstration; what definition is, and what things are definable. And let usfirst discuss certain difficulties which these questions raise, beginning whatwe have to say with a point most intimately connected with our immedi-ately preceding remarks, namely the doubt that might be felt as to whetheror not it is possible to know the same thing in the same relation, both bydefinition and by demonstration. It might, I mean, be urged that defini-tion is held to concern essential nature and is in every case universal andaffirmative; whereas, on the other hand, some conclusions are negative andsome are not universal; e.g. all in the second figure are negative, none inthe third are universal. And again, not even all affirmative conclusions inthe first figure are definable, e.g. ‘every triangle has its angles equal to tworight angles’. An argument proving this difference between demonstrationand definition is that to have scientific knowledge of the demonstrable isidentical with possessing a demonstration of it: hence if demonstration ofsuch conclusions as these is possible, there clearly cannot also be definitionof them. If there could, one might know such a conclusion also in virtue ofits definition without possessing the demonstration of it; for there is nothingto stop our having the one without the other.
Induction too will sufficiently convince us of this difference; for never yetby defining anything - essential attribute or accident - did we get knowledgeof it. Again, if to define is to acquire knowledge of a substance, at any ratesuch attributes are not substances.
It is evident, then, that not everything demonstrable can be defined.What then? Can everything definable be demonstrated, or not? There is oneof our previous arguments which covers this too. Of a single thing qua singlethere is a single scientific knowledge. Hence, since to know the demonstra-ble scientifically is to possess the demonstration of it, an impossible conse-quence will follow: - possession of its definition without its demonstrationwill give knowledge of the demonstrable.
Moreover, the basic premisses of demonstrations are definitions, and ithas already been shown that these will be found indemonstrable; either thebasic premisses will be demonstrable and will depend on prior premisses,and the regress will be endless; or the primary truths will be indemonstrabledefinitions.
But if the definable and the demonstrable are not wholly the same, maythey yet be partially the same? Or is that impossible, because there can be nodemonstration of the definable? There can be none, because definition is ofthe essential nature or being of something, and all demonstrations evidently
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posit and assume the essential nature - mathematical demonstrations, for ex-ample, the nature of unity and the odd, and all the other sciences likewise.Moreover, every demonstration proves a predicate of a subject as attachingor as not attaching to it, but in definition one thing is not predicated of an-other; we do not, e.g. predicate animal of biped nor biped of animal, noryet figure of plane - plane not being figure nor figure plane. Again, to proveessential nature is not the same as to prove the fact of a connexion. Now def-inition reveals essential nature, demonstration reveals that a given attributeattaches or does not attach to a given subject; but different things require dif-ferent demonstrations - unless the one demonstration is related to the otheras part to whole. I add this because if all triangles have been proved to pos-sess angles equal to two right angles, then this attribute has been proved toattach to isosceles; for isosceles is a part of which all triangles constitute thewhole. But in the case before us the fact and the essential nature are not sorelated to one another, since the one is not a part of the other.
So it emerges that not all the definable is demonstrable nor all the demon-strable definable; and we may draw the general conclusion that there is noidentical object of which it is possible to possess both a definition and ademonstration. It follows obviously that definition and demonstration areneither identical nor contained either within the other: if they were, theirobjects would be related either as identical or as whole and part.
Part 4 Whether syllogism is possible
So much, then, for the first stage of our problem. The next step is to raise thequestion whether syllogism - i.e. demonstration - of the definable nature ispossible or, as our recent argument assumed, impossible.
We might argue it impossible on the following grounds: - (a) syllogismproves an attribute of a subject through the middle term; on the other hand(b) its definable nature is both ‘peculiar’ to a subject and predicated of itas belonging to its essence. But in that case (1) the subject, its definition,and the middle term connecting them must be reciprocally predicable of oneanother; for if A is to C, obviously A is ‘peculiar’ to B and B to C - in fact allthree terms are ‘peculiar’ to one another: and further (2) if A inheres in theessence of all B and B is predicated universally of all C as belonging to C’sessence, A also must be predicated of C as belonging to its essence.
If one does not take this relation as thus duplicated - if, that is, A is predi-cated as being of the essence of B, but B is not of the essence of the subjects ofwhich it is predicated - A will not necessarily be predicated of C as belongingto its essence. So both premisses will predicate essence, and consequently Balso will be predicated of C as its essence. Since, therefore, both premissesdo predicate essence - i.e. definable form - C’s definable form will appear in
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the middle term before the conclusion is drawn.We may generalize by supposing that it is possible to prove the essential
nature of man. Let C be man, A man’s essential nature - two-footed animal,or aught else it may be. Then, if we are to syllogize, A must be predicatedof all B. But this premiss will be mediated by a fresh definition, which con-sequently will also be the essential nature of man. Therefore the argumentassumes what it has to prove, since B too is the essential nature of man. It is,however, the case in which there are only the two premisses - i.e. in whichthe premisses are primary and immediate - which we ought to investigate,because it best illustrates the point under discussion.
Thus they who prove the essential nature of soul or man or anythingelse through reciprocating terms beg the question. It would be begging thequestion, for example, to contend that the soul is that which causes its ownlife, and that what causes its own life is a self-moving number; for one wouldhave to postulate that the soul is a self-moving number in the sense of beingidentical with it. For if A is predicable as a mere consequent of B and B ofC, A will not on that account be the definable form of C: A will merely bewhat it was true to say of C. Even if A is predicated of all B inasmuch asB is identical with a species of A, still it will not follow: being an animal ispredicated of being a man - since it is true that in all instances to be humanis to be animal, just as it is also true that every man is an animal - but not asidentical with being man.
We conclude, then, that unless one takes both the premisses as predicat-ing essence, one cannot infer that A is the definable form and essence of C:but if one does so take them, in assuming B one will have assumed, beforedrawing the conclusion, what the definable form of C is; so that there hasbeen no inference, for one has begged the question.
Part 5 The method of division a not a process of inference
Nor, as was said in my formal logic, is the method of division a process of in-ference at all, since at no point does the characterization of the subject follownecessarily from the premising of certain other facts: division demonstratesas little as does induction. For in a genuine demonstration the conclusionmust not be put as a question nor depend on a concession, but must follownecessarily from its premisses, even if the respondent deny it. The definerasks ‘Is man animal or inanimate?’ and then assumes - he has not inferred- that man is animal. Next, when presented with an exhaustive division ofanimal into terrestrial and aquatic, he assumes that man is terrestrial. More-over, that man is the complete formula, terrestrial-animal, does not follownecessarily from the premisses: this too is an assumption, and equally an as-sumption whether the division comprises many differentiae or few. (Indeed
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as this method of division is used by those who proceed by it, even truthsthat can be inferred actually fail to appear as such.) For why should not thewhole of this formula be true of man, and yet not exhibit his essential natureor definable form? Again, what guarantee is there against an unessential ad-dition, or against the omission of the final or of an intermediate determinantof the substantial being?
The champion of division might here urge that though these lapses dooccur, yet we can solve that difficulty if all the attributes we assume are con-stituents of the definable form, and if, postulating the genus, we produceby division the requisite uninterrupted sequence of terms, and omit noth-ing; and that indeed we cannot fail to fulfil these conditions if what is to bedivided falls whole into the division at each stage, and none of it is omit-ted; and that this - the dividendum - must without further question be (ulti-mately) incapable of fresh specific division. Nevertheless, we reply, divisiondoes not involve inference; if it gives knowledge, it gives it in another way.Nor is there any absurdity in this: induction, perhaps, is not demonstrationany more than is division, et it does make evident some truth. Yet to state adefinition reached by division is not to state a conclusion: as, when conclu-sions are drawn without their appropriate middles, the alleged necessity bywhich the inference follows from the premisses is open to a question as tothe reason for it, so definitions reached by division invite the same question.
Thus to the question ‘What is the essential nature of man?’ the dividerreplies ‘Animal, mortal, footed, biped, wingless’; and when at each step heis asked ‘Why?’, he will say, and, as he thinks, proves by division, that allanimal is mortal or immortal: but such a formula taken in its entirety is notdefinition; so that even if division does demonstrate its formula, definitionat any rate does not turn out to be a conclusion of inference.
Part 6 The definable form must not fall within thesyllogism
Can we nevertheless actually demonstrate what a thing essentially and sub-stantially is, but hypothetically, i.e. by premising (1) that its definable formis constituted by the ‘peculiar’ attributes of its essential nature; (2) that suchand such are the only attributes of its essential nature, and that the completesynthesis of them is peculiar to the thing; and thus - since in this synthe-sis consists the being of the thing - obtaining our conclusion? Or is the truththat, since proof must be through the middle term, the definable form is oncemore assumed in this minor premiss too?
Further, just as in syllogizing we do not premise what syllogistic infer-ence is (since the premisses from which we conclude must be related aswhole and part), so the definable form must not fall within the syllogism
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but remain outside the premisses posited. It is only against a doubt as toits having been a syllogistic inference at all that we have to defend our ar-gument as conforming to the definition of syllogism. It is only when someone doubts whether the conclusion proved is the definable form that wehave to defend it as conforming to the definition of definable form whichwe assumed. Hence syllogistic inference must be possible even without theexpress statement of what syllogism is or what definable form is.
The following type of hypothetical proof also begs the question. If evil isdefinable as the divisible, and the definition of a thing’s contrary - if it hasone the contrary of the thing’s definition; then, if good is the contrary of eviland the indivisible of the divisible, we conclude that to be good is essentiallyto be indivisible. The question is begged because definable form is assumedas a premiss, and as a premiss which is to prove definable form. ‘But notthe same definable form’, you may object. That I admit, for in demonstra-tions also we premise that ‘this’ is predicable of ‘that’; but in this premiss theterm we assert of the minor is neither the major itself nor a term identical indefinition, or convertible, with the major.
Again, both proof by division and the syllogism just described are opento the question why man should be animal-biped-terrestrial and not merelyanimal and terrestrial, since what they premise does not ensure that thepredicates shall constitute a genuine unity and not merely belong to a singlesubject as do musical and grammatical when predicated of the same man.
Part 7 How then by definition shall we prove essentialnature?
How then by definition shall we prove substance or essential nature? Wecannot show it as a fresh fact necessarily following from the assumption ofpremisses admitted to be facts - the method of demonstration: we may notproceed as by induction to establish a universal on the evidence of groupsof particulars which offer no exception, because induction proves not whatthe essential nature of a thing is but that it has or has not some attribute.Therefore, since presumably one cannot prove essential nature by an appealto sense perception or by pointing with the finger, what other method re-mains?
To put it another way: how shall we by definition prove essential na-ture? He who knows what human - or any other - nature is, must know alsothat man exists; for no one knows the nature of what does not exist - onecan know the meaning of the phrase or name ‘goat-stag’ but not what theessential nature of a goat-stag is. But further, if definition can prove whatis the essential nature of a thing, can it also prove that it exists? And howwill it prove them both by the same process, since definition exhibits one
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single thing and demonstration another single thing, and what human na-ture is and the fact that man exists are not the same thing? Then too wehold that it is by demonstration that the being of everything must be proved- unless indeed to be were its essence; and, since being is not a genus, it isnot the essence of anything. Hence the being of anything as fact is matterfor demonstration; and this is the actual procedure of the sciences, for thegeometer assumes the meaning of the word triangle, but that it is possessedof some attribute he proves. What is it, then, that we shall prove in definingessential nature? Triangle? In that case a man will know by definition whata thing’s nature is without knowing whether it exists. But that is impossible.
Moreover it is clear, if we consider the methods of defining actually inuse, that definition does not prove that the thing defined exists: since evenif there does actually exist something which is equidistant from a centre, yetwhy should the thing named in the definition exist? Why, in other words,should this be the formula defining circle? One might equally well call itthe definition of mountain copper. For definitions do not carry a furtherguarantee that the thing defined can exist or that it is what they claim todefine: one can always ask why.
Since, therefore, to define is to prove either a thing’s essential nature orthe meaning of its name, we may conclude that definition, if it in no senseproves essential nature, is a set of words signifying precisely what a namesignifies. But that were a strange consequence; for (1) both what is not sub-stance and what does not exist at all would be definable, since even non-existents can be signified by a name: (2) all sets of words or sentences wouldbe definitions, since any kind of sentence could be given a name; so that weshould all be talking in definitions, and even the Iliad would be a defini-tion: (3) no demonstration can prove that any particular name means anyparticular thing: neither, therefore, do definitions, in addition to revealingthe meaning of a name, also reveal that the name has this meaning. It ap-pears then from these considerations that neither definition and syllogismnor their objects are identical, and further that definition neither demon-strates nor proves anything, and that knowledge of essential nature is not tobe obtained either by definition or by demonstration.
Part 8 Whether essential nature is demonstrable
We must now start afresh and consider which of these conclusions are soundand which are not, and what is the nature of definition, and whether essen-tial nature is in any sense demonstrable and definable or in none.
Now to know its essential nature is, as we said, the same as to know thecause of a thing’s existence, and the proof of this depends on the fact that athing must have a cause. Moreover, this cause is either identical with the es-
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sential nature of the thing or distinct from it; and if its cause is distinct fromit, the essential nature of the thing is either demonstrable or indemonstra-ble. Consequently, if the cause is distinct from the thing’s essential natureand demonstration is possible, the cause must be the middle term, and, theconclusion proved being universal and affirmative, the proof is in the firstfigure. So the method just examined of proving it through another essentialnature would be one way of proving essential nature, because a conclusioncontaining essential nature must be inferred through a middle which is anessential nature just as a ‘peculiar’ property must be inferred through a mid-dle which is a ‘peculiar’ property; so that of the two definable natures of asingle thing this method will prove one and not the other.
Now it was said before that this method could not amount to demonstra-tion of essential nature - it is actually a dialectical proof of it - so let us beginagain and explain by what method it can be demonstrated. When we areaware of a fact we seek its reason, and though sometimes the fact and thereason dawn on us simultaneously, yet we cannot apprehend the reason amoment sooner than the fact; and clearly in just the same way we cannot ap-prehend a thing’s definable form without apprehending that it exists, sincewhile we are ignorant whether it exists we cannot know its essential nature.Moreover we are aware whether a thing exists or not sometimes through ap-prehending an element in its character, and sometimes accidentally, as, forexample, when we are aware of thunder as a noise in the clouds, of eclipseas a privation of light, or of man as some species of animal, or of the soulas a self-moving thing. As often as we have accidental knowledge that thething exists, we must be in a wholly negative state as regards awareness ofits essential nature; for we have not got genuine knowledge even of its exis-tence, and to search for a thing’s essential nature when we are unaware thatit exists is to search for nothing. On the other hand, whenever we apprehendan element in the thing’s character there is less difficulty. Thus it follows thatthe degree of our knowledge of a thing’s essential nature is determined bythe sense in which we are aware that it exists. Let us then take the follow-ing as our first instance of being aware of an element in the essential nature.Let A be eclipse, C the moon, B the earth’s acting as a screen. Now to askwhether the moon is eclipsed or not is to ask whether or not B has occurred.But that is precisely the same as asking whether A has a defining condition;and if this condition actually exists, we assert that A also actually exists. Oragain we may ask which side of a contradiction the defining condition ne-cessitates: does it make the angles of a triangle equal or not equal to tworight angles? When we have found the answer, if the premisses are immedi-ate, we know fact and reason together; if they are not immediate, we knowthe fact without the reason, as in the following example: let C be the moon,A eclipse, B the fact that the moon fails to produce shadows though she is
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full and though no visible body intervenes between us and her. Then if B,failure to produce shadows in spite of the absence of an intervening body, isattributable A to C, and eclipse, is attributable to B, it is clear that the moonis eclipsed, but the reason why is not yet clear, and we know that eclipseexists, but we do not know what its essential nature is. But when it is clearthat A is attributable to C and we proceed to ask the reason of this fact, weare inquiring what is the nature of B: is it the earth’s acting as a screen, or themoon’s rotation or her extinction? But B is the definition of the other term,viz. in these examples, of the major term A; for eclipse is constituted by theearth acting as a screen. Thus, (1) ‘What is thunder?’ ‘The quenching of firein cloud’, and (2) ‘Why does it thunder?’ ‘Because fire is quenched in thecloud’, are equivalent. Let C be cloud, A thunder, B the quenching of fire.Then B is attributable to C, cloud, since fire is quenched in it; and A, noise,is attributable to B; and B is assuredly the definition of the major term A. Ifthere be a further mediating cause of B, it will be one of the remaining partialdefinitions of A.
We have stated then how essential nature is discovered and becomesknown, and we see that, while there is no syllogism - i.e. no demonstrativesyllogism - of essential nature, yet it is through syllogism, viz. demonstra-tive syllogism, that essential nature is exhibited. So we conclude that neithercan the essential nature of anything which has a cause distinct from itself beknown without demonstration, nor can it be demonstrated; and this is whatwe contended in our preliminary discussions.
Part 9 There are essential natures which are immediate
Now while some things have a cause distinct from themselves, others havenot. Hence it is evident that there are essential natures which are immediate,that is are basic premisses; and of these not only that they are but also whatthey are must be assumed or revealed in some other way. This too is theactual procedure of the arithmetician, who assumes both the nature and theexistence of unit. On the other hand, it is possible (in the manner explained)to exhibit through demonstration the essential nature of things which havea ‘middle’, i.e. a cause of their substantial being other than that being itself;but we do not thereby demonstrate it.
Part 10 Defining definition
Since definition is said to be the statement of a thing’s nature, obviously onekind of definition will be a statement of the meaning of the name, or of anequivalent nominal formula. A definition in this sense tells you, e.g. themeaning of the phrase ‘triangular character’. When we are aware that trian-
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gle exists, we inquire the reason why it exists. But it is difficult thus to learnthe definition of things the existence of which we do not genuinely know -the cause of this difficulty being, as we said before, that we only know ac-cidentally whether or not the thing exists. Moreover, a statement may bea unity in either of two ways, by conjunction, like the Iliad, or because itexhibits a single predicate as inhering not accidentally in a single subject.
That then is one way of defining definition. Another kind of definitionis a formula exhibiting the cause of a thing’s existence. Thus the former sig-nifies without proving, but the latter will clearly be a quasi-demonstrationof essential nature, differing from demonstration in the arrangement of itsterms. For there is a difference between stating why it thunders, and stat-ing what is the essential nature of thunder; since the first statement will be‘Because fire is quenched in the clouds’, while the statement of what the na-ture of thunder is will be ‘The noise of fire being quenched in the clouds’.Thus the same statement takes a different form: in one form it is continu-ous demonstration, in the other definition. Again, thunder can be defined asnoise in the clouds, which is the conclusion of the demonstration embody-ing essential nature. On the other hand the definition of immediates is anindemonstrable positing of essential nature.
We conclude then that definition is (a) an indemonstrable statement ofessential nature, or (b) a syllogism of essential nature differing from demon-stration in grammatical form, or (c) the conclusion of a demonstration givingessential nature.
Our discussion has therefore made plain (1) in what sense and of whatthings the essential nature is demonstrable, and in what sense and of whatthings it is not; (2) what are the various meanings of the term definition,and in what sense and of what things it proves the essential nature, and inwhat sense and of what things it does not; (3) what is the relation of defi-nition to demonstration, and how far the same thing is both definable anddemonstrable and how far it is not.
Part 11 We have scientific knowledge when we know thecause
We think we have scientific knowledge when we know the cause, and thereare four causes: (1) the definable form, (2) an antecedent which necessitates aconsequent, (3) the efficient cause, (4) the final cause. Hence each of these canbe the middle term of a proof, for (a) though the inference from antecedent tonecessary consequent does not hold if only one premiss is assumed - two isthe minimum - still when there are two it holds on condition that they havea single common middle term. So it is from the assumption of this singlemiddle term that the conclusion follows necessarily. The following example
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will also show this. Why is the angle in a semicircle a right angle? - or fromwhat assumption does it follow that it is a right angle? Thus, let A be rightangle, B the half of two right angles, C the angle in a semicircle. Then B isthe cause in virtue of which A, right angle, is attributable to C, the angle ina semicircle, since B=A and the other, viz. C,=B, for C is half of two rightangles. Therefore it is the assumption of B, the half of two right angles, fromwhich it follows that A is attributable to C, i.e. that the angle in a semicir-cle is a right angle. Moreover, B is identical with (b) the defining form ofA, since it is what A’s definition signifies. Moreover, the formal cause hasalready been shown to be the middle. (c) ‘Why did the Athenians becomeinvolved in the Persian war?’ means ‘What cause originated the waging ofwar against the Athenians?’ and the answer is, ‘Because they raided Sardiswith the Eretrians’, since this originated the war. Let A be war, B unpro-voked raiding, C the Athenians. Then B, unprovoked raiding, is true of C,the Athenians, and A is true of B, since men make war on the unjust aggres-sor. So A, having war waged upon them, is true of B, the initial aggressors,and B is true of C, the Athenians, who were the aggressors. Hence here toothe cause - in this case the efficient cause - is the middle term. (d) This is noless true where the cause is the final cause. E.g. why does one take a walkafter supper? For the sake of one’s health. Why does a house exist? For thepreservation of one’s goods. The end in view is in the one case health, inthe other preservation. To ask the reason why one must walk after supper isprecisely to ask to what end one must do it. Let C be walking after supper, Bthe non-regurgitation of food, A health. Then let walking after supper pos-sess the property of preventing food from rising to the orifice of the stomach,and let this condition be healthy; since it seems that B, the non-regurgitationof food, is attributable to C, taking a walk, and that A, health, is attributableto B. What, then, is the cause through which A, the final cause, inheres in C?It is B, the non-regurgitation of food; but B is a kind of definition of A, for Awill be explained by it. Why is B the cause of A’s belonging to C? Because tobe in a condition such as B is to be in health. The definitions must be trans-posed, and then the detail will become clearer. Incidentally, here the order ofcoming to be is the reverse of what it is in proof through the efficient cause:in the efficient order the middle term must come to be first, whereas in theteleological order the minor, C, must first take place, and the end in viewcomes last in time.
The same thing may exist for an end and be necessitated as well. Forexample, light shines through a lantern (1) because that which consists ofrelatively small particles necessarily passes through pores larger than thoseparticles - assuming that light does issue by penetration - and (2) for an end,namely to save us from stumbling. If then, a thing can exist through twocauses, can it come to be through two causes - as for instance if thunder be
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a hiss and a roar necessarily produced by the quenching of fire, and alsodesigned, as the Pythagoreans say, for a threat to terrify those that lie in Tar-tarus? Indeed, there are very many such cases, mostly among the processesand products of the natural world; for nature, in different senses of the term‘nature’, produces now for an end, now by necessity.
Necessity too is of two kinds. It may work in accordance with a thing’snatural tendency, or by constraint and in opposition to it; as, for instance,by necessity a stone is borne both upwards and downwards, but not by thesame necessity.
Of the products of man’s intelligence some are never due to chance ornecessity but always to an end, as for example a house or a statue; others,such as health or safety, may result from chance as well.
It is mostly in cases where the issue is indeterminate (though only wherethe production does not originate in chance, and the end is consequentlygood), that a result is due to an end, and this is true alike in nature or in art.By chance, on the other hand, nothing comes to be for an end.
Part 12 Middle term as cause
The effect may be still coming to be, or its occurrence may be past or future,yet the cause will be the same as when it is actually existent - for it is themiddle which is the cause - except that if the effect actually exists the causeis actually existent, if it is coming to be so is the cause, if its occurrence ispast the cause is past, if future the cause is future. For example, the moonwas eclipsed because the earth intervened, is becoming eclipsed because theearth is in process of intervening, will be eclipsed because the earth willintervene, is eclipsed because the earth intervenes.
To take a second example: assuming that the definition of ice is solidifiedwater, let C be water, A solidified, B the middle, which is the cause, namelytotal failure of heat. Then B is attributed to C, and A, solidification, to B: icewhen B is occurring, has formed when B has occurred, and will form whenB shall occur.
This sort of cause, then, and its effect come to be simultaneously whenthey are in process of becoming, and exist simultaneously when they actu-ally exist; and the same holds good when they are past and when they arefuture. But what of cases where they are not simultaneous? Can causes andeffects different from one another form, as they seem to us to form, a continu-ous succession, a past effect resulting from a past cause different from itself,a future effect from a future cause different from it, and an effect which iscoming-to-be from a cause different from and prior to it? Now on this the-ory it is from the posterior event that we reason (and this though these laterevents actually have their source of origin in previous events – a fact which
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shows that also when the effect is coming-to-be we still reason from the pos-terior event), and from the event we cannot reason (we cannot argue thatbecause an event A has occurred, therefore an event B has occurred subse-quently to A but still in the past - and the same holds good if the occurrenceis future) - cannot reason because, be the time interval definite or indefinite,it will never be possible to infer that because it is true to say that A occurred,therefore it is true to say that B, the subsequent event, occurred; for in theinterval between the events, though A has already occurred, the latter state-ment will be false. And the same argument applies also to future events; i.e.one cannot infer from an event which occurred in the past that a future eventwill occur. The reason of this is that the middle must be homogeneous, pastwhen the extremes are past, future when they are future, coming to be whenthey are coming-to-be, actually existent when they are actually existent; andthere cannot be a middle term homogeneous with extremes respectively pastand future. And it is a further difficulty in this theory that the time intervalcan be neither indefinite nor definite, since during it the inference will befalse. We have also to inquire what it is that holds events together so thatthe coming-to-be now occurring in actual things follows upon a past event.It is evident, we may suggest, that a past event and a present process cannotbe ‘contiguous’, for not even two past events can be ‘contiguous’. For pastevents are limits and atomic; so just as points are not ‘contiguous’ neither arepast events, since both are indivisible. For the same reason a past event and apresent process cannot be ‘contiguous’, for the process is divisible, the eventindivisible. Thus the relation of present process to past event is analogous tothat of line to point, since a process contains an infinity of past events. Thesequestions, however, must receive a more explicit treatment in our generaltheory of change.
The following must suffice as an account of the manner in which themiddle would be identical with the cause on the supposition that coming-to-be is a series of consecutive events: for in the terms of such a series toothe middle and major terms must form an immediate premiss; e.g. we arguethat, since C has occurred, therefore A occurred: and C‘s occurrence wasposterior, A’s prior; but C is the source of the inference because it is nearerto the present moment, and the starting-point of time is the present. We nextargue that, since D has occurred, therefore C occurred. Then we concludethat, since D has occurred, therefore A must have occurred; and the cause isC, for since D has occurred C must have occurred, and since C has occurredA must previously have occurred.
If we get our middle term in this way, will the series terminate in animmediate premiss, or since, as we said, no two events are ‘contiguous’, willa fresh middle term always intervene because there is an infinity of middles?No: though no two events are ‘contiguous’, yet we must start from a premiss
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consisting of a middle and the present event as major. The like is true offuture events too, since if it is true to say that D will exist, it must be a priortruth to say that A will exist, and the cause of this conclusion is C; for if D willexist, C will exist prior to D, and if C will exist, A will exist prior to it. Andhere too the same infinite divisibility might be urged, since future events arenot ‘contiguous’. But here too an immediate basic premiss must be assumed.And in the world of fact this is so: if a house has been built, then blocks musthave been quarried and shaped. The reason is that a house having been builtnecessitates a foundation having been laid, and if a foundation has been laidblocks must have been shaped beforehand. Again, if a house will be built,blocks will similarly be shaped beforehand; and proof is through the middlein the same way, for the foundation will exist before the house.
Now we observe in Nature a certain kind of circular process of coming-to-be; and this is possible only if the middle and extreme terms are recipro-cal, since conversion is conditioned by reciprocity in the terms of the proof.This - the convertibility of conclusions and premisses - has been proved inour early chapters, and the circular process is an instance of this. In actualfact it is exemplified thus: when the earth had been moistened an exhalationwas bound to rise, and when an exhalation had risen cloud was bound toform, and from the formation of cloud rain necessarily resulted and by thefall of rain the earth was necessarily moistened: but this was the starting-point, so that a circle is completed; for posit any one of the terms and anotherfollows from it, and from that another, and from that again the first.
Some occurrences are universal (for they are, or come-to-be what theyare, always and in ever case); others again are not always what they are butonly as a general rule: for instance, not every man can grow a beard, but itis the general rule. In the case of such connexions the middle term too mustbe a general rule. For if A is predicated universally of B and B of C, A toomust be predicated always and in every instance of C, since to hold in everyinstance and always is of the nature of the universal. But we have assumed aconnexion which is a general rule; consequently the middle term B must alsobe a general rule. So connexions which embody a general rule - i.e. whichexist or come to be as a general rule - will also derive from immediate basicpremisses.
Part 13 The elements predicated as constituting thedefinable form
We have already explained how essential nature is set out in the terms of ademonstration, and the sense in which it is or is not demonstrable or defin-able; so let us now discuss the method to be adopted in tracing the elementspredicated as constituting the definable form.
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Now of the attributes which inhere always in each several thing there aresome which are wider in extent than it but not wider than its genus (by at-tributes of wider extent mean all such as are universal attributes of each sev-eral subject, but in their application are not confined to that subject). whilean attribute may inhere in every triad, yet also in a subject not a triad - as be-ing inheres in triad but also in subjects not numbers at all - odd on the otherhand is an attribute inhering in every triad and of wider application (inher-ing as it does also in pentad), but which does not extend beyond the genus oftriad; for pentad is a number, but nothing outside number is odd. It is suchattributes which we have to select, up to the exact point at which they areseverally of wider extent than the subject but collectively coextensive withit; for this synthesis must be the substance of the thing. For example everytriad possesses the attributes number, odd, and prime in both senses, i.e. notonly as possessing no divisors, but also as not being a sum of numbers. This,then, is precisely what triad is, viz. a number, odd, and prime in the formerand also the latter sense of the term: for these attributes taken severally ap-ply, the first two to all odd numbers, the last to the dyad also as well as to thetriad, but, taken collectively, to no other subject. Now since we have shownabove that attributes predicated as belonging to the essential nature are nec-essary and that universals are necessary, and since the attributes which weselect as inhering in triad, or in any other subject whose attributes we se-lect in this way, are predicated as belonging to its essential nature, triad willthus possess these attributes necessarily. Further, that the synthesis of themconstitutes the substance of triad is shown by the following argument. If itis not identical with the being of triad, it must be related to triad as a genusnamed or nameless. It will then be of wider extent than triad - assuming thatwider potential extent is the character of a genus. If on the other hand thissynthesis is applicable to no subject other than the individual triads, it willbe identical with the being of triad, because we make the further assump-tion that the substance of each subject is the predication of elements in itsessential nature down to the last differentia characterizing the individuals.It follows that any other synthesis thus exhibited will likewise be identicalwith the being of the subject.
The author of a hand-book on a subject that is a generic whole shoulddivide the genus into its first infimae species-number e.g. into triad anddyad - and then endeavour to seize their definitions by the method we havedescribed - the definition, for example, of straight line or circle or right angle.After that, having established what the category is to which the subalterngenus belongs - quantity or quality, for instance - he should examine theproperties ‘peculiar’ to the species, working through the proximate commondifferentiae. He should proceed thus because the attributes of the generacompounded of the infimae species will be clearly given by the definitions
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of the species; since the basic element of them all is the definition, i.e. thesimple infirma species, and the attributes inhere essentially in the simpleinfimae species, in the genera only in virtue of these.
Divisions according to differentiae are a useful accessory to this method.What force they have as proofs we did, indeed, explain above, but thatmerely towards collecting the essential nature they may be of use we willproceed to show. They might, indeed, seem to be of no use at all, but ratherto assume everything at the start and to be no better than an initial assump-tion made without division. But, in fact, the order in which the attributesare predicated does make a difference – it matters whether we say animal-tame-biped, or biped-animal-tame. For if every definable thing consists oftwo elements and ‘animal-tame’ forms a unity, and again out of this and thefurther differentia man (or whatever else is the unity under construction)is constituted, then the elements we assume have necessarily been reachedby division. Again, division is the only possible method of avoiding theomission of any element of the essential nature. Thus, if the primary genusis assumed and we then take one of the lower divisions, the dividendumwill not fall whole into this division: e.g. it is not all animal which is ei-ther whole-winged or split-winged but all winged animal, for it is wingedanimal to which this differentiation belongs. The primary differentiation ofanimal is that within which all animal falls. The like is true of every othergenus, whether outside animal or a subaltern genus of animal; e.g. the pri-mary differentiation of bird is that within which falls every bird, of fish thatwithin which falls every fish. So, if we proceed in this way, we can be surethat nothing has been omitted: by any other method one is bound to omitsomething without knowing it.
To define and divide one need not know the whole of existence. Yet somehold it impossible to know the differentiae distinguishing each thing fromevery single other thing without knowing every single other thing; and onecannot, they say, know each thing without knowing its differentiae, sinceeverything is identical with that from which it does not differ, and otherthan that from which it differs. Now first of all this is a fallacy: not ev-ery differentia precludes identity, since many differentiae inhere in thingsspecifically identical, though not in the substance of these nor essentially.Secondly, when one has taken one’s differing pair of opposites and assumedthat the two sides exhaust the genus, and that the subject one seeks to defineis present in one or other of them, and one has further verified its presencein one of them; then it does not matter whether or not one knows all theother subjects of which the differentiae are also predicated. For it is obviousthat when by this process one reaches subjects incapable of further differ-entiation one will possess the formula defining the substance. Moreover, topostulate that the division exhausts the genus is not illegitimate if the op-
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posites exclude a middle; since if it is the differentia of that genus, anythingcontained in the genus must lie on one of the two sides.
In establishing a definition by division one should keep three objects inview: (1) the admission only of elements in the definable form, (2) the ar-rangement of these in the right order, (3) the omission of no such elements.The first is feasible because one can establish genus and differentia throughthe topic of the genus, just as one can conclude the inherence of an accidentthrough the topic of the accident. The right order will be achieved if theright term is assumed as primary, and this will be ensured if the term se-lected is predicable of all the others but not all they of it; since there must beone such term. Having assumed this we at once proceed in the same waywith the lower terms; for our second term will be the first of the remainder,our third the first of those which follow the second in a ‘contiguous’ series,since when the higher term is excluded, that term of the remainder which is‘contiguous’ to it will be primary, and so on. Our procedure makes it clearthat no elements in the definable form have been omitted: we have taken thedifferentia that comes first in the order of division, pointing out that animal,e.g. is divisible exhaustively into A and B, and that the subject accepts one ofthe two as its predicate. Next we have taken the differentia of the whole thusreached, and shown that the whole we finally reach is not further divisible -i.e. that as soon as we have taken the last differentia to form the concrete to-tality, this totality admits of no division into species. For it is clear that thereis no superfluous addition, since all these terms we have selected are ele-ments in the definable form; and nothing lacking, since any omission wouldhave to be a genus or a differentia. Now the primary term is a genus, andthis term taken in conjunction with its differentiae is a genus: moreover thedifferentiae are all included, because there is now no further differentia; ifthere were, the final concrete would admit of division into species, which,we said, is not the case.
To resume our account of the right method of investigation: We muststart by observing a set of similar - i.e. specifically identical - individuals,and consider what element they have in common. We must then apply thesame process to another set of individuals which belong to one species andare generically but not specifically identical with the former set. When wehave established what the common element is in all members of this sec-ond species, and likewise in members of further species, we should againconsider whether the results established possess any identity, and persevereuntil we reach a single formula, since this will be the definition of the thing.But if we reach not one formula but two or more, evidently the definien-dum cannot be one thing but must be more than one. I may illustrate mymeaning as follows. If we were inquiring what the essential nature of prideis, we should examine instances of proud men we know of to see what, as
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such, they have in common; e.g. if Alcibiades was proud, or Achilles andAjax were proud, we should find on inquiring what they all had in com-mon, that it was intolerance of insult; it was this which drove Alcibiadesto war, Achilles wrath, and Ajax to suicide. We should next examine othercases, Lysander, for example, or Socrates, and then if these have in commonindifference alike to good and ill fortune, I take these two results and inquirewhat common element have equanimity amid the vicissitudes of life and im-patience of dishonour. If they have none, there will be two genera of pride.Besides, every definition is always universal and commensurate: the physi-cian does not prescribe what is healthy for a single eye, but for all eyes or fora determinate species of eye. It is also easier by this method to define the sin-gle species than the universal, and that is why our procedure should be fromthe several species to the universal genera - this for the further reason toothat equivocation is less readily detected in genera than in infimae species.Indeed, perspicuity is essential in definitions, just as inferential movement isthe minimum required in demonstrations; and we shall attain perspicuity ifwe can collect separately the definition of each species through the group ofsingulars which we have established e.g. the definition of similarity not un-qualified but restricted to colours and to figures; the definition of acuteness,but only of sound - and so proceed to the common universal with a carefulavoidance of equivocation. We may add that if dialectical disputation mustnot employ metaphors, clearly metaphors and metaphorical expressions areprecluded in definition: otherwise dialectic would involve metaphors.
Part 14 The method of selection of analyses and divisions
In order to formulate the connexions we wish to prove we have to select ouranalyses and divisions. The method of selection consists in laying down thecommon genus of all our subjects of investigation - if e.g. they are animals,we lay down what the properties are which inhere in every animal. Theseestablished, we next lay down the properties essentially connected with thefirst of the remaining classes - e.g. if this first subgenus is bird, the essentialproperties of every bird - and so on, always characterizing the proximatesubgenus. This will clearly at once enable us to say in virtue of what char-acter the subgenera - man, e.g. or horse - possess their properties. Let A beanimal, B the properties of every animal, C D E various species of animal.Then it is clear in virtue of what character B inheres in D - namely A - andthat it inheres in C and E for the same reason: and throughout the remainingsubgenera always the same rule applies.
We are now taking our examples from the traditional class-names, butwe must not confine ourselves to considering these. We must collect anyother common character which we observe, and then consider with what
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species it is connected and what.properties belong to it. For example, as thecommon properties of horned animals we collect the possession of a thirdstomach and only one row of teeth. Then since it is clear in virtue of whatcharacter they possess these attributes - namely their horned character - thenext question is, to what species does the possession of horns attach?
Yet a further method of selection is by analogy: for we cannot find a sin-gle identical name to give to a squid‘s pounce, a fish’s spine, and an animal’sbone, although these too possess common properties as if there were a singleosseous nature.
Part 15 Identical and subordinate connexions
Some connexions that require proof are identical in that they possess anidentical ‘middle’ e.g. a whole group might be proved through ‘reciprocalreplacement’ - and of these one class are identical in genus, namely all thosewhose difference consists in their concerning different subjects or in theirmode of manifestation. This latter class may be exemplified by the ques-tions as to the causes respectively of echo, of reflection, and of the rainbow:the connexions to be proved which these questions embody are identicalgenerically, because all three are forms of repercussion; but specifically theyare different.
Other connexions that require proof only differ in that the ‘middle’ of theone is subordinate to the ‘middle’ of the other. For example: Why does theNile rise towards the end of the month? Because towards its close the monthis more stormy. Why is the month more stormy towards its close? Becausethe moon is waning. Here the one cause is subordinate to the other.
Part 16 Whether, when the effect is present the cause also ispresent
The question might be raised with regard to cause and effect whether whenthe effect is present the cause also is present; whether, for instance, if a plantsheds its leaves or the moon is eclipsed, there is present also the cause of theeclipse or of the fall of the leaves - the possession of broad leaves, let us say, inthe latter case, in the former the earth’s interposition. For, one might argue,if this cause is not present, these phenomena will have some other cause: ifit is present, its effect will be at once implied by it - the eclipse by the earth’sinterposition, the fall of the leaves by the possession of broad leaves; but ifso, they will be logically coincident and each capable of proof through theother. Let me illustrate: Let A be deciduous character, B the possession ofbroad leaves, C vine. Now if A inheres in B (for every broad-leaved plant isdeciduous), and B in C (every vine possessing broad leaves); then A inheres
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in C (every vine is deciduous), and the middle term B is the cause. But wecan also demonstrate that the vine has broad leaves because it is deciduous.Thus, let D be broad-leaved, E deciduous, F vine. Then E inheres in F (sinceevery vine is deciduous), and D in E (for every deciduous plant has broadleaves): therefore every vine has broad leaves, and the cause is its deciduouscharacter. If, however, they cannot each be the cause of the other (for cause isprior to effect, and the earth‘s interposition is the cause of the moon’s eclipseand not the eclipse of the interposition) - if, then, demonstration throughthe cause is of the reasoned fact and demonstration not through the causeis of the bare fact, one who knows it through the eclipse knows the fact ofthe earth’s interposition but not the reasoned fact. Moreover, that the eclipseis not the cause of the interposition, but the interposition of the eclipse, isobvious because the interposition is an element in the definition of eclipse,which shows that the eclipse is known through the interposition and notvice versa.
On the other hand, can a single effect have more than one cause? Onemight argue as follows: if the same attribute is predicable of more than onething as its primary subject, let B be a primary subject in which A inheres,and C another primary subject of A, and D and E primary subjects of B andC respectively. A will then inhere in D and E, and B will be the cause of A‘sinherence in D, C of A’s inherence in E. The presence of the cause thus neces-sitates that of the effect, but the presence of the effect necessitates the pres-ence not of all that may cause it but only of a cause which yet need not be thewhole cause. We may, however, suggest that if the connexion to be provedis always universal and commensurate, not only will the cause be a wholebut also the effect will be universal and commensurate. For instance, decid-uous character will belong exclusively to a subject which is a whole, and, ifthis whole has species, universally and commensurately to those species -i.e. either to all species of plant or to a single species. So in these universaland commensurate connexions the ‘middle’ and its effect must reciprocate,i.e. be convertible. Supposing, for example, that the reason why trees aredeciduous is the coagulation of sap, then if a tree is deciduous, coagulationmust be present, and if coagulation is present - not in any subject but in atree - then that tree must be deciduous.
Part 17 Must identical effects have identical causes?
Can the cause of an identical effect be not identical in every instance of theeffect but different? Or is that impossible? Perhaps it is impossible if theeffect is demonstrated as essential and not as inhering in virtue of a symp-tom or an accident - because the middle is then the definition of the majorterm - though possible if the demonstration is not essential. Now it is possi-
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ble to consider the effect and its subject as an accidental conjunction, thoughsuch conjunctions would not be regarded as connexions demanding scien-tific proof. But if they are accepted as such, the middle will correspond tothe extremes, and be equivocal if they are equivocal, generically one if theyare generically one. Take the question why proportionals alternate. Thecause when they are lines, and when they are numbers, is both different andidentical; different in so far as lines are lines and not numbers, identical as in-volving a given determinate increment. In all proportionals this is so. Again,the cause of likeness between colour and colour is other than that betweenfigure and figure; for likeness here is equivocal, meaning perhaps in the lat-ter case equality of the ratios of the sides and equality of the angles, in thecase of colours identity of the act of perceiving them, or something else ofthe sort. Again, connexions requiring proof which are identical by analogymiddles also analogous.
The truth is that cause, effect, and subject are reciprocally predicable inthe following way. If the species are taken severally, the effect is wider thanthe subject (e.g. the possession of external angles equal to four right angles isan attribute wider than triangle or are), but it is coextensive with the speciestaken collectively (in this instance with all figures whose external angles areequal to four right angles). And the middle likewise reciprocates, for themiddle is a definition of the major; which is incidentally the reason why allthe sciences are built up through definition.
We may illustrate as follows. Deciduous is a universal attribute of vine,and is at the same time of wider extent than vine; and of fig, and is of widerextent than fig: but it is not wider than but coextensive with the totality of thespecies. Then if you take the middle which is proximate, it is a definition ofdeciduous. I say that, because you will first reach a middle next the subject,and a premiss asserting it of the whole subject, and after that a middle - thecoagulation of sap or something of the sort - proving the connexion of thefirst middle with the major: but it is the coagulation of sap at the junction ofleaf-stalk and stem which defines deciduous.
If an explanation in formal terms of the inter-relation of cause and effectis demanded, we shall offer the following. Let A be an attribute of all B,and B of every species of D, but so that both A and B are wider than theirrespective subjects. Then B will be a universal attribute of each species ofD (since I call such an attribute universal even if it is not commensurate,and I call an attribute primary universal if it is commensurate, not with eachspecies severally but with their totality), and it extends beyond each of themtaken separately.
Thus, B is the cause of A’s inherence in the species of D: consequentlyA must be of wider extent than B; otherwise why should B be the cause ofA’s inherence in D any more than A the cause of B’s inherence in D? Now
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if A is an attribute of all the species of E, all the species of E will be unitedby possessing some common cause other than B: otherwise how shall we beable to say that A is predicable of all of which E is predicable, while E is notpredicable of all of which A can be predicated? I mean how can there failto be some special cause of A’s inherence in E, as there was of A’s inherencein all the species of D? Then are the species of E, too, united by possessingsome common cause? This cause we must look for. Let us call it C.
We conclude, then, that the same effect may have more than one cause,but not in subjects specifically identical. For instance, the cause of longevityin quadrupeds is lack of bile, in birds a dry constitution - or certainly some-thing different.
Part 18 Which of multiple middles is the cause?
If immediate premisses are not reached at once, and there is not merely onemiddle but several middles, i.e. several causes; is the cause of the property’sinherence in the several species the middle which is proximate to the pri-mary universal, or the middle which is proximate to the species? Clearlythe cause is that nearest to each species severally in which it is manifested,for that is the cause of the subject’s falling under the universal. To illustrateformally: C is the cause of B’s inherence in D; hence C is the cause of A‘sinherence in D, B of A’s inherence in C, while the cause of A’s inherence in Bis B itself.
Part 19 How basic premisses become known.
As regards syllogism and demonstration, the definition of, and the condi-tions required to produce each of them, are now clear, and with that also thedefinition of, and the conditions required to produce, demonstrative knowl-edge, since it is the same as demonstration. As to the basic premisses, howthey become known and what is the developed state of knowledge of themis made clear by raising some preliminary problems.
We have already said that scientific knowledge through demonstrationis impossible unless a man knows the primary immediate premisses. Butthere are questions which might be raised in respect of the apprehension ofthese immediate premisses: one might not only ask whether it is of the samekind as the apprehension of the conclusions, but also whether there is or isnot scientific knowledge of both; or scientific knowledge of the latter, and ofthe former a different kind of knowledge; and, further, whether the devel-oped states of knowledge are not innate but come to be in us, or are innatebut at first unnoticed. Now it is strange if we possess them from birth; forit means that we possess apprehensions more accurate than demonstration
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and fail to notice them. If on the other hand we acquire them and do not pre-viously possess them, how could we apprehend and learn without a basisof pre-existent knowledge? For that is impossible, as we used to find in thecase of demonstration. So it emerges that neither can we possess them frombirth, nor can they come to be in us if we are without knowledge of themto the extent of having no such developed state at all. Therefore we mustpossess a capacity of some sort, but not such as to rank higher in accuracythan these developed states. And this at least is an obvious characteristicof all animals, for they possess a congenital discriminative capacity whichis called sense-perception. But though sense-perception is innate in all an-imals, in some the sense-impression comes to persist, in others it does not.So animals in which this persistence does not come to be have either noknowledge at all outside the act of perceiving, or no knowledge of objects ofwhich no impression persists; animals in which it does come into being haveperception and can continue to retain the sense-impression in the soul: andwhen such persistence is frequently repeated a further distinction at oncearises between those which out of the persistence of such sense-impressionsdevelop a power of systematizing them and those which do not. So out ofsense-perception comes to be what we call memory, and out of frequentlyrepeated memories of the same thing develops experience; for a number ofmemories constitute a single experience. From experience again - i.e. fromthe universal now stabilized in its entirety within the soul, the one besidethe many which is a single identity within them all - originate the skill ofthe craftsman and the knowledge of the man of science, skill in the sphere ofcoming to be and science in the sphere of being.
We conclude that these states of knowledge are neither innate in a deter-minate form, nor developed from other higher states of knowledge, but fromsense-perception. It is like a rout in battle stopped by first one man makinga stand and then another, until the original formation has been restored. Thesoul is so constituted as to be capable of this process.
Let us now restate the account given already, though with insufficientclearness. When one of a number of logically indiscriminable particularshas made a stand, the earliest universal is present in the soul: for thoughthe act of sense-perception is of the particular, its content is universal - isman, for example, not the man Callias. A fresh stand is made among theserudimentary universals, and the process does not cease until the indivisibleconcepts, the true universals, are established: e.g. such and such a species ofanimal is a step towards the genus animal, which by the same process is astep towards a further generalization.
Thus it is clear that we must get to know the primary premisses by induc-tion; for the method by which even sense-perception implants the universalis inductive. Now of the thinking states by which we grasp truth, some are
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unfailingly true, others admit of error-opinion, for instance, and calculation,whereas scientific knowing and intuition are always true: further, no otherkind of thought except intuition is more accurate than scientific knowledge,whereas primary premisses are more knowable than demonstrations, and allscientific knowledge is discursive. From these considerations it follows thatthere will be no scientific knowledge of the primary premisses, and sinceexcept intuition nothing can be truer than scientific knowledge, it will be in-tuition that apprehends the primary premisses - a result which also followsfrom the fact that demonstration cannot be the originative source of demon-stration, nor, consequently, scientific knowledge of scientific knowledge.If,therefore, it is the only other kind of true thinking except scientific know-ing, intuition will be the originative source of scientific knowledge. And theoriginative source of science grasps the original basic premiss, while scienceas a whole is similarly
Volume 4 Book Part 0
Volume 5 TOPICS
Book I Preliminary considerations
Part 1 What reasoning is
Our treatise proposes to find a line of inquiry whereby we shall be able toreason from opinions that are generally accepted about every problem pro-pounded to us, and also shall ourselves, when standing up to an argument,avoid saying anything that will obstruct us. First, then, we must say whatreasoning is, and what its varieties are, in order to grasp dialectical reason-ing: for this is the object of our search in the treatise before us.
Now reasoning is an argument in which, certain things being laid down,something other than these necessarily comes about through them.
(a) It is a ‘demonstration’, when the premisses from which the reasoningstarts are true and primary, or are such that our knowledge of them hasoriginally come through premisses which are primary and true:
(b) reasoning, on the other hand, is ‘dialectical’, if it reasons from opin-ions that are generally accepted. Things are ‘true’ and ‘primary’ which arebelieved on the strength not of anything else but of themselves: for in regardto the first principles of science it is improper to ask any further for the whyand wherefore of them; each of the first principles should command beliefin and by itself. On the other hand, those opinions are ‘generally accepted’which are accepted by every one or by the majority or by the philosophers -i.e. by all, or by the majority, or by the most notable and illustrious of them.Again
(c), reasoning is ‘contentious’ if it starts from opinions that seem to begenerally accepted, but are not really such, or again if it merely seems toreason from opinions that are or seem to be generally accepted. For not everyopinion that seems to be generally accepted actually is generally accepted.For in none of the opinions which we call generally accepted is the illusionentirely on the surface, as happens in the case of the principles of contentiousarguments; for the nature of the fallacy in these is obvious immediately, and
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as a rule even to persons with little power of comprehension. So then, of thecontentious reasonings mentioned, the former really deserves to be called‘reasoning’ as well, but the other should be called ‘contentious reasoning’,but not ‘reasoning’, since it appears to reason, but does not really do so.Further
(d), besides all the reasonings we have mentioned there are the mis-reasonings that start from the premisses peculiar to the special sciences,as happens (for example) in the case of geometry and her sister sciences.For this form of reasoning appears to differ from the reasonings mentionedabove; the man who draws a false figure reasons from things that are neithertrue and primary, nor yet generally accepted. For he does not fall within thedefinition; he does not assume opinions that are received either by every oneor by the majority or by philosophers - that is to say, by all, or by most, or bythe most illustrious of them - but he conducts his reasoning upon assump-tions which, though appropriate to the science in question, are not true; forhe effects his mis-reasoning either by describing the semicircles wrongly orby drawing certain lines in a way in which they could not be drawn.
The foregoing must stand for an outline survey of the species of reason-ing. In general, in regard both to all that we have already discussed and tothose which we shall discuss later, we may remark that that amount of dis-tinction between them may serve, because it is not our purpose to give theexact definition of any of them; we merely want to describe them in outline;we consider it quite enough from the point of view of the line of inquirybefore us to be able to recognize each of them in some sort of way.
Part 2 For what purposes the treatise is useful
Next in order after the foregoing, we must say for how many and for whatpurposes the treatise is useful. They are three - intellectual training, casualencounters, and the philosophical sciences. That it is useful as a training isobvious on the face of it. The possession of a plan of inquiry will enableus more easily to argue about the subject proposed. For purposes of casualencounters, it is useful because when we have counted up the opinions heldby most people, we shall meet them on the ground not of other people’sconvictions but of their own, while we shift the ground of any argumentthat they appear to us to state unsoundly. For the study of the philosophicalsciences it is useful, because the ability to raise searching difficulties on bothsides of a subject will make us detect more easily the truth and error aboutthe several points that arise. It has a further use in relation to the ultimatebases of the principles used in the several sciences. For it is impossible todiscuss them at all from the principles proper to the particular science inhand, seeing that the principles are the prius of everything else: it is through
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the opinions generally held on the particular points that these have to bediscussed, and this task belongs properly, or most appropriately, to dialectic:for dialectic is a process of criticism wherein lies the path to the principles ofall inquiries.
Part 3 On the way to proceed
We shall be in perfect possession of the way to proceed when we are in aposition like that which we occupy in regard to rhetoric and medicine andfaculties of that kind: this means the doing of that which we choose with thematerials that are available. For it is not every method that the rhetoricianwill employ to persuade, or the doctor to heal; still, if he omits none of theavailable means, we shall say that his grasp of the science is adequate.
Part 4 Of what parts our inquiry consists
First, then, we must see of what parts our inquiry consists. Now if we wereto grasp (a) with reference to how many, and what kind of, things argu-ments take place, and with what materials they start, and (h) how we are tobecome well supplied with these, we should have sufficiently won our goal.Now the materials with which arguments start are equal in number, and areidentical, with the subjects on which reasonings take place. For argumentsstart with ‘propositions’, while the subjects on which reasonings take placeare ‘problems’. Now every proposition and every problem indicates either agenus or a peculiarity or an accident - for the differentia too, applying as itdoes to a class (or genus), should be ranked together with the genus. Since,however, of what is peculiar to anything part signifies its essence, while partdoes not, let us divide the ‘peculiar’ into both the aforesaid parts, and callthat part which indicates the essence a ‘definition’, while of the remainderlet us adopt the terminology which is generally current about these things,and speak of it as a ‘property’. What we have said, then, makes it clear thataccording to our present division, the elements turn out to be four, all told,namely either property or definition or genus or accident. Do not let anyone suppose us to mean that each of these enunciated by itself constitutes aproposition or problem, but only that it is from these that both problems andpropositions are formed. The difference between a problem and a proposi-tion is a difference in the turn of the phrase. For if it be put in this way,‘"An animal that walks on two feet" is the definition of man, is it not?’ or‘"Animal" is the genus of man, is it not?’ the result is a proposition: but ifthus, ‘Is "an animal that walks on two feet" a definition of man or no?’ [or‘Is "animal" his genus or no?’] the result is a problem. Similarly too in othercases. Naturally, then, problems and propositions are equal in number: for
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out of every proposition you will make a problem if you change the turn ofthe phrase.
Part 5 Definition, property, genus, and accident
We must now say what are ‘definition’, ‘property’, ‘genus’, and ‘accident’. A‘definition’ is a phrase signifying a thing’s essence. It is rendered in the formeither of a phrase in lieu of a term, or of a phrase in lieu of another phrase; forit is sometimes possible to define the meaning of a phrase as well. Peoplewhose rendering consists of a term only, try it as they may, clearly do notrender the definition of the thing in question, because a definition is alwaysa phrase of a certain kind. One may, however, use the word ‘definitory’also of such a remark as ‘The "becoming" is "beautiful"’, and likewise alsoof the question, ‘Are sensation and knowledge the same or different?’, forargument about definitions is mostly concerned with questions of samenessand difference. In a word we may call ‘definitory’ everything that falls underthe same branch of inquiry as definitions; and that all the above-mentionedexamples are of this character is clear on the face of them. For if we are able toargue that two things are the same or are different, we shall be well suppliedby the same turn of argument with lines of attack upon their definitions aswell: for when we have shown that they are not the same we shall havedemolished the definition. Observe, please, that the converse of this laststatement does not hold: for to show that they are the same is not enoughto establish a definition. To show, however, that they are not the same isenough of itself to overthrow it.
A ‘property’ is a predicate which does not indicate the essence of a thing,but yet belongs to that thing alone, and is predicated convertibly of it. Thusit is a property of man to-be-capable of learning grammar: for if A be aman, then he is capable of learning grammar, and if he be capable of learn-ing grammar, he is a man. For no one calls anything a ‘property’ whichmay possibly belong to something else, e.g. ‘sleep’ in the case of man, eventhough at a certain time it may happen to belong to him alone. That is to say,if any such thing were actually to be called a property, it will be called not a‘property’ absolutely, but a ‘temporary’ or a ‘relative’ property: for ‘being onthe right hand side’ is a temporary property, while ‘two-footed’ is in pointof fact ascribed as a property in certain relations; e.g. it is a property of manrelatively to a horse and a dog. That nothing which may belong to anythingelse than A is a convertible predicate of A is clear: for it does not necessarilyfollow that if something is asleep it is a man.
A ‘genus’ is what is predicated in the category of essence of a numberof things exhibiting differences in kind. We should treat as predicates in thecategory of essence all such things as it would be appropriate to mention
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in reply to the question, ‘What is the object before you?’; as, for example,in the case of man, if asked that question, it is appropriate to say ‘He is ananimal’. The question, ‘Is one thing in the same genus as another or in adifferent one?’ is also a ‘generic’ question; for a question of that kind as wellfalls under the same branch of inquiry as the genus: for having argued that‘animal’ is the genus of man, and likewise also of ox, we shall have arguedthat they are in the same genus; whereas if we show that it is the genus ofthe one but not of the other, we shall have argued that these things are notin the same genus.
An ‘accident’ is (i) something which, though it is none of the foregoing -i.e. neither a definition nor a property nor a genus yet belongs to the thing:(something which may possibly either belong or not belong to any one andthe self-same thing, as (e.g.) the ‘sitting posture’ may belong or not belongto some self-same thing. Likewise also ‘whiteness’, for there is nothing toprevent the same thing being at one time white, and at another not white.Of the definitions of accident the second is the better: for if he adopts thefirst, any one is bound, if he is to understand it, to know already what ‘def-inition’ and ‘genus’ and ‘property’ are, whereas the second is sufficient ofitself to tell us the essential meaning of the term in question. To Accidentare to be attached also all comparisons of things together, when expressedin language that is drawn in any kind of way from what happens (accidit) tobe true of them; such as, for example, the question, ‘Is the honourable or theexpedient preferable?’ and ‘Is the life of virtue or the life of self-indulgencethe pleasanter?’, and any other problem which may happen to be phrasedin terms like these. For in all such cases the question is ‘to which of the twodoes the predicate in question happen (accidit) to belong more closely?’ It isclear on the face of it that there is nothing to prevent an accident from becom-ing a temporary or relative property. Thus the sitting posture is an accident,but will be a temporary property, whenever a man is the only person sitting,while if he be not the only one sitting, it is still a property relatively to thosewho are not sitting. So then, there is nothing to prevent an accident from be-coming both a relative and a temporary property; but a property absolutelyit will never be.
Part 6 Remarks made in criticism of definitions
We must not fail to observe that all remarks made in criticism of a ‘prop-erty’ and ‘genus’ and ‘accident’ will be applicable to ‘definitions’ as well.For when we have shown that the attribute in question fails to belong onlyto the term defined, as we do also in the case of a property, or that the genusrendered in the definition is not the true genus, or that any of the thingsmentioned in the phrase used does not belong, as would be remarked also
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in the case of an accident, we shall have demolished the definition; so that,to use the phrase previously employed, all the points we have enumeratedmight in a certain sense be called ‘definitory’. But we must not on this ac-count expect to find a single line of inquiry which will apply universally tothem all: for this is not an easy thing to find, and, even were one found, itwould be very obscure indeed, and of little service for the treatise before us.Rather, a special plan of inquiry must be laid down for each of the classeswe have distinguished, and then, starting from the rules that are appropri-ate in each case, it will probably be easier to make our way right throughthe task before us. So then, as was said before, we must outline a divisionof our subject, and other questions we must relegate each to the particularbranch to which it most naturally belongs, speaking of them as ‘definitory’and ‘generic’ questions. The questions I mean have practically been alreadyassigned to their several branches.
Part 7 Senses borne by the term ’Sameness’
First of all we must define the number of senses borne by the term ‘Same-ness’. Sameness would be generally regarded as falling, roughly speaking,into three divisions. We generally apply the term numerically or specificallyor generically - numerically in cases where there is more than one name butonly one thing, e.g. ‘doublet’ and ‘cloak’; specifically, where there is morethan one thing, but they present no differences in respect of their species,as one man and another, or one horse and another: for things like this thatfall under the same species are said to be ‘specifically the same’. Similarly,too, those things are called generically the same which fall under the samegenus, such as a horse and a man. It might appear that the sense in whichwater from the same spring is called ‘the same water’ is somehow differentand unlike the senses mentioned above: but really such a case as this oughtto be ranked in the same class with the things that in one way or another arecalled ‘the same’ in view of unity of species. For all such things seem to beof one family and to resemble one another. For the reason why all water issaid to be specifically the same as all other water is because of a certain like-ness it bears to it, and the only difference in the case of water drawn fromthe same spring is this, that the likeness is more emphatic: that is why wedo not distinguish it from the things that in one way or another are called‘the same’ in view of unity of species. It is generally supposed that the term‘the same’ is most used in a sense agreed on by every one when applied towhat is numerically one. But even so, it is apt to be rendered in more thanone sense; its most literal and primary use is found whenever the samenessis rendered in reference to an alternative name or definition, as when a cloakis said to be the same as a doublet, or an animal that walks on two feet is
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said to be the same as a man: a second sense is when it is rendered in refer-ence to a property, as when what can acquire knowledge is called the sameas a man, and what naturally travels upward the same as fire: while a thirduse is found when it is rendered in reference to some term drawn from Ac-cident, as when the creature who is sitting, or who is musical, is called thesame as Socrates. For all these uses mean to signify numerical unity. Thatwhat I have just said is true may be best seen where one form of appellationis substituted for another. For often when we give the order to call one ofthe people who are sitting down, indicating him by name, we change ourdescription, whenever the person to whom we give the order happens notto understand us; he will, we think, understand better from some accidentalfeature; so we bid him call to us ‘the man who is sitting’ or ‘who is convers-ing over there’ - clearly supposing ourselves to be indicating the same objectby its name and by its accident.
Part 8 Confirming the senses of ’definition’
Of ‘sameness’ then, as has been said, three senses are to be distinguished.Now one way to confirm that the elements mentioned above are those out ofwhich and through which and to which arguments proceed, is by induction:for if any one were to survey propositions and problems one by one, it wouldbe seen that each was formed either from the definition of something orfrom its property or from its genus or from its accident. Another way toconfirm it is through reasoning. For every predicate of a subject must ofnecessity be either convertible with its subject or not: and if it is convertible,it would be its definition or property, for if it signifies the essence, it is thedefinition; if not, it is a property: for this was what a property is, viz. whatis predicated convertibly, but does not signify the essence. If, on the otherhand, it is not predicated convertibly of the thing, it either is or is not one ofthe terms contained in the definition of the subject: and if it be one of thoseterms, then it will be the genus or the differentia, inasmuch as the definitionconsists of genus and differentiae; whereas, if it be not one of those terms,clearly it would be an accident, for accident was said to be what belongs asan attribute to a subject without being either its definition or its genus or aproperty.
Part 9 Categories of predicate
Next, then, we must distinguish between the classes of predicates in whichthe four orders in question are found. These are ten in number: Essence,Quantity, Quality, Relation, Place, Time, Position, State, Activity, Passivity.For the accident and genus and property and definition of anything will al-
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ways be in one of these categories: for all the propositions found throughthese signify either something’s essence or its quality or quantity or someone of the other types of predicate. It is clear, too, on the face of it thatthe man who signifies something’s essence signifies sometimes a substance,sometimes a quality, sometimes some one of the other types of predicate.For when man is set before him and he says that what is set there is ‘a man’or ‘an animal’, he states its essence and signifies a substance; but when awhite colour is set before him and he says that what is set there is ‘white’ oris ‘a colour’, he states its essence and signifies a quality. Likewise, also, ifa magnitude of a cubit be set before him and he says that what is set thereis a magnitude of a cubit, he will be describing its essence and signifying aquantity. Likewise, also, in the other cases: for each of these kinds of pred-icate, if either it be asserted of itself, or its genus be asserted of it, signifiesan essence: if, on the other hand, one kind of predicate is asserted of anotherkind, it does not signify an essence, but a quantity or a quality or one of theother kinds of predicate. Such, then, and so many, are the subjects on whicharguments take place, and the materials with which they start. How we areto acquire them, and by what means we are to become well supplied withthem, falls next to be told.
Part 10 Dialectical propositions and problems
First, then, a definition must be given of a ‘dialectical proposition’ and a ‘di-alectical problem’. For it is not every proposition nor yet every problem thatis to be set down as dialectical: for no one in his senses would make a propo-sition of what no one holds, nor yet make a problem of what is obvious toeverybody or to most people: for the latter admits of no doubt, while to theformer no one would assent. Now a dialectical proposition consists in ask-ing something that is held by all men or by most men or by the philosophers,i.e. either by all, or by most, or by the most notable of these, provided it benot contrary to the general opinion; for a man would probably assent to theview of the philosophers, if it be not contrary to the opinions of most men.Dialectical propositions also include views which are like those generally ac-cepted; also propositions which contradict the contraries of opinions that aretaken to be generally accepted, and also all opinions that are in accordancewith the recognized arts. Thus, supposing it to be a general opinion that theknowledge of contraries is the same, it might probably pass for a generalopinion also that the perception of contraries is the same: also, supposingit to be a general opinion that there is but one single science of grammar, itmight pass for a general opinion that there is but one science of flute-playingas well, whereas, if it be a general opinion that there is more than one sci-ence of grammar, it might pass for a general opinion that there is more than
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one science of flute-playing as well: for all these seem to be alike and akin.Likewise, also, propositions contradicting the contraries of general opinionswill pass as general opinions: for if it be a general opinion that one oughtto do good to one’s friends, it will also be a general opinion that one oughtnot to do them harm. Here, that one ought to do harm to one’s friends iscontrary to the general view, and that one ought not to do them harm is thecontradictory of that contrary. Likewise also, if one ought to do good toone’s friends, one ought not to do good to one’s enemies: this too is the con-tradictory of the view contrary to the general view; the contrary being thatone ought to do good to one’s enemies. Likewise, also, in other cases. Also,on comparison, it will look like a general opinion that the contrary predicatebelongs to the contrary subject: e.g. if one ought to do good to one’s friends,one ought also to do evil to one’s enemies. it might appear also as if doinggood to one’s friends were a contrary to doing evil to one’s enemies: butwhether this is or is not so in reality as well will be stated in the course of thediscussion upon contraries. Clearly also, all opinions that are in accordancewith the arts are dialectical propositions; for people are likely to assent tothe views held by those who have made a study of these things, e.g. on aquestion of medicine they will agree with the doctor, and on a question ofgeometry with the geometrician; and likewise also in other cases.
Part 11 Theses
A dialectical problem is a subject of inquiry that contributes either to choiceand avoidance, or to truth and knowledge, and that either by itself, or as ahelp to the solution of some other such problem. It must, moreover, be some-thing on which either people hold no opinion either way, or the masses holda contrary opinion to the philosophers, or the philosophers to the masses,or each of them among themselves. For some problems it is useful to knowwith a view to choice or avoidance, e.g. whether pleasure is to be chosenor not, while some it is useful to know merely with a view to knowledge,e.g. whether the universe is eternal or not: others, again, are not useful inand by themselves for either of these purposes, but yet help us in regardto some such problems; for there are many things which we do not wish toknow in and by themselves, but for the sake of other things, in order thatthrough them we may come to know something else. Problems also includequestions in regard to which reasonings conflict (the difficulty then beingwhether so-and so is so or not, there being convincing arguments for bothviews); others also in regard to which we have no argument because they areso vast, and we find it difficult to give our reasons, e.g. the question whetherthe universe is eternal or no: for into questions of that kind too it is possibleto inquire.
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Problems, then, and propositions are to be defined as aforesaid. A ‘thesis’is a supposition of some eminent philosopher that conflicts with the generalopinion; e.g. the view that contradiction is impossible, as Antisthenes said;or the view of Heraclitus that all things are in motion; or that Being is one, asMelissus says: for to take notice when any ordinary person expresses viewscontrary to men’s usual opinions would be silly. Or it may be a view aboutwhich we have a reasoned theory contrary to men’s usual opinions, e.g. theview maintained by the sophists that what is need not in every case eitherhave come to be or be eternal: for a musician who is a grammarian ‘is’ sowithout ever having ‘come to be’ so, or being so eternally. For even if a mandoes not accept this view, he might do so on the ground that it is reasonable.
Now a ‘thesis’ also is a problem, though a problem is not always a thesis,inasmuch as some problems are such that we have no opinion about themeither way. That a thesis, however, also forms a problem, is clear: for itfollows of necessity from what has been said that either the mass of mendisagree with the philosophers about the thesis, or that the one or the otherclass disagree among themselves, seeing that the thesis is a supposition inconflict with general opinion. Practically all dialectical problems indeed arenow called ‘theses’. But it should make no difference whichever descriptionis used; for our object in thus distinguishing them has not been to create aterminology, but to recognize what differences happen to be found betweenthem.
Not every problem, nor every thesis, should be examined, but only onewhich might puzzle one of those who need argument, not punishment orperception. For people who are puzzled to know whether one ought to hon-our the gods and love one’s parents or not need punishment, while thosewho are puzzled to know whether snow is white or not need perception.The subjects should not border too closely upon the sphere of demonstra-tion, nor yet be too far removed from it: for the former cases admit of nodoubt, while the latter involve difficulties too great for the art of the trainer.
Part 12 Species of dialectical arguments
Having drawn these definitions, we must distinguish how many speciesthere are of dialectical arguments. There is on the one hand Induction, onthe other Reasoning. Now what reasoning is has been said before: inductionis a passage from individuals to universals, e.g. the argument that suppos-ing the skilled pilot is the most effective, and likewise the skilled charioteer,then in general the skilled man is the best at his particular task. Inductionis the more convincing and clear: it is more readily learnt by the use of thesenses, and is applicable generally to the mass of men, though reasoning ismore forcible and effective against contradictious people.
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Part 13 Four sources of arguments
The classes, then, of things about which, and of things out of which, argu-ments are constructed, are to be distinguished in the way we have said be-fore. The means whereby we are to become well supplied with reasoningsare four:
(1) the securing of propositions;(2) the power to distinguish in how many senses particular expression is
used;(3) the discovery of the differences of things;(4) the investigation of likeness. The last three, as well, are in a certain
sense propositions: for it is possible to make a proposition corresponding toeach of them, e.g.
(1) ‘The desirable may mean either the honourable or the pleasant or theexpedient’; and
(2) Sensation differs from knowledge in that the latter may be recoveredagain after it has been lost, while the former cannot; and
(3) The relation of the healthy to health is like that of the vigorous tovigour. The first proposition depends upon the use of one term in severalsenses, the second upon the differences of things, the third upon their like-nesses.
Part 14 Three divisions of propositions and problems
Propositions should be selected in a number of ways corresponding to thenumber of distinctions drawn in regard to the proposition: thus one mayfirst take in hand the opinions held by all or by most men or by the philoso-phers, i.e. by all, or most, or the most notable of them; or opinions contraryto those that seem to be generally held; and, again, all opinions that are inaccordance with the arts. We must make propositions also of the contradic-tories of opinions contrary to those that seem to be generally held, as waslaid down before. It is useful also to make them by selecting not only thoseopinions that actually are accepted, but also those that are like these, e.g.‘The perception of contraries is the same’ - the knowledge of them being so -and ‘we see by admission of something into ourselves, not by an emission’;for so it is, too, in the case of the other senses; for in hearing we admit some-thing into ourselves; we do not emit; and we taste in the same way. Likewisealso in the other cases. Moreover, all statements that seem to be true in allor in most cases, should be taken as a principle or accepted position; forthey are posited by those who do not also see what exception there may be.We should select also from the written handbooks of argument, and shoulddraw up sketch-lists of them upon each several kind of subject, putting them
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down under separate headings, e.g. ‘On Good’, or ‘On Life’ - and that ‘OnGood’ should deal with every form of good, beginning with the category ofessence. In the margin, too, one should indicate also the opinions of individ-ual thinkers, e.g. ‘Empedocles said that the elements of bodies were four’:for any one might assent to the saying of some generally accepted authority.
Of propositions and problems there are - to comprehend the matter inoutline - three divisions: for some are ethical propositions, some are on nat-ural philosophy, while some are logical. Propositions such as the followingare ethical, e.g. ‘Ought one rather to obey one’s parents or the laws, if theydisagree?’; such as this are logical, e.g. ‘Is the knowledge of opposites thesame or not?’; while such as this are on natural philosophy, e.g. ‘Is the uni-verse eternal or not?’ Likewise also with problems. The nature of each ofthe aforesaid kinds of proposition is not easily rendered in a definition, butwe have to try to recognize each of them by means of the familiarity at-tained through induction, examining them in the light of the illustrationsgiven above.
For purposes of philosophy we must treat of these things according totheir truth, but for dialectic only with an eye to general opinion. All propo-sitions should be taken in their most universal form; then, the one shouldbe made into many. E.g. ‘The knowledge of opposites is the same’; next,‘The knowledge of contraries is the same’, and that ‘of relative terms’. In thesame way these two should again be divided, as long as division is possible,e.g. the knowledge of ‘good and evil’, of ‘white and black’, or ‘cold and hot’.Likewise also in other cases.
Part 15 The number of senses a term bears
On the formation, then, of propositions, the above remarks are enough. Asregards the number of senses a term bears, we must not only treat of thoseterms which bear different senses, but we must also try to render their def-initions; e.g. we must not merely say that justice and courage are called‘good’ in one sense, and that what conduces to vigour and what conduces tohealth are called so in another, but also that the former are so called becauseof a certain intrinsic quality they themselves have, the latter because theyare productive of a certain result and not because of any intrinsic quality inthemselves. Similarly also in other cases.
Whether a term bears a number of specific meanings or one only, may beconsidered by the following means. First, look and see if its contrary bears anumber of meanings, whether the discrepancy between them be one of kindor one of names. For in some cases a difference is at once displayed even inthe names; e.g. the contrary of ‘sharp’ in the case of a note is ‘flat’, while inthe case of a solid edge it is ‘dull’. Clearly, then, the contrary of ‘sharp’ bears
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several meanings, and if so, also does ‘sharp’; for corresponding to each ofthe former terms the meaning of its contrary will be different. For ‘sharp’will not be the same when contrary to ‘dull’ and to ‘flat’, though ‘sharp’ isthe contrary of each. Again Barhu (‘flat’, ‘heavy’) in the case of a note has‘sharp’ as its contrary, but in the case of a solid mass ‘light’, so that Barhu isused with a number of meanings, inasmuch as its contrary also is so used.Likewise, also, ‘fine’ as applied to a picture has ‘ugly’ as its contrary, but, asapplied to a house, ‘ramshackle’; so that ‘fine’ is an ambiguous term.
In some cases there is no discrepancy of any sort in the names used, buta difference of kind between the meanings is at once obvious: e.g. in thecase of ‘clear’ and ‘obscure’: for sound is called ‘clear’ and ‘obscure’, just as‘colour’ is too. As regards the names, then, there is no discrepancy, but thedifference in kind between the meanings is at once obvious: for colour is notcalled ‘clear’ in a like sense to sound. This is plain also through sensation:for of things that are the same in kind we have the same sensation, whereaswe do not judge clearness by the same sensation in the case of sound andof colour, but in the latter case we judge by sight, in the former by hearing.Likewise also with ‘sharp’ and ‘dull’ in regard to flavours and solid edges:here in the latter case we judge by touch, but in the former by taste. For hereagain there is no discrepancy in the names used, in the case either of theoriginal terms or of their contraries: for the contrary also of sharp in eithersense is ‘dull’.
Moreover, see if one sense of a term has a contrary, while another hasabsolutely none; e.g. the pleasure of drinking has a contrary in the pain ofthirst, whereas the pleasure of seeing that the diagonal is incommensuratewith the side has none, so that ‘pleasure’ is used in more than one sense.To ‘love’ also, used of the frame of mind, has to ‘hate’ as its contrary, whileas used of the physical activity (kissing) it has none: clearly, therefore, to‘love’ is an ambiguous term. Further, see in regard to their intermediates, ifsome meanings and their contraries have an intermediate, others have none,or if both have one but not the same one, e.g. ‘clear’ and ‘obscure’ in thecase of colours have ‘grey’ as an intermediate, whereas in the case of soundthey have none, or, if they have, it is ‘harsh’, as some people say that a harshsound is intermediate. ‘Clear’, then, is an ambiguous term, and likewise also‘obscure’. See, moreover, if some of them have more than one intermediate,while others have but one, as is the case with ‘clear’ and ‘obscure’, for inthe case of colours there are numbers of intermediates, whereas in regard tosound there is but one, viz. ‘harsh’.
Again, in the case of the contradictory opposite, look and see if it bearsmore than one meaning. For if this bears more than one meaning, then theopposite of it also will be used in more than one meaning; e.g. ‘to fail to see’a phrase with more than one meaning, viz. (1) to fail to possess the power of
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sight, (2) to fail to put that power to active use. But if this has more than onemeaning, it follows necessarily that ‘to see’ also has more than one meaning:for there will be an opposite to each sense of ‘to fail to see’; e.g. the oppositeof ‘not to possess the power of sight’ is to possess it, while of ‘not to put thepower of sight to active use’, the opposite is to put it to active use.
Moreover, examine the case of terms that denote the privation or pres-ence of a certain state: for if the one term bears more than one meaning, thenso will the remaining term: e.g. if ‘to have sense’ be used with more than onemeaning, as applied to the soul and to the body, then ‘to be wanting in sense’too will be used with more than one meaning, as applied to the soul and tothe body. That the opposition between the terms now in question dependsupon the privation or presence of a certain state is clear, since animals natu-rally possess each kind of ‘sense’, both as applied to the soul and as appliedto the body.
Moreover, examine the inflected forms. For if ‘justly’ has more than onemeaning, then ‘just’, also, will be used with more than one meaning; forthere will be a meaning of ‘just’ to each of the meanings of ‘justly’; e.g. if theword ‘justly’ be used of judging according to one’s own opinion, and alsoof judging as one ought, then ‘just’ also will be used in like manner. In thesame way also, if ‘healthy’ has more than one meaning, then ‘healthily’ alsowill be used with more than one meaning: e.g. if ‘healthy’ describes bothwhat produces health and what preserves health and what betokens health,then ‘healthily’ also will be used to mean ‘in such a way as to produce’ or‘preserve’ or ‘betoken’ health. Likewise also in other cases, whenever theoriginal term bears more than one meaning, the inflexion also that is formedfrom it will be used with more than one meaning, and vice versa.
Look also at the classes of the predicates signified by the term, and seeif they are the same in all cases. For if they are not the same, then clearlythe term is ambiguous: e.g. ‘good’ in the case of food means ‘productiveof pleasure’, and in the case of medicine ‘productive of health’, whereas asapplied to the soul it means to be of a certain quality, e.g. temperate orcourageous or just: and likewise also, as applied to ‘man’. Sometimes itsignifies what happens at a certain time, as (e.g.) the good that happensat the right time: for what happens at the right time is called good. Often itsignifies what is of certain quantity, e.g. as applied to the proper amount: forthe proper amount too is called good. So then the term ‘good’ is ambiguous.In the same way also ‘clear’, as applied to a body, signifies a colour, but inregard to a note it denotes what is ‘easy to hear’. ‘Sharp’, too, is in a closelysimilar case: for the same term does not bear the same meaning in all itsapplications: for a sharp note is a swift note, as the mathematical theorists ofharmony tell us, whereas a sharp (acute) angle is one that is less than a rightangle, while a sharp dagger is one containing a sharp angle (point).
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Look also at the genera of the objects denoted by the same term, andsee if they are different without being subaltern, as (e.g.) ‘donkey’, whichdenotes both the animal and the engine. For the definition of them thatcorresponds to the name is different: for the one will be declared to be ananimal of a certain kind, and the other to be an engine of a certain kind. If,however, the genera be subaltern, there is no necessity for the definitionsto be different. Thus (e.g.) ‘animal’ is the genus of ‘raven’, and so is ‘bird’.Whenever therefore we say that the raven is a bird, we also say that it is acertain kind of animal, so that both the genera are predicated of it. Likewisealso whenever we call the raven a ‘flying biped animal’, we declare it to bea bird: in this way, then, as well, both the genera are predicated of raven,and also their definition. But in the case of genera that are not subaltern thisdoes not happen, for whenever we call a thing an ‘engine’, we do not call itan animal, nor vice versa.
Look also and see not only if the genera of the term before you are dif-ferent without being subaltern, but also in the case of its contrary: for if itscontrary bears several senses, clearly the term before you does so as well.
It is useful also to look at the definition that arises from the use of theterm in combination, e.g. of a ’clear (lit. white) body’ of a ‘clear note’. Forthen if what is peculiar in each case be abstracted, the same expression oughtto remain over. This does not happen in the case of ambiguous terms, e.g.in the cases just mentioned. For the former will be body possessing suchand such a colour, while the latter will be ‘a note easy to hear’. Abstract,then, ‘a body’ and ‘a note’, and the remainder in each case is not the same.It should, however, have been had the meaning of ‘clear’ in each case beensynonymous.
Often in the actual definitions as well ambiguity creeps in unawares, andfor this reason the definitions also should be examined. If (e.g.) any onedescribes what betokens and what produces health as ‘related commensu-rably to health’, we must not desist but go on to examine in what sense hehas used the term ‘commensurably’ in each case, e.g. if in the latter case itmeans that ‘it is of the right amount to produce health’, whereas in the for itmeans that ‘it is such as to betoken what kind of state prevails’.
Moreover, see if the terms cannot be compared as ‘more or less’ or as‘in like manner’, as is the case (e.g.) with a ‘clear’ (lit. white) sound anda ‘clear’ garment, and a ‘sharp’ flavour and a ‘sharp’ note. For neither arethese things said to be clear or sharp ‘in a like degree’, nor yet is the onesaid to be clearer or sharper than the other. ‘Clear’, then, and ‘sharp’ areambiguous. For synonyms are always comparable; for they will always beused either in like manner, or else in a greater degree in one case.
Now since of genera that are different without being subaltern the dif-ferentiae also are different in kind, e.g. those of ‘animal’ and ‘knowledge’
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(for the differentiae of these are different), look and see if the meanings com-prised under the same term are differentiae of genera that are different with-out being subaltern, as e.g. ‘sharp’ is of a ‘note’ and a ‘solid’. For being‘sharp’ differentiates note from note, and likewise also one solid from an-other. ‘Sharp’, then, is an ambiguous term: for it forms differentiae of generathat are different without being subaltern.
Again, see if the actual meanings included under the same term them-selves have different differentiae, e.g. ‘colour’ in bodies and ‘colour’ intunes: for the differentiae of ‘colour’ in bodies are ‘sight-piercing’ and ‘sightcompressing’, whereas ‘colour’ in melodies has not the same differentiae.Colour, then, is an ambiguous term; for things that are the same have thesame differentiae.
Moreover, since the species is never the differentia of anything, look andsee if one of the meanings included under the same term be a species andanother a differentia, as (e.g.) ‘clear’ (lit. white) as applied to a body is aspecies of colour, whereas in the case of a note it is a differentia; for one noteis differentiated from another by being ‘clear’.
Part 16 Difference should be examined in same genera
The presence, then, of a number of meanings in a term may be investigatedby these and like means. The differences which things present to each othershould be examined within the same genera, e.g. ‘Wherein does justice differfrom courage, and wisdom from temperance?’ - for all these belong to thesame genus; and also from one genus to another, provided they be not verymuch too far apart, e.g. ‘Wherein does sensation differ from knowledge?’:for in the case of genera that are very far apart, the differences are entirelyobvious.
Part 17 Likeness should be studied in different genera
Likeness should be studied, first, in the case of things belonging to differentgenera, the formulae being ’A:B = C:D’ (e.g. as knowledge stands to theobject of knowledge, so is sensation related to the object of sensation), and‘As A is in B, so is C in D’ (e.g. as sight is in the eye, so is reason in the soul,and as is a calm in the sea, so is windlessness in the air). Practice is moreespecially needed in regard to terms that are far apart; for in the case of therest, we shall be more easily able to see in one glance the points of likeness.We should also look at things which belong to the same genus, to see if anyidentical attribute belongs to them all, e.g. to a man and a horse and a dog;for in so far as they have any identical attribute, in so far they are alike.
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Part 18 It is useful to study difference in meaning of a term
It is useful to have examined the number of meanings of a term both forclearness’ sake (for a man is more likely to know what it is he asserts, if itbas been made clear to him how many meanings it may have), and also witha view to ensuring that our reasonings shall be in accordance with the actualfacts and not addressed merely to the term used. For as long as it is not clearin how many senses a term is used, it is possible that the answerer and thequestioner are not directing their minds upon the same thing: whereas whenonce it has been made clear how many meanings there are, and also uponwhich of them the former directs his mind when he makes his assertion, thequestioner would then look ridiculous if he failed to address his argumentto this. It helps us also both to avoid being misled and to mislead by falsereasoning: for if we know the number of meanings of a term, we shall cer-tainly never be misled by false reasoning, but shall know if the questionerfails to address his argument to the same point; and when we ourselves putthe questions we shall be able to mislead him, if our answerer happens notto know the number of meanings of our terms. This, however, is not possi-ble in all cases, but only when of the many senses some are true and othersare false. This manner of argument, however, does not belong properly todialectic; dialecticians should therefore by all means beware of this kind ofverbal discussion, unless any one is absolutely unable to discuss the subjectbefore him in any other way.
The discovery of the differences of things helps us both in reasoningsabout sameness and difference, and also in recognizing what any particularthing is. That it helps us in reasoning about sameness and difference is clear:for when we have discovered a difference of any kind whatever between theobjects before us, we shall already have shown that they are not the same:while it helps us in recognizing what a thing is, because we usually distin-guish the expression that is proper to the essence of each particular thing bymeans of the differentiae that are proper to it.
The examination of likeness is useful with a view both to inductive argu-ments and to hypothetical reasonings, and also with a view to the renderingof definitions. It is useful for inductive arguments, because it is by meansof an induction of individuals in cases that are alike that we claim to bringthe universal in evidence: for it is not easy to do this if we do not know thepoints of likeness. It is useful for hypothetical reasonings because it is a gen-eral opinion that among similars what is true of one is true also of the rest.If, then, with regard to any of them we are well supplied with matter fora discussion, we shall secure a preliminary admission that however it is inthese cases, so it is also in the case before us: then when we have shown theformer we shall have shown, on the strength of the hypothesis, the matter
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before us as well: for we have first made the hypothesis that however it is inthese cases, so it is also in the case before us, and have then proved the pointas regards these cases. It is useful for the rendering of definitions because, ifwe are able to see in one glance what is the same in each individual case ofit, we shall be at no loss into what genus we ought to put the object beforeus when we define it: for of the common predicates that which is most def-initely in the category of essence is likely to be the genus. Likewise, also, inthe case of objects widely divergent, the examination of likeness is useful forpurposes of definition, e.g. the sameness of a calm at sea, and windlessnessin the air (each being a form of rest), and of a point on a line and the unit innumber - each being a starting point. If, then, we render as the genus whatis common to all the cases, we shall get the credit of defining not inappropri-ately. Definition-mongers too nearly always render them in this way: theydeclare the unit to be the startingpoint of number, and the point the starting-point of a line. It is clear, then, that they place them in that which is commonto both as their genus.
The means, then, whereby reasonings are effected, are these: the com-monplace rules, for the observance of which the aforesaid means are useful,are as follows.
Book II On various argumentativetechniques
Part 1 Of problems some are universal, others particular
Of problems some are universal, others particular. Universal problems aresuch as ‘Every pleasure is good’ and ‘No pleasure is good’; particular prob-lems are such as ‘Some pleasure is good’ and ‘Some pleasure is not good’.The methods of establishing and overthrowing a view universally are com-mon to both kinds of problems; for when we have shown that a predicate be-longs in every case, we shall also have shown that it belongs in some cases.Likewise, also, if we show that it does not belong in any case, we shall alsohave shown that it does not belong in every case.
First, then, we must speak of the methods of overthrowing a view univer-sally, because such are common to both universal and particular problems,and because people more usually introduce theses asserting a predicate thandenying it, while those who argue with them overthrow it. The conversionof an appropriate name which is drawn from the element ‘accident’ is anextremely precarious thing; for in the case of accidents and in no other it ispossible for something to be true conditionally and not universally. Names
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drawn from the elements ‘definition’ and ‘property’ and ‘genus’ are boundto be convertible; e.g. if ‘to be an animal that walks on two feet is an attributeof S’, then it will be true by conversion to say that ‘S is an animal that walkson two feet’. Likewise, also, if drawn from the genus; for if ‘to be an animalis an attribute of S’, then ‘S is an animal’. The same is true also in the caseof a property; for if ‘to be capable of learning grammar is an attribute of S’,then ‘S will be capable of learning grammar’. For none of these attributescan possibly belong or not belong in part; they must either belong or not be-long absolutely. In the case of accidents, on the other hand, there is nothingto prevent an attribute (e.g. whiteness or justice) belonging in part, so thatit is not enough to show that whiteness or justice is an attribute of a man inorder to show that he is white or just; for it is open to dispute it and say thathe is white or just in part only. Conversion, then, is not a necessary processin the case of accidents.
We must also define the errors that occur in problems. They are of twokinds, caused either by false statement or by transgression of the establisheddiction. For those who make false statements, and say that an attribute be-longs to thing which does not belong to it, commit error; and those whocall objects by the names of other objects (e.g. calling a planetree a ‘man’)transgress the established terminology.
Part 2 Mistaken accidental ascription
Now one commonplace rule is to look and see if a man has ascribed as anaccident what belongs in some other way. This mistake is most commonlymade in regard to the genera of things, e.g. if one were to say that white hap-pens (accidit) to be a colour - for being a colour does not happen by accidentto white, but colour is its genus. The assertor may of course define it so inso many words, saying (e.g.) that ‘Justice happens (accidit) to be a virtue’;but often even without such definition it is obvious that he has rendered thegenus as an accident; e.g. suppose that one were to say that whiteness iscoloured or that walking is in motion. For a predicate drawn from the genusis never ascribed to the species in an inflected form, but always the generaare predicated of their species literally; for the species take on both the nameand the definition of their genera. A man therefore who says that white is‘coloured’ has not rendered ‘coloured’ as its genus, seeing that he has usedan inflected form, nor yet as its property or as its definition: for the defini-tion and property of a thing belong to it and to nothing else, whereas manythings besides white are coloured, e.g. a log, a stone, a man, and a horse.Clearly then he renders it as an accident.
Another rule is to examine all cases where a predicate has been eitherasserted or denied universally to belong to something. Look at them species
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by species, and not in their infinite multitude: for then the inquiry will pro-ceed more directly and in fewer steps. You should look and begin with themost primary groups, and then proceed in order down to those that are notfurther divisible: e.g. if a man has said that the knowledge of opposites isthe same, you should look and see whether it be so of relative oppositesand of contraries and of terms signifying the privation or presence of certainstates, and of contradictory terms. Then, if no clear result be reached so farin these cases, you should again divide these until you come to those thatare not further divisible, and see (e.g.) whether it be so of just deeds andunjust, or of the double and the half, or of blindness and sight, or of beingand not-being: for if in any case it be shown that the knowledge of them isnot the same we shall have demolished the problem. Likewise, also, if thepredicate belongs in no case. This rule is convertible for both destructiveand constructive purposes: for if, when we have suggested a division, thepredicate appears to hold in all or in a large number of cases, we may thenclaim that the other should actually assert it universally, or else bring a neg-ative instance to show in what case it is not so: for if he does neither of thesethings, a refusal to assert it will make him look absurd.
Another rule is to make definitions both of an accident and of its subject,either of both separately or else of one of them, and then look and see if any-thing untrue has been assumed as true in the definitions. Thus (e.g.) to seeif it is possible to wrong a god, ask what is ‘to wrong’? For if it be ‘to injuredeliberately’, clearly it is not possible for a god to be wronged: for it is im-possible that God should be injured. Again, to see if the good man is jealous,ask who is the ‘jealous’ man and what is ‘jealousy’. For if ‘jealousy’ is painat the apparent success of some well-behaved person, clearly the good manis not jealous: for then he would be bad. Again, to see if the indignant manis jealous, ask who each of them is: for then it will be obvious whether thestatement is true or false; e.g. if he is ‘jealous’ who grieves at the successes ofthe good, and he is ‘indignant’ who grieves at the successes of the evil, thenclearly the indignant man would not be jealous. A man should substitutedefinitions also for the terms contained in his definitions, and not stop untilhe comes to a familiar term: for often if the definition be rendered whole, thepoint at issue is not cleared up, whereas if for one of the terms used in thedefinition a definition be stated, it becomes obvious.
Moreover, a man should make the problem into a proposition for himself,and then bring a negative instance against it: for the negative instance willbe a ground of attack upon the assertion. This rule is very nearly the sameas the rule to look into cases where a predicate has been attributed or denieduniversally: but it differs in the turn of the argument.
Moreover, you should define what kind of things should be called asmost men call them, and what should not. For this is useful both for estab-
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lishing and for overthrowing a view: e.g. you should say that we ought touse our terms to mean the same things as most people mean by them, butwhen we ask what kind of things are or are not of such and such a kind,we should not here go with the multitude: e.g. it is right to call ‘healthy’whatever tends to produce health, as do most men: but in saying whetherthe object before us tends to produce health or not, we should adopt thelanguage no longer of the multitude but of the doctor.
Part 3 Attributions to terms used in several senses
Moreover, if a term be used in several senses, and it has been laid down thatit is or that it is not an attribute of S, you should show your case of one of itsseveral senses, if you cannot show it of both. This rule is to be observed incases where the difference of meaning is undetected; for supposing this to beobvious, then the other man will object that the point which he himself ques-tioned has not been discussed, but only the other point. This commonplacerule is convertible for purposes both of establishing and of overthrowing aview. For if we want to establish a statement, we shall show that in one sensethe attribute belongs, if we cannot show it of both senses: whereas if we areoverthrowing a statement, we shall show that in one sense the attribute doesnot belong, if we cannot show it of both senses. Of course, in overthrowing astatement there is no need to start the discussion by securing any admission,either when the statement asserts or when it denies the attribute universally:for if we show that in any case whatever the attribute does not belong, weshall have demolished the universal assertion of it, and likewise also if weshow that it belongs in a single case, we shall demolish the universal denialof it. Whereas in establishing a statement we ought to secure a preliminaryadmission that if it belongs in any case whatever, it belongs universally, sup-posing this claim to be a plausible one. For it is not enough to discuss a singleinstance in order to show that an attribute belongs universally; e.g. to arguethat if the soul of man be immortal, then every soul is immortal, so that aprevious admission must be secured that if any soul whatever be immortal,then every soul is immortal. This is not to be done in every case, but onlywhenever we are not easily able to quote any single argument applying toall cases in common, as (e.g.) the geometrician can argue that the trianglehas its angles equal to two right angles.
If, again, the variety of meanings of a term be obvious, distinguish howmany meanings it has before proceeding either to demolish or to establish it:e.g. supposing ‘the right’ to mean ‘the expedient’ or ‘the honourable’, youshould try either to establish or to demolish both descriptions of the subjectin question; e.g. by showing that it is honourable and expedient, or that it isneither honourable nor expedient. Supposing, however, that it is impossible
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to show both, you should show the one, adding an indication that it is truein the one sense and not in the other. The same rule applies also when thenumber of senses into which it is divided is more than two.
Again, consider those expressions whose meanings are many, but differnot by way of ambiguity of a term, but in some other way: e.g. ‘The scienceof many things is one’: here ‘many things’ may mean the end and the meansto that end, as (e.g.) medicine is the science both of producing health and ofdieting; or they may be both of them ends, as the science of contraries is saidto be the same (for of contraries the one is no more an end than the other); oragain they may be an essential and an accidental attribute, as (e.g.) the es-sential fact that the triangle has its angles equal to two right angles, and theaccidental fact that the equilateral figure has them so: for it is because of theaccident of the equilateral triangle happening to be a triangle that we knowthat it has its angles equal to two right angles. If, then, it is not possible inany sense of the term that the science of many things should be the same,it clearly is altogether impossible that it should be so; or, if it is possible insome sense, then clearly it is possible. Distinguish as many meanings as arerequired: e.g. if we want to establish a view, we should bring forward allsuch meanings as admit that view and should divide them only into thosemeanings which also are required for the establishment of our case: whereasif we want to overthrow a view, we should bring forward all that do not ad-mit that view, and leave the rest aside. We must deal also in these cases aswell with any uncertainty about the number of meanings involved. Further,that one thing is, or is not, ‘of’ another should be established by means ofthe same commonplace rules; e.g. that a particular science is of a particularthing, treated either as an end or as a means to its end, or as accidentally con-nected with it; or again that it is not ‘of’ it in any of the aforesaid ways. Thesame rule holds true also of desire and all other terms that have more thanone object. For the ‘desire of X’ may mean the desire of it as an end (e.g. thedesire of health) or as a means to an end (e.g. the desire of being doctored),or as a thing desired accidentally, as, in the case of wine, the sweet-toothedperson desires it not because it is wine but because it is sweet. For essentiallyhe desires the sweet, and only accidentally the wine: for if it be dry, he nolonger desires it. His desire for it is therefore accidental. This rule is usefulin dealing with relative terms: for cases of this kind are generally cases ofrelative terms.
Part 4 It is well to alter a term into one more familiar
Moreover, it is well to alter a term into one more familiar, e.g. to substitute‘clear’ for ‘exact’ in describing a conception, and ‘being fussy’ for ‘beingbusy’: for when the expression is made more familiar, the thesis becomes
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easier to attack. This commonplace rule also is available for both purposesalike, both for establishing and for overthrowing a view.
In order to show that contrary attributes belong to the same thing, lookat its genus; e.g. if we want to show that rightness and wrongness are pos-sible in regard to perception, and to perceive is to judge, while it is possibleto judge rightly or wrongly, then in regard to perception as well rightnessand wrongness must be possible. In the present instance the proof proceedsfrom the genus and relates to the species: for ‘to judge’ is the genus of ‘to-perceive’; for the man who perceives judges in a certain way. But per contrait may proceed from the species to the genus: for all the attributes that be-long to the species belong to the genus as well; e.g. if there is a bad anda good knowledge there is also a bad and a good disposition: for ‘disposi-tion’ is the genus of knowledge. Now the former commonplace argument isfallacious for purposes of establishing a view, while the second is true. Forthere is no necessity that all the attributes that belong to the genus shouldbelong also to the species; for ‘animal’ is flying and quadruped, but not so‘man’. All the attributes, on the other hand, that belong to the species mustof necessity belong also to the genus; for if ‘man’ is good, then animal also isgood. On the other hand, for purposes of overthrowing a view, the formerargument is true while the latter is fallacious; for all the attributes which donot belong to the genus do not belong to the species either; whereas all thosethat are wanting to the species are not of necessity wanting to the genus.
Since those things of which the genus is predicated must also of necessityhave one of its species predicated of them, and since those things that arepossessed of the genus in question, or are described by terms derived fromthat genus, must also of necessity be possessed of one of its species or bedescribed by terms derived from one of its species (e.g. if to anything theterm ‘scientific knowledge’ be applied, then also there will be applied to itthe term ‘grammatical’ or ‘musical’ knowledge, or knowledge of one of theother sciences; and if any one possesses scientific knowledge or is describedby a term derived from ‘science’, then he will also possess grammatical ormusical knowledge or knowledge of one of the other sciences, or will bedescribed by a term derived from one of them, e.g. as a ‘grammarian’ ora ‘musician’) - therefore if any expression be asserted that is in any wayderived from the genus (e.g. that the soul is in motion), look and see whetherit be possible for the soul to be moved with any of the species of motion;whether (e.g.) it can grow or be destroyed or come to be, and so forth withall the other species of motion. For if it be not moved in any of these ways,clearly it does not move at all. This commonplace rule is common for bothpurposes, both for overthrowing and for establishing a view: for if the soulmoves with one of the species of motion, clearly it does move; while if itdoes not move with any of the species of motion, clearly it does not move.
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If you are not well equipped with an argument against the assertion, lookamong the definitions, real or apparent, of the thing before you, and if one isnot enough, draw upon several. For it will be easier to attack people whencommitted to a definition: for an attack is always more easily made on defi-nitions.
Moreover, look and see in regard to the thing in question, what it iswhose reality conditions the reality of the thing in question, or what it iswhose reality necessarily follows if the thing in question be real: if you wishto establish a view inquire what there is on whose reality the reality of thething in question will follow (for if the former be shown to be real, then thething in question will also have been shown to be real); while if you want tooverthrow a view, ask what it is that is real if the thing in question be real,for if we show that what follows from the thing in question is unreal, weshall have demolished the thing in question.
Moreover, look at the time involved, to see if there be any discrepancyanywhere: e.g. suppose a man to have stated that what is being nourishedof necessity grows: for animals are always of necessity being nourished, butthey do not always grow. Likewise, also, if he has said that knowing is re-membering: for the one is concerned with past time, whereas the other hasto do also with the present and the future. For we are said to know thingspresent and future (e.g. that there will be an eclipse), whereas it is impossibleto remember anything save what is in the past.
Part 5 Drawing an opponent into a refutable statement
Moreover, there is the sophistic turn of argument, whereby we draw ouropponent into the kind of statement against which we shall be well sup-plied with lines of argument. This process is sometimes a real necessity,sometimes an apparent necessity, sometimes neither an apparent nor a realnecessity. It is really necessary whenever the answerer has denied any viewthat would be useful in attacking the thesis, and the questioner thereuponaddresses his arguments to the support of this view, and when moreoverthe view in question happens to be one of a kind on which he has a goodstock of lines of argument. Likewise, also, it is really necessary whenever he(the questioner) first, by an induction made by means of the view laid down,arrives at a certain statement and then tries to demolish that statement: forwhen once this has been demolished, the view originally laid down is de-molished as well. It is an apparent necessity, when the point to which thediscussion comes to be directed appears to be useful, and relevant to thethesis, without being really so; whether it be that the man who is standingup to the argument has refused to concede something, or whether he (thequestioner) has first reached it by a plausible induction based upon the the-
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sis and then tries to demolish it. The remaining case is when the point towhich the discussion comes to be directed is neither really nor apparentlynecessary, and it is the answerer’s luck to be confuted on a mere side issueYou should beware of the last of the aforesaid methods; for it appears to bewholly disconnected from, and foreign to, the art of dialectic. For this rea-son, moreover, the answerer should not lose his temper, but assent to thosestatements that are of no use in attacking the thesis, adding an indicationwhenever he assents although he does not agree with the view. For, as arule, it increases the confusion of questioners if, after all propositions of thiskind have been granted them, they can then draw no conclusion.
Moreover, any one who has made any statement whatever has in a cer-tain sense made several statements, inasmuch as each statement has a num-ber of necessary consequences: e.g. the man who said ‘X is a man’ has alsosaid that it is an animal and that it is animate and a biped and capable of ac-quiring reason and knowledge, so that by the demolition of any single oneof these consequences, of whatever kind, the original statement is demol-ished as well. But you should beware here too of making a change to a moredifficult subject: for sometimes the consequence, and sometimes the originalthesis, is the easier to demolish.
Part 6 On dichotomies
In regard to subjects which must have one and one only of two predicates,as (e.g.) a man must have either a disease or health, supposing we are wellsupplied as regards the one for arguing its presence or absence, we shall bewell equipped as regards the remaining one as well. This rule is convertiblefor both purposes: for when we have shown that the one attribute belongs,we shall have shown that the remaining one does not belong; while if weshow that the one does not belong, we shall have shown that the remainingone does belong. Clearly then the rule is useful for both purposes.
Moreover, you may devise a line of attack by reinterpreting a term inits literal meaning, with the implication that it is most fitting so to take itrather than in its established meaning: e.g. the expression ‘strong at heart’will suggest not the courageous man, according to the use now established,but the man the state of whose heart is strong; just as also the expression‘of a good hope’ may be taken to mean the man who hopes for good things.Likewise also ‘well-starred’ may be taken to mean the man whose star isgood, as Xenocrates says ‘well-starred is he who has a noble soul’. ‘For aman’s star is his soul.’
Some things occur of necessity, others usually, others however it maychance; if therefore a necessary event has been asserted to occur usually, orif a usual event (or, failing such an event itself, its contrary) has been stated
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to occur of necessity, it always gives an opportunity for attack. For if a neces-sary event has been asserted to occur usually, clearly the speaker has deniedan attribute to be universal which is universal, and so has made a mistake:and so he has if he has declared the usual attribute to be necessary: for thenhe declares it to belong universally when it does not so belong. Likewisealso if he has declared the contrary of what is usual to be necessary. For thecontrary of a usual attribute is always a comparatively rare attribute: e.g. ifmen are usually bad, they are comparatively seldom good, so that his mis-take is even worse if he has declared them to be good of necessity. The sameis true also if he has declared a mere matter of chance to happen of neces-sity or usually; for a chance event happens neither of necessity nor usually.If the thing happens usually, then even supposing his statement does notdistinguish whether he meant that it happens usually or that it happens nec-essarily, it is open to you to discuss it on the assumption that he meant thatit happens necessarily: e.g. if he has stated without any distinction that dis-inherited persons are bad, you may assume in discussing it that he meansthat they are so necessarily.
Moreover, look and see also if he has stated a thing to be an accidentof itself, taking it to be a different thing because it has a different name, asProdicus used to divide pleasures into joy and delight and good cheer: for allthese are names of the same thing, to wit, Pleasure. If then any one says thatjoyfulness is an accidental attribute of cheerfulness, he would be declaring itto be an accidental attribute of itself.
Part 7 Contraries and their conjunctions
Inasmuch as contraries can be conjoined with each other in six ways, andfour of these conjunctions constitute a contrariety, we must grasp the sub-ject of contraries, in order that it may help us both in demolishing and inestablishing a view. Well then, that the modes of conjunction are six is clear:for either (1) each of the contrary verbs will be conjoined to each of the con-trary objects; and this gives two modes: e.g. to do good to friends and to doevil to enemies, or per contra to do evil to friends and to do good to enemies.Or else (2) both verbs may be attached to one object; and this too gives twomodes, e.g. to do good to friends and to do evil to friends, or to do good toenemies and to do evil to enemies. Or (3) a single verb may be attached toboth objects: and this also gives two modes; e.g. to do good to friends andto do good to enemies, or to do evil to friends and evil to enemies.
The first two then of the aforesaid conjunctions do not constitute anycontrariety; for the doing of good to friends is not contrary to the doing ofevil to enemies: for both courses are desirable and belong to the same dis-position. Nor is the doing of evil to friends contrary to the doing of good to
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enemies: for both of these are objectionable and belong to the same disposi-tion: and one objectionable thing is not generally thought to be the contraryof another, unless the one be an expression denoting an excess, and the otheran expression denoting a defect: for an excess is generally thought to belongto the class of objectionable things, and likewise also a defect. But the otherfour all constitute a contrariety. For to do good to friends is contrary to thedoing of evil to friends: for it proceeds from the contrary disposition, andthe one is desirable, and the other objectionable. The case is the same alsoin regard to the other conjunctions: for in each combination the one courseis desirable, and the other objectionable, and the one belongs to a reason-able disposition and the other to a bad. Clearly, then, from what has beensaid, the same course has more than one contrary. For the doing of good tofriends has as its contrary both the doing of good to enemies and the doingof evil to friends. Likewise, if we examine them in the same way, we shallfind that the contraries of each of the others also are two in number. Selecttherefore whichever of the two contraries is useful in attacking the thesis.
Moreover, if the accident of a thing have a contrary, see whether it be-longs to the subject to which the accident in question has been declared tobelong: for if the latter belongs the former could not belong; for it is impos-sible that contrary predicates should belong at the same time to the samething.
Or again, look and see if anything has been said about something, of sucha kind that if it be true, contrary predicates must necessarily belong to thething: e.g. if he has said that the ‘Ideas’ exist in us. For then the result will bethat they are both in motion and at rest, and moreover that they are objectsboth of sensation and of thought. For according to the views of those whoposit the existence of Ideas, those Ideas are at rest and are objects of thought;while if they exist in us, it is impossible that they should be unmoved: forwhen we move, it follows necessarily that all that is in us moves with us aswell. Clearly also they are objects of sensation, if they exist in us: for it isthrough the sensation of sight that we recognize the Form present in eachindividual.
Again, if there be posited an accident which has a contrary, look andsee if that which admits of the accident will admit of its contrary as well:for the same thing admits of contraries. Thus (e.g.) if he has asserted thathatred follows anger, hatred would in that case be in the ‘spirited faculty’:for that is where anger is. You should therefore look and see if its contrary,to wit, friendship, be also in the ‘spirited faculty’: for if not - if friendshipis in the faculty of desire - then hatred could not follow anger. Likewisealso if he has asserted that the faculty of desire is ignorant. For if it werecapable of ignorance, it would be capable of knowledge as well: and this isnot generally held - I mean that the faculty of desire is capable of knowledge.
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For purposes, then, of overthrowing a view, as has been said, this rule shouldbe observed: but for purposes of establishing one, though the rule will nothelp you to assert that the accident actually belongs, it will help you to assertthat it may possibly belong. For having shown that the thing in questionwill not admit of the contrary of the accident asserted, we shall have shownthat the accident neither belongs nor can possibly belong; while on the otherhand, if we show that the contrary belongs, or that the thing is capable of thecontrary, we shall not indeed as yet have shown that the accident asserteddoes belong as well; our proof will merely have gone to this point, that it ispossible for it to belong.
Part 8 Look for arguments among contradictories
Seeing that the modes of opposition are four in number, you should look forarguments among the contradictories of your terms, converting the order oftheir sequence, both when demolishing and when establishing a view, andyou should secure them by means of induction - such arguments (e.g.) asthat man be an animal, what is not an animal is not a man: and likewisealso in other instances of contradictories. For in those cases the sequence isconverse: for ‘animal’ follows upon ‘man’ but ‘not-animal’ does not followupon ‘not-man’, but conversely ‘not-man’ upon ‘not-animal’. In all cases,therefore, a postulate of this sort should be made, (e.g.) that ‘If the hon-ourable is pleasant, what is not pleasant is not honourable, while if the latterbe untrue, so is the former’. Likewise, also, ‘If what is not pleasant be nothonourable, then what is honourable is pleasant’. Clearly, then, the conver-sion of the sequence formed by contradiction of the terms of the thesis is amethod convertible for both purposes.
Then look also at the case of the contraries of S and P in the thesis, andsee if the contrary of the one follows upon the contrary of the other, eitherdirectly or conversely, both when you are demolishing and when you areestablishing a view: secure arguments of this kind as well by means of in-duction, so far as may be required. Now the sequence is direct in a case suchas that of courage and cowardice: for upon the one of them virtue follows,and vice upon the other; and upon the one it follows that it is desirable, whileupon the other it follows that it is objectionable. The sequence, therefore, inthe latter case also is direct; for the desirable is the contrary of the objec-tionable. Likewise also in other cases. The sequence is, on the other hand,converse in such a case as this: Health follows upon vigour, but disease doesnot follow upon debility; rather debility follows upon disease. In this case,then, clearly the sequence is converse. Converse sequence is, however, rarein the case of contraries; usually the sequence is direct. If, therefore, thecontrary of the one term does not follow upon the contrary of the other ei-
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ther directly or conversely, clearly neither does the one term follow uponthe other in the statement made: whereas if the one followed the other inthe case of the contraries, it must of necessity do so as well in the originalstatement.
You should look also into cases of the privation or presence of a state inlike manner to the case of contraries. Only, in the case of such privations theconverse sequence does not occur: the sequence is always bound to be direct:e.g. as sensation follows sight, while absence of sensation follows blindness.For the opposition of sensation to absence of sensation is an opposition ofthe presence to the privation of a state: for the one of them is a state, and theother the privation of it.
The case of relative terms should also be studied in like manner to thatof a state and its privation: for the sequence of these as well is direct; e.g. if3/1 is a multiple, then 1/3 is a fraction: for 3/1 is relative to 1/3, and so is amultiple to a fraction. Again, if knowledge be a conceiving, then also the ob-ject of knowledge is an object of conception; and if sight be a sensation, thenalso the object of sight is an object of sensation. An objection may be madethat there is no necessity for the sequence to take place, in the case of relativeterms, in the way described: for the object of sensation is an object of knowl-edge, whereas sensation is not knowledge. The objection is, however, notgenerally received as really true; for many people deny that there is knowl-edge of objects of sensation. Moreover, the principle stated is just as usefulfor the contrary purpose, e.g. to show that the object of sensation is not anobject of knowledge, on the ground that neither is sensation knowledge.
Part 9 Co-ordinates and inflected forms of the terms
Again look at the case of the co-ordinates and inflected forms of the termsin the thesis, both in demolishing and in establishing it. By co-ordinatesare meant terms such as the following: ‘Just deeds’ and the ‘just man’ arecoordinates of ‘justice’, and ‘courageous deeds’ and the ‘courageous man’are co-ordinates of courage. Likewise also things that tend to produce andto preserve anything are called co-ordinates of that which they tend to pro-duce and to preserve, as e.g. ‘healthy habits’ are co-ordinates of ‘health’and a ‘vigorous constitutional’ of a ‘vigorous constitution’ and so forth alsoin other cases. ‘Co-ordinate’, then, usually describes cases such as these,whereas ‘inflected forms’ are such as the following: ‘justly’, ‘courageously’,‘healthily’, and such as are formed in this way. It is usually held that wordswhen used in their inflected forms as well are co-ordinates, as (e.g.) ‘justly’in relation to justice, and ‘courageously’ to courage; and then ‘co-ordinate’describes all the members of the same kindred series, e.g. ‘justice’, ‘just’,of a man or an act, ‘justly’. Clearly, then, when any one member, whatever
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its kind, of the same kindred series is shown to be good or praiseworthy,then all the rest as well come to be shown to be so: e.g. if ‘justice’ be some-thing praiseworthy, then so will ‘just’, of a man or thing, and ‘justly’ connotesomething praiseworthy. Then ‘justly’ will be rendered also ‘praiseworthily’,derived will by the same inflexion from ‘the praiseworthy’ whereby ‘justly’is derived from ‘justice’.
Look not only in the case of the subject mentioned, but also in the case ofits contrary, for the contrary predicate: e.g. argue that good is not necessarilypleasant; for neither is evil painful: or that, if the latter be the case, so is theformer. Also, if justice be knowledge, then injustice is ignorance: and if‘justly’ means ‘knowingly’ and ‘skilfully’, then ‘unjustly’ means ‘ignorantly’and ‘unskilfully’: whereas if the latter be not true, neither is the former, as inthe instance given just now: for ‘unjustly’ is more likely to seem equivalentto ‘skilfully’ than to ‘unskilfully’. This commonplace rule has been statedbefore in dealing with the sequence of contraries; for all we are claimingnow is that the contrary of P shall follow the contrary of S.
Moreover, look at the modes of generation and destruction of a thing, andat the things which tend to produce or to destroy it, both in demolishingand in establishing a view. For those things whose modes of generationrank among good things, are themselves also good; and if they themselvesbe good, so also are their modes of generation. If, on the other hand, theirmodes of generation be evil, then they themselves also are evil. In regardto modes of destruction the converse is true: for if the modes of destructionrank as good things, then they themselves rank as evil things; whereas if themodes of destruction count as evil, they themselves count as good. The sameargument applies also to things tending to produce and destroy: for thingswhose productive causes are good, themselves also rank as good; whereas ifcauses destructive of them are good, they themselves rank as evil.
Part 10 Look at things which are like the subject
Again, look at things which are like the subject in question, and see if theyare in like case; e.g. if one branch of knowledge has more than one object, soalso will one opinion; and if to possess sight be to see, then also to possesshearing will be to hear. Likewise also in the case of other things, both thosewhich are and those which are generally held to be like. The rule in questionis useful for both purposes; for if it be as stated in the case of some one likething, it is so with the other like things as well, whereas if it be not so in thecase of some one of them, neither is it so in the case of the others. Look andsee also whether the cases are alike as regards a single thing and a numberof things: for sometimes there is a discrepancy. Thus, if to ‘know’ a thing beto ‘think of’ it, then also to ‘know many things’ is to ‘be thinking of many
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things’; whereas this is not true; for it is possible to know many things butnot to be thinking of them. If, then, the latter proposition be not true, neitherwas the former that dealt with a single thing, viz. that to ‘know’ a thing is to‘think of’ it.
Moreover, argue from greater and less degrees. In regard to greater de-grees there are four commonplace rules. One is: See whether a greater de-gree of the predicate follows a greater degree of the subject: e.g. if pleasurebe good, see whether also a greater pleasure be a greater good: and if to do awrong be evil, see whether also to do a greater wrong is a greater evil. Nowthis rule is of use for both purposes: for if an increase of the accident followsan increase of the subject, as we have said, clearly the accident belongs; whileif it does not follow, the accident does not belong. You should establish thisby induction. Another rule is: If one predicate be attributed to two subjects;then supposing it does not belong to the subject to which it is the more likelyto belong, neither does it belong where it is less likely to belong; while if itdoes belong where it is less likely to belong, then it belongs as well where itis more likely. Again: If two predicates be attributed to one subject, then ifthe one which is more generally thought to belong does not belong, neitherdoes the one that is less generally thought to belong; or, if the one that is lessgenerally thought to belong does belong, so also does the other. Moreover:If two predicates be attributed to two subjects, then if the one which is moreusually thought to belong to the one subject does not belong, neither doesthe remaining predicate belong to the remaining subject; or, if the one whichis less usually thought to belong to the one subject does belong, so too doesthe remaining predicate to the remaining subject.
Moreover, you can argue from the fact that an attribute belongs, or isgenerally supposed to belong, in a like degree, in three ways, viz. thosedescribed in the last three rules given in regard to a greater degree.’ For sup-posing that one predicate belongs, or is supposed to belong, to two subjectsin a like degree, then if it does not belong to the one, neither does it belongto the other; while if it belongs to the one, it belongs to the remaining oneas well. Or, supposing two predicates to belong in a like degree to the samesubject, then, if the one does not belong, neither does the remaining one;while if the one does belong, the remaining one belongs as well. The caseis the same also if two predicates belong in a like degree to two subjects;for if the one predicate does not belong to the one subject, neither does theremaining predicate belong to the remaining subject, while if the one pred-icate does belong to the one subject, the remaining predicate belongs to theremaining subject as well.
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Part 11 Matters of degree
You can argue, then, from greater or less or like degrees of truth in the afore-said number of ways. Moreover, you should argue from the addition of onething to another. If the addition of one thing to another makes that othergood or white, whereas formerly it was not white or good, then the thingadded will be white or good - it will possess the character it imparts to thewhole as well. Moreover, if an addition of something to a given object in-tensifies the character which it had as given, then the thing added will itselfas well be of that character. Likewise, also, in the case of other attributes.The rule is not applicable in all cases, but only in those in which the excessdescribed as an ‘increased intensity’ is found to take place. The above ruleis, however, not convertible for overthrowing a view. For if the thing addeddoes not make the other good, it is not thereby made clear whether in itselfit may not be good: for the addition of good to evil does not necessarilymake the whole good, any more than the addition of white to black makesthe whole white.
Again, any predicate of which we can speak of greater or less degreesbelongs also absolutely: for greater or less degrees of good or of white willnot be attributed to what is not good or white: for a bad thing will never besaid to have a greater or less degree of goodness than another, but always ofbadness. This rule is not convertible, either, for the purpose of overthrowinga predication: for several predicates of which we cannot speak of a greaterdegree belong absolutely: for the term ‘man’ is not attributed in greater andless degrees, but a man is a man for all that.
You should examine in the same way predicates attributed in a given re-spect, and at a given time and place: for if the predicate be possible in somerespect, it is possible also absolutely. Likewise, also, is what is predicated ata given time or place: for what is absolutely impossible is not possible eitherin any respect or at any place or time. An objection may be raised that in agiven respect people may be good by nature, e.g. they may be generous ortemperately inclined, while absolutely they are not good by nature, becauseno one is prudent by nature. Likewise, also, it is possible for a destructiblething to escape destruction at a given time, whereas it is not possible for it toescape absolutely. In the same way also it is a good thing at certain places tofollow see and such a diet, e.g. in infected areas, though it is not a good thingabsolutely. Moreover, in certain places it is possible to live singly and alone,but absolutely it is not possible to exist singly and alone. In the same wayalso it is in certain places honourable to sacrifice one’s father, e.g. among theTriballi, whereas, absolutely, it is not honourable. Or possibly this may indi-cate a relativity not to places but to persons: for it is all the same whereverthey may be: for everywhere it will be held honourable among the Triballi
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themselves, just because they are Triballi. Again, at certain times it is a goodthing to take medicines, e.g. when one is ill, but it is not so absolutely. Orpossibly this again may indicate a relativity not to a certain time, but to a cer-tain state of health: for it is all the same whenever it occurs, if only one be inthat state. A thing is ‘absolutely’ so which without any addition you are pre-pared to say is honourable or the contrary. Thus (e.g.) you will deny that tosacrifice one’s father is honourable: it is honourable only to certain persons:it is not therefore honourable absolutely. On the other hand, to honour thegods you will declare to be honourable without adding anything, becausethat is honourable absolutely. So that whatever without any addition is gen-erally accounted to be honourable or dishonourable or anything else of thatkind, will be said to be so ‘absolutely’.
Book III Which is the more desirable oftwo or more things
Part 1 In themselves
The question which is the more desirable, or the better, of two or morethings, should be examined upon the following lines: only first of all it mustbe clearly laid down that the inquiry we are making concerns not things thatare widely divergent and that exhibit great differences from one another (fornobody raises any doubt whether happiness or wealth is more desirable),but things that are nearly related and about which we commonly discuss forwhich of the two we ought rather to vote, because we do not see any advan-tage on either side as compared with the other. Clearly, in such cases if wecan show a single advantage, or more than one, our judgement will recordour assent that whichever side happens to have the advantage is the moredesirable.
First, then, that which is more lasting or secure is more desirable thanthat which is less so: and so is that which is more likely to be chosen by theprudent or by the good man or by the right law, or by men who are good inany particular line, when they make their choice as such, or by the experts inregard to any particular class of things; i.e. either whatever most of them orwhat all of them would choose; e.g. in medicine or in carpentry those thingsare more desirable which most, or all, doctors would choose; or, in general,whatever most men or all men or all things would choose, e.g. the good:for everything aims at the good. You should direct the argument you intendto employ to whatever purpose you require. Of what is ‘better’ or ‘moredesirable’ the absolute standard is the verdict of the better science, though
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relatively to a given individual the standard may be his own particular sci-ence.
In the second place, that which is known as ‘an x’ is more desirable thanthat which does not come within the genus ‘x’ - e.g. justice than a just man;for the former falls within the genus ‘good’, whereas the other does not, andthe former is called ‘a good’, whereas the latter is not: for nothing whichdoes not happen to belong to the genus in question is called by the genericname; e.g. a ‘white man’ is not ‘a colour’. Likewise also in other cases.
Also, that which is desired for itself is more desirable than that which isdesired for something else; e.g. health is more desirable than gymnastics: forthe former is desired for itself, the latter for something else. Also, that whichis desirable in itself is more desirable than what is desirable per accidens; e.g.justice in our friends than justice in our enemies: for the former is desirablein itself, the latter per accidens: for we desire that our enemies should bejust per accidens, in order that they may do us no harm. This last principleis the same as the one that precedes it, with, however, a different turn ofexpression. For we desire justice in our friends for itself, even though it willmake no difference to us, and even though they be in India; whereas in ourenemies we desire it for something else, in order that they may do us noharm.
Also, that which is in itself the cause of good is more desirable than whatis so per accidens, e.g. virtue than luck (for the former in itself, and thelatter per accidens, the cause of good things), and so in other cases of thesame kind. Likewise also in the case of the contrary; for what is in itself thecause of evil is more objectionable than what is so per accidens, e.g. vice andchance: for the one is bad in itself, whereas chance is so per accidens.
Also, what is good absolutely is more desirable than what is good for aparticular person, e.g. recovery of health than a surgical operation; for theformer is good absolutely, the latter only for a particular person, viz. theman who needs an operation. So too what is good by nature is more desir-able than the good that is not so by nature, e.g. justice than the just man;for the one is good by nature, whereas in the other case the goodness is ac-quired. Also the attribute is more desirable which belongs to the better andmore honourable subject, e.g. to a god rather than to a man, and to the soulrather than to the body. So too the property of the better thing is better thanthe property of the worse; e.g. the property of God than the property of man:for whereas in respect of what is common in both of them they do not differat all from each other, in respect of their properties the one surpasses theother. Also that is better which is inherent in things better or prior or morehonourable: thus (e.g.) health is better than strength and beauty: for the for-mer is inherent in the moist and the dry, and the hot and the cold, in fact inall the primary constituents of an animal, whereas the others are inherent in
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what is secondary, strength being a feature of the sinews and bones, whilebeauty is generally supposed to consist in a certain symmetry of the limbs.Also the end is generally supposed to be more desirable than the means,and of two means, that which lies nearer the end. In general, too, a meansdirected towards the end of life is more desirable than a means to anythingelse, e.g. that which contributes to happiness than that which contributesto prudence. Also the competent is more desirable than the incompetent.Moreover, of two productive agents that one is more desirable whose endis better; while between a productive agent and an end we can decide bya proportional sum whenever the excess of the one end over the other isgreater than that of the latter over its own productive means: e.g. suppos-ing the excess of happiness over health to be greater than that of health overwhat produces health, then what produces happiness is better than health.For what produces happiness exceeds what produces health just as muchas happiness exceeds health. But health exceeds what produces health bya smaller amount; ergo, the excess of what produces happiness over whatproduces health is greater than that of health over what produces health.Clearly, therefore, what produces happiness is more desirable than health:for it exceeds the same standard by a greater amount. Moreover, what isin itself nobler and more precious and praiseworthy is more desirable thanwhat is less so, e.g. friendship than wealth, and justice than strength. For theformer belong in themselves to the class of things precious and praisewor-thy, while the latter do so not in themselves but for something else: for noone prizes wealth for itself but always for something else, whereas we prizefriendship for itself, even though nothing else is likely to come to us from it.
Part 2 In their consequences
Moreover, whenever two things are very much like one another, and we can-not see any superiority in the one over the other of them, we should look atthem from the standpoint of their consequences. For the one which is fol-lowed by the greater good is the more desirable: or, if the consequences beevil, that is more desirable which is followed by the less evil. For thoughboth may be desirable, yet there may possibly be some unpleasant conse-quence involved to turn the scale. Our survey from the point of view ofconsequences lies in two directions, for there are prior consequences andlater consequences: e.g. if a man learns, it follows that he was ignorant be-fore and knows afterwards. As a rule, the later consequence is the better toconsider. You should take, therefore, whichever of the consequences suitsyour purpose.
Moreover, a greater number of good things is more desirable than asmaller, either absolutely or when the one is included in the other, viz. the
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smaller number in the greater. An objection may be raised suppose in someparticular case the one is valued for the sake of the other; for then the twotogether are not more desirable than the one; e.g. recovery of health andhealth, than health alone, inasmuch as we desire recovery of health for thesake of health. Also it is quite possible for what is not good, together withwhat is, to be more desirable than a greater number of good things, e.g. thecombination of happiness and something else which is not good may bemore desirable than the combination of justice and courage. Also, the samethings are more valuable if accompanied than if unaccompanied by pleasure,and likewise when free from pain than when attended with pain.
Also, everything is more desirable at the season when it is of greater con-sequence; e.g. freedom from pain in old age more than in youth: for it isof greater consequence in old age. On the same principle also, prudence ismore desirable in old age; for no man chooses the young to guide him, be-cause he does not expect them to be prudent. With courage, the converseis the case, for it is in youth that the active exercise of courage is more im-peratively required. Likewise also with temperance; for the young are moretroubled by their passions than are their elders.
Also, that is more desirable which is more useful at every season or atmost seasons, e.g. justice and temperance rather than courage: for they arealways useful, while courage is only useful at times. Also, that one of twothings which if all possess, we do not need the other thing, is more desirablethan that which all may possess and still we want the other one as well. Takethe case of justice and courage; if everybody were just, there would be no usefor courage, whereas all might be courageous, and still justice would be ofuse.
Moreover, judge by the destructions and losses and generations and ac-quisitions and contraries of things: for things whose destruction is moreobjectionable are themselves more desirable. Likewise also with the lossesand contraries of things; for a thing whose loss or whose contrary is moreobjectionable is itself more desirable. With the generations or acquisitionsof things the opposite is the case: for things whose acquisition or gener-ation is more desirable are themselves also desirable. Another common-place rule is that what is nearer to the good is better and more desirable,i.e. what more nearly resembles the good: thus justice is better than a justman. Also, that which is more like than another thing to something betterthan itself, as e.g. some say that Ajax was a better man than Odysseus be-cause he was more like Achilles. An objection may be raised to this that itis not true: for it is quite possible that Ajax did not resemble Achilles morenearly than Odysseus in the points which made Achilles the best of them,and that Odysseus was a good man, though unlike Achilles. Look also tosee whether the resemblance be that of a caricature, like the resemblance of
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a monkey to a man, whereas a horse bears none: for the monkey is not themore handsome creature, despite its nearer resemblance to a man. Again, inthe case of two things, if one is more like the better thing while another ismore like the worse, then that is likely to be better which is more like the bet-ter. This too, however, admits of an objection: for quite possibly the one onlyslightly resembles the better, while the other strongly resembles the worse,e.g. supposing the resemblance of Ajax to Achilles to be slight, while that ofOdysseus to Nestor is strong. Also it may be that the one which is like thebetter type shows a degrading likeness, whereas the one which is like theworse type improves upon it: witness the likeness of a horse to a donkey,and that of a monkey to a man.
Another rule is that the more conspicuous good is more desirable thanthe less conspicuous, and the more difficult than the easier: for we appreciatebetter the possession of things that cannot be easily acquired. Also the morepersonal possession is more desirable than the more widely shared. Also,that which is more free from connexion with evil: for what is not attendedby any unpleasantness is more desirable than what is so attended.
Moreover, if A be without qualification better than B, then also the bestof the members of A is better than the best of the members of B; e.g. if Manbe better than Horse, then also the best man is better than the best horse.Also, if the best in A be better than the best in B, then also A is better than Bwithout qualification; e.g. if the best man be better than the best horse, thenalso Man is better than Horse without qualification.
Moreover, things which our friends can share are more desirable thanthose they cannot. Also, things which we like rather to do to our friendare more desirable than those we like to do to the man in the street, e.g.just dealing and the doing of good rather than the semblance of them: forwe would rather really do good to our friends than seem to do so, whereastowards the man in the street the converse is the case.
Also, superfluities are better than necessities, and are sometimes moredesirable as well: for the good life is better than mere life, and good life is asuperfluity, whereas mere life itself is a necessity. Sometimes, though, whatis better is not also more desirable: for there is no necessity that because itis better it should also be more desirable: at least to be a philosopher is bet-ter than to make money, but it is not more desirable for a man who lacksthe necessities of life. The expression ‘superfluity’ applies whenever a manpossesses the necessities of life and sets to work to secure as well other no-ble acquisitions. Roughly speaking, perhaps, necessities are more desirable,while superfluities are better.
Also, what cannot be got from another is more desirable than what canbe got from another as well, as (e.g.) is the case of justice compared withcourage. Also, A is more desirable if A is desirable without B, but not B
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without A: power (e.g.) is not desirable without prudence, but prudence isdesirable without power. Also, if of two things we repudiate the one in orderto be thought to possess the other, then that one is more desirable which wewish to be thought to possess; thus (e.g.) we repudiate the love of hard workin order that people may think us geniuses.
Moreover, that is more desirable in whose absence it is less blameworthyfor people to be vexed; and that is more desirable in whose absence it is moreblameworthy for a man not to be vexed.
Part 3 The particular virtue of species
Moreover, of things that belong to the same species one which possesses thepeculiar virtue of the species is more desirable than one which does not. Ifboth possess it, then the one which possesses it in a greater degree is moredesirable.
Moreover, if one thing makes good whatever it touches, while anotherdoes not, the former is more desirable, just as also what makes things warmis warmer than what does not. If both do so, then that one is more desirablewhich does so in a greater degree, or if it render good the better and moreimportant object - if (e.g.), the one makes good the soul, and the other thebody.
Moreover, judge things by their inflexions and uses and actions andworks, and judge these by them: for they go with each other: e.g. if‘justly’ means something more desirable than ‘courageously’, then also jus-tice means something more desirable than courage; and if justice be moredesirable than courage, then also ‘justly’ means something more desirablethan ‘courageously’. Similarly also in the other cases.
Moreover, if one thing exceeds while the other falls short of the samestandard of good, the one which exceeds is the more desirable; or if the oneexceeds an even higher standard. Nay more, if there be two things bothpreferable to something, the one which is more highly preferable to it ismore desirable than the less highly preferable. Moreover, when the excessof a thing is more desirable than the excess of something else, that thing isitself also more desirable than the other, as (e.g.) friendship than money: foran excess of friendship is more desirable than an excess of money. So alsothat of which a man would rather that it were his by his own doing is moredesirable than what he would rather get by another’s doing, e.g. friendsthan money. Moreover, judge by means of an addition, and see if the addi-tion of A to the same thing as B makes the whole more desirable than doesthe addition of B. You must, however, beware of adducing a case in whichthe common term uses, or in some other way helps the case of, one of thethings added to it, but not the other, as (e.g.) if you took a saw and a sickle
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in combination with the art of carpentry: for in the combination the saw isa more desirable thing, but it is not a more desirable thing without qualifi-cation. Again, a thing is more desirable if, when added to a lesser good, itmakes the whole greater good. Likewise, also, you should judge by means ofsubtraction: for the thing upon whose subtraction the remainder is a lessergood may be taken to be a greater good, whichever it be whose subtractionmakes the remainder a lesser good.
Also, if one thing be desirable for itself, and the other for the look of it, theformer is more desirable, as (e.g.) health than beauty. A thing is defined asbeing desired for the look of it if, supposing no one knew of it, you would notcare to have it. Also, it is more desirable both for itself and for the look of it,while the other thing is desirable on the one ground alone. Also, whicheveris the more precious for itself, is also better and more desirable. A thingmay be taken to be more precious in itself which we choose rather for itself,without anything else being likely to come of it.
Moreover, you should distinguish in how many senses ‘desirable’ isused, and with a view to what ends, e.g. expediency or honour or pleasure.For what is useful for all or most of them may be taken to be more desir-able than what is not useful in like manner. If the same characters belong toboth things you should look and see which possesses them more markedly,i.e. which of the two is the more pleasant or more honourable or more ex-pedient. Again, that is more desirable which serves the better purpose, e.g.that which serves to promote virtue more than that which serves to promotepleasure. Likewise also in the case of objectionable things; for that is moreobjectionable which stands more in the way of what is desirable, e.g. diseasemore than ugliness: for disease is a greater hindrance both to pleasure andto being good.
Moreover, argue by showing that the thing in question is in like measureobjectionable and desirable: for a thing of such a character that a man mightwell desire and object to it alike is less desirable than the other which isdesirable only.
Part 4 The more desirable is desirable
Comparisons of things together should therefore be conducted in the man-ner prescribed. The same commonplace rules are useful also for showingthat anything is simply desirable or objectionable: for we have only to sub-tract the excess of one thing over another. For if what is more precious bemore desirable, then also what is precious is desirable; and if what is moreuseful be more desirable, then also what is useful is desirable. Likewise, also,in the case of other things which admit of comparisons of that kind. For insome cases in the very course of comparing the things together we at once
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assert also that each of them, or the one of them, is desirable, e.g. wheneverwe call the one good ‘by nature’ and the other ‘not by nature’: for dearlywhat is good by nature is desirable.
Part 5 Comparative degrees and amounts
The commonplace rules relating to comparative degrees and amounts oughtto be taken in the most general possible form: for when so taken they arelikely to be useful in a larger number of instances. It is possible to rendersome of the actual rules given above more universal by a slight alterationof the expression, e.g. that what by nature exhibits such and such a qualityexhibits that quality in a greater degree than what exhibits it not by nature.Also, if one thing does, and another does not, impart such and such a qualityto that which possesses it, or to which it belongs, then whichever does im-part it is of that quality in greater degree than the one which does not impartit; and if both impart it, then that one exhibits it in a greater degree whichimparts it in a greater degree.
Moreover, if in any character one thing exceeds and another falls shortof the same standard; also, if the one exceeds something which exceeds agiven standard, while the other does not reach that standard, then clearlythe first-named thing exhibits that character in a greater degree. Moreover,you should judge by means of addition, and see if A when added to the samething as B imparts to the whole such and such a character in a more markeddegree than B, or if, when added to a thing which exhibits that characterin a less degree, it imparts that character to the whole in a greater degree.Likewise, also, you may judge by means of subtraction: for a thing uponwhose subtraction the remainder exhibits such and such a character in a lessdegree, itself exhibits that character in a greater degree. Also, things exhibitsuch and such a character in a greater degree if more free from admixturewith their contraries; e.g. that is whiter which is more free from admixturewith black. Moreover, apart from the rules given above, that has such andsuch a character in greater degree which admits in a greater degree of thedefinition proper to the given character; e.g. if the definition of ‘white’ be‘a colour which pierces the vision’, then that is whiter which is in a greaterdegree a colour that pierces the vision.
Part 6 Universals entail particulars
If the question be put in a particular and not in a universal form, in the firstplace the universal constructive or destructive commonplace rules that havebeen given may all be brought into use. For in demolishing or establishinga thing universally we also show it in particular: for if it be true of all, it is
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true also of some, and if untrue of all, it is untrue of some. Especially handyand of general application are the commonplace rules that are drawn fromthe opposites and co-ordinates and inflexions of a thing: for public opin-ion grants alike the claim that if all pleasure be good, then also all pain isevil, and the claim that if some pleasure be good, then also some pain isevil. Moreover, if some form of sensation be not a capacity, then also someform of failure of sensation is not a failure of capacity. Also, if the object ofconception is in some cases an object of knowledge, then also some form ofconceiving is knowledge. Again, if what is unjust be in some cases good,then also what is just is in some cases evil; and if what happens justly is insome cases evil, then also what happens unjustly is in some cases good. Also,if what is pleasant is in some cases objectionable, then pleasure is in somecases an objectionable thing. On the same principle, also, if what is pleasantis in some cases beneficial, then pleasure is in some cases a beneficial thing.The case is the same also as regards the things that destroy, and the pro-cesses of generation and destruction. For if anything that destroys pleasureor knowledge be in some cases good, then we may take it that pleasure orknowledge is in some cases an evil thing. Likewise, also, if the destructionof knowledge be in some cases a good thing or its production an evil thing,then knowledge will be in some cases an evil thing; e.g. if for a man to forgethis disgraceful conduct be a good thing, and to remember it be an evil thing,then the knowledge of his disgraceful conduct may be taken to be an evilthing. The same holds also in other cases: in all such cases the premiss andthe conclusion are equally likely to be accepted.
Moreover you should judge by means of greater or smaller or like de-grees: for if some member of another genus exhibit such and such a char-acter in a more marked degree than your object, while no member of thatgenus exhibits that character at all, then you may take it that neither doesthe object in question exhibit it; e.g. if some form of knowledge be good ina greater degree than pleasure, while no form of knowledge is good, thenyou may take it that pleasure is not good either. Also, you should judge by asmaller or like degree in the same way: for so you will find it possible bothto demolish and to establish a view, except that whereas both are possibleby means of like degrees, by means of a smaller degree it is possible only toestablish, not to overthrow. For if a certain form of capacity be good in a likedegree to knowledge, and a certain form of capacity be good, then so also isknowledge; while if no form of capacity be good, then neither is knowledge.If, too, a certain form of capacity be good in a less degree than knowledge,and a certain form of capacity be good, then so also is knowledge; but if noform of capacity be good, there is no necessity that no form of knowledgeeither should be good. Clearly, then, it is only possible to establish a view bymeans of a less degree.
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Not only by means of another genus can you overthrow a view, but alsoby means of the same, if you take the most marked instance of the characterin question; e.g. if it be maintained that some form of knowledge is good,then, suppose it to be shown that prudence is not good, neither will anyother kind be good, seeing that not even the kind upon which there is mostgeneral agreement is so. Moreover, you should go to work by means ofan hypothesis; you should claim that the attribute, if it belongs or does notbelong in one case, does so in a like degree in all, e.g. that if the soul ofman be immortal, so are other souls as well, while if this one be not so,neither are the others. If, then, it be maintained that in some instance theattribute belongs, you must show that in some instance it does not belong:for then it will follow, by reason of the hypothesis, that it does not belongto any instance at all. If, on the other hand, it be maintained that it doesnot belong in some instance, you must show that it does belong in someinstance, for in this way it will follow that it belongs to all instances. It isclear that the maker of the hypothesis universalizes the question, whereas itwas stated in a particular form: for he claims that the maker of a particularadmission should make a universal admission, inasmuch as he claims thatif the attribute belongs in one instance, it belongs also in all instances alike.
If the problem be indefinite, it is possible to overthrow a statement inonly one way; e.g. if a man has asserted that pleasure is good or is not good,without any further definition. For if he meant that a particular pleasure isgood, you must show universally that no pleasure is good, if the propositionin question is to be demolished. And likewise, also, if he meant that someparticular pleasure is not good you must show universally that all pleasureis good: it is impossible to demolish it in any other way. For if we showthat some particular pleasure is not good or is good, the proposition in ques-tion is not yet demolished. It is clear, then, that it is possible to demolish anindefinite statement in one way only, whereas it can be established in twoways: for whether we show universally that all pleasure is good, or whetherwe show that a particular pleasure is good, the proposition in question willhave been proved. Likewise, also, supposing we are required to argue thatsome particular pleasure is not good, if we show that no pleasure is goodor that a particular pleasure is not good, we shall have produced an argu-ment in both ways, both universally and in particular, to show that someparticular pleasure is not good. If, on the other hand, the statement madebe definite, it will be possible to demolish it in two ways; e.g. if it be main-tained that it is an attribute of some particular pleasure to be good, while ofsome it is not: for whether it be shown that all pleasure, or that no pleasure,is good, the proposition in question will have been demolished. If, however,he has stated that only one single pleasure is good, it is possible to demolishit in three ways: for by showing that all pleasure, or that no pleasure, or that
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more than one pleasure, is good, we shall have demolished the statementin question. If the statement be made still more definite, e.g. that prudencealone of the virtues is knowledge, there are four ways of demolishing it: forif it be shown that all virtue is knowledge, or that no virtue is so, or that someother virtue (e.g. justice) is so, or that prudence itself is not knowledge, theproposition in question will have been demolished.
It is useful also to take a look at individual instances, in cases where someattribute has been said to belong or not to belong, as in the case of universalquestions. Moreover, you should take a glance among genera, dividing themby their species until you come to those that are not further divisible, as hasbeen said before: for whether the attribute is found to belong in all cases orin none, you should, after adducing several instances, claim that he shouldeither admit your point universally, or else bring an objection showing inwhat case it does not hold. Moreover, in cases where it is possible to makethe accident definite either specifically or numerically, you should look andsee whether perhaps none of them belongs, showing e.g. that time is notmoved, nor yet a movement, by enumerating how many species there areof movement: for if none of these belong to time, clearly it does not move,nor yet is a movement. Likewise, also, you can show that the soul is not anumber, by dividing all numbers into either odd or even: for then, if the soulbe neither odd nor even, clearly it is not a number.
In regard then to Accident, you should set to work by means like these,and in this manner.
Book IV The relationship betweengenus and species
Part 1 Species are distinguished by essential properties
Next we must go on to examine questions relating to Genus and Property.These are elements in the questions that relate to definitions, but dialecti-cians seldom address their inquiries to these by themselves. If, then, a genusbe suggested for something that is, first take a look at all objects which be-long to the same genus as the thing mentioned, and see whether the genussuggested is not predicated of one of them, as happens in the case of an ac-cident: e.g. if ‘good’ be laid down to be the genus of ‘pleasure’, see whethersome particular pleasure be not good: for, if so, clearly ‘good’ is not thegenus of pleasure: for the genus is predicated of all the members of the samespecies. Secondly, see whether it be predicated not in the category of essence,but as an accident, as ‘white’ is predicated of ‘snow’, or ‘self-moved’ of the
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soul. For ‘snow’ is not a kind of ‘white’, and therefore ‘white’ is not the genusof snow, nor is the soul a kind of ‘moving object’: its motion is an accidentof it, as it often is of an animal to walk or to be walking. Moreover, ‘moving’does not seem to indicate the essence, but rather a state of doing or of havingsomething done to it. Likewise, also, ‘white’: for it indicates not the essenceof snow, but a certain quality of it. So that neither of them is predicated inthe category of ‘essence’.
Especially you should take a look at the definition of Accident, and seewhether it fits the genus mentioned, as (e.g.) is also the case in the instancesjust given. For it is possible for a thing to be and not to be self-moved, andlikewise, also, for it to be and not to be white. So that neither of these at-tributes is the genus but an accident, since we were saying that an accidentis an attribute which can belong to a thing and also not belong.
Moreover, see whether the genus and the species be not found in thesame division, but the one be a substance while the other is a quality, orthe one be a relative while the other is a quality, as (e.g.) ‘slow’ and ‘swan’are each a substance, while ‘white’ is not a substance but a quality, so that‘white’ is not the genus either of ‘snow’ or of ‘swan’. Again, ‘knowledge’ isa relative, while ‘good’ and ‘noble’ are each a quality, so that good, or no-ble, is not the genus of knowledge. For the genera of relatives ought them-selves also to be relatives, as is the case with ‘double’: for ‘multiple’, whichis the genus of ‘double’, is itself also a relative. To speak generally, the genusought to fall under the same division as the species: for if the species be asubstance, so too should be the genus, and if the species be a quality, so toothe genus should be a quality; e.g. if white be a quality, so too should colourbe. Likewise, also, in other cases.
Again, see whether it be necessary or possible for the genus to partake ofthe object which has been placed in the genus. ‘To partake’ is defined as ‘toadmit the definition of that which is partaken.’ Clearly, therefore, the speciespartake of the genera, but not the genera of the species: for the species ad-mits the definition of the genus, whereas the genus does not admit that ofthe species. You must look, therefore, and see whether the genus renderedpartakes or can possibly partake of the species, e.g. if any one were to renderanything as genus of ‘being’ or of ‘unity’: for then the result will be that thegenus partakes of the species: for of everything that is, ‘being’ and ‘unity’are predicated, and therefore their definition as well.
Moreover, see if there be anything of which the species rendered is true,while the genus is not so, e.g. supposing ‘being’ or ‘object of knowledge’were stated to be the genus of ‘object of opinion’. For ‘object of opinion’ willbe a predicate of what does not exist; for many things which do not existare objects of opinion; whereas that ‘being’ or ‘object of knowledge’ is notpredicated of what does not exist is clear. So that neither ‘being’ nor ‘object
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of knowledge’ is the genus of ‘object of opinion’: for of the objects of whichthe species is predicated, the genus ought to be predicated as well.
Again, see whether the object placed in the genus be quite unable to par-take of any of its species: for it is impossible that it should partake of thegenus if it do not partake of any of its species, except it be one of the speciesreached by the first division: these do partake of the genus alone. If, there-fore, ‘Motion’ be stated as the genus of pleasure, you should look and see ifpleasure be neither locomotion nor alteration, nor any of the rest of the givenmodes of motion: for clearly you may then take it that it does not partakeof any of the species, and therefore not of the genus either, since what par-takes of the genus must necessarily partake of one of the species as well: sothat pleasure could not be a species of Motion, nor yet be one of the individ-ual phenomena comprised under the term ‘motion’. For individuals as wellpartake in the genus and the species, as (e.g.) an individual man partakes ofboth ‘man’ and ‘animal’.
Moreover, see if the term placed in the genus has a wider denotationthan the genus, as (e.g.) ‘object of opinion’ has, as compared with ‘being’:for both what is and what is not are objects of opinion, so that ‘object ofopinion’ could not be a species of being: for the genus is always of widerdenotation than the species. Again, see if the species and its genus have anequal denotation; suppose, for instance, that of the attributes which go witheverything, one were to be stated as a species and the other as its genus, asfor example Being and Unity: for everything has being and unity, so thatneither is the genus of the other, since their denotation is equal. Likewise,also, if the ‘first’ of a series and the ‘beginning’ were to be placed one underthe other: for the beginning is first and the first is the beginning, so thateither both expressions are identical or at any rate neither is the genus of theother. The elementary principle in regard to all such cases is that the genushas a wider denotation than the species and its differentia: for the differentiaas well has a narrower denotation than the genus.
See also whether the genus mentioned fails, or might be generallythought to fail, to apply to some object which is not specifically differentfrom the thing in question; or, if your argument be constructive, whether itdoes so apply. For all things that are not specifically different have the samegenus. If, therefore, it be shown to apply to one, then clearly it applies toall, and if it fails to apply to one, clearly it fails to apply to any; e.g. if anyone who assumes ‘indivisible lines’ were to say that the ‘indivisible’ is theirgenus. For the aforesaid term is not the genus of divisible lines, and thesedo not differ as regards their species from indivisible: for straight lines arenever different from each other as regards their species.
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Part 2 Species falling under more than one genus
Look and see, also, if there be any other genus of the given species whichneither embraces the genus rendered nor yet falls under it, e.g. suppose anyone were to lay down that ‘knowledge’ is the genus of justice. For virtue isits genus as well, and neither of these genera embraces the remaining one, sothat knowledge could not be the genus of justice: for it is generally acceptedthat whenever one species falls under two genera, the one is embraced bythe other. Yet a principle of this kind gives rise to a difficulty in some cases.For some people hold that prudence is both virtue and knowledge, and thatneither of its genera is embraced by the other: although certainly not ev-erybody admits that prudence is knowledge. If, however, any one were toadmit the truth of this assertion, yet it would still be generally agreed to benecessary that the genera of the same object must at any rate be subordinateeither the one to the other or both to the same, as actually is the case withvirtue and knowledge. For both fall under the same genus; for each of themis a state and a disposition. You should look, therefore, and see whetherneither of these things is true of the genus rendered; for if the genera besubordinate neither the one to the other nor both to the same, then what isrendered could not be the true genus.
Look, also, at the genus of the genus rendered, and so continually at thenext higher genus, and see whether all are predicated of the species, andpredicated in the category of essence: for all the higher genera should bepredicated of the species in the category of essence. If, then, there be any-where a discrepancy, clearly what is rendered is not the true genus. [Again,see whether either the genus itself, or one of its higher genera, partakes ofthe species: for the higher genus does not partake of any of the lower.] If,then, you are overthrowing a view, follow the rule as given: if establishingone, then - suppose that what has been named as genus be admitted to be-long to the species, only it be disputed whether it belongs as genus - it isenough to show that one of its higher genera is predicated of the species inthe category of essence. For if one of them be predicated in the categoryof essence, all of them, both higher and lower than this one, if predicatedat all of the species, will be predicated of it in the category of essence: sothat what has been rendered as genus is also predicated in the category ofessence. The premiss that when one genus is predicated in the category ofessence, all the rest, if predicated at all, will be predicated in the categoryof essence, should be secured by induction. Supposing, however, that it bedisputed whether what has been rendered as genus belongs at all, it is notenough to show that one of the higher genera is predicated of the speciesin the category of essence: e.g. if any one has rendered ‘locomotion’ as thegenus of walking, it is not enough to show that walking is ‘motion’ in order
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to show that it is ‘locomotion’, seeing that there are other forms of motion aswell; but one must show in addition that walking does not partake of any ofthe species of motion produced by the same division except locomotion. Forof necessity what partakes of the genus partakes also of one of the speciesproduced by the first division of the genus. If, therefore, walking does notpartake either of increase or decrease or of the other kinds of motion, clearlyit would partake of locomotion, so that locomotion would be the genus ofwalking.
Again, look among the things of which the given species is predicatedas genus, and see if what is rendered as its genus be also predicated in thecategory of essence of the very things of which the species is so predicated,and likewise if all the genera higher than this genus are so predicated as well.For if there be anywhere a discrepancy, clearly what has been rendered is notthe true genus: for had it been the genus, then both the genera higher thanit, and it itself, would all have been predicated in the category of essence ofthose objects of which the species too is predicated in the category of essence.If, then, you are overthrowing a view, it is useful to see whether the genusfails to be predicated in the category of essence of those things of which thespecies too is predicated. If establishing a view, it is useful to see whether itis predicated in the category of essence: for if so, the result will be that thegenus and the species will be predicated of the same object in the categoryof essence, so that the same object falls under two genera: the genera musttherefore of necessity be subordinate one to the other, and therefore if it beshown that the one we wish to establish as genus is not subordinate to thespecies, clearly the species would be subordinate to it, so that you may takeit as shown that it is the genus.
Look, also, at the definitions of the genera, and see whether they applyboth to the given species and to the objects which partake of the species. Forof necessity the definitions of its genera must be predicated of the speciesand of the objects which partake of the species: if, then, there be anywhere adiscrepancy, clearly what has been rendered is not the genus.
Again, see if he has rendered the differentia as the genus, e.g. ‘immor-tal’ as the genus of ‘God’. For ‘immortal’ is a differentia of ‘living being’,seeing that of living beings some are mortal and others immortal. Clearly,then, a bad mistake has been made; for the differentia of a thing is never itsgenus. And that this is true is clear: for a thing’s differentia never signifiesits essence, but rather some quality, as do ‘walking’ and ‘biped’.
Also, see whether he has placed the differentia inside the genus, e.g. bytaking ‘odd’ as a ‘number’. For ‘odd’ is a differentia of number, not a species.Nor is the differentia generally thought to partake of the genus: for whatpartakes of the genus is always either a species or an individual, whereasthe differentia is neither a species nor an individual. Clearly, therefore, the
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differentia does not partake of the genus, so that ‘odd’ too is no species buta differentia, seeing that it does not partake of the genus.
Moreover, see whether he has placed the genus inside the species, e.g.by taking ‘contact’ to be a ‘juncture’, or ‘mixture’ a ‘fusion’, or, as in Plato‘sdefinition, ’locomotion‘ to be the same as ’carriage’. For there is no necessitythat contact should be juncture: rather, conversely, juncture must be contact:for what is in contact is not always joined, though what is joined is alwaysin contact. Likewise, also, in the remaining instances: for mixture is not al-ways a ‘fusion’ (for to mix dry things does not fuse them), nor is locomotionalways ‘carriage’. For walking is not generally thought to be carriage: for‘carriage’ is mostly used of things that change one place for another involun-tarily, as happens in the case of inanimate things. Clearly, also, the species,in the instances given, has a wider denotation than the genus, whereas itought to be vice versa.
Again, see whether he has placed the differentia inside the species, bytaking (e.g.) ‘immortal’ to be ‘a god’. For the result will be that the specieshas an equal or wider denotation: and this cannot be, for always the dif-ferentia has an equal or a wider denotation than the species. Moreover, seewhether he has placed the genus inside the differentia, by making ‘colour’(e.g.) to be a thing that ‘pierces’, or ‘number’ a thing that is ‘odd’. Also, see ifhe has mentioned the genus as differentia: for it is possible for a man to bringforward a statement of this kind as well, e.g. that ‘mixture’ is the differentiaof ‘fusion’, or that change of place’ is the differentia of ‘carriage’. All suchcases should be examined by means of the same principles: for they dependupon common rules: for the genus should have a wider denotation that itsdifferentia, and also should not partake of its differentia; whereas, if it berendered in this manner, neither of the aforesaid requirements can be satis-fied: for the genus will both have a narrower denotation than its differentia,and will partake of it.
Again, if no differentia belonging to the genus be predicated of the givenspecies, neither will the genus be predicated of it; e.g. of ‘soul’ neither‘odd’ nor ‘even’ is predicated: neither therefore is ‘number’. Moreover, seewhether the species is naturally prior and abolishes the genus along withitself: for the contrary is the general view. Moreover, if it be possible for thegenus stated, or for its differentia, to be absent from the alleged species, e.g.for ‘movement’ to be absent from the ‘soul’, or ‘truth and falsehood’ from‘opinion’, then neither of the terms stated could be its genus or its differen-tia: for the general view is that the genus and the differentia accompany thespecies, as long as it exists.
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Part 3 Species partaking of contratries of the genus
Look and see, also, if what is placed in the genus partakes or could possiblypartake of any contrary of the genus: for in that case the same thing willat the same time partake of contrary things, seeing that the genus is neverabsent from it, while it partakes, or can possibly partake, of the contrarygenus as well. Moreover, see whether the species shares in any characterwhich it is utterly impossible for any member of the genus to have. Thus(e.g.) if the soul has a share in life, while it is impossible for any number tolive, then the soul could not be a species of number.
You should look and see, also, if the species be a homonym of the genus,and employ as your elementary principles those already stated for dealingwith homonymity: for the genus and the species are synonymous.
Seeing that of every genus there is more than one species, look and seeif it be impossible that there should be another species than the given onebelonging to the genus stated: for if there should be none, then clearly whathas been stated could not be a genus at all.
Look and see, also, if he has rendered as genus a metaphorical expres-sion, describing (e.g. ‘temperance’ as a ‘harmony’: a ‘harmony’: for a genusis always predicated of its species in its literal sense, whereas ‘harmony’ ispredicated of temperance not in a literal sense but metaphorically: for a har-mony always consists in notes.
Moreover, if there be any contrary of the species, examine it. The ex-amination may take different forms; first of all see if the contrary as wellbe found in the same genus as the species, supposing the genus to have nocontrary; for contraries ought to be found in the same genus, if there be nocontrary to the genus. Supposing, on the other hand, that there is a con-trary to the genus, see if the contrary of the species be found in the contrarygenus: for of necessity the contrary species must be in the contrary genus,if there be any contrary to the genus. Each of these points is made plain bymeans of induction. Again, see whether the contrary of the species be notfound in any genus at all, but be itself a genus, e.g. ‘good’: for if this be notfound in any genus, neither will its contrary be found in any genus, but willitself be a genus, as happens in the case of ‘good’ and ‘evil’: for neither ofthese is found in a genus, but each of them is a genus. Moreover, see if bothgenus and species be contrary to something, and one pair of contraries havean intermediary, but not the other. For if the genera have an intermediary, soshould their species as well, and if the species have, so should their generaas well, as is the case with (1) virtue and vice and (2) justice and injustice: foreach pair has an intermediary. An objection to this is that there is no inter-mediary between health and disease, although there is one between evil andgood. Or see whether, though there be indeed an intermediary between both
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pairs, i.e. both between the species and between the genera, yet it be not sim-ilarly related, but in one case be a mere negation of the extremes, whereas inthe other case it is a subject. For the general view is that the relation shouldbe similar in both cases, as it is in the cases of virtue and vice and of justiceand injustice: for the intermediaries between both are mere negations. More-over, whenever the genus has no contrary, look and see not merely whetherthe contrary of the species be found in the same genus, but the intermediateas well: for the genus containing the extremes contains the intermediates aswell, as (e.g.) in the case of white and black: for ‘colour’ is the genus bothof these and of all the intermediate colours as well. An objection may beraised that ‘defect’ and ‘excess’ are found in the same genus (for both arein the genus ‘evil’), whereas ‘moderate amount’, the intermediate betweenthem, is found not in ‘evil’ but in ‘good’. Look and see also whether, whilethe genus has a contrary, the species has none; for if the genus be contraryto anything, so too is the species, as virtue to vice and justice to injustice.
Likewise. also, if one were to look at other instances, one would come tosee clearly a fact like this. An objection may be raised in the case of healthand disease: for health in general is the contrary of disease, whereas a par-ticular disease, being a species of disease, e.g. fever and ophthalmia and anyother particular disease, has no contrary.
If, therefore, you are demolishing a view, there are all these ways inwhich you should make your examination: for if the aforesaid charactersdo not belong to it, clearly what has been rendered is not the genus. If, onthe other hand, you are establishing a view, there are three ways: in the firstplace, see whether the contrary of the species be found in the genus stated,suppose the genus have no contrary: for if the contrary be found in it, clearlythe species in question is found in it as well. Moreover, see if the interme-diate species is found in the genus stated: for whatever genus contains theintermediate contains the extremes as well. Again, if the genus have a con-trary, look and see whether also the contrary species is found in the contrarygenus: for if so, clearly also the species in question is found in the genus inquestion.
Again, consider in the case of the inflexions and the co-ordinates ofspecies and genus, and see whether they follow likewise, both in demol-ishing and in establishing a view. For whatever attribute belongs or doesnot belong to one belongs or does not belong at the same time to all; e.g. ifjustice be a particular form of knowledge, then also ‘justly’ is ‘knowingly’and the just man is a man of knowledge: whereas if any of these things benot so, then neither is any of the rest of them.
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Part 4 Things that bear a like relation to one another
Again, consider the case of things that bear a like relation to one another.Thus (e.g.) the relation of the pleasant to pleasure is like that of the useful tothe good: for in each case the one produces the other. If therefore pleasure bea kind of ‘good’, then also the pleasant will be a kind of ‘useful’: for clearlyit may be taken to be productive of good, seeing that pleasure is good. In thesame way also consider the case of processes of generation and destruction;if (e.g.) to build be to be active, then to have built is to have been active, andif to learn be to recollect, then also to have learnt is to have recollected, andif to be decomposed be to be destroyed, then to have been decomposed isto have been destroyed, and decomposition is a kind of destruction. Con-sider also in the same way the case of things that generate or destroy, andof the capacities and uses of things; and in general, both in demolishing andin establishing an argument, you should examine things in the light of anyresemblance of whatever description, as we were saying in the case of gen-eration and destruction. For if what tends to destroy tends to decompose,then also to be destroyed is to be decomposed: and if what tends to generatetends to produce, then to be generated is to be produced, and generation isproduction. Likewise, also, in the case of the capacities and uses of things:for if a capacity be a disposition, then also to be capable of something is tobe disposed to it, and if the use of anything be an activity, then to use it is tobe active, and to have used it is to have been active.
If the opposite of the species be a privation, there are two ways of demol-ishing an argument, first of all by looking to see if the opposite be foundin the genus rendered: for either the privation is to be found absolutelynowhere in the same genus, or at least not in the same ultimate genus: e.g. ifthe ultimate genus containing sight be sensation, then blindness will not be asensation. Secondly, if there be a sensation. Secondly, if there be a privationopposed to both genus and species, but the opposite of the species be notfound in the opposite of the genus, then neither could the species renderedbe in the genus rendered. If, then, you are demolishing a view, you shouldfollow the rule as stated; but if establishing one there is but one way: for ifthe opposite species be found in the opposite genus, then also the species inquestion would be found in the genus in question: e.g. if ‘blindness’ be aform of ‘insensibility’, then ‘sight’ is a form of ‘sensation’.
Again, look at the negations of the genus and species and convert theorder of terms, according to the method described in the case of Accident:e.g. if the pleasant be a kind of good, what is not good is not pleasant. Forwere this no something not good as well would then be pleasant. That, how-ever, cannot be, for it is impossible, if ‘good’ be the genus of pleasant, thatanything not good should be pleasant: for of things of which the genus is
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not predicated, none of the species is predicated either. Also, in establishinga view, you should adopt the same method of examination: for if what isnot good be not pleasant, then what is pleasant is good, so that ‘good’ is thegenus of ‘pleasant’.
If the species be a relative term, see whether the genus be a relative termas well: for if the species be a relative term, so too is the genus, as is the casewith ‘double’ and ‘multiple’: for each is a relative term. If, on the other hand,the genus be a relative term, there is no necessity that the species shouldbe so as well: for ‘knowledge’is a relative term, but not so ‘grammar’. Orpossibly not even the first statement would be generally considered true: forvirtue is a kind of ‘noble’ and a kind of ‘good’ thing, and yet, while ‘virtue’is a relative term, ‘good’ and ‘noble’ are not relatives but qualities. Again,see whether the species fails to be used in the same relation when called byits own name, and when called by the name of its genus: e.g. if the term‘double’ be used to mean the double of a ‘half’, then also the term ‘multiple’ought to be used to mean multiple of a ‘half’. Otherwise ‘multiple’ could notbe the genus of ‘double’.
Moreover, see whether the term fail to be used in the same relation bothwhen called by the name of its genus, and also when called by those of allthe genera of its genus. For if the double be a multiple of a half, then ‘inexcess of’ will also be used in relation to a ‘half’: and, in general, the doublewill be called by the names of all the higher genera in relation to a ‘half’. Anobjection may be raised that there is no necessity for a term to be used inthe same relation when called by its own name and when called by that ofits genus: for ‘knowledge’ is called knowledge ‘of an object’, whereas it iscalled a ‘state’ and ‘disposition’ not of an ‘object’ but of the ‘soul’.
Again, see whether the genus and the species be used in the same way inrespect of the inflexions they take, e.g. datives and genitives and all the rest.For as the species is used, so should the genus be as well, as in the case of‘double’ and its higher genera: for we say both ‘double of’ and ‘multiple of’a thing. Likewise, also, in the case of ‘knowledge’: for both knowledge itselfand its genera, e.g. ‘disposition’ and ‘state’, are said to be ‘of’ something. Anobjection may be raised that in some cases it is not so: for we say ‘superiorto’ and ‘contrary to’ so and so, whereas ‘other’, which is the genus of theseterms, demands not ‘to’ but ‘than’: for the expression is ‘other than’ so andso.
Again, see whether terms used in like case relationships fail to yield alike construction when converted, as do ‘double’ and ‘multiple’. For eachof these terms takes a genitive both in itself and in its converted form: forwe say both ‘a half of’ and ‘a fraction of’ something. The case is the samealso as regards both ‘knowledge’ and ‘conception’: for these take a genitive,and by conversion an ‘object of knowledge’ and an ‘object of conception’ are
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both alike used with a dative. If, then, in any cases the constructions afterconversion be not alike, clearly the one term is not the genus of the other.
Again, see whether the species and the genus fail to be used in relationto an equal number of things: for the general view is that the uses of bothare alike and equal in number, as is the case with ‘present’ and ‘grant’. For apresent is of something or to some one, and also a ‘grant’ is of something andto some one: and ‘grant’ is the genus of ‘present’, for a ‘present’ is a ‘grantthat need not be returned’. In some cases, however, the number of relationsin which the terms are used happens not to be equal, for while ‘double’ isdouble of something, we speak of ‘in excess’ or ‘greater’ in something, aswell as of or than something: for what is in excess or greater is always inexcess in something, as well as in excess of something. Hence the termsin question are not the genera of ‘double’, inasmuch as they are not usedin relation to an equal number of things with the species. Or possibly it isnot universally true that species and genus are used in relation to an equalnumber of things.
See, also, if the opposite of the species have the opposite of the genus asits genus, e.g. whether, if ‘multiple’ be the genus of ‘double’, ‘fraction’ bealso the genus of ‘half’. For the opposite of the genus should always be thegenus of the opposite species. If, then, any one were to assert that knowledgeis a kind of sensation, then also the object of knowledge will have to be akind of object of sensation, whereas it is not: for an object of knowledge isnot always an object of sensation: for objects of knowledge include some ofthe objects of intuition as well. Hence ‘object of sensation’ is not the genusof ‘object of knowledge’: and if this be so, neither is ‘sensation’ the genus of‘knowledge’.
Seeing that of relative terms some are of necessity found in, or used of,the things in relation to which they happen at any time to be used (e.g. ‘dis-position’ and ‘state’ and ‘balance’; for in nothing else can the aforesaid termspossibly be found except in the things in relation to which they are used),while others need not be found in the things in relation to which they areused at any time, though they still may be (e.g. if the term ‘object of knowl-edge’ be applied to the soul: for it is quite possible that the knowledge ofitself should be possessed by the soul itself, but it is not necessary, for it ispossible for this same knowledge to be found in some one else), while forothers, again, it is absolutely impossible that they should be found in thethings in relation to which they happen at any time to be used (as e.g. thatthe contrary should be found in the contrary or knowledge in the object ofknowledge, unless the object of knowledge happen to be a soul or a man) -you should look, therefore, and see whether he places a term of one kind in-side a genus that is not of that kind, e.g. suppose he has said that ‘memory’is the ‘abiding of knowledge’. For ‘abiding’ is always found in that which
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abides, and is used of that, so that the abiding of knowledge also will befound in knowledge. Memory, then, is found in knowledge, seeing that itis the abiding of knowledge. But this is impossible, for memory is alwaysfound in the soul. The aforesaid commonplace rule is common to the subjectof Accident as well: for it is all the same to say that ‘abiding’ is the genus ofmemory, or to allege that it is an accident of it. For if in any way whatevermemory be the abiding of knowledge, the same argument in regard to it willapply.
Part 5 Placing what is a ’state’ inside the genus ’activity’
Again, see if he has placed what is a ‘state’ inside the genus ‘activity’, or anactivity inside the genus ‘state’, e.g. by defining ‘sensation’ as ‘movementcommunicated through the body’: for sensation is a ‘state’, whereas move-ment is an ‘activity’. Likewise, also, if he has said that memory is a ‘statethat is retentive of a conception’, for memory is never a state, but rather anactivity.
They also make a bad mistake who rank a ‘state’ within the ‘capacity’that attends it, e.g. by defining ‘good temper’ as the ‘control of anger’, and‘courage’ and ‘justice’ as ‘control of fears’ and of ‘gains’: for the terms ‘coura-geous’ and ‘good-tempered’ are applied to a man who is immune from pas-sion, whereas ‘self-controlled’ describes the man who is exposed to passionand not led by it. Quite possibly, indeed, each of the former is attended bya capacity such that, if he were exposed to passion, he would control it andnot be led by it: but, for all that, this is not what is meant by being ‘coura-geous’ in the one case, and ‘good tempered’ in the other; what is meant is anabsolute immunity from any passions of that kind at all.
Sometimes, also, people state any kind of attendant feature as the genus,e.g. ‘pain’ as the genus of ‘anger’ and ‘conception’ as that of ‘conviction’.For both of the things in question follow in a certain sense upon the givenspecies, but neither of them is genus to it. For when the angry man feels pain,the pain bas appeared in him earlier than the anger: for his anger is not thecause of his pain, but his pain of his anger, so that anger emphatically isnot pain. By the same reasoning, neither is conviction conception: for it ispossible to have the same conception even without being convinced of it,whereas this is impossible if conviction be a species of conception: for it isimpossible for a thing still to remain the same if it be entirely transferred outof its species, just as neither could the same animal at one time be, and atanother not be, a man. If, on the other hand, any one says that a man whohas a conception must of necessity be also convinced of it, then ‘conception’and ‘conviction’ will be used with an equal denotation, so that not even socould the former be the genus of the latter: for the denotation of the genus
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should be wider.See, also, whether both naturally come to be anywhere in the same thing:
for what contains the species contains the genus as well: e.g. what contains‘white’ contains ‘colour’ as well, and what contains ‘knowledge of gram-mar’ contains ‘knowledge’ as well. If, therefore, any one says that ‘shame’ is‘fear’, or that ‘anger’ is ‘pain’, the result will be that genus and species arenot found in the same thing: for shame is found in the ‘reasoning’ faculty,whereas fear is in the ‘spirited’ faculty, and ‘pain’ is found in the faculty of‘desires’. (for in this pleasure also is found), whereas ‘anger’ is found in the‘spirited’ faculty. Hence the terms rendered are not the genera, seeing thatthey do not naturally come to be in the same faculty as the species. Likewise,also, if ‘friendship’ be found in the faculty of desires, you may take it that itis not a form of ‘wishing’: for wishing is always found in the ‘reasoning’ fac-ulty. This commonplace rule is useful also in dealing with Accident: for theaccident and that of which it is an accident are both found in the same thing,so that if they do not appear in the same thing, clearly it is not an accident.
Again, see if the species partakes of the genus attributed only in someparticular respect: for it is the general view that the genus is not thus im-parted only in some particular respect: for a man is not an animal in a par-ticular respect, nor is grammar knowledge in a particular respect only. Like-wise also in other instances. Look, therefore, and see if in the case of any ofits species the genus be imparted only in a certain respect; e.g. if ‘animal’ hasbeen described as an ‘object of perception’ or of ‘sight’. For an animal is anobject of perception or of sight in a particular respect only; for it is in respectof its body that it is perceived and seen, not in respect of its soul, so that -‘object of sight’ and ‘object of perception’ could not be the genus of ‘animal’.
Sometimes also people place the whole inside the part without detection,defining (e.g.) ‘animal’ as an ‘animate body’; whereas the part is not pred-icated in any sense of the whole, so that ‘body’ could not be the genus ofanimal, seeing that it is a part.
See also if he has put anything that is blameworthy or objectionable intothe class ‘capacity’ or ‘capable’, e.g. by defining a ‘sophist’ or a ‘slanderer’, ora ‘thief’ as ‘one who is capable of secretly thieving other people’s property’.For none of the aforesaid characters is so called because he is ‘capable’ in oneof these respects: for even God and the good man are capable of doing badthings, but that is not their character: for it is always in respect of their choicethat bad men are so called. Moreover, a capacity is always a desirable thing:for even the capacities for doing bad things are desirable, and therefore it iswe say that even God and the good man possess them; for they are capable(we say) of doing evil. So then ‘capacity’ can never be the genus of anythingblameworthy. Else, the result will be that what is blameworthy is sometimesdesirable: for there will be a certain form of capacity that is blameworthy.
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Also, see if he has put anything that is precious or desirable for its ownsake into the class ‘capacity’ or ‘capable’ or ‘productive’ of anything. Forcapacity, and what is capable or productive of anything, is always desirablefor the sake of something else.
Or see if he has put anything that exists in two genera or more into oneof them only. For some things it is impossible to place in a single genus,e.g. the ‘cheat’ and the ‘slanderer’: for neither he who has the will withoutthe capacity, nor he who has the capacity without the will, is a slandereror cheat, but he who has both of them. Hence he must be put not into onegenus, but into both the aforesaid genera.
Moreover, people sometimes in converse order render genus as differen-tia, and differentia as genus, defining (e.g.) astonishment as ‘excess of won-derment’ and conviction as ‘vehemence of conception’. For neither ‘excess’nor ‘vehemence’ is the genus, but the differentia: for astonishment is usuallytaken to be an ‘excessive wonderment’, and conviction to be a ‘vehementconception’, so that ‘wonderment’ and ‘conception’ are the genus, while ‘ex-cess’ and ‘vehemence’ are the differentia. Moreover, if any one renders ‘ex-cess’ and ‘vehemence’ as genera, then inanimate things will be convincedand astonished. For ‘vehemence’ and ‘excess’ of a thing are found in a thingwhich is thus vehement and in excess. If, therefore, astonishment be excessof wonderment the astonishment will be found in the wonderment, so that‘wonderment’ will be astonished! Likewise, also, conviction will be foundin the conception, if it be ‘vehemence of conception’, so that the conceptionwill be convinced. Moreover, a man who renders an answer in this style willin consequence find himself calling vehemence vehement and excess exces-sive: for there is such a thing as a vehement conviction: if then convictionbe ‘vehemence’, there would be a ‘vehement vehemence’. Likewise, also,there is such a thing as excessive astonishment: if then astonishment be anexcess, there would be an ‘excessive excess’. Whereas neither of these thingsis generally believed, any more than that knowledge is a knower or motiona moving thing.
Sometimes, too, people make the bad mistake of putting an affection intothat which is affected, as its genus, e.g. those who say that immortality iseverlasting life: for immortality seems to be a certain affection or accidentalfeature of life. That this saying is true would appear clear if any one were toadmit that a man can pass from being mortal and become immortal: for noone will assert that he takes another life, but that a certain accidental featureor affection enters into this one as it is. So then ‘life’ is not the genus ofimmortality.
Again, see if to an affection he has ascribed as genus the object of whichit is an affection, by defining (e.g.) wind as ‘air in motion’. Rather, windis ‘a movement of air’: for the same air persists both when it is in motion
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and when it is still. Hence wind is not ‘air’ at all: for then there would alsohave been wind when the air was not in motion, seeing that the same airwhich formed the wind persists. Likewise, also, in other cases of the kind.Even, then, if we ought in this instance to admit the point that wind is ‘airin motion’, yet we should accept a definition of the kind, not about all thosethings of which the genus is not true, but only in cases where the genusrendered is a true predicate. For in some cases, e.g. ‘mud’ or ‘snow’, it isnot generally held to be true. For people tell you that snow is ‘frozen water’and mud is earth mixed with moisture, whereas snow is not water, nor mudearth, so that neither of the terms rendered could be the genus: for the genusshould be true of all its species. Likewise neither is wine ‘fermented water’,as Empedocles speaks of ‘water fermented in wood’; for it simply is notwater at all.
Part 6 If the term rendered fails to be the genus of anything
Moreover, see whether the term rendered fail to be the genus of anythingat all; for then clearly it also fails to be the genus of the species mentioned.Examine the point by seeing whether the objects that partake of the genusfail to be specifically different from one another, e.g. white objects: for thesedo not differ specifically from one another, whereas of a genus the speciesare always different, so that ‘white’ could not be the genus of anything.
Again, see whether he has named as genus or differentia some featurethat goes with everything: for the number of attributes that follow every-thing is comparatively large: thus (e.g.) ‘Being’ and ‘Unity’ are among thenumber of attributes that follow everything. If, therefore, he has rendered‘Being’ as a genus, clearly it would be the genus of everything, seeing thatit is predicated of everything; for the genus is never predicated of anythingexcept of its species. Hence Unity, inter alia, will be a species of Being. Theresult, therefore, is that of all things of which the genus is predicated, thespecies is predicated as well, seeing that Being and Unity are predicates ofabsolutely everything, whereas the predication of the species ought to be ofnarrower range. If, on the other hand, he has named as differentia some at-tribute that follows everything, clearly the denotation of the differentia willbe equal to, or wider than, that of the genus. For if the genus, too, be someattribute that follows everything, the denotation of the differentia will beequal to its denotation, while if the genus do not follow everything, it willbe still wider.
Moreover, see if the description ‘inherent in S’ be used of the genus ren-dered in relation to its species, as it is used of ‘white’ in the case of snow,thus showing clearly that it could not be the genus: for ‘true of S’ is the onlydescription used of the genus in relation to its species. Look and see also if
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the genus fails to be synonymous with its species. For the genus is alwayspredicated of its species synonymously.
Moreover, beware, whenever both species and genus have a contrary,and he places the better of the contraries inside the worse genus: for the re-sult will be that the remaining species will be found in the remaining genus,seeing that contraries are found in contrary genera, so that the better specieswill be found in the worse genus and the worse in the better: whereas theusual view is that of the better species the genus too is better. Also see ifhe has placed the species inside the worse and not inside the better genus,when it is at the same time related in like manner to both, as (e.g.) if he hasdefined the ‘soul’ as a ‘form of motion’ or ‘a form of moving thing’. For thesame soul is usually thought to be a principle alike of rest and of motion,so that, if rest is the better of the two, this is the genus into which the soulshould have been put.
Moreover, judge by means of greater and less degrees: if overthrowinga view, see whether the genus admits of a greater degree, whereas neitherthe species itself does so, nor any term that is called after it: e.g. if virtueadmits of a greater degree, so too does justice and the just man: for one manis called ‘more just than another’. If, therefore, the genus rendered admits ofa greater degree, whereas neither the species does so itself nor yet any termcalled after it, then what has been rendered could not be the genus.
Again, if what is more generally, or as generally, thought to be the genusbe not so, clearly neither is the genus rendered. The commonplace rule inquestion is useful especially in cases where the species appears to have sev-eral predicates in the category of essence, and where no distinction has beendrawn between them, and we cannot say which of them is genus; e.g. both‘pain’ and the ‘conception of a slight’ are usually thought to be predicatesof anger in the category of essence: for the angry man is both in pain andalso conceives that he is slighted. The same mode of inquiry may be appliedalso to the case of the species, by comparing it with some other species: for ifthe one which is more generally, or as generally, thought to be found in thegenus rendered be not found therein, then clearly neither could the speciesrendered be found therein.
In demolishing a view, therefore, you should follow the rule as stated. Inestablishing one, on the other hand, the commonplace rule that you shouldsee if both the genus rendered and the species admit of a greater degree willnot serve: for even though both admit it, it is still possible for one not to bethe genus of the other. For both ‘beautiful’ and ‘white’ admit of a greaterdegree, and neither is the genus of the other. On the other hand, the com-parison of the genera and of the species one with another is of use: e.g. sup-posing A and B to have a like claim to be genus, then if one be a genus, soalso is the other. Likewise, also, if what has less claim be a genus, so also is
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what has more claim: e.g. if ‘capacity’ have more claim than ‘virtue’ to be thegenus of self-control, and virtue be the genus, so also is capacity. The sameobservations will apply also in the case of the species. For instance, suppos-ing A and B to have a like claim to be a species of the genus in question, thenif the one be a species, so also is the other: and if that which is less generallythought to be so be a species, so also is that which is more generally thoughtto be so.
Moreover, to establish a view, you should look and see if the genus ispredicated in the category of essence of those things of which it has beenrendered as the genus, supposing the species rendered to be not one singlespecies but several different ones: for then clearly it will be the genus. If, onthe other, the species rendered be single, look and see whether the genus bepredicated in the category of essence of other species as well: for then, again,the result will be that it is predicated of several different species.
Since some people think that the differentia, too, is a predicate of the var-ious species in the category of essence, you should distinguish the genusfrom the differentia by employing the aforesaid elementary principles - (a)that the genus has a wider denotation than the differentia; (b) that in ren-dering the essence of a thing it is more fitting to state the genus than thedifferentia: for any one who says that ‘man’ is an ‘animal’ shows what manis better than he who describes him as ‘walking’; also (c) that the differentiaalways signifies a quality of the genus, whereas the genus does not do thisof the differentia: for he who says ‘walking’ describes an animal of a cer-tain quality, whereas he who says ‘animal’ describes an animal of a certainquality, whereas he who says ‘animal’ does not describe a walking thing ofa certain quality.
The differentia, then, should be distinguished from the genus in thismanner. Now seeing it is generally held that if what is musical, in beingmusical, possesses knowledge in some respect, then also ‘music’ is a partic-ular kind of ‘knowledge’; and also that if what walks is moved in walking,then ‘walking’ is a particular kind of ‘movement’; you should therefore ex-amine in the aforesaid manner any genus in which you want to establish theexistence of something; e.g. if you wish to prove that ‘knowledge’ is a formof ‘conviction’, see whether the knower in knowing is convinced: for thenclearly knowledge would be a particular kind of conviction. You shouldproceed in the same way also in regard to the other cases of this kind.
Moreover, seeing that it is difficult to distinguish whatever always fol-lows along with a thing, and is not convertible with it, from its genus, ifA follows B universally, whereas B does not follow A universally - as e.g.‘rest’ always follows a ‘calm’ and ‘divisibility’ follows ‘number’, but notconversely (for the divisible is not always a number, nor rest a calm) - youmay yourself assume in your treatment of them that the one which always
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follows is the genus, whenever the other is not convertible with it: if, on theother hand, some one else puts forward the proposition, do not accept it uni-versally. An objection to it is that ‘not-being’ always follows what is ‘comingto be’ (for what is coming to be is not) and is not convertible with it (for whatis not is not always coming to be), and that still ‘not-being’ is not the genusof ‘coming to be’: for ‘not-being’ has not any species at all. Questions, then,in regard to Genus should be investigated in the ways described.
Book V Whether an attribute is or is nota property
Part 1 Essential and Relative Properties
The question whether the attribute stated is or is not a property, should beexamined by the following methods:
Any ‘property’ rendered is always either essential and permanent or rel-ative and temporary: e.g. it is an ‘essential property’ of man to be ‘by naturea civilized animal’: a ‘relative property’ is one like that of the soul in relationto the body, viz. that the one is fitted to command, and the other to obey: a‘permanent property’ is one like the property which belongs to God, of beingan ‘immortal living being’: a ‘temporary property’ is one like the propertywhich belongs to any particular man of walking in the gymnasium.
[The rendering of a property ‘relatively’ gives rise either to two problemsor to four. For if he at the same time render this property of one thing anddeny it of another, only two problems arise, as in the case of a statement thatit is a property of a man, in relation to a horse, to be a biped. For one mighttry both to show that a man is not a biped, and also that a horse is a biped: inboth ways the property would be upset. If on the other hand he render oneapiece of two attributes to each of two things, and deny it in each case of theother, there will then be four problems; as in the case of a statement that itis a property of a man in relation to a horse for the former to be a biped andthe latter a quadruped. For then it is possible to try to show both that a manis not naturally a biped, and that he is a quadruped, and also that the horseboth is a biped, and is not a quadruped. If you show any of these at all, theintended attribute is demolished.]
An ‘essential’ property is one which is rendered of a thing in comparisonwith everything else and distinguishes the said thing from everything else,as does ‘a mortal living being capable of receiving knowledge’ in the caseof man. A ‘relative’ property is one which separates its subject off not fromeverything else but only from a particular definite thing, as does the prop-
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erty which virtue possesses, in comparison with knowledge, viz. that theformer is naturally produced in more than one faculty, whereas the latter isproduced in that of reason alone, and in those who have a reasoning faculty.A ‘permanent’ property is one which is true at every time, and never fails,like being ‘compounded of soul and body’, in the case of a living creature. A‘temporary’ property is one which is true at some particular time, and doesnot of necessity always follow; as, of some particular man, that he walks inthe market-place.
To render a property ‘relatively’ to something else means to state the dif-ference between them as it is found either universally and always, or gen-erally and in most cases: thus a difference that is found universally and al-ways, is one such as man possesses in comparison with a horse, viz. beinga biped: for a man is always and in every case a biped, whereas a horseis never a biped at any time. On the other hand, a difference that is foundgenerally and in most cases, is one such as the faculty of reason possessesin comparison with that of desire and spirit, in that the former commands,while the latter obeys: for the reasoning faculty does not always command,but sometimes also is under command, nor is that of desire and spirit alwaysunder command, but also on occasion assumes the command, whenever thesoul of a man is vicious.
Of ‘properties’ the most ‘arguable’ are the essential and permanent andthe relative. For a relative property gives rise, as we said before, to severalquestions: for of necessity the questions arising are either two or four, orthat arguments in regard to these are several. An essential and a permanentproperty you can discuss in relation to many things, or can observe in re-lation to many periods of time: if essential, discuss it in comparison withmany things: for the property ought to belong to its subject in comparisonwith every single thing that is, so that if the subject be not distinguished byit in comparison with everything else, the property could not have been ren-dered correctly. So a permanent property you should observe in relation tomany periods of time; for if it does not or did not, or is not going to, belong,it will not be a property. On the other hand, about a temporary property wedo not inquire further than in regard to the time called ‘the present’; and soarguments in regard to it are not many; whereas an arguable question is onein regard to which it is possible for arguments both numerous and good toarise.
The so-called ‘relative’ property, then, should be examined by means ofthe commonplace arguments relating to Accident, to see whether it belongsto the one thing and not to the other: on the other hand, permanent andessential properties should be considered by the following methods.
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Part 2 Correct rendition of properties
First, see whether the property has or has not been rendered correctly. Ofa rendering being incorrect or correct, one test is to see whether the termsin which the property is stated are not or are more intelligible - for de-structive purposes, whether they are not so, and for constructive purposes,whether they are so. Of the terms not being more intelligible, one test is tosee whether the property which he renders is altogether more unintelligiblethan the subject whose property he has stated: for, if so, the property willnot have been stated correctly. For the object of getting a property consti-tuted is to be intelligible: the terms therefore in which it is rendered shouldbe more intelligible: for in that case it will be possible to conceive it moreadequately, e.g. any one who has stated that it is a property of ‘fire’ to ‘beara very close resemblance to the soul’, uses the term ‘soul’, which is less in-telligible than ‘fire’ - for we know better what fire is than what soul is - , andtherefore a ‘very close resemblance to the soul’ could not be correctly statedto be a property of fire. Another test is to see whether the attribution of A(property) to B (subject) fails to be more intelligible. For not only should theproperty be more intelligible than its subject, but also it should be somethingwhose attribution to the particular subject is a more intelligible attribution.For he who does not know whether it is an attribute of the particular subjectat all, will not know either whether it belongs to it alone, so that whicheverof these results happens, its character as a property becomes obscure. Thus(e.g.) a man who has stated that it is a property of fire to be ‘the primary ele-ment wherein the soul is naturally found’, has introduced a subject which isless intelligible than ‘fire’, viz. whether the soul is found in it, and whether itis found there primarily; and therefore to be ‘the primary element in whichthe soul is naturally found’ could not be correctly stated to be a property of‘fire’. On the other hand, for constructive purposes, see whether the termsin which the property is stated are more intelligible, and if they are more in-telligible in each of the aforesaid ways. For then the property will have beencorrectly stated in this respect: for of constructive arguments, showing thecorrectness of a rendering, some will show the correctness merely in this re-spect, while others will show it without qualification. Thus (e.g.) a man whohas said that the ‘possession of sensation’ is a property of ‘animal’ has bothused more intelligible terms and has rendered the property more intelligiblein each of the aforesaid senses; so that to ‘possess sensation’ would in thisrespect have been correctly rendered as a property of ‘animal’.
Next, for destructive purposes, see whether any of the terms rendered inthe property is used in more than one sense, or whether the whole expres-sion too signifies more than one thing. For then the property will not havebeen correctly stated. Thus (e.g.) seeing that to ‘being natural sentient’ signi-
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fies more than one thing, viz. (1) to possess sensation, (2) to use one’s sensa-tion, being naturally sentient, could not be a correct statement of a propertyof ‘animal’. The reason why the term you use, or the whole expression sig-nifying the property, should not bear more than one meaning is this, thatan expression bearing more than one meaning makes the object describedobscure, because the man who is about to attempt an argument is in doubtwhich of the various senses the expression bears: and this will not do, forthe object of rendering the property is that he may understand. Moreover,in addition to this, it is inevitable that those who render a property after thisfashion should be somehow refuted whenever any one addresses his syllo-gism to that one of the term’s several meanings which does not agree. Forconstructive purposes, on the other hand, see whether both all the terms andalso the expression as a whole avoid bearing more than one sense: for thenthe property will have been correctly stated in this respect. Thus (e.g.) seeingthat ‘body’ does not bear several meanings, nor quickest to move upwardsin space, nor yet the whole expression made by putting them together, itwould be correct in this respect to say that it is a property of fire to be the‘body quickest to move upwards in space’.
Next, for destructive purposes, see if the term of which he renders theproperty is used in more than one sense, and no distinction has been drawnas to which of them it is whose property he is stating: for then the propertywill not have been correctly rendered. The reasons why this is so are quiteclear from what has been said above: for the same results are bound to fol-low. Thus (e.g.) seeing that ‘the knowledge of this’ signifies many things forit means
(1) the possession of knowledge by it,(2) the use of its knowledge by it,(3) the existence of knowledge about it,(4) the use of knowledge about it- no property of the ‘knowledge of this’ could be rendered correctly un-
less he draw a distinction as to which of these it is whose property he isrendering. For constructive purposes, a man should see if the term of whichhe is rendering the property avoids bearing many senses and is one and sim-ple: for then the property will have been correctly stated in this respect. Thus(e.g.) seeing that ‘man’ is used in a single sense, ‘naturally civilized animal’would be correctly stated as a property of man.
Next, for destructive purposes, see whether the same term has been re-peated in the property. For people often do this undetected in rendering‘properties’ also, just as they do in their ‘definitions’ as well: but a prop-erty to which this has happened will not have been correctly stated: for therepetition of it confuses the hearer; thus inevitably the meaning becomes ob-scure, and further, such people are thought to babble. Repetition of the same
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term is likely to happen in two ways; one is, when a man repeatedly usesthe same word, as would happen if any one were to render, as a propertyof fire, ‘the body which is the most rarefied of bodies’ (for he has repeatedthe word ‘body’); the second is, if a man replaces words by their definitions,as would happen if any one were to render, as a property of earth, ‘the sub-stance which is by its nature most easily of all bodies borne downwards inspace’, and were then to substitute ‘substances of such and such a kind’ forthe word ‘bodies’: for ‘body’ and ‘a substance of such and such a kind’ meanone and the same thing. For he will have repeated the word ‘substance’, andaccordingly neither of the properties would be correctly stated. For con-structive purposes, on the other hand, see whether he avoids ever repeatingthe same term; for then the property will in this respect have been correctlyrendered. Thus (e.g.) seeing that he who has stated ‘animal capable of ac-quiring knowledge’ as a property of man has avoided repeating the sameterm several times, the property would in this respect have been correctlyrendered of man.
Next, for destructive purposes, see whether he has rendered in the prop-erty any such term as is a universal attribute. For one which does not dis-tinguish its subject from other things is useless, and it is the business of thelanguage Of ‘properties’, as also of the language of definitions, to distin-guish. In the case contemplated, therefore, the property will not have beencorrectly rendered. Thus (e.g.) a man who has stated that it is a propertyof knowledge to be a ‘conception incontrovertible by argument, because ofits unity’, has used in the property a term of that kind, viz. ‘unity’, whichis a universal attribute; and therefore the property of knowledge could nothave been correctly stated. For constructive purposes, on the other hand, seewhether he has avoided all terms that are common to everything and useda term that distinguishes the subject from something: for then the propertywill in this respect have been correctly stated. Thus (e.g.) inasmuch as hewho has said that it is a property of a ‘living creature’ to ‘have a soul’ hasused no term that is common to everything, it would in this respect havebeen correctly stated to be a property of a ‘living creature’ to ‘have a soul’.
Next, for destructive purposes see whether he renders more than oneproperty of the same thing, without a definite proviso that he is stating morethan one: for then the property will not have been correctly stated. For justas in the case of definitions too there should be no further addition beside theexpression which shows the essence, so too in the case of properties nothingfurther should be rendered beside the expression that constitutes the prop-erty mentioned: for such an addition is made to no purpose. Thus (e.g.) aman who has said that it is a property of fire to be ‘the most rarefied andlightest body’ has rendered more than one property (for each term is a truepredicate of fire alone); and so it could not be a correctly stated property
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of fire to be ‘the most rarefied and lightest body’. On the other hand, forconstructive purposes, see whether he has avoided rendering more than oneproperty of the same thing, and has rendered one only: for then the prop-erty will in this respect have been correctly stated. Thus (e.g.) a man whohas said that it is a property of a liquid to be a ‘body adaptable to everyshape’ has rendered as its property a single character and not several, andso the property of ‘liquid’ would in this respect have been correctly stated.
Part 3 Correct rendition of properties (continued)
Next, for destructive purposes, see whether he has employed either the ac-tual subject whose property he is rendering, or any of its species: for thenthe property will not have been correctly stated. For the object of renderingthe property is that people may understand: now the subject itself is just asunintelligible as it was to start with, while any one of its species is posteriorto it, and so is no more intelligible. Accordingly it is impossible to under-stand anything further by the use of these terms. Thus (e.g.) any one whohas said that it is property of ‘animal’ to be ‘the substance to which "man"belongs as a species’ has employed one of its species, and therefore the prop-erty could not have been correctly stated. For constructive purposes, on theother hand, see whether he avoids introducing either the subject itself or anyof its species: for then the property will in this respect have been correctlystated. Thus (e.g.) a man who has stated that it is a property of a living crea-ture to be ‘compounded of soul and body’ has avoided introducing amongthe rest either the subject itself or any of its species, and therefore in this re-spect the property of a ‘living creature’ would have been correctly rendered.
You should inquire in the same way also in the case of other terms that door do not make the subject more intelligible: thus, for destructive purposes,see whether he has employed anything either opposite to the subject or, ingeneral, anything simultaneous by nature with it or posterior to it: for thenthe property will not have been correctly stated. For an opposite is simul-taneous by nature with its opposite, and what is simultaneous by nature oris posterior to it does not make its subject more intelligible. Thus (e.g.) anyone who has said that it is a property of good to be ‘the most direct oppositeof evil’, has employed the opposite of good, and so the property of goodcould not have been correctly rendered. For constructive purposes, on theother hand, see whether he has avoided employing anything either oppositeto, or, in general, simultaneous by nature with the subject, or posterior to it:for then the property will in this respect have been correctly rendered. Thus(e.g.) a man who has stated that it is a property of knowledge to be ‘themost convincing conception’ has avoided employing anything either oppo-site to, or simultaneous by nature with, or posterior to, the subject; and so
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the property of knowledge would in this respect have been correctly stated.Next, for destructive purposes, see whether he has rendered as property
something that does not always follow the subject but sometimes ceases tobe its property: for then the property will not have been correctly described.For there is no necessity either that the name of the subject must also be trueof anything to which we find such an attribute belonging; nor yet that thename of the subject will be untrue of anything to which such an attribute isfound not to belong. Moreover, in addition to this, even after he has ren-dered the property it will not be clear whether it belongs, seeing that it isthe kind of attribute that may fall: and so the property will not be clear.Thus (e.g.) a man who has stated that it is a property of animal ‘sometimesto move and sometimes to stand still’ rendered the kind of property whichsometimes is not a property, and so the property could not have been cor-rectly stated. For constructive purposes, on the other hand, see whether hehas rendered something that of necessity must always be a property: forthen the property will have been in this respect correctly stated. Thus (e.g.)a man who has stated that it is a property of virtue to be ‘what makes its pos-sessor good’ has rendered as property something that always follows, andso the property of virtue would in this respect have been correctly rendered.
Next, for destructive purposes, see whether in rendering the property ofthe present time he has omitted to make a definite proviso that it is the prop-erty of the present time which he is rendering: for else the property will nothave been correctly stated. For in the first place, any unusual procedure al-ways needs a definite proviso: and it is the usual procedure for everybody torender as property some attribute that always follows. In the second place,a man who omits to provide definitely whether it was the property of thepresent time which he intended to state, is obscure: and one should not giveany occasion for adverse criticism. Thus (e.g.) a man who has stated it asthe property of a particular man ‘to be sitting with a particular man’, statesthe property of the present time, and so he cannot have rendered the prop-erty correctly, seeing that he has described it without any definite proviso.For constructive purposes, on the other hand, see whether, in rendering theproperty of the present time, he has, in stating it, made a definite provisothat it is the property of the present time that he is stating: for then the prop-erty will in this respect have been correctly stated. Thus (e.g.) a man whohas said that it is the property of a particular man ‘to be walking now’, hasmade this distinction in his statement, and so the property would have beencorrectly stated.
Next, for destructive purposes, see whether he has rendered a propertyof the kind whose appropriateness is not obvious except by sensation: forthen the property will not have been correctly stated. For every sensibleattribute, once it is taken beyond the sphere of sensation, becomes uncertain.
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For it is not clear whether it still belongs, because it is evidenced only bysensation. This principle will be true in the case of any attributes that do notalways and necessarily follow. Thus (e.g.) any one who has stated that itis a property of the sun to be ‘the brightest star that moves over the earth’,has used in describing the property an expression of that kind, viz. ‘to moveover the earth’, which is evidenced by sensation; and so the sun’s propertycould not have been correctly rendered: for it will be uncertain, wheneverthe sun sets, whether it continues to move over the earth, because sensationthen fails us. For constructive purposes, on the other hand, see whether hehas rendered the property of a kind that is not obvious to sensation, or, if itbe sensible, must clearly belong of necessity: for then the property will inthis respect have been correctly stated. Thus (e.g.) a man who has statedthat it is a property of a surface to be ‘the primary thing that is coloured’,has introduced amongst the rest a sensible quality, ‘to be coloured’, but stilla quality such as manifestly always belongs, and so the property of ‘surface’would in this respect have been correctly rendered.
Next, for destructive purposes, see whether he has rendered the defini-tion as a property: for then the property will not have been correctly stated:for the property of a thing ought not to show its essence. Thus (e.g.) a manwho has said that it is the property of man to be ‘a walking, biped animal’has rendered a property of man so as to signify his essence, and so the prop-erty of man could not have been correctly rendered. For constructive pur-poses, on the other hand, see whether the property which he has renderedforms a predicate convertible with its subject, without, however, signifyingits essence: for then the property will in this respect have been correctly ren-dered. Thus (e.g.) he who has stated that it is a property of man to be a‘naturally civilized animal’ has rendered the property so as to be convertiblewith its subject, without, however, showing its essence, and so the propertyof ‘man’ would in this respect have been correctly rendered.
Next, for destructive purposes, see whether he has rendered the prop-erty without having placed the subject within its essence. For of properties,as also of definitions, the first term to be rendered should be the genus, andthen the rest of it should be appended immediately afterwards, and shoulddistinguish its subject from other things. Hence a property which is notstated in this way could not have been correctly rendered. Thus (e.g.) aman who has said that it is a property of a living creature to ‘have a soul’has not placed ‘living creature’ within its essence, and so the property of aliving creature could not have been correctly stated. For constructive pur-poses, on the other hand, see whether a man first places within its essencethe subject whose property he is rendering, and then appends the rest: forthen the property will in this respect have been correctly rendered. Thus(e.g.) he who has stated that is a property of man to be an ‘animal capable
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of receiving knowledge’, has rendered the property after placing the subjectwithin its essence, and so the property of ‘man’ would in this respect havebeen correctly rendered.
Part 4 Whether what is stated is or is not a Property
The inquiry, then, whether the property has been correctly rendered or no,should be made by these means. The question, on the other hand, whetherwhat is stated is or is not a property at all, you should examine from thefollowing points of view. For the commonplace arguments which establishabsolutely that the property is accurately stated will be the same as thosethat constitute it a property at all: accordingly they will be described in thecourse of them.
Firstly, then, for destructive purposes, take a look at each subject of whichhe has rendered the property, and see (e.g.) if it fails to belong to any of themat all, or to be true of them in that particular respect, or to be a property ofeach of them in respect of that character of which he has rendered the prop-erty: for then what is stated to be a property will not be a property. Thus,for example, inasmuch as it is not true of the geometrician that he ‘cannotbe deceived by an argument’ (for a geometrician is deceived when his fig-ure is misdrawn), it could not be a property of the man of science that heis not deceived by an argument. For constructive purposes, on the otherhand, see whether the property rendered be true of every instance, and truein that particular respect: for then what is stated not to be a property willbe a property. Thus, for example, in as much as the description ‘an animalcapable of receiving knowledge’ is true of every man, and true of him quaman, it would be a property of man to be ‘an animal capable of receivingknowledge’. commonplace rule means - for destructive purposes, see if thedescription fails to be true of that of which the name is true; and if the namefails to be true of that of which the description is true: for constructive pur-poses, on the other hand, see if the description too is predicated of that ofwhich the name is predicated, and if the name too is predicated of that ofwhich the description is predicated.]
Next, for destructive purposes, see if the description fails to apply tothat to which the name applies, and if the name fails to apply to that towhich the description applies: for then what is stated to be a property willnot be a property. Thus (e.g.) inasmuch as the description ‘a living beingthat partakes of knowledge’ is true of God, while ‘man’ is not predicated ofGod, to be a living being that partakes of knowledge could not be a propertyof man. For constructive purposes, on the other hand, see if the name aswell be predicated of that of which the description is predicated, and if thedescription as well be predicated of that of which the name is predicated.
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For then what is stated not to be a property will be a property. Thus (e.g.)the predicate ‘living creature’ is true of that of which ‘having a soul’ is true,and ‘having a soul’ is true of that of which the predicate ‘living creature’ istrue; and so ‘having a soul’ would be a property of ‘living creature’.
Next, for destructive purposes, see if he has rendered a subject as a prop-erty of that which is described as ‘in the subject’: for then what has beenstated to be a property will not be a property. Thus (e.g.) inasmuch ashe who has rendered ‘fire’ as the property of ‘the body with the most rar-efied particles’, has rendered the subject as the property of its predicate, ‘fire’could not be a property of ‘the body with the most rarefied particles’. Thereason why the subject will not be a property of that which is found in thesubject is this, that then the same thing will be the property of a number ofthings that are specifically different. For the same thing has quite a num-ber of specifically different predicates that belong to it alone, and the subjectwill be a property of all of these, if any one states the property in this way.For constructive purposes, on the other hand, see if he has rendered whatis found in the subject as a property of the subject: for then what has beenstated not to be a property will be a property, if it be predicated only of thethings of which it has been stated to be the property. Thus (e.g.) he who hassaid that it is a property of ‘earth’ to be ‘specifically the heaviest body’ hasrendered of the subject as its property something that is said of the thing inquestion alone, and is said of it in the manner in which a property is predi-cated, and so the property of earth would have been rightly stated.
Next, for destructive purposes, see if he has rendered the property aspartaken of: for then what is stated to be a property will not be a prop-erty. For an attribute of which the subject partakes is a constituent part ofits essence: and an attribute of that kind would be a differentia applying tosome one species. E.g. inasmuch as he who has said that ‘walking on twofeet’ is property of man has rendered the property as partaken of, ‘walkingon two feet’ could not be a property of ‘man’. For constructive purposes, onthe other hand, see if he has avoided rendering the property as partaken of,or as showing the essence, though the subject is predicated convertibly withit: for then what is stated not to be a property will be a property. Thus (e.g.)he who has stated that to be ‘naturally sentient’ is a property of ‘animal’ hasrendered the property neither as partaken of nor as showing the essence,though the subject is predicated convertibly with it; and so to be ‘naturallysentient’ would be a property of ‘animal’.
Next, for destructive purposes, see if the property cannot possibly be-long simultaneously, but must belong either as posterior or as prior to theattribute described in the name: for then what is stated to be a property willnot be a property either never, or not always. Thus (e.g.) inasmuch as itis possible for the attribute ‘walking through the market-place’ to belong to
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an object as prior and as posterior to the attribute ‘man’, ‘walking throughthe market-place’ could not be a property of ‘man’ either never, or not al-ways. For constructive purposes, on the other hand, see if it always and ofnecessity belongs simultaneously, without being either a definition or a dif-ferentia: for then what is stated not to be a property will be a property. Thus(e.g.) the attribute ‘an animal capable of receiving knowledge’ always and ofnecessity belongs simultaneously with the attribute ‘man’, and is neither dif-ferentia nor definition of its subject, and so ‘an animal capable of receivingknowledge’ would be a property of ‘man’.
Next, for destructive purposes, see if the same thing fails to be a propertyof things that are the same as the subject, so far as they are the same: for thenwhat is stated to be a property will not be a property. Thus, for example,inasmuch as it is no property of a ‘proper object of pursuit’ to ‘appear good tocertain persons’, it could not be a property of the ‘desirable’ either to ‘appeargood to certain persons’: for ‘proper object of pursuit’ and ‘desirable’ meanthe same. For constructive purposes, on the other hand, see if the same thingbe a property of something that is the same as the subject, in so far as it isthe same. For then is stated not to be a property will be a property. Thus(e.g.) inasmuch as it is called a property of a man, in so far as he is a man, ‘tohave a tripartite soul’, it would also be a property of a mortal, in so far as heis a mortal, to have a tripartite soul. This commonplace rule is useful also indealing with Accident: for the same attributes ought either to belong or notbelong to the same things, in so far as they are the same.
Next, for destructive purposes, see if the property of things that are thesame in kind as the subject fails to be always the same in kind as the allegedproperty: for then neither will what is stated to be the property of the subjectin question. Thus (e.g.) inasmuch as a man and a horse are the same in kind,and it is not always a property of a horse to stand by its own initiative, itcould not be a property of a man to move by his own initiative; for to standand to move by his own initiative are the same in kind, because they belongto each of them in so far as each is an ‘animal’. For constructive purposes,on the other hand, see if of things that are the same in kind as the subjectthe property that is the same as the alleged property is always true: for thenwhat is stated not to be a property will be a property. Thus (e.g.) since itis a property of man to be a ‘walking biped,’ it would also be a property ofa bird to be a ‘flying biped’: for each of these is the same in kind, in so faras the one pair have the sameness of species that fall under the same genus,being under the genus ‘animal’, while the other pair have that of differentiaeof the genus, viz. of ‘animal’. This commonplace rule is deceptive wheneverone of the properties mentioned belongs to some one species only while theother belongs to many, as does ‘walking quadruped’.
Inasmuch as ‘same’ and ‘different’ are terms used in several senses, it
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is a job to render to a sophistical questioner a property that belongs to onething and that only. For an attribute that belongs to something qualifiedby an accident will also belong to the accident taken along with the subjectwhich it qualifies; e.g. an attribute that belongs to ‘man’ will belong also to‘white man’, if there be a white man, and one that belongs to ‘white man’will belong also to ‘man’. One might, then, bring captious criticism againstthe majority of properties, by representing the subject as being one thing initself, and another thing when combined with its accident, saying, for ex-ample, that ‘man’ is one thing, and ‘white man’ another, and moreover byrepresenting as different a certain state and what is called after that state. Foran attribute that belongs to the state will belong also to what is called afterthat state, and one that belongs to what is called after a state will belong alsoto the state: e.g. inasmuch as the condition of the scientist is called after hisscience, it could not be a property of ‘science’ that it is ‘incontrovertible byargument’; for then the scientist also will be incontrovertible by argument.For constructive purposes, however, you should say that the subject of anaccident is not absolutely different from the accident taken along with itssubject; though it is called ‘another’ thing because the mode of being of thetwo is different: for it is not the same thing for a man to be a man and fora white man to be a white man. Moreover, you should take a look along atthe inflections, and say that the description of the man of science is wrong:one should say not ‘it’ but ‘he is incontrovertible by argument’; while thedescription of Science is wrong too: one should say not ‘it’ but ‘she is incon-trovertible by argument’. For against an objector who sticks at nothing thedefence should stick at nothing.
Part 5 Natural properties cannot be essential
Next, for destructive purposes, see if, while intending to render an attributethat naturally belongs, he states it in his language in such a way as to indicateone that invariably belongs: for then it would be generally agreed that whathas been stated to be a property is upset. Thus (e.g.) the man who hassaid that ‘biped’ is a property of man intends to render the attribute thatnaturally belongs, but his expression actually indicates one that invariablybelongs: accordingly, ‘biped’ could not be a property of man: for not everyman is possessed of two feet. For constructive purposes, on the other hand,see if he intends to render the property that naturally belongs, and indicatesit in that way in his language: for then the property will not be upset in thisrespect. Thus (e.g.) he who renders as a property of ‘man’ the phrase ‘ananimal capable of receiving knowledge’ both intends, and by his languageindicates, the property that belongs by nature, and so ‘an animal capable ofreceiving knowledge’ would not be upset or shown in that respect not to be
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a property of man.Moreover, as regards all the things that are called as they are primarily
after something else, or primarily in themselves, it is a job to render theproperty of such things. For if you render a property as belonging to thesubject that is so called after something else, then it will be true of its primarysubject as well; whereas if you state it of its primary subject, then it will bepredicated also of the thing that is so called after this other. Thus (e.g.) ifany one renders , ‘coloured’ as the property of ‘surface’, ‘coloured’ will betrue of body as well; whereas if he render it of ‘body’, it will be predicatedalso of ‘surface’. Hence the name as well will not be true of that of which thedescription is true.
In the case of some properties it mostly happens that some error is in-curred because of a failure to define how as well as to what things the prop-erty is stated to belong. For every one tries to render as the property ofa thing something that belongs to it either naturally, as ‘biped’ belongs to‘man’, or actually, as ‘having four fingers’ belongs to a particular man, orspecifically, as ‘consisting of most rarefied particles’ belongs to ‘fire’, or ab-solutely, as ‘life’ to ‘living being’, or one that belongs to a thing only as calledafter something else, as ‘wisdom’ to the ‘soul’, or on the other hand primar-ily, as ‘wisdom’ to the ‘rational faculty’, or because the thing is in a certainstate, as ‘incontrovertible by argument’ belongs to a ‘scientist’ (for simplyand solely by reason of his being in a certain state will he be ‘incontrovertibleby argument’), or because it is the state possessed by something, as ‘incon-trovertible by argument’ belongs to ‘science’, or because it is partaken of, as‘sensation’ belongs to ‘animal’ (for other things as well have sensation, e.g.man, but they have it because they already partake of ‘animal’), or becauseit partakes of something else, as ‘life’ belongs to a particular kind of ‘livingbeing’. Accordingly he makes a mistake if he has failed to add the word‘naturally’, because what belongs naturally may fail to belong to the thing towhich it naturally belongs, as (e.g.) it belongs to a man to have two feet: sotoo he errs if he does not make a definite proviso that he is rendering whatactually belongs, because one day that attribute will not be what it now is,e.g. the man’s possession of four fingers. So he errs if he has not shown thathe states a thing to be such and such primarily, or that he calls it so aftersomething else, because then its name too will not be true of that of whichthe description is true, as is the case with ‘coloured’, whether rendered as aproperty of ‘surface’ or of ‘body’. So he errs if he has not said beforehandthat he has rendered a property to a thing either because that thing possessesa state, or because it is a state possessed by something; because then it willnot be a property. For, supposing he renders the property to something asbeing a state possessed, it will belong to what possesses that state; whilesupposing he renders it to what possesses the state, it will belong to the state
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possessed, as did ‘incontrovertible by argument’ when stated as a propertyof ‘science’ or of the ‘scientist’. So he errs if he has not indicated beforehandthat the property belongs because the thing partakes of, or is partaken of by,something; because then the property will belong to certain other things aswell. For if he renders it because its subject is partaken of, it will belong tothe things which partake of it; whereas if he renders it because its subjectpartakes of something else, it will belong to the things partaken of, as (e.g.)if he were to state ‘life’ to be a property of a ‘particular kind of living being’,or just of ‘living being’. So he errs if he has not expressly distinguished theproperty that belongs specifically, because then it will belong only to one ofthe things that fall under the term of which he states the property: for thesuperlative belongs only to one of them, e.g. ‘lightest’ as applied to ‘fire’.Sometimes, too, a man may even add the word ‘specifically’, and still makea mistake. For the things in question should all be of one species, wheneverthe word ‘specifically’ is added: and in some cases this does not occur, as itdoes not, in fact, in the case of fire. For fire is not all of one species; for livecoals and flame and light are each of them ‘fire’, but are of different species.The reason why, whenever ‘specifically’ is added, there should not be anyspecies other than the one mentioned, is this, that if there be, then the prop-erty in question will belong to some of them in a greater and to others ina less degree, as happens with ‘consisting of most rarefied particles’ in thecase of fire: for ‘light’ consists of more rarefied particles than live coals andflame. And this should not happen unless the name too be predicated in agreater degree of that of which the description is truer; otherwise the rulethat where the description is truer the name too should be truer is not ful-filled. Moreover, in addition to this, the same attribute will be the propertyboth of the term which has it absolutely and of that element therein whichhas it in the highest degree, as is the condition of the property ‘consistingof most rarefied particles’ in the case of ‘fire’: for this same attribute willbe the property of ‘light’ as well: for it is ‘light’ that ‘consists of the mostrarefied particles’. If, then, any one else renders a property in this way oneshould attack it; for oneself, one should not give occasion for this objection,but should define in what manner one states the property at the actual timeof making the statement.
Next, for destructive purposes, see if he has stated a thing as a propertyof itself: for then what has been stated to be a property will not be a property.For a thing itself always shows its own essence, and what shows the essenceis not a property but a definition. Thus (e.g.) he who has said that ‘becoming’is a property of ‘beautiful’ has rendered the term as a property of itself (for‘beautiful’ and ‘becoming’ are the same); and so ‘becoming’ could not be aproperty of ‘beautiful’. For constructive purposes, on the other hand, see ifhe has avoided rendering a thing as a property of itself, but has yet stated
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a convertible predicate: for then what is stated not to be a property will bea property. Thus he who has stated ‘animate substance’ as a property of‘living-creature’ has not stated ‘living-creature’ as a property of itself, buthas rendered a convertible predicate, so that ‘animate substance’ would be aproperty of ‘living-creature’.
Next, in the case of things consisting of like parts, you should look andsee, for destructive purposes, if the property of the whole be not true of thepart, or if that of the part be not predicated of the whole: for then whathas been stated to be the property will not be a property. In some cases ithappens that this is so: for sometimes in rendering a property in the caseof things that consist of like parts a man may have his eye on the whole,while sometimes he may address himself to what is predicated of the part:and then in neither case will it have been rightly rendered. Take an instancereferring to the whole: the man who has said that it is a property of the ‘sea’to be ‘the largest volume of salt water’, has stated the property of somethingthat consists of like parts, but has rendered an attribute of such a kind asis not true of the part (for a particular sea is not ‘the largest volume of saltwater’); and so ‘the largest volume of salt water’ could not be a property ofthe ‘sea’. Now take one referring to the part: the man who has stated that itis a property of ‘air’ to be ‘breathable’ has stated the property of somethingthat consists of like parts, but he has stated an attribute such as, though trueof some air, is still not predicable of the whole (for the whole of the air isnot breathable); and so ‘breathable’ could not be a property of ‘air’. Forconstructive purposes, on the other hand, see whether, while it is true ofeach of the things with similar parts, it is on the other hand a property ofthem taken as a collective whole: for then what has been stated not to be aproperty will be a property. Thus (e.g.) while it is true of earth everywherethat it naturally falls downwards, it is a property of the various particularpieces of earth taken as ‘the Earth’, so that it would be a property of ‘earth’‘naturally to fall downwards’.
Part 6 The point of view of the respective opposites
Next, look from the point of view of the respective opposites, and first (a)from that of the contraries, and see, for destructive purposes, if the contraryof the term rendered fails to be a property of the contrary subject. For thenneither will the contrary of the first be a property of the contrary of the sec-ond. Thus (e.g.) inasmuch as injustice is contrary to justice, and the lowestevil to the highest good, but ‘to be the highest good’ is not a property of‘justice’, therefore ‘to be the lowest evil’ could not be a property of ‘injus-tice’. For constructive purposes, on the other hand, see if the contrary is theproperty of the contrary: for then also the contrary of the first will be the
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property of the contrary of the second. Thus (e.g.) inasmuch as evil is con-trary to good, and objectionable to desirable, and ‘desirable’ is a property of‘good’, ‘objectionable’ would be a property of ‘evil’.
Secondly (h) look from the point of view of relative opposites and see,for destructive purposes, if the correlative of the term rendered fails to be aproperty of the correlative of the subject: for then neither will the correlativeof the first be a property of the correlative of the second. Thus (e.g.) inas-much as ‘double’ is relative to ‘half’, and ‘in excess’ to ‘exceeded’, while ‘inexcess’ is not a property of ‘double’, ‘exceeded’ could not be a property of‘half’. For constructive purposes, on the other hand, see if the correlative ofthe alleged property is a property of the subject’s correlative: for then alsothe correlative of the first will be a property of the correlative of the second:e.g. inasmuch as ‘double’ is relative to ‘half’, and the proportion 1:2 is rel-ative to the proportion 2:1, while it is a property of ‘double’ to be ‘in theproportion of 2 to 1’, it would be a property of ‘half’ to be ‘in the proportionof 1 to 2’.
Thirdly (c) for destructive purposes, see if an attribute described in termsof a state (X) fails to be a property of the given state (Y): for then neither willthe attribute described in terms of the privation (of X) be a property of theprivation (of Y). Also if, on the other hand, an attribute described in termsof the privation (of X) be not a property of the given privation (of Y), neitherwill the attribute described in terms of the state (X) be a property of thestate (Y). Thus, for example, inasmuch as it is not predicated as a propertyof ‘deafness’ to be a ‘lack of sensation’, neither could it be a property of‘hearing’ to be a ‘sensation’. For constructive purposes, on the other hand,see if an attribute described in terms of a state (X) is a property of the givenstate (Y): for then also the attribute that is described in terms of the privation(of X) will be a property of the privation (of Y). Also, if an attribute describedin terms of a privation (of X) be a property of the privation (of Y), then alsothe attribute that is described in terms of the state (X) will be a property of thestate (Y). Thus (e.g.) inasmuch as ‘to see’ is a property of ‘sight’, inasmuch aswe have sight, ‘failure to see’ would be a property of ‘blindness’, inasmuchas we have not got the sight we should naturally have.
Next, look from the point of view of positive and negative terms; andfirst (a) from the point of view of the predicates taken by themselves. Thiscommon-place rule is useful only for a destructive purpose. Thus (e.g.) seeif the positive term or the attribute described in terms of it is a property ofthe subject: for then the negative term or the attribute described in termsof it will not be a property of the subject. Also if, on the other hand, thenegative term or the attribute described in terms of it is a property of thesubject, then the positive term or the attribute described in terms of it willnot be a property of the subject: e.g. inasmuch as ‘animate’ is a property of
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‘living creature’, ‘inanimate’ could not be a property of ‘living creature’.Secondly (b) look from the point of view of the predicates, positive or
negative, and their respective subjects; and see, for destructive purposes, ifthe positive term falls to be a property of the positive subject: for then neitherwill the negative term be a property of the negative subject. Also, if thenegative term fails to be a property of the negative subject, neither will thepositive term be a property of the positive subject. Thus (e.g.) inasmuch as‘animal’ is not a property of ‘man’, neither could ‘not-animal’ be a propertyof ‘not-man’. Also if ‘not-animal’ seems not to be a property of ‘not-man’,neither will ‘animal’ be a property of ‘man’. For constructive purposes, onthe other hand, see if the positive term is a property of the positive subject:for then the negative term will be a property of the negative subject as well.Also if the negative term be a property of the negative subject, the positivewill be a property of the positive as well. Thus (e.g.) inasmuch as it is aproperty of ‘not-living being’ ‘not to live’, it would be a property of ‘livingbeing’ ‘to live’: also if it seems to be a property of ‘living being’ ‘to live’, itwill also seem to be a property of ‘not-living being’ ‘not to live’.
Thirdly (c) look from the point of view of the subjects taken by them-selves, and see, for destructive purposes, if the property rendered is a prop-erty of the positive subject: for then the same term will not be a property ofthe negative subject as well. Also, if the term rendered be a property of thenegative subject, it will not be a property of the positive. Thus (e.g.) inas-much as ‘animate’ is a property of ‘living creature’, ‘animate’ could not bea property of ‘not-living creature’. For constructive purposes, on the otherhand, if the term rendered fails to be a property of the affirmative subject itwould be a property of the negative. This commonplace rule is, however,deceptive: for a positive term is not a property of a negative, or a negativeof a positive. For a positive term does not belong at all to a negative, while anegative term, though it belongs to a positive, does not belong as a property.
Next, look from the point of view of the coordinate members of a divi-sion, and see, for destructive purposes, if none of the co-ordinate members(parallel with the property rendered) be a property of any of the remainingset of co-ordinate members (parallel with the subject): for then neither willthe term stated be a property of that of which it is stated to be a property.Thus (e.g.) inasmuch as ‘sensible living being’ is not a property of any ofthe other living beings, ‘intelligible living being’ could not be a property ofGod. For constructive purposes, on the other hand, see if some one or otherof the remaining co-ordinate members (parallel with the property rendered)be a property of each of these co-ordinate members (parallel with the sub-ject): for then the remaining one too will be a property of that of which ithas been stated not to be a property. Thus (e.g.) inasmuch as it is a propertyof ‘wisdom’ to be essentially ‘the natural virtue of the rational faculty’, then,
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taking each of the other virtues as well in this way, it would be a property of‘temperance’ to be essentially ‘the natural virtue of the faculty of desire’.
Next, look from the point of view of the inflexions, and see, for destruc-tive purposes, if the inflexion of the property rendered fails to be a propertyof the inflexion of the subject: for then neither will the other inflexion be aproperty of the other inflexion. Thus (e.g.) inasmuch as ‘beautifully’ is nota property of ‘justly’, neither could ‘beautiful’ be a property of ‘just’. Forconstructive purposes, on the other hand, see if the inflexion of the propertyrendered is a property of the inflexion of the subject: for then also the otherinflexion will be a property of the other inflexion. Thus (e.g.) inasmuch as‘walking biped’ is a property of man, it would also be any one’s property‘as a man’ to be described ‘as a walking biped’. Not only in the case of theactual term mentioned should one look at the inflexions, but also in the caseof its opposites, just as has been laid down in the case of the former com-monplace rules as well.’ Thus, for destructive purposes, see if the inflexionof the opposite of the property rendered fails to be the property of the in-flexion of the opposite of the subject: for then neither will the inflexion ofthe other opposite be a property of the inflexion of the other opposite. Thus(e.g.) inasmuch as ‘well’ is not a property of ‘justly’, neither could ‘badly’ bea property of ‘unjustly’. For constructive purposes, on the other hand, see ifthe inflexion of the opposite of the property originally suggested is a prop-erty of the inflexion of the opposite of the original subject: for then also theinflexion of the other opposite will be a property of the inflexion of the otheropposite. Thus (e.g.) inasmuch as ‘best’ is a property of ‘the good’, ‘worst’also will be a property of ‘the evil’.
Part 7 The point of view of things that are in a like relation
Next, look from the point of view of things that are in a like relation, andsee, for destructive purposes, if what is in a relation like that of the propertyrendered fails to be a property of what is in a relation like that of the subject:for then neither will what is in a relation like that of the first be a propertyof what is in a relation like that of the second. Thus (e.g.) inasmuch as therelation of the builder towards the production of a house is like that of thedoctor towards the production of health, and it is not a property of a doctorto produce health, it could not be a property of a builder to produce a house.For constructive purposes, on the other hand, see if what is in a relation likethat of the property rendered is a property of what is in a relation like thatof the subject: for then also what is in a relation like that of the first will be aproperty of what is in a relation like that of the second. Thus (e.g.) inasmuchas the relation of a doctor towards the possession of ability to produce healthis like that of a trainer towards the possession of ability to produce vigour,
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and it is a property of a trainer to possess the ability to produce vigour, itwould be a property of a doctor to possess the ability to produce health.
Next look from the point of view of things that are identically related,and see, for destructive purposes, if the predicate that is identically relatedtowards two subjects fails to be a property of the subject which is identicallyrelated to it as the subject in question; for then neither will the predicate thatis identically related to both subjects be a property of the subject which isidentically related to it as the first. If, on the other hand, the predicate whichis identically related to two subjects is the property of the subject which isidentically related to it as the subject in question, then it will not be a prop-erty of that of which it has been stated to be a property. (e.g.) inasmuchas prudence is identically related to both the noble and the base, since it isknowledge of each of them, and it is not a property of prudence to be knowl-edge of the noble, it could not be a property of prudence to be knowledge ofthe base. If, on the other hand, it is a property of prudence to be the knowl-edge of the noble, it could not be a property of it to be the knowledge of thebase.] For it is impossible for the same thing to be a property of more thanone subject. For constructive purposes, on the other hand, this common-place rule is of no use: for what is ‘identically related’ is a single predicate inprocess of comparison with more than one subject.
Next, for destructive purposes, see if the predicate qualified by the verb‘to be’ fails to be a property of the subject qualified by the verb ‘to be’: forthen neither will the destruction of the one be a property of the other quali-fied by the verb ‘to be destroyed’, nor will the ‘becoming’the one be a prop-erty of the other qualified by the verb ‘to become’. Thus (e.g.) inasmuch asit is not a property of ‘man’ to be an animal, neither could it be a property ofbecoming a man to become an animal; nor could the destruction of an ani-mal be a property of the destruction of a man. In the same way one shouldderive arguments also from ‘becoming’ to ‘being’ and ‘being destroyed’, andfrom ‘being destroyed’ to ‘being’ and to ‘becoming’ exactly as they have justbeen given from ‘being’ to ‘becoming’ and ‘being destroyed’. For construc-tive purposes, on the other hand, see if the subject set down as qualified bythe verb ‘to be’ has the predicate set down as so qualified, as its property: forthen also the subject qualified by the very ‘to become’ will have the predi-cate qualified by ‘to become’ as its property, and the subject qualified by theverb ‘to be destroyed’ will have as its property the predicate rendered withthis qualification. Thus, for example, inasmuch as it is a property of man tobe a mortal, it would be a property of becoming a man to become a mortal,and the destruction of a mortal would be a property of the destruction of aman. In the same way one should derive arguments also from ‘becoming’and ‘being destroyed’ both to ‘being’ and to the conclusions that follow fromthem, exactly as was directed also for the purpose of destruction.
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Next take a look at the ‘idea’ of the subject stated, and see, for destructivepurposes, if the suggested property fails to belong to the ‘idea’ in question,or fails to belong to it in virtue of that character which causes it to bear thedescription of which the property was rendered: for then what has beenstated to be a property will not be a property. Thus (e.g.) inasmuch as ‘be-ing motionless’ does not belong to ‘man-himself’ qua ‘man’, but qua ‘idea’,it could not be a property of ‘man’ to be motionless. For constructive pur-poses, on the other hand, see if the property in question belongs to the idea,and belongs to it in that respect in virtue of which there is predicated ofit that character of which the predicate in question has been stated not tobe a property: for then what has been stated not to be a property will bea property. Thus (e.g.) inasmuch as it belongs to ‘living-creature-itself’ tobe compounded of soul and body, and further this belongs to it qua ‘living-creature’, it would be a property of ‘living-creature’ to be compounded ofsoul and body.
Part 8 The point of view of greater and less degrees
Next look from the point of view of greater and less degrees, and first (a) fordestructive purposes, see if what is more-P fails to be a property of what ismore-S: for then neither will what is less-P be a property of what is less-S, norleast-P of least-S, nor most-P of most-S, nor P simply of S simply. Thus (e.g.)inasmuch as being more highly coloured is not a property of what is more abody, neither could being less highly coloured be a property of what is lessa body, nor being coloured be a property of body at all. For constructivepurposes, on the other hand, see if what is more-P is a property of what ismore-S: for then also what is less-P will be a property of what is less S, andleast-P of least-S, and most-P of most-S, and P simply of S simply. Thus (e.g.)inasmuch as a higher degree of sensation is a property of a higher degree oflife, a lower degree of sensation also would be a property of a lower degreeof life, and the highest of the highest and the lowest of the lowest degree,and sensation simply of life simply.
Also you should look at the argument from a simple predication to thesame qualified types of predication, and see, for destructive purposes, if Psimply fails to be a property of S simply; for then neither will more-P bea property of more-S, nor less-P of less-S, nor most-P of most-S, nor least-P of least-S. Thus (e.g.) inasmuch as ‘virtuous’ is not a property of ‘man’,neither could ‘more virtuous’ be a property of what is ‘more human’. Forconstructive purposes, on the other hand, see if P simply is a property ofS simply: for then more P also will be a property of more-S, and less-P ofless-S, and least-P of least-S, and most-P of most-S. Thus (e.g.) a tendency tomove upwards by nature is a property of fire, and so also a greater tendency
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to move upwards by nature would be a property of what is more fiery. Inthe same way too one should look at all these matters from the point of viewof the others as well.
Secondly (b) for destructive purposes, see if the more likely property failsto be a property of the more likely subject: for then neither will the less likelyproperty be a property of the less likely subject. Thus (e.g.) inasmuch as‘perceiving’ is more likely to be a property of ‘animal’ than ‘knowing’ of‘man’, and ‘perceiving’ is not a property of ‘animal’, ‘knowing’ could notbe a property of ‘man’. For constructive purposes, on the other hand, see ifthe less likely property is a property of the less likely subject; for then toothe more likely property will be a property of the more likely subject. Thus(e.g.) inasmuch as ‘to be naturally civilized’ is less likely to be a property ofman than ‘to live’ of an animal, and it is a property of man to be naturallycivilized, it would be a property of animal to live.
Thirdly (c) for destructive purposes, see if the predicate fails to be a prop-erty of that of which it is more likely to be a property: for then neither willit be a property of that of which it is less likely to be a property: while if itis a property of the former, it will not be a property of the latter. Thus (e.g.)inasmuch as ‘to be coloured’ is more likely to be a property of a ‘surface’than of a ‘body’, and it is not a property of a surface, ‘to be coloured’ couldnot be a property of ‘body’; while if it is a property of a ‘surface’, it could notbe a property of a ‘body’. For constructive purposes, on the other hand, thiscommonplace rule is not of any use: for it is impossible for the same thingto be a property of more than one thing.
Fourthly (d) for destructive purposes, see if what is more likely to be aproperty of a given subject fails to be its property: for then neither will whatis less likely to be a property of it be its property. Thus (e.g.) inasmuchas ‘sensible’ is more likely than ‘divisible’ to be a property of ‘animal’, and‘sensible’ is not a property of animal, ‘divisible’ could not be a property ofanimal. For constructive purposes, on the other hand, see if what is lesslikely to be a property of it is a property; for then what is more likely to bea property of it will be a property as well. Thus, for example, inasmuch as‘sensation’ is less likely to be a property of ‘animal’ than ‘life’, and ‘sensation’is a property of animal, ‘life’ would be a property of animal.
Next, look from the point of view of the attributes that belong in a likemanner, and
first (a) for destructive purposes, see if what is as much a property failsto be a property of that of which it is as much a property: for then neitherwill that which is as much a property as it be a property of that of whichit is as much a property. Thus (e.g.) inasmuch as ‘desiring’ is as much aproperty of the faculty of desire as ‘reasoning’ is a property of the facultyof reason, and desiring is not a property of the faculty of desire, reasoning
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could not be a property of the faculty of reason. For constructive purposes,on the other hand, see if what is as much a property is a property of that ofwhich it is as much a property: for then also what is as much a property asit will be a property of that of which it is as much a property. Thus (e.g.)inasmuch as it is as much a property of ‘the faculty of reason’ to be ‘theprimary seat of wisdom’ as it is of ‘the faculty of desire’ to be ‘the primaryseat of temperance’, and it is a property of the faculty of reason to be theprimary seat of wisdom, it would be a property of the faculty of desire to bethe primary seat of temperance.
Secondly (b) for destructive purposes, see if what is as much a propertyof anything fails to be a property of it: for then neither will what is as mucha property be a property of it. Thus (e.g.) inasmuch as ‘seeing’ is as much aproperty of man as ‘hearing’, and ‘seeing’ is not a property of man, ‘hearing’could not be a property of man. For constructive purposes, on the otherhand, see if what is as much a property of it is its property: for then whatis as much a property of it as the former will be its property as well. Thus(e.g.) it is as much a property of the soul to be the primary possessor of apart that desires as of a part that reasons, and it is a property of the soul tobe the primary possessor of a part that desires, and so it be a property of thesoul to be the primary possessor of a part that reasons.
Thirdly (c) for destructive purposes, see if it fails to be a property of thatof which it is as much a property: for then neither will it be a property of thatof which it is as much a property as of the former, while if it be a property ofthe former, it will not be a property of the other. Thus (e.g.) inasmuch as ‘toburn’ is as much a property of ‘flame’ as of ‘live coals’, and ‘to burn’ is not aproperty of flame, ‘to burn’ could not be a property of live coals: while if it isa property of flame, it could not be a property of live coals. For constructivepurposes, on the other hand, this commonplace rule is of no use.
The rule based on things that are ‘in a like relation’ differs from the rulebased on attributes that belong ‘in a like manner,’ because the former pointis secured by analogy, not from reflection on the belonging of any attribute,while the latter is judged by a comparison based on the fact that an attributebelongs.
Next, for destructive purposes, see if in rendering the property poten-tially, he has also through that potentiality rendered the property relativelyto something that does not exist, when the potentiality in question cannotbelong to what does not exist: for then what is stated to be a property willnot be a property. Thus (e.g.) he who has said that ‘breathable’ is a propertyof ‘air’ has, on the one hand, rendered the property potentially (for that is‘breathable’ which is such as can be breathed), and on the other hand hasalso rendered the property relatively to what does not exist: - for while airmay exist, even though there exist no animal so constituted as to breathe the
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air, it is not possible to breathe it if no animal exist: so that it will not, either,be a property of air to be such as can be breathed at a time when there existsno animal such as to breathe it and so it follows that ‘breathable’ could notbe a property of air.
For constructive purposes, see if in rendering the property potentially herenders the property either relatively to something that exists, or to some-thing that does not exist, when the potentiality in question can belong towhat does not exist: for then what has been stated not to be a property willbe a property. Thus e.g.) he who renders it as a property of ‘being’ to be‘capable of being acted upon or of acting’, in rendering the property poten-tially, has rendered the property relatively to something that exists: for when‘being’ exists, it will also be capable of being acted upon or of acting in a cer-tain way: so that to be ‘capable of being acted upon or of acting’ would be aproperty of ‘being’.
Next, for destructive purposes, see if he has stated the property in the su-perlative: for then what has been stated to be a property will not be a prop-erty. For people who render the property in that way find that of the objectof which the description is true, the name is not true as well: for thoughthe object perish the description will continue in being none the less; for itbelongs most nearly to something that is in being. An example would besupposing any one were to render ‘the lightest body’ as a property of ‘fire’:for, though fire perish, there eh re will still be some form of body that is thelightest, so that ‘the lightest body’ could not be a property of fire. For con-structive purposes, on the other hand, see if he has avoided rendering theproperty in the superlative: for then the property will in this respect havebeen property of man has not rendered the property correctly stated. Thus(e.g.) inasmuch as he in the superlative, the property would in who states ‘anaturally civilized animal’ as a this respect have been correctly stated.
Book VI The discussion of definitions
Part 1 The five parts of the discussion of definitions
The discussion of Definitions falls into five parts. For you have to showeither
(1) that it is not true at all to apply the expression as well to that to whichthe term is applied (for the definition of Man ought to be true of every man);or
(2) that though the object has a genus, he has failed to put the objectdefined into the genus, or to put it into the appropriate genus (for the framerof a definition should first place the object in its genus, and then append
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its differences: for of all the elements of the definition the genus is usuallysupposed to be the principal mark of the essence of what is defined): or
(3) that the expression is not peculiar to the object (for, as we said aboveas well, a definition ought to be peculiar): or else
(4) see if, though he has observed all the aforesaid cautions, he has yetfailed to define the object, that is, to express its essence.
(5) It remains, apart from the foregoing, to see if he has defined it, butdefined it incorrectly.
Whether, then, the expression be not also true of that of which the termis true you should proceed to examine according to the commonplace rulesthat relate to Accident. For there too the question is always ‘Is so and so trueor untrue?’: for whenever we argue that an accident belongs, we declare it tobe true, while whenever we argue that it does not belong, we declare it to beuntrue. If, again, he has failed to place the object in the appropriate genus, orif the expression be not peculiar to the object, we must go on to examine thecase according to the commonplace rules that relate to genus and property.
It remains, then, to prescribe how to investigate whether the object hasbeen either not defined at all, or else defined incorrectly. First, then, we mustproceed to examine if it has been defined incorrectly: for with anything it iseasier to do it than to do it correctly. Clearly, then, more mistakes are madein the latter task on account of its greater difficulty. Accordingly the attackbecomes easier in the latter case than in the former.
Incorrectness falls into two branches: (1) first, the use of obscure lan-guage (for the language of a definition ought to be the very clearest possible,seeing that the whole purpose of rendering it is to make something known);(secondly, if the expression used be longer than is necessary: for all addi-tional matter in a definition is superfluous. Again, each of the aforesaidbranches is divided into a number of others.
Part 2 Obscurity
One commonplace rule, then, in regard to obscurity is, See if the meaningintended by the definition involves an ambiguity with any other, e.g. ‘Be-coming is a passage into being’, or ‘Health is the balance of hot and coldelements’. Here ‘passage’ and ‘balance’ are ambiguous terms: it is accord-ingly not clear which of the several possible senses of the term he intendsto convey. Likewise also, if the term defined be used in different sensesand he has spoken without distinguishing between them: for then it is notclear to which of them the definition rendered applies, and one can thenbring a captious objection on the ground that the definition does not applyto all the things whose definition he has rendered: and this kind of thing isparticularly easy in the case where the definer does not see the ambiguity
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of his terms. Or, again, the questioner may himself distinguish the varioussenses of the term rendered in the definition, and then institute his argumentagainst each: for if the expression used be not adequate to the subject in anyof its senses, it is clear that he cannot have defined it in any sense aright.
Another rule is, See if he has used a metaphorical expression, as, for in-stance, if he has defined knowledge as ‘unsupplantable’, or the earth as a‘nurse’, or temperance as a ‘harmony’. For a metaphorical expression is al-ways obscure. It is possible, also, to argue sophistically against the user ofa metaphorical expression as though he had used it in its literal sense: forthe definition stated will not apply to the term defined, e.g. in the case oftemperance: for harmony is always found between notes. Moreover, if har-mony be the genus of temperance, then the same object will occur in twogenera of which neither contains the other: for harmony does not containvirtue, nor virtue harmony. Again, see if he uses terms that are unfamil-iar, as when Plato describes the eye as ‘brow-shaded’, or a certain spider as‘poison-fanged’, or the marrow as ‘boneformed’. For an unusual phrase isalways obscure.
Sometimes a phrase is used neither ambiguously, nor yet metaphorically,nor yet literally, as when the law is said to be the ‘measure’ or ‘image’ of thethings that are by nature just. Such phrases are worse than metaphor; for thelatter does make its meaning to some extent clear because of the likeness in-volved; for those who use metaphors do so always in view of some likeness:whereas this kind of phrase makes nothing clear; for there is no likeness tojustify the description ‘measure’ or ‘image’, as applied to the law, nor is thelaw ordinarily so called in a literal sense. So then, if a man says that thelaw is literally a ‘measure’ or an ‘image’, he speaks falsely: for an image issomething produced by imitation, and this is not found in the case of thelaw. If, on the other hand, he does not mean the term literally, it is clear thathe has used an unclear expression, and one that is worse than any sort ofmetaphorical expression.
Moreover, see if from the expression used the definition of the contrarybe not clear; for definitions that have been correctly rendered also indicatetheir contraries as well. Or, again, see if, when it is merely stated by itself, itis not evident what it defines: just as in the works of the old painters, unlessthere were an inscription, the figures used to be unrecognizable.
Part 3 Redundancy
If, then, the definition be not clear, you should proceed to examine on linessuch as these. If, on the other hand, he has phrased the definition redun-dantly, first of all look and see whether he has used any attribute that be-longs universally, either to real objects in general, or to all that fall under
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the same genus as the object defined: for the mention of this is sure to beredundant. For the genus ought to divide the object from things in general,and the differentia from any of the things contained in the same genus. Nowany term that belongs to everything separates off the given object from ab-solutely nothing, while any that belongs to all the things that fall under thesame genus does not separate it off from the things contained in the samegenus. Any addition, then, of that kind will be pointless.
Or see if, though the additional matter may be peculiar to the given term,yet even when it is struck out the rest of the expression too is peculiar andmakes clear the essence of the term. Thus, in the definition of man, the ad-dition ‘capable of receiving knowledge’ is superfluous; for strike it out, andstill the expression is peculiar and makes clear his essence. Speaking gen-erally, everything is superfluous upon whose removal the remainder stillmakes the term that is being defined clear. Such, for instance, would alsobe the definition of the soul, assuming it to be stated as a ‘self-moving num-ber’; for the soul is just ‘the self-moving’, as Plato defined it. Or perhapsthe expression used, though appropriate, yet does not declare the essence, ifthe word ‘number’ be eliminated. Which of the two is the real state of thecase it is difficult to determine clearly: the right way to treat the matter in allcases is to be guided by convenience. Thus (e.g.) it is said that the definitionof phlegm is the ‘undigested moisture that comes first off food’. Here theaddition of the word ‘undigested’ is superfluous, seeing that ‘the first’ is oneand not many, so that even when ‘undigested’ is left out the definition willstill be peculiar to the subject: for it is impossible that both phlegm and alsosomething else should both be the first to arise from the food. Or perhapsthe phlegm is not absolutely the first thing to come off the food, but only thefirst of the undigested matters, so that the addition ‘undigested’ is required;for stated the other way the definition would not be true unless the phlegmcomes first of all.
Moreover, see if anything contained in the definition fails to apply to ev-erything that falls under the same species: for this sort of definition is worsethan those which include an attribute belonging to all things universally. Forin that case, if the remainder of the expression be peculiar, the whole too willbe peculiar: for absolutely always, if to something peculiar anything what-ever that is true be added, the whole too becomes peculiar. Whereas if anypart of the expression do not apply to everything that falls under the samespecies, it is impossible that the expression as a whole should be peculiar: forit will not be predicated convertibly with the object; e.g. ‘a walking bipedanimal six feet high’: for an expression of that kind is not predicated con-vertibly with the term, because the attribute ‘six feet high’ does not belongto everything that falls under the same species.
Again, see if he has said the same thing more than once, saying (e.g.) ‘de-
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sire’ is a ‘conation for the pleasant’. For ‘desire’ is always ‘for the pleasant’,so that what is the same as desire will also be ‘for the pleasant’. Accordinglyour definition of desire becomes ‘conation-for-the-pleasant’: for the word‘desire’ is the exact equivalent of the words ‘conation for-the-pleasant’, sothat both alike will be ‘for the pleasant’. Or perhaps there is no absurdityin this; for consider this instance: - ‘Man is a biped’: therefore, what is thesame as man is a biped: but ‘a walking biped animal’ is the same as man,and therefore walking biped animal is a ‘biped’. But this involves no realabsurdity. For ‘biped’ is not a predicate of ‘walking animal’: if it were, thenwe should certainly have ‘biped’ predicated twice of the same thing; but asa matter of fact the subject said to be a biped is ‘a walking biped animal’, sothat the word ‘biped’ is only used as a predicate once. Likewise also in thecase of ‘desire’ as well: for it is not ‘conation’ that is said to be ‘for the pleas-ant’, but rather the whole idea, so that there too the predication is only madeonce. Absurdity results, not when the same word is uttered twice, but whenthe same thing is more than once predicated of a subject; e.g. if he says, likeXenocrates, that wisdom defines and contemplates reality: for definition isa certain type of contemplation, so that by adding the words ‘and contem-plates’ over again he says the same thing twice over. Likewise, too, those failwho say that ‘cooling’ is ‘the privation of natural heat’. For all privation is aprivation of some natural attribute, so that the addition of the word ‘natural’is superfluous: it would have been enough to say ‘privation of heat’, for theword ‘privation’ shows of itself that the heat meant is natural heat.
Again, see if a universal have been mentioned and then a particular caseof it be added as well, e.g. ‘Equity is a remission of what is expedient andjust’; for what is just is a branch of what is expedient and is therefore in-cluded in the latter term: its mention is therefore redundant, an additionof the particular after the universal has been already stated. So also, if hedefines ‘medicine’ as ‘knowledge of what makes for health in animals andmen’, or ‘the law’ as ‘the image of what is by nature noble and just’; for whatis just is a branch of what is noble, so that he says the same thing more thanonce.
Part 4 Intelligibility, priority, circularity
Whether, then, a man defines a thing correctly or incorrectly you should pro-ceed to examine on these and similar lines. But whether he has mentionedand defined its essence or no, should be examined as follows: First of all,see if he has failed to make the definition through terms that are prior andmore intelligible. For the reason why the definition is rendered is to makeknown the term stated, and we make things known by taking not any ran-dom terms, but such as are prior and more intelligible, as is done in demon-
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strations (for so it is with all teaching and learning); accordingly, it is clearthat a man who does not define through terms of this kind has not definedat all. Otherwise, there will be more than one definition of the same thing:for clearly he who defines through terms that are prior and more intelligiblehas also framed a definition, and a better one, so that both would then bedefinitions of the same object. This sort of view, however, does not generallyfind acceptance: for of each real object the essence is single: if, then, thereare to be a number of definitions of the same thing, the essence of the objectwill be the same as it is represented to be in each of the definitions, and theserepresentations are not the same, inasmuch as the definitions are different.Clearly, then, any one who has not defined a thing through terms that areprior and more intelligible has not defined it at all.
The statement that a definition has not been made through more intelli-gible terms may be understood in two senses, either supposing that its termsare absolutely less intelligible, or supposing that they are less intelligible tous: for either sense is possible. Thus absolutely the prior is more intelligiblethan the posterior, a point, for instance, than a line, a line than a plane, anda plane than a solid; just as also a unit is more intelligible than a number;for it is the prius and starting-point of all number. Likewise, also, a letter ismore intelligible than a syllable. Whereas to us it sometimes happens thatthe converse is the case: for the solid falls under perception most of all - morethan a plane - and a plane more than a line, and a line more than a point; formost people learn things like the former earlier than the latter; for any or-dinary intelligence can grasp them, whereas the others require an exact andexceptional understanding.
Absolutely, then, it is better to try to make what is posterior knownthrough what is prior, inasmuch as such a way of procedure is more sci-entific. Of course, in dealing with persons who cannot recognize thingsthrough terms of that kind, it may perhaps be necessary to frame the ex-pression through terms that are intelligible to them. Among definitions ofthis kind are those of a point, a line, and a plane, all of which explain theprior by the posterior; for they say that a point is the limit of a line, a line ofa plane, a plane of a solid. One must, however, not fail to observe that thosewho define in this way cannot show the essential nature of the term theydefine, unless it so happens that the same thing is more intelligible both tous and also absolutely, since a correct definition must define a thing throughits genus and its differentiae, and these belong to the order of things whichare absolutely more intelligible than, and prior to, the species. For annul thegenus and differentia, and the species too is annulled, so that these are priorto the species. They are also more intelligible; for if the species be known, thegenus and differentia must of necessity be known as well (for any one whoknows what a man is knows also what ‘animal’ and ‘walking’ are), whereas
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if the genus or the differentia be known it does not follow of necessity thatthe species is known as well: thus the species is less intelligible. Moreover,those who say that such definitions, viz. those which proceed from whatis intelligible to this, that, or the other man, are really and truly definitions,will have to say that there are several definitions of one and the same thing.For, as it happens, different things are more intelligible to different people,not the same things to all; and so a different definition would have to be ren-dered to each several person, if the definition is to be constructed from whatis more intelligible to particular individuals. Moreover, to the same peopledifferent things are more intelligible at different times; first of all the objectsof sense; then, as they become more sharpwitted, the converse; so that thosewho hold that a definition ought to be rendered through what is more intelli-gible to particular individuals would not have to render the same definitionat all times even to the same person. It is clear, then, that the right way to de-fine is not through terms of that kind, but through what is absolutely moreintelligible: for only in this way could the definition come always to be oneand the same. Perhaps, also, what is absolutely intelligible is what is intel-ligible, not to all, but to those who are in a sound state of understanding,just as what is absolutely healthy is what is healthy to those in a sound stateof body. All such points as this ought to be made very precise, and madeuse of in the course of discussion as occasion requires. The demolition of adefinition will most surely win a general approval if the definer happens tohave framed his expression neither from what is absolutely more intelligiblenor yet from what is so to us.
One form, then, of the failure to work through more intelligible termsis the exhibition of the prior through the posterior, as we remarked before.Another form occurs if we find that the definition has been rendered of whatis at rest and definite through what is indefinite and in motion: for what isstill and definite is prior to what is indefinite and in motion.
Of the failure to use terms that are prior there are three forms:(1) The first is when an opposite has been defined through its opposite,
e.g.i. good through evil: for opposites are always simultaneous by nature.Some people think, also, that both are objects of the same science, so that theone is not even more intelligible than the other. One must, however, observethat it is perhaps not possible to define some things in any other way, e.g.the double without the half, and all the terms that are essentially relative:for in all such cases the essential being is the same as a certain relation tosomething, so that it is impossible to understand the one term without theother, and accordingly in the definition of the one the other too must beembraced. One ought to learn up all such points as these, and use them asoccasion may seem to require.
(2) Another is - if he has used the term defined itself. This passes unob-
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served when the actual name of the object is not used, e.g. supposing anyone had defined the sun as a star that appears ‘by day’. For in bringing in‘day’ he brings in the sun. To detect errors of this sort, exchange the wordfor its definition, e.g. the definition of ‘day’ as the ‘passage of the sun overthe earth’. Clearly, whoever has said ‘the passage of the sun over the earth’has said ‘the sun’, so that in bringing in the ‘day’ he has brought in the sun.
(3) Again, see if he has defined one coordinate member of a division byanother, e.g. ‘an odd number’ as ‘that which is greater by one than an evennumber’. For the co-ordinate members of a division that are derived fromthe same genus are simultaneous by nature and ‘odd’ and ‘even’ are suchterms: for both are differentiae of number.
Likewise also, see if he has defined a superior through a subordinateterm, e.g. ‘An "even number" is "a number divisible into halves"’, or ‘"thegood" is a "state of virtue"’. For ‘half’ is derived from ‘two’, and ‘two’ is aneven number: virtue also is a kind of good, so that the latter terms are subor-dinate to the former. Moreover, in using the subordinate term one is boundto use the other as well: for whoever employs the term ‘virtue’ employs theterm ‘good’, seeing that virtue is a certain kind of good: likewise, also, who-ever employs the term ‘half’ employs the term ‘even’, for to be ‘divided inhalf’ means to be divided into two, and two is even.
Part 5 When an object in a genus has not been placed in it
Generally speaking, then, one commonplace rule relates to the failure toframe the expression by means of terms that are prior and more intelligi-ble: and of this the subdivisions are those specified above. A second is, seewhether, though the object is in a genus, it has not been placed in a genus.This sort of error is always found where the essence of the object does notstand first in the expression, e.g. the definition of ‘body’ as ‘that which hasthree dimensions’, or the definition of ‘man’, supposing any one to give it,as ‘that which knows how to count’: for it is not stated what it is that hasthree dimensions, or what it is that knows how to count: whereas the genusis meant to indicate just this, and is submitted first of the terms in the defini-tion.
Moreover, see if, while the term to be defined is used in relation to manythings, he has failed to render it in relation to all of them; as (e.g.) if he de-fine ‘grammar’ as the ‘knowledge how to write from dictation’: for he oughtalso to say that it is a knowledge how to read as well. For in renderingit as ‘knowledge of writing’ has no more defined it than by rendering it as‘knowledge of reading’: neither in fact has succeeded, but only he who men-tions both these things, since it is impossible that there should be more thanone definition of the same thing. It is only, however, in some cases that what
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has been said corresponds to the actual state of things: in some it does not,e.g. all those terms which are not used essentially in relation to both things:as medicine is said to deal with the production of disease and health; for itis said essentially to do the latter, but the former only by accident: for it isabsolutely alien to medicine to produce disease. Here, then, the man whorenders medicine as relative to both of these things has not defined it anybetter than he who mentions the one only. In fact he has done it perhapsworse, for any one else besides the doctor is capable of producing disease.
Moreover, in a case where the term to be defined is used in relation toseveral things, see if he has rendered it as relative to the worse rather than tothe better; for every form of knowledge and potentiality is generally thoughtto be relative to the best.
Again, if the thing in question be not placed in its own proper genus, onemust examine it according to the elementary rules in regard to genera, as hasbeen said before.
Moreover, see if he uses language which transgresses the genera of thethings he defines, defining, e.g. justice as a ‘state that produces equality’ or‘distributes what is equal’: for by defining it so he passes outside the sphereof virtue, and so by leaving out the genus of justice he fails to express itsessence: for the essence of a thing must in each case bring in its genus. It isthe same thing if the object be not put into its nearest genus; for the man whoputs it into the nearest one has stated all the higher genera, seeing that all thehigher genera are predicated of the lower. Either, then, it ought to be put intoits nearest genus, or else to the higher genus all the differentiae ought to beappended whereby the nearest genus is defined. For then he would not haveleft out anything: but would merely have mentioned the subordinate genusby an expression instead of by name. On the other hand, he who mentionsmerely the higher genus by itself, does not state the subordinate genus aswell: in saying ‘plant’ a man does not specify ‘a tree’.
Part 6 Whether the differentiae be those of the genus
Again, in regard to the differentiae, we must examine in like mannerwhether the differentiae, too, that he has stated be those of the genus. Forif a man has not defined the object by the differentiae peculiar to it, or hasmentioned something such as is utterly incapable of being a differentia ofanything, e.g. ‘animal’ or ‘substance’, clearly he has not defined it at all: forthe aforesaid terms do not differentiate anything at all. Further, we must seewhether the differentia stated possesses anything that is co-ordinate withit in a division; for, if not, clearly the one stated could not be a differen-tia of the genus. For a genus is always divided by differentiae that are co-ordinate members of a division, as, for instance, by the terms ‘walking’, ‘fly-
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ing’, ‘aquatic’, and ‘biped’. Or see if, though the contrasted differentia exists,it yet is not true of the genus, for then, clearly, neither of them could be a dif-ferentia of the genus; for differentiae that are co-ordinates in a division withthe differentia of a thing are all true of the genus to which the thing belongs.Likewise, also, see if, though it be true, yet the addition of it to the genus failsto make a species. For then, clearly, this could not be a specific differentia ofthe genus: for a specific differentia, if added to the genus, always makes aspecies. If, however, this be no true differentia, no more is the one adduced,seeing that it is a co-ordinate member of a division with this.
Moreover, see if he divides the genus by a negation, as those do whodefine line as ‘length without breadth’: for this means simply that it has notany breadth. The genus will then be found to partake of its own species: for,since of everything either an affirmation or its negation is true, length mustalways either lack breadth or possess it, so that ‘length’ as well, i.e. the genusof ‘line’, will be either with or without breadth. But ‘length without breadth’is the definition of a species, as also is ‘length with breadth’: for ‘withoutbreadth’ and ‘with breadth’ are differentiae, and the genus and differentiaconstitute the definition of the species. Hence the genus would admit ofthe definition of its species. Likewise, also, it will admit of the definitionof the differentia, seeing that one or the other of the aforesaid differentiaeis of necessity predicated of the genus. The usefulness of this principle isfound in meeting those who assert the existence of ‘Ideas’: for if absolutelength exist, how will it be predicable of the genus that it has breadth orthat it lacks it? For one assertion or the other will have to be true of ‘length’universally, if it is to be true of the genus at all: and this is contrary to thefact: for there exist both lengths which have, and lengths which have not,breadth. Hence the only people against whom the rule can be employed arethose who assert that a genus is always numerically one; and this is what isdone by those who assert the real existence of the ‘Ideas’; for they allege thatabsolute length and absolute animal are the genus.
It may be that in some cases the definer is obliged to employ a negation aswell, e.g. in defining privations. For ‘blind’ means a thing which cannot seewhen its nature is to see. There is no difference between dividing the genusby a negation, and dividing it by such an affirmation as is bound to havea negation as its co-ordinate in a division, e.g. supposing he had definedsomething as ‘length possessed of breadth’; for co-ordinate in the divisionwith that which is possessed of breadth is that which possesses no breadthand that only, so that again the genus is divided by a negation.
Again, see if he rendered the species as a differentia, as do those whodefine ‘contumely’ as ‘insolence accompanied by jeering’; for jeering is akind of insolence, i.e. it is a species and not a differentia.
Moreover, see if he has stated the genus as the differentia, e.g. Virtue is
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a good or noble state: for ‘good’ is the genus of ‘virtue’. Or possibly ‘good’here is not the genus but the differentia, on the principle that the same thingcannot be in two genera of which neither contains the other: for ‘good’ doesnot include ‘state’, nor vice versa: for not every state is good nor every gooda ‘state’. Both, then, could not be genera, and consequently, if ‘state’ is thegenus of virtue, clearly ‘good’ cannot be its genus: it must rather be thedifferentia. Moreover, ‘a state’ indicates the essence of virtue, whereas ‘good’indicates not the essence but a quality: and to indicate a quality is generallyheld to be the function of the differentia. See, further, whether the differentiarendered indicates an individual rather than a quality: for the general viewis that the differentia always expresses a quality.
Look and see, further, whether the differentia belongs only by accidentto the object defined. For the differentia is never an accidental attribute, anymore than the genus is: for the differentia of a thing cannot both belong andnot belong to it.
Moreover, if either the differentia or the species, or any of the thingswhich are under the species, is predicable of the genus, then he could nothave defined the term. For none of the aforesaid can possibly be predicatedof the genus, seeing that the genus is the term with the widest range of all.Again, see if the genus be predicated of the differentia; for the general view isthat the genus is predicated, not of the differentia, but of the objects of whichthe differentia is predicated. Animal (e.g.) is predicated of ‘man’ or ‘ox’ orother walking animals, not of the actual differentia itself which we predicateof the species. For if ‘animal’ is to be predicated of each of its differentiae,then ‘animal’ would be predicated of the species several times over; for thedifferentiae are predicates of the species. Moreover, the differentiae will beall either species or individuals, if they are animals; for every animal is eithera species or an individual.
Likewise you must inquire also if the species or any of the objects thatcome under it is predicated of the differentia: for this is impossible, seeingthat the differentia is a term with a wider range than the various species.Moreover, if any of the species be predicated of it, the result will be that thedifferentia is a species: if, for instance, ‘man’ be predicated, the differentia isclearly the human race. Again, see if the differentia fails to be prior to thespecies: for the differentia ought to be posterior to the genus, but prior to thespecies.
Look and see also if the differentia mentioned belongs to a differentgenus, neither contained in nor containing the genus in question. For thegeneral view is that the same differentia cannot be used of two non-subalterngenera. Else the result will be that the same species as well will be in twonon-subaltern genera: for each of the differentiae imports its own genus, e.g.‘walking’ and ‘biped’ import with them the genus ‘animal’. If, then, each of
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the genera as well is true of that of which the differentia is true, it clearlyfollows that the species must be in two non-subaltern genera. Or perhapsit is not impossible for the same differentia to be used of two non-subalterngenera, and we ought to add the words ‘except they both be subordinatemembers of the same genus’. Thus ‘walking animal’ and ‘flying animal’ arenon-subaltern genera, and ‘biped’ is the differentia of both. The words ‘ex-cept they both be subordinate members of the same genus’ ought thereforeto be added; for both these are subordinate to ‘animal’. From this possibility,that the same differentia may be used of two non-subaltern genera, it is clearalso that there is no necessity for the differentia to carry with it the wholeof the genus to which it belongs, but only the one or the other of its limbstogether with the genera that are higher than this, as ‘biped’ carries with iteither ‘flying’ or ‘walking animal’.
See, too, if he has rendered ‘existence in’ something as the differentia ofa thing’s essence: for the general view is that locality cannot differentiatebetween one essence and another. Hence, too, people condemn those whodivide animals by means of the terms ‘walking’ and ‘aquatic’, on the groundthat ‘walking’ and ‘aquatic’ indicate mere locality. Or possibly in this casethe censure is undeserved; for ‘aquatic’ does not mean ‘in’ anything; nordoes it denote a locality, but a certain quality: for even if the thing be on thedry land, still it is aquatic: and likewise a land-animal, even though it bein the water, will still be a and not an aquatic-animal. But all the same, ifever the differentia does denote existence in something, clearly he will havemade a bad mistake.
Again, see if he has rendered an affection as the differentia: for every af-fection, if intensified, subverts the essence of the thing, while the differentiais not of that kind: for the differentia is generally considered rather to pre-serve that which it differentiates; and it is absolutely impossible for a thingto exist without its own special differentia: for if there be no ‘walking’, therewill be no ‘man’. In fact, we may lay down absolutely that a thing cannothave as its differentia anything in respect of which it is subject to alteration:for all things of that kind, if intensified, destroy its essence. If, then, a manhas rendered any differentia of this kind, he has made a mistake: for weundergo absolutely no alteration in respect of our differentiae.
Again, see if he has failed to render the differentia of a relative term rela-tively to something else; for the differentiae of relative terms are themselvesrelative, as in the case also of knowledge. This is classed as speculative, prac-tical and productive; and each of these denotes a relation: for it speculatesupon something, and produces something and does something.
Look and see also if the definer renders each relative term relatively to itsnatural purpose: for while in some cases the particular relative term can beused in relation to its natural purpose only and to nothing else, some can be
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used in relation to something else as well. Thus sight can only be used forseeing, but a strigil can also be used to dip up water. Still, if any one were todefine a strigil as an instrument for dipping water, he has made a mistake:for that is not its natural function. The definition of a thing’s natural functionis ‘that for which it would be used by the prudent man, acting as such, andby the science that deals specially with that thing’.
Or see if, whenever a term happens to be used in a number of relations,he has failed to introduce it in its primary relation: e.g. by defining ‘wisdom’as the virtue of ‘man’ or of the ‘soul,’ rather than of the ‘reasoning faculty’:for ‘wisdom’ is the virtue primarily of the reasoning faculty: for it is in virtueof this that both the man and his soul are said to be wise.
Moreover, if the thing of which the term defined has been stated to bean affection or disposition, or whatever it may be, be unable to admit it, thedefiner has made a mistake. For every disposition and every affection isformed naturally in that of which it is an affection or disposition, as knowl-edge, too, is formed in the soul, being a disposition of soul. Sometimes,however, people make bad mistakes in matters of this sort, e.g. all thosewho say that ‘sleep’ is a ‘failure of sensation’, or that ‘perplexity’ is a stateof ‘equality between contrary reasonings’, or that ‘pain’ is a ‘violent disrup-tion of parts that are naturally conjoined’. For sleep is not an attribute ofsensation, whereas it ought to be, if it is a failure of sensation. Likewise,perplexity is not an attribute of opposite reasonings, nor pain of parts natu-rally conjoined: for then inanimate things will be in pain, since pain will bepresent in them. Similar in character, too, is the definition of ‘health’, say, asa ‘balance of hot and cold elements’: for then health will be necessarily ex-hibited by the hot and cold elements: for balance of anything is an attributeinherent in those things of which it is the balance, so that health would bean attribute of them. Moreover, people who define in this way put effect forcause, or cause for effect. For the disruption of parts naturally conjoined isnot pain, but only a cause of pain: nor again is a failure of sensation sleep,but the one is the cause of the other: for either we go to sleep because sensa-tion fails, or sensation fails because we go to sleep. Likewise also an equalitybetween contrary reasonings would be generally considered to be a causeof perplexity: for it is when we reflect on both sides of a question and findeverything alike to be in keeping with either course that we are perplexedwhich of the two we are to do.
Moreover, with regard to all periods of time look and see whether therebe any discrepancy between the differentia and the thing defined: e.g. sup-posing the ‘immortal’ to be defined as a ‘living thing immune at present fromdestruction’. For a living thing that is immune ‘at present’ from destructionwill be immortal ‘at present’. Possibly, indeed, in this case this result doesnot follow, owing to the ambiguity of the words ‘immune at present from
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destruction’: for it may mean either that the thing has not been destroyedat present, or that it cannot be destroyed at present, or that at present it issuch that it never can be destroyed. Whenever, then, we say that a livingthing is at present immune from destruction, we mean that it is at present aliving thing of such a kind as never to be destroyed: and this is equivalentto saying that it is immortal, so that it is not meant that it is immortal only atpresent. Still, if ever it does happen that what has been rendered accordingto the definition belongs in the present only or past, whereas what is meantby the word does not so belong, then the two could not be the same. So,then, this commonplace rule ought to be followed, as we have said.
Part 7 Whether application of a term is consistent with itsdefinition
You should look and see also whether the term being defined is appliedin consideration of something other than the definition rendered. Suppose(e.g.) a definition of ‘justice’ as the ‘ability to distribute what is equal’. Thiswould not be right, for ‘just’ describes rather the man who chooses, than theman who is able to distribute what is equal: so that justice could not be anability to distribute what is equal: for then also the most just man would bethe man with the most ability to distribute what is equal.
Moreover, see if the thing admits of degrees, whereas what is renderedaccording to the definition does not, or, vice versa, what is rendered accord-ing to the definition admits of degrees while the thing does not. For eitherboth must admit them or else neither, if indeed what is rendered accordingto the definition is the same as the thing. Moreover, see if, while both of themadmit of degrees, they yet do not both become greater together: e.g. supposesexual love to be the desire for intercourse: for he who is more intensely inlove has not a more intense desire for intercourse, so that both do not be-come intensified at once: they certainly should, however, had they been thesame thing.
Moreover, suppose two things to be before you, see if the term to be de-fined applies more particularly to the one to which the content of the defini-tion is less applicable. Take, for instance, the definition of ‘fire’ as the ‘bodythat consists of the most rarefied particles’. For ‘fire’ denotes flame ratherthan light, but flame is less the body that consists of the most rarefied par-ticles than is light: whereas both ought to be more applicable to the samething, if they had been the same. Again, see if the one expression appliesalike to both the objects before you, while the other does not apply to bothalike, but more particularly to one of them.
Moreover, see if he renders the definition relative to two things takenseparately: thus, the beautiful ‘is’ what is pleasant to the eyes or to the ears":
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or ‘the real’ is ‘what is capable of being acted upon or of acting’. For thenthe same thing will be both beautiful and not beautiful, and likewise will beboth real and not real. For ‘pleasant to the ears’ will be the same as ‘beau-tiful’, so that ‘not pleasant to the ears’ will be the same as ‘not beautiful’:for of identical things the opposites, too, are identical, and the opposite of‘beautiful’ is ‘not beautiful’, while of ‘pleasant to the ears’ the opposite is‘not pleasant to the cars’: clearly, then, ‘not pleasant to the ears’ is the samething as ‘not beautiful’. If, therefore, something be pleasant to the eyes butnot to the ears, it will be both beautiful and not beautiful. In like manner weshall show also that the same thing is both real and unreal.
Moreover, of both genera and differentiae and all the other terms ren-dered in definitions you should frame definitions in lieu of the terms, andthen see if there be any discrepancy between them.
Part 8 Definitions of terms which are relative
If the term defined be relative, either in itself or in respect of its genus, seewhether the definition fails to mention that to which the term, either in itselfor in respect of its genus, is relative, e.g. if he has defined ‘knowledge’ asan ‘incontrovertible conception’ or ‘wishing’ as ‘painless conation’. For ofeverything relative the essence is relative to something else, seeing that thebeing of every relative term is identical with being in a certain relation tosomething. He ought, therefore, to have said that knowledge is ‘conceptionof a knowable’ and that wishing is ‘conation for a good’. Likewise, also, if hehas defined ‘grammar’ as ‘knowledge of letters’: whereas in the definitionthere ought to be rendered either the thing to which the term itself is relative,or that, whatever it is, to which its genus is relative. Or see if a relativeterm has been described not in relation to its end, the end in anything beingwhatever is best in it or gives its purpose to the rest. Certainly it is what isbest or final that should be stated, e.g. that desire is not for the pleasant butfor pleasure: for this is our purpose in choosing what is pleasant as well.
Look and see also if that in relation to which he has rendered the term bea process or an activity: for nothing of that kind is an end, for the completionof the activity or process is the end rather than the process or activity itself.Or perhaps this rule is not true in all cases, for almost everybody prefers thepresent experience of pleasure to its cessation, so that they would count theactivity as the end rather than its completion.
Again see in some cases if he has failed to distinguish the quantity orquality or place or other differentiae of an object; e.g. the quality and quan-tity of the honour the striving for which makes a man ambitious: for all menstrive for honour, so that it is not enough to define the ambitious man ashim who strives for honour, but the aforesaid differentiae must be added.
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Likewise, also, in defining the covetous man the quantity of money he aimsat, or in the case of the incontinent man the quality of the pleasures, shouldbe stated. For it is not the man who gives way to any sort of pleasure what-ever who is called incontinent, but only he who gives way to a certain kindof pleasure. Or again, people sometimes define night as a ‘shadow on theearth’, or an earthquake as ‘a movement of the earth’, or a cloud as ‘conden-sation of the air’, or a wind as a ‘movement of the air’; whereas they oughtto specify as well quantity, quality, place, and cause. Likewise, also, in othercases of the kind: for by omitting any differentiae whatever he fails to statethe essence of the term. One should always attack deficiency. For a move-ment of the earth does not constitute an earthquake, nor a movement of theair a wind, irrespective of its manner and the amount involved.
Moreover, in the case of conations, and in any other cases where it ap-plies, see if the word ‘apparent’ is left out, e.g. ‘wishing is a conation afterthe good’, or ‘desire is a conation after the pleasant’ - instead of saying ‘theapparently good’, or ‘pleasant’. For often those who exhibit the conation donot perceive what is good or pleasant, so that their aim need not be reallygood or pleasant, but only apparently so. They ought, therefore, to haverendered the definition also accordingly. On the other hand, any one whomaintains the existence of Ideas ought to be brought face to face with hisIdeas, even though he does render the word in question: for there can be noIdea of anything merely apparent: the general view is that an Idea is alwaysspoken of in relation to an Idea: thus absolute desire is for the absolutelypleasant, and absolute wishing is for the absolutely good; they therefore can-not be for an apparent good or an apparently pleasant: for the existence ofan absolutely-apparently-good or pleasant would be an absurdity.
Part 9 Definitions of state, of relatives, of contraries
Moreover, if the definition be of the state of anything, look at what is in thestate, while if it be of what is in the state, look at the state: and likewise alsoin other cases of the kind. Thus if the pleasant be identical with the benefi-cial, then, too, the man who is pleased is benefited. Speaking generally, indefinitions of this sort it happens that what the definer defines is in a sensemore than one thing: for in defining knowledge, a man in a sense definesignorance as well, and likewise also what has knowledge and what lacks it,and what it is to know and to be ignorant. For if the first be made clear, theothers become in a certain sense clear as well. We have, then, to be on ourguard in all such cases against discrepancy, using the elementary principlesdrawn from consideration of contraries and of coordinates.
Moreover, in the case of relative terms, see if the species is rendered asrelative to a species of that to which the genus is rendered as relative, e.g.
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supposing belief to be relative to some object of belief, see whether a par-ticular belief is made relative to some particular object of belief: and, if amultiple be relative to a fraction, see whether a particular multiple be maderelative to a particular fraction. For if it be not so rendered, clearly a mistakehas been made.
See, also, if the opposite of the term has the opposite definition, whether(e.g.) the definition of ‘half’ is the opposite of that of ‘double’: for if ‘dou-ble’ is ‘that which exceeds another by an equal amount to that other’, ‘half’is ‘that which is exceeded by an amount equal to itself’. In the same way,too, with contraries. For to the contrary term will apply the definition thatis contrary in some one of the ways in which contraries are conjoined. Thus(e.g.) if ‘useful’ = ‘productive of good’, ‘injurious’ = ‘productive of evil’ or‘destructive of good’, for one or the other of thee is bound to be contraryto the term originally used. Suppose, then, neither of these things to be thecontrary of the term originally used, then clearly neither of the definitionsrendered later could be the definition of the contrary of the term originallydefined: and therefore the definition originally rendered of the original termhas not been rightly rendered either. Seeing, moreover, that of contraries,the one is sometimes a word forced to denote the privation of the other, as(e.g.) inequality is generally held to be the privation of equality (for ‘un-equal’ merely describes things that ‘are not equal’), it is therefore clear thatthat contrary whose form denotes the privation must of necessity be definedthrough the other; whereas the other cannot then be defined through theone whose form denotes the privation; for else we should find that each isbeing interpreted by the other. We must in the case of contrary terms keepan eye on this mistake, e.g. supposing any one were to define equality asthe contrary of inequality: for then he is defining it through the term whichdenotes privation of it. Moreover, a man who so defines is bound to use inhis definition the very term he is defining; and this becomes clear, if for theword we substitute its definition. For to say ‘inequality’ is the same as to say‘privation of equality’. Therefore equality so defined will be ‘the contrary ofthe privation of equality’, so that he would have used the very word to bedefined. Suppose, however, that neither of the contraries be so formed as todenote privation, but yet the definition of it be rendered in a manner like theabove, e.g. suppose ‘good’ to be defined as ‘the contrary of evil’, then, sinceit is clear that ‘evil’ too will be ‘the contrary of good’ (for the definition ofthings that are contrary in this must be rendered in a like manner), the resultagain is that he uses the very term being defined: for ‘good’ is inherent in thedefinition of ‘evil’. If, then, ‘good’ be the contrary of evil, and evil be noth-ing other than the ‘contrary of good’, then ‘good’ will be the ‘contrary of thecontrary of good’. Clearly, then, he has used the very word to be defined.
Moreover, see if in rendering a term formed to denote privation, he has
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failed to render the term of which it is the privation, e.g. the state, or con-trary, or whatever it may be whose privation it is: also if he has omitted toadd either any term at all in which the privation is naturally formed, or elsethat in which it is naturally formed primarily, e.g. whether in defining ‘igno-rance’ a privation he has failed to say that it is the privation of ‘knowledge’;or has failed to add in what it is naturally formed, or, though he has addedthis, has failed to render the thing in which it is primarily formed, placing it(e.g.) in ‘man’ or in ‘the soul’, and not in the ‘reasoning faculty’: for if in anyof these respects he fails, he has made a mistake. Likewise, also, if he hasfailed to say that ‘blindness’ is the ‘privation of sight in an eye’: for a properrendering of its essence must state both of what it is the privation and whatit is that is deprived.
Examine further whether he has defined by the expression ‘a privation’a term that is not used to denote a privation: thus a mistake of this sort alsowould be generally thought to be incurred in the case of ‘error’ by any onewho is not using it as a merely negative term. For what is generally thoughtto be in error is not that which has no knowledge, but rather that which hasbeen deceived, and for this reason we do not talk of inanimate things or ofchildren as ‘erring’. ‘Error’, then, is not used to denote a mere privation ofknowledge.
Part 10 Like inflexions, ambiguous terms
Moreover, see whether the like inflexions in the definition apply to the likeinflexions of the term; e.g. if ‘beneficial’ means ‘productive of health’, does‘beneficially’ mean ’productively of health‘ and a ’benefactor‘ a ’producer ofhealth’?
Look too and see whether the definition given will apply to the Idea aswell. For in some cases it will not do so; e.g. in the Platonic definition wherehe adds the word ‘mortal’ in his definitions of living creatures: for the Idea(e.g. the absolute Man) is not mortal, so that the definition will not fit theIdea. So always wherever the words ‘capable of acting on’ or ‘capable of be-ing acted upon’ are added, the definition and the Idea are absolutely boundto be discrepant: for those who assert the existence of Ideas hold that theyare incapable of being acted upon, or of motion. In dealing with these peopleeven arguments of this kind are useful.
Further, see if he has rendered a single common definition of terms thatare used ambiguously. For terms whose definition corresponding their com-mon name is one and the same, are synonymous; if, then, the definition ap-plies in a like manner to the whole range of the ambiguous term, it is not trueof any one of the objects described by the term. This is, moreover, what hap-pens to Dionysius’ definition of ‘life’ when stated as ‘a movement of a crea-
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ture sustained by nutriment, congenitally present with it’: for this is foundin plants as much as in animals, whereas ‘life’ is generally understood tomean not one kind of thing only, but to be one thing in animals and anotherin plants. It is possible to hold the view that life is a synonymous term and isalways used to describe one thing only, and therefore to render the definitionin this way on purpose: or it may quite well happen that a man may see theambiguous character of the word, and wish to render the definition of theone sense only, and yet fail to see that he has rendered a definition commonto both senses instead of one peculiar to the sense he intends. In either case,whichever course he pursues, he is equally at fault. Since ambiguous termssometimes pass unobserved, it is best in questioning to treat such terms asthough they were synonymous (for the definition of the one sense will notapply to the other, so that the answerer will be generally thought not to havedefined it correctly, for to a synonymous term the definition should applyin its full range), whereas in answering you should yourself distinguish be-tween the senses. Further, as some answerers call ‘ambiguous’ what is reallysynonymous, whenever the definition rendered fails to apply universally,and, vice versa, call synonymous what is really ambiguous supposing theirdefinition applies to both senses of the term, one should secure a prelimi-nary admission on such points, or else prove beforehand that so-and-so isambiguous or synonymous, as the case may be: for people are more readyto agree when they do not foresee what the consequence will be. If, how-ever, no admission has been made, and the man asserts that what is reallysynonymous is ambiguous because the definition he has rendered will notapply to the second sense as well, see if the definition of this second mean-ing applies also to the other meanings: for if so, this meaning must clearlybe synonymous with those others. Otherwise, there will be more than onedefinition of those other meanings, for there are applicable to them two dis-tinct definitions in explanation of the term, viz. the one previously renderedand also the later one. Again, if any one were to define a term used in sev-eral senses, and, finding that his definition does not apply to them all, wereto contend not that the term is ambiguous, but that even the term does notproperly apply to all those senses, just because his definition will not do soeither, then one may retort to such a man that though in some things onemust not use the language of the people, yet in a question of terminologyone is bound to employ the received and traditional usage and not to upsetmatters of that sort.
Part 11 Complex terms, equimembrals
Suppose now that a definition has been rendered of some complex term, takeaway the definition of one of the elements in the complex, and see if also the
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rest of the definition defines the rest of it: if not, it is clear that neither doesthe whole definition define the whole complex. Suppose, e.g. that some onehas defined a ‘finite straight line’ as ‘the limit of a finite plane, such that itscentre is in a line with its extremes’; if now the definition of a ‘finite line’ bethe ‘limit of a finite plane’, the rest (viz. ‘such that its centre is in a line withits extremes’) ought to be a definition of ‘straight’. But an infinite straightline has neither centre nor extremes and yet is straight so that this remainderdoes not define the remainder of the term.
Moreover, if the term defined be a compound notion, see if the defini-tion rendered be equimembral with the term defined. A definition is saidto be equimembral with the term defined when the number of the elementscompounded in the latter is the same as the number of nouns and verbs inthe definition. For the exchange in such cases is bound to be merely one ofterm for term, in the case of some if not of all, seeing that there are no moreterms used now than formerly; whereas in a definition terms ought to berendered by phrases, if possible in every case, or if not, in the majority. Forat that rate, simple objects too could be defined by merely calling them by adifferent name, e.g. ‘cloak’ instead of ‘doublet’.
The mistake is even worse, if actually a less well known term be sub-stituted, e.g. ‘pellucid mortal’ for ‘white man’: for it is no definition, andmoreover is less intelligible when put in that form.
Look and see also whether, in the exchange of words, the sense fails stillto be the same. Take, for instance, the explanation of ‘speculative knowl-edge’ as ‘speculative conception’: for conception is not the same as knowl-edge - as it certainly ought to be if the whole is to be the same too: for thoughthe word ‘speculative’ is common to both expressions, yet the remainder isdifferent.
Moreover, see if in replacing one of the terms by something else he hasexchanged the genus and not the differentia, as in the example just given:for ‘speculative’ is a less familiar term than knowledge; for the one is thegenus and the other the differentia, and the genus is always the most famil-iar term of all; so that it is not this, but the differentia, that ought to have beenchanged, seeing that it is the less familiar. It might be held that this criticismis ridiculous: because there is no reason why the most familiar term shouldnot describe the differentia, and not the genus; in which case, clearly, theterm to be altered would also be that denoting the genus and not the differ-entia. If, however, a man is substituting for a term not merely another termbut a phrase, clearly it is of the differentia rather than of the genus that adefinition should be rendered, seeing that the object of rendering the defi-nition is to make the subject familiar; for the differentia is less familiar thanthe genus.
If he has rendered the definition of the differentia, see whether the defi-
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nition rendered is common to it and something else as well: e.g. wheneverhe says that an odd number is a ‘number with a middle’, further definitionis required of how it has a middle: for the word ‘number’ is common to bothexpressions, and it is the word ‘odd’ for which the phrase has been substi-tuted. Now both a line and a body have a middle, yet they are not ‘odd’; sothat this could not be a definition of ‘odd’. If, on the other hand, the phrase‘with a middle’ be used in several senses, the sense here intended requiresto be defined. So that this will either discredit the definition or prove that itis no definition at all.
Part 12 Reality, relatives, imperfection, desirables
Again, see if the term of which he renders the definition is a reality, whereaswhat is contained in the definition is not, e.g. Suppose ‘white’ to be definedas ‘colour mingled with fire’: for what is bodiless cannot be mingled withbody, so that ‘colour’ ‘mingled with fire’ could not exist, whereas ‘white’does exist.
Moreover, those who in the case of relative terms do not distinguish towhat the object is related, but have described it only so as to include it amongtoo large a number of things, are wrong either wholly or in part; e.g. supposesome one to have defined ‘medicine’ as a science of ‘Reality’. For if medicinebe not a science of anything that is real, the definition is clearly altogetherfalse; while if it be a science of some real thing, but not of another, it is partlyfalse; for it ought to hold of all reality, if it is said to be of Reality essentiallyand not accidentally: as is the case with other relative terms: for every objectof knowledge is a term relative to knowledge: likewise, also, with other rel-ative terms, inasmuch as all such are convertible. Moreover, if the right wayto render account of a thing be to render it as it is not in itself but acciden-tally, then each and every relative term would be used in relation not to onething but to a number of things. For there is no reason why the same thingshould not be both real and white and good, so that it would be a correctrendering to render the object in relation to any one whatsoever of these, ifto render what it is accidentally be a correct way to render it. It is, moreover,impossible that a definition of this sort should be peculiar to the term ren-dered: for not only but the majority of the other sciences too, have for theirobject some real thing, so that each will be a science of reality. Clearly, then,such a definition does not define any science at all; for a definition ought tobe peculiar to its own term, not general.
Sometimes, again, people define not the thing but only the thing in agood or perfect condition. Such is the definition of a rhetorician as ‘one whocan always see what will persuade in the given circumstances, and omitnothing’; or of a thief, as ‘one who pilfers in secret’: for clearly, if they each
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do this, then the one will be a good rhetorician, and the other a good thief:whereas it is not the actual pilfering in secret, but the wish to do it, thatconstitutes the thief.
Again, see if he has rendered what is desirable for its own sake as de-sirable for what it produces or does, or as in any way desirable because ofsomething else, e.g. by saying that justice is ‘what preserves the laws’ orthat wisdom is ‘what produces happiness’; for what produces or preservessomething else is one of the things desirable for something else. It mightbe said that it is possible for what is desirable in itself to be desirable forsomething else as well: but still to define what is desirable in itself in sucha way is none the less wrong: for the essence contains par excellence whatis best in anything, and it is better for a thing to be desirable in itself than tobe desirable for something else, so that this is rather what the definition tooought to have indicated.
Part 13 Product and sum
See also whether in defining anything a man has defined it as an ‘A and B’,or as a ‘product of A and B’ or as an ‘A+B’. If he defines it as ‘A and B’,the definition will be true of both and yet of neither of them; suppose, e.g.justice to be defined as ‘temperance and courage.’ For if of two persons eachhas one of the two only, both and yet neither will be just: for both togetherhave justice, and yet each singly fails to have it. Even if the situation heredescribed does not so far appear very absurd because of the occurrence ofthis kind of thing in other cases also (for it is quite possible for two men tohave a mina between them, though neither of them has it by himself), yetleast that they should have contrary attributes surely seems quite absurd;and yet this will follow if the one be temperate and yet a coward, and theother, though brave, be a profligate; for then both will exhibit both justiceand injustice: for if justice be temperance and bravery, then injustice will becowardice and profligacy. In general, too, all the ways of showing that thewhole is not the same as the sum of its parts are useful in meeting the typejust described; for a man who defines in this way seems to assert that theparts are the same as the whole. The arguments are particularly appropriatein cases where the process of putting the parts together is obvious, as in ahouse and other things of that sort: for there, clearly, you may have the partsand yet not have the whole, so that parts and whole cannot be the same.
If, however, he has said that the term being defined is not ‘A and B’ butthe ‘product of A and B’, look and see in the first place if A and B cannotin the nature of things have a single product: for some things are so relatedto one another that nothing can come of them, e.g. a line and a number.Moreover, see if the term that has been defined is in the nature of things
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found primarily in some single subject, whereas the things which he hassaid produce it are not found primarily in any single subject, but each ina separate one. If so, clearly that term could not be the product of thesethings: for the whole is bound to be in the same things wherein its parts are,so that the whole will then be found primarily not in one subject only, butin a number of them. If, on the other hand, both parts and whole are foundprimarily in some single subject, see if that medium is not the same, but onething in the case of the whole and another in that of the parts. Again, seewhether the parts perish together with the whole: for it ought to happen,vice versa, that the whole perishes when the parts perish; when the wholeperishes, there is no necessity that the parts should perish too. Or again,see if the whole be good or evil, and the parts neither, or, vice versa, if theparts be good or evil and the whole neither. For it is impossible either for aneutral thing to produce something good or bad, or for things good or badto produce a neutral thing. Or again, see if the one thing is more distinctlygood than the other is evil, and yet the product be no more good than evil,e.g. suppose shamelessness be defined as ‘the product of courage and falseopinion’: here the goodness of courage exceeds the evil of false opinion;accordingly the product of these ought to have corresponded to this excess,and to be either good without qualification, or at least more good than evil.Or it may be that this does not necessarily follow, unless each be in itselfgood or bad; for many things that are productive are not good in themselves,but only in combination; or, per contra, they are good taken singly, and bador neutral in combination. What has just been said is most clearly illustratedin the case of things that make for health or sickness; for some drugs are suchthat each taken alone is good, but if they are both administered in a mixture,bad.
Again, see whether the whole, as produced from a better and worse, failsto be worse than the better and better than the worse element. This again,however, need not necessarily be the case, unless the elements compoundedbe in themselves good; if they are not, the whole may very well not be good,as in the cases just instanced.
Moreover, see if the whole be synonymous with one of the elements: forit ought not to be, any more than in the case of syllables: for the syllable isnot synonymous with any of the letters of which it is made up.
Moreover, see if he has failed to state the manner of their composition: forthe mere mention of its elements is not enough to make the thing intelligible.For the essence of any compound thing is not merely that it is a product ofso-and-so, but that it is a product of them compounded in such and such away, just as in the case of a house: for here the materials do not make a houseirrespective of the way they are put together.
If a man has defined an object as ‘A+B’, the first thing to be said is that
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‘A+B’ means the same either as ‘A and B’, or as the ‘product of A and B.’ for‘honey+water’ means either the honey and the water, or the ‘drink made ofhoney and water’. If, then, he admits that ‘A+B’ is the same as either of thesetwo things, the same criticisms will apply as have already been given formeeting each of them. Moreover, distinguish between the different senses inwhich one thing may be said to be ‘+’ another, and see if there is none of themin which A could be said to exist ‘+ B.’ Thus e.g. supposing the expressionto mean that they exist either in some identical thing capable of containingthem (as e.g. justice and courage are found in the soul), or else in the sameplace or in the same time, and if this be in no way true of the A and B inquestion, clearly the definition rendered could not hold of anything, as thereis no possible way in which A can exist B. If, however, among the varioussenses above distinguished, it be true that A and B are each found in thesame time as the other, look and see if possibly the two are not used in thesame relation. Thus e.g. suppose courage to have been defined as ‘daringwith right reasoning’: here it is possible that the person exhibits daring inrobbery, and right reasoning in regard to the means of health: but he mayhave ‘the former quality + the latter’ at the same time, and not as yet becourageous! Moreover, even though both be used in the same relation aswell, e.g. in relation to medical treatment (for a man may exhibit both daringand right reasoning in respect of medical treatment), still, none the less, noteven this combination of ‘the one + the other’ makes him ‘courageous’. Forthe two must not relate to any casual object that is the same, any more thaneach to a different object; rather, they must relate to the function of courage,e.g. meeting the perils of war, or whatever is more properly speaking itsfunction than this.
Some definitions rendered in this form fail to come under the aforesaiddivision at all, e.g. a definition of anger as ‘pain with a consciousness ofbeing slighted’. For what this means to say is that it is because of a con-sciousness of this sort that the pain occurs; but to occur ‘because of’ a thingis not the same as to occur ‘+ a thing’ in any of its aforesaid senses.
Part 14 Definitions as composites or contraries
Again, if he have described the whole compounded as the ‘composition’ ofthese things (e.g. ‘a living creature’ as a ‘composition of soul and body’),first of all see whether he has omitted to state the kind of composition, as(e.g.) in a definition of ‘flesh’ or ‘bone’ as the ‘composition of fire, earth,and air’. For it is not enough to say it is a composition, but you should alsogo on to define the kind of composition: for these things do not form fleshirrespective of the manner of their composition, but when compounded inone way they form flesh, when in another, bone. It appears, moreover, that
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neither of the aforesaid substances is the same as a ‘composition’ at all: fora composition always has a decomposition as its contrary, whereas neitherof the aforesaid has any contrary. Moreover, if it is equally probable thatevery compound is a composition or else that none is, and every kind ofliving creature, though a compound, is never a composition, then no othercompound could be a composition either.
Again, if in the nature of a thing two contraries are equally liable to oc-cur, and the thing has been defined through the one, clearly it has not beendefined; else there will be more than one definition of the same thing; forhow is it any more a definition to define it through this one than through theother, seeing that both alike are naturally liable to occur in it? Such is the def-inition of the soul, if defined as a substance capable of receiving knowledge:for it has a like capacity for receiving ignorance.
Also, even when one cannot attack the definition as a whole for lack ofacquaintance with the whole, one should attack some part of it, if one knowsthat part and sees it to be incorrectly rendered: for if the part be demolished,so too is the whole definition. Where, again, a definition is obscure, oneshould first of all correct and reshape it in order to make some part of it clearand get a handle for attack, and then proceed to examine it. For the answereris bound either to accept the sense as taken by the questioner, or else himselfto explain clearly whatever it is that his definition means. Moreover, justas in the assemblies the ordinary practice is to move an emendation of theexisting law and, if the emendation is better, they repeal the existing law,so one ought to do in the case of definitions as well: one ought oneself topropose a second definition: for if it is seen to be better, and more indicativeof the object defined, clearly the definition already laid down will have beendemolished, on the principle that there cannot be more than one definitionof the same thing.
In combating definitions it is always one of the chief elementary princi-ples to take by oneself a happy shot at a definition of the object before one,or to adopt some correctly expressed definition. For one is bound, with themodel (as it were) before one’s eyes, to discern both any shortcoming in anyfeatures that the definition ought to have, and also any superfluous addition,so that one is better supplied with lines of attack.
As to definitions, then, let so much suffice.
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Book VII Whether two things are ’thesame’ or ’different’
Part 1 Inflections, accidents, categories, degrees...
Whether two things are ‘the same’ or ‘different’, in the most literal of themeanings ascribed to ‘sameness’ (and we said that ‘the same’ applies in themost literal sense to what is numerically one), may be examined in the lightof their inflexions and coordinates and opposites. For if justice be the sameas courage, then too the just man is the same as the brave man, and ‘justly’is the same as ‘bravely’. Likewise, too, in the case of their opposites: for iftwo things be the same, their opposites also will be the same, in any of therecognized forms of opposition. For it is the same thing to take the oppositeof the one or that of the other, seeing that they are the same. Again it may beexamined in the light of those things which tend to produce or to destroy thethings in question of their formation and destruction, and in general of anything that is related in like manner to each. For where things are absolutelythe same, their formations and destructions also are the same, and so are thethings that tend to produce or to destroy them. Look and see also, in a casewhere one of two things is said to be something or other in a superlativedegree, if the other of these alleged identical things can also be described bya superlative in the same respect. Thus Xenocrates argues that the happy lifeand the good life are the same, seeing that of all forms of life the good lifeis the most desirable and so also is the happy life: for ‘the most desirable’and the greatest‘ apply but to one thing.’ Likewise also in other cases of thekind. Each, however, of the two things termed ‘greatest’ or ‘most desirable’must be numerically one: otherwise no proof will have been given that theyare the same; for it does not follow because Peloponnesians and Spartansare the bravest of the Greeks, that Peloponnesians are the same as Spartans,seeing that ‘Peloponnesian’ is not any one person nor yet ‘Spartan’; it onlyfollows that the one must be included under the other as ‘Spartans’ are under‘Peloponnesians’: for otherwise, if the one class be not included under theother, each will be better than the other. For then the Peloponnesians arebound to be better than the Spartans, seeing that the one class is not includedunder the other; for they are better than anybody else. Likewise also theSpartans must perforce be better than the Peloponnesians; for they too arebetter than anybody else; each then is better than the other! Clearly thereforewhat is styled ‘best’ and ‘greatest’ must be a single thing, if it is to be provedto be ‘the same’ as another. This also is why Xenocrates fails to prove hiscase: for the happy life is not numerically single, nor yet the good life, so
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that it does not follow that, because they are both the most desirable, theyare therefore the same, but only that the one falls under the other.
Again, look and see if, supposing the one to be the same as something,the other also is the same as it: for if they be not both the same as the samething, clearly neither are they the same as one another.
Moreover, examine them in the light of their accidents or of the things ofwhich they are accidents: for any accident belonging to the one must belongalso to the other, and if the one belong to anything as an accident, so mustthe other also. If in any of these respects there is a discrepancy, clearly theyare not the same.
See further whether, instead of both being found in one class of predi-cates, the one signifies a quality and the other a quantity or relation. Again,see if the genus of each be not the same, the one being ‘good’ and the other‘evil’, or the one being ‘virtue’ and the other ‘knowledge’: or see if, thoughthe genus is the same, the differentiae predicted of either be not the same,the one (e.g.) being distinguished as a ‘speculative’ science, the other as a‘practical’ science. Likewise also in other cases.
Moreover, from the point of view of ‘degrees’, see if the one admits anincrease of degree but not the other, or if though both admit it, they do notadmit it at the same time; just as it is not the case that a man desires inter-course more intensely, the more intensely he is in love, so that love and thedesire for intercourse are not the same.
Moreover, examine them by means of an addition, and see whether theaddition of each to the same thing fails to make the same whole; or if the sub-traction of the same thing from each leaves a different remainder. Suppose(e.g.) that he has declared ‘double a half’ to be the same as ‘a multiple of ahalf’: then, subtracting the words ‘a half’ from each, the remainders ought tohave signified the same thing: but they do not; for ‘double’ and ‘a multipleof’ do not signify the same thing.
Inquire also not only if some impossible consequence results directlyfrom the statement made, that A and B are the same, but also whether itis possible for a supposition to bring it about; as happens to those who as-sert that ‘empty’ is the same as ‘full of air’: for clearly if the air be exhausted,the vessel will not be less but more empty, though it will no longer be full ofair. So that by a supposition, which may be true or may be false (it makes nodifference which), the one character is annulled and not the other, showingthat they are not the same.
Speaking generally, one ought to be on the look-out for any discrepancyanywhere in any sort of predicate of each term, and in the things of whichthey are predicated. For all that is predicated of the one should be predicatedalso of the other, and of whatever the one is a predicate, the other should bea predicate of it as well.
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Moreover, as ‘sameness’ is a term used in many senses, see whetherthings that are the same in one way are the same also in a different way.For there is either no necessity or even no possibility that things that are thesame specifically or generically should be numerically the same, and it iswith the question whether they are or are not the same in that sense that weare concerned.
Moreover, see whether the one can exist without the other; for, if so, theycould not be the same.
Part 2 Constraints on definitions apply to sameness
Such is the number of the commonplace rules that relate to ‘sameness’. It isclear from what has been said that all the destructive commonplaces relatingto sameness are useful also in questions of definition, as was said before: forif what is signified by the term and by the expression be not the same, clearlythe expression rendered could not be a definition. None of the constructivecommonplaces, on the other hand, helps in the matter of definition; for itis not enough to show the sameness of content between the expression andthe term, in order to establish that the former is a definition, but a definitionmust have also all the other characters already announced.
Part 3 Reasoning to a thing’s definition
This then is the way, and these the arguments, whereby the attempt to de-molish a definition should always be made. If, on the other hand, we desireto establish one, the first thing to observe is that few if any who engage indiscussion arrive at a definition by reasoning: they always assume some-thing of the kind as their starting points - both in geometry and in arithmeticand the other studies of that kind. In the second place, to say accuratelywhat a definition is, and how it should be given, belongs to another inquiry.At present it concerns us only so far as is required for our present purpose,and accordingly we need only make the bare statement that to reason toa thing’s definition and essence is quite possible. For if a definition is anexpression signifying the essence of the thing and the predicates containedtherein ought also to be the only ones which are predicated of the thing inthe category of essence; and genera and differentiae are so predicated in thatcategory: it is obvious that if one were to get an admission that so and so arethe only attributes predicated in that category, the expression containing soand so would of necessity be a definition; for it is impossible that anythingelse should be a definition, seeing that there is not anything else predicatedof the thing in the category of essence.
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That a definition may thus be reached by a process of reasoning is obvi-ous. The means whereby it should be established have been more preciselydefined elsewhere, but for the purposes of the inquiry now before us thesame commonplace rules serve. For we have to examine into the contrariesand other opposites of the thing, surveying the expressions used both aswholes and in detail: for if the opposite definition defines that opposite term,the definition given must of necessity be that of the term before us. Seeing,however, that contraries may be conjoined in more than one way, we haveto select from those contraries the one whose contrary definition seems mostobvious. The expressions, then, have to be examined each as a whole in theway we have said, and also in detail as follows. First of all, see that thegenus rendered is correctly rendered; for if the contrary thing be found inthe contrary genus to that stated in the definition, and the thing before youis not in that same genus, then it would clearly be in the contrary genus: forcontraries must of necessity be either in the same genus or in contrary gen-era. The differentiae, too, that are predicated of contraries we expect to becontrary, e.g. those of white and black, for the one tends to pierce the vision,while the other tends to compress it. So that if contrary differentiae to thosein the definition are predicated of the contrary term, then those rendered inthe definition would be predicated of the term before us. Seeing, then, thatboth the genus and the differentiae have been rightly rendered, clearly theexpression given must be the right definition. It might be replied that thereis no necessity why contrary differentiae should be predicated of contraries,unless the contraries be found within the same genus: of things whose gen-era are themselves contraries it may very well be that the same differentiais used of both, e.g. of justice and injustice; for the one is a virtue and theother a vice of the soul: ‘of the soul’, therefore, is the differentia in both cases,seeing that the body as well has its virtue and vice. But this much at least istrue, that the differentiae of contraries are either contrary or else the same.If, then, the contrary differentia to that given be predicated of the contraryterm and not of the one in hand, clearly the differentia stated must be pred-icated of the latter. Speaking generally, seeing that the definition consists ofgenus and differentiae, if the definition of the contrary term be apparent, thedefinition of the term before you will be apparent also: for since its contraryis found either in the same genus or in the contrary genus, and likewise alsothe differentiae predicated of opposites are either contrary to, or the same as,each other, clearly of the term before you there will be predicated either thesame genus as of its contrary, while, of its differentiae, either all are contraryto those of its contrary, or at least some of them are so while the rest remainthe same; or, vice versa, the differentiae will be the same and the genera con-trary; or both genera and differentiae will be contrary. And that is all; forthat both should be the same is not possible; else contraries will have the
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same definition.Moreover, look at it from the point of view of its inflexions and coor-
dinates. For genera and definitions are bound to correspond in either case.Thus if forgetfulness be the loss of knowledge, to forget is to lose knowledge,and to have forgotten is to have lost knowledge. If, then, any one whateverof these is agreed to, the others must of necessity be agreed to as well. Like-wise, also, if destruction is the decomposition of the thing’s essence, then tobe destroyed is to have its essence decomposed, and ‘destructively’ means‘in such a way as to decompose its essence’; if again ‘destructive’ means ‘aptto decompose something’s essence’, then also ‘destruction’ means ‘the de-composition of its essence’. Likewise also with the rest: an admission of anyone of them whatever, and all the rest are admitted too.
Moreover, look at it from the point of view of things that stand in rela-tions that are like each other. For if ‘healthy’ means ‘productive of health’,‘vigorous’ too will mean ‘productive of vigour’, and ‘useful’ will mean ‘pro-ductive of good.’ For each of these things is related in like manner to its ownpeculiar end, so that if one of them is defined as ‘productive of’ that end,this will also be the definition of each of the rest as well.
Moreover, look at it from the point of and like degrees, in all the ways inwhich it is possible to establish a result by comparing two and two together.Thus if A defines a better than B defines and B is a definition of so too is A ofa. Further, if A’s claim to define a is like B’s to define B, and B defines B, thenA too defines a. This examination from the point of view of greater degreesis of no use when a single definition is compared with two things, or twodefinitions with one thing; for there cannot possibly be one definition of twothings or two of the same thing.
Part 4 The most handy of the commonplace arguments
The most handy of all the commonplace arguments are those just mentionedand those from co-ordinates and inflexions, and these therefore are thosewhich it is most important to master and to have ready to hand: for theyare the most useful on the greatest number of occasions. Of the rest, too,the most important are those of most general application: for these are themost effective, e.g. that you should examine the individual cases, and thenlook to see in the case of their various species whether the definition applies.For the species is synonymous with its individuals. This sort of inquiry isof service against those who assume the existence of Ideas, as has been saidbefore. Moreover see if a man has used a term metaphorically, or predicatedit of itself as though it were something different. So too if any other of thecommonplace rules is of general application and effective, it should be em-ployed.
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Part 5 It is more difficult to establish than to overthrow adefinition
That it is more difficult to establish than to overthrow a definition, is obvi-ous from considerations presently to be urged. For to see for oneself, andto secure from those whom one is questioning, an admission of premissesof this sort is no simple matter, e.g. that of the elements of the definitionrendered the one is genus and the other differentia, and that only the genusand differentiae are predicated in the category of essence. Yet without thesepremisses it is impossible to reason to a definition; for if any other things aswell are predicated of the thing in the category of essence, there is no tellingwhether the formula stated or some other one is its definition, for a defini-tion is an expression indicating the essence of a thing. The point is clear alsofrom the following: It is easier to draw one conclusion than many. Now indemolishing a definition it is sufficient to argue against one point only (forif we have overthrown any single point whatsoever, we shall have demol-ished the definition); whereas in establishing a definition, one is bound tobring people to the view that everything contained in the definition is at-tributable. Moreover, in establishing a case, the reasoning brought forwardmust be universal: for the definition put forward must be predicated of ev-erything of which the term is predicated, and must moreover be convertible,if the definition rendered is to be peculiar to the subject. In overthrowing aview, on the other hand, there is no longer any necessity to show one’s pointuniversally: for it is enough to show that the formula is untrue of any one ofthe things embraced under the term.
Further, even supposing it should be necessary to overthrow somethingby a universal proposition, not even so is there any need to prove the con-verse of the proposition in the process of overthrowing the definition. Formerely to show that the definition fails to be predicated of every one of thethings of which the term is predicated, is enough to overthrow it universally:and there is no need to prove the converse of this in order to show that theterm is predicated of things of which the expression is not predicated. More-over, even if it applies to everything embraced under the term, but not to italone, the definition is thereby demolished.
The case stands likewise in regard to the property and genus of a termalso. For in both cases it is easier to overthrow than to establish. As regardsthe property this is clear from what has been said: for as a rule the property isrendered in a complex phrase, so that to overthrow it, it is only necessary todemolish one of the terms used, whereas to establish it is necessary to reasonto them all. Then, too, nearly all the other rules that apply to the definitionwill apply also to the property of a thing. For in establishing a propertyone has to show that it is true of everything included under the term in
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question, whereas to overthrow one it is enough to show in a single caseonly that it fails to belong: further, even if it belongs to everything fallingunder the term, but not to that only, it is overthrown in this case as well, aswas explained in the case of the definition. In regard to the genus, it is clearthat you are bound to establish it in one way only, viz. by showing that itbelongs in every case, while of overthrowing it there are two ways: for ifit has been shown that it belongs either never or not in a certain case, theoriginal statement has been demolished. Moreover, in establishing a genusit is not enough to show that it belongs, but also that it belongs as genus hasto be shown; whereas in overthrowing it, it is enough to show its failure tobelong either in some particular case or in every case. It appears, in fact, asthough, just as in other things to destroy is easier than to create, so in thesematters too to overthrow is easier than to establish.
In the case of an accidental attribute the universal proposition is easierto overthrow than to establish; for to establish it, one has to show that itbelongs in every case, whereas to overthrow it, it is enough to show thatit does not belong in one single case. The particular proposition is, on thecontrary, easier to establish than to overthrow: for to establish it, it is enoughto show that it belongs in a particular instance, whereas to overthrow it, ithas to be shown that it never belongs at all.
It is clear also that the easiest thing of all is to overthrow a definition. Foron account of the number of statements involved we are presented in the def-inition with the greatest number of points for attack, and the more plentifulthe material, the quicker an argument comes: for there is more likelihood ofa mistake occurring in a large than in a small number of things. Moreover,the other rules too may be used as means for attacking a definition: for ifeither the formula be not peculiar, or the genus rendered be the wrong one,or something included in the formula fail to belong, the definition is therebydemolished. On the other hand, against the others we cannot bring all of thearguments drawn from definitions, nor yet of the rest: for only those relatingto accidental attributes apply generally to all the aforesaid kinds of attribute.For while each of the aforesaid kinds of attribute must belong to the thingin question, yet the genus may very well not belong as a property withoutas yet being thereby demolished. Likewise also the property need not be-long as a genus, nor the accident as a genus or property, so long as theydo belong. So that it is impossible to use one set as a basis of attack uponthe other except in the case of definition. Clearly, then, it is the easiest ofall things to demolish a definition, while to establish one is the hardest. Forthere one both has to establish all those other points by reasoning (i.e. thatthe attributes stated belong, and that the genus rendered is the true genus,and that the formula is peculiar to the term), and moreover, besides this,that the formula indicates the essence of the thing; and this has to be done
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correctly.Of the rest, the property is most nearly of this kind: for it is easier to
demolish, because as a rule it contains several terms; while it is the hardest toestablish, both because of the number of things that people must be broughtto accept, and, besides this, because it belongs to its subject alone and ispredicated convertibly with its subject.
The easiest thing of all to establish is an accidental predicate: for in othercases one has to show not only that the predicate belongs, but also that it be-longs in such and such a particular way: whereas in the case of the accidentit is enough to show merely that it belongs. On the other hand, an accidentalpredicate is the hardest thing to overthrow, because it affords the least ma-terial: for in stating accident a man does not add how the predicate belongs;and accordingly, while in other cases it is possible to demolish what is saidin two ways, by showing either that the predicate does not belong, or thatit does not belong in the particular way stated, in the case of an accidentalpredicate the only way to demolish it is to show that it does not belong atall.
The commonplace arguments through which we shall be well suppliedwith lines of argument with regard to our several problems have now beenenumerated at about sufficient length.
Book VIII Arrangement and method inposing questions
Part 1 The premisses which have to be adopted
Next there fall to be discussed the problems of arrangement and method inpitting questions. Any one who intends to frame questions must, first of all,select the ground from which he should make his attack; secondly, he mustframe them and arrange them one by one to himself; thirdly and lastly, hemust proceed actually to put them to the other party. Now so far as the selec-tion of his ground is concerned the problem is one alike for the philosopherand the dialectician; but how to go on to arrange his points and frame hisquestions concerns the dialectician only: for in every problem of that kinda reference to another party is involved. Not so with the philosopher, andthe man who is investigating by himself: the premisses of his reasoning,although true and familiar, may be refused by the answerer because theylie too near the original statement and so he foresees what will follow if hegrants them: but for this the philosopher does not care. Nay, he may possi-bly be even anxious to secure axioms as familiar and as near to the question
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in hand as possible: for these are the bases on which scientific reasonings arebuilt up.
The sources from which one’s commonplace arguments should be drawnhave already been described: we have now to discuss the arrangement andformation of questions and first to distinguish the premisses, other than thenecessary premisses, which have to be adopted. By necessary premissesare meant those through which the actual reasoning is constructed. Thosewhich are secured other than these are of four kinds; they serve either in-ductively to secure the universal premiss being granted, or to lend weight tothe argument, or to conceal the conclusion, or to render the argument moreclear. Beside these there is no other premiss which need be secured: these arethe ones whereby you should try to multiply and formulate your questions.Those which are used to conceal the conclusion serve a controversial pur-pose only; but inasmuch as an undertaking of this sort is always conductedagainst another person, we are obliged to employ them as well.
The necessary premisses through which the reasoning is effected, oughtnot to be propounded directly in so many words. Rather one should soaras far aloof from them as possible. Thus if one desires to secure an admis-sion that the knowledge of contraries is one, one should ask him to admit itnot of contraries, but of opposites: for, if he grants this, one will then arguethat the knowledge of contraries is also the same, seeing that contraries areopposites; if he does not, one should secure the admission by induction, byformulating a proposition to that effect in the case of some particular pair ofcontraries. For one must secure the necessary premisses either by reasoningor by induction, or else partly by one and partly by the other, although anypropositions which are too obvious to be denied may be formulated in somany words. This is because the coming conclusion is less easily discernedat the greater distance and in the process of induction, while at the sametime, even if one cannot reach the required premisses in this way, it is stillopen to one to formulate them in so many words. The premisses, other thanthese, that were mentioned above, must be secured with a view to the lat-ter. The way to employ them respectively is as follows: Induction shouldproceed from individual cases to the universal and from the known to theunknown; and the objects of perception are better known, to most people ifnot invariably. Concealment of one’s plan is obtained by securing throughprosyllogisms the premisses through which the proof of the original propo-sition is going to be constructed - and as many of them as possible. Thisis likely to be effected by making syllogisms to prove not only the neces-sary premisses but also some of those which are required to establish them.Moreover, do not state the conclusions of these premisses but draw themlater one after another; for this is likely to keep the answerer at the greatestpossible distance from the original proposition. Speaking generally, a man
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who desires to get information by a concealed method should so put hisquestions that when he has put his whole argument and has stated the con-clusion, people still ask ‘Well, but why is that?’ This result will be securedbest of all by the method above described: for if one states only the final con-clusion, it is unclear how it comes about; for the answerer does not foreseeon what grounds it is based, because the previous syllogisms have not beenmade articulate to him: while the final syllogism, showing the conclusion, islikely to be kept least articulate if we lay down not the secured propositionson which it is based, but only the grounds on which we reason to them.
It is a useful rule, too, not to secure the admissions claimed as the basesof the syllogisms in their proper order, but alternately those that conduceto one conclusion and those that conduce to another; for, if those which gotogether are set side by side, the conclusion that will result from them ismore obvious in advance.
One should also, wherever possible, secure the universal premiss bya definition relating not to the precise terms themselves but to their co-ordinates; for people deceive themselves, whenever the definition is taken inregard to a co-ordinate, into thinking that they are not making the admissionuniversally. An instance would be, supposing one had to secure the admis-sion that the angry man desires vengeance on account of an apparent slight,and were to secure this, that ‘anger’ is a desire for vengeance on account ofan apparent slight: for, clearly, if this were secured, we should have univer-sally what we intend. If, on the other hand, people formulate propositionsrelating to the actual terms themselves, they often find that the answerer re-fuses to grant them because on the actual term itself he is readier with hisobjection, e.g. that the ‘angry man’ does not desire vengeance, because webecome angry with our parents, but we do not desire vengeance on them.Very likely the objection is not valid; for upon some people it is vengeanceenough to cause them pain and make them sorry; but still it gives a certainplausibility and air of reasonableness to the denial of the proposition. In thecase, however, of the definition of ‘anger’ it is not so easy to find an objection.
Moreover, formulate your proposition as though you did so not for itsown sake, but in order to get at something else: for people are shy of grantingwhat an opponent’s case really requires. Speaking generally, a questionershould leave it as far as possible doubtful whether he wishes to secure anadmission of his proposition or of its opposite: for if it be uncertain whattheir opponent’s argument requires, people are more ready to say what theythemselves think.
Moreover, try to secure admissions by means of likeness: for such ad-missions are plausible, and the universal involved is less patent; e.g. makethe other person admit that as knowledge and ignorance of contraries is thesame, so too perception of contraries is the same; or vice versa, that since the
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perception is the same, so is the knowledge also. This argument resemblesinduction, but is not the same thing; for in induction it is the universal whoseadmission is secured from the particulars, whereas in arguments from like-ness, what is secured is not the universal under which all the like cases fall.
It is a good rule also, occasionally to bring an objection against oneself:for answerers are put off their guard against those who appear to be argu-ing impartially. It is useful too, to add that ‘So and so is generally held orcommonly said’; for people are shy of upsetting the received opinion un-less they have some positive objection to urge: and at the same time theyare cautious about upsetting such things because they themselves too findthem useful. Moreover, do not be insistent, even though you really requirethe point: for insistence always arouses the more opposition. Further, for-mulate your premiss as though it were a mere illustration: for people admitthe more readily a proposition made to serve some other purpose, and notrequired on its own account. Moreover, do not formulate the very proposi-tion you need to secure, but rather something from which that necessarilyfollows: for people are more willing to admit the latter, because it is not soclear from this what the result will be, and if the one has been secured, theother has been secured also. Again, one should put last the point whichone most wishes to have conceded; for people are specially inclined to denythe first questions put to them, because most people in asking questions putfirst the points which they are most eager to secure. On the other hand, indealing with some people propositions of this sort should be put forwardfirst: for ill-tempered men admit most readily what comes first, unless theconclusion that will result actually stares them in the face, while at the closeof an argument they show their ill-temper. Likewise also with those whoconsider themselves smart at answering: for when they have admitted mostof what you want they finally talk clap-trap to the effect that the conclusiondoes not follow from their admissions: yet they say ‘Yes’ readily, confidentin their own character, and imagining that they cannot suffer any reverse.Moreover, it is well to expand the argument and insert things that it doesnot require at all, as do those who draw false geometrical figures: for in themultitude of details the whereabouts of the fallacy is obscured. For this rea-son also a questioner sometimes evades observation as he adds in a cornerwhat, if he formulated it by itself, would not be granted.
For concealment, then, the rules which should be followed are the above.Ornament is attained by induction and distinction of things closely akin.What sort of process induction is obvious: as for distinction, an instance ofthe kind of thing meant is the distinction of one form of knowledge as betterthan another by being either more accurate, or concerned with better objects;or the distinction of sciences into speculative, practical, and productive. Foreverything of this kind lends additional ornament to the argument, though
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there is no necessity to say them, so far as the conclusion goes.For clearness, examples and comparisons should be adduced, and let the
illustrations be relevant and drawn from things that we know, as in Homerand not as in Choerilus; for then the proposition is likely to become clearer.
Part 2 Syllogism and demonstration versus induction
In dialectics, syllogism should be employed in reasoning against dialecti-cians rather than against the crowd: induction, on the other hand, is mostuseful against the crowd. This point has been treated previously as well.In induction, it is possible in some cases to ask the question in its universalform, but in others this is not easy, because there is no established generalterm that covers all the resemblances: in this case, when people need to se-cure the universal, they use the phrase ‘in all cases of this sort’. But it is oneof the very hardest things to distinguish which of the things adduced are ‘ofthis sort’, and which are not: and in this connexion people often throw dustin each others’ eyes in their discussion, the one party asserting the likenessof things that are not alike, and the other disputing the likeness of things thatare. One ought, therefore, to try oneself to coin a word to cover all things ofthe given sort, so as to leave no opportunity either to the answerer to dis-pute, and say that the thing advanced does not answer to a like description,or to the questioner to suggest falsely that it does answer to a like descrip-tion, for many things appear to answer to like descriptions that do not reallydo so.
If one has made an induction on the strength of several cases and yetthe answerer refuses to grant the universal proposition, then it is fair to de-mand his objection. But until one has oneself stated in what cases it is so,it is not fair to demand that he shall say in what cases it is not so: for oneshould make the induction first, and then demand the objection. One ought,moreover, to claim that the objections should not be brought in reference tothe actual subject of the proposition, unless that subject happen to be theone and only thing of the kind, as for instance two is the one prime numberamong the even numbers: for, unless he can say that this subject is uniqueof its kind, the objector ought to make his objection in regard to some other.People sometimes object to a universal proposition, and bring their objectionnot in regard to the thing itself, but in regard to some homonym of it: thusthey argue that a man can very well have a colour or a foot or a hand otherthan his own, for a painter may have a colour that is not his own, and a cookmay have a foot that is not his own. To meet them, therefore, you shoulddraw the distinction before putting your question in such cases: for so longas the ambiguity remains undetected, so long will the objection to the propo-sition be deemed valid. If, however, he checks the series of questions by an
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objection in regard not to some homonym, but to the actual thing asserted,the questioner should withdraw the point objected to, and form the remain-der into a universal proposition, until he secures what he requires; e.g. in thecase of forgetfulness and having forgotten: for people refuse to admit thatthe man who has lost his knowledge of a thing has forgotten it, because ifthe thing alters, he has lost knowledge of it, but he has not forgotten it. Ac-cordingly the thing to do is to withdraw the part objected to, and assert theremainder, e.g. that if a person have lost knowledge of a thing while it stillremains, he then has forgotten it. One should similarly treat those who ob-ject to the statement that ‘the greater the good, the greater the evil that is itsopposite’: for they allege that health, which is a less good thing than vigour,has a greater evil as its opposite: for disease is a greater evil than debility. Inthis case too, therefore, we have to withdraw the point objected to; for whenit has been withdrawn, the man is more likely to admit the proposition, e.g.that ‘the greater good has the greater evil as its opposite, unless the one goodinvolves the other as well’, as vigour involves health. This should be donenot only when he formulates an objection, but also if, without so doing, herefuses to admit the point because he foresees something of the kind: for ifthe point objected to be withdrawn, he will be forced to admit the proposi-tion because he cannot foresee in the rest of it any case where it does not holdtrue: if he refuse to admit it, then when asked for an objection he certainlywill be unable to render one. Propositions that are partly false and partlytrue are of this type: for in the case of these it is possible by withdrawinga part to leave the rest true. If, however, you formulate the proposition onthe strength of many cases and he has no objection to bring, you may claimthat he shall admit it: for a premiss is valid in dialectics which thus holds inseveral instances and to which no objection is forthcoming.
Whenever it is possible to reason to the same conclusion either through orwithout a reduction per impossibile, if one is demonstrating and not arguingdialectically it makes no difference which method of reasoning be adopted,but in argument with another reasoning per impossibile should be avoided.For where one has reasoned without the reduction per impossibile, no dis-pute can arise; if, on the other hand, one does reason to an impossible con-clusion, unless its falsehood is too plainly manifest, people deny that it isimpossible, so that the questioners do not get what they want.
One should put forward all propositions that hold true of several cases,and to which either no objection whatever appears or at least not any on thesurface: for when people cannot see any case in which it is not so, they admitit for true.
The conclusion should not be put in the form of a question; if it be, andthe man shakes his head, it looks as if the reasoning had failed. For often,even if it be not put as a question but advanced as a consequence, people
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deny it, and then those who do not see that it follows upon the previousadmissions do not realize that those who deny it have been refuted: when,then, the one man merely asks it as a question without even saying that itso follows, and the other denies it, it looks altogether as if the reasoning hadfailed.
Not every universal question can form a dialectical proposition as ordi-narily understood, e.g. ‘What is man?’ or ‘How many meanings has "thegood"?’ For a dialectical premiss must be of a form to which it is possible toreply ‘Yes’ or ‘No’, whereas to the aforesaid it is not possible. For this reasonquestions of this kind are not dialectical unless the questioner himself drawsdistinctions or divisions before expressing them, e.g. ‘Good means this, orthis, does it not?’ For questions of this sort are easily answered by a Yes ora No. Hence one should endeavour to formulate propositions of this kindin this form. It is at the same time also perhaps fair to ask the other manhow many meanings of ‘the good’ there are, whenever you have yourselfdistinguished and formulated them, and he will not admit them at all.
Any one who keeps on asking one thing for a long time is a bad inquirer.For if he does so though the person questioned keeps on answering the ques-tions, clearly he asks a large number of questions, or else asks the same ques-tion a large number of times: in the one case he merely babbles, in the otherhe fails to reason: for reasoning always consists of a small number of pre-misses. If, on the other hand, he does it because the person questioned doesnot answer the questions, he is at fault in not taking him to task or breakingoff the discussion.
Part 3 Sources of difficulty in discussion
There are certain hypotheses upon which it is at once difficult to bring, andeasy to stand up to, an argument. Such (e.g.) are those things which standfirst and those which stand last in the order of nature. For the former requiredefinition, while the latter have to be arrived at through many steps if onewishes to secure a continuous proof from first principles, or else all discus-sion about them wears the air of mere sophistry: for to prove anything isimpossible unless one begins with the appropriate principles, and connectsinference with inference till the last are reached. Now to define first princi-ples is just what answerers do not care to do, nor do they pay any attentionif the questioner makes a definition: and yet until it is clear what it is that isproposed, it is not easy to discuss it. This sort of thing happens particularlyin the case of the first principles: for while the other propositions are shownthrough these, these cannot be shown through anything else: we are obligedto understand every item of that sort by a definition. The inferences, too, thatlie too close to the first principle are hard to treat in argument: for it is not
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possible to bring many arguments in regard to them, because of the smallnumber of those steps, between the conclusion and the principle, wherebythe succeeding propositions have to be shown. The hardest, however, of alldefinitions to treat in argument are those that employ terms about which,in the first place, it is uncertain whether they are used in one sense or sev-eral, and, further, whether they are used literally or metaphorically by thedefiner. For because of their obscurity, it is impossible to argue upon suchterms; and because of the impossibility of saying whether this obscurity isdue to their being used metaphorically, it is impossible to refute them.
In general, it is safe to suppose that, whenever any problem proves in-tractable, it either needs definition or else bears either several senses, or ametaphorical sense, or it is not far removed from the first principles; or elsethe reason is that we have yet to discover in the first place just this - in whichof the aforesaid directions the source of our difficulty lies: when we havemade this clear, then obviously our business must be either to define or todistinguish, or to supply the intermediate premisses: for it is through thesethat the final conclusions are shown.
It often happens that a difficulty is found in discussing or arguing a givenposition because the definition has not been correctly rendered: e.g. ‘Hasone thing one contrary or many?’: here when the term ‘contraries’ has beenproperly defined, it is easy to bring people to see whether it is possible for thesame thing to have several contraries or not: in the same way also with otherterms requiring definition. It appears also in mathematics that the difficultyin using a figure is sometimes due to a defect in definition; e.g. in provingthat the line which cuts the plane parallel to one side divides similarly boththe line which it cuts and the area; whereas if the definition be given, the factasserted becomes immediately clear: for the areas have the same fractionsubtracted from them as have the sides: and this is the definition of ‘the sameratio’. The most primary of the elementary principles are without exceptionvery easy to show, if the definitions involved, e.g. the nature of a line or ofa circle, be laid down; only the arguments that can be brought in regard toeach of them are not many, because there are not many intermediate steps.If, on the other hand, the definition of the starting-points be not laid down,to show them is difficult and may even prove quite impossible. The caseof the significance of verbal expressions is like that of these mathematicalconceptions.
One may be sure then, whenever a position is hard to discuss, that oneor other of the aforesaid things has happened to it. Whenever, on the otherhand, it is a harder task to argue to the point claimed, i.e. the premiss, thanto the resulting position, a doubt may arise whether such claims should beadmitted or not: for if a man is going to refuse to admit it and claim that youshall argue to it as well, he will be giving the signal for a harder undertaking
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than was originally proposed: if, on the other hand, he grants it, he willbe giving the original thesis credence on the strength of what is less crediblethan itself. If, then, it is essential not to enhance the difficulty of the problem,he had better grant it; if, on the other hand, it be essential to reason throughpremisses that are better assured, he had better refuse. In other words, inserious inquiry he ought not to grant it, unless he be more sure about it thanabout the conclusion; whereas in a dialectical exercise he may do so if he ismerely satisfied of its truth. Clearly, then, the circumstances under whichsuch admissions should be claimed are different for a mere questioner andfor a serious teacher.
Part 4 The business of a good answerer
As to the formulation, then, and arrangement of one’s questions, aboutenough has been said.
With regard to the giving of answers, we must first define what is thebusiness of a good answerer, as of a good questioner. The business of thequestioner is so to develop the argument as to make the answerer utter themost extravagant paradoxes that necessarily follow because of his position:while that of the answerer is to make it appear that it is not he who is re-sponsible for the absurdity or paradox, but only his position: for one may,perhaps, distinguish between the mistake of taking up a wrong position tostart with, and that of not maintaining it properly, when once taken up.
Part 5 Premisses generally accepted or rejected withoutqualification
Inasmuch as no rules are laid down for those who argue for the sake oftraining and of examination: - and the aim of those engaged in teachingor learning is quite different from that of those engaged in a competition; asis the latter from that of those who discuss things together in the spirit ofinquiry: for a learner should always state what he thinks: for no one is eventrying to teach him what is false; whereas in a competition the business ofthe questioner is to appear by all means to produce an effect upon the other,while that of the answerer is to appear unaffected by him; on the other hand,in an assembly of disputants discussing in the spirit not of a competition butof an examination and inquiry, there are as yet no articulate rules about whatthe answerer should aim at, and what kind of things he should and shouldnot grant for the correct or incorrect defence of his position: - inasmuch,then, as we have no tradition bequeathed to us by others, let us try to saysomething upon the matter for ourselves.
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The thesis laid down by the answerer before facing the questioner’s ar-gument is bound of necessity to be one that is either generally accepted orgenerally rejected or else is neither: and moreover is so accepted or rejectedeither absolutely or else with a restriction, e.g. by some given person, bythe speaker or by some one else. The manner, however, of its acceptance orrejection, whatever it be, makes no difference: for the right way to answer,i.e. to admit or to refuse to admit what has been asked, will be the samein either case. If, then, the statement laid down by the answerer be gener-ally rejected, the conclusion aimed at by the questioner is bound to be onegenerally accepted, whereas if the former be generally accepted, the latter isgenerally rejected: for the conclusion which the questioner tries to draw isalways the opposite of the statement laid down. If, on the other hand, whatis laid down is generally neither rejected nor accepted, the conclusion willbe of the same type as well.
Now since a man who reasons correctly demonstrates his proposed con-clusion from premisses that are more generally accepted, and more familiar,it is clear that:
(1) where the view laid down by him is one that generally is absolutelyrejected, the answerer ought not to grant either what is thus absolutely notaccepted at all, or what is accepted indeed, but accepted less generally thanthe questioner’s conclusion. For if the statement laid down by the answererbe generally rejected, the conclusion aimed at by the questioner will be onethat is generally accepted, so that the premisses secured by the questionershould all be views generally accepted, and more generally accepted thanhis proposed conclusion, if the less familiar is to be inferred through themore familiar. Consequently, if any of the questions put to him be not of thischaracter, the answerer should not grant them.
(2) If, on the other hand, the statement laid down by the answerer begenerally accepted without qualification, clearly the conclusion sought bythe questioner will be one generally rejected without qualification. Accord-ingly, the answerer should admit all views that are generally accepted and,of those that are not generally accepted, all that are less generally rejectedthan the conclusion sought by the questioner. For then he will probably bethought to have argued sufficiently well.
(3) Likewise, too, if the statement laid down by the answerer be neitherrejected generally nor generally accepted; for then, too, anything that ap-pears to be true should be granted, and, of the views not generally accepted,any that are more generally accepted than the questioner’s conclusion; forin that case the result will be that the arguments will be more generally ac-cepted.
If, then, the view laid down by the answerer be one that is generallyaccepted or rejected without qualification, then the views that are accepted
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absolutely must be taken as the standard of comparison: whereas if the viewlaid down be one that is not generally accepted or rejected, but only by theanswerer, then the standard whereby the latter must judge what is generallyaccepted or not, and must grant or refuse to grant the point asked, is himself.If, again, the answerer be defending some one else’s opinion, then clearly itwill be the latter’s judgement to which he must have regard in granting ordenying the various points. This is why those, too, who introduce other’sopinions, e.g. that ‘good and evil are the same thing, as Heraclitus says,’refuse to admit the impossibility of contraries belonging at the same time tothe same thing; not because they do not themselves believe this, but becauseon Heraclitus’ principles one has to say so. The same thing is done also bythose who take on the defence of one another’s positions; their aim being tospeak as would the man who stated the position.
Part 6 What the aims of the answerer should be
It is clear, then, what the aims of the answerer should be, whether the po-sition he lays down be a view generally accepted without qualification oraccepted by some definite person. Now every question asked is bound toinvolve some view that is either generally held or generally rejected or nei-ther, and is also bound to be either relevant to the argument or irrelevant:if then it be a view generally accepted and irrelevant, the answerer shouldgrant it and remark that it is the accepted view: if it be a view not gener-ally accepted and irrelevant, he should grant it but add a comment that it isnot generally accepted, in order to avoid the appearance of being a simple-ton. If it be relevant and also be generally accepted, he should admit thatit is the view generally accepted but say that it lies too close to the origi-nal proposition, and that if it be granted the problem proposed collapses.If what is claimed by the questioner be relevant but too generally rejected,the answerer, while admitting that if it be granted the conclusion sought fol-lows, should yet protest that the proposition is too absurd to be admitted.Suppose, again, it be a view that is neither rejected generally nor generallyaccepted, then, if it be irrelevant to the argument, it may be granted withoutrestriction; if, however, it be relevant, the answerer should add the commentthat, if it be granted, the original problem collapses. For then the answererwill not be held to be personally accountable for what happens to him, if hegrants the several points with his eyes open, and also the questioner will beable to draw his inference, seeing that all the premisses that are more gener-ally accepted than the conclusion are granted him. Those who try to draw aninference from premisses more generally rejected than the conclusion clearlydo not reason correctly: hence, when men ask these things, they ought notto be granted.
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Part 7 Terms used obscurely
The questioner should be met in a like manner also in the case of terms usedobscurely, i.e. in several senses. For the answerer, if he does not understand,is always permitted to say ‘I do not understand’: he is not compelled to reply‘Yes’ or ‘No’ to a question which may mean different things. Clearly, then, inthe first place, if what is said be not clear, he ought not to hesitate to say thathe does not understand it; for often people encounter some difficulty fromassenting to questions that are not clearly put. If he understands the questionand yet it covers many senses, then supposing what it says to be universallytrue or false, he should give it an unqualified assent or denial: if, on theother hand, it be partly true and partly false, he should add a comment thatit bears different senses, and also that in one it is true, in the other false: for ifhe leave this distinction till later, it becomes uncertain whether originally aswell he perceived the ambiguity or not. If he does not foresee the ambiguity,but assents to the question having in view the one sense of the words, then,if the questioner takes it in the other sense, he should say, ‘That was not whatI had in view when I admitted it; I meant the other sense’: for if a term orexpression covers more than one thing, it is easy to disagree. If, however,the question is both clear and simple, he should answer either ‘Yes’ or ‘No’.
Part 8 A premiss relates to a constituent in the reasoning
A premiss in reasoning always either is one of the constituent elements inthe reasoning, or else goes to establish one of these: (and you can alwaystell when it is secured in order to establish something else by the fact of anumber of similar questions being put: for as a rule people secure their uni-versal by means either of induction or of likeness): - accordingly the partic-ular propositions should all be admitted, if they are true and generally held.On the other hand, against the universal one should try to bring some neg-ative instance; for to bring the argument to a standstill without a negativeinstance, either real or apparent, shows ill-temper. If, then, a man refuses togrant the universal when supported by many instances, although he has nonegative instance to show, he obviously shows ill-temper. If, moreover, hecannot even attempt a counter-proof that it is not true, far more likely is heto be thought ill-tempered - although even counter-proof is not enough: forwe often hear arguments that are contrary to common opinions, whose so-lution is yet difficult, e.g. the argument of Zeno that it is impossible to moveor to traverse the stadium; - but still, this is no reason for omitting to assertthe opposites of these views. If, then, a man refuses to admit the proposi-tion without having either a negative instance or some counter-argument tobring against it, clearly he is ill-tempered: for ill-temper in argument consists
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in answering in ways other than the above, so as to wreck the reasoning.
Part 9 Before advancing a position, test it
Before maintaining either a thesis or a definition the answerer should try hishand at attacking it by himself; for clearly his business is to oppose thosepositions from which questioners demolish what he has laid down.
He should beware of maintaining a hypothesis that is generally rejected:and this it may be in two ways: for it may be one which results in absurdstatements, e.g. suppose any one were to say that everything is in motionor that nothing is; and also there are all those which only a bad characterwould choose, and which are implicitly opposed to men’s wishes, e.g. thatpleasure is the good, and that to do injustice is better than to suffer it. Forpeople then hate him, supposing him to maintain them not for the sake ofargument but because he really thinks them.
Part 10 Demolish the point on which the fallacy depends
Of all arguments that reason to a false conclusion the right solution is todemolish the point on which the fallacy that occurs depends: for the demo-lition of any random point is no solution, even though the point demolishedbe false. For the argument may contain many falsehoods, e.g. suppose someone to secure the premisses, ‘He who sits, writes’ and ‘Socrates is sitting’: forfrom these it follows that ‘Socrates is writing’. Now we may demolish theproposition ‘Socrates is sitting’, and still be no nearer a solution of the argu-ment; it may be true that the point claimed is false; but it is not on that thatfallacy of the argument depends: for supposing that any one should happento be sitting and not writing, it would be impossible in such a case to applythe same solution. Accordingly, it is not this that needs to be demolished,but rather that ‘He who sits, writes’: for he who sits does not always write.He, then, who has demolished the point on which the fallacy depends, hasgiven the solution of the argument completely. Any one who knows that it ison such and such a point that the argument depends, knows the solution ofit, just as in the case of a figure falsely drawn. For it is not enough to object,even if the point demolished be a falsehood, but the reason of the fallacyshould also be proved: for then it would be clear whether the man makeshis objection with his eyes open or not.
There are four possible ways of preventing a man from working his ar-gument to a conclusion. It can be done either by demolishing the point onwhich the falsehood that comes about depends, or by stating an objectiondirected against the questioner: for often when a solution has not as a mat-ter of fact been brought, yet the questioner is rendered thereby unable to
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pursue the argument any farther. Thirdly, one may object to the questionsasked: for it may happen that what the questioner wants does not followfrom the questions he has asked because he has asked them badly, whereasif something additional be granted the conclusion comes about. If, then, thequestioner be unable to pursue his argument farther, the objection wouldproperly be directed against the questioner; if he can do so, then it would beagainst his questions. The fourth and worst kind of objection is that whichis directed to the time allowed for discussion: for some people bring objec-tions of a kind which would take longer to answer than the length of thediscussion in hand.
There are then, as we said, four ways of making objections: but of themthe first alone is a solution: the others are just hindrances and stumbling-blocks to prevent the conclusions.
Part 11 Five kinds of criticism of arguments
Adverse criticism of an argument on its own merits, and of it when pre-sented in the form of questions, are two different things. For often thefailure to carry through the argument correctly in discussion is due to theperson questioned, because he will not grant the steps of which a correctargument might have been made against his position: for it is not in thepower of the one side only to effect properly a result that depends on bothalike. Accordingly it sometimes becomes necessary to attack the speaker andnot his position, when the answerer lies in wait for the points that are con-trary to the questioner and becomes abusive as well: when people lose theirtempers in this way, their argument becomes a contest, not a discussion.Moreover, since arguments of this kind are held not for the sake of instruc-tion but for purposes of practice and examination, clearly one has to reasonnot only to true conclusions, but also to false ones, and not always throughtrue premisses, but sometimes through false as well. For often, when a trueproposition is put forward, the dialectician is compelled to demolish it: andthen false propositions have to be formulated. Sometimes also when a falseproposition is put forward, it has to be demolished by means of false propo-sitions: for it is possible for a given man to believe what is not the fact morefirmly than the truth. Accordingly, if the argument be made to depend onsomething that he holds, it will be easier to persuade or help him. He, how-ever, who would rightly convert any one to a different opinion should doso in a dialectical and not in a contentious manner, just as a geometricianshould reason geometrically, whether his conclusion be false or true: whatkind of syllogisms are dialectical has already been said. The principle thata man who hinders the common business is a bad partner, clearly appliesto an argument as well; for in arguments as well there is a common aim in
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view, except with mere contestants, for these cannot both reach the samegoal; for more than one cannot possibly win. It makes no difference whetherhe effects this as answerer or as questioner: for both he who asks contentiousquestions is a bad dialectician, and also he who in answering fails to grantthe obvious answer or to understand the point of the questioner’s inquiry.What has been said, then, makes it clear that adverse criticism is not to bepassed in a like strain upon the argument on its own merits, and upon thequestioner: for it may very well be that the argument is bad, but that thequestioner has argued with the answerer in the best possible way: for whenmen lose their tempers, it may perhaps be impossible to make one’s infer-ences straight-forwardly as one would wish: we have to do as we can.
Inasmuch as it is indeterminate when people are claiming the admissionof contrary things, and when they are claiming what originally they set outto prove - for often when they are talking by themselves they say contrarythings, and admit afterwards what they have previously denied; for whichreason they often assent, when questioned, to contrary things and to whatoriginally had to be proved - the argument is sure to become vitiated. Theresponsibility, however, for this rests with the answerer, because while refus-ing to grant other points, he does grant points of that kind. It is, then, clearthat adverse criticism is not to be passed in a like manner upon questionersand upon their arguments.
In itself an argument is liable to five kinds of adverse criticism:(1) The first is when neither the proposed conclusion nor indeed any con-
clusion at all is drawn from the questions asked, and when most, if not all, ofthe premisses on which the conclusion rests are false or generally rejected,when, moreover, neither any withdrawals nor additions nor both togethercan bring the conclusions about.
(2) The second is, supposing the reasoning, though constructed from thepremisses, and in the manner, described above, were to be irrelevant to theoriginal position.
(3) The third is, supposing certain additions would bring an inferenceabout but yet these additions were to be weaker than those that were put asquestions and less generally held than the conclusion.
(4) Again, supposing certain withdrawals could effect the same: forsometimes people secure more premisses than are necessary, so that it isnot through them that the inference comes about.
(5) Moreover, suppose the premisses be less generally held and less credi-ble than the conclusion, or if, though true, they require more trouble to provethan the proposed view.
One must not claim that the reasoning to a proposed view shall in ev-ery case equally be a view generally accepted and convincing: for it is adirect result of the nature of things that some subjects of inquiry shall be
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easier and some harder, so that if a man brings people to accept his pointfrom opinions that are as generally received as the case admits, he has ar-gued his case correctly. Clearly, then, not even the argument itself is opento the same adverse criticism when taken in relation to the proposed conclu-sion and when taken by itself. For there is nothing to prevent the argumentbeing open to reproach in itself, and yet commendable in relation to the pro-posed conclusion, or again, vice versa, being commendable in itself, and yetopen to reproach in relation to the proposed conclusion, whenever there aremany propositions both generally held and also true whereby it could easilybe proved. It is possible also that an argument, even though brought to aconclusion, may sometimes be worse than one which is not so concluded,whenever the premisses of the former are silly, while its conclusion is not so;whereas the latter, though requiring certain additions, requires only such asare generally held and true, and moreover does not rest as an argument onthese additions. With those which bring about a true conclusion by meansof false premisses, it is not fair to find fault: for a false conclusion must ofnecessity always be reached from a false premiss, but a true conclusion maysometimes be drawn even from false premisses; as is clear from the Analyt-ics.
Whenever by the argument stated something is demonstrated, but thatsomething is other than what is wanted and has no bearing whatever on theconclusion, then no inference as to the latter can be drawn from it: and ifthere appears to be, it will be a sophism, not a proof. A philosopheme is ademonstrative inference: an epichireme is a dialectical inference: a sophismis a contentious inference: an aporeme is an inference that reasons dialecti-cally to a contradiction.
If something were to be shown from premisses, both of which are viewsgenerally accepted, but not accepted with like conviction, it may very wellbe that the conclusion shown is something held more strongly than either. If,on the other hand, general opinion be for the one and neither for nor againstthe other, or if it be for the one and against the other, then, if the pro andcon be alike in the case of the premisses, they will be alike for the conclusionalso: if, on the other hand, the one preponderates, the conclusion too willfollow suit.
It is also a fault in reasoning when a man shows something through along chain of steps, when he might employ fewer steps and those alreadyincluded in his argument: suppose him to be showing (e.g.) that one opinionis more properly so called than another, and suppose him to make his pos-tulates as follows: ‘x-in-itself is more fully x than anything else’: ‘there gen-uinely exists an object of opinion in itself’: therefore ‘the object-of-opinion-in-itself is more fully an object of opinion than the particular objects of opin-ion’. Now ‘a relative term is more fully itself when its correlate is more fully
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itself’: and ‘there exists a genuine opinion-in-itself, which will be "opinion"in a more accurate sense than the particular opinions’: and it has been pos-tulated both that ‘a genuine opinion-in-itself exists’, and that ‘x-in-itself ismore fully x than anything else’: therefore ‘this will be opinion in a more ac-curate sense’. Wherein lies the viciousness of the reasoning? Simply in thatit conceals the ground on which the argument depends.
Part 12 An argument is called fallacious in four senses
An argument is clear in one, and that the most ordinary, sense, if it be sobrought to a conclusion as to make no further questions necessary: in an-other sense, and this is the type most usually advanced, when the proposi-tions secured are such as compel the conclusion, and the argument is con-cluded through premisses that are themselves conclusions: moreover, it is soalso if some step is omitted that generally is firmly accepted.
An argument is called fallacious in four senses:(1) when it appears to be brought to a conclusion, and is not really so -
what is called ‘contentious’ reasoning:(2) when it comes to a conclusion but not to the conclusion proposed -
which happens principally in the case of reductiones ad impossibile:(3) when it comes to the proposed conclusion but not according to the
mode of inquiry appropriate to the case, as happens when a non-medicalargument is taken to be a medical one, or one which is not geometrical for ageometrical argument, or one which is not dialectical for dialectical, whetherthe result reached be true or false:
(4) if the conclusion be reached through false premisses: of this type theconclusion is sometimes false, sometimes true: for while a false conclusionis always the result of false premisses, a true conclusion may be drawn evenfrom premisses that are not true, as was said above as well.
Fallacy in argument is due to a mistake of the arguer rather than of theargument: yet it is not always the fault of the arguer either, but only whenhe is not aware of it: for we often accept on its merits in preference to manytrue ones an argument which demolishes some true proposition if it does sofrom premisses as far as possible generally accepted. For an argument of thatkind does demonstrate other things that are true: for one of the premisseslaid down ought never to be there at all, and this will then be demonstrated.If, however, a true conclusion were to be reached through premisses thatare false and utterly childish, the argument is worse than many argumentsthat lead to a false conclusion, though an argument which leads to a falseconclusion may also be of this type. Clearly then the first thing to ask inregard to the argument in itself is, ‘Has it a conclusion?’; the second, ‘Isthe conclusion true or false?’; the third, ‘Of what kind of premisses does it
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consist?’: for if the latter, though false, be generally accepted, the argumentis dialectical, whereas if, though true, they be generally rejected, it is bad: ifthey be both false and also entirely contrary to general opinion, clearly it isbad, either altogether or else in relation to the particular matter in hand.
Part 13 People seem to beg their original question in fiveways
Of the ways in which a questioner may beg the original question and alsobeg contraries the true account has been given in the Analytics; but an ac-count on the level of general opinion must be given now.
People appear to beg their original question in five ways: the first andmost obvious being if any one begs the actual point requiring to be shown:this is easily detected when put in so many words; but it is more apt to es-cape detection in the case of different terms, or a term and an expression, thatmean the same thing. A second way occurs whenever any one begs univer-sally something which he has to demonstrate in a particular case: suppose(e.g.) he were trying to prove that the knowledge of contraries is one andwere to claim that the knowledge of opposites in general is one: for thenhe is generally thought to be begging, along with a number of other things,that which he ought to have shown by itself. A third way is if any one wereto beg in particular cases what he undertakes to show universally: e.g. ifhe undertook to show that the knowledge of contraries is always one, andbegged it of certain pairs of contraries: for he also is generally consideredto be begging independently and by itself what, together with a number ofother things, he ought to have shown. Again, a man begs the question ifhe begs his conclusion piecemeal: supposing e.g. that he had to show thatmedicine is a science of what leads to health and to disease, and were toclaim first the one, then the other; or, fifthly, if he were to beg the one or theother of a pair of statements that necessarily involve one other; e.g. if he hadto show that the diagonal is incommensurable with the side, and were to begthat the side is incommensurable with the diagonal.
The ways in which people assume contraries are equal in number tothose in which they beg their original question. For it would happen,
firstly, if any one were to beg an opposite affirmation and negation;secondly, if he were to beg the contrary terms of an antithesis, e.g. that
the same thing is good and evil;thirdly, suppose any one were to claim something universally and then
proceed to beg its contradictory in some particular case, e.g. if having se-cured that the knowledge of contraries is one, he were to claim that theknowledge of what makes for health or for disease is different; or,
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fourthly, suppose him, after postulating the latter view, to try to secureuniversally the contradictory statement. Again,
fifthly, suppose a man begs the contrary of the conclusion which neces-sarily comes about through the premisses laid down; and this would happensuppose, even without begging the opposites in so many words, he were tobeg two premisses such that this contradictory statement that is opposite tothe first conclusion will follow from them. The securing of contraries differsfrom begging the original question in this way: in the latter case the mistakelies in regard to the conclusion; for it is by a glance at the conclusion that wetell that the original question has been begged: whereas contrary views liein the premisses, viz. in a certain relation which they bear to one another.
Part 14 Training and practice in arguments
The best way to secure training and practice in arguments of this kind is inthe first place to get into the habit of converting the arguments. For in thisway we shall be better equipped for dealing with the proposition stated, andafter a few attempts we shall know several arguments by heart. For by ‘con-version’ of an argument is meant the taking the reverse of the conclusiontogether with the remaining propositions asked and so demolishing one ofthose that were conceded: for it follows necessarily that if the conclusion beuntrue, some one of the premisses is demolished, seeing that, given all thepremisses, the conclusion was bound to follow. Always, in dealing with anyproposition, be on the look-out for a line of argument both pro and con: andon discovering it at once set about looking for the solution of it: for in thisway you will soon find that you have trained yourself at the same time inboth asking questions and answering them. If we cannot find any one elseto argue with, we should argue with ourselves. Select, moreover, argumentsrelating to the same thesis and range them side by side: for this producesa plentiful supply of arguments for carrying a point by sheer force, and inrefutation also it is of great service, whenever one is well stocked with argu-ments pro and con: for then you find yourself on your guard against con-trary statements to the one you wish to secure. Moreover, as contributing toknowledge and to philosophic wisdom the power of discerning and holdingin one view the results of either of two hypotheses is no mean instrument;for it then only remains to make a right choice of one of them. For a taskof this kind a certain natural ability is required: in fact real natural abilityjust is the power right to choose the true and shun the false. Men of naturalability can do this; for by a right liking or disliking for whatever is proposedto them they rightly select what is best.
It is best to know by heart arguments upon those questions which are ofmost frequent occurrence, and particularly in regard to those propositions
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which are ultimate: for in discussing these answerers frequently give up indespair. Moreover, get a good stock of definitions: and have those of familiarand primary ideas at your fingers’ ends: for it is through these that reason-ings are effected. You should try, moreover, to master the heads under whichother arguments mostly tend to fall. For just as in geometry it is useful to bepractised in the elements, and in arithmetic to have the multiplication tableup to ten at one‘s fingers’ ends - and indeed it makes a great difference inone’s knowledge of the multiples of other numbers too - likewise also in ar-guments it is a great advantage to be well up in regard to first principles, andto have a thorough knowledge of premisses at the tip of one’s tongue. Forjust as in a person with a trained memory, a memory of things themselvesis immediately caused by the mere mention of their loci, so these habits toowill make a man readier in reasoning, because he has his premisses classi-fied before his mind’s eye, each under its number. It is better to commit tomemory a premiss of general application than an argument: for it is difficultto be even moderately ready with a first principle, or hypothesis.
Moreover, you should get into the habit of turning one argument intoseveral, and conceal your procedure as darkly as you can: this kind of effectis best produced by keeping as far as possible away from topics akin to thesubject of the argument. This can be done with arguments that are entirelyuniversal, e.g. the statement that ‘there cannot be one knowledge of morethan one thing’: for that is the case with both relative terms and contrariesand co-ordinates.
Records of discussions should be made in a universal form, even thoughone has argued only some particular case: for this will enable one to turna single rule into several. A like rule applies in Rhetoric as well to en-thymemes. For yourself, however, you should as far as possible avoid uni-versalizing your reasonings. You should, moreover, always examine ar-guments to see whether they rest on principles of general application: forall particular arguments really reason universally, as well, i.e. a particulardemonstration always contains a universal demonstration, because it is im-possible to reason at all without using universals.
You should display your training in inductive reasoning against a youngman, in deductive against an expert. You should try, moreover, to securefrom those skilled in deduction their premisses, from inductive reasonerstheir parallel cases; for this is the thing in which they are respectively trained.In general, too, from your exercises in argumentation you should try to carryaway either a syllogism on some subject or a refutation or a proposition oran objection, or whether some one put his question properly or improperly(whether it was yourself or some one else) and the point which made it theone or the other. For this is what gives one ability, and the whole object oftraining is to acquire ability, especially in regard to propositions and objec-
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tions. For it is the skilled propounder and objector who is, speaking gener-ally, a dialectician. To formulate a proposition is to form a number of thingsinto one - for the conclusion to which the argument leads must be taken gen-erally, as a single thing - whereas to formulate an objection is to make onething into many; for the objector either distinguishes or demolishes, partlygranting, partly denying the statements proposed.
Do not argue with every one, nor practise upon the man in the street:for there are some people with whom any argument is bound to degenerate.For against any one who is ready to try all means in order to seem not to bebeaten, it is indeed fair to try all means of bringing about one’s conclusion:but it is not good form. Wherefore the best rule is, not lightly to engage withcasual acquaintances, or bad argument is sure to result. For you see how inpractising together people cannot refrain from contentious argument.
It is best also to have ready-made arguments relating to those questionsin which a very small stock will furnish us with arguments serviceable ona very large number of occasions. These are those that are universal, andthose in regard to which it is rather difficult to produce points for ourselvesfrom matters of everyday
Volume 5 Book Part 0
Volume 6 ON SOPHISTICALREFUTATIONS
Section I Introduction
Part 1 Distinguishing between genuine and sophisticalarguments
Let us now discuss sophistic refutations, i.e. what appear to be refutationsbut are really fallacies instead. We will begin in the natural order with thefirst.
That some reasonings are genuine, while others seem to be so but are not,is evident. This happens with arguments, as also elsewhere, through a cer-tain likeness between the genuine and the sham. For physically some peopleare in a vigorous condition, while others merely seem to be so by blowingand rigging themselves out as the tribesmen do their victims for sacrifice;and some people are beautiful thanks to their beauty, while others seem tobe so, by dint of embellishing themselves. So it is, too, with inanimate things;for of these, too, some are really silver and others gold, while others are notand merely seem to be such to our sense; e.g. things made of litharge andtin seem to be of silver, while those made of yellow metal look golden. Inthe same way both reasoning and refutation are sometimes genuine, some-times not, though inexperience may make them appear so: for inexperiencedpeople obtain only, as it were, a distant view of these things. For reasoningrests on certain statements such that they involve necessarily the assertion ofsomething other than what has been stated, through what has been stated:refutation is reasoning involving the contradictory of the given conclusion.Now some of them do not really achieve this, though they seem to do sofor a number of reasons; and of these the most prolific and usual domain isthe argument that turns upon names only. It is impossible in a discussion tobring in the actual things discussed: we use their names as symbols insteadof them; and therefore we suppose that what follows in the names, follows
346 Introduction
in the things as well, just as people who calculate suppose in regard to theircounters. But the two cases (names and things) are not alike. For names arefinite and so is the sum-total of formulae, while things are infinite in num-ber. Inevitably, then, the same formulae, and a single name, have a numberof meanings. Accordingly just as, in counting, those who are not clever inmanipulating their counters are taken in by the experts, in the same way inarguments too those who are not well acquainted with the force of namesmisreason both in their own discussions and when they listen to others. Forthis reason, then, and for others to be mentioned later, there exists both rea-soning and refutation that is apparent but not real. Now for some people itis better worth while to seem to be wise, than to be wise without seemingto be (for the art of the sophist is the semblance of wisdom without the re-ality, and the sophist is one who makes money from an apparent but unrealwisdom); for them, then, it is clearly essential also to seem to accomplish thetask of a wise man rather than to accomplish it without seeming to do so.To reduce it to a single point of contrast it is the business of one who knowsa thing, himself to avoid fallacies in the subjects which he knows and to beable to show up the man who makes them; and of these accomplishmentsthe one depends on the faculty to render an answer, and the other upon thesecuring of one. Those, then, who would be sophists are bound to study theclass of arguments aforesaid: for it is worth their while: for a faculty of thiskind will make a man seem to be wise, and this is the purpose they happento have in view.
Clearly, then, there exists a class of arguments of this kind, and it is atthis kind of ability that those aim whom we call sophists. Let us now goon to discuss how many kinds there are of sophistical arguments, and howmany in number are the elements of which this faculty is composed, andhow many branches there happen to be of this inquiry, and the other factorsthat contribute to this art.
Part 2 Four kinds of arguments used in discussion
Of arguments in dialogue form there are four classes: Didactic, Dialectical,Examination-arguments, and Contentious arguments. Didactic argumentsare those that reason from the principles appropriate to each subject and notfrom the opinions held by the answerer (for the learner should take things ontrust): dialectical arguments are those that reason from premisses generallyaccepted, to the contradictory of a given thesis: examination-arguments arethose that reason from premisses which are accepted by the answerer andwhich any one who pretends to possess knowledge of the subject is boundto know - in what manner, has been defined in another treatise: contentiousarguments are those that reason or appear to reason to a conclusion from
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premisses that appear to be generally accepted but are not so. The subject,then, of demonstrative arguments has been discussed in the Analytics, whilethat of dialectic arguments and examination-arguments has been discussedelsewhere: let us now proceed to speak of the arguments used in competi-tions and contests.
Section II Sophistical questions andarguments
Part 3 Five objectives of argument
First we must grasp the number of aims entertained by those who argue ascompetitors and rivals to the death. These are five in number, refutation, fal-lacy, paradox, solecism, and fifthly to reduce the opponent in the discussionto babbling - i.e. to constrain him to repeat himself a number of times: or itis to produce the appearance of each of these things without the reality. Forthey choose if possible plainly to refute the other party, or as the second bestto show that he is committing some fallacy, or as a third best to lead him intoparadox, or fourthly to reduce him to solecism, i.e. to make the answerer, inconsequence of the argument, to use an ungrammatical expression; or, as alast resort, to make him repeat himself.
Part 4 Six sophistical methods involving language
There are two styles of refutation: for some depend on the language used,while some are independent of language. Those ways of producing the falseappearance of an argument which depend on language are six in number:they are ambiguity, amphiboly, combination, division of words, accent, formof expression. Of this we may assure ourselves both by induction, and bysyllogistic proof based on this - and it may be on other assumptions as well- that this is the number of ways in which we might fall to mean the samething by the same names or expressions. Arguments such as the followingdepend upon ambiguity. ‘Those learn who know: for it is those who knowtheir letters who learn the letters dictated to them’. For to ‘learn’ is ambigu-ous; it signifies both ‘to understand’ by the use of knowledge, and also ‘toacquire knowledge’. Again, ‘Evils are good: for what needs to be is good,and evils must needs be’. For ‘what needs to be’ has a double meaning: itmeans what is inevitable, as often is the case with evils, too (for evil of somekind is inevitable), while on the other hand we say of good things as wellthat they ‘need to be’. Moreover, ‘The same man is both seated and standing
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and he is both sick and in health: for it is he who stood up who is stand-ing, and he who is recovering who is in health: but it is the seated man whostood up, and the sick man who was recovering’. For ‘The sick man does soand so’, or ‘has so and so done to him’ is not single in meaning: sometimesit means ‘the man who is sick or is seated now’, sometimes ‘the man whowas sick formerly’. Of course, the man who was recovering was the sickman, who really was sick at the time: but the man who is in health is notsick at the same time: he is ‘the sick man’ in the sense not that he is sick now,but that he was sick formerly. Examples such as the following depend uponamphiboly: ‘I wish that you the enemy may capture’. Also the thesis, ‘Theremust be knowledge of what one knows’: for it is possible by this phraseto mean that knowledge belongs to both the knower and the known. Also,‘There must be sight of what one sees: one sees the pillar: ergo the pillar hassight’. Also, ‘What you profess to-be, that you profess to-be: you profess astone to-be: ergo you profess-to-be a stone’. Also, ‘Speaking of the silent ispossible’: for ‘speaking of the silent’ also has a double meaning: it may meanthat the speaker is silent or that the things of which he speaks are so. Thereare three varieties of these ambiguities and amphibolies: (1) When either theexpression or the name has strictly more than one meaning, e.g. aetos andthe ‘dog’; (2) when by custom we use them so; (3) when words that have asimple sense taken alone have more than one meaning in combination; e.g.‘knowing letters’. For each word, both ‘knowing’ and ‘letters’, possibly has asingle meaning: but both together have more than one - either that the lettersthemselves have knowledge or that someone else has it of them.
Amphiboly and ambiguity, then, depend on these modes of speech.Upon the combination of words there depend instances such as the follow-ing: ‘A man can walk while sitting, and can write while not writing’. For themeaning is not the same if one divides the words and if one combines themin saying that ‘it is possible to walk-while-sitting’ and write while not writ-ing]. The same applies to the latter phrase, too, if one combines the words‘to write-while-not-writing’: for then it means that he has the power to writeand not to write at once; whereas if one does not combine them, it meansthat when he is not writing he has the power to write. Also, ‘He now if hehas learnt his letters’. Moreover, there is the saying that ‘One single thing ifyou can carry a crowd you can carry too’.
Upon division depend the propositions that 5 is 2 and 3, and odd, andthat the greater is equal: for it is that amount and more besides. For thesame phrase would not be thought always to have the same meaning whendivided and when combined, e.g. ‘I made thee a slave once a free man’, and‘God-like Achilles left fifty a hundred men’.
An argument depending upon accent it is not easy to construct in un-written discussion; in written discussions and in poetry it is easier. Thus
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(e.g.) some people emend Homer against those who criticize as unnaturalhis expression το μεν ου καταπυτηεται ομβρο. For they solve the difficulty bya change of accent, pronouncing the ου with an acuter accent. Also, in thepassage about Agamemnon’s dream, they say that Zeus did not himself say‘We grant him the fulfilment of his prayer’, but that he bade the dream grantit. Instances such as these, then, turn upon the accentuation.
Others come about owing to the form of expression used, when what isreally different is expressed in the same form, e.g. a masculine thing by afeminine termination, or a feminine thing by a masculine, or a neuter by ei-ther a masculine or a feminine; or, again, when a quality is expressed by atermination proper to quantity or vice versa, or what is active by a passiveword, or a state by an active word, and so forth with the other divisions pre-viously laid down. For it is possible to use an expression to denote what doesnot belong to the class of actions at all as though it did so belong. Thus (e.g.)‘flourishing’ is a word which in the form of its expression is like ‘cutting’or ‘building’: yet the one denotes a certain quality - i.e. a certain condition- while the other denotes a certain action. In the same manner also in theother instances.
Refutations, then, that depend upon language are drawn from thesecommon-place rules. Of fallacies, on the other hand, that are independent oflanguage there are seven kinds:
(1) that which depends upon Accident:(2) the use of an expression absolutely or not absolutely but with some
qualification of respect or place, or time, or relation:(3) that which depends upon ignorance of what ‘refutation’ is:(4) that which depends upon the consequent:(5) that which depends upon assuming the original conclusion:(6) stating as cause what is not the cause:(7) the making of more than one question into one.
Part 5 Seven fallacies unconnected with language
Fallacies, then, that depend on Accident occur whenever any attribute isclaimed to belong in like manner to a thing and to its accident. For sincethe same thing has many accidents there is no necessity that all the sameattributes should belong to all of a thing’s predicates and to their subject aswell. Thus (e.g.), ‘If Coriscus be different from "man", he is different fromhimself: for he is a man’: or ‘If he be different from Socrates, and Socratesbe a man, then’, they say, ‘he has admitted that Coriscus is different from aman, because it so happens (accidit) that the person from whom he said thathe (Coriscus) is different is a man’.
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Those that depend on whether an expression is used absolutely or in acertain respect and not strictly, occur whenever an expression used in a par-ticular sense is taken as though it were used absolutely, e.g. in the argument‘If what is not is the object of an opinion, then what is not is’: for it is not thesame thing ‘to be x’ and ‘to be’ absolutely. Or again, ‘What is, is not, if it isnot a particular kind of being, e.g. if it is not a man.’ For it is not the samething ‘not to be x’ and ‘not to be’ at all: it looks as if it were, because of thecloseness of the expression, i.e. because ‘to be x’ is but little different from‘to be’, and ‘not to be x’ from ‘not to be’. Likewise also with any argumentthat turns upon the point whether an expression is used in a certain respector used absolutely. Thus e.g. ‘Suppose an Indian to be black all over, butwhite in respect of his teeth; then he is both white and not white.’ Or if bothcharacters belong in a particular respect, then, they say, ‘contrary attributesbelong at the same time’. This kind of thing is in some cases easily seen byany one, e.g. suppose a man were to secure the statement that the Ethiopianis black, and were then to ask whether he is white in respect of his teeth; andthen, if he be white in that respect, were to suppose at the conclusion of hisquestions that therefore he had proved dialectically that he was both whiteand not white. But in some cases it often passes undetected, viz. in all caseswhere, whenever a statement is made of something in a certain respect, itwould be generally thought that the absolute statement follows as well; andalso in all cases where it is not easy to see which of the attributes ought to berendered strictly. A situation of this kind arises, where both the opposite at-tributes belong alike: for then there is general support for the view that onemust agree absolutely to the assertion of both, or of neither: e.g. if a thing ishalf white and half black, is it white or black?
Other fallacies occur because the terms ‘proof’ or ‘refutation’ have notbeen defined, and because something is left out in their definition. For torefute is to contradict one and the same attribute - not merely the name,but the reality - and a name that is not merely synonymous but the samename-and to confute it from the propositions granted, necessarily, withoutincluding in the reckoning the original point to be proved, in the same re-spect and relation and manner and time in which it was asserted. A ‘falseassertion’ about anything has to be defined in the same way. Some people,however, omit some one of the said conditions and give a merely apparentrefutation, showing (e.g.) that the same thing is both double and not double:for two is double of one, but not double of three. Or, it may be, they showthat it is both double and not double of the same thing, but not that it is soin the same respect: for it is double in length but not double in breadth. Or,it may be, they show it to be both double and not double of the same thingand in the same respect and manner, but not that it is so at the same time:and therefore their refutation is merely apparent. One might, with some vi-
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olence, bring this fallacy into the group of fallacies dependent on languageas well.
Those that depend on the assumption of the original point to be proved,occur in the same way, and in as many ways, as it is possible to beg theoriginal point; they appear to refute because men lack the power to keeptheir eyes at once upon what is the same and what is different.
The refutation which depends upon the consequent arises because peo-ple suppose that the relation of consequence is convertible. For whenever,suppose A is, B necessarily is, they then suppose also that if B is, A necessar-ily is. This is also the source of the deceptions that attend opinions based onsense-perception. For people often suppose bile to be honey because honeyis attended by a yellow colour: also, since after rain the ground is wet in con-sequence, we suppose that if the ground is wet, it has been raining; whereasthat does not necessarily follow. In rhetoric proofs from signs are based onconsequences. For when rhetoricians wish to show that a man is an adul-terer, they take hold of some consequence of an adulterous life, viz. thatthe man is smartly dressed, or that he is observed to wander about at night.There are, however, many people of whom these things are true, while thecharge in question is untrue. It happens like this also in real reasoning; e.g.Melissus’ argument, that the universe is eternal, assumes that the universehas not come to be (for from what is not nothing could possibly come tobe) and that what has come to be has done so from a first beginning. If,therefore, the universe has not come to be, it has no first beginning, and istherefore eternal. But this does not necessarily follow: for even if what hascome to be always has a first beginning, it does not also follow that what hasa first beginning has come to be; any more than it follows that if a man in afever be hot, a man who is hot must be in a fever.
The refutation which depends upon treating as cause what is not a cause,occurs whenever what is not a cause is inserted in the argument, as thoughthe refutation depended upon it. This kind of thing happens in argumentsthat reason ad impossible: for in these we are bound to demolish one of thepremisses. If, then, the false cause be reckoned in among the questions thatare necessary to establish the resulting impossibility, it will often be thoughtthat the refutation depends upon it, e.g. in the proof that the ‘soul’ and ‘life’are not the same: for if coming-to-be be contrary to perishing, then a par-ticular form of perishing will have a particular form of coming-to-be as itscontrary: now death is a particular form of perishing and is contrary to life:life, therefore, is a coming to-be, and to live is to come-to-be. But this isimpossible: accordingly, the ‘soul’ and ‘life’ are not the same. Now this isnot proved: for the impossibility results all the same, even if one does notsay that life is the same as the soul, but merely says that life is contrary todeath, which is a form of perishing, and that perishing has ‘coming-to-be’
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as its contrary. Arguments of that kind, then, though not inconclusive abso-lutely, are inconclusive in relation to the proposed conclusion. Also even thequestioners themselves often fail quite as much to see a point of that kind.
Such, then, are the arguments that depend upon the consequent andupon false cause. Those that depend upon the making of two questionsinto one occur whenever the plurality is undetected and a single answer isreturned as if to a single question. Now, in some cases, it is easy to see thatthere is more than one, and that an answer is not to be given, e.g. ‘Does theearth consist of sea, or the sky?’ But in some cases it is less easy, and thenpeople treat the question as one, and either confess their defeat by failing toanswer the question, or are exposed to an apparent refutation. Thus ‘Is Aand is B a man?’ ‘Yes.’ ‘Then if any one hits A and B, he will strike a man’(singular), ‘not men’ (plural). Or again, where part is good and part bad, ‘isthe whole good or bad?’ For whichever he says, it is possible that he mightbe thought to expose himself to an apparent refutation or to make an appar-ently false statement: for to say that something is good which is not good,or not good which is good, is to make a false statement. Sometimes, how-ever, additional premisses may actually give rise to a genuine refutation; e.g.suppose a man were to grant that the descriptions ‘white’ and ‘naked’ and‘blind’ apply to one thing and to a number of things in a like sense. For if‘blind’ describes a thing that cannot see though nature designed it to see, itwill also describe things that cannot see though nature designed them to doso. Whenever, then, one thing can see while another cannot, they will eitherboth be able to see or else both be blind; which is impossible.
Part 6 Further discussion of these sophistical refutations
The right way, then, is either to divide apparent proofs and refutations asabove, or else to refer them all to ignorance of what ‘refutation’ is, and makethat our starting-point: for it is possible to analyse all the aforesaid modesof fallacy into breaches of the definition of a refutation. In the first place, wemay see if they are inconclusive: for the conclusion ought to result from thepremisses laid down, so as to compel us necessarily to state it and not merelyto seem to compel us. Next we should also take the definition bit by bit, andtry the fallacy thereby. For of the fallacies that consist in language, somedepend upon a double meaning, e.g. ambiguity of words and of phrases,and the fallacy of like verbal forms (for we habitually speak of everythingas though it were a particular substance) - while fallacies of combinationand division and accent arise because the phrase in question or the term asaltered is not the same as was intended. Even this, however, should be thesame, just as the thing signified should be as well, if a refutation or proofis to be effected; e.g. if the point concerns a doublet, then you should draw
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the conclusion of a ‘doublet’, not of a ‘cloak’. For the former conclusion alsowould be true, but it has not been proved; we need a further question toshow that ‘doublet’ means the same thing, in order to satisfy any one whoasks why you think your point proved.
Fallacies that depend on Accident are clear cases of ignoratio elenchiwhen once ‘proof’ has been defined. For the same definition ought to holdgood of ‘refutation’ too, except that a mention of ‘the contradictory’ is hereadded: for a refutation is a proof of the contradictory. If, then, there is noproof as regards an accident of anything, there is no refutation. For suppos-ing, when A and B are, C must necessarily be, and C is white, there is nonecessity for it to be white on account of the syllogism. So, if the trianglehas its angles equal to two right-angles, and it happens to be a figure, or thesimplest element or starting point, it is not because it is a figure or a startingpoint or simplest element that it has this character. For the demonstrationproves the point about it not qua figure or qua simplest element, but quatriangle. Likewise also in other cases. If, then, refutation is a proof, an ar-gument which argued per accidens could not be a refutation. It is, however,just in this that the experts and men of science generally suffer refutation atthe hand of the unscientific: for the latter meet the scientists with reasoningsconstituted per accidens; and the scientists for lack of the power to draw dis-tinctions either say ‘Yes’ to their questions, or else people suppose them tohave said ‘Yes’, although they have not.
Those that depend upon whether something is said in a certain respectonly or said absolutely, are clear cases of ignoratio elenchi because the affir-mation and the denial are not concerned with the same point. For of ‘whitein a certain respect’ the negation is ‘not white in a certain respect’, while of‘white absolutely’ it is ‘not white, absolutely’. If, then, a man treats the ad-mission that a thing is ‘white in a certain respect’ as though it were said tobe white absolutely, he does not effect a refutation, but merely appears to doso owing to ignorance of what refutation is.
The clearest cases of all, however, are those that were previously de-scribed as depending upon the definition of a ‘refutation’: and this is alsowhy they were called by that name. For the appearance of a refutation isproduced because of the omission in the definition, and if we divide falla-cies in the above manner, we ought to set ‘Defective definition’ as a commonmark upon them all.
Those that depend upon the assumption of the original point and uponstating as the cause what is not the cause, are clearly shown to be cases ofignoratio elenchi through the definition thereof. For the conclusion ought tocome about ‘because these things are so’, and this does not happen wherethe premisses are not causes of it: and again it should come about withouttaking into account the original point, and this is not the case with those
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arguments which depend upon begging the original point.Those that depend upon the assumption of the original point and upon
stating as the cause what is not the cause, are clearly shown to be cases ofignoratio elenchi through the definition thereof. For the conclusion ought tocome about ‘because these things are so’, and this does not happen wherethe premisses are not causes of it: and again it should come about withouttaking into account the original point, and this is not the case with thosearguments which depend upon begging the original point.
Those that depend upon the consequent are a branch of Accident: forthe consequent is an accident, only it differs from the accident in this, thatyou may secure an admission of the accident in the case of one thing only(e.g. the identity of a yellow thing and honey and of a white thing andswan), whereas the consequent always involves more than one thing: forwe claim that things that are the same as one and the same thing are alsothe same as one another, and this is the ground of a refutation dependenton the consequent. It is, however, not always true, e.g. suppose that and Bare the same as C per accidens; for both ‘snow’ and the ‘swan’ are the sameas something ‘white’. Or again, as in Melissus’ argument, a man assumesthat to ‘have been generated’ and to ‘have a beginning’ are the same thing,or to ‘become equal’ and to ‘assume the same magnitude’. For because whathas been generated has a beginning, he claims also that what has a beginninghas been generated, and argues as though both what has been generated andwhat is finite were the same because each has a beginning. Likewise also inthe case of things that are made equal he assumes that if things that assumeone and the same magnitude become equal, then also things that becomeequal assume one magnitude: i.e. he assumes the consequent. Inasmuch,then, as a refutation depending on accident consists in ignorance of what arefutation is, clearly so also does a refutation depending on the consequent.We shall have further to examine this in another way as well.
Those fallacies that depend upon the making of several questions intoone consist in our failure to dissect the definition of ‘proposition’. For aproposition is a single statement about a single thing. For the same defi-nition applies to ‘one single thing only’ and to the ‘thing’, simply, e.g. to‘man’ and to ‘one single man only’ and likewise also in other cases. If, then,a ‘single proposition’ be one which claims a single thing of a single thing,a ‘proposition’, simply, will also be the putting of a question of that kind.Now since a proof starts from propositions and refutation is a proof, refu-tation, too, will start from propositions. If, then, a proposition is a singlestatement about a single thing, it is obvious that this fallacy too consists inignorance of what a refutation is: for in it what is not a proposition appearsto be one. If, then, the answerer has returned an answer as though to asingle question, there will be a refutation; while if he has returned one not
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really but apparently, there will be an apparent refutation of his thesis. Allthe types of fallacy, then, fall under ignorance of what a refutation is, someof them because the contradiction, which is the distinctive mark of a refuta-tion, is merely apparent, and the rest failing to conform to the definition of aproof.
Part 7 On the sources of these fallacies
The deception comes about in the case of arguments that depend on ambigu-ity of words and of phrases because we are unable to divide the ambiguousterm (for some terms it is not easy to divide, e.g. ‘unity’, ‘being’, and ‘same-ness’), while in those that depend on combination and division, it is becausewe suppose that it makes no difference whether the phrase be combined ordivided, as is indeed the case with most phrases. Likewise also with thosethat depend on accent: for the lowering or raising of the voice upon a phraseis thought not to alter its meaning-with any phrase, or not with many. Withthose that depend on the of expression it is because of the likeness of expres-sion. For it is hard to distinguish what kind of things are signified by thesame and what by different kinds of expression: for a man who can do thisis practically next door to the understanding of the truth. A special reasonwhy a man is liable to be hurried into assent to the fallacy is that we supposeevery predicate of everything to be an individual thing, and we understandit as being one with the thing: and we therefore treat it as a substance: for itis to that which is one with a thing or substance, as also to substance itself,that ‘individually’ and ‘being’ are deemed to belong in the fullest sense. Forthis reason, too, this type of fallacy is to be ranked among those that dependon language; in the first place, because the deception is effected the morereadily when we are inquiring into a problem in company with others thanwhen we do so by ourselves (for an inquiry with another person is carriedon by means of speech, whereas an inquiry by oneself is carried on quite asmuch by means of the object itself); secondly a man is liable to be deceived,even when inquiring by himself, when he takes speech as the basis of hisinquiry: moreover the deception arises out of the likeness (of two differentthings), and the likeness arises out of the language. With those fallacies thatdepend upon Accident, deception comes about because we cannot distin-guish the sameness and otherness of terms, i.e. their unity and multiplicity,or what kinds of predicate have all the same accidents as their subject. Like-wise also with those that depend on the Consequent: for the consequent is abranch of Accident. Moreover, in many cases appearances point to this-andthe claim is made that if is inseparable from B, so also is B from With thosethat depend upon an imperfection in the definition of a refutation, and withthose that depend upon the difference between a qualified and an absolute
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statement, the deception consists in the smallness of the difference involved;for we treat the limitation to the particular thing or respect or manner ortime as adding nothing to the meaning, and so grant the statement univer-sally. Likewise also in the case of those that assume the original point, andthose of false cause, and all that treat a number of questions as one: for in allof them the deception lies in the smallness of the difference: for our failureto be quite exact in our definition of ‘premiss’ and of ‘proof’ is due to theaforesaid reason.
Part 8 Apparent and sophistical syllogisms
Since we know on how many points apparent syllogisms depend, we knowalso on how many sophistical syllogisms and refutations may depend. By asophistical refutation and syllogism I mean not only a syllogism or refutationwhich appears to be valid but is not, but also one which, though it is valid,only appears to be appropriate to the thing in question. These are thosewhich fail to refute and prove people to be ignorant according to the natureof the thing in question, which was the function of the art of examination.Now the art of examining is a branch of dialectic: and this may prove a falseconclusion because of the ignorance of the answerer. Sophistic refutationson the other hand, even though they prove the contradictory of his thesis,do not make clear whether he is ignorant: for sophists entangle the scientistas well with these arguments.
That we know them by the same line of inquiry is clear: for the same con-siderations which make it appear to an audience that the points required forthe proof were asked in the questions and that the conclusion was proved,would make the answerer think so as well, so that false proof will occurthrough all or some of these means: for what a man has not been asked butthinks he has granted, he would also grant if he were asked. Of course, insome cases the moment we add the missing question, we also show up itsfalsity, e.g. in fallacies that depend on language and on solecism. If then, fal-lacious proofs of the contradictory of a thesis depend on their appearing torefute, it is clear that the considerations on which both proofs of false conclu-sions and an apparent refutation depend must be the same in number. Nowan apparent refutation depends upon the elements involved in a genuineone: for the failure of one or other of these must make the refutation merelyapparent, e.g. that which depends on the failure of the conclusion to followfrom the argument (the argument ad impossible) and that which treats twoquestions as one and so depends upon a flaw in the premiss, and that whichdepends on the substitution of an accident for an essential attribute, and-abranch of the last-that which depends upon the consequent: more over, theconclusion may follow not in fact but only verbally: then, instead of prov-
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ing the contradictory universally and in the same respect and relation andmanner, the fallacy may be dependent on some limit of extent or on one orother of these qualifications: moreover, there is the assumption of the orig-inal point to be proved, in violation of the clause ‘without reckoning in theoriginal point’. Thus we should have the number of considerations on whichthe fallacious proofs depend: for they could not depend on more, but all willdepend on the points aforesaid.
A sophistical refutation is a refutation not absolutely but relatively tosome one: and so is a proof, in the same way. For unless that which dependsupon ambiguity assumes that the ambiguous term has a single meaning, andthat which depends on like verbal forms assumes that substance is the onlycategory, and the rest in the same way, there will be neither refutations norproofs, either absolutely or relatively to the answerer: whereas if they do as-sume these things, they will stand, relatively to the answerer; but absolutelythey will not stand: for they have not secured a statement that does have asingle meaning, but only one that appears to have, and that only from thisparticular man.
Part 9 Scientific and dialectical reasoning
The number of considerations on which depend the refutations of those whoare refuted, we ought not to try to grasp without a knowledge of everythingthat is. This, however, is not the province of any special study: for possiblythe sciences are infinite in number, so that obviously demonstrations maybe infinite too. Now refutations may be true as well as false: for wheneverit is possible to demonstrate something, it is also possible to refute the manwho maintains the contradictory of the truth; e.g. if a man has stated thatthe diagonal is commensurate with the side of the square, one might refutehim by demonstrating that it is incommensurate. Accordingly, to exhaustall possible refutations we shall have to have scientific knowledge of every-thing: for some refutations depend upon the principles that rule in geome-try and the conclusions that follow from these, others upon those that rulein medicine, and others upon those of the other sciences. For the matter ofthat, the false refutations likewise belong to the number of the infinite: foraccording to every art there is false proof, e.g. according to geometry thereis false geometrical proof, and according to medicine there is false medicalproof. By ‘according to the art’, I mean ‘according to the principles of it’.Clearly, then, it is not of all refutations, but only of those that depend upondialectic that we need to grasp the common-place rules: for these stand ina common relation to every art and faculty. And as regards the refutationthat is according to one or other of the particular sciences it is the task of thatparticular scientist to examine whether it is merely apparent without being
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real, and, if it be real, what is the reason for it: whereas it is the businessof dialecticians so to examine the refutation that proceeds from the commonfirst principles that fall under no particular special study. For if we graspthe startingpoints of the accepted proofs on any subject whatever we graspthose of the refutations current on that subject. For a refutation is the proofof the contradictory of a given thesis, so that either one or two proofs of thecontradictory constitute a refutation. We grasp, then, the number of con-siderations on which all such depend: if, however, we grasp this, we alsograsp their solutions as well; for the objections to these are the solutions ofthem. We also grasp the number of considerations on which those refuta-tions depend, that are merely apparent-apparent, I mean, not to everybody,but to people of a certain stamp; for it is an indefinite task if one is to in-quire how many are the considerations that make them apparent to the manin the street. Accordingly it is clear that the dialectician’s business is to beable to grasp on how many considerations depends the formation, throughthe common first principles, of a refutation that is either real or apparent, i.e.either dialectical or apparently dialectical, or suitable for an examination.
Part 10 Argument against the word, and against the thought
It is no true distinction between arguments which some people draw whenthey say that some arguments are directed against the expression, and oth-ers against the thought expressed: for it is absurd to suppose that some ar-guments are directed against the expression and others against the thought,and that they are not the same. For what is failure to direct an argumentagainst the thought except what occurs whenever a man does not in usingthe expression think it to be used in his question in the same sense in whichthe person questioned granted it? And this is the same thing as to direct theargument against the expression. On the other hand, it is directed againstthe thought whenever a man uses the expression in the same sense whichthe answerer had in mind when he granted it. If now any (i.e. both thequestioner and the person questioned), in dealing with an expression withmore than one meaning, were to suppose it to have one meaning-as e.g. itmay be that ‘Being’ and ‘One’ have many meanings, and yet both the an-swerer answers and the questioner puts his question supposing it to be one,and the argument is to the effect that ‘All things are one’ - will this discus-sion be directed any more against the expression than against the thoughtof the person questioned? If, on the other hand, one of them supposes theexpression to have many meanings, it is clear that such a discussion will notbe directed against the thought. Such being the meanings of the phrases inquestion, they clearly cannot describe two separate classes of argument. For,in the first place, it is possible for any such argument as bears more than
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one meaning to be directed against the expression and against the thought,and next it is possible for any argument whatsoever; for the fact of being di-rected against the thought consists not in the nature of the argument, but inthe special attitude of the answerer towards the points he concedes. Next, allof them may be directed to the expression. For ‘to be directed against the ex-pression’ means in this doctrine ‘not to be directed against the thought’. Forif not all are directed against either expression or thought, there will be cer-tain other arguments directed neither against the expression nor against thethought, whereas they say that all must be one or the other, and divide themall as directed either against the expression or against the thought, whileothers (they say) there are none. But in point of fact those that depend onmere expression are only a branch of those syllogisms that depend on a mul-tiplicity of meanings. For the absurd statement has actually been made thatthe description ‘dependent on mere expression’ describes all the argumentsthat depend on language: whereas some of these are fallacies not becausethe answerer adopts a particular attitude towards them, but because the ar-gument itself involves the asking of a question such as bears more than onemeaning.
It is, too, altogether absurd to discuss Refutation without first discussingProof: for a refutation is a proof, so that one ought to discuss proof as wellbefore describing false refutation: for a refutation of that kind is a merelyapparent proof of the contradictory of a thesis. Accordingly, the reason ofthe falsity will be either in the proof or in the contradiction (for mentionof the ‘contradiction’ must be added), while sometimes it is in both, if therefutation be merely apparent. In the argument that speaking of the silent ispossible it lies in the contradiction, not in the proof; in the argument that onecan give what one does not possess, it lies in both; in the proof that Homer’spoem is a figure through its being a cycle it lies in the proof. An argumentthat does not fail in either respect is a true proof.
But, to return to the point whence our argument digressed, are math-ematical reasonings directed against the thought, or not? And if any onethinks ‘triangle’ to be a word with many meanings, and granted it in somedifferent sense from the figure which was proved to contain two right an-gles, has the questioner here directed his argument against the thought ofthe former or not?
Moreover, if the expression bears many senses, while the answerer doesnot understand or suppose it to have them, surely the questioner here hasdirected his argument against his thought! Or how else ought he to puthis question except by suggesting a distinction-suppose one‘s question to bespeaking of the silent possible or not?’ - as follows, ‘Is the answer "No" inone sense, but "Yes" in another?’ If, then, any one were to answer that itwas not possible in any sense and the other were to argue that it was, has
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not his argument been directed against the thought of the answerer? Yethis argument is supposed to be one of those that depend on the expression.There is not, then, any definite kind of arguments that is directed againstthe thought. Some arguments are, indeed, directed against the expression:but these are not all even apparent refutations, let alone all refutations. Forthere are also apparent refutations which do not depend upon language, e.g.those that depend upon accident, and others.
If, however, any one claims that one should actually draw the distinction,and say, ‘By "speaking of the silent" I mean, in one sense this and in the othersense that’, surely to claim this is in the first place absurd (for sometimes thequestioner does not see the ambiguity of his question, and he cannot pos-sibly draw a distinction which he does not think to be there): in the secondplace, what else but this will didactic argument be? For it will make manifestthe state of the case to one who has never considered, and does not know orsuppose that there is any other meaning but one. For what is there to pre-vent the same thing also happening to us in cases where there is no doublemeaning? ‘Are the units in four equal to the twos? Observe that the twosare contained in four in one sense in this way, in another sense in that’. Also,‘Is the knowledge of contraries one or not? Observe that some contrariesare known, while others are unknown’. Thus the man who makes this claimseems to be unaware of the difference between didactic and dialectical ar-gument, and of the fact that while he who argues didactically should notask questions but make things clear himself, the other should merely askquestions.
Part 11 Dialectical versus contentious and sophisticalreasoning
Moreover, to claim a ‘Yes’ or ‘No’ answer is the business not of a man whois showing something, but of one who is holding an examination. For theart of examining is a branch of dialectic and has in view not the man whohas knowledge, but the ignorant pretender. He, then, is a dialectician whoregards the common principles with their application to the particular mat-ter in hand, while he who only appears to do this is a sophist. Now forcontentious and sophistical reasoning: (1) one such is a merely apparent rea-soning, on subjects on which dialectical reasoning is the proper method ofexamination, even though its conclusion be true: for it misleads us in regardto the cause: also (2) there are those misreasonings which do not conform tothe line of inquiry proper to the particular subject, but are generally thoughtto conform to the art in question. For false diagrams of geometrical figuresare not contentious (for the resulting fallacies conform to the subject of theart) - any more than is any false diagram that may be offered in proof of
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a truth - e.g. Hippocrates’ figure or the squaring of the circle by means ofthe lunules. But Bryson’s method of squaring the circle, even if the circle isthereby squared, is still sophistical because it does not conform to the sub-ject in hand. So, then, any merely apparent reasoning about these things isa contentious argument, and any reasoning that merely appears to conformto the subject in hand, even though it be genuine reasoning, is a contentiousargument: for it is merely apparent in its conformity to the subject-matter, sothat it is deceptive and plays foul. For just as a foul in a race is a definite typeof fault, and is a kind of foul fighting, so the art of contentious reasoning isfoul fighting in disputation: for in the former case those who are resolved towin at all costs snatch at everything, and so in the latter case do contentiousreasoners. Those, then, who do this in order to win the mere victory are gen-erally considered to be contentious and quarrelsome persons, while thosewho do it to win a reputation with a view to making money are sophisti-cal. For the art of sophistry is, as we said, a kind of art of money-makingfrom a merely apparent wisdom, and this is why they aim at a merely ap-parent demonstration: and quarrelsome persons and sophists both employthe same arguments, but not with the same motives: and the same argu-ment will be sophistical and contentious, but not in the same respect; rather,it will be contentious in so far as its aim is an apparent victory, while in sofar as its aim is an apparent wisdom, it will be sophistical: for the art ofsophistry is a certain appearance of wisdom without the reality. The con-tentious argument stands in somewhat the same relation to the dialecticalas the drawer of false diagrams to the geometrician; for it beguiles by mis-reasoning from the same principles as dialectic uses, just as the drawer ofa false diagram beguiles the geometrician. But whereas the latter is not acontentious reasoner, because he bases his false diagram on the principlesand conclusions that fall under the art of geometry, the argument which issubordinate to the principles of dialectic will yet clearly be contentious asregards other subjects. Thus, e.g. though the squaring of the circle by meansof the lunules is not contentious, Bryson’s solution is contentious: and theformer argument cannot be adapted to any subject except geometry, becauseit proceeds from principles that are peculiar to geometry, whereas the lattercan be adapted as an argument against all the number of people who do notknow what is or is not possible in each particular context: for it will applyto them all. Or there is the method whereby Antiphon squared the circle.Or again, an argument which denied that it was better to take a walk afterdinner, because of Zeno’s argument, would not be a proper argument for adoctor, because Zeno’s argument is of general application. If, then, the re-lation of the contentious argument to the dialectical were exactly like thatof the drawer of false diagrams to the geometrician, a contentious argumentupon the aforesaid subjects could not have existed. But, as it is, the dialec-
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tical argument is not concerned with any definite kind of being, nor does itshow anything, nor is it even an argument such as we find in the generalphilosophy of being. For all beings are not contained in any one kind, nor, ifthey were, could they possibly fall under the same principles. Accordingly,no art that is a method of showing the nature of anything proceeds by ask-ing questions: for it does not permit a man to grant whichever he likes ofthe two alternatives in the question: for they will not both of them yield aproof. Dialectic, on the other hand, does proceed by questioning, whereasif it were concerned to show things, it would have refrained from puttingquestions, even if not about everything, at least about the first principlesand the special principles that apply to the particular subject in hand. Forsuppose the answerer not to grant these, it would then no longer have hadany grounds from which to argue any longer against the objection. Dialec-tic is at the same time a mode of examination as well. For neither is the artof examination an accomplishment of the same kind as geometry, but onewhich a man may possess, even though he has not knowledge. For it is pos-sible even for one without knowledge to hold an examination of one who iswithout knowledge, if also the latter grants him points taken not from thingthat he knows or from the special principles of the subject under discussionbut from all that range of consequences attaching to the subject which a manmay indeed know without knowing the theory of the subject, but which ifhe do not know, he is bound to be ignorant of the theory. So then clearlythe art of examining does not consist in knowledge of any definite subject.For this reason, too, it deals with everything: for every ‘theory’ of anythingemploys also certain common principles. Hence everybody, including evenamateurs, makes use in a way of dialectic and the practice of examining:for all undertake to some extent a rough trial of those who profess to knowthings. What serves them here is the general principles: for they know theseof themselves just as well as the scientist, even if in what they say they seemto the latter to go wildly astray from them. All, then, are engaged in refuta-tion; for they take a hand as amateurs in the same task with which dialectic isconcerned professionally; and he is a dialectician who examines by the helpof a theory of reasoning. Now there are many identical principles which aretrue of everything, though they are not such as to constitute a particular na-ture, i.e. a particular kind of being, but are like negative terms, while otherprinciples are not of this kind but are special to particular subjects; accord-ingly it is possible from these general principles to hold an examination oneverything, and that there should be a definite art of so doing, and, more-over, an art which is not of the same kind as those which demonstrate. Thisis why the contentious reasoner does not stand in the same condition in allrespects as the drawer of a false diagram: for the contentious reasoner willnot be given to misreasoning from any definite class of principles, but will
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deal with every class.These, then, are the types of sophistical refutations: and that it belongs to
the dialectician to study these, and to be able to effect them, is not difficultto see: for the investigation of premisses comprises the whole of this study.
Part 12 Exposing fallacious and paradoxical sophisms
So much, then, for apparent refutations. As for showing that the answerer iscommitting some fallacy, and drawing his argument into paradox - for thiswas the second item of the sophist’s programme - in the first place, then,this is best brought about by a certain manner of questioning and throughthe question. For to put the question without framing it with reference toany definite subject is a good bait for these purposes: for people are moreinclined to make mistakes when they talk at large, and they talk at largewhen they have no definite subject before them. Also the putting of severalquestions, even though the position against which one is arguing be quitedefinite, and the claim that he shall say only what he thinks, create abun-dant opportunity for drawing him into paradox or fallacy, and also, whetherto any of these questions he replies ‘Yes’ or replies ‘No’, of leading him onto statements against which one is well off for a line of attack. Nowadays,however, men are less able to play foul by these means than they were for-merly: for people rejoin with the question, ‘What has that to do with theoriginal subject?’ It is, too, an elementary rule for eliciting some fallacy orparadox that one should never put a controversial question straight away,but say that one puts it from the wish for information: for the process ofinquiry thus invited gives room for an attack.
A rule specially appropriate for showing up a fallacy is the sophisticrule, that one should draw the answerer on to the kind of statements againstwhich one is well supplied with arguments: this can be done both properlyand improperly, as was said before. Again, to draw a paradoxical statement,look and see to what school of philosophers the person arguing with youbelongs, and then question him as to some point wherein their doctrine isparadoxical to most people: for with every school there is some point of thatkind. It is an elementary rule in these matters to have a collection of the spe-cial ‘theses’ of the various schools among your propositions. The solutionrecommended as appropriate here, too, is to point out that the paradox doesnot come about because of the argument: whereas this is what his opponentalways really wants.
Moreover, argue from men’s wishes and their professed opinions. Forpeople do not wish the same things as they say they wish: they say whatwill look best, whereas they wish what appears to be to their interest: e.g.they say that a man ought to die nobly rather than to live in pleasure, and
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to live in honest poverty rather than in dishonourable riches; but they wishthe opposite. Accordingly, a man who speaks according to his wishes mustbe led into stating the professed opinions of people, while he who speaksaccording to these must be led into admitting those that people keep hiddenaway: for in either case they are bound to introduce a paradox; for they willspeak contrary either to men’s professed or to their hidden opinions.
The widest range of common-place argument for leading men into para-doxical statement is that which depends on the standards of Nature and ofthe Law: it is so that both Callicles is drawn as arguing in the Gorgias, andthat all the men of old supposed the result to come about: for nature (theysaid) and law are opposites, and justice is a fine thing by a legal standard,but not by that of nature. Accordingly, they said, the man whose statementagrees with the standard of nature you should meet by the standard of thelaw, but the man who agrees with the law by leading him to the facts of na-ture: for in both ways paradoxical statements may be committed. In theirview the standard of nature was the truth, while that of the law was theopinion held by the majority. So that it is clear that they, too, used to tryeither to refute the answerer or to make him make paradoxical statements,just as the men of to-day do as well.
Some questions are such that in both forms the answer is paradoxical;e.g. ‘Ought one to obey the wise or one’s father?’ and ‘Ought one to dowhat is expedient or what is just?’ and ‘Is it preferable to suffer injusticeor to do an injury?’ You should lead people, then, into views opposite tothe majority and to the philosophers; if any one speaks as do the expertreasoners, lead him into opposition to the majority, while if he speaks asdo the majority, then into opposition to the reasoners. For some say that ofnecessity the happy man is just, whereas it is paradoxical to the many that aking should be happy. To lead a man into paradoxes of this sort is the sameas to lead him into the opposition of the standards of nature and law: forthe law represents the opinion of the majority, whereas philosophers speakaccording to the standard of nature and the truth.
Part 13 Making someone babble
Paradoxes, then, you should seek to elicit by means of these common-placerules. Now as for making any one babble, we have already said what wemean by ‘to babble’. This is the object in view in all arguments of the fol-lowing kind: If it is all the same to state a term and to state its definition, the‘double’ and ‘double of half’ are the same: if then ‘double’ be the ‘double ofhalf’, it will be the ‘double of half of half’. And if, instead of ‘double’, ‘dou-ble of half’ be again put, then the same expression will be repeated threetimes, ‘double of half of half of half’. Also ‘desire is of the pleasant, isn’t it?’
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desire is conation for the pleasant: accordingly, ‘desire’ is ‘conation for thepleasant for the pleasant’.
All arguments of this kind occur in dealing (1) with any relative termswhich not only have relative genera, but are also themselves relative, and arerendered in relation to one and the same thing, as e.g. conation is conationfor something, and desire is desire of something, and double is double ofsomething, i.e. double of half: also in dealing (2) with any terms which,though they be not relative terms at all, yet have their substance, viz. thethings of which they are the states or affections or what not, indicated as wellin their definition, they being predicated of these things. Thus e.g. ‘odd’ is a‘number containing a middle’: but there is an ‘odd number’: therefore thereis a ‘number-containing-a-middle number’. Also, if snubness be a concavityof the nose, and there be a snub nose, there is therefore a ‘concave-nose nose’.
People sometimes appear to produce this result, without really produc-ing it, because they do not add the question whether the expression ‘double’,just by itself, has any meaning or no, and if so, whether it has the same mean-ing, or a different one; but they draw their conclusion straight away. Still itseems, inasmuch as the word is the same, to have the same meaning as well.
Part 14 Solecism
We have said before what kind of thing ‘solecism’ is. It is possible both tocommit it, and to seem to do so without doing so, and to do so withoutseeming to do so. Suppose, as Protagoras used to say that ‘wrath’ (µῆνις)and ‘helmet’ (πήλνξ) are masculine: according to him a man who calls wratha ‘destructress’ (oὐλoµένην) commits a solecism, though he does not seemto do so to other people, where he who calls it a ‘destructor’ (oὐλόµενην)commits no solecism though he seems to do so. It is clear, then, that any onecould produce this effect by art as well: and for this reason many argumentsseem to lead to solecism which do not really do so, as happens in the case ofrefutations.
Almost all apparent solecisms depend upon the word ‘this’ (τόδε) andupon occasions when the inflection denotes neither a masculine nor a fem-inine object but a neuter. For ‘he’ (ουτος) signifies a masculine, and ‘she’(αυτε) feminine; but ‘this’ (τουτο), though meant to signify a neuter, oftenalso signifies one or other of the former: e.g. ‘What is this?’ ‘It is Calliope’;‘it is a log’; ‘it is Coriscus’. Now in the masculine and feminine the inflec-tions are all different, whereas in the neuter some are and some are not.Often, then, when ‘this’ (τουτο) has been granted, people reason as if ‘him’(τουτον) had been said: and likewise also they substitute one inflection foranother. The fallacy comes about because ‘this’ (τουτο) is a common form ofseveral inflections: for ‘this’ signifies sometimes ‘his’ (ουτος) and sometimes
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‘him’ (τουτον). It should signify them alternately; when combined with ‘is’(εστι) it should be ‘he’, while with ‘being’ it should be ‘him’: e.g. ‘Coriscus(Κοπισκος) is’, but ‘being Coriscus’ (Κοπισκον). It happens in the same wayin the case of feminine nouns as well, and in the case of the so-called ‘chat-tels’ that have feminine or masculine designations. For only those nameswhich end in o and n, have the designation proper to a chattel, e.g. ξυλον(‘log’), σςηοινιον (‘rope’); those which do not end so have that of a masculineor feminine object, though some of them we apply to chattels: e.g. ασκος(‘wineskin’) is a masculine noun, and κλινε (‘bed’) a feminine. For this rea-son in cases of this kind as well there will be a difference of the same sortbetween a construction with ‘is’ (εστι) or with ‘being’ (το ειναι). Also, Sole-cism resembles in a certain way those refutations which are said to dependon the like expression of unlike things. For, just as there we come upon a ma-terial solecism, so here we come upon a verbal: for ‘man’ is both a ‘matter’for expression and also a ‘word’: and so is ‘white’.
It is clear, then, that for solecisms we must try to construct our argumentout of the aforesaid inflections.
These, then, are the types of contentious arguments, and the subdivisionsof those types, and the methods for conducting them aforesaid. But it makesno little difference if the materials for putting the question be arranged ina certain manner with a view to concealment, as in the case of dialectics.Following then upon what we have said, this must be discussed first.
Part 15 How to ask questions effectively
With a view then to refutation, one resource is length - for it is difficult tokeep several things in view at once; and to secure length the elementaryrules that have been stated before should be employed. One resource, on theother hand, is speed; for when people are left behind they look ahead less.Moreover, there is anger and contentiousness, for when agitated everybodyis less able to take care of himself. Elementary rules for producing angerare to make a show of the wish to play foul, and to be altogether shameless.Moreover, there is the putting of one’s questions alternately, whether onehas more than one argument leading to the same conclusion, or whether onehas arguments to show both that something is so, and that it is not so: forthe result is that he has to be on his guard at the same time either againstmore than one line, or against contrary lines, of argument. In general, allthe methods described before of producing concealment are useful also forpurposes of contentious argument: for the object of concealment is to avoiddetection, and the object of this is to deceive.
To counter those who refuse to grant whatever they suppose to help one’sargument, one should put the question negatively, as though desirous of the
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opposite answer, or at any rate as though one put the question without prej-udice; for when it is obscure what answer one wants to secure, people areless refractory. Also when, in dealing with particulars, a man grants theindividual case, when the induction is done you should often not put theuniversal as a question, but take it for granted and use it: for sometimespeople themselves suppose that they have granted it, and also appear to theaudience to have done so, for they remember the induction and assume thatthe questions could not have been put for nothing. In cases where there is noterm to indicate the universal, still you should avail yourself of the resem-blance of the particulars to suit your purpose; for resemblance often escapesdetection. Also, with a view to obtaining your premiss, you ought to putit in your question side by side with its contrary. E.g. if it were necessaryto secure the admission that ‘A man should obey his father in everything’,ask ‘Should a man obey his parents in everything, or disobey them in every-thing?’; and to secure that ‘A number multiplied by a large number is a largenumber’, ask ‘Should one agree that it is a large number or a small one?’ Forthen, if compelled to choose, one will be more inclined to think it a large one:for the placing of their contraries close beside them makes things look big tomen, both relatively and absolutely, and worse and better.
A strong appearance of having been refuted is often produced by themost highly sophistical of all the unfair tricks of questioners, when withoutproving anything, instead of putting their final proposition as a question,they state it as a conclusion, as though they had proved that ‘Therefore so-and-so is not true’
It is also a sophistical trick, when a paradox has been laid down, first topropose at the start some view that is generally accepted, and then claimthat the answerer shall answer what he thinks about it, and to put one‘squestion on matters of that kind in the form ’Do you think that...?’ For then,if the question be taken as one of the premisses of one’s argument, either arefutation or a paradox is bound to result; if he grants the view, a refutation;if he refuses to grant it or even to admit it as the received opinion, a paradox;if he refuses to grant it, but admits that it is the received opinion, somethingvery like a refutation, results.
Moreover, just as in rhetorical discourses, so also in those aimed at refuta-tion, you should examine the discrepancies of the answerer’s position eitherwith his own statements, or with those of persons whom he admits to sayand do aright, moreover with those of people who are generally supposed tobear that kind of character, or who are like them, or with those of the major-ity or of all men. Also just as answerers, too, often, when they are in processof being confuted, draw a distinction, if their confutation is just about to takeplace, so questioners also should resort to this from time to time to counterobjectors, pointing out, supposing that against one sense of the words the
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objection holds, but not against the other, that they have taken it in the lattersense, as e.g. Cleophon does in the Mandrobulus. They should also break offtheir argument and cut down their other lines of attack, while in answering,if a man perceives this being done beforehand, he should put in his objec-tion and have his say first. One should also lead attacks sometimes againstpositions other than the one stated, on the understood condition that onecannot find lines of attack against the view laid down, as Lycophron didwhen ordered to deliver a eulogy upon the lyre. To counter those who de-mand ‘Against what are you directing your effort?’, since one is generallythought bound to state the charge made, while, on the other hand, someways of stating it make the defence too easy, you should state as your aimonly the general result that always happens in refutations, namely the con-tradiction of his thesis -viz. that your effort is to deny what he has affirmed,or to affirm what he denied: don’t say that you are trying to show that theknowledge of contraries is, or is not, the same. One must not ask one’s con-clusion in the form of a premiss, while some conclusions should not even beput as questions at all; one should take and use it as granted.
Section III Responding to sophisticalarguments
Part 16 Sophistries must be answered as well as understood
We have now therefore dealt with the sources of questions, and the methodsof questioning in contentious disputations: next we have to speak of answer-ing, and of how solutions should be made, and of what requires them, andof what use is served by arguments of this kind.
The use of them, then, is, for philosophy, twofold. For in the first place,since for the most part they depend upon the expression, they put us in abetter condition for seeing in how many senses any term is used, and whatkind of resemblances and what kind of differences occur between thingsand between their names. In the second place they are useful for one’s ownpersonal researches; for the man who is easily committed to a fallacy bysome one else, and does not perceive it, is likely to incur this fate of himselfalso on many occasions. Thirdly and lastly, they further contribute to one’sreputation, viz. the reputation of being well trained in everything, and notinexperienced in anything: for that a party to arguments should find faultwith them, if he cannot definitely point out their weakness, creates a suspi-cion, making it seem as though it were not the truth of the matter but merely
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inexperience that put him out of temper.Answerers may clearly see how to meet arguments of this kind, if our
previous account was right of the sources whence fallacies came, and alsoour distinctions adequate of the forms of dishonesty in putting questions.But it is not the same thing take an argument in one’s hand and then to seeand solve its faults, as it is to be able to meet it quickly while being subjectedto questions: for what we know, we often do not know in a different context.Moreover, just as in other things speed is enhanced by training, so it is witharguments too, so that supposing we are unpractised, even though a pointbe clear to us, we are often too late for the right moment. Sometimes too ithappens as with diagrams; for there we can sometimes analyse the figure,but not construct it again: so too in refutations, though we know the thingon which the connexion of the argument depends, we still are at a loss tosplit the argument apart.
Part 17 Refutation by fraudulent artifice, equivocation,amphiboly
First then, just as we say that we ought sometimes to choose to prove some-thing in the general estimation rather than in truth, so also we have some-times to solve arguments rather in the general estimation than according tothe truth. For it is a general rule in fighting contentious persons, to treatthem not as refuting, but as merely appearing to refute: for we say that theydon’t really prove their case, so that our object in correcting them must be todispel the appearance of it. For if refutation be an unambiguous contradic-tion arrived at from certain views, there could be no need to draw distinc-tions against amphiboly and ambiguity: they do not effect a proof. The onlymotive for drawing further distinctions is that the conclusion reached lookslike a refutation. What, then, we have to beware of, is not being refuted,but seeming to be, because of course the asking of amphibolies and of ques-tions that turn upon ambiguity, and all the other tricks of that kind, concealeven a genuine refutation, and make it uncertain who is refuted and who isnot. For since one has the right at the end, when the conclusion is drawn,to say that the only denial made of One’s statement is ambiguous, no mat-ter how precisely he may have addressed his argument to the very samepoint as oneself, it is not clear whether one has been refuted: for it is notclear whether at the moment one is speaking the truth. If, on the other hand,one had drawn a distinction, and questioned him on the ambiguous term orthe amphiboly, the refutation would not have been a matter of uncertainty.Also what is incidentally the object of contentious arguers, though less sonowadays than formerly, would have been fulfilled, namely that the per-son questioned should answer either ‘Yes’ or ‘No’: whereas nowadays the
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improper forms in which questioners put their questions compel the partyquestioned to add something to his answer in correction of the faultinessof the proposition as put: for certainly, if the questioner distinguishes hismeaning adequately, the answerer is bound to reply either ‘Yes’ or ‘No’.
If any one is going to suppose that an argument which turns upon am-biguity is a refutation, it will be impossible for an answerer to escape beingrefuted in a sense: for in the case of visible objects one is bound of necessityto deny the term one has asserted, and to assert what one has denied. For theremedy which some people have for this is quite unavailing. They say, notthat Coriscus is both musical and unmusical, but that this Coriscus is musi-cal and this Coriscus unmusical. But this will not do, for to say ‘this Coriscusis unmusical’, or ‘musical’, and to say ‘this Coriscus’ is so, is to use the sameexpression: and this he is both affirming and denying at once. ‘But perhapsthey do not mean the same.’ Well, nor did the simple name in the formercase: so where is the difference? If, however, he is to ascribe to the one per-son the simple title ‘Coriscus’, while to the other he is to add the prefix ‘one’or ‘this’, he commits an absurdity: for the latter is no more applicable to theone than to the other: for to whichever he adds it, it makes no difference.
All the same, since if a man does not distinguish the senses of an amphi-boly, it is not clear whether he has been confuted or has not been confuted,and since in arguments the right to distinguish them is granted, it is evidentthat to grant the question simply without drawing any distinction is a mis-take, so that, even if not the man himself, at any rate his argument looks asthough it had been refuted. It often happens, however, that, though theysee the amphiboly, people hesitate to draw such distinctions, because of thedense crowd of persons who propose questions of the kind, in order thatthey may not be thought to be obstructionists at every turn: then, thoughthey would never have supposed that that was the point on which the argu-ment turned, they often find themselves faced by a paradox. Accordingly,since the right of drawing the distinction is granted, one should not hesitate,as has been said before.
If people never made two questions into one question, the fallacy thatturns upon ambiguity and amphiboly would not have existed either, buteither genuine refutation or none. For what is the difference between asking‘Are Callias and Themistocles musical?’ and what one might have asked ifthey, being different, had had one name? For if the term applied means morethan one thing, he has asked more than one question. If then it be not rightto demand simply to be given a single answer to two questions, it is evidentthat it is not proper to give a simple answer to any ambiguous question,not even if the predicate be true of all the subjects, as some claim that oneshould. For this is exactly as though he had asked ‘Are Coriscus and Calliasat home or not at home?’, supposing them to be both in or both out: for in
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both cases there is a number of propositions: for though the simple answerbe true, that does not make the question one. For it is possible for it to be trueto answer even countless different questions when put to one, all togetherwith either a ‘Yes’ or a ‘No’: but still one should not answer them with asingle answer: for that is the death of discussion. Rather, the case is likeas though different things has actually had the same name applied to them.If then, one should not give a single answer to two questions, it is evidentthat we should not say simply ‘Yes’ or ‘No’ in the case of ambiguous termseither: for the remark is simply a remark, not an answer at all, althoughamong disputants such remarks are loosely deemed to be answers, becausethey do not see what the consequence is.
As we said, then, inasmuch as certain refutations are generally taken forsuch, though not such really, in the same way also certain solutions will begenerally taken for solutions, though not really such. Now these, we say,must sometimes be advanced rather than the true solutions in contentiousreasonings and in the encounter with ambiguity. The proper answer in say-ing what one thinks is to say ‘Granted’; for in that way the likelihood of beingrefuted on a side issue is minimized. If, on the other hand, one is compelledto say something paradoxical, one should then be most careful to add that ‘itseems’ so: for in that way one avoids the impression of being either refutedor paradoxical. Since it is clear what is meant by ‘begging the original ques-tion’, and people think that they must at all costs overthrow the premissesthat lie near the conclusion, and plead in excuse for refusing to grant himsome of them that he is begging the original question, so whenever any oneclaims from us a point such as is bound to follow as a consequence from ourthesis, but is false or paradoxical, we must plead the same: for the necessaryconsequences are generally held to be a part of the thesis itself. Moreover,whenever the universal has been secured not under a definite name, but bya comparison of instances, one should say that the questioner assumes itnot in the sense in which it was granted nor in which he proposed it in thepremiss: for this too is a point upon which a refutation often depends.
If one is debarred from these defences one must pass to the argumentthat the conclusion has not been properly shown, approaching it in the lightof the aforesaid distinction between the different kinds of fallacy.
In the case, then, of names that are used literally one is bound to answereither simply or by drawing a distinction: the tacit understandings impliedin our statements, e.g. in answer to questions that are not put clearly butelliptically-it is upon this that the consequent refutation depends. For exam-ple, ‘Is what belongs to Athenians the property of Athenians?’ Yes. ‘And soit is likewise in other cases. But observe; man belongs to the animal king-dom, doesn’t he?’ Yes. ‘Then man is the property of the animal kingdom.’But this is a fallacy: for we say that man ‘belongs to’ the animal kingdom
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because he is an animal, just as we say that Lysander ‘belongs to’ the Spar-tans, because he is a Spartan. It is evident, then, that where the premiss putforward is not clear, one must not grant it simply.
Whenever of two things it is generally thought that if the one is true theother is true of necessity, whereas, if the other is true, the first is not true ofnecessity, one should, if asked which of them is true, grant the smaller one:for the larger the number of premisses, the harder it is to draw a conclusionfrom them. If, again, the sophist tries to secure that has a contrary whileB has not, suppose what he says is true, you should say that each has acontrary, only for the one there is no established name.
Since, again, in regard to some of the views they express, most peoplewould say that any one who did not admit them was telling a falsehood,while they would not say this in regard to some, e.g. to any matters whereonopinion is divided (for most people have no distinct view whether the soul ofanimals is destructible or immortal), accordingly (1) it is uncertain in whichof two senses the premiss proposed is usually meant-whether as maximsare (for people call by the name of ‘maxims’ both true opinions and generalassertions) or like the doctrine ‘the diagonal of a square is incommensuratewith its side’: and moreover (2) whenever opinions are divided as to thetruth, we then have subjects of which it is very easy to change the terminol-ogy undetected. For because of the uncertainty in which of the two sensesthe premiss contains the truth, one will not be thought to be playing anytrick, while because of the division of opinion, one will not be thought to betelling a falsehood. Change the terminology therefore, for the change willmake the position irrefutable.
Moreover, whenever one foresees any question coming, one should putin one‘s objection and have one’s say beforehand: for by doing so one islikely to embarrass the questioner most effectually.
Part 18 Making a distinction versus demolishing a premiss
Inasmuch as a proper solution is an exposure of false reasoning, showing onwhat kind of question the falsity depends, and whereas ‘false reasoning’ hasa double meaning - for it is used either if a false conclusion has been proved,or if there is only an apparent proof and no real one - there must be both thekind of solution just described, and also the correction of a merely apparentproof, so as to show upon which of the questions the appearance depends.Thus it comes about that one solves arguments that are properly reasonedby demolishing them, whereas one solves merely apparent arguments bydrawing distinctions. Again, inasmuch as of arguments that are properlyreasoned some have a true and others a false conclusion, those that are falsein respect of their conclusion it is possible to solve in two ways; for it is
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possible both by demolishing one of the premisses asked, and by showingthat the conclusion is not the real state of the case: those, on the other hand,that are false in respect of the premisses can be solved only by a demolitionof one of them; for the conclusion is true. So that those who wish to solvean argument should in the first place look and see if it is properly reasoned,or is unreasoned; and next, whether the conclusion be true or false, in orderthat we may effect the solution either by drawing some distinction or bydemolishing something, and demolishing it either in this way or in that,as was laid down before. There is a very great deal of difference betweensolving an argument when being subjected to questions and when not: forto foresee traps is difficult, whereas to see them at one’s leisure is easier.
Part 19 Equivocal premisses versus equivocal conclusions
Of the refutations, then, that depend upon ambiguity and amphiboly somecontain some question with more than one meaning, while others containa conclusion bearing a number of senses: e.g. in the proof that ‘speakingof the silent’ is possible, the conclusion has a double meaning, while in theproof that ‘he who knows does not understand what he knows’ one of thequestions contains an amphiboly. Also the double-edged saying is true inone context but not in another: it means something that is and somethingthat is not.
Whenever, then, the many senses lie in the conclusion no refutation takesplace unless the sophist secures as well the contradiction of the conclusionhe means to prove; e.g. in the proof that ‘seeing of the blind’ is possible: forwithout the contradiction there was no refutation. Whenever, on the otherhand, the many senses lie in the questions, there is no necessity to begin bydenying the double-edged premiss: for this was not the goal of the argumentbut only its support. At the start, then, one should reply with regard to anambiguity, whether of a term or of a phrase, in this manner, that ‘in onesense it is so, and in another not so’, as e.g. that ‘speaking of the silent’ isin one sense possible but in another not possible: also that in one sense ‘oneshould do what must needs be done’, but not in another: for ‘what mustneeds be’ bears a number of senses. If, however, the ambiguity escapes one,one should correct it at the end by making an addition to the question: ‘Isspeaking of the silent possible?’ ‘No, but to speak of while he is silent ispossible.’ Also, in cases which contain the ambiguity in their premisses,one should reply in like manner: ‘Do people-then not understand what theyknow? "Yes, but not those who know it in the manner described’: for it isnot the same thing to say that ‘those who know cannot understand what theyknow’, and to say that ‘those who know something in this particular mannercannot do so’. In general, too, even though he draws his conclusion in a quite
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unambiguous manner, one should contend that what he has negated is notthe fact which one has asserted but only its name; and that therefore there isno refutation.
Part 20 Fallacies involving division and combination ofwords
It is evident also how one should solve those refutations that depend uponthe division and combination of words: for if the expression means some-thing different when divided and when combined, as soon as one’s oppo-nent draws his conclusion one should take the expression in the contraryway. All such expressions as the following depend upon the combination ordivision of the words: ‘Was X being beaten with that with which you sawhim being beaten?’ and ‘Did you see him being beaten with that with whichhe was being beaten?’ This fallacy has also in it an element of amphiboly inthe questions, but it really depends upon combination. For the meaning thatdepends upon the division of the words is not really a double meaning (forthe expression when divided is not the same), unless also the word that ispronounced, according to its breathing, as eros and eros is a case of doublemeaning. (In writing, indeed, a word is the same whenever it is written ofthe same letters and in the same manner - and even there people nowadaysput marks at the side to show the pronunciation - but the spoken words arenot the same.) Accordingly an expression that depends upon division is notan ambiguous one. It is evident also that not all refutations depend uponambiguity as some people say they do.
The answerer, then, must divide the expression: for ‘I-saw-a-man-being-beaten with my eyes’ is not the same as to say ‘I saw a man being-beaten-with-my-eyes’. Also there is the argument of Euthydemus proving ‘Thenyou know now in Sicily that there are triremes in Piraeus’: and again, ‘Can agood man who is a cobbler be bad?’ ‘No.’ ‘But a good man may be a bad cob-bler: therefore a good cobbler will be bad.’ Again, ‘Things the knowledge ofwhich is good, are good things to learn, aren’t they?’ ‘Yes.’ ‘The knowledge,however, of evil is good: therefore evil is a good thing to know.’ ‘Yes. But,you see, evil is both evil and a thing-to-learn, so that evil is an evil-thing-to-learn, although the knowledge of evils is good.’ Again, ‘Is it true to sayin the present moment that you are born?’ ‘Yes.’ ‘Then you are born in thepresent moment.’ ‘No; the expression as divided has a different meaning:for it is true to say-in-the-present-moment that "you are born", but not "Youare born-in-the-present-moment".’ Again, ‘Could you do what you can, andas you can?’ ‘Yes.’ ‘But when not harping, you have the power to harp: andtherefore you could harp when not harping.’ ‘No: he has not the power toharp-while-not-harping; merely, when he is not doing it, he has the power
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to do it.’ Some people solve this last refutation in another way as well. For,they say, if he has granted that he can do anything in the way he can, stillit does not follow that he can harp when not harping: for it has not beengranted that he will do anything in every way in which he can; and it is notthe same thing ‘to do a thing in the way he can’ and ‘to do it in every way inwhich he can’. But evidently they do not solve it properly: for of argumentsthat depend upon the same point the solution is the same, whereas this willnot fit all cases of the kind nor yet all ways of putting the questions: it isvalid against the questioner, but not against his argument.
Part 21 Accentuation
Accentuation gives rise to no fallacious arguments, either as written or asspoken, except perhaps some few that might be made up; e.g. the followingargument. ‘Is oὗ καταλύεις (where you lodge) a house?’ ‘Yes.’ ‘Is then oὐκαταλύεις (you do not lodge) the negation of καταλύεις’ (you lodge) ‘Yes.’‘But you said that oὗ καταλύεις is a house: therefore the house is a negation.’How one should solve this, is clear: for the word does not mean the samewhen spoken with an acuter and when spoken with a graver accent.
Part 22 Identical expressions for distinct things
It is clear also how one must meet those fallacies that depend on the identicalexpressions of things that are not identical, seeing that we are in possessionof the kinds of predications. For the one man, say, has granted, when asked,that a term denoting a substance does not belong as an attribute, while theother has shown that some attribute belongs which is in the Category ofRelation or of Quantity, but is usually thought to denote a substance becauseof its expression; e.g. in the following argument: ‘Is it possible to be doingand to have done the same thing at the same time?’ ‘No.’ ‘But, you see, it issurely possible to be seeing and to have seen the same thing at the same time,and in the same aspect.’ Again, ‘Is any mode of passivity a mode of activity?’‘No.’ ‘Then "he is cut", "he is burnt", "he is struck by some sensible object"are alike in expression and all denote some form of passivity, while again "tosay", "to run", "to see" are like one like one another in expression: but, yousee, "to see" is surely a form of being struck by a sensible object; thereforeit is at the same time a form of passivity and of activity.’ Suppose, however,that in that case any one, after granting that it is not possible to do and tohave done the same thing in the same time, were to say that it is possibleto see and to have seen it, still he has not yet been refuted, suppose him tosay that ‘to see’ is not a form of ‘doing’ (activity) but of ‘passivity’: for thisquestion is required as well, though he is supposed by the listener to have
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already granted it, when he granted that ‘to cut’ is a form of present, and‘to have cut’ a form of past, activity, and so on with the other things thathave a like expression. For the listener adds the rest by himself, thinkingthe meaning to be alike: whereas really the meaning is not alike, though itappears to be so because of the expression. The same thing happens here ashappens in cases of ambiguity: for in dealing with ambiguous expressionsthe tyro in argument supposes the sophist to have negated the fact which he(the tyro) affirmed, and not merely the name: whereas there still wants thequestion whether in using the ambiguous term he had a single meaning inview: for if he grants that that was so, the refutation will be effected.
Like the above are also the following arguments. It is asked if a manhas lost what he once had and afterwards has not: for a man will no longerhave ten dice even though he has only lost one die. No: rather it is that hehas lost what he had before and has not now; but there is no necessity forhim to have lost as much or as many things as he has not now. So then,he asks the questions as to what he has, and draws the conclusion as to thewhole number that he has: for ten is a number. If then he had asked to beginwith, whether a man no longer having the number of things he once hadhas lost the whole number, no one would have granted it, but would havesaid ‘Either the whole number or one of them’. Also there is the argumentthat ‘a man may give what he has not got’: for he has not got only one die.No: rather it is that he has given not what he had not got, but in a manner inwhich he had not got it, viz. just the one. For the word ‘only’ does not signifya particular substance or quality or number, but a manner relation, e.g. thatit is not coupled with any other. It is therefore just as if he had asked ‘Coulda man give what he has not got?’ and, on being given the answer ‘No’, wereto ask if a man could give a thing quickly when he had not got it quickly,and, on this being granted, were to conclude that ‘a man could give what hehad not got’. It is quite evident that he has not proved his point: for to ‘givequickly’ is not to give a thing, but to give in a certain manner; and a mancould certainly give a thing in a manner in which he has not got it, e.g. hemight have got it with pleasure and give it with pain.
Like these are also all arguments of the following kind: ‘Could a manstrike a blow with a hand which he has not got, or see with an eye whichhe has not got?’ For he has not got only one eye. Some people solve thiscase, where a man has more than one eye, or more than one of anything else,by saying also that he has only one. Others also solve it as they solve therefutation of the view that ‘what a man has, he has received’: for A gaveonly one vote; and certainly B, they say, has only one vote from A. Others,again, proceed by demolishing straight away the proposition asked, and ad-mitting that it is quite possible to have what one has not received; e.g. tohave received sweet wine, but then, owing to its going bad in the course of
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receipt, to have it sour. But, as was said also above, all these persons directtheir solutions against the man, not against his argument. For if this were agenuine solution, then, suppose any one to grant the opposite, he could findno solution, just as happens in other cases; e.g. suppose the true solution tobe ‘So-and-so is partly true and partly not’, then, if the answerer grants theexpression without any qualification, the sophist’s conclusion follows. If, onthe other hand, the conclusion does not follow, then that could not be thetrue solution: and what we say in regard to the foregoing examples is that,even if all the sophist’s premisses be granted, still no proof is effected.
Moreover, the following too belong to this group of arguments. ‘If some-thing be in writing did some one write it?’ ‘Yes.’ ‘But it is now in writing thatyou are seated-a false statement, though it was true at the time when it waswritten: therefore the statement that was written is at the same time false andtrue.’ But this is fallacious, for the falsity or truth of a statement or opinionindicates not a substance but a quality: for the same account applies to thecase of an opinion as well. Again, ‘Is what a learner learns what he learns?’‘Yes.’ ‘But suppose some one learns "slow" quick’. Then his (the sophist’s)words denote not what the learner learns but how he learns it. Also, ‘Doesa man tread upon what he walks through?’ ‘Yes.’ ‘But X walks through awhole day.’ No, rather the words denote not what he walks through, butwhen he walks; just as when any one uses the words ‘to drink the cup’ hedenotes not what he drinks, but the vessel out of which he drinks. Also, ‘Is iteither by learning or by discovery that a man knows what he knows?’ ‘Yes.’‘But suppose that of a pair of things he has discovered one and learned theother, the pair is not known to him by either method.’ No: ‘what’ he knows,means ‘every single thing’ he knows, individually; but this does not mean‘all the things’ he knows, collectively. Again, there is the proof that thereis a ‘third man’ distinct from Man and from individual men. But that is afallacy, for ‘Man’, and indeed every general predicate, denotes not an indi-vidual substance, but a particular quality, or the being related to somethingin a particular manner, or something of that sort. Likewise also in the caseof ‘Coriscus’ and ‘Coriscus the musician’ there is the problem, ‘Are they thesame or different?’ For the one denotes an individual substance and theother a quality, so that it cannot be isolated; though it is not the isolationwhich creates the ‘third man’, but the admission that it is an individual sub-stance. For ‘Man’ cannot be an individual substance, as Callias is. Nor is thecase improved one whit even if one were to call the clement he has isolatednot an individual substance but a quality: for there will still be the one be-side the many, just as ‘Man’ was. It is evident then that one must not grantthat what is a common predicate applying to a class universally is an indi-vidual substance, but must say that denotes either a quality, or a relation, ora quantity, or something of that kind.
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Part 23 Summary on answers for arguments depending onlanguage
It is a general rule in dealing with arguments that depend on language thatthe solution always follows the opposite of the point on which the argumentturns: e.g. if the argument depends upon combination, then the solutionconsists in division; if upon division, then in combination. Again, if it de-pends on an acute accent, the solution is a grave accent; if on a grave accent,it is an acute. If it depends on ambiguity, one can solve it by using the oppo-site term; e.g. if you find yourself calling something inanimate, despite yourprevious denial that it was so, show in what sense it is alive: if, on the otherhand, one has declared it to be inanimate and the sophist has proved it tobe animate, say how it is inanimate. Likewise also in a case of amphiboly.If the argument depends on likeness of expression, the opposite will be thesolution. ‘Could a man give what he has not got?’ ‘No, not what he has notgot’; but he could give it in a way in which he has not got it, e.g. one dieby itself. ‘Does a man know either by learning or by discovery each thingthat he knows, singly? but not the things that he knows, collectively.’ Also aman treads, perhaps, on any thing he walks through, but not on the time hewalks through. Likewise also in the case of the other examples.
Part 24 Dealing with arguments which depend on accident
In dealing with arguments that depend on Accident, one and the same solu-tion meets all cases. For since it is indeterminate when an attribute should beascribed to a thing, in cases where it belongs to the accident of the thing, andsince in some cases it is generally agreed and people admit that it belongs,while in others they deny that it need belong, we should therefore, as soonas the conclusion has been drawn, say in answer to them all alike, that thereis no need for such an attribute to belong. One must, however, be preparedto adduce an example of the kind of attribute meant. All arguments suchas the following depend upon Accident. ‘Do you know what I am going toask you? you know the man who is approaching’, or ‘the man in the mask’?‘Is the statue your work of art?’ or ‘Is the dog your father?’ ‘Is the productof a small number with a small number a small number?’ For it is evidentin all these cases that there is no necessity for the attribute which is true ofthe thing’s accident to be true of the thing as well. For only to things thatare indistinguishable and one in essence is it generally agreed that all thesame attributes belong; whereas in the case of a good thing, to be good is notthe same as to be going to be the subject of a question; nor in the case of aman approaching, or wearing a mask, is ‘to be approaching’ the same thingas ‘to be Coriscus’, so that suppose I know Coriscus, but do not know the
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man who is approaching, it still isn’t the case that I both know and do notknow the same man; nor, again, if this is mine and is also a work of art, is ittherefore my work of art, but my property or thing or something else. (Thesolution is after the same manner in the other cases as well.)
Some solve these refutations by demolishing the original propositionasked: for they say that it is possible to know and not to know the samething, only not in the same respect: accordingly, when they don’t know theman who is coming towards them, but do know Corsicus, they assert thatthey do know and don’t know the same object, but not in the same respect.Yet, as we have already remarked, the correction of arguments that dependupon the same point ought to be the same, whereas this one will not standif one adopts the same principle in regard not to knowing something, but tobeing, or to being is a in a certain state, e.g. suppose that X is father, and isalso yours: for if in some cases this is true and it is possible to know and notto know the same thing, yet with that case the solution stated has nothingto do. Certainly there is nothing to prevent the same argument from havinga number of flaws; but it is not the exposition of any and every fault thatconstitutes a solution: for it is possible for a man to show that a false con-clusion has been proved, but not to show on what it depends, e.g. in thecase of Zeno’s argument to prove that motion is impossible. So that evenif any one were to try to establish that this doctrine is an impossible one,he still is mistaken, and even if he proved his case ten thousand times over,still this is no solution of Zeno’s argument: for the solution was all along anexposition of false reasoning, showing on what its falsity depends. If thenhe has not proved his case, or is trying to establish even a true proposition,or a false one, in a false manner, to point this out is a true solution. Possi-bly, indeed, the present suggestion may very well apply in some cases: butin these cases, at any rate, not even this would be generally agreed: for heknows both that Coriscus is Coriscus and that the approaching figure is ap-proaching. To know and not to know the same thing is generally thoughtto be possible, when e.g. one knows that X is white, but does not realizethat he is musical: for in that way he does know and not know the samething, though not in the same respect. But as to the approaching figure andCoriscus he knows both that it is approaching and that he is Coriscus.
A like mistake to that of those whom we have mentioned is that of thosewho solve the proof that every number is a small number: for if, when theconclusion is not proved, they pass this over and say that a conclusion hasbeen proved and is true, on the ground that every number is both great andsmall, they make a mistake.
Some people also use the principle of ambiguity to solve the aforesaidreasonings, e.g. the proof that ‘X is your father’, or ‘son’, or ‘slave’. Yet it isevident that if the appearance a proof depends upon a plurality of meanings,
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the term, or the expression in question, ought to bear a number of literalsenses, whereas no one speaks of A as being ‘B’s child’ in the literal sense,if B is the child’s master, but the combination depends upon Accident. ‘Is Ayours?’ ‘Yes.’ ‘And is A a child?’ ‘Yes.’ ‘Then the child A is yours,’ becausehe happens to be both yours and a child; but he is not ‘your child’.
There is also the proof that ‘something "of evils" is good’; for wisdomis a ‘knowledge "of evils"’. But the expression that this is ‘of so and-so’(=‘so-and-so’s’) has not a number of meanings: it means that it is ‘so-and-so’s property’. We may suppose of course, on the other hand, that it has anumber of meanings-for we also say that man is ‘of the animals’, though nottheir property; and also that any term related to ‘evils’ in a way expressedby a genitive case is on that account a so-and-so ‘of evils’, though it is notone of the evils-but in that case the apparently different meanings seem todepend on whether the term is used relatively or absolutely. ‘Yet it is con-ceivably possible to find a real ambiguity in the phrase "Something of evilsis good".’ Perhaps, but not with regard to the phrase in question. It wouldoccur more nearly, suppose that ‘A servant is good of the wicked’; thoughperhaps it is not quite found even there: for a thing may be ‘good’ and be‘X’s’ without being at the same time ‘X’s good’. Nor is the saying that ‘Manis of the animals’ a phrase with a number of meanings: for a phrase does notbecome possessed of a number of meanings merely suppose we express itelliptically: for we express ‘Give me the Iliad’ by quoting half a line of it, e.g.‘Give me "Sing, goddess, of the wrath..."’
Part 25 Arguments depending on expressions not validabsolutely
Those arguments which depend upon an expression that is valid of a partic-ular thing, or in a particular respect, or place, or manner, or relation, and notvalid absolutely, should be solved by considering the conclusion in relationto its contradictory, to see if any of these things can possibly have happenedto it. For it is impossible for contraries and opposites and an affirmative anda negative to belong to the same thing absolutely; there is, however, nothingto prevent each from belonging in a particular respect or relation or man-ner, or to prevent one of them from belonging in a particular respect andthe other absolutely. So that if this one belongs absolutely and that one in aparticular respect, there is as yet no refutation. This is a feature one has tofind in the conclusion by examining it in comparison with its contradictory.
All arguments of the following kind have this feature: ‘Is it possible forwhat is-not to be? "No." But, you see, it is something, despite its not being.’Likewise also, Being will not be; for it will not he some particular form ofbeing. ‘Is it possible for the same man at the same time to be a keeper and
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a breaker of his oath?’ ‘Can the same man at the same time both obey anddisobey the same man?’ Or isn’t it the case that being something in par-ticular and Being are not the same? On the other hand, Not-being, even ifit be something, need not also have absolute ‘being’ as well. Nor if a mankeeps his oath in this particular instance or in this particular respect, is hebound also to be a keeper of oaths absolutely, but he who swears that he willbreak his oath, and then breaks it, keeps this particular oath only; he is nota keeper of his oath: nor is the disobedient man ‘obedient’, though he obeysone particular command. The argument is similar, also, as regards the prob-lem whether the same man can at the same time say what is both false andtrue: but it appears to be a troublesome question because it is not easy to seein which of the two connexions the word ‘absolutely’ is to be rendered-with‘true’ or with ‘false’. There is, however, nothing to prevent it from being falseabsolutely, though true in some particular respect or relation, i.e. being truein some things, though not ‘true’ absolutely. Likewise also in cases of someparticular relation and place and time. For all arguments of the followingkind depend upon this. ‘Is health, or wealth, a good thing?’ ‘Yes.’ ‘But tothe fool who does not use it aright it is not a good thing: therefore it is bothgood and not good.’ ‘Is health, or political power, a good thing?’ ‘Yes. "Butsometimes it is not particularly good: therefore the same thing is both goodand not good to the same man.’ Or rather there is nothing to prevent a thing,though good absolutely, being not good to a particular man, or being goodto a particular man, and yet not good or here. ‘Is that which the prudentman would not wish, an evil?’ ‘Yes.’ ‘But to get rid of, he would not wishthe good: therefore the good is an evil.’ But that is a mistake; for it is not thesame thing to say ‘The good is an evil’ and ‘to get rid of the good is an evil’.Likewise also the argument of the thief is mistaken. For it is not the casethat if the thief is an evil thing, acquiring things is also evil: what he wishes,therefore, is not what is evil but what is good; for to acquire something goodis good. Also, disease is an evil thing, but not to get rid of disease. ‘Is thejust preferable to the unjust, and what takes place justly to what takes placeunjustly?’ ‘Yes.’ ‘But to to be put to death unjustly is preferable.’ ‘Is it justthat each should have his own?’ ‘Yes.’ ‘But whatever decisions a man comesto on the strength of his personal opinion, even if it be a false opinion, arevalid in law: therefore the same result is both just and unjust.’ Also, shouldone decide in favour of him who says what is unjust?’ ‘The former.’ ’Butyou see, it is just for the injured party to say fully the things he has suffered;and these are fallacies. For because to suffer a thing unjustly is preferable,unjust ways are not therefore preferable, though in this particular case theunjust may very well be better than the just. Also, to have one’s own is just,while to have what is another’s is not just: all the same, the decision in ques-tion may very well be a just decision, whatever it be that the opinion of the
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man who gave the decision supports: for because it is just in this particularcase or in this particular manner, it is not also just absolutely. Likewise also,though things are unjust, there is nothing to prevent the speaking of thembeing just: for because to speak of things is just, there is no necessity that thethings should be just, any more than because to speak of things be of use, thethings need be of use. Likewise also in the case of what is just. So that it isnot the case that because the things spoken of are unjust, the victory goes tohim who speaks unjust things: for he speaks of things that are just to speakof, though absolutely, i.e. to suffer, they are unjust.
Part 26 Comparing the conclusion with its contradictory
Refutations that depend on the definition of a refutation must, according tothe plan sketched above, be met by comparing together the conclusion withits contradictory, and seeing that it shall involve the same attribute in thesame respect and relation and manner and time. If this additional questionbe put at the start, you should not admit that it is impossible for the samething to be both double and not double, but grant that it is possible, only notin such a way as was agreed to constitute a refutation of your case. All thefollowing arguments depend upon a point of that kind. ‘Does a man whoknows A to be A, know the thing called A?’ and in the same way, ‘is onewho is ignorant that A is A ignorant of the thing called A?’ ‘Yes.’ ‘But onewho knows that Coriscus is Coriscus might be ignorant of the fact that heis musical, so that he both knows and is ignorant of the same thing.’ ‘Is athing four cubits long greater than a thing three cubits long?’ ‘Yes.’ ‘But athing might grow from three to four cubits in length;’ now what is ‘greater’is greater than a ‘less’: accordingly the thing in question will be both greaterand less than itself in the same respect.
Part 27 Begging the question
As to refutations that depend on begging and assuming the original pointto be proved, suppose the nature of the question to be obvious, one shouldnot grant it, even though it be a view generally held, but should tell him thetruth. Suppose, however, that it escapes one, then, thanks to the badness ofarguments of that kind, one should make one’s error recoil upon the ques-tioner, and say that he has brought no argument: for a refutation must beproved independently of the original point. Secondly, one should say thatthe point was granted under the impression that he intended not to use it asa premiss, but to reason against it, in the opposite way from that adopted inrefutations on side issues.
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Part 28 Refutations reaching their conclusion through theconsequent
Also, those refutations that bring one to their conclusion through the conse-quent you should show up in the course of the argument itself. The mode inwhich consequences follow is twofold. For the argument either is that as theuniversal follows on its particular-as (e.g.) ‘animal’ follows from ‘man’-sodoes the particular on its universal: for the claim is made that if A is alwaysfound with B, then B also is always found with A. Or else it proceeds byway of the opposites of the terms involved: for if A follows B, it is claimedthat A’s opposite will follow B’s opposite. On this latter claim the argumentof Melissus also depends: for he claims that because that which has cometo be has a beginning, that which has not come to be has none, so that ifthe heaven has not come to be, it is also eternal. But that is not so; for thesequence is vice versa.
Part 29 Refutations whose reasoning depends on someaddition
In the case of any refutations whose reasoning depends on some addition,look and see if upon its subtraction the absurdity follows none the less: andthen if so, the answerer should point this out, and say that he granted theaddition not because he really thought it, but for the sake of the argument,whereas the questioner has not used it for the purpose of his argument at all.
Part 30 Refutations which make several questions into one
To meet those refutations which make several questions into one, one shoulddraw a distinction between them straight away at the start. For a questionmust be single to which there is a single answer, so that one must not affirmor deny several things of one thing, nor one thing of many, but one of one.But just as in the case of ambiguous terms, an attribute belongs to a termsometimes in both its senses, and sometimes in neither, so that a simple an-swer does one, as it happens, no harm despite the fact that the question isnot simple, so it is in these cases of double questions too. Whenever, then,the several attributes belong to the one subject, or the one to the many, theman who gives a simple answer encounters no obstacle even though he hascommitted this mistake: but whenever an attribute belongs to one subjectbut not to the other, or there is a question of a number of attributes belong-ing to a number of subjects and in one sense both belong to both, while inanother sense, again, they do not, then there is trouble, so that one must be-ware of this. Thus (e.g.) in the following arguments: Supposing to be good
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and B evil, you will, if you give a single answer about both, be compelled tosay that it is true to call these good, and that it is true to call them evil andlikewise to call them neither good nor evil (for each of them has not eachcharacter), so that the same thing will be both good and evil and neithergood nor evil. Also, since everything is the same as itself and different fromanything else, inasmuch as the man who answers double questions simplycan be made to say that several things are ‘the same’ not as other things but‘as themselves’, and also that they are different from themselves, it followsthat the same things must be both the same as and different from themselves.Moreover, if what is good becomes evil while what is evil is good, then theymust both become two. So of two unequal things each being equal to itself,it will follow that they are both equal and unequal to themselves.
Now these refutations fall into the province of other solutions as well: for‘both’ and ‘all’ have more than one meaning, so that the resulting affirmationand denial of the same thing does not occur, except verbally: and this is notwhat we meant by a refutation. But it is clear that if there be not put a singlequestion on a number of points, but the answerer has affirmed or denied oneattribute only of one subject only, the absurdity will not come to pass.
Part 31 Those who draw one into repetition
With regard to those who draw one into repeating the same thing a num-ber of times, it is clear that one must not grant that predications of relativeterms have any meaning in abstraction by themselves, e.g. that ‘double’ isa significant term apart from the whole phrase ‘double of half’ merely onthe ground that it figures in it. For ten figures in ‘ten minus one’ and in ‘notdo’, and generally the affirmation in the negation; but for all that, supposeany one were to say, ‘This is not white’, he does not say that it is white. Thebare word ‘double’, one may perhaps say, has not even any meaning at all,any more than has ‘the’ in ‘the half’: and even if it has a meaning, yet it hasnot the same meaning as in the combination. Nor is ‘knowledge’ the samething in a specific branch of it (suppose it, e.g. to be ‘medical knowledge’)as it is in general: for in general it was the ‘knowledge of the knowable’. Inthe case of terms that are predicated of the terms through which they are de-fined, you should say the same thing, that the term defined is not the samein abstraction as it is in the whole phrase. For ‘concave’ has a general mean-ing which is the same in the case of a snub nose, and of a bandy leg, butwhen added to either substantive nothing prevents it from differentiating itsmeaning; in fact it bears one sense as applied to the nose, and another asapplied to the leg: for in the former connexion it means ‘snub’ and in thelatter ‘bandyshaped’; i.e. it makes no difference whether you say ‘a snubnose’ or ‘a concave nose’. Moreover, the expression must not be granted in
Volume 6 Book III Part 31
Refuting solecisms 385
the nominative case: for it is a falsehood. For snubness is not a concave nosebut something (e.g. an affection) belonging to a nose: hence, there is no ab-surdity in supposing that the snub nose is a nose possessing the concavitythat belongs to a nose.
Part 32 Refuting solecisms
With regard to solecisms, we have previously said what it is that appears tobring them about; the method of their solution will be clear in the course ofthe arguments themselves. Solecism is the result aimed at in all argumentsof the following kind: ‘Is a thing truly that which you truly call it?’ ‘Yes’.‘But, speaking of a stone, you call him real: therefore of a stone it followsthat "him is real".’ No: rather, talking of a stone means not saying ‘which’but ‘whom’, and not ‘that’ but ‘him’. If, then, any one were to ask, ‘Is a stonehim whom you truly call him?’ he would be generally thought not to bespeaking good Greek, any more than if he were to ask, ‘Is he what you callher?’ Speak in this way of a ‘stick’ or any neuter word, and the differencedoes not break out. For this reason, also, no solecism is incurred, supposeany one asks, ‘Is a thing what you say it to be?’ ‘Yes’. ‘But, speaking of astick, you call it real: therefore, of a stick it follows that it is real.’ ‘Stone’,however, and ‘he’ have masculine designations. Now suppose some onewere to ask, ‘Can "he" be a she" (a female)?’, and then again, ‘Well, but isnot he Coriscus?’ and then were to say, ‘Then he is a "she",’ he has notproved the solecism, even if the name ‘Coriscus’ does signify a ‘she’, if, onthe other hand, the answerer does not grant this: this point must be put asan additional question: while if neither is it the fact nor does he grant it, thenthe sophist has not proved his case either in fact or as against the person hehas been questioning. In like manner, then, in the above instance as well itmust be definitely put that ‘he’ means the stone. If, however, this neitheris so nor is granted, the conclusion must not be stated: though it followsapparently, because the case (the accusative), that is really unlike, appears tobe like the nominative. ‘Is it true to say that this object is what you call it byname?’ ‘Yes’. ‘But you call it by the name of a shield: this object thereforeis "of a shield".’ No: not necessarily, because the meaning of ‘this object’is not ‘of a shield’ but ‘a shield’: ‘of a shield’ would be the meaning of ‘thisobject’s’. Nor again if ‘He is what you call him by name’, while ‘the nameyou call him by is Cleon’s‘, is he therefore ’Cleon‘s’: for he is not ‘Cleon’s’,for what was said was that ‘He, not his, is what I call him by name’. For thequestion, if put in the latter way, would not even be Greek. ‘Do you knowthis?’ ‘Yes.’ ‘But this is he: therefore you know he’. No: rather ‘this’ has notthe same meaning in ‘Do you know this?’ as in ‘This is a stone’; in the firstit stands for an accusative, in the second for a nominative case. ‘When you
ON SOPHISTICAL REFUTATIONS
386 Responding to sophistical arguments
have understanding of anything, do you understand it?’ ‘Yes.’ ‘But you haveunderstanding of a stone: therefore you understand of a stone.’ No: the onephrase is in the genitive, ‘of a stone’, while the other is in the accusative, ‘astone’: and what was granted was that ‘you understand that, not of that, ofwhich you have understanding’, so that you understand not ‘of a stone’, but‘the stone’.
Thus that arguments of this kind do not prove solecism but merely ap-pear to do so, and both why they so appear and how you should meet them,is clear from what has been said.
Part 33 Degrees of difficulty in refutation of fallacies
We must also observe that of all the arguments aforesaid it is easier withsome to see why and where the reasoning leads the hearer astray, while withothers it is more difficult, though often they are the same arguments as theformer. For we must call an argument the same if it depends upon the samepoint; but the same argument is apt to be thought by some to depend on dic-tion, by others on accident, and by others on something else, because eachof them, when worked with different terms, is not so clear as it was. Ac-cordingly, just as in fallacies that depend on ambiguity, which are generallythought to be the silliest form of fallacy, some are clear even to the man inthe street (for humorous phrases nearly all depend on diction; e.g. ‘The mangot the cart down from the stand’; and ‘Where are you bound?’ ‘To the yardarm’; and ‘Which cow will calve afore?’ ‘Neither, but both behind;’ and ‘Isthe North wind clear?’ ‘No, indeed; for it has murdered the beggar and themerchant." Is he a Good enough-King?’ ‘No, indeed; a Rob-son’: and so withthe great majority of the rest as well), while others appear to elude the mostexpert (and it is a symptom of this that they often fight about their terms,e.g. whether the meaning of ‘Being’ and ‘One’ is the same in all their appli-cations or different; for some think that ‘Being’ and ‘One’ mean the same;while others solve the argument of Zeno and Parmenides by asserting that‘One’ and ‘Being’ are used in a number of senses), likewise also as regardsfallacies of Accident and each of the other types, some of the arguments willbe easier to see while others are more difficult; also to grasp to which classa fallacy belongs, and whether it is a refutation or not a refutation, is notequally easy in all cases.
An incisive argument is one which produces the greatest perplexity: forthis is the one with the sharpest fang. Now perplexity is twofold, one whichoccurs in reasoned arguments, respecting which of the propositions askedone is to demolish, and the other in contentious arguments, respecting themanner in which one is to assent to what is propounded. Therefore it is insyllogistic arguments that the more incisive ones produce the keenest heart-
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Degrees of difficulty in refutation of fallacies 387
searching. Now a syllogistic argument is most incisive if from premissesthat are as generally accepted as possible it demolishes a conclusion that isaccepted as generally as possible. For the one argument, if the contradictoryis changed about, makes all the resulting syllogisms alike in character: foralways from premisses that are generally accepted it will prove a conclusion,negative or positive as the case may be, that is just as generally accepted; andtherefore one is bound to feel perplexed. An argument, then, of this kind isthe most incisive, viz. the one that puts its conclusion on all fours with thepropositions asked; and second comes the one that argues from premisses,all of which are equally convincing: for this will produce an equal perplexityas to what kind of premiss, of those asked, one should demolish. Herein isa difficulty: for one must demolish something, but what one must demolishis uncertain. Of contentious arguments, on the other hand, the most incisiveis the one which, in the first place, is characterized by an initial uncertaintywhether it has been properly reasoned or not; and also whether the solutiondepends on a false premiss or on the drawing of a distinction; while, of therest, the second place is held by that whose solution clearly depends upona distinction or a demolition, and yet it does not reveal clearly which it isof the premisses asked, whose demolition, or the drawing of a distinctionwithin it, will bring the solution about, but even leaves it vague whether itis on the conclusion or on one of the premisses that the deception depends.
Now sometimes an argument which has not been properly reasoned issilly, supposing the assumptions required to be extremely contrary to thegeneral view or false; but sometimes it ought not to be held in contempt.For whenever some question is left out, of the kind that concerns both thesubject and the nerve of the argument, the reasoning that has both failed tosecure this as well, and also failed to reason properly, is silly; but when whatis omitted is some extraneous question, then it is by no means to be lightlydespised, but the argument is quite respectable, though the questioner hasnot put his questions well.
Just as it is possible to bring a solution sometimes against the argument,at others against the questioner and his mode of questioning, and at othersagainst neither of these, likewise also it is possible to marshal one’s questionsand reasoning both against the thesis, and against the answerer and againstthe time, whenever the solution requires a longer time to examine than theperiod available.
ON SOPHISTICAL REFUTATIONS
388 Epilogue
Section IV Epilogue
Part 34 Review and conclusions
As to the number, then, and kind of sources whence fallacies arise in discus-sion, and how we are to show that our opponent is committing a fallacy andmake him utter paradoxes; moreover, by the use of what materials solescismis brought about, and how to question and what is the way to arrange thequestions; moreover, as to the question what use is served by all argumentsof this kind, and concerning the answerer’s part, both as a whole in general,and in particular how to solve arguments and solecisms-on all these thingslet the foregoing discussion suffice. It remains to recall our original proposaland to bring our discussion to a close with a few words upon it.
Our programme was, then, to discover some faculty of reasoning aboutany theme put before us from the most generally accepted premisses thatthere are. For that is the essential task of the art of discussion (dialectic) andof examination (peirastic). Inasmuch, however, as it is annexed to it, on ac-count of the near presence of the art of sophistry (sophistic), not only to beable to conduct an examination dialectically but also with a show of knowl-edge, we therefore proposed for our treatise not only the aforesaid aim ofbeing able to exact an account of any view, but also the aim of ensuring thatin standing up to an argument we shall defend our thesis in the same man-ner by means of views as generally held as possible. The reason of this wehave explained; for this, too, was why Socrates used to ask questions andnot to answer them; for he used to confess that he did not know. We havemade clear, in the course of what precedes, the number both of the pointswith reference to which, and of the materials from which, this will be ac-complished, and also from what sources we can become well supplied withthese: we have shown, moreover, how to question or arrange the question-ing as a whole, and the problems concerning the answers and solutions to beused against the reasonings of the questioner. We have also cleared up theproblems concerning all other matters that belong to the same inquiry intoarguments. In addition to this we have been through the subject of Fallacies,as we have already stated above.
That our programme, then, has been adequately completed is clear. Butwe must not omit to notice what has happened in regard to this inquiry.For in the case of all discoveries the results of previous labours that havebeen handed down from others have been advanced bit by bit by those whohave taken them on, whereas the original discoveries generally make ad-vance that is small at first though much more useful than the developmentwhich later springs out of them. For it may be that in everything, as the say-
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Review and conclusions 389
ing is, ‘the first start is the main part’: and for this reason also it is the mostdifficult; for in proportion as it is most potent in its influence, so it is small-est in its compass and therefore most difficult to see: whereas when this isonce discovered, it is easier to add and develop the remainder in connexionwith it. This is in fact what has happened in regard to rhetorical speechesand to practically all the other arts: for those who discovered the beginningsof them advanced them in all only a little way, whereas the celebrities ofto-day are the heirs (so to speak) of a long succession of men who have ad-vanced them bit by bit, and so have developed them to their present form,Tisias coming next after the first founders, then Thrasymachus after Tisias,and Theodorus next to him, while several people have made their severalcontributions to it: and therefore it is not to be wondered at that the arthas attained considerable dimensions. Of this inquiry, on the other hand,it was not the case that part of the work had been thoroughly done before,while part had not. Nothing existed at all. For the training given by thepaid professors of contentious arguments was like the treatment of the mat-ter by Gorgias. For they used to hand out speeches to be learned by heart,some rhetorical, others in the form of question and answer, each side sup-posing that their arguments on either side generally fall among them. Andtherefore the teaching they gave their pupils was ready but rough. For theyused to suppose that they trained people by imparting to them not the artbut its products, as though any one professing that he would impart a formof knowledge to obviate any pain in the feet, were then not to teach a manthe art of shoe-making or the sources whence he can acquire anything of thekind, but were to present him with several kinds of shoes of all sorts: for hehas helped him to meet his need, but has not imparted an art to him. More-over, on the subject of Rhetoric there exists much that has been said longago, whereas on the subject of reasoning we had nothing else of an earlierdate to speak of at all, but were kept at work for a long time in experimentalresearches. If, then, it seems to you after inspection that, such being the situ-ation as it existed at the start, our investigation is in a satisfactory conditioncompared with the other inquiries that have been developed by tradition,there must remain for all of you, or for our students, the task of extendingus your pardon for the shortcomings of the inquiry, and for the discoveriesthereof your
ON SOPHISTICAL REFUTATIONS
Index
abnormal, 18absolute, 243, 264, 301, 307, 309, 350,
355, 381absolutely-apparently-good, 307abstract, 225abstraction, 167, 384accidens, 244, 353, 354accident, 51, 89, 95, 112, 149, 153, 154,
160, 187, 188, 203, 206, 213–217, 228–230, 232, 236–238,241, 253, 254, 261, 264, 265,271, 280, 281, 293, 300, 302,317, 318, 323, 324, 349, 353–356, 360, 378, 380, 386
accidit, 215, 229, 349Achilles, 204, 246, 247, 348acquaintance, 316, 344action, 2, 3, 7, 9, 20, 38, 176, 349actuality, 49, 63adulterer, 351adulterous, 351Aetos, 348affection, 2, 3, 17, 20, 137, 141, 142,
266, 303, 304, 385affirmation, 3, 23–25, 31, 33–40, 42,
44, 45, 50, 52, 53, 55, 68, 76,79, 105–107, 125, 145, 161,170, 179, 301, 341, 353, 384
Agamemnon, 349Ajax, 204, 246, 247Alcibiades, 204
alteration, 7, 28, 181, 250, 255, 303amphiboly, 347, 348, 369, 370, 373,
374, 378anacharsis, 162analogous, 156, 199, 207analyse, 102, 352, 369analysed, 103analyses, 204analysis, 100, 183analytic, 173analytics, 40, 53, 143, 186, 339, 341,
347ancient, 26animal-biped-terrestrial, 192animal-man, 43animal-man-white, 81animal-tame, 202animal-tame-biped, 202animal-white-garment, 74, 75animal-white-inanimate, 75animal-white-man, 74, 75animal-white-pitch, 75animal-white-raven, 75animal-white-snow, 75animal-white-swan, 75antecedent, 130, 145, 172, 196antecedently, 145antecedents, 89–93, 180Antiphon, 361Antisthenes, 220antithesis, 23, 341
392 INDEX
aporeme, 339aquatic, 2, 190, 301, 303aquatic-animal, 303arc, 112argue, 9, 20, 28, 37, 53, 102, 130, 139,
152, 160, 183, 189, 199, 205,206, 212, 214, 215, 228, 231,235, 240–242, 249, 252, 293,294, 317, 322, 325, 327–329,331–333, 338–340, 342–344,347, 353, 354, 359, 360, 362–364, 369, 387
argumentation, 343Aristomenes, 97arithmetic, 154–157, 162, 180, 319,
343arithmetician, 146, 156, 195art, 94, 111, 185, 198, 220, 235, 249,
346, 356, 357, 360–362, 365,378, 379, 388, 389
arts, 9, 137, 218, 219, 221, 389assert, 44, 63, 83, 144, 145, 192, 194,
230, 238, 250, 263, 266, 301,309, 313, 318, 329, 335, 370,379
assertion, 3, 34, 53, 67, 69, 79, 83, 99,162, 227, 230, 231, 234, 256,301, 345, 350, 372
assertoric, 73–80astronomical, 94astronomy, 94, 157, 162Athenians, 138, 197, 371Athens, 9atomic, 163–165, 199atomically, 163–165attributable, 160, 166, 168, 169, 176,
181, 195, 197, 322attribute, 5, 10, 11, 13, 50, 54, 72, 83,
90, 94, 100, 145, 146, 148–151, 154–156, 161, 163–168,171–177, 185–189, 192, 193,201, 206–208, 215, 217, 226,
229, 231, 232, 235, 236, 241,244, 252–254, 260, 267, 270,272, 274, 276, 279–285, 291,294–296, 302, 304, 323, 349,350, 356, 375, 378, 382–384
attributed, 57, 198, 230, 241, 242, 265attribution, 54, 71, 83, 164, 173, 272author, 201authority, 222axiom, 145axioms, 145, 154, 157, 158, 183, 324
babble, 273, 330, 364Barhu, 223base, 85, 147, 156, 159, 167, 212, 234,
288, 291, 325, 326, 347, 351,361
basic, 145, 146, 151, 152, 155–157, 159,173, 174, 177, 179, 180, 182,183, 188, 195, 200, 202, 208,210
basis, 2, 209, 323, 355battle, 209begging, 130, 131, 190, 341, 342, 354,
371, 382beginning, 13, 21, 70, 84, 86, 188, 222,
255, 351, 354, 383being-beaten-with-my-eyes, 374beleif, 134belief, 98, 138, 139, 146, 164, 211, 308believe, 146, 153, 157, 164, 184, 211,
266, 334, 337biped, 13, 42, 43, 67, 115, 171, 189,
191, 225, 235, 257, 270, 271,277, 280–282, 287, 295, 296,301–303
biped-animal-tame, 202bird, 12, 13, 202, 204, 225, 280birds, 12, 208born, 18, 65, 374born-in-the-present-moment, 374borne, 198, 216, 274
INDEX 393
Caeneus, 160calculate, 346calculation, 183, 210Callias, 34, 50, 88, 158, 171, 209, 370,
377Callicles, 364Calliope, 365capacity, 7, 16–18, 24, 49, 105, 209,
251, 261, 264–266, 269, 316carpentry, 243, 249cars, 306cart, 386casuistries, 34category, 1, 3, 9, 10, 17, 19–21, 100,
171, 201, 214, 217, 218, 222,228, 253, 254, 256, 257, 268,269, 317, 319, 322, 357, 375
causative, 38, 176cause, 16–18, 26, 27, 131, 132, 144–
146, 149, 152, 153, 156, 161,162, 164, 176, 177, 182, 185,187, 190, 193–200, 205–208,240, 244, 264, 289, 304, 307,326, 349, 351–354, 356, 360
caused, 17, 136, 229, 343centaur, 186ceteris, 178change, 7, 8, 24, 28, 48, 142, 152, 166,
181, 199, 214, 217, 235, 258,349, 372
characteristic, 5, 6, 17, 20, 25, 42, 69,160, 176, 209
characterization, 190characterized, 94, 171, 178, 387characterizing, 201, 204charioteer, 220Choerilus, 328circle, 14, 20, 139, 147, 154, 155, 160,
193, 200, 201, 331, 361circles, 160circular, 20, 116, 117, 119, 147, 148,
162, 200
circularity, 296circularly, 148clap-trap, 327classification, 39, 148classified, 343Cleophon, 368co-ordinate, 2, 113, 239, 251, 260, 286,
299–301, 321, 326, 343cobbler, 374coexist, 183coextensive, 201, 207combination, 3, 25, 31, 42, 43, 225,
237, 246, 249, 314, 315, 347,348, 352, 355, 374, 378, 380,384
combine, 36, 42, 43, 45, 348combined, 18, 43, 170, 281, 348, 355,
366, 374combines, 348come-to-be, 200, 351coming-to-be, 198–200, 351command, 211, 270, 271, 381commands, 271commendable, 339commensurably, 225commensurate, 84, 95, 103, 145, 148–
151, 155, 173, 176–178, 182,185, 187, 204, 206, 207, 357
commensurately, 149–151, 154, 155,175–178, 181, 182, 184, 206
commit, 229, 234, 343, 364, 365, 368,370, 383
complete, 15, 167, 179, 190, 191composed, 14, 93, 148, 346composite, 1–3, 25, 31, 33, 34, 43, 44,
51, 96compound, 100, 148, 311, 314, 316comprehend, 12, 95, 222comprehension, 143, 212conation, 296, 306, 307, 365conation-for-the-pleasant, 296conceivably, 380
394 INDEX
conceive, 272concept, 209conception, 33, 232, 239, 251, 262,
264, 266, 268, 274, 275, 306,311, 331
confute, 350connexion, 12, 83, 132, 146, 149, 152–
155, 162–164, 168, 176, 181,182, 184, 186, 189, 200, 204–207, 247, 328, 369, 381, 384,389
connote, 240consciousness, 315consequence, 43, 44, 54, 56, 58, 71,
72, 77, 80, 146, 162, 173, 188,193, 235, 245, 246, 266, 310,318, 329, 347, 351, 362, 371,383
consequent, 47, 49, 89, 91, 147, 149,172, 190, 196, 349, 351, 352,354–356, 371, 383
contingency, 44, 46contingent, 45–47, 152contradict, 34, 130, 218, 350contradiction, 35, 36, 43, 44, 129, 130,
140, 145, 158, 159, 194, 220,238, 339, 355, 359, 368, 369,373
contradictious, 220contradictory, 34–38, 41, 42, 44, 45,
47, 48, 50–53, 72, 76, 84, 120–126, 128, 129, 134, 149, 166,219, 221, 223, 230, 238, 341,342, 345, 346, 353, 356–359,380, 382, 387
contraries, 9–11, 19–26, 28, 35, 41, 50–53, 76, 92, 98–100, 102, 103,105, 128–130, 140, 165, 183,218, 219, 221–223, 230, 232,236–240, 246, 250, 259, 268,284, 294, 307, 308, 315, 316,320, 325, 326, 331, 334, 341–
343, 360, 367, 368, 380contrariety, 129, 236, 237contrary, 6–11, 19–21, 24–28, 34–36,
39, 41, 47–52, 68, 91, 95, 99,110, 112, 120–126, 129, 130,134–136, 139, 140, 147, 149,154, 157, 159, 164–166, 170,180, 192, 218–223, 225, 233,235–240, 243, 244, 246, 258–260, 262, 263, 268, 284, 285,294, 301, 304, 308, 309, 313,316, 320, 323, 331, 335, 337,338, 341, 342, 350–352, 364,366, 367, 372, 374, 387
converse, 14, 116, 117, 214, 238–240,246, 247, 266, 297, 298, 322
conversely, 27, 90, 161, 165, 238, 239,258, 269
convert, 54, 55, 90, 103, 104, 120, 261,337
converted, 55, 61, 62, 65, 67–70, 73,74, 78–82, 90, 93, 103, 104,117, 118, 120–123, 138, 166,262
convertibility, 76, 200convertible, 54, 58–61, 63, 65, 66, 68–
70, 75–77, 80, 88, 90, 91, 104,108, 117, 130, 131, 136–138,142, 148, 168, 192, 206, 214,217, 229–231, 235, 238, 242,269, 270, 277, 284, 312, 322,351
convertibly, 214, 217, 279, 295, 324converting, 60, 63, 78, 79, 116, 119,
238, 342converts, 55coordinate, 163, 239, 286, 299, 307,
317, 321copulation, 33Coriscus, 175, 349, 365, 366, 370, 377–
379, 382, 385corollary, 173
INDEX 395
Corsicus, 379counter-argument, 335counter-proof, 335covetous, 307cowardice, 25, 183, 238, 313
dative, 100, 262, 263definable, 171, 185, 188–194, 196, 200,
202, 203define, 1, 4, 10, 12, 22, 28, 31, 45, 53,
55, 100, 146, 148, 188, 193,202, 204, 214, 216, 228–230,282, 283, 293, 297–299, 301,304, 306–308, 310–313, 315,316, 321, 330–332
definiendum, 203definite, 3, 6, 9, 15, 39, 42, 57, 89, 94,
108, 145, 158, 181, 199, 252,253, 270, 274, 276, 282, 298,334, 360–363, 371
definition, 1, 3–6, 12, 15, 20, 32, 39, 44,68–72, 88, 89, 95, 102, 146,147, 153, 155–158, 160, 170,173, 176, 184, 188–193, 195–198, 201–204, 206–208, 212–218, 220, 222, 225, 227–230,234, 250, 252–254, 257, 258,267, 273, 274, 277, 280, 283,292–299, 301, 304–313, 315,316, 319–323, 326, 330, 331,336, 343, 350, 352–356, 364,365, 382
definition-mongers, 228definitive, 34definitory, 214, 216demonstrable, 98, 145, 146, 155, 157,
167, 168, 172, 173, 177, 181,182, 188, 189, 193, 194, 196,200
demonstrate, 60, 61, 66, 88, 89, 94,102, 117, 130, 152, 162, 191,195, 206, 340, 341, 357, 362
demonstrative, 53, 69, 138, 141, 145,147, 148, 151–153, 156, 157,160, 173, 179, 195, 208, 339,347
denial, 23, 31–42, 44, 45, 50, 52, 53, 64,68, 105–107, 179, 231, 326,335, 353, 369, 378, 384
denotation, 255, 258, 264, 267, 269denote, 19, 32, 35, 39, 151, 224, 303,
308, 309, 349, 375, 377denoted, 13, 225denotes, 145, 224, 225, 303, 305, 308,
349, 365, 377denoting, 39, 237, 311, 375deny, 34, 35, 44, 68, 83, 84, 128, 158,
174, 182, 190, 239, 243, 270,327, 329, 330, 368, 370, 378,383
derivative, 18, 19derivatively, 1derive, 1, 12, 200, 288derived, 12, 18, 19, 21, 141, 174, 177,
180, 182, 233, 240, 299derives, 1, 156, 178dialectic, 94, 153, 158, 160, 204, 213,
222, 227, 235, 328, 329, 347,356, 357, 360–362, 366, 388
dialectical, 42, 53, 54, 94, 131, 138,143, 145, 160, 167, 170, 173,178, 182, 194, 204, 211, 218–220, 329, 330, 332, 337, 339–341, 346, 350, 357, 358, 360–362, 388
dialectician, 53, 227, 253, 324, 328,337, 338, 344, 358, 360, 362,363
didactic, 346, 360didactically, 360differentia, 2, 5, 6, 95, 151, 156, 171,
190, 201–203, 213, 217, 225–227, 255, 257, 258, 266, 267,269, 279, 280, 295, 297–304,
396 INDEX
306, 307, 311, 318–320, 322differentiate, 6, 27, 202, 226, 300, 303,
384Dionesius, 309disconnexion, 163disposition, 11, 16, 17, 19, 29, 233,
236, 237, 256, 261–263, 304divide, 96, 141, 201, 202, 213, 230,
232, 236, 295, 303, 352, 353,355, 359, 374
divided, 27, 191, 222, 232, 293, 299–301, 348, 355, 372, 374
dividendum, 191, 202divider, 191divides, 95, 301, 331, 348dividing, 95, 253, 301divined, 185does-not-enjoy-health, 41drink, 315, 377drinkable, 102drinking, 223drugs, 314
earthquake, 68, 186, 307Einai, 366elders, 246element, 37, 39, 171, 173, 174, 180,
185, 194, 202–204, 206, 228,272, 283, 314, 353, 374
elementary, 255, 259, 269, 300, 307,316, 331, 363, 366
elenchi, 353, 354embarrass, 372emendation, 316emotions, 142Empedocles, 222, 267enthymeme, 141, 143enthymemes, 343entities, 4, 180entity, 175, 176enumerated, 18, 28, 29, 216, 324enumerating, 253
enumeration, 40, 138epic, 160epichireme, 339equality, 10, 11, 150, 176, 187, 207,
300, 304, 308equidistant, 193equilateral, 151, 232equilaterals, 151equimembral, 311equivalent, 22, 35, 36, 41, 42, 44, 48,
51, 159, 168, 187, 195, 240,296, 305
equivocal, 34, 159, 176, 207, 373equivocally, 1, 49equivocation, 204, 369Eretrians, 197ergo, 245, 348Eros, 374essence, 51, 94, 136, 151, 163, 189,
190, 193, 213, 214, 217, 218,222, 227, 228, 253, 254, 256,257, 268, 269, 274, 277–279,283, 293, 295–297, 299, 300,302, 303, 306, 307, 309, 313,314, 319, 321–323, 378
essential, 13, 15, 143, 148–157, 170–174, 176, 180, 184, 185, 187–196, 200–204, 206, 215, 232,253, 270, 271, 281, 297, 298,332, 346, 356, 388
essentially, 15, 148, 149, 151, 152, 154,155, 168, 171, 172, 185, 191,192, 202, 204, 232, 286, 287,298, 300, 312
ethical, 222Ethiopian, 350Euthydemus, 374evidence, 95, 138, 148, 192, 227evil-thing-to-learn, 374expression, 2
father, 242, 243, 364, 367, 378, 379
INDEX 397
flute-player, 162flute-playing, 218, 219foreign, 33, 235formal, 159, 190, 197, 207foundation, 147, 200function, 44, 175, 302, 304, 315, 356fundamental, 146, 154, 167, 183, 184
geniuses, 248genus, 2–6, 20, 26, 27, 89, 95, 99, 101,
110–114, 149, 152–158, 163–165, 167, 171, 174, 180, 181,183, 191, 193, 201–205, 209,213–218, 225, 226, 228, 229,233, 244, 251–270, 277, 280,292–295, 297–303, 306, 307,311, 318–323, 365
geometer, 156, 157, 159, 162, 193geometrical, 85, 154, 156, 159, 160,
162, 327, 337, 340, 357, 360geometrician, 102, 219, 231, 278, 337,
361geometry, 26, 154, 156, 157, 159, 162,
180, 183, 212, 219, 319, 343,357, 361, 362
gnomon, 28Gorgias, 364, 389grammar, 1, 2, 5, 18–20, 214, 218, 229,
262, 265, 299, 306grammarian, 1, 220, 233grammatical, 2, 3, 18, 19, 192, 196,
233Greek, 317, 385gymnasium, 270gymnastics, 244
hand-book, 201handbooks, 221harmonic, 154–156, 162, 180harmony, 224, 259, 294harp, 374, 375harp-while-not-harping, 374
harping, 374, 375have
to have, 29having, 2, 12, 23, 68, 89, 133, 141, 161,
164, 174, 177, 186–188, 192,197, 200, 201, 203, 209, 215,220, 238, 254, 277, 279, 282,329, 335, 341, 367, 376, 379
Heraclitus, 220, 334Hippocrates, 361Homer, 44, 328, 349, 359homogeneous, 156, 181, 199homonym, 259, 328, 329honour, 26, 220, 243, 249, 306honourable, 26, 215, 221, 231, 238,
242–244, 249hypotheses, 60, 132, 157, 167, 178,
330, 342hypothesi, 78, 101, 107, 111, 112, 117,
126, 136, 137, 142, 166hypothesis, 84, 93, 103, 124–132, 145,
146, 153, 157, 227, 228, 252,336, 343
hypothetical, 83, 84, 93, 102, 103, 172,192, 227
hypothetically, 83, 84, 172, 191
idea, 289, 296, 307, 309ideal, 175ideas, 237, 301, 307, 309, 321, 343identical, 1, 52, 68, 90–93, 97, 100,
101, 105, 107, 117, 125, 128–131, 136, 141, 149, 151, 154,158, 166, 171, 174, 176, 182,183, 185, 187–190, 192, 193,197, 199, 201–203, 205–208,213, 226, 255, 288, 306, 307,315, 317, 362, 375
identity, 7, 24, 34, 92, 155, 183, 185,202, 203, 207, 209, 354
ignorance, 11, 57, 98, 135, 145, 164,237, 240, 307, 309, 316, 326,
398 INDEX
349, 352–356ignorant, 135, 153, 162, 194, 237, 245,
307, 356, 360, 362, 382ignorantly, 240ignoratio, 353, 354Iliad, 193, 196, 380illogical, 160illusion, 211image, 294, 296images, 31immediate, 138, 139, 145, 147, 153,
155, 161, 163, 164, 167–169,173, 174, 177, 179, 183, 184,190, 194, 195, 199, 200, 208
immediately, 128, 134, 140, 168, 173,181, 188, 211, 277, 331, 343
imperatively, 246imperceptible, 182imperfect, 53, 54, 60, 70, 71, 73, 74, 76,
80, 83, 119impossibile, 58, 60–63, 71–73, 75, 81,
83, 84, 92, 93, 103, 123–126,128, 131, 132, 158, 175, 179,180, 329, 340
impossibilities, 48impossibility, 44, 48, 71, 72, 92, 93,
132, 171, 174, 179, 185, 331,334, 351
indefinite, 15, 32, 39, 41, 43, 53, 54, 57,59–62, 68–70, 74, 75, 77, 78,80, 81, 89, 160, 183, 199, 252,298, 358
indemonstrable, 145–147, 155, 174,180, 184, 188, 194, 196
independent, 31–33, 44, 132, 147, 341,347, 349, 382
indeterminate, 24, 160, 177, 198, 338,378
India, 244Indian, 350indicative, 316individual, 1–7, 14, 20, 26, 34–37, 41,
44, 88, 98, 142, 150, 158, 172,175, 201, 203, 220, 222, 227,228, 237, 244, 253, 255, 257,298, 302, 321, 325, 355, 367,377
indivisible, 146, 173, 174, 192, 199,209, 255
induction, 25, 86, 138, 139, 143, 147,161, 167, 188, 190–192, 209,217, 220, 222, 227, 234, 238,241, 256, 259, 325, 327, 328,335, 347, 367
inductive, 85, 143, 160, 209, 227, 325,343
inequality, 10, 308infer, 84, 108, 127, 142, 152, 153, 160,
179, 190, 199inference, 17, 41, 74, 85, 97, 99, 125,
148, 155, 161, 164–167, 176,179, 182, 190–192, 196, 199,204, 330, 334, 338, 339
inferring, 108, 116infers, 84, 153infima, 201, 202, 204infinite, 146, 168–173, 200, 230, 311,
346, 357infinity, 168, 169, 173, 174, 199inflection, 281, 317, 365, 366inflexion, 224, 240, 248, 251, 260, 262,
287, 309, 317, 321inhere, 95, 146, 149, 151–155, 161–
163, 167, 168, 170, 173–180,184, 185, 189, 196, 197, 201–208, 244, 267, 304, 308
integrity, 19intermediate, 21–24, 139, 163, 168,
172, 191, 223, 260, 331intermediates, 22, 169, 173, 174, 223,
260intuit, 182intuition, 174, 182, 184, 185, 210, 263
INDEX 399
justice, 16, 18, 19, 26, 89, 100, 139, 183,222, 226, 229, 239, 240, 244–248, 253, 256, 259, 260, 264,268, 284, 300, 305, 313, 315,317, 320, 364
king, 364kingdom, 371kopiskon, 366kopiskos, 366
limit, 88, 151, 159, 168, 177, 297, 311,357
logic, 190logical, 39, 44, 46, 48, 222logically, 205, 209logicians, 95love, 26, 137, 146, 220, 223, 248, 305,
318lover, 137lunules, 139, 361Lyceum, 3, 21Lycophron, 368lyre, 368Lysander, 204, 372
magnitude, 154, 156, 184, 218, 354Mandrobulus, 368mathematician, 162mathematics, 143, 159, 160, 162, 167,
183, 189, 224, 331, 359meanings, 36, 99, 196, 222–224, 226,
227, 231, 232, 273, 310, 317,330, 346, 358, 359, 379, 380
medical, 315, 340, 357, 384medicine, 56, 128–130, 159, 162, 183,
213, 219, 224, 232, 243, 296,300, 312, 341, 357
Melissus, 220, 351, 354, 383Meno, 135, 144metaphysical, 185method, 4, 27, 91, 93–95, 106, 126,
128, 131, 147, 155, 158, 170,
190–194, 200–205, 209, 213,228, 235, 238, 261, 262, 270,271, 324, 326, 329, 347, 360–362, 366, 368, 377, 385
Miccalus, 97modality, 71mode, 50, 54, 68–70, 79, 80, 93, 130,
168, 185, 205, 236, 238, 240,255, 268, 281, 340, 348, 352,362, 375, 383, 387
model, 316money, 177, 185, 247, 248, 307, 346,
361mortal, 95, 191, 257, 266, 270, 280,
288, 309, 311Motion, 28multiple, 208, 239, 254, 262, 263, 308,
318multiplication, 343multiplicity, 173, 355, 359multiplied, 367music, 20, 84, 89, 111, 142, 167, 174,
269musical, 43, 97, 106, 149, 159, 175,
192, 217, 233, 269, 370, 379,382
musician, 170, 175, 220, 233, 377
necessary, 12, 15, 16, 21–28, 34, 35,37–39, 45–49, 51, 54–86, 89,90, 92, 93, 95–97, 101, 107–109, 116–120, 123–126, 133,136–138, 141, 142, 146–149,151–153, 157, 158, 161, 164,165, 173, 179, 181, 183, 184,189, 190, 192, 196–198, 200–202, 211, 214, 224, 229, 234–237, 240, 242, 254–256, 263,277, 293, 297, 304, 314, 322,325, 327, 332, 337, 338, 340–342, 345, 350–353, 367, 371,385
400 INDEX
necessitate, 13, 116, 153, 194, 196,197, 200, 206
necessity, 21–23, 36–38, 44, 45, 47–49,54, 55, 58, 60, 62, 63, 66–68,70, 71, 76, 97, 102, 108, 125,146, 147, 149, 152, 153, 181,191, 198, 217, 220, 225, 233–236, 239, 247, 251, 257–259,262–264, 271, 276, 277, 280,297, 298, 301, 303, 308, 314,319–322, 328, 333, 339, 349,353, 364, 370, 372, 373, 376,378, 382
negated, 374, 376negation, 24, 25, 76, 105–107, 125,
145, 161, 162, 164, 169, 179,260, 261, 301, 341, 353, 375,384
negative, 3, 23, 32–36, 39–41, 44, 45,47, 51, 54–82, 85, 87, 88, 90,91, 99, 100, 103–105, 108–129, 131–134, 136, 140, 158,164–170, 175, 178–180, 188,194, 230, 285, 286, 309, 335,362, 380, 387
Nestor, 247nexus, 153, 158Nile, 205nominal, 195nominative, 100, 385nonexistent, 39nonnecessary, 153notable, 211, 218, 221
obscure, 216, 223, 272, 273, 276, 293,294, 316, 367
obscured, 327obscurely, 335obscuring, 86obscurity, 293, 331observation, 162, 327observations, 269
observe, 92, 150, 200, 204, 214, 215,271, 297, 298, 319, 360, 371,386
observed, 184, 185, 231, 238, 293, 351observers, 162observing, 203obstructionists, 370occurs, 7, 161, 162, 164, 182, 243, 298,
315, 336, 341, 351, 358, 386Odysseus, 246, 247olcontradictories, 128ombro, 349opine, 50, 136, 184, 185opines, 184, 185opinion, 7, 14, 44, 88, 131, 140, 157,
175, 176, 184, 185, 211, 218–220, 222, 224, 227, 240, 251,254, 255, 258, 314, 327, 334,337, 339–341, 350, 364, 367,372, 377, 381
opposite, 16, 21–25, 34, 36–38, 40, 41,43, 44, 48–50, 58, 68, 69, 79,107, 120, 128, 129, 134, 137,140, 149, 152, 154, 158, 159,202, 203, 222–224, 230, 246,251, 261, 263, 275, 284, 285,287, 298, 304, 306, 308, 317,320, 325, 326, 329, 333, 335,341, 342, 350, 364, 367, 377,378, 380, 382, 383
opposition, 21, 68, 120, 128, 140, 145,198, 224, 238, 239, 317, 327,364
oppositions, 129optical, 154, 162optician, 162optics, 156, 159, 162oratory, 26orifice, 197origin, 18, 198original, 12, 58, 74, 84, 86, 87, 93, 96,
116, 120–122, 124, 126–128,
INDEX 401
130–132, 140, 148, 158, 209,210, 223, 224, 235, 239, 287,308, 323–325, 332, 334, 338,341, 342, 349–351, 353, 354,356, 357, 363, 371, 379, 382,388
originally, 57, 75, 77, 83, 90, 120, 122,125, 211, 234, 287, 308, 332,335, 338
originate, 17, 198, 209originated, 197ostensive, 83, 84, 92, 93, 126, 128, 131ostensively, 62, 83, 92, 126, 128, 131
paradox, 146, 332, 347, 363, 364, 367,370, 388
paradoxical, 363, 364, 371Parmenides, 386pellucid, 311Peloponnesian, 317penetration, 197people, 9, 16, 18, 19, 38, 141, 144, 185,
212, 214, 217–220, 223, 228,231, 234, 239, 242, 248, 256,264–267, 269, 273, 275, 292,297, 298, 301, 303, 304, 307,309, 310, 312, 322, 324–329,331, 335–339, 341, 344–346,349–353, 356, 358, 361, 363–367, 370–372, 374–376, 378,379, 389
perceive, 181, 182, 233, 307, 368perceived, 14, 135, 187, 265, 335perceives, 233, 368perceiving, 14, 207, 209, 290perceptible, 12, 14, 162perceptibles, 14perception, 11, 12, 14, 17, 102, 181,
182, 187, 192, 209, 218, 220,221, 233, 265, 297, 325–327
perfect, 53, 54, 56–58, 60, 62, 63, 69–71, 73–75, 82, 83, 85, 86, 213,
312perfected, 76, 84perfectly, 58Persian, 197phenomena, 94, 205, 255Philo, 32philosopheme, 339philosopher, 162, 220, 247, 324philosophers, 211, 212, 218–221, 363,
364philosophic, 342philosophical, 212philosophy, 94, 185, 222, 362, 368Phocians, 138, 139Piraeus, 374Pittacus, 141place, 20Plato, 258, 294, 295Platonic, 309play, 363, 366poem, 359poet, 44poetry, 33, 348political, 381position, 20positive, 21possibility, 14, 19, 44, 46, 48, 55, 63,
68–75, 98, 158, 160, 183, 303,319
posterior, 26, 27, 49, 143, 146, 147,178, 186, 198, 199, 275, 279,280, 297, 298, 302
postulate, 157, 190, 202, 238postulated, 151, 340postulates, 157, 178, 339postulating, 191, 342potential, 49, 55, 178, 201potentialities, 49potentiality, 38, 39, 44, 49, 291, 292,
300poverty, 364power, 7, 17, 25, 49, 88, 96, 209, 212,
402 INDEX
221, 223, 224, 248, 337, 342,348, 351, 353, 374, 381
practicable, 49practical, 185, 303, 318, 327practically, 20, 162, 166, 216, 220, 355,
389practice, 226, 316, 337, 342, 362practise, 344practised, 343practising, 344prayer, 33, 349predicability, 2, 71predicable, 1–3, 5, 6, 32, 57, 90, 143,
148, 151, 155, 158, 160–163,166, 169, 172–174, 181, 182,185, 186, 189, 190, 192, 203,206–208, 284, 301, 302
predicate, 2–6, 32, 34–37, 39, 41–43,45, 47, 49, 54, 57, 64, 77, 87–91, 97, 100, 101, 108, 109,128, 131, 132, 134, 138, 143–145, 149, 150, 153, 155, 158–161, 164, 168–172, 174, 176,181, 189, 196, 203, 214, 215,217–219, 228–230, 240–242,254, 267, 269, 274, 277, 279,284, 288–290, 296, 302, 318,324, 355, 370, 377
predication, 1prejudice, 367premise, 152, 191, 192premised, 165premises, 140premising, 190, 191premiss, 42, 53–89, 91–94, 96–100,
102, 104, 108–124, 126–134,136, 138–140, 143–148, 152–161, 163–170, 172, 174, 175,177–184, 188–192, 194–196,199, 200, 207–212, 251, 256,322, 324–327, 329–340, 342,343, 346, 347, 351–354, 356,
363, 367, 368, 371–373, 377,382, 387, 388
presence, 1primary, 3–6, 14, 39, 49, 91, 145, 146,
150–152, 155–157, 163, 168,169, 174, 176, 180, 182, 183,188, 190, 202, 203, 206–212,216, 230, 244, 272, 277, 282,291, 304, 331, 343
prime, 148, 201, 328principal, 49, 53, 88, 89, 94, 96, 108,
130, 182, 183, 211–213, 258,259, 269, 293, 307, 316, 330,331, 334, 343, 346, 357, 358,360–362
principally, 340principle, 45, 49, 51, 130, 135, 143,
221, 239, 244, 246, 251, 255,256, 268, 277, 301, 302, 316,330, 331, 337, 343, 379
prior, 9, 14, 26, 27, 49, 53, 88, 130, 138,145–147, 150, 156, 168, 169,172, 174, 178–180, 188, 198–200, 206, 244, 245, 258, 279,280, 296–299, 302
priority, 26, 180, 296prius, 212, 297privation, 22–25, 40, 187, 194, 224,
230, 239, 261, 285, 296, 301,308, 309
privative, 21–25, 106, 149professors, 389proof, 31, 57, 59, 61, 64, 66–68, 70, 71,
74, 77–83, 87, 91, 92, 94, 95,103, 106, 108, 110, 112, 113,115–119, 121, 122, 126, 127,131, 139–141, 145, 147, 150–152, 154–161, 163, 167, 169–174, 176–179, 183, 191–194,196, 197, 200, 205, 207, 233,238, 317, 325, 330, 339, 347,350–360, 362, 369, 372, 373,
INDEX 403
377, 379, 380proofs, 85, 119, 131, 151, 153, 155,
172, 173, 180, 202, 351, 352,356–358
property, 14, 23, 24, 95, 151, 154, 155,177, 181, 187, 194, 197, 208,213–215, 217, 229, 244, 253,265, 270–293, 322–324, 371,379, 380
proposition, 5, 6, 21, 23, 25–27, 31–48,50, 52, 54, 55, 64, 67–69, 71–86, 89–93, 96, 98, 108, 116–119, 121, 124, 127, 131, 133,135, 141, 145, 148, 152, 153,159, 164, 165, 169, 172, 174,178–180, 213, 214, 217–222,230, 235, 241, 252, 253, 270,322, 323, 325–331, 334–337,339, 340, 342–344, 348, 350,354, 363, 367, 370, 371, 376,379, 386, 387
prosyllogism, 90, 170prosyllogisms, 86, 179, 325protagoras, 365punishment, 220pupil, 145, 157, 167pupils, 389Pythagorean, 198
quadrangular, 18, 19quadruped, 233, 270, 280quadrupeds, 208quale, 171qualia, 183qualitative, 28qualitatively, 6quality, 2, 6–8, 10, 11, 16–20, 22–24,
28, 29, 37, 50, 51, 70, 74, 79,93, 99, 121, 154, 166, 171,176, 201, 217, 218, 222, 224,250, 254, 257, 262, 269, 277,302, 303, 306, 307, 315, 318,
349, 376, 377quanta, 183quantified, 171, 172quantitative, 6, 9, 10quantitatively, 146quantities, 8, 9, 11quantity, 2, 6, 8–11, 19, 29, 201, 217,
218, 224, 306, 307, 318, 349,375, 377
quarter-tone, 174quasi-demonstration, 196
race, 302, 361rare, 18, 236, 238rarefied, 274, 275, 279, 282, 283, 305ratio, 187, 331rational, 49, 184, 282, 286ratios, 207raven, 57, 59, 62, 73, 113, 225real, 1, 37–39, 42, 51, 167, 168, 175,
184, 234, 294–297, 301, 306,312, 335, 342, 346, 351, 358,372, 373, 380, 385
reality, 37, 176, 219, 234, 296, 312, 346,347, 350, 361
realization, 49realize, 330, 379realized, 33, 49reason, 4, 7, 12, 17, 36, 44, 48, 55, 59,
73, 89, 98, 103, 105, 107–109,116, 118, 129–131, 133, 140,143, 152, 153, 158–160, 162,167, 177, 182, 184, 186, 187,191, 194–200, 204, 206, 207,211, 212, 216, 225, 226, 235,252, 271, 273, 279, 282, 283,290, 291, 296, 309, 311, 312,319, 322, 326, 327, 329–332,334–338, 343, 346, 351, 355,356, 358, 359, 362, 365, 366,382, 385, 387–389
reasonable, 220, 237
404 INDEX
reasonableness, 326reasonably, 26reasoned, 152, 153, 155, 156, 161–163,
176, 177, 180, 182, 184, 206,220, 329, 372, 373, 386, 387
reasoner, 361, 362reasoners, 343, 361, 364reasoning, 69, 84, 103, 139, 143, 160,
167, 176, 181, 211, 212, 217,220, 227, 264, 265, 271, 290,304, 309, 315, 319, 320, 322–325, 328–330, 335, 336, 338–340, 343, 345, 346, 351, 357,360–362, 372, 379, 383, 386–389
reasonings, 129, 212, 213, 219, 221,227, 228, 304, 325, 343, 345,353, 359, 371, 379, 388
reasons, 102, 173, 177, 211, 212, 219,273, 291, 333, 339, 345
rebut, 131recall, 388reduce, 62, 96, 98, 102, 105, 128, 346,
347reduced, 63, 83, 92, 103, 105, 188reduces, 147reducible, 84reducing, 63, 96reductio, 58, 63, 76, 77, 81, 83, 93, 131,
132, 158, 175, 179, 180reduction, 61, 67, 92, 93, 103–105,
123, 126, 131, 139, 329reductiones, 84, 340reductions, 84redundancy, 294redundant, 295, 296redundantly, 294refer, 16, 35, 84, 122, 142, 352reference, 3, 5, 6, 9–12, 14–16, 18–23,
25, 26, 29, 31, 34, 35, 40, 41,49, 56, 64, 72, 83, 88, 91, 94,98, 100, 102, 104, 120, 129,
131, 133, 134, 140, 213, 216,217, 324, 328, 363, 388
referred, 173, 182referring, 83, 284refers, 29reflect, 304reflection, 205, 291refutable, 141, 234refutation, 120, 121, 123, 130, 131,
133, 134, 342, 343, 345–347,349–360, 362, 363, 365–371,373–376, 379, 380, 382–384,386
refute, 88, 91, 95, 120, 121, 126, 159,331, 347, 350, 351, 356, 357,364, 369
refuted, 87, 99, 120–124, 131, 273, 330,357, 367, 369–371, 375
refuting, 94, 105, 108, 369, 385relation, 2–4, 8, 10, 11, 13, 15, 19–21,
23, 44, 46, 47, 54, 56–62, 64,65, 73–79, 81, 83, 84, 86–88,93, 94, 99, 104–107, 112, 114,129, 135, 136, 138, 139, 162,168, 187–189, 196, 199, 212,217, 221, 239, 260–263, 267,270, 271, 287, 291, 298–300,303, 304, 306, 307, 312, 315,318, 339, 341, 342, 349–352,357, 361, 365, 375–377, 380–382
relation-white-animal-pitch, 75relation-white-animal-snow, 75relations, 57, 63, 73, 76, 78, 79, 87,
91, 93, 99, 109, 129, 214, 263,304, 321
relationships, 262relative, 8–15, 18, 20, 21, 23, 42, 73, 88,
137, 177, 214, 215, 222, 230,232, 239, 254, 262, 263, 270,271, 285, 298, 300, 303, 305–308, 312, 339, 343, 365, 384
INDEX 405
relatively, 140, 157, 197, 214, 215, 244,270, 271, 291, 292, 303, 357,367, 380
relativity, 242, 243remarked, 215, 298, 379rest, 20rhetoric, 33, 213, 343, 351, 389rhetorical, 138, 143, 367, 389rhetorician, 213, 312, 313rhetoricians, 351right-angles, 353rightly, 107, 152, 233, 279, 284, 308,
320, 337, 342rightness, 233robbery, 315
sameness, 214, 216, 217, 227, 228, 280,317, 319, 355
satisfactory, 389satisfied, 145, 258, 332satisfy, 353say-in-the-present-moment, 374schoinion, 366school, 146, 363schools, 363scientific, 131, 144–148, 151–154, 156,
159, 162, 163, 167, 172, 181,182, 184, 188, 196, 207, 208,210, 233, 297, 325, 357
scientifically, 149, 188scientist, 281–283, 356, 357, 362scientists, 353Scythians, 162sea, 226, 228, 284, 352sea-fight, 37, 39secret, 312, 313secretly, 265self-contradictory, 130self-identical, 183semicircle, 143, 197semicircles, 85, 212
sensation, 214, 221, 223, 226, 237, 239,251, 261, 263, 264, 272, 273,276, 277, 282, 285, 289, 290,304
sense-impression, 209sense-impressions, 209sense-perception, 161, 167, 178, 182,
209, 351sense-perceptions, 182sentence, 31–33, 39–42, 45, 53, 193sentences, 33, 35, 193sentient, 272, 273, 279separate, 8, 33, 42, 43, 47, 128, 155,
167, 175, 222, 295, 314, 358separated, 10separately, 150, 151, 204, 207, 230, 305separates, 270, 295separation, 31sequence, 26, 27, 39, 48, 107, 191,
238–240, 383sequences, 46, 47series, 132, 134, 146, 163, 166, 168–
173, 181, 199, 203, 239, 240,255, 328
servant, 380set, 10, 24, 25, 40, 54, 98, 101, 178, 182,
193, 200, 203, 218, 253, 286,288, 323, 326, 338, 342, 353
sets, 146, 193, 247, 277sexual, 137, 305shameless, 366shamelessness, 314sharpwitted, 298shoe-making, 389shoemaker, 43shoes, 389Sicily, 374sick, 10, 348sickle, 248sickly, 16, 103, 140sign, 32, 99, 141, 142signal, 331
406 INDEX
significance, 11, 13, 31, 32, 36, 41, 331significant, 31–33, 36, 384signified, 95, 193, 224, 318, 319, 352,
355signifies, 66, 149, 176, 193, 196, 197,
213, 217, 218, 224, 257, 269,272, 273, 318, 347, 365
signify, 2, 6, 171, 217, 218, 277, 318,365, 366, 376, 385
signifying, 24, 171, 193, 214, 218, 230,273, 277, 319
signs, 140–142, 153, 351similar, 11, 45, 55, 57, 59, 65–67, 69,
74, 76–79, 82, 92, 98, 104–106, 110, 121, 122, 131, 134,135, 138, 139, 163, 165, 170,176, 185, 203, 224, 260, 284,296, 304, 335, 381
similarity, 11, 97, 204similarly, 5, 7–11, 13, 14, 16–18, 20,
23, 26, 28, 32–34, 38, 39, 43,52, 54, 56, 62–64, 67–69, 76–81, 86, 87, 89, 91–94, 97, 100,101, 103, 104, 106–115, 117,120–124, 126–129, 131, 132,134–137, 139, 140, 166–168,174, 180, 200, 210, 213, 216,222, 248, 260, 329, 331
similars, 140, 227simple, 1, 25, 31, 33, 34, 43, 44, 55, 64,
67–69, 71, 76, 100, 147, 174,177, 202, 273, 289, 311, 322,335, 348, 370, 371, 383
simply, 29, 38, 43, 64, 65, 70, 72, 101,116, 134, 149, 150, 158, 249,267, 282, 289, 301, 340, 354,370–372, 384
simultaneous, 27sine, 179solecism, 347, 356, 365, 366, 385, 386,
388sophism, 339
sophist, 144, 265, 346, 360, 363, 372,373, 376–378, 385
sophistic, 234, 345, 356, 363, 388sophistical, 281, 345–347, 352, 356,
357, 360, 361, 363, 367, 368sophistically, 151, 294sophistry, 330, 361, 388sophists, 34, 152, 220, 346, 356, 361Spartan, 317, 372state, 20subaltern, 201, 202, 225, 226subclasses, 2subdivision, 299, 366subgenera, 204subgenus, 204subject
of affirmation, 39universal, 34
subject-genus, 154, 183, 184subject-matter, 45, 361subjoined, 40subordinate, 2, 89, 91, 108–110, 129,
130, 139, 154, 162, 164–167,205, 256, 257, 299, 300, 303,361
subordinated, 162, 166subsist, 6, 23, 50, 52subsisting, 26, 47subsists, 4, 50subspecies, 27substance, 2–8, 10, 14, 15, 23, 49, 58,
59, 94, 96, 148, 149, 171, 172,176, 180, 184, 188, 192, 193,201, 202, 218, 254, 274, 275,284, 300, 316, 352, 355, 357,365, 375–377
substantial, 171, 172, 191, 195substantially, 171, 191substantival, 32substantive, 384substitute, 187, 230, 232, 274, 308, 365substituted, 80, 84, 98, 147, 217, 311,
INDEX 407
312substituting, 311substitution, 62, 93, 356substratum, 162, 168, 170, 172, 180subverts, 303suicide, 204supposition, 15, 38, 123, 124, 128–
130, 147, 165, 176, 199, 220,318
syllogism, 53, 54, 56–64, 69–104, 108–110, 113, 116–136, 138, 141,143–146, 148, 152, 154, 157,158, 160–164, 167, 169, 174,176, 179, 180, 189, 191–193,195, 196, 208, 273, 326, 328,343, 353, 356
definition, 53perfect, 54
syllogistic, 53, 78, 79, 81, 85, 86, 97,139, 143, 159, 191, 192, 347,386, 387
syllogistically, 53, 83, 84, 86, 89, 92–96, 123, 130, 138
syllogize, 190symbol, 32, 36symbolize, 31, 157symbols, 31, 345synonymous, 225, 259, 268, 309, 310,
314, 321, 350synonymously, 268synonyms, 225synthesis, 191, 201system, 174systematizing, 209
teleological, 197Thebans, 138, 139Themistocles, 370Theodorus, 389theorem, 132, 154–156, 159theorists, 224theory, 147, 162, 198, 199, 220, 362
theses, 219, 220, 228, 363thesis, 84, 86, 97, 99, 113, 128, 130,
131, 133, 145, 146, 220, 232,234, 235, 237–239, 332, 333,336, 342, 346, 348, 355, 356,358, 359, 368, 371, 387, 388
time, 20touto, 365, 366triad, 201triangle, 20, 85, 98, 132, 135, 143, 144,
148–151, 175–178, 182, 187,188, 193, 194, 196, 207, 231,232, 353, 359
triangular, 18–20, 156, 195triballi, 242, 243tripartite, 280trireme, 374tyro, 376
units, 156, 183, 360unity, 33, 42, 43, 156, 189, 192, 196,
202, 216, 217, 254, 255, 267,274, 355
universe, 10, 219, 222, 351univocal, 6univocally, 1, 5, 6
vague, 387valid, 58, 60, 85, 165, 326, 328, 329,
356, 375, 380, 381validly, 160
wisdom, 57, 99, 111, 185, 226, 282,286, 291, 296, 304, 313, 342,346, 361, 380
wise, 41, 141, 304, 346, 364wit, 185, 236, 237
Xenocrates, 235, 296, 317Xulon, 366
Zeno, 132, 335, 361, 379, 386Zeus, 349
