Aristotle Organon

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THE ORGANON

By Aristotle, 350 B.C.E



Categories

1

Things are said to be named'equivocally' when, though they have acommon name, the definitioncorresponding with the name differs foreach. Thus, a real man and a figure ina picture can both lay claim to thename 'animal'; yet these are

equivocally so named, for, though theyhave a common name, the definitioncorresponding with the name differs foreach. For should any one define in whatsense each is an animal, his definitionin the one case will be appropriate tothat case only.

On the other hand, things are said to be named 'univocally' which have both

the name and the definition answeringto the name in common. A man and an oxare both 'animal', and these areunivocally so named, inasmuch as notonly the name, but also the definition,

is the same in both cases: for if a manshould state in what sense each is ananimal, the statement in the one casewould be identical with that in theother.



Things are said to be named'derivatively', which derive their namefrom some other name, but differ fromit in termination. Thus the grammarianderives his name from the word'grammar', and the courageous man fromthe word 'courage'.

2

Forms of speech are either simple orcomposite. 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 never present in a subject. Thus 'man' is predicable of the individual man, and

is never present in a subject.

By being 'present in a subject' I donot mean present as parts are presentin a whole, but being incapable of

existence apart from the said subject.

Some things, again, are present in asubject, but are never predicable of asubject. For instance, a certain point



of grammatical knowledge is present inthe mind, but is not predicable of anysubject; or again, a certain whiteness

may be present in the body (for colourrequires a material basis), yet it isnever predicable of anything.

Other things, again, are both predicable of a subject and present in

a subject. Thus while knowledge is present in the human mind, it is

predicable of grammar.

There is, lastly, a class of thingswhich are neither present in a subjectnor predicable of a subject, such asthe individual man or the individualhorse. But, to speak more generally,that which is individual and has thecharacter of a unit is never predicableof a subject. Yet in some cases thereis nothing to prevent such being

present in a subject. Thus a certain point of grammatical knowledge is present in a subject.

3

When one thing is predicated ofanother, all that which is predicableof the predicate will be predicable



also of the subject. Thus, 'man' is predicated of the individual man; but

'animal' is predicated of 'man'; itwill, therefore, be predicable of theindividual man also: for the individual

man is both 'man' and 'animal'.

If genera are different and co-ordinate, their differentiae arethemselves different in kind. Take asan instance the genus 'animal' and the

genus 'knowledge'. 'With feet', 'two-footed', 'winged', 'aquatic', aredifferentiae of 'animal'; the speciesof knowledge are not distinguished bythe same differentiae. One species ofknowledge does not differ from anotherin being 'two-footed'.

But where one genus is subordinate toanother, there is nothing to preventtheir having the same differentiae: forthe greater class is predicated of thelesser, so that all the differentiae ofthe predicate will be differentiae alsoof the subject.

4

Expressions which are in no waycomposite signify substance, quantity,



quality, relation, place, time, position, state, action, or affection.

To sketch my meaning roughly, examplesof substance are 'man' or 'the horse',of quantity, such terms as 'two cubitslong' or 'three cubits long', ofquality, such attributes as 'white','grammatical'. 'Double', 'half','greater', fall under the category ofrelation; 'in a the market place', 'inthe Lyceum', under that of place;

'yesterday', 'last year', under that oftime. 'Lying', 'sitting', are termsindicating position, 'shod', 'armed',state; 'to lance', 'to cauterize',action; 'to be lanced', 'to becauterized', affection.

No one of these terms, in and byitself, involves an affirmation; it is

by the combination of such terms that positive or negative statements arise.

For every assertion must, as isadmitted, be either true or false,whereas expressions which are not inany way composite such as 'man',

'white', 'runs', 'wins', cannot beeither true or false.



5

Substance, in the truest and primaryand most definite sense of the word, isthat which is neither predicable of asubject nor present in a subject; forinstance, the individual man or horse.But in a secondary sense those thingsare called substances within which, asspecies, the primary substances areincluded; also those which, as genera,

include the species. For instance, theindividual man is included in thespecies 'man', and the genus to whichthe species belongs is 'animal'; these,therefore-that is to say, the species'man' and the genus 'animal,-are termedsecondary substances.

It is plain from what has been saidthat both the name and the definitionof the predicate must be predicable ofthe subject. For instance, 'man' is

predicted of the individual man. Now inthis case the name of the species man'is applied to the individual, for we

use the term 'man' in describing theindividual; and the definition of 'man'will also be predicated of theindividual man, for the individual manis both man and animal. Thus, both the



name and the definition of the speciesare predicable of the individual.

With regard, on the other hand, tothose things which are present in asubject, it is generally the case thatneither their name nor their definitionis predicable of that in which they are

present. Though, however, thedefinition is never predicable, thereis nothing in certain cases to prevent

the name being used. For instance,'white' being present in a body is

predicated of that in which it is present, for a body is called white:

the definition, however, of the colourwhite' is never predicable of the body.

Everything except primary substances iseither predicable of a primarysubstance or present in a primarysubstance. This becomes evident byreference to particular instances whichoccur. 'Animal' is predicated of thespecies 'man', therefore of theindividual man, for if there were no

individual man of whom it could be predicated, it could not be predicated

of the species 'man' at all. Again,colour is present in body, therefore inindividual bodies, for if there were no



individual body in which it was present, it could not be present in body at all. Thus everything except primary substances is either predicated

of primary substances, or is present inthem, and if these last did not exist,it would be impossible for anythingelse to exist.

Of secondary substances, the species is more truly substance than the genus,

being more nearly related to primarysubstance. For if any one should renderan account of what a primary substanceis, he would render a more instructiveaccount, and one more proper to thesubject, by stating the species than bystating the genus. Thus, he would givea more instructive account of anindividual man by stating that he was

man than by stating that he was animal,for the former description is peculiarto the individual in a greater degree,while the latter is too general. Again,the man who gives an account of thenature of an individual tree will give

a more instructive account by mentioning the species 'tree' than by mentioning the genus 'plant'.



Moreover, primary substances are most properly called substances in virtue of

the fact that they are the entitieswhich underlie every. else, and thateverything else is either predicated ofthem or present in them. Now the samerelation which subsists between primarysubstance and everything else subsistsalso between the species and the genus:for the species is to the genus assubject is to predicate, since the

genus is predicated of the species,whereas the species cannot be

predicated of the genus. Thus we have asecond ground for asserting that thespecies is more truly substance thanthe genus.

Of species themselves, except in thecase of such as are genera, no one is

more truly substance than another. Weshould not give a more appropriateaccount of the individual man bystating the species to which he

belonged, than we should of anindividual horse by adopting the same

method of definition. In the same way,of primary substances, no one is moretruly substance than another; anindividual man is not more trulysubstance than an individual ox.







substance cannot be present in asubject.

Yet this is not peculiar to substance,for it is also the case thatdifferentiae cannot be present insubjects. The characteristics'terrestrial' and 'two-footed' are

predicated of the species 'man', butnot present in it. For they are not in

man. Moreover, the definition of the

differentia may be predicated of thatof which the differentia itself is

predicated. For instance, if thecharacteristic 'terrestrial' is

predicated of the species 'man', thedefinition also of that characteristic

may be used to form the predicate ofthe species 'man': for 'man' isterrestrial.

The fact that the parts of substancesappear to be present in the whole, asin a subject, should not make usapprehensive lest we should have toadmit that such parts are not

substances: for in explaining the phrase 'being present in a subject', we

stated' that we meant 'otherwise thanas parts in a whole'.





differentia forms the predicate, theseare predicated univocally.

All substance appears to signify thatwhich is individual. In the case of

primary substance this is indisputablytrue, for the thing is a unit. In thecase of secondary substances, when wespeak, for instance, of 'man' or'animal', our form of speech gives theimpression that we are here also

indicating that which is individual, but the impression is not strictly

true; for a secondary substance is notan individual, but a class with acertain qualification; for it is notone and single as a primary substanceis; the words 'man', 'animal', are

predicable of more than one subject.

Yet species and genus do not merelyindicate quality, like the term'white'; 'white' indicates quality andnothing further, but species and genusdetermine the quality with reference toa substance: they signify substance

qualitatively differentiated. Thedeterminate qualification covers alarger field in the case of the genusthat in that of the species: he whouses the word 'animal' is herein using



a word of wider extension than he whouses the word 'man'.

Another mark of substance is that ithas no contrary. What could be thecontrary of any primary substance, suchas the individual man or animal? It hasnone. Nor can the species or the genushave a contrary. Yet thischaracteristic is not peculiar tosubstance, but is true of many other

things, such as quantity. There isnothing that forms the contrary of 'twocubits long' or of 'three cubits long',or of 'ten', or of any such term. A man

may contend that 'much' is the contraryof 'little', or 'great' of 'small', butof definite quantitative terms nocontrary exists.

Substance, again, does not appear toadmit of variation of degree. I do not

mean by this that one substance cannot be more or less truly substance than

another, for it has already beenstated' that this is the case; but that

no single substance admits of varyingdegrees within itself. For instance,one particular substance, 'man', cannot

be more or less man either than himselfat some other time or than some other





everything that is not substance. Butone and the selfsame substance, whileretaining its identity, is yet capableof admitting contrary qualities. Thesame individual person is at one timewhite, at another black, at one timewarm, at another cold, at one timegood, at another bad. This capacity isfound nowhere else, though it might be

maintained that a statement or opinionwas an exception to the rule. The same

statement, it is agreed, can be bothtrue and false. For if the statement'he is sitting' is true, yet, when the

person in question has risen, the samestatement will be false. The sameapplies to opinions. For if any onethinks truly that a person is sitting,yet, when that person has risen, thissame opinion, if still held, will befalse. Yet although this exception may

be allowed, there is, nevertheless, adifference in the manner in which thething takes place. It is by themselveschanging that substances admit contraryqualities. It is thus that that which

was hot becomes cold, for it hasentered into a different state.Similarly that which was white becomes

black, and that which was bad good, bya process of change; and in the same



way in all other cases it is bychanging that substances are capable ofadmitting contrary qualities. Butstatements and opinions themselvesremain unaltered in all respects: it is

by the alteration in the facts of thecase that the contrary quality comes to

be theirs. The statement 'he issitting' remains unaltered, but it isat one time true, at another false,according to circumstances. What has

been said of statements applies also toopinions. Thus, in respect of the

manner in which the thing takes place,it is the peculiar mark of substancethat it should be capable of admittingcontrary qualities; for it is by itselfchanging that it does so.

If, then, a man should make thisexception and contend that statementsand opinions are capable of admittingcontrary qualities, his contention isunsound. For statements and opinionsare said to have this capacity, not

because they themselves undergo

modification, but because this modification occurs in the case of

something else. The truth or falsity ofa statement depends on facts, and noton any power on the part of the







Moreover, it is a discrete quantity forits parts have no common boundary.There is no common boundary at whichthe syllables join, but each isseparate and distinct from the rest.

A line, on the other hand, is acontinuous quantity, for it is possibleto find a common boundary at which its

parts join. In the case of the line,this common boundary is the point; in

the case of the plane, it is the line:for the parts of the plane have also acommon boundary. Similarly you can finda common boundary in the case of the

parts of a solid, namely either a lineor a plane.

Space and time also belong to thisclass of quantities. Time, past,

present, and future, forms a continuouswhole. Space, likewise, is a continuousquantity; for the parts of a solidoccupy a certain space, and these havea common boundary; it follows that the

parts of space also, which are occupied

by the parts of the solid, have thesame common boundary as the parts ofthe solid. Thus, not only time, butspace also, is a continuous quantity,for its parts have a common boundary.







taken, to the effect that it lasted ayear, or something of that sort. In thesame way, he would explain the size ofa white object in terms of surface, forhe would state the area which itcovered. Thus the things already

mentioned, and these alone, are intheir intrinsic nature quantities;nothing else can claim the name in itsown right, but, if at all, only in asecondary sense.

Quantities have no contraries. In thecase of definite quantities this isobvious; thus, there is nothing that isthe 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 thecontrary of 'little', and 'great' of'small'. But these are notquantitative, but relative; things arenot great or small absolutely, they areso called rather as the result of anact of comparison. For instance, a

mountain is called small, a grain

large, in virtue of the fact that thelatter is greater than others of itskind, the former less. Thus there is areference here to an external standard,for if the terms 'great' and 'small'





in comparison with one thing, and greatin comparison with another, so that thesame thing comes to be both small andgreat at one and the same time, and isof such a nature as to admit contraryqualities 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 capableof admitting contrary qualities, yet no

one is at the same time both sick andhealthy, nothing is at the same time

both white and black. Nor is thereanything which is qualified in contraryways at one and the same time.

Moreover, if these were contraries,they would themselves be contrary tothemselves. For if 'great' is thecontrary of 'small', and the same thingis both great and small at the sametime, then 'small' or 'great' is thecontrary of itself. But this isimpossible. The term 'great',therefore, is not the contrary of the

term 'small', nor 'much' of 'little'. And even though a man should call these

terms not relative but quantitative,they would not have contraries.



It is in the case of space thatquantity most plausibly appears toadmit of a contrary. For men define theterm 'above' as the contrary of'below', when it is the region at thecentre they mean by 'below'; and thisis so, because nothing is farther fromthe extremities of the universe thanthe region at the centre. Indeed, itseems that in defining contraries ofevery kind men have recourse to a

spatial metaphor, for they say thatthose things are contraries which,within the same class, are separated bythe greatest possible distance.

Quantity does not, it appears, admit ofvariation of degree. One thing cannot

be two cubits long in a greater degreethan another. Similarly with regard tonumber: what is 'three' is not moretruly three than what is 'five' isfive; nor is one set of three moretruly three than another set. Again,one period of time is not said to be

more truly time than another. Nor is

there any other kind of quantity, ofall that have been mentioned, withregard to which variation of degree can

be predicated. The category of







with son with another; for the mountainclaims this attribute by comparisonwith something. Again, that which iscalled similar must be similar tosomething else, and all other suchattributes have this externalreference. It is to be noted that lyingand standing and sitting are particularattitudes, but attitude is itself arelative term. To lie, to stand, to beseated, are not themselves attitudes,

but take their name from the aforesaidattitudes.

It is possible for relatives to havecontraries. Thus virtue has a contrary,vice, these both being relatives;knowledge, too, has a contrary,ignorance. But this is not the mark ofall relatives; 'double' and 'triple'have no contrary, nor indeed has anysuch term.

It also appears that relatives canadmit of variation of degree. For'like' and 'unlike', 'equal' and

'unequal', have the modifications'more' and 'less' applied to them, andeach of these is relative in character:for the terms 'like' and 'unequal' bear'unequal' bear a reference to something











termed, then, when all other attributesare removed and that alone is left invirtue of which it was stated to becorrelative, the stated correlationwill be found to have disappeared.

For suppose the correlative of 'theslave' should be said to be 'the man',or the correlative of 'the wing"the

bird'; if the attribute 'master' bewithdrawn from' the man', the

correlation between 'the man' and 'theslave' will cease to exist, for if the

man is not a master, the slave is not aslave. Similarly, if the attribute'winged' be withdrawn from 'the bird','the wing' will no longer be relative;for if the so-called correlative is notwinged, it follows that 'the wing' hasno correlative.

Thus it is essential that thecorrelated terms should be exactlydesignated; if there is a nameexisting, the statement will be easy;if not, it is doubtless our duty to

construct names. When the terminologyis thus correct, it is evident that allcorrelatives are interdependent.







not exist, it follows that perceptionalso ceases to exist. Thus theannihilation of the perceptibleinvolves that of perception.

But the annihilation of perception doesnot involve that of the perceptible.For if the animal is annihilated, itfollows that perception also isannihilated, but perceptibles such as

body, heat, sweetness, bitterness, and

so on, will remain.

Again, perception is generated at thesame time as the perceiving subject,for it comes into existence at the sametime as the animal. But the perceptiblesurely exists before perception; forfire and water and such elements, outof which the animal is itself composed,exist before the animal is an animal atall, and before perception. Thus itwould seem that the perceptible exists

before perception.

It may be questioned whether it is true

that no substance is relative, as seemsto be the case, or whether exception isto be made in the case of certainsecondary substances. With regard to

primary substances, it is quite true









relatives, and, this being the case, itwould be true to say that no substanceis relative in character. It is perhapsa difficult matter, in such cases, to

make a positive statement without moreexhaustive examination, but to haveraised questions with regard to detailsis not without advantage.

8

By 'quality' I mean that in virtue ofwhich people are said to be such andsuch.

Quality is a term that is used in manysenses. One sort of quality let us call'habit' or 'disposition'. Habit differsfrom disposition in being more lastingand more firmly established. Thevarious kinds of knowledge and ofvirtue are habits, for knowledge, evenwhen acquired only in a moderatedegree, is, it is agreed, abiding inits character and difficult todisplace, unless some great mental

upheaval takes place, through diseaseor any such cause. The virtues, also,such as justice, self-restraint, and soon, are not easily dislodged ordismissed, so as to give place to vice.









which admit them are affected. What is meant is that these said qualities are

capable of producing an 'affection' inthe way of perception. For sweetnesshas the power of affecting the sense oftaste; heat, that of touch; and so itis with the rest of these qualities.

Whiteness and blackness, however, andthe other colours, are not said to beaffective qualities in this sense, but

-because they themselves are theresults of an affection. It is plainthat many changes of colour take place

because of affections. When a man isashamed, he blushes; when he is afraid,he becomes pale, and so on. So true isthis, that when a man is by natureliable to such affections, arising fromsome concomitance of elements in hisconstitution, it is a probableinference that he has the correspondingcomplexion of skin. For the samedisposition of bodily elements, whichin the former instance was momentarily

present in the case of an access of

shame, might be a result of a man'snatural temperament, so as to producethe corresponding colouring also as anatural characteristic. All conditions,therefore, of this kind, if caused by





and which has its origin in certaindeep-seated affections is called aquality. I mean such conditions asinsanity, irascibility, and so on: for

people are said to be mad or irasciblein virtue of these. Similarly thoseabnormal psychic states which are notinborn, but arise from the concomitanceof certain other elements, and aredifficult to remove, or altogether

permanent, are called qualities, for in

virtue of them men are said to be suchand such.

Those, however, which arise from causeseasily rendered ineffective are calledaffections, not qualities. Suppose thata man is irritable when vexed: he isnot even spoken of as a bad-tempered

man, when in such circumstances heloses his temper somewhat, but ratheris said to be affected. Such conditionsare 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 andcurvedness and any other qualities ofthis type; each of these defines athing as being such and such. Because







exists for the quality, that whichtakes its character from the qualityhas a name that is not a derivative.For instance, the upright man takes hischaracter from the possession of thequality of integrity, but the namegiven him is not derived from the word'integrity'. Yet this does not occuroften.

We may therefore state that those

things are said to be possessed of somespecific quality which have a namederived from that of the aforesaidquality, or which are in some other waydependent on it.

One quality may be the contrary ofanother; thus justice is the contraryof injustice, whiteness of blackness,and so on. The things, also, which aresaid to be such and such in virtue ofthese qualities, may be contrary theone to the other; for that which isunjust is contrary to that which isjust, that which is white to that which

is black. This, however, is not alwaysthe case. Red, yellow, and suchcolours, though qualities, have nocontraries.







for to neither is the definition of thecircle appropriate. In short, if thedefinition of the term proposed is notapplicable to both objects, they cannot

be compared. Thus it is not allqualities which admit of variation ofdegree.

Whereas none of the characteristics Ihave mentioned are peculiar to quality,the fact that likeness and unlikeness

can be predicated with reference toquality only, gives to that categoryits distinctive feature. One thing islike another only with reference tothat in virtue of which it is such andsuch; thus this forms the peculiar markof quality.

We must not be disturbed because it may be argued that, though proposing to

discuss the category of quality, wehave included in it many relativeterms. We did say that habits anddispositions were relative. In

practically all such cases the genus is

relative, the individual not. Thusknowledge, as a genus, is explained byreference to something else, for we

mean a knowledge of something. But particular branches of knowledge are



not thus explained. The knowledge ofgrammar is not relative to anythingexternal, nor is the knowledge of

music, but these, if relative at all,are relative only in virtue of theirgenera; thus grammar is said be theknowledge of something, not the grammarof something; similarly music is theknowledge of something, not the musicof something.

Thus individual branches of knowledgeare not relative. And it is because we

possess these individual branches ofknowledge that we are said to be suchand such. It is these that we actually

possess: we are called experts becausewe possess knowledge in some particular

branch. Those particular branches,therefore, of knowledge, in virtue ofwhich we are sometimes said to be suchand such, are themselves qualities, andare not relative. Further, if anythingshould happen to fall within both thecategory of quality and that ofrelation, there would be nothing

extraordinary in classing it under boththese heads.



9

Action and affection both admit ofcontraries and also of variation ofdegree. Heating is the contrary ofcooling, being heated of being cooled,

being glad of being vexed. Thus theyadmit of contraries. They also admit ofvariation of degree: for it is possibleto heat in a greater or less degree;also to be heated in a greater or less

degree. Thus action and affection alsoadmit of variation of degree. So much,then, is stated with regard to thesecategories.

We spoke, moreover, of the category of position when we were dealing with that

of relation, and stated that such termsderived their names from those of thecorresponding attitudes.

As for the rest, time, place, state,since they are easily intelligible, Isay no more about them than was said atthe beginning, that in the category of

state are included such states as'shod', 'armed', in that of place 'inthe Lyceum' and so on, as was explained

before.







have no intermediate, but those in thecase of which no such necessityobtains, always have an intermediate.Thus disease and health are naturally

present in the body of an animal, andit is necessary that either the one orthe other should be present in the bodyof an animal. Odd and even, again, are

predicated of number, and it isnecessary that the one or the othershould be present in numbers. Now there

is no intermediate between the terms ofeither of these two pairs. On the otherhand, in those contraries with regardto which no such necessity obtains, wefind an intermediate. Blackness andwhiteness are naturally present in the

body, but it is not necessary thateither the one or the other should be

present in the body, inasmuch as it isnot true to say that everybody must bewhite or black. Badness and goodness,again, are predicated of man, and of

many other things, but it is notnecessary that either the one qualityor the other should be present in that

of which they are predicated: it is nottrue to say that everything that may begood or bad must be either good or bad.These pairs of contraries haveintermediates: the intermediates



between white and black are grey,sallow, and all the other colours thatcome between; the intermediate betweengood and bad is that which is neitherthe one nor the other.

Some intermediate qualities have names,such as grey and sallow and all theother colours that come between whiteand black; in other cases, however, itis not easy to name the intermediate,

but we must define it as that which isnot either extreme, as in the case ofthat which is neither good nor bad,neither just nor unjust.

(iii) 'privatives' and 'Positives' havereference to the same subject. Thus,sight and blindness have reference tothe eye. It is a universal rule thateach of a pair of opposites of thistype has reference to that to which the

particular 'positive' is natural. Wesay that that is capable of some

particular faculty or possession hassuffered privation when the faculty or

possession in question is in no way present in that in which, and at the

time at which, it should naturally be present. We do not call that toothless

which has not teeth, or that blind















impossible. There may be a change from possession to privation, but not from privation to possession. The man who

has become blind does not regain hissight; the man who has become bald doesnot regain his hair; the man who haslost his teeth does not grow his grow anew set. (iv) Statements opposed asaffirmation and negation belong

manifestly to a class which isdistinct, for in this case, and in this

case only, it is necessary for the oneopposite to be true and the otherfalse.

Neither in the case of contraries, norin the case of correlatives, nor in thecase of 'positives' and 'privatives',is it necessary for one to be true andthe other false. Health and disease arecontraries: neither of them is true orfalse. 'Double' and 'half' are opposedto each other as correlatives: neitherof them is true or false. The case isthe same, of course, with regard to'positives' and 'privatives' such as

'sight' and 'blindness'. In short,where there is no sort of combinationof words, truth and falsity have no

place, and all the opposites we have





is not yet able to acquire the power ofvision, both are false, as also ifSocrates is altogether non-existent.

But in the case of affirmation andnegation, whether the subject exists ornot, one is always false and the othertrue. For manifestly, if Socratesexists, one of the two propositions'Socrates is ill', 'Socrates is notill', is true, and the other false.

This is likewise the case if he doesnot exist; for if he does not exist, tosay that he is ill is false, to saythat he is not ill is true. Thus it isin the case of those opposites only,which are opposite in the sense inwhich the term is used with referenceto affirmation and negation, that therule holds good, that one of the pair

must be true and the other false.

11

That the contrary of a good is an evilis shown by induction: the contrary of

health is disease, of courage,cowardice, and so on. But the contraryof an evil is sometimes a good,sometimes an evil. For defect, which isan evil, has excess for its contrary,



this also being an evil, and the mean.which is a good, is equally thecontrary of the one and of the other.It is only in a few cases, however,that we see instances of this: in most,the contrary of an evil is a good.

In the case of contraries, it is notalways necessary that if one exists theother should also exist: for if all

become healthy there will be health and

no disease, and again, if everythingturns white, there will be white, butno black. Again, since the fact thatSocrates is ill is the contrary of thefact that Socrates is well, and twocontrary conditions cannot both obtainin one and the same individual at thesame time, both these contraries couldnot exist at once: for if that Socrateswas well was a fact, then that Socrateswas ill could not possibly be one.

It is plain that contrary attributes must needs be present in subjects which belong to the same species or genus.

Disease and health require as theirsubject the body of an animal; whiteand black require a body, withoutfurther qualification; justice and











species. These are distinguished withinthe same genus, and are opposed each toeach, for the genus 'animal' has the'winged', the 'terrestrial', and the'water' species, and no one of these is

prior or posterior to another; on thecontrary, all such things appear to be'simultaneous' in nature. Each of thesealso, the terrestrial, the winged, andthe water species, can be divided againinto subspecies. Those species, then,

also will be 'simultaneous' point ofnature, which, belonging to the samegenus, are distinguished each from each

by one and the same method ofdifferentiation.

But genera are prior to species, forthe sequence of their being cannot bereversed. If there is the species'water-animal', there will be the genus'animal', but granted the being of thegenus 'animal', it does not follownecessarily that there will be thespecies 'water-animal'.

Those things, therefore, are said to be'simultaneous' in nature, the being ofeach of which involves that of theother, while at the same time neitheris in any way the cause of the other's







the contrary of motion downwards andvice versa.

In the case of that sort of motionwhich yet remains, of those that have

been enumerated, it is not easy tostate what is its contrary. It appearsto have no contrary, unless one shoulddefine the contrary here also either as'rest in its quality' or as 'change inthe direction of the contrary quality',

just as we defined the contrary ofchange of place either as rest in a

place or as change in the reversedirection. For a thing is altered whenchange of quality takes place;therefore either rest in its quality orchange in the direction of the contrary

may be called the contrary of thisqualitative form of motion. In this way

becoming white is the contrary of becoming black; there is alteration in

the contrary direction, since a changeof a qualitative nature takes place.

15

The term 'to have' is used in varioussenses. In the first place it is usedwith reference to habit or dispositionor any other quality, for we are said



to 'have' a piece of knowledge or avirtue. Then, again, it has referenceto quantity, as, for instance, in thecase of a man's height; for he is saidto 'have' a height of three or fourcubits. It is used, moreover, withregard to apparel, a man being said to'have' a coat or tunic; or in respectof something which we have on a part ofourselves, as a ring on the hand: or inrespect of something which is a part of

us, as hand or foot. The term refersalso to content, as in the case of avessel and wheat, or of a jar and wine;a jar is said to 'have' wine, and acorn-measure wheat. The expression insuch cases has reference to content. Orit refers to that which has beenacquired; we are said to 'have' a houseor 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 use ofit we mean simply that the husbandlives with the wife.

Other senses of the word might perhaps be found, but the most ordinary ones

have all been enumerated.







a noun or name-it is only so when it becomes a symbol; inarticulate sounds,

such as those which brutes produce, aresignificant, yet none of theseconstitutes a noun.

The expression ‘not-man’ is not a noun.There is indeed no recognized term bywhich we may denote such an expression,for it is not a sentence or a 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 ofthese cases of a noun is in otherrespects the same as that of the noun

proper, but, when coupled with ‘is’,‘was’, or will be’, they do not, asthey are, form a proposition eithertrue or false, and this the noun properalways does, under these conditions.Take the words ‘of Philo is’ or ‘of or‘of Philo is not’; these words do not,as they stand, form either a true or a

false proposition.







meaning, but does not constitute a proposition, either positive or

negative. It is only when other wordsare added that the whole will form anaffirmation or denial. But if weseparate one syllable of the word‘human’ from the other, it has no

meaning; similarly in the word ‘mouse’,the part ‘ouse’ has no meaning initself, but is merely a sound. Incomposite words, indeed, the parts

contribute to the meaning of the whole;yet, as has been pointed out, they havenot an independent meaning.

Every sentence has meaning, not as being the natural means by which a physical faculty is realized, but, as

we have said, by convention. Yet everysentence is not a proposition; onlysuch are propositions as have in themeither truth or falsity. Thus a prayeris a sentence, but is neither true norfalse.

Let us therefore dismiss all other

types of sentence but the proposition,for this last concerns our presentinquiry, whereas the investigation ofthe others belongs rather to the studyof rhetoric or of poetry.







is present or of something which isnot, and since these same affirmationsand denials are possible with referenceto those times which lie outside the

present, it would be possible tocontradict any affirmation or denial.Thus it is plain that every affirmationhas an opposite denial, and similarlyevery denial an opposite affirmation.

We will call such a pair of

propositions a pair of contradictories.Those positive and negative

propositions are said to becontradictory which have the samesubject and predicate. The identity ofsubject and of predicate must not be‘equivocal’. Indeed there aredefinitive qualifications besides this,which we make to meet the casuistriesof sophists.

7

Some things are universal, othersindividual. By the term ‘universal’ I

mean that which is of such a nature asto be predicated of many subjects, by‘individual’ that which is not thus

predicated. Thus ‘man’ is a universal,‘Callias’ an individual.



Our propositions necessarily sometimesconcern a universal subject, sometimesan individual.

If, then, a man states a positive and anegative proposition of universalcharacter with regard to a universal,these two propositions are ‘contrary’.By the expression ‘a proposition ofuniversal character with regard to 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 contrary. As instances of propositions made with

regard to a universal, but not ofuniversal character, we may take the‘propositions ‘man is white’, ‘man isnot white’. ‘Man’ is a universal, butthe proposition is not made as ofuniversal character; for the word

‘every’ does not make the subject auniversal, but rather gives the

proposition a universal character. If,however, both predicate and subject aredistributed, the proposition thus



constituted is contrary to truth; noaffirmation will, under suchcircumstances, be true. The proposition‘every man is every animal’ is anexample of this type.

An affirmation is opposed to a denialin the sense which I denote by the term‘contradictory’, when, while thesubject remains the same, theaffirmation is of universal character

and the denial is not. The affirmation‘every man is white’ is thecontradictory of the denial ‘not every

man is white’, or again, the proposition ‘no man is white’ is the

contradictory of the proposition ‘some men are white’. But propositions are

opposed as contraries when both theaffirmation and the denial areuniversal, as in the sentences ‘every

man 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, but the

contradictories of a pair of contrariescan sometimes both be true withreference to the same subject; forinstance ‘not every man is white’ andsome men are white’ are both true. Of



such corresponding positive andnegative propositions as refer touniversals and have a universalcharacter, one must be true and theother false. This is the case also whenthe reference is to individuals, as inthe propositions ‘Socrates is white’,‘Socrates is not white’.

When, on the other hand, the referenceis to universals, but the propositions

are not universal, it is not always thecase that one is true and the otherfalse, for it is possible to statetruly that man is white and that man isnot white and that man is beautiful andthat man is not beautiful; for if a manis deformed he is the reverse of

beautiful, also if he is progressingtowards beauty he is not yet beautiful.

This statement might seem at firstsight to carry with it a contradiction,owing to the fact that the proposition‘man is not white’ appears to beequivalent to the proposition ‘no man

is white’. This, however, is not thecase, nor are they necessarily at thesame time true or false.



It is evident also that the denialcorresponding to a single affirmationis itself single; for the denial mustdeny just that which the affirmationaffirms concerning the same subject,and must correspond with theaffirmation both in the universal or

particular character of the subject andin the distributed or undistributedsense in which it is understood.

For instance, the affirmation ‘Socratesis white’ has its proper denial in the

proposition ‘Socrates is not white’. Ifanything else be negatively predicatedof the subject or if anything else bethe subject though the predicate remainthe same, the denial will not be thedenial proper to that affirmation, buton that is distinct.

The denial proper to the affirmation‘every man is white’ is ‘not every manis white’; that proper to theaffirmation ‘some men are white’ is ‘no

man is white’, while that proper to the

affirmation ‘man is white’ is ‘man isnot white’.

We have shown further that a singledenial is contradictorily opposite to a



single affirmation and we haveexplained which these are; we have alsostated that contrary are distinct fromcontradictory propositions and whichthe contrary are; also that with regardto a pair of opposite propositions itis not always the case that one is trueand the other false. We have pointedout, moreover, what the reason of thisis and under what circumstances thetruth of the one involves the falsity

of the other.

8

An affirmation or denial is single, ifit indicates some one fact about someone subject; it matters not whether thesubject is universal and whether thestatement has a universal character, orwhether this is not so. Such single

propositions are: ‘every man is white’,‘not every man is white’;’man iswhite’,’man is not white’; ‘no man iswhite’, ‘some men are white’; providedthe word ‘white’ has one meaning. If,

on the other hand, one word has two meanings which do not combine to form

one, the affirmation is not single. Forinstance, if a man should establish thesymbol ‘garment’ as significant both of





true and the other false; whereas whenthe subject is universal, but the

propositions are not of a universalcharacter, there is no such necessity.

We have discussed this type also in a previous chapter.

When the subject, however, isindividual, and that which is

predicated of it relates to the future,the case is altered. For if all

propositions whether positive ornegative are either true or false, thenany given predicate must either belongto the subject or not, so that if one

man affirms that an event of a givencharacter will take place and anotherdenies it, it is plain that thestatement of the one will correspondwith 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 tothe future.

Thus, if it is true to say that a thing

is white, it must necessarily be white;if the reverse proposition is true, itwill of necessity not be white. Again,if it is white, the proposition statingthat it is white was true; if it is not





it was always true to say that a thingis or will be, it is not possible thatit should not be or not be about to be,and when a thing cannot not come to be,it is impossible that it should notcome to be, and when it is impossiblethat it should not come to be, it mustcome to be. All, then, that is about to

be must of necessity take place. Itresults from this that nothing isuncertain or fortuitous, for if it were

fortuitous it would not be necessary.

Again, to say that neither theaffirmation nor the denial is true,

maintaining, let us say, that an eventneither will take place nor will nottake place, is to take up a positionimpossible to defend. In the first

place, though facts should prove theone proposition false, the oppositewould still be untrue. Secondly, if itwas true to say that a thing was bothwhite and large, both these qualities

must necessarily belong to it; and ifthey will belong to it the next day,

they must necessarily belong to it thenext day. But if an event is neither totake place nor not to take place thenext day, the element of chance will beeliminated. For example, it would be



necessary that a sea-fight shouldneither take place nor fail to take

place on the next day.

These awkward results and others of thesame kind follow, if it is anirrefragable law that of every pair ofcontradictory propositions, whetherthey have regard to universals and arestated as universally applicable, orwhether they have regard to

individuals, one must be true and theother false, and that there are no realalternatives, but that all that is ortakes place is the outcome ofnecessity. There would be no need todeliberate or to take trouble, on thesupposition that if we should adopt acertain course, a certain result wouldfollow, while, if we did not, theresult would not follow. For a man may

predict an event ten thousand years beforehand, and another may predict the

reverse; that which was truly predictedat the moment in the past will ofnecessity take place in the fullness of

time.

Further, it makes no difference whether people have or have not actually made

the contradictory statements. For it is





events also therefore may either take place or not take place. There are many

obvious instances of this. It is possible that this coat may be cut in

half, and yet it may not be cut inhalf, but wear out first. In the sameway, it is possible that it should not

be cut in half; unless this were so, itwould not be possible that it shouldwear out first. So it is therefore withall other events which possess this

kind of potentiality. It is therefore plain that it is not of necessity that

everything is or takes place; but insome instances there are realalternatives, in which case theaffirmation is no more true and no morefalse than the denial; while someexhibit a predisposition and generaltendency in one direction or the other,and yet can issue in the oppositedirection by exception.

Now that which is must needs be when itis, and that which is not must needsnot be when it is not. Yet it cannot be

said without qualification that allexistence and non-existence is theoutcome of necessity. For there is adifference between saying that thatwhich is, when it is, must needs be,





true and the other false, but we cannotsay determinately that this or that isfalse, but must leave the alternativeundecided. One may indeed be morelikely to be true than the other, butit cannot be either actually true oractually false. It is therefore plainthat it is not necessary that of anaffirmation and a denial one should betrue and the other false. For in thecase of that which exists potentially,

but not actually, the rule whichapplies to that which exists actuallydoes not hold good. The case is ratheras we have indicated.

10

An affirmation is the statement of afact with regard to a subject, and thissubject is either a noun or that whichhas no name; the subject and predicatein an affirmation must each denote asingle thing. I have already explained’what is meant by a noun and by thatwhich has no name; for I stated that

the expression ‘not-man’ was not anoun, in the proper sense of the word,

but an indefinite noun, denoting as itdoes in a certain sense a single thing.Similarly the expression ‘does not



enjoy health’ is not a verb proper, butan indefinite verb. Every affirmation,then, and every denial, will consist ofa noun and a verb, either definite orindefinite.

There can be no affirmation or denialwithout a verb; for the expressions‘is’, ‘will be’, ‘was’, ‘is coming to

be’, and the like are verbs accordingto our definition, since besides their

specific meaning they convey the notionof time. Thus the primary affirmationand denial are ‘as follows: ‘man is’,‘man is not’. Next to these, there arethe propositions: ‘not-man is’, ‘not-

man is not’. Again we have the propositions: ‘every man is, ‘every man

is not’, ‘all that is not-man is’, ‘allthat is not-man is not’. The sameclassification holds good with regardto such periods of time as lie outsidethe present.

When the verb ‘is’ is used as a thirdelement in the sentence, there can be

positive and negative propositions oftwo sorts. Thus in the sentence ‘man isjust’ the verb ‘is’ is used as a thirdelement, call it verb or noun, whichyou will. Four propositions, therefore,





A'. Affirmation B'. DenialEvery man is just Not every man is just

\ /

X/ \D'. Denial C'. Affirmation

Yet here it is not possible, in thesame way as in the former case, thatthe propositions joined in the table bya diagonal line should both be true;

though under certain circumstances thisis the case.

We have thus set out two pairs ofopposite propositions; there are

moreover two other pairs, if a term beconjoined with ‘not-man’, the latterforming a kind of subject. Thus:

A." B." Not-man is just Not-man is not just

\ /X

D." / \ C." Not-man is not not-just Not-man is not-just

This is an exhaustive enumeration ofall the pairs of opposite propositionsthat can possibly be framed. This lastgroup should remain distinct from thosewhich preceded it, since it employs asits subject the expression ‘not-man’.



When the verb ‘is’ does not fit the

structure of the sentence (forinstance, when the verbs ‘walks’,‘enjoys health’ are used), that schemeapplies, which 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 inthese propositions use the expression‘not every man’. The negative must beattached to the word ‘man’, for theword ‘every’ does not give to thesubject a universal significance, butimplies that, as a subject, it isdistributed. This is plain from thefollowing pairs: ‘man enjoys health’,‘man does not enjoy health’; ‘not-manenjoys health’, ‘not man does not enjoyhealth’. These propositions differ fromthe former in being indefinite and notuniversal in character. Thus the

adjectives ‘every’ and no additionalsignificance except that the subject,whether in a positive or in a negativesentence, is distributed. The rest of



the sentence, therefore, will in eachcase be the same.

Since the contrary of the proposition‘every animal is just’ is ‘no animal isjust’, it is plain that these two

propositions will never both be true atthe same time or with reference to thesame subject. Sometimes, however, thecontradictories of these contrarieswill both be true, as in the instance

before us: the propositions ‘not everyanimal is just’ and ‘some animals arejust’ are both true.

Further, the proposition ‘no man isjust’ follows from the proposition‘every man is not just’ and the

proposition ‘not every man is notjust’, which is the opposite of ‘every

man is not-just’, follows from the proposition ‘some men 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 thetrue one, a certain positive

proposition is also true. Thus, if thequestion were asked Socrates wise?’ and





is not man is not just’ is equivalentto the proposition ‘nothing that is not

man is just’.

The conversion of the position ofsubject and predicate in a sentenceinvolves no difference in its meaning.Thus we say ‘man is white’ and ‘whiteis man’. If these were not equivalent,there would be more than onecontradictory to the same proposition,

whereas it has been demonstrated’ thateach proposition has one propercontradictory and one only. For of the

proposition ‘man is white’ theappropriate contradictory is ‘man isnot white’, and of the proposition‘white is man’, if its meaning bedifferent, the contradictory willeither 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 thelatter of these is the contradictory ofthe proposition ‘man is white’; thusthere will be two contradictories to

one proposition.

It is evident, therefore, that theinversion of the relative position of



subject and predicate does not affectthe sense of affirmations and denials.

11

There is no unity about an affirmationor denial which, either positively ornegatively, predicates one thing of

many subjects, or many things of thesame subject, unless that which isindicated by the many is really some

one thing. do not apply this word ‘one’to those things which, though they havea single recognized name, yet do notcombine to form a unity. Thus, man may

be an animal, and biped, anddomesticated, but these three

predicates combine to form a unity. Onthe other hand, the predicates ‘white’,‘man’, and ‘walking’ do not thuscombine. Neither, therefore, if thesethree form the subject of anaffirmation, nor if they form its

predicate, is there any unity aboutthat affirmation. In both cases theunity is linguistic, but not real.

If therefore the dialectical questionis a request for an answer, i.e. eitherfor the admission of a premiss or forthe admission of one of two



contradictories-and the premiss isitself always one of twocontradictories-the answer to such aquestion as contains the above

predicates cannot be a single proposition. For as I have explained in

the Topics, question is not a singleone, even if the answer asked for istrue.

At the same time it is plain that a

question of the form ‘what is it?’ isnot a dialectical question, for adialectical questioner must by the formof his question give his opponent thechance of announcing one of twoalternatives, whichever he wishes. He

must therefore put the question into a more definite form, and inquire, e.g..

whether man has such and such acharacteristic or not.

Some combinations of predicates aresuch that the separate predicates uniteto form a single predicate. Let usconsider under what conditions this is

and is not possible. We may eitherstate in two separate propositions that

man is an animal and that man is a biped, or we may combine the two, and

state that man is an animal with two



feet. Similarly we may use ‘man’ and‘white’ as separate predicates, orunite them into one. Yet if a man is ashoemaker and is also good, we cannotconstruct a composite proposition andsay that he is a good shoemaker. Forif, whenever two separate predicatestruly belong to a subject, it followsthat the predicate resulting from theircombination also truly belongs to thesubject, many absurd results ensue. For

instance, a man is man and white.Therefore, if predicates may always becombined, he is a white man. Again, ifthe predicate ‘white’ belongs to him,then the combination of that predicatewith the former composite predicatewill be permissible. Thus it will beright to say that he is a white man soon indefinitely. Or, again, we maycombine the predicates ‘musical’,‘white’, and ‘walking’, and these may

be combined many times. Similarly we may say that Socrates is Socrates and a man, and that therefore he is the man

Socrates, or that Socrates is a man and

a biped, and that therefore he is atwo-footed man. Thus it is manifestthat if man states unconditionally that

predicates can always be combined, manyabsurd consequences ensue.



We will now explain what ought to be

laid down.

Those predicates, and terms forming thesubject of predication, which areaccidental either to the same subjector to one another, do not combine toform a unity. Take the proposition ‘manis white of complexion and musical’.

Whiteness and being musical do not

coalesce to form a unity, for they belong only accidentally to the same

subject. Nor yet, if it were true tosay that that which is white is

musical, would the terms ‘musical’ and‘white’ form a unity, for it is onlyincidentally that that which is musicalis white; the combination of the twowill, therefore, not form a unity.

Thus, again, whereas, if a man is bothgood and a shoemaker, we cannot combinethe two propositions and say simplythat he is a good shoemaker, we are, atthe same time, able to combine the

predicates ‘animal’ and ‘biped’ and saythat a man is an animal with two feet,for these predicates are notaccidental.



Those predicates, again, cannot form aunity, of which the one is implicit inthe other: thus we cannot combine the

predicate ‘white’ again and again withthat which already contains the notion‘white’, nor is it right to call a manan animal-man or a two-footed man; forthe notions ‘animal’ and ‘biped’ areimplicit in the word ‘man’. On theother hand, it is possible to predicatea term simply of any one instance, and

to say that some one particular man isa man or that some one white man is awhite man.

Yet this is not always possible:indeed, when in the adjunct there issome opposite which involves acontradiction, the predication of thesimple term is impossible. Thus it isnot right to call a dead man a man.

When, however, this is not the case, itis not impossible.

Yet the facts of the case might rather be stated thus: when some such opposite

elements are present, resolution isnever possible, but when they are not

present, resolution is nevertheless notalways possible. Take the proposition‘Homer is so-and-so’, say ‘a poet’;



does it follow that Homer is, or doesit not? The verb ‘is’ is here used ofHomer only incidentally, the

proposition being that Homer is a poet,not that he is, in the independentsense of the word.

Thus, in the case of those predicationswhich have within them no contradictionwhen the nouns are expanded intodefinitions, and wherein the predicates

belong to the subject in their own proper sense and not in any indirect

way, the individual may be the subjectof the simple propositions as well asof the composite. But in the case ofthat which is not, it is not true tosay that because it is the object ofopinion, it is; for the opinion heldabout it is that it is not, not that itis.

12

As these distinctions have been made,we must consider the mutual relation of

those affirmations and denials whichassert or deny possibility orcontingency, impossibility ornecessity: for the subject is notwithout difficulty.



We admit that of composite expressions

those are contradictory each to eachwhich have the verb ‘to be’ its

positive and negative formrespectively. Thus the contradictory ofthe proposition ‘man is’ is ‘man isnot’, not ‘not-man is’, and thecontradictory of ‘man is white’ is ‘manis not white’, not ‘man is not-white’.For otherwise, since either the

positive or the negative proposition istrue of any subject, it will turn outtrue to say that a piece of wood is a

man that is not white.

Now if this is the case, in those propositions which do not contain the

verb ‘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’ merelyequivalent to saying ‘man is walking’.

If then this rule is universal, the

contradictory of ‘it may be’ is may not be’, not ‘it cannot be’.

Now it appears that the same thing both may and may not be; for instance,





contradictory of this is ‘it is notcontingent that it should be’. Thesimilar propositions, such as ‘it isnecessary’ and ‘it is impossible’, may

be dealt with in the same manner. Forit comes about that just as in theformer instances the verbs ‘is’ and ‘isnot’ were added to the subject-matterof the sentence ‘white’ and ‘man’, sohere ‘that it should be’ and ‘that itshould not be’ are the subject-matter

and ‘is possible’, ‘is contingent’, areadded. These indicate that a certainthing is or is not possible, just as inthe former instances ‘is’ and ‘is not’indicated that certain things were orwere not the case.

The contradictory, then, of ‘it may not be’ is not ‘it cannot be’, but ‘it

cannot not be’, and the contradictoryof ‘it may be’ is not ‘it may not be’,

but cannot be’. Thus the propositions‘it may be’ and ‘it may not be’ appeareach to imply the other: for, sincethese two propositions are not

contradictory, the same thing both mayand may not be. But the propositions‘it may be’ and ‘it cannot be’ cannever be true of the same subject atthe same time, for they are



contradictory. Nor can the propositions‘it may not be’ and ‘it cannot not be’

be at once true of the same subject.

The propositions which have to do withnecessity are governed by the same

principle. The contradictory of ‘it isnecessary that it should be’, is not‘it is necessary that it should not

be,’ but ‘it is not necessary that itshould be’, and the contradictory of

‘it is necessary that it should not be’is ‘it is not necessary that it shouldnot be’.

Again, the contradictory of ‘it isimpossible that it should be’ is not‘it is impossible that it should not

be’ but ‘it is not impossible that itshould be’, and the contradictory of‘it is impossible that it should not

be’ is ‘it is not impossible that itshould not be’.

To generalize, we must, as has beenstated, define the clauses ‘that it

should be’ and ‘that it should not be’as the subject-matter of the

propositions, and in making these termsinto affirmations and denials we mustcombine them with ‘that it should be’



and ‘that it should not be’respectively.

We must consider the following pairs ascontradictory propositions:

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.

13

Logical sequences follow in due coursewhen we have arranged the propositionsthus. From the proposition ‘it may be’it follows that it is contingent, andthe relation is reciprocal. It followsalso that it is not impossible and notnecessary.

From the proposition ‘it may not be’ or‘it is contingent that it should not

be’ it follows that it is not necessarythat it should not be and that it is



not impossible that it should not be.From the proposition ‘it cannot be’ or‘it is not contingent’ it follows thatit is necessary that it should not beand that it is impossible that itshould be. From the proposition ‘itcannot not be’ or ‘it is not contingentthat it should not be’ it follows thatit is necessary that it should be andthat it is impossible that it shouldnot be.

Let us consider these statements by thehelp of a table:

A. B.It may be. It cannot be.It is contingent. It is not contingent.It is not impossible It is impossible that it

that it should be. should be.It is not necessary It is necessary that it

that it should be. should not be.

C. D.It may not be. It cannot not be.It is contingent that it It is not contingent that

should not be. it should not be.It is not impossible It is impossible thatit

that it should not be. should not be.It is not necessary that It is necessary that it

it should not be. should be.

Now the propositions ‘it is impossiblethat it should be’ and ‘it is notimpossible that it should be’ areconsequent upon the propositions ‘it

may be’, ‘it is contingent’, and ‘it



cannot be’, ‘it is not contingent’, thecontradictories upon thecontradictories. But there isinversion. The negative of the

proposition ‘it is impossible’ isconsequent upon the proposition ‘it may

be’ and the corresponding positive inthe first case upon the negative in thesecond. For ‘it is impossible’ is a

positive proposition and ‘it is notimpossible’ is negative.

We must investigate the relationsubsisting between these propositionsand those which predicate necessity.That there is a distinction is clear.In this case, contrary propositionsfollow respectively from contradictory

propositions, and the contradictory propositions belong to separate

sequences. For the proposition ‘it isnot necessary that it should be’ is notthe negative of ‘it is necessary thatit should not be’, for both these

propositions may be true of the samesubject; for when it is necessary that

a thing should not be, it is notnecessary that it should be. The reasonwhy the propositions predicatingnecessity do not follow in the samekind of sequence as the rest, lies in



the fact that the proposition ‘it isimpossible’ is equivalent, when usedwith a contrary subject, to the

proposition ‘it is necessary’. For whenit is impossible that a thing should

be, it is necessary, not that it should be, but that it should not be, and when

it is impossible that a thing shouldnot be, it is necessary that it should

be. Thus, if the propositions predicating impossibility or non-

impossibility follow without change ofsubject from those predicating

possibility or non-possibility, those predicating necessity must follow 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 thecontradictory propositions predicatingnecessity should be thus arranged. Forwhen it is necessary that a thingshould be, it is possible that itshould be. (For if not, the opposite

follows, since one or the other mustfollow; so, if it is not possible, itis impossible, and it is thusimpossible that a thing should be,



which must necessarily be; which isabsurd.)

Yet from the proposition ‘it may be’ itfollows that it is not impossible, andfrom that it follows that it is notnecessary; it comes about thereforethat the thing which must necessarily

be need not be; which is absurd. Butagain, the proposition ‘it is necessarythat it should be’ does not follow from

the proposition ‘it may be’, nor doesthe proposition ‘it is necessary thatit should not be’. For the proposition‘it may be’ implies a twofold

possibility, while, if either of thetwo former propositions is true, thetwofold possibility vanishes. For if athing may be, it may also not be, butif it is necessary that it should be orthat it should not be, one of the twoalternatives will be excluded. Itremains, therefore, that the

proposition ‘it is not necessary thatit should not be’ follows from the

proposition ‘it may be’. For this is

true also of that which mustnecessarily be.

Moreover the proposition ‘it is notnecessary that it should not be’ is the



contradictory of that which followsfrom the proposition ‘it cannot be’;for ‘it cannot be’ is followed by ‘itis impossible that it should be’ and by‘it is necessary that it should not

be’, and the contradictory of this isthe proposition ‘it is not necessarythat it should not be’. Thus in thiscase also contradictory propositionsfollow contradictory in the wayindicated, and no logical

impossibilities occur when they arethus arranged.

It may be questioned whether the proposition ‘it may be’ follows from

the proposition ‘it is necessary thatit should be’. If not, thecontradictory must follow, namely thatit cannot be, or, if a man should

maintain that this is not thecontradictory, then the proposition ‘it

may not be’.

Now both of these are false of thatwhich necessarily is. At the same time,

it is thought that if a thing may becut it may also not be cut, if a thing

may be it may also not be, and thus itwould follow that a thing which mustnecessarily be may possibly not be;



which is false. It is evident, then,that it is not always the case thatthat which may be or may walk possessesalso a potentiality in the otherdirection. There are exceptions. In thefirst place we must except those thingswhich possess a potentiality not inaccordance with a rational principle,as fire possesses the potentiality ofgiving out heat, that is, an irrationalcapacity. Those potentialities which

involve a rational principle are potentialities of more than one result,

that is, of contrary results; thosethat are irrational are not always thusconstituted. As I have said, firecannot both heat and not heat, neitherhas anything that is always actual anytwofold potentiality. Yet some even ofthose potentialities which areirrational admit of opposite results.However, thus much has been said toemphasize the truth that it is notevery potentiality which admits ofopposite results, even where the wordis used always in the same sense.

But in some cases the word is usedequivocally. For the term ‘possible’ isambiguous, being used in the one casewith reference to facts, to that which



is actualized, as when a man is said tofind walking possible because he isactually walking, and generally when acapacity is predicated because it isactually realized; in the other case,with reference to a state in whichrealization is conditionally

practicable, as when a man is said tofind walking possible because undercertain conditions he would walk. Thislast sort of potentiality belongs only

to that which can be in motion, theformer can exist also in the case ofthat which has not this power. Both ofthat which is walking and is actual,and of that which has the capacitythough not necessarily realized, it istrue to say that it is not impossiblethat it should walk (or, in the othercase, that it should be), but while wecannot predicate this latter kind of

potentiality of that which is necessaryin the unqualified sense of the word,we can predicate the former.

Our conclusion, then, is this: that

since the universal is consequent uponthe particular, that which is necessaryis also possible, though not in everysense in which the word may be used.



We may perhaps state that necessity andits absence are the initial principlesof existence and non-existence, andthat all else must be regarded as

posterior to these.

It is plain from what has been saidthat that which is of necessity isactual. Thus, if that which is eternalis prior, actuality also is prior to

potentiality. Some things are

actualities without potentiality,namely, the primary substances; asecond class consists of those thingswhich are actual but also potential,whose actuality is in nature prior totheir potentiality, though posterior intime; a third class comprises thosethings which are never actualized, butare pure potentialities.

14

The question arises whether anaffirmation finds its contrary in a

denial or in another affirmation;whether the proposition ‘every man isjust’ finds its contrary in the

proposition ‘no man is just’, or in the proposition ‘every man is unjust’. Take



the propositions ‘Callias is just’,‘Callias is not just’, ‘Callias isunjust’; we have to discover which ofthese form contraries.

Now if the spoken word corresponds withthe judgement of the mind, and if, inthought, that judgement is the contraryof another, which pronounces a contraryfact, in the way, for instance, inwhich the judgement ‘every man is just’

pronounces a contrary to that pronounced by the judgement ‘every man

is unjust’, the same must needs holdgood with regard to spokenaffirmations.

But if, in thought, it is not thejudgement which pronounces a contraryfact that is the contrary of another,then one affirmation will not find itscontrary in another, but rather in thecorresponding denial. We must thereforeconsider which true judgement is thecontrary of the false, that which formsthe denial of the false judgement or

that which affirms the contrary fact.

Let me illustrate. There is a truejudgement 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 tothe true? And if they are one and thesame, which mode of expression formsthe contrary?

It is an error to suppose thatjudgements are to be defined ascontrary in virtue of the fact thatthey have contrary subjects; for the

judgement concerning a good thing, thatit is good, and that concerning a badthing, that it is bad, may be one andthe same, and whether they are so ornot, they both represent the truth. Yetthe subjects here are contrary. Butjudgements are not contrary becausethey have contrary subjects, but

because they are to the contraryeffect.

Now if we take the judgement that thatwhich is good is good, and another thatit is not good, and if there are at thesame time other attributes, which do

not and cannot belong to the good, we must nevertheless refuse to treat as

the contraries of the true judgementthose which opine that some otherattribute subsists which does not



subsist, as also those that opine thatsome other attribute does not subsistwhich does subsist, for both theseclasses of judgement are of unlimitedcontent.

Those judgements must rather be termedcontrary to the true judgements, inwhich error is present. Now thesejudgements are those which areconcerned with the starting points of

generation, and generation is the passing from one extreme to its

opposite; therefore error is a liketransition.

Now that which is good is both good andnot bad. The first quality is part ofits essence, the second accidental; forit is by accident that it is not bad.But if that true judgement is mostreally true, which concerns thesubject’s intrinsic nature, then thatfalse judgement likewise is most reallyfalse, which concerns its intrinsicnature. Now the judgement that that is

good is not good is a false judgementconcerning its intrinsic nature, thejudgement that it is bad is oneconcerning that which is accidental.Thus the judgement which denies the



true judgement is more really falsethan that which positively asserts the

presence of the contrary quality. Butit is the man who forms that judgementwhich is contrary to the true who is

most thoroughly deceived, forcontraries are among the things whichdiffer most widely within the sameclass. If then of the two judgementsone is contrary to the true judgement,

but that which is contradictory is the

more truly contrary, then the latter,it seems, is the real contrary. Thejudgement that that which is good is

bad is composite. For presumably the man who forms that judgement must at

the same time understand that thatwhich is good is not good.

Further, the contradictory is eitheralways the contrary or never;therefore, if it must necessarily be soin all other cases, our conclusion inthe case just dealt with would seem to

be correct. Now where terms have nocontrary, that judgement is false,

which forms the negative of the true;for instance, he who thinks a man isnot a man forms a false judgement. Ifthen in these cases the negative is the



contrary, then the principle isuniversal in its application.

Again, the judgement that that which isnot good is not good is parallel withthe judgement that that which is goodis good. Besides these there is thejudgement that that which is good isnot good, parallel with the judgementthat that that is not good is good. Letus consider, therefore, what would form

the contrary of the true judgement thatthat which is not good is not good. Thejudgement that it is bad would, ofcourse, fail to meet the case, sincetwo true judgements are never contraryand this judgement might be true at thesame time as that with which it isconnected. For since some things whichare not good are bad, both judgements

may be true. Nor is the judgement thatit is not bad the contrary, for thistoo might be true, since both qualities

might be predicated of the samesubject. It remains, therefore, that ofthe judgement concerning that which is

not good, that it is not good, thecontrary judgement is that it is good;for this is false. In the same way,

moreover, the judgement concerning thatwhich is good, that it is not good, is



the contrary of the judgement that itis good.

It is evident that it will make nodifference if we universalize the

positive judgement, for the universalnegative judgement will form thecontrary. For instance, the contrary ofthe judgement that everything that isgood is good is that nothing that isgood is good. For the judgement that

that which is good is good, if thesubject be understood in a universalsense, is equivalent to the judgementthat whatever is good is good, and thisis identical with the judgement thateverything that is good is good. We maydeal similarly with judgementsconcerning that which is not good.

If therefore this is the rule withjudgements, and if spoken affirmationsand denials are judgements expressed inwords, it is plain that the universaldenial is the contrary of theaffirmation about the same subject.

Thus the propositions ‘everything goodis good’, ‘every man is good’, have fortheir contraries the propositions‘nothing good is good’, ‘no man isgood’. The contradictory propositions,





Prior Analytics

Book I

1

We must first state the subject of ourinquiry and the faculty to which it

belongs: its subject is demonstrationand the faculty that carries it outdemonstrative science. We must next

define a premiss, a term, and asyllogism, and the nature of a perfectand of an imperfect syllogism; andafter that, the inclusion ornoninclusion of one term in another asin a whole, and what we mean by

predicating one term of all, or none,of another.

A premiss then is a sentence affirmingor denying one thing of another. Thisis either universal or particular orindefinite. By universal I mean thestatement that something belongs to allor none of something else; by

particular that it belongs to some ornot to some or not to all; byindefinite that it does or does not

belong, without any mark to showwhether it is universal or particular,



e.g. ‘contraries are subjects of thesame science’, or ‘pleasure is notgood’. The demonstrative premissdiffers from the dialectical, becausethe demonstrative premiss is theassertion of one of two contradictorystatements (the demonstrator does notask for his premiss, but lays it down),whereas the dialectical premiss dependson the adversary’s choice between twocontradictories. But this will make no

difference to the production of asyllogism in either case; for both thedemonstrator and the dialectician arguesyllogistically after stating thatsomething does or does not belong tosomething else. Therefore a syllogistic

premiss without qualification will bean affirmation or denial of somethingconcerning something else in the way wehave described; it will bedemonstrative, if it is true andobtained through the first principlesof its science; while a dialectical

premiss is the giving of a choice between two contradictories, when a man

is proceeding by question, but when heis syllogizing it is the assertion ofthat which is apparent and generallyadmitted, as has been said in theTopics. The nature then of a premiss



and the difference between syllogistic,demonstrative, and dialectical

premisses, may be taken as sufficientlydefined by us in relation to our

present need, but will be statedaccurately in the sequel.

I call that a term into which the premiss is resolved, i.e. both the predicate 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 ofnecessity from their being so. I mean

by the last phrase that they producethe consequence, and by this, that nofurther term is required from withoutin order to make the consequencenecessary.

I call that a perfect syllogism whichneeds nothing other than what has beenstated to make plain what necessarily

follows; a syllogism is imperfect, ifit needs either one or more

propositions, which are indeed thenecessary consequences of the terms set



down, but have not been expresslystated as premisses.

That one term should be included inanother as in a whole is the same asfor the other to be predicated of allof the first. And we say that one termis predicated of all of another,whenever no instance of the subject can

be found of which the other term cannot be asserted: ‘to be predicated of none’

must be understood in the same way.

2

Every premiss states that somethingeither is or must be or may be theattribute of something else; of

premisses of these three kinds some areaffirmative, others negative, inrespect of each of the three modes ofattribution; again some affirmative andnegative premisses are universal,others particular, others indefinite.It is necessary then that in universalattribution the terms of the negative

premiss should be convertible, e.g. ifno pleasure is good, then no good will

be pleasure; the terms of theaffirmative must be convertible, nothowever, universally, but in part, e.g.



if every pleasure,is good, some good must be pleasure; the particular

affirmative must convert in part (forif some pleasure is good, then somegood will be pleasure); but the

particular negative need not convert,for if some animal is not man, it doesnot follow that some man is not animal.

First then take a universal negativewith 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 ifevery B is A then some A is B. For ifno A were B, then no B could be A. Butwe assumed that every B is A. Similarlytoo, if the premiss is particular. Forif some B is A, then some of the As

must be B. For if none were, then no Bwould be A. But if some B is not A,there is no necessity that some of the

As should not be B; e.g. let B standfor animal and A for man. Not everyanimal is a man; but every man is ananimal.

3

The same manner of conversion will holdgood also in respect of necessary



premisses. The universal negativeconverts universally; each of theaffirmatives converts into a

particular. If it is necessary that noB is A, it is necessary also that no Ais B. For if it is possible that some Ais B, it would be possible also thatsome B is A. If all or some B is A ofnecessity, it is necessary also thatsome A is B: for if there were nonecessity, neither would some of the Bs

be A necessarily. But the particularnegative 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 andwhat is not necessary and what is

potential is possible), affirmativestatements will all convert in a mannersimilar to those described. For if itis possible that all or some B is A, itwill be possible that some A is B. Forif that were not possible, then no Bcould possibly be A. This has been

already proved. But in negativestatements the case is different.

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, itis possible that man is not horse, orthat no garment is white. For in theformer case the one term necessarilydoes not belong to the other; in thelatter there is no necessity that itshould: and the premiss converts likeother negative statements. For if it is

possible for no man to be a horse, itis also admissible for no horse to be a

man; and if it is admissible for nogarment to be white, it is alsoadmissible for nothing white to be agarment. For if any white thing must bea garment, then some garment willnecessarily be white. This has beenalready proved. The particular negativealso must be treated like those dealtwith above. But if anything is said to

be possible because it is the generalrule and natural (and it is in this waywe define the possible), the negative

premisses can no longer be convertedlike the simple negatives; theuniversal negative premiss does not

convert, and the particular does. Thiswill be plain when we speak about the

possible. At present we may take this much as clear in addition to what has been said: the statement that it is





a whole, the extremes must be related by a perfect syllogism. I call that

term middle which is itself containedin another and contains another initself: in position also this comes inthe middle. By extremes I mean boththat term which is itself contained inanother and that in which another iscontained. If A is predicated of all B,and B of all C, A must be predicated ofall C: we have already explained what

we mean by ‘predicated of all’.Similarly also, if A is predicated ofno B, and B of all C, it is necessarythat no C will be A.

But if the first term belongs to allthe middle, but the middle to none ofthe last term, there will be nosyllogism in respect of the extremes;for nothing necessary follows from theterms being so related; for it is

possible that the first should belongeither to all or to none of the last,so that neither a particular nor auniversal conclusion is necessary. But

if there is no necessary consequence,there cannot be a syllogism by means ofthese premisses. As an example of auniversal affirmative relation betweenthe extremes we may take the terms



animal, man, horse; of a universalnegative relation, the terms animal,

man, stone. Nor again can syllogism beformed when neither the first term

belongs to any of the middle, nor the middle to any of the last. As an

example of a positive relation betweenthe extremes take the terms science,line, medicine: of a negative relationscience, line, unit.

If then the terms are universallyrelated, it is clear in this figurewhen a syllogism will be possible andwhen not, and that if a syllogism is

possible the terms must be related asdescribed, and if they are so relatedthere will be a syllogism.

But if one term is related universally,the other in part only, to its subject,there must be a perfect syllogismwhenever universality is posited withreference to the major term eitheraffirmatively or negatively, and

particularity with reference to the

minor term affirmatively: but wheneverthe universality is posited in relationto the minor term, or the terms arerelated in any other way, a syllogismis impossible. I call that term the



major in which the middle is containedand that term the minor which comesunder the middle. Let all B be A andsome C be B. Then if ‘predicated ofall’ means what was said above, it isnecessary that some C is A. And if no Bis A but some C is B, it is necessarythat some C is not A. The meaning of‘predicated of none’ has also beendefined. So there will be a perfectsyllogism. This holds good also if the

premiss BC should be indefinite, provided that it is affirmative: for we

shall have the same syllogism whetherthe premiss is indefinite or

particular.

But if the universality is posited withrespect to the minor term eitheraffirmatively or negatively, asyllogism will not be possible, whetherthe major premiss is positive ornegative, indefinite or particular:e.g. if some B is or is not A, and allC is B. As an example of a positiverelation between the extremes take the

terms good, state, wisdom: of anegative relation, good, state,ignorance. Again if no C is B, but someB is or is not A or not every B is A,there cannot be a syllogism. Take the



terms white, horse, swan: white, horse,raven. The same terms may be taken alsoif the premiss BA is indefinite.

Nor when the major premiss isuniversal, whether affirmative ornegative, and the minor premiss isnegative and particular, can there be asyllogism, whether the minor premiss beindefinite or particular: e.g. if all Bis A and some C is not B, or if not all

C is B. For the major term may be predicable both of all and of none of

the minor, to some of which the middleterm cannot be attributed. Suppose theterms are animal, man, white: next takesome of the white things of which manis not predicated-swan and snow: animalis predicated of all of the one, but ofnone of the other. Consequently therecannot be a syllogism. Again let no B

be A, but let some C not be B. Take theterms inanimate, man, white: then takesome white things of which man is not

predicated-swan and snow: the terminanimate is predicated of all of the

one, of none of the other.

Further since it is indefinite to saysome C is not B, and it is true thatsome C is not B, whether no C is B, or



not all C is B, and since if terms areassumed such that no C is B, nosyllogism follows (this has already

been stated) it is clear that thisarrangement of terms will not afford asyllogism: otherwise one would have

been possible with a universal negative minor premiss. A similar proof may also be given if the universal premiss is

negative.

Nor can there in any way be a syllogismif both the relations of subject and

predicate are particular, either positively or negatively, or the one

negative and the other affirmative, orone indefinite and the other definite,or both indefinite. Terms common to allthe above are animal, white, horse:animal, white, stone.

It is clear then from what has beensaid that if there is a syllogism inthis figure with a particularconclusion, the terms must be relatedas we have stated: if they are related

otherwise, no syllogism is possibleanyhow. It is evident also that all thesyllogisms in this figure are perfect(for they are all completed by means ofthe premisses originally taken) and



that all conclusions are proved by thisfigure, viz. universal and particular,affirmative and negative. Such a figureI call the first.

5

Whenever the same thing belongs to allof one subject, and to none of another,or to all of each subject or to none ofeither, I call such a figure the

second; by middle term in it I meanthat which is predicated of bothsubjects, by extremes the terms ofwhich this is said, by major extremethat which lies near the middle, by

minor that which is further away fromthe middle. The middle term standsoutside the extremes, and is first in

position. A syllogism cannot be perfectanyhow in this figure, but it may bevalid whether the terms are relateduniversally or not.

If then the terms are relateduniversally a syllogism will be

possible, whenever the middle belongsto all of one subject and to none ofanother (it does not matter which hasthe negative relation), but in no otherway. Let M be predicated of no N, but



of all O. Since, then, the negativerelation is convertible, N will belongto no M: but M was assumed to belong toall O: consequently N will belong to noO. This has already been proved. Againif M belongs to all N, but to no O,then N will belong to no O. For if M

belongs to no O, O belongs to no M: but M (as was said) belongs to all N: O

then will belong to no N: for the firstfigure has again been formed. But since

the negative relation is convertible, Nwill belong to no O. Thus it will bethe same syllogism that proves bothconclusions.

It is possible to prove these resultsalso by reductio ad impossibile.

It is clear then that a syllogism isformed when the terms are so related,

but not a perfect syllogism; fornecessity is not perfectly established

merely from the original premisses;others also are needed.

But if M is predicated of every N andO, there cannot be a syllogism. Termsto illustrate a positive relation

between the extremes are substance,animal, man; a negative relation,



substance, animal, number-substance being the middle term.

Nor is a syllogism possible when M is predicated neither of any N nor of any

O. Terms to illustrate a positiverelation are line, animal, man: anegative relation, line, animal, stone.

It is clear then that if a syllogism isformed when the terms are universally

related, the terms must be related aswe stated at the outset: for if theyare otherwise related no necessaryconsequence follows.

If the middle term is relateduniversally to one of the extremes, a

particular negative syllogism mustresult whenever the middle term isrelated universally to the majorwhether positively or negatively, and

particularly to 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 particularis affirmative: if the universal isaffirmative, the particular isnegative. For if M belongs to no N, butto some O, it is necessary that N does



not belong to some O. For since thenegative statement is convertible, Nwill belong to no M: but M was admittedto belong to some O: therefore N willnot belong to some O: for the result isreached by means of the first figure.

Again if M belongs to all N, but not tosome O, it is necessary that N does not

belong to some O: for if N belongs toall O, and M is predicated also of all

N, 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 toall O, we shall conclude that N doesnot belong to all O: the proof is thesame as the above. But if M is

predicated of all O, but not of all N,there will be no syllogism. Take theterms animal, substance, raven; animal,white, raven. Nor will there be aconclusion when M is predicated of noO, but of some N. Terms to illustrate a

positive relation between the extremesare animal, substance, unit: a negativerelation, animal, substance, science.

If then the universal statement isopposed to the particular, we havestated when a syllogism will be

possible and when not: but if the premisses are similar in form, I mean



both negative or both affirmative, asyllogism will not be possible anyhow.First let them be negative, and let the

major premiss be universal, e.g. let M belong to no N, and not to some O. It

is possible then for N to belong eitherto all O or to no O. Terms toillustrate the negative relation are

black, snow, animal. But it is not possible to find terms of which the

extremes are related positively and

universally, if M belongs to some O,and does not belong to some O. For if N

belonged to all O, but M to no N, then M would belong to no O: but we assumed

that it belongs to some O. In this waythen it is not admissible to taketerms: our point must be proved fromthe indefinite nature of the particularstatement. For since it is true that Mdoes not belong to some O, even if it

belongs to no O, and since if 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 before beuniversal, e.g. let M belong to all Nand to some O. It is possible then for

N to belong to all O or to no O. Terms



to illustrate the negative relation arewhite, swan, stone. But it is not

possible to take terms to illustratethe universal affirmative relation, forthe reason already stated: the point

must be proved from the indefinitenature of the particular statement. Butif the minor premiss is universal, and

M belongs to no O, and not to some N,it is possible for N to belong eitherto all O or to no O. Terms for the

positive relation are white, animal,raven: for the negative relation,white, stone, raven. If the premissesare affirmative, terms for the negativerelation are white, animal, snow; forthe positive relation, white, animal,swan. Evidently then, whenever the

premisses are similar in form, and oneis universal, the other particular, asyllogism can, not be formed anyhow.

Nor is one possible if the middle term belongs to some of each of the

extremes, or does not belong to some ofeither, or belongs to some of the one,not to some of the other, or belongs to

neither universally, or is related tothem indefinitely. Common terms for allthe above are white, animal, man:white, animal, inanimate. It is clearthen from what has been said that if



the terms are related to one another inthe way stated, a syllogism results ofnecessity; and if there is a syllogism,the terms must be so related. But it isevident also that all the syllogisms inthis figure are imperfect: for all are

made perfect by certain supplementarystatements, which either are containedin the terms of necessity or areassumed as hypotheses, i.e. when we

prove per impossibile. And it is

evident that an affirmative conclusionis not attained by means of thisfigure, but all are negative, whetheruniversal or particular.

6

But if one term belongs to all, andanother to none, of a third, or if both

belong to all, or to none, of it, Icall such a figure the third; by middleterm in it I mean that of which boththe predicates are predicated, byextremes I mean the predicates, by the

major extreme that which is further

from the middle, by the minor thatwhich is nearer to it. The middle termstands outside the extremes, and islast in position. A syllogism cannot be

perfect in this figure either, but it



may be valid whether the terms arerelated universally or not to the

middle term.

If they are universal, whenever both Pand R belong to S, it follows that Pwill 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 todemonstrate this also per impossibileand by exposition. 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 belongto 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 someR. This may be demonstrated in the sameway as before by converting the premissRS. It might be proved also per

impossibile, as in the former cases.But if R belongs to no S, P to all S,there will be no syllogism. Terms forthe positive relation are animal,



horse, man: for the negative relationanimal, inanimate, man.

Nor can there be a syllogism when bothterms are asserted of no S. Terms forthe positive relation are animal,horse, inanimate; for the negativerelation 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 relateduniversally. For whenever both theterms are affirmative, there will be asyllogism to prove that one extreme

belongs to some of the other; but whenthey are negative, no syllogism will be

possible. But when one is negative, theother affirmative, if the major isnegative, the minor affirmative, therewill be a syllogism to prove that theone extreme does not belong to some ofthe other: but if the relation isreversed, no syllogism will be

possible. If one term is related

universally to the middle, the other in part only, when both are affirmative

there must be a syllogism, no matterwhich of the premisses is universal.For if R belongs to all S, P to some S,



P must belong to some R. For since theaffirmative statement is convertible Swill belong to some P: consequentlysince R belongs to all S, and S to someP, R must also belong to some P:therefore P must belong to some R.

Again if R belongs to some S, and P toall S, P must belong to some R. This

may be demonstrated in the same way asthe preceding. And it is possible to

demonstrate it also per impossibile and by exposition, as in the former cases.

But if one term is affirmative, theother negative, and if the affirmativeis 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 tosome R. For if P belongs to all R, andR belongs to all S, then P will belongto all S: but we assumed that it didnot. Proof is possible also withoutreduction ad impossibile, if one of theSs be taken to which P does not belong.

But whenever the major is affirmative,no syllogism will be possible, e.g. ifP belongs to all S and R does not

belong to some S. Terms for the



universal affirmative relation areanimate, man, animal. For the universalnegative relation it is not possible toget terms, if R belongs to some S, anddoes not belong to some S. For if P

belongs to all S, and R to some S, thenP will belong to some R: but we assumedthat it belongs to no R. We must putthe matter as before.’ Since theexpression ‘it does not belong to some’is indefinite, it may be used truly of

that also which belongs to none. But ifR belongs to no S, no syllogism is

possible, as has been shown. Clearlythen no syllogism will be possiblehere.

But if the negative term is universal,whenever the major is negative and the

minor affirmative there will be asyllogism. For if P belongs to no S,and R belongs to some S, P will not

belong to some R: for we shall have thefirst figure again, if the premiss RSis converted.

But when the minor is negative, therewill be no syllogism. Terms for the

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 bothare stated in the negative, but one isuniversal, the other particular. Whenthe minor is related universally to the

middle, take the terms animal, science,wild; animal, man, wild. When the majoris related universally to the middle,take as terms for a negative relation

raven, snow, white. For a positiverelation terms cannot be found, if R

belongs to some S, and does not belongto some S. For if P belongs to all R,and R to some S, then P belongs to someS: but we assumed that it belongs to noS. Our point, then, must be proved fromthe indefinite nature of the particularstatement.

Nor is a syllogism possible anyhow, ifeach of the extremes belongs to some ofthe middle or does not belong, or one

belongs and the other does not to someof the middle, or one belongs to some

of the middle, the other not to all, orif the premisses are indefinite. Commonterms for all are animal, man, white:animal, inanimate, white.



It is clear then in this figure alsowhen a syllogism will be possible, andwhen not; and that if the terms are asstated, a syllogism results ofnecessity, and if there is a syllogism,the terms must be so related. It isclear also that all the syllogisms inthis figure are imperfect (for all are

made perfect by certain supplementaryassumptions), and that it will not be

possible to reach a universal

conclusion by means of this figure,whether negative or affirmative.

7

It is evident also that in all thefigures, whenever a proper syllogismdoes not result, if both the terms areaffirmative or negative nothingnecessary follows at all, but if one isaffirmative, the other negative, and ifthe negative is stated universally, asyllogism 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 premisses areconverted it is necessary that C doesnot belong to some A. Similarly also inthe other figures: a syllogism alwaysresults by means of conversion. It is



evident also that the substitution ofan indefinite for a particularaffirmative will effect the samesyllogism in all the figures.

It is clear too that all the imperfectsyllogisms are made perfect by means ofthe first figure. For all are broughtto a conclusion either ostensively or

per impossibile. In both ways the firstfigure is formed: if they are made

perfect ostensively, because (as wesaw) all are brought to a conclusion by

means of conversion, and conversion produces the first figure: if they are proved per impossibile, because on the

assumption of the false statement thesyllogism comes about by means of thefirst figure, e.g. in the last figure,if A and B belong to all C, it followsthat A belongs to some B: for if A

belonged to no B, and B belongs to allC, A would belong to no C: but (as westated) it belongs to all C. Similarlyalso with the rest.

It is possible also to reduce allsyllogisms to the universal syllogismsin the first figure. Those in thesecond figure are clearly made perfect

by these, though not all in the same



way; the universal syllogisms are made perfect by converting the negative premiss, each of the particular

syllogisms by reductio ad impossibile.In the first figure particularsyllogisms are indeed made perfect bythemselves, but it is possible also to

prove them by means of the secondfigure, reducing them ad impossibile,e.g. if A belongs to all B, and B tosome 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 of thesecond figure. Similarly alsodemonstration will be possible in thecase of the negative. For if A belongsto no B, and B belongs to some C, Awill not belong to some C: for if it

belonged to all C, and belongs to no B,then B will belong to no C: and this(as we saw) is the middle figure.Consequently, since all syllogisms inthe middle figure can be reduced touniversal syllogisms in the firstfigure, and since particular syllogisms

in the first figure can be reduced tosyllogisms in the middle figure, it isclear that particular syllogisms can bereduced to universal syllogisms in thefirst figure. Syllogisms in the third



figure, if the terms are universal, aredirectly made perfect by means of thosesyllogisms; but, when one of the

premisses is particular, by means ofthe particular syllogisms in the firstfigure: and these (we have seen) may bereduced to the universal syllogisms inthe first figure: consequently also the

particular syllogisms in the thirdfigure may be so reduced. It is clearthen that all syllogisms may be reduced

to the universal syllogisms in thefirst figure.

We have stated then how syllogismswhich prove that something belongs ordoes not belong to something else areconstituted, both how syllogisms of thesame figure are constituted inthemselves, and how syllogisms ofdifferent figures are related to oneanother.

8

Since there is a difference according

as something belongs, necessarily belongs, or may belong to something

else (for many things belong indeed, but not necessarily, others neither

necessarily nor indeed at all, but it



is possible for them to belong), it isclear that there will be differentsyllogisms to prove each of theserelations, and syllogisms withdifferently related terms, onesyllogism concluding from what isnecessary, another from what is, athird from what is possible.

There is hardly any difference betweensyllogisms from necessary premisses and

syllogisms from premisses which merelyassert. When the terms are put in thesame way, then, whether something

belongs or necessarily belongs (or doesnot belong) to something else, asyllogism will or will not result alikein both cases, the only difference

being the addition of the expression‘necessarily’ to the terms. For thenegative statement is convertible alikein both cases, and we should give thesame account of the expressions ‘to becontained in something as in a whole’and ‘to be predicated of all ofsomething’. With the exceptions to be

made below, the conclusion will be proved to be necessary by means of

conversion, in the same manner as inthe case of simple predication. But inthe middle figure when the universal



statement is affirmative, and the particular negative, and again in the

third figure when the universal isaffirmative and the particularnegative, the demonstration will nottake the same form, but it is necessary

by the ‘exposition’ of a part of thesubject of the particular negative

proposition, to which the predicatedoes not belong, to make the syllogismin reference to this: with terms so

chosen the conclusion will necessarilyfollow. But if the relation isnecessary in respect of the part taken,it must hold of some of that term inwhich this part is included: for the

part taken is just some of that. Andeach of the resulting syllogisms is inthe appropriate figure.

9

It happens sometimes also that when one premiss is necessary the conclusion is

necessary, not however when either premiss is necessary, but only when the

major is, e.g. if A is taken asnecessarily belonging or not belongingto B, but B is taken as simply

belonging to C: for if the premissesare taken in this way, A will



necessarily belong or not belong to C.For since necessarily belongs, or doesnot belong, to every B, and since C isone of the Bs, it is clear that for Calso the positive or the negativerelation to A will hold necessarily.But if the major premiss is notnecessary, but the minor is necessary,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 besuch that it is possible that A should

belong to none of it. Further, anexample also makes it clear that theconclusion not be necessary, e.g. if Awere movement, B animal, C man: man isan animal necessarily, but an animaldoes not move necessarily, nor does

man. Similarly also if the major premiss is negative; for the proof is

the same.

In particular syllogisms, if theuniversal premiss is necessary, then

the conclusion will be necessary; butif the particular, the conclusion willnot be necessary, whether the universal

premiss is negative or affirmative.First let the universal be necessary,



and let A belong to all B necessarily, but let B simply belong to some C: it

is necessary then that A belongs tosome C necessarily: for C falls underB, and A was assumed to belongnecessarily to all B. Similarly also ifthe syllogism should be negative: forthe proof will be the same. But if the

particular premiss is necessary, theconclusion will not be necessary: forfrom the denial of such a conclusion

nothing impossible results, just as itdoes not in the universal syllogisms.The same is true of negativesyllogisms. Try the terms movement,animal, white.

10

In the second figure, if the negative premiss is necessary, then the

conclusion will be necessary, but ifthe affirmative, not necessary. Firstlet the negative be necessary; let A be

possible of no B, and simply belong toC. Since then the negative statement is

convertible, B is possible of no A. But A belongs to all C; consequently B is possible of no C. For C falls under A.

The same result would be obtained ifthe minor premiss were negative: for if



A is possible be of no C, C is possibleof no A: but A belongs to all B,consequently C is possible of none ofthe Bs: for again we have obtained thefirst figure. Neither then is B

possible of C: for conversion is possible without modifying the

relation.

But if the affirmative premiss isnecessary, the conclusion will not be

necessary. Let A belong to all Bnecessarily, but to no C simply. Ifthen the negative premiss is converted,the first figure results. But it has

been proved in the case of the firstfigure that if the negative major

premiss is not necessary the conclusionwill not be necessary either. Thereforethe same result will obtain here.Further, if the conclusion isnecessary, it follows that Cnecessarily does not belong to some A.For if B necessarily belongs to no C, Cwill necessarily belong to no B. But Bat any rate must belong to some A, if

it is true (as was assumed) that Anecessarily belongs to all B.Consequently it is necessary that Cdoes not belong to some A. But nothing

prevents such an A being taken that it



is possible for C to belong to all ofit. Further one might show by anexposition of terms that the conclusionis not necessary without qualification,though it is a necessary conclusionfrom the premisses. For example let A

be animal, B man, C white, and let the premisses be assumed to correspond to

what we had before: it is possible thatanimal should belong to nothing white.

Man then will not belong to anything

white, but not necessarily: for it is possible for man to be born white, not

however so long as animal belongs tonothing white. Consequently under theseconditions the conclusion will benecessary, but it is not necessarywithout qualification.

Similar results will obtain also in particular syllogisms. For whenever the

negative premiss is both universal andnecessary, then the conclusion will benecessary: but whenever the affirmative

premiss is universal, the negative particular, the conclusion will not be

necessary. First then let the negative premiss be both universal and

necessary: let it be possible for no Bthat A should belong to it, and let Asimply belong to some C. Since the



negative statement is convertible, itwill be possible for no A that B should

belong to it: but A belongs to some C;consequently B necessarily does not

belong to some of the Cs. Again let theaffirmative premiss be both universaland necessary, and let the major

premiss be affirmative. If then Anecessarily belongs to all B, but doesnot belong to some C, it is clear thatB will not belong to some C, but not

necessarily. For the same terms can beused to demonstrate the point, whichwere used in the universal syllogisms.

Nor again, if the negative statement isnecessary but particular, will theconclusion be necessary. The point can

be demonstrated by means of the sameterms.

11

In the last figure when the terms arerelated universally to the middle, and

both premisses are affirmative, if oneof the two is necessary, then the

conclusion will be necessary. But ifone is negative, the other affirmative,whenever the negative is necessary theconclusion also will be necessary, butwhenever the affirmative is necessary



the conclusion will not be necessary.First let both the premisses beaffirmative, and let A and B belong toall C, and let AC be necessary. Sincethen B belongs to all C, C also will

belong to some B, because the universalis convertible into the particular:consequently if A belongs necessarilyto all C, and C belongs to some B, itis necessary that A should belong tosome B also. For B is under C. The

first figure then is formed. A similar proof will be given also if BC is

necessary. For C is convertible withsome A: consequently if B belongsnecessarily to all C, it will belongnecessarily also to some A.

Again let AC be negative, BCaffirmative, and let the negative

premiss be necessary. Since then C isconvertible with some B, but Anecessarily belongs to no C, A willnecessarily not belong to some Beither: for B is under C. But if theaffirmative is necessary, the

conclusion will not be necessary. Forsuppose BC is affirmative andnecessary, while AC is negative and notnecessary. Since then the affirmativeis convertible, C also will belong to



some B necessarily: consequently if A belongs to none of the Cs, while C belongs to some of the Bs, A will not belong to some of the Bs-but not of

necessity; for it has been proved, inthe case of the first figure, that ifthe negative premiss is not necessary,neither will the conclusion benecessary. Further, the point may be

made clear by considering the terms.Let the term A be ‘good’, let that

which B signifies be ‘animal’, let theterm C be ‘horse’. It is possible thenthat the term good should belong to nohorse, and it is necessary that theterm animal should belong to everyhorse: but it is not necessary thatsome animal should not be good, sinceit is possible for every animal to begood. Or if that is not possible, takeas the term ‘awake’ or ‘asleep’: forevery animal can accept these.

If, then, the premisses are universal,we have stated when the conclusion will

be necessary. But if one premiss is

universal, the other particular, and if both are affirmative, whenever the

universal is necessary the conclusionalso must be necessary. Thedemonstration is the same as before;



for the particular affirmative also isconvertible. If then it is necessarythat B should belong to all C, and Afalls under C, it is necessary that Bshould belong to some A. But if B must

belong to some A, then A must belong tosome B: for conversion is possible.Similarly also if AC should benecessary and universal: for B fallsunder C. But if the particular premissis necessary, the conclusion will not

be necessary. Let the premiss BC be both particular and necessary, and let A belong to all C, not however

necessarily. If the proposition BC isconverted the first figure is formed,and the universal premiss is notnecessary, but the particular isnecessary. But when the premisses werethus, the conclusion (as we proved wasnot necessary: consequently it is nothere either. Further, the point isclear if we look at the terms. Let A bewaking, B biped, and C animal. It isnecessary that B should belong to someC, but it is possible for A to belong

to C, and that A should belong to B isnot necessary. For there is nonecessity that some biped should beasleep or awake. Similarly and by meansof the same terms proof can be made,



should the proposition AC be both particular and necessary.

But if one premiss is affirmative, theother negative, whenever the universalis both negative and necessary theconclusion also will be necessary. Forif 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

affirmative proposition is necessary,whether universal or particular, or thenegative is particular, the conclusionwill not be necessary. The proof ofthis by reduction will be the same as

before; but if terms are wanted, whenthe universal affirmative is necessary,take the terms ‘waking’-’animal’-’man’,‘man’ being middle, and when theaffirmative is particular andnecessary, take the terms ‘waking’-’animal’-’white’: for it is necessarythat animal should belong to some whitething, but it is possible that wakingshould belong to none, and it is not

necessary that waking should not belongto some animal. But when the negative

proposition being particular isnecessary, take the terms ‘biped’,



‘moving’, ‘animal’, ‘animal’ being middle.

12

It is clear then that a simpleconclusion is not reached unless both

premisses are simple assertions, but anecessary conclusion is possiblealthough one only of the premisses isnecessary. But in both cases, whether

the syllogisms are affirmative ornegative, it is necessary that one

premiss should be similar to theconclusion. I mean by ‘similar’, if theconclusion is a simple assertion, the

premiss must be simple; if theconclusion is necessary, the premiss

must be necessary. Consequently thisalso is clear, that the conclusion will

be neither necessary nor simple unlessa necessary or simple premiss isassumed.

13

Perhaps enough has been said about the proof of necessity, how it comes about

and how it differs from the proof of asimple statement. We proceed to discussthat which is possible, when and how



and by what means it can be proved. Iuse the terms ‘to be possible’ and ‘the

possible’ of that which is notnecessary but, being assumed, resultsin nothing impossible. We say indeedambiguously of the necessary that it is

possible. But that my definition of the possible is correct is clear from the phrases by which we deny or on the

contrary affirm possibility. For theexpressions ‘it is not possible to

belong’, ‘it is impossible to belong’,and ‘it is necessary not to belong’ areeither identical or follow from oneanother; consequently their oppositesalso, ‘it is possible to belong’, ‘itis not impossible to belong’, and ‘itis not necessary not to belong’, willeither be identical or follow from oneanother. For of everything theaffirmation or the denial holds good.That which is possible then will be notnecessary and that which is notnecessary will be possible. It resultsthat all premisses in the mode of

possibility are convertible into one

another. I mean not that theaffirmative are convertible into thenegative, but that those which areaffirmative in form admit of conversion

by opposition, e.g. ‘it is possible to



belong’ may be converted into ‘it is possible not to belong’, and ‘it is possible for A to belong to all B’ into

‘it is possible for A to belong to noB’ or ‘not to all B’, and ‘it is

possible for A to belong to some B’into ‘it is possible for A not to

belong to some B’. And similarly theother propositions in this mode can beconverted. For since that which is

possible is not necessary, and that

which is not necessary may possibly not belong, it is clear that if it is possible that A should belong to B, it

is possible also that it should not belong to B: and if it is possible that

it should belong to all, it is also possible that it should not belong to

all. The same holds good in the case of particular affirmations: for the proof

is identical. And such premisses areaffirmative 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 generally and fallshort of necessity, e.g. man’s turninggrey or growing or decaying, or



generally what naturally belongs to athing (for this has not its necessityunbroken, since man’s existence is notcontinuous for ever, although if a mandoes exist, it comes about eithernecessarily or generally). In anothersense the expression means theindefinite, which can be both thus andnot thus, e.g. an animal’s walking oran earthquake’s taking place while itis walking, or generally what happens

by chance: for none of these inclines by nature in the one way more than in

the opposite.

That which is possible in each of itstwo senses is convertible into itsopposite, not however in the same way:

but what is natural is convertible because it does not necessarily belong

(for in this sense it is possible thata man should not grow grey) and what isindefinite is convertible because itinclines this way no more than that.Science and demonstrative syllogism arenot concerned with things which are

indefinite, because the middle term isuncertain; but they are concerned withthings that are natural, and as a rulearguments and inquiries are made aboutthings which are possible in this



sense. Syllogisms indeed can be madeabout the former, but it is unusual atany rate to inquire about them.

These matters will be treated moredefinitely in the sequel; our businessat present is to state the moods andnature of the syllogism made from

possible premisses. The expression ‘itis possible for this to belong to that’

may be understood in two senses: ‘that’

may mean either that to which ‘that’ belongs or that to which it may belong;

for the expression ‘A is possible ofthe subject of B’ means that it is

possible either of that of which B isstated or of that of which B may

possibly be stated. It makes nodifference whether we say, A is

possible of the subject of B, or all Badmits of A. It is clear then that theexpression ‘A may possibly belong toall B’ might be used in two senses.First then we must state the nature andcharacteristics of the syllogism whicharises if B is possible of the subject

of C, and A is possible of the subjectof B. For thus both premisses areassumed in the mode of possibility; butwhenever A is possible of that of whichB is true, one premiss is a simple



assertion, the other a problematic.Consequently we must start from

premisses which are similar in form, asin the other cases.

14

Whenever A may possibly belong to allB, and B to all C, there will be a

perfect syllogism to prove that A may possibly belong to all C. This is clear

from the definition: for it was in thisway that we explained ‘to be possiblefor one term to belong to all ofanother’. Similarly if it is possiblefor A to belong no B, and for B to

belong to all C, then it is possiblefor A to belong to no C. For thestatement that it is possible for A notto belong to that of which B may betrue means (as we saw) that none ofthose things which can possibly fallunder the term B is left out ofaccount. But whenever A may belong toall B, and B may belong to no C, thenindeed no syllogism results from the

premisses assumed, but if the premissBC is converted after the manner of

problematic propositions, the samesyllogism results as before. For sinceit is possible that B should belong to



no C, it is possible also that itshould belong to all C. This has beenstated above. Consequently if B is

possible for all C, and A is possiblefor all B, the same syllogism againresults. Similarly if in both the

premisses the negative is joined with‘it is possible’: e.g. if A may belongto none of the Bs, and B to none of theCs. No syllogism results from theassumed premisses, but if they are

converted we shall have the samesyllogism as before. It is clear thenthat if the minor premiss is negative,or if both premisses are negative,either no syllogism results, or if oneit is not perfect. For the necessityresults from the conversion.

But if one of the premisses isuniversal, the other particular, whenthe major premiss is universal therewill be a perfect syllogism. For if Ais possible for all B, and B for someC, then A is possible for some C. Thisis clear from the definition of being

possible. Again if A may belong to noB, and B may belong to some of the Cs,it is necessary that A may possibly not

belong to some of the Cs. The proof isthe same as above. But if the



particular premiss is negative, and theuniversal is affirmative, the majorstill being universal and the minor

particular, e.g. A is possible for allB, B may possibly not belong to some C,then a clear syllogism does not resultfrom the assumed premisses, but if the

particular premiss is converted and itis laid down that B possibly may belongto some C, we shall have the sameconclusion as before, as in the cases

given at the beginning.

But if the major premiss is the minoruniversal, whether both areaffirmative, or negative, or differentin quality, or if both are indefiniteor particular, in no way will asyllogism be possible. For nothing

prevents B from reaching beyond A, sothat as predicates cover unequal areas.Let C be that by which B extends beyond

A. To C it is not possible that Ashould belong-either to all or to noneor to some or not to some, since

premisses in the mode of possibility

are convertible and it is possible forB to belong to more things than A can.Further, this is obvious if we taketerms; for if the premisses are asassumed, the major term is both



possible for none of the minor and must belong to all of it. Take as terms

common to all the cases underconsideration ‘animal’-’white’-’man’,where the major belongs necessarily tothe minor; ‘animal’-’white’-’garment’,where it is not possible that the majorshould belong to the minor. It is clearthen that if the terms are related inthis manner, no syllogism results. Forevery syllogism proves that something

belongs either simply or necessarily or possibly. It is clear that there is no proof of the first or of the second.

For the affirmative is destroyed by thenegative, and the negative by theaffirmative. There remains the proof of

possibility. But this is impossible.For it has been proved that if theterms are related in this manner it is

both necessary that the major should belong to all the minor and not possible that it should belong to any.

Consequently there cannot be asyllogism to prove the possibility; forthe necessary (as we stated) is not

possible.

It is clear that if the terms areuniversal in possible premisses asyllogism always results in the first



figure, whether they are affirmative ornegative, only a perfect syllogismresults in the first case, an imperfectin the second. But possibility must beunderstood according to the definitionlaid down, not as covering necessity.This is sometimes forgotten.

15

If one premiss is a simple proposition,

the other a problematic, whenever the major premiss indicates possibility all

the syllogisms will be perfect andestablish possibility in the sensedefined; but whenever the minor premissindicates possibility all thesyllogisms will be imperfect, and thosewhich are negative will establish not

possibility according to thedefinition, but that the major does notnecessarily belong to any, or to all,of the minor. For if this is so, we sayit is possible that it should belong tonone or not to all. Let A be possiblefor 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 perfect

syllogism results. Likewise if the premiss AB is negative, and the premiss



BC is affirmative, the former stating possible, the latter simple

attribution, a perfect syllogismresults proving that A possibly belongsto no C.

It is clear that perfect syllogismsresult if the minor premiss statessimple belonging: but that syllogismswill result if the modality of the

premisses is reversed, must be proved

per impossibile. At the same time itwill be evident that they areimperfect: for the proof proceeds notfrom the premisses assumed. First we

must state that if B’s being followsnecessarily from A’s being, B’s

possibility will follow necessarilyfrom A’s possibility. Suppose, theterms 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,and if that which is impossible, whenit is impossible, could not happen, andif at the same time A is possible and B

impossible, it would be possible for Ato happen without B, and if to happen,then to be. For that which hashappened, when it has happened, is. Butwe must take the impossible and the



possible not only in the sphere of becoming, but also in the spheres of

truth and predicability, and thevarious other spheres in which we speakof the possible: for it will be alikein 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: fornothing follows of necessity from the

being of some one thing, but from two

at least, i.e. when the premisses arerelated in the manner stated to be thatof the syllogism. For if C is

predicated of D, and D of F, then C isnecessarily predicated of F. And ifeach is possible, the conclusion alsois possible. If then, for example, oneshould indicate the premisses by A, andthe conclusion by B, it would not onlyresult that if A is necessary B isnecessary, but also that if A is

possible, B is possible.

Since this is proved it is evident thatif a false and not impossible

assumption is made, the consequence ofthe assumption will also be false andnot impossible: e.g. if A is false, butnot impossible, and if B is theconsequence of A, B also will be false



but not impossible. For since it has been proved that if B’s being is the

consequence of A’s being, then B’s possibility will follow from A’s possibility (and A is assumed to be possible), consequently B will be possible: for if it were impossible,

the same thing would at the same time be possible and impossible.

Since we have defined these points, let

A belong to all B, and B be possiblefor all C: it is necessary then thatshould be a possible attribute for allC. Suppose that it is not possible, butassume that B belongs to all C: this isfalse but not impossible. If then A isnot possible for C but B belongs to allC, then A is not possible for all B:for a syllogism is formed in the thirddegree. But it was assumed that A is a

possible attribute for all B. It isnecessary then that A is possible forall C. For though the assumption we

made is false and not impossible, theconclusion is impossible. It is

possible also in the first figure to bring about the impossibility, by

assuming that B belongs to C. For if B belongs to all C, and A is possible for

all B, then A would be possible for all



C. But the assumption was made that Ais not possible for all C.

We must understand ‘that which belongsto all’ with no limitation in respectof time, e.g. to the present or to a

particular period, but simply withoutqualification. For it is by the help ofsuch premisses that we make syllogisms,since if the premiss is understood withreference to the present moment, there

cannot be a syllogism. For nothing perhaps prevents ‘man’ belonging at a particular time to everything that is moving, i.e. if nothing else were moving: but ‘moving’ is possible for

every horse; yet ‘man’ is possible forno horse. Further let the major term be‘animal’, the middle ‘moving’, the the

minor ‘man’. The premisses then will beas before, but the conclusionnecessary, not possible. For man isnecessarily animal. It is clear thenthat the universal must be understoodsimply, without limitation in respectof time.

Again let the premiss AB be universaland negative, and assume that A belongsto no B, but B possibly belongs to allC. These propositions being laid down,



it is necessary that A possibly belongsto no C. Suppose that it cannot belong,and that B belongs to C, as above. Itis necessary then that A belongs tosome B: for we have a syllogism in thethird figure: but this is impossible.Thus it will be possible for A to

belong to no C; for if at is supposedfalse, the consequence is an impossibleone. This syllogism then does notestablish that which is possible

according to the definition, but thatwhich does not necessarily belong toany part of the subject (for this isthe contradictory of the assumptionwhich was made: for it was supposedthat A necessarily belongs to some C,

but the syllogism per impossibileestablishes the contradictory which isopposed to this). Further, it is clearalso from an example that theconclusion will not establish

possibility. Let A be ‘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 belongsto no C: so the conclusion does notestablish possibility. But neither isit always necessary. Let A be ‘moving’,





but if the problematic premiss isconverted, we shall have a syllogism.Suppose that A belongs to no B, and B

may possibly belong to no C. Throughthese comes nothing necessary. But if Bis assumed to be possible for all C(and this is true) and if the premiss

AB remains as before, we shall againhave the same syllogism. But if it beassumed that B does not belong to anyC, instead of possibly not belonging,

there cannot be a syllogism anyhow,whether the premiss AB is negative oraffirmative. As common instances of anecessary and positive relation we maytake the terms white-animal-snow: of anecessary and negative relation, white-animal-pitch. Clearly then if the termsare universal, and one of the premissesis assertoric, the other problematic,whenever the minor premiss is

problematic a syllogism always results,only sometimes it results from the

premisses that are taken, sometimes itrequires the conversion of one premiss.

We have stated when each of these

happens and the reason why. But if oneof the relations is universal, theother particular, then whenever the

major premiss is universal and problematic, whether affirmative or



negative, and the particular isaffirmative and assertoric, there will

be a perfect syllogism, just as whenthe terms are universal. Thedemonstration is the same as before.But whenever the major premiss isuniversal, but assertoric, not

problematic, and the minor is particular and problematic, whether both premisses are negative or

affirmative, or one is negative, the

other affirmative, in all cases therewill be an imperfect syllogism. Onlysome of them will be proved perimpossibile, others by the conversionof the problematic premiss, as has beenshown above. And a syllogism will be

possible by means of conversion whenthe major premiss is universal andassertoric, whether positive ornegative, and the minor particular,negative, and problematic, e.g. if A

belongs to all B or to no B, and B may possibly not belong to some C. For if

the premiss BC is converted in respectof possibility, a syllogism results.

But whenever the particular premiss isassertoric and negative, there cannot

be a syllogism. As instances of the positive relation we may take the terms

white-animal-snow; of the negative,



white-animal-pitch. For thedemonstration must be made through theindefinite nature of the particular

premiss. But if the minor premiss isuniversal, and the major particular,whether either premiss is negative oraffirmative, problematic or assertoric,nohow is a syllogism possible. Nor is asyllogism possible when the premissesare particular or indefinite, whether

problematic or assertoric, or the one

problematic, the other assertoric. Thedemonstration is the same as above. Asinstances of the necessary and positiverelation we may take the terms animal-white-man; of the necessary andnegative relation, animal-white-garment. It is evident then that if the

major premiss is universal, a syllogismalways results, but if the minor isuniversal nothing at all can ever be

proved.

16

Whenever one premiss is necessary, theother 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 theconclusion will be problematic, notassertoric, whether the premisses areuniversal or not: but if one isaffirmative, the other negative, whenthe affirmative is necessary theconclusion will be problematic, notnegative assertoric; but when thenegative is necessary the conclusionwill be problematic negative, andassertoric negative, whether the

premisses are universal or not.Possibility in the conclusion must beunderstood in the same manner as

before. There cannot be an inference tothe necessary negative proposition: for‘not necessarily to belong’ isdifferent 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 imperfectsyllogism to prove that A may belong to

all C. That it is imperfect is clearfrom 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 A may belong to all C, not that A does belong to all C: and it is perfect, not

imperfect: for it is completed directlythrough the original premisses.

But if the premisses are not similar inquality, suppose first that thenegative premiss is necessary, and letnecessarily A not be possible for anyB, but let B be possible for all C. It

is necessary then that A belongs to noC. For suppose A to belong to all C orto some C. Now we assumed that A is not

possible for any B. Since then thenegative proposition is convertible, Bis not possible for any A. But A issupposed to belong to all C or to someC. Consequently B will not be possiblefor any C or for all C. But it wasoriginally laid down that B is possiblefor all C. And it is clear that the

possibility of belonging can beinferred, since the fact of not

belonging is inferred. Again, let theaffirmative premiss be necessary, and

let A possibly not belong to any B, andlet B necessarily belong to all C. Thesyllogism will be perfect, but it willestablish a problematic negative, notan assertoric negative. For the major



premiss was problematic, and further itis not possible to prove the assertoricconclusion per impossibile. For if itwere supposed that A belongs to some C,and it is laid down that A possiblydoes not belong to any B, no impossiblerelation between B and C follows fromthese premisses. But if the minor

premiss is negative, when it is problematic a syllogism is possible by

conversion, 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 forthe positive relation-white-animal-snow, and for the negative relation-white-animal-pitch.

The same relation will obtain in particular syllogisms. Whenever the

negative proposition is necessary, theconclusion will be negative assertoric:e.g. if it is not possible that Ashould belong to any B, but B may

belong to some of the Cs, it is

necessary that A should not belong tosome of the Cs. For if A belongs to allC, but cannot belong to any B, neithercan B belong to any A. So if A belongsto all C, to none of the Cs can B



belong. But it was laid down that B may belong to some C. But when the particular affirmative in the negative

syllogism, e.g. BC the minor premiss,or the universal proposition in theaffirmative syllogism, e.g. AB the

major premiss, is necessary, there willnot be an assertoric conclusion. Thedemonstration is the same as before.But if the minor premiss is universal,and problematic, whether affirmative or

negative, and the major premiss is particular and necessary, there cannot be a syllogism. Premisses of this kind

are possible both where the relation is positive and necessary, e.g. animal-

white-man, and where it is necessaryand negative, e.g. animal-white-garment. But when the universal isnecessary, the particular problematic,if the universal is negative we maytake the terms animal-white-raven toillustrate the positive relation, oranimal-white-pitch to illustrate thenegative; and if the universal isaffirmative we may take the terms

animal-white-swan to illustrate the positive relation, and animal-white-

snow to illustrate the negative andnecessary relation. Nor again is asyllogism possible when the premisses



are indefinite, or both particular.Terms applicable in either case toillustrate the positive relation areanimal-white-man: to illustrate thenegative, animal-white-inanimate. Forthe relation of animal to some white,and of white to some inanimate, is bothnecessary and positive and necessaryand negative. Similarly if the relationis problematic: so the terms may beused for all cases.

Clearly then from what has been said asyllogism results or not from similarrelations of the terms whether we aredealing with simple existence ornecessity, with this exception, that ifthe negative premiss is assertoric theconclusion is problematic, but if thenegative premiss is necessary theconclusion is both problematic andnegative assertoric. [It is clear alsothat all the syllogisms are imperfectand are perfected by means of thefigures above mentioned.]

17

In the second figure whenever both premisses are problematic, no syllogism

is possible, whether the premisses are



affirmative or negative, universal or particular. But when one premiss is

assertoric, the other problematic, ifthe affirmative is assertoric nosyllogism is possible, but if theuniversal negative is assertoric aconclusion can always be drawn.Similarly when one premiss isnecessary, the other problematic. Herealso we must understand the term‘possible’ in the conclusion, in the

same sense as before.

First we must point out that thenegative problematic proposition is notconvertible, e.g. if A may belong to noB, it does not follow that B may belongto no A. For suppose it to follow andassume that B may belong to no A. Sincethen problematic affirmations areconvertible with negations, whetherthey are contraries or contradictories,and since B may belong to no A, it isclear that B may belong to all A. Butthis is false: for if all this can bethat, it does not follow that all that

can be this: consequently the negative proposition is not convertible.

Further, these propositions are notincompatible, ‘A may belong to no B’,‘B necessarily does not belong to some



of the As’; e.g. it is possible that no man should be white (for it is also possible that every man should be

white), but it is not true to say thatit is possible that no white thingshould be a man: for many white thingsare necessarily not men, and thenecessary (as we saw) other than the

possible.

Moreover it is not possible to prove

the convertibility of these propositions by a reductio ad absurdum,

i.e. by claiming assent to thefollowing argument: ‘since it is falsethat B may belong to no A, it is truethat it cannot belong to no A, for theone statement is the contradictory ofthe other. But if this is so, it istrue that B necessarily belongs to someof the As: consequently A necessarily

belongs to some of the Bs. But this isimpossible.’ The argument cannot beadmitted, for it does not follow thatsome A is necessarily B, if it is not

possible that no A should be B. For the

latter expression is used in twosenses, one if A some is necessarily B,another if some A is necessarily not B.For it is not true to say that thatwhich necessarily does not belong to



some of the As may possibly not belongto 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 itis not possible for C to belong to allD, it necessarily does not belong tosome D, he would make a falseassumption: for it does belong to allD, but because in some cases it belongsnecessarily, therefore we say that it

is not possible for it to belong toall. Hence both the propositions ‘Anecessarily belongs to some B’ and ‘Anecessarily does not belong to some B’are opposed to the proposition ‘A

belongs to all B’. Similarly also theyare opposed to the proposition ‘A may

belong to no B’. It is clear then thatin relation to what is possible and not

possible, in the sense originallydefined, we must assume, not that Anecessarily belongs to some B, but that

A necessarily does not belong to someB. But if this is assumed, no absurdityresults: consequently no syllogism. It

is clear from what has been said thatthe negative proposition is notconvertible.



This being proved, suppose it possiblethat A may belong to no B and to all C.By means of conversion no syllogismwill result: for the major premiss, ashas been said, is not convertible. Norcan a proof be obtained by a reductioad absurdum: for if it is assumed thatB can belong to all C, no falseconsequence results: for A may belong

both to all C and to no C. In general,if there is a syllogism, it is clear

that its conclusion will be problematic because neither of the premisses is

assertoric; and this must be eitheraffirmative or negative. But neither is

possible. Suppose the conclusion isaffirmative: it will be proved by anexample that the predicate cannot

belong to the subject. Suppose theconclusion is negative: it will be

proved that it is not problematic butnecessary. Let A be white, B man, Chorse. It is possible then for A to

belong to all of the one and to none ofthe other. But it is not possible for Bto belong nor not to belong to C. That

it is not possible for it to belong, isclear. For no horse is a man. Neitheris it possible for it not to belong.For it is necessary that no horseshould be a man, but the necessary we



found to be different from the possible. No syllogism then results. A

similar proof can be given if the major premiss is negative, the minor

affirmative, or if both are affirmativeor negative. The demonstration can be

made by means of the same terms. Andwhenever one premiss is universal, theother particular, or both are

particular or indefinite, or inwhatever other way the premisses can be

altered, the proof will always proceedthrough the same terms. Clearly then,if both the premisses are problematic,no syllogism results.

18

But if one premiss is assertoric, theother problematic, if the affirmativeis assertoric and the negative

problematic no syllogism will be possible, whether the premisses are

universal or particular. The proof isthe same as above, and by means of thesame terms. But when the affirmative

premiss is problematic, and thenegative assertoric, we shall have asyllogism. Suppose A belongs to no B,

but can belong to all C. If thenegative proposition is converted, B





before. Again if both the relations arenegative, and the assertoric

proposition is universal, although noconclusion follows from the actual

premisses, a syllogism can be obtained by converting the problematic premiss

into its complementary affirmative as before. But if the negative proposition

is assertoric, but particular, nosyllogism is possible, whether theother premiss is affirmative or

negative. Nor can a conclusion be drawnwhen both premisses are indefinite,whether affirmative or negative, or

particular. The proof is the same and by the same terms.

19

If one of the premisses is necessary,the other problematic, then if thenegative is necessary a syllogisticconclusion can be drawn, not merely anegative problematic but also anegative assertoric conclusion; but ifthe affirmative premiss is necessary,

no conclusion is possible. Suppose that A necessarily belongs to no B, but may belong to all C. If the negative premiss is converted B will belong to

no A: but A ex hypothesi is capable of



belonging to all C: so once more aconclusion is drawn by the first figurethat B may belong to no C. But at thesame time it is clear that B will not

belong to any C. For assume that itdoes: then if A cannot belong to any B,and B belongs to some of the Cs, Acannot belong to some of the Cs: but exhypothesi it may belong to all. Asimilar proof can be given if the minor

premiss is negative. Again let the

affirmative proposition be necessary,and the other problematic; i.e. supposethat A may belong to no B, butnecessarily belongs to all C. When theterms are arranged in this way, nosyllogism is possible. For (1) itsometimes turns out that B necessarilydoes 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; Clearly then we cannot draw a problematic conclusion; for that which

is necessary is admittedly distinctfrom that which is possible. (2) Nor

again can we draw a necessaryconclusion: for that presupposes that

both premisses are necessary, or at anyrate the negative premiss. (3) Furtherit is possible also, when the terms are



so arranged, that B should belong to C:for nothing prevents C falling under B,

A being possible for all B, andnecessarily belonging to C; e.g. if Cstands for ‘awake’, B for ‘animal’, Afor ‘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 bethe negative assertion, if the relation

must be positive when the terms arerelated as above. Nor can the oppositeaffirmations be established:consequently no syllogism is possible.

A similar proof is possible if the major premiss is affirmative.

But if the premisses are similar inquality, when they are negative asyllogism can always be formed byconverting the problematic premiss intoits complementary affirmative as

before. Suppose A necessarily does not belong to B, and possibly may not belong to C: if the premisses are

converted B belongs to no A, and A may possibly belong to all C: thus we have

the first figure. Similarly if the minor premiss is negative. But if the premisses are affirmative there cannot



be a syllogism. Clearly the conclusioncannot be a negative assertoric or anegative necessary proposition becauseno negative premiss has been laid downeither in the assertoric or in thenecessary mode. Nor can the conclusion

be a problematic negative proposition.For if the terms are so related, thereare cases in which B necessarily willnot belong to C; e.g. suppose that A iswhite, B swan, C man. Nor can the

opposite affirmations be established,since we have shown a case in which Bnecessarily does not belong to C. Asyllogism then is not possible at all.

Similar relations will obtain in particular syllogisms. For whenever the

negative proposition is universal andnecessary, a syllogism will always be

possible to prove both a problematicand a negative assertoric proposition(the proof proceeds by conversion); butwhen the affirmative proposition isuniversal and necessary, no syllogisticconclusion can be drawn. This can be

proved in the same way as for universal propositions, and by the same terms. Nor is a syllogistic conclusion possible when both premisses are

affirmative: this also may be proved as



above. But when both premisses arenegative, and the premiss thatdefinitely disconnects two terms isuniversal and necessary, though nothingfollows necessarily from the premissesas they are stated, a conclusion can bedrawn as above if the problematic

premiss is converted into itscomplementary affirmative. But if bothare indefinite or particular, nosyllogism can be formed. The same proof

will serve, and the same terms.

It is clear then from what has beensaid that if the universal and negative

premiss is necessary, a syllogism isalways possible, proving not merely anegative problematic, but also anegative assertoric proposition; but ifthe affirmative premiss is necessary noconclusion can be drawn. It is cleartoo that a syllogism is possible or notunder the same conditions whether the

mode of the premisses is assertoric ornecessary. And it is clear that all thesyllogisms are imperfect, and are

completed by means of the figures mentioned.



20

In the last figure a syllogism is possible whether both or only one of

the premisses is problematic. When the premisses are problematic the

conclusion will be problematic; andalso when one premiss is problematic,the other assertoric. But when theother premiss is necessary, if it isaffirmative the conclusion will be

neither necessary or assertoric; but ifit is negative the syllogism willresult in a negative assertoric

proposition, as above. In these also we must understand the expression

‘possible’ in the conclusion in thesame way as before.

First let the premisses be problematicand suppose that both A and B may

possibly belong to every C. Since thenthe affirmative proposition isconvertible into a particular, and B

may possibly belong to every C, itfollows that C may possibly belong to

some B. So, if A is possible for everyC, and C is possible for some of theBs, then A is possible for some of theBs. For we have got the first figure.

And A if may possibly belong to no C,



but B may possibly belong to all C, itfollows that A may possibly not belongto some B: for we shall have the firstfigure again by conversion. But if both

premisses should be negative nonecessary consequence will follow fromthem as they are stated, but if the

premisses are converted into theircorresponding affirmatives there will

be a syllogism as before. For if A andB may possibly not belong to C, if ‘may

possibly belong’ is substituted weshall again have the first 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 arrangement

of the terms as in the case ofassertoric propositions. Suppose that A

may possibly belong to all C, and B tosome C. We shall have the first figureagain if the particular premiss isconverted. For if A is possible for allC, and C for some of the Bs, then A is

possible for some of the Bs. Similarlyif the proposition BC is universal.

Likewise also if the proposition AC isnegative, and the proposition BCaffirmative: for we shall again havethe first figure by conversion. But if

both premisses should be negative-the



one universal and the other particular-although no syllogistic conclusion willfollow from the premisses as they are

put, it will follow if they areconverted, as above. But when both

premisses are indefinite or particular,no syllogism can be formed: for A must

belong sometimes to all B and sometimesto no B. To illustrate the affirmativerelation take the terms animal-man-white; to illustrate the negative, take

the terms horse-man-white—white beingthe middle term.

21

If one premiss is pure, the other problematic, the conclusion will be problematic, not pure; and a syllogism

will be possible under the samearrangement of the terms as before.First let the premisses be affirmative:suppose that A belongs to all C, and B

may possibly belong to all C. If the proposition BC is converted, we shall

have the first figure, and the

conclusion that A may possibly belongto some of the Bs. For when one of the

premisses in the first figure is problematic, the conclusion also (as we

saw) is problematic. Similarly 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 conclusion will be problematic: for the first figure is

obtained once more, and it has been proved that if one premiss is problematic in that figure the

conclusion also will be problematic.But if the minor premiss BC isnegative, or if both premisses are

negative, no syllogistic conclusion can be drawn from the premisses as they

stand, but if they are converted asyllogism is obtained as before.

If one of the premisses is universal,the other particular, then when bothare affirmative, or when the universalis negative, the particularaffirmative, we shall have the samesort of syllogisms: for all arecompleted by means of the first figure.So it is clear that we shall have not a

pure but a problematic syllogisticconclusion. But if the affirmative

premiss is universal, the negative particular, the proof will proceed by a

reductio ad impossibile. Suppose that B belongs to all C, and A may possibly

not belong to some C: it follows that



may possibly not belong to some B. Forif A necessarily belongs to all B, andB (as has been assumed) belongs to allC, A will necessarily belong to all C:for this has been proved before. But itwas assumed at the outset that A may

possibly not belong to some C.

Whenever both premisses are indefiniteor particular, no syllogism will be

possible. The demonstration is the same

as was given in the case of universal premisses, and proceeds by means of the

same terms.

22

If one of the premisses is necessary,the other problematic, when the

premisses are affirmative a problematicaffirmative conclusion can always bedrawn; when one proposition isaffirmative, the other negative, if theaffirmative is necessary a problematicnegative can be inferred; but if thenegative proposition is necessary both

a problematic and a pure negativeconclusion are possible. But anecessary negative conclusion will not

be possible, any more than in the otherfigures. Suppose first that the



premisses are affirmative, i.e. that Anecessarily belongs to all C, and B may

possibly belong to all C. Since then A must belong to all C, and C may belong

to some B, it follows that A may (notdoes) belong to some B: for so itresulted in the first figure. A similar

proof may be given if the propositionBC is necessary, and AC is problematic.

Again suppose one proposition isaffirmative, the other negative, the

affirmative being necessary: i.e.suppose A may possibly belong to no C,

but B necessarily belongs to all C. Weshall have the first figure once more:and-since the negative premiss is

problematic-it is clear that theconclusion will be problematic: forwhen the premisses stand thus in thefirst figure, the conclusion (as wefound) is problematic. But if thenegative premiss is necessary, theconclusion will be not only that A may

possibly not belong to some B but alsothat it does not belong to some B. Forsuppose that A necessarily does not

belong to C, but B may belong to all C.If the affirmative proposition BC isconverted, we shall have the firstfigure, and the negative premiss isnecessary. But when the premisses stood



thus, it resulted that A might possiblynot belong to some C, and that it didnot belong to some C; consequently hereit follows that A does not belong tosome B. But when the minor premiss isnegative, if it is problematic we shallhave a syllogism by altering the

premiss into its complementaryaffirmative, as before; but if it isnecessary no syllogism can be formed.For A sometimes necessarily belongs to

all B, and sometimes cannot possibly belong to any B. To illustrate the

former take the terms sleep-sleepinghorse-man; to illustrate the lattertake the terms sleep-waking horse-man.

Similar results will obtain if one ofthe terms is related universally to the

middle, the other in part. If both premisses are affirmative, the

conclusion will be problematic, not pure; and also when one premiss is

negative, the other affirmative, thelatter being necessary. But when thenegative premiss is necessary, the

conclusion also will be a pure negative proposition; for the same kind of proof

can be given whether the terms areuniversal or not. For the syllogisms

must be made perfect by means of the



first figure, so that a result whichfollows in the first figure followsalso in the third. But when the minor

premiss is negative and universal, ifit is problematic a syllogism can beformed by means of conversion; but ifit is necessary a syllogism is not

possible. The proof will follow thesame course as where the premisses areuniversal; and the same terms may beused.

It is clear then in this figure alsowhen and how a syllogism can be formed,and when the conclusion is problematic,and when it is pure. It is evident alsothat all syllogisms in this figure areimperfect, and that they are made

perfect by means of the first figure.

23

It is clear from what has been saidthat the syllogisms in these figuresare made perfect by means of universalsyllogisms in the first figure and are

reduced to them. That every syllogismwithout qualification can be sotreated, will be clear presently, whenit has been proved that every syllogism



is formed through one or other of thesefigures.

It is necessary that everydemonstration and every syllogismshould prove either that something

belongs or that it does not, and thiseither universally or in part, andfurther either ostensively orhypothetically. One sort ofhypothetical proof is the reductio ad

impossibile. Let us speak first ofostensive syllogisms: for after thesehave been pointed out the truth of ourcontention will be clear with regard tothose which are proved per impossibile,and in general hypothetically.

If then one wants to provesyllogistically A of B, either as anattribute of it or as not an attributeof it, one must assert something ofsomething else. If now A should beasserted of B, the propositionoriginally in question will have beenassumed. But if A should be asserted of

C, but C should not be asserted ofanything, nor anything of it, noranything else of A, no syllogism will

be possible. For nothing necessarilyfollows from the assertion of some one



thing concerning some other singlething. Thus we must take another

premiss as well. If then A be assertedof something else, or something else of

A, or something different of C, nothing prevents a syllogism being formed, but

it will not be in relation to B throughthe premisses taken. Nor when C belongsto something else, and that tosomething else and so on, no connexionhowever being made with B, will a

syllogism be possible concerning A inits relation to B. For in general westated that no syllogism can establishthe attribution of one thing toanother, unless some middle term istaken, which is somehow related to each

by way of predication. For thesyllogism in general is made out of

premisses, and a syllogism referring tothis out of premisses with the samereference, and a syllogism relatingthis to that proceeds through premisseswhich relate this to that. But it isimpossible to take a premiss inreference to B, if we neither affirm

nor deny anything of it; or again totake a premiss relating A to B, if wetake nothing common, but affirm or deny

peculiar attributes of each. So we musttake something midway between the two,



which will connect the predications, ifwe are to have a syllogism relatingthis to that. If then we must takesomething common in relation to both,and this is possible in three ways(either by predicating A of C, and C ofB, or C of both, or both of C), andthese are the figures of which we havespoken, it is clear that everysyllogism must be made in one or otherof these figures. The argument is the

same if several middle terms should benecessary to establish the relation toB; for the figure will be the samewhether there is one middle term or

many.

It is clear then that the ostensivesyllogisms are effected by means of theaforesaid figures; these considerationswill show that reductiones ad also areeffected in the same way. For all whoeffect an argument per impossibileinfer syllogistically what is false,and prove the original conclusionhypothetically when something

impossible results from the assumptionof its contradictory; e.g. that thediagonal of the square isincommensurate with the side, becauseodd numbers are equal to evens if it is



supposed to be commensurate. One inferssyllogistically that odd numbers comeout equal to evens, and one proveshypothetically the incommensurabilityof the diagonal, since a falsehoodresults through contradicting this. Forthis we found to be reasoning perimpossibile, viz. proving somethingimpossible by means of an hypothesisconceded at the beginning.Consequently, since the falsehood is

established in reductions adimpossibile by an ostensive syllogism,and the original conclusion is provedhypothetically, and we have alreadystated that ostensive syllogisms areeffected by means of these figures, itis evident that syllogisms perimpossibile also will be made throughthese figures. Likewise all the otherhypothetical syllogisms: for in everycase the syllogism leads up to the

proposition that is substituted for theoriginal thesis; but the originalthesis is reached by means of aconcession or some other hypothesis.

But if this is true, everydemonstration and every syllogism must

be formed by means of the three figures mentioned above. But when this has been

shown it is clear that every syllogism



is perfected by means of the firstfigure and is reducible to theuniversal syllogisms in this figure.

24

Further in every syllogism one of the premisses must be affirmative, and

universality must be present: unlessone of the premisses is universaleither a syllogism will not be

possible, or it will not refer to thesubject proposed, or the original

position will be begged. Suppose wehave to prove that pleasure in music isgood. If one should claim as a premissthat pleasure is good without adding‘all’, no syllogism will be possible;if one should claim that some pleasureis good, then if it is different from

pleasure in music, it is not relevantto the subject proposed; if it is thisvery pleasure, one is assuming thatwhich was proposed at the outset to be

proved. This is more obvious ingeometrical proofs, e.g. that the

angles at the base of an isoscelestriangle are equal. Suppose the lines Aand B have been drawn to the centre. Ifthen one should assume that the angle

AC is equal to the angle BD, without



claiming generally that angles ofsemicircles are equal; and again if oneshould assume that the angle C is equalto the angle D, without the additionalassumption that every angle of asegment is equal to every other angleof the same segment; and further if oneshould assume that when equal anglesare taken from the whole angles, whichare themselves equal, the remainders Eand F are equal, he will beg the thing

to be proved, unless he also statesthat when equals are taken from equalsthe remainders are equal.

It is clear then that in everysyllogism there must be a universal

premiss, and that a universal statementis proved only when all the premissesare universal, while a particularstatement is proved both from twouniversal premisses and from one only:consequently if the conclusion isuniversal, the premisses also must beuniversal, but if the premisses areuniversal it is possible that the

conclusion may not be universal. And itis clear also that in every syllogismeither both or one of the premisses

must be like the conclusion. I mean notonly in being affirmative or negative,



but also in being necessary, pure, problematic. We must consider also the

other forms of predication.

It is clear also when a syllogism ingeneral can be made and when it cannot;and when a valid, when a perfectsyllogism can be formed; and that if asyllogism is formed the terms must bearranged in one of the ways that have

been mentioned.

25

It is clear too that everydemonstration will proceed throughthree terms and no more, unless thesame conclusion is established bydifferent pairs of propositions; e.g.the conclusion E may be establishedthrough the propositions A and B, andthrough the propositions C and D, orthrough the propositions A and B, or Aand C, or B and C. For nothing preventsthere being several middles for thesame terms. But in that case there is

not one but several syllogisms. Oragain when each of the propositions Aand B is obtained by syllogisticinference, e.g. by means of D and E,and again B by means of F and G. Or one





or (ii) A or B, either (i) thesyllogisms will be more than one, or(ii) the same thing happens to beinferred by means of several terms onlyin the sense which we saw to be

possible. But if (iii) the conclusionis other than E or A or B, thesyllogisms will be many, andunconnected with one another. But if Cis not so related to D as to make asyllogism, the propositions will have

been assumed to no purpose, unless forthe sake of induction or of obscuringthe argument or something of the sort.

(2) But if from the propositions A andB there follows not E but some otherconclusion, and if from C and D either

A or B follows or something else, thenthere are several syllogisms, and theydo not establish the conclusion

proposed: for we assumed that thesyllogism proved E. And if noconclusion follows from C and D, itturns out that these propositions have

been assumed to no purpose, and the

syllogism does not prove the original proposition.



So it is clear that every demonstrationand every syllogism will proceedthrough three terms only.

This being evident, it is clear that asyllogistic conclusion follows from two

premisses and not from more than two.For the three terms make two premisses,unless a new premiss is assumed, as wassaid at the beginning, to perfect thesyllogisms. It is clear therefore that

in whatever syllogistic argument the premisses through which the main

conclusion follows (for some of the preceding conclusions must be premisses) are not even in number, this

argument either has not been drawnsyllogistically or it has assumed morethan was necessary to establish itsthesis.

If then syllogisms are taken withrespect to their main premisses, everysyllogism will consist of an evennumber of premisses and an odd numberof terms (for the terms exceed the

premisses by one), and the conclusionswill be half the number of the

premisses. But whenever a conclusion isreached by means of prosyllogisms or by

means of several continuous middle



terms, e.g. the proposition AB by meansof the middle terms C and D, the numberof the terms will similarly exceed thatof the premisses by one (for the extraterm must either be added outside orinserted: but in either case it followsthat the relations of predication areone fewer than the terms related), andthe premisses will be equal in numberto the relations of predication. The

premisses however will not always be

even, the terms odd; but they willalternate-when the premisses are even,the terms must be odd; when the termsare even, the premisses must be odd:for along with one term one premiss isadded, if a term is added from anyquarter. Consequently since the

premisses were (as we saw) even, andthe terms odd, we must make themalternately even and odd at eachaddition. But the conclusions will notfollow the same arrangement either inrespect 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 theconclusion is drawn not in relation tothe single term last added, but inrelation to all the rest, e.g. if to

ABC the term D is added, two



conclusions are thereby added, one inrelation to A, the other in relation toB. Similarly with any furtheradditions. And similarly too if theterm is inserted in the middle: for inrelation to one term only, a syllogismwill not be constructed. Consequentlythe conclusions will be much morenumerous than the terms or the

premisses.

26

Since we understand the subjects withwhich syllogisms are concerned, whatsort of conclusion is established ineach figure, and in how many moods thisis done, it is evident to us both whatsort of problem is difficult and whatsort is easy to prove. For that whichis concluded in many figures andthrough many moods is easier; thatwhich is concluded in few figures andthrough few moods is more difficult toattempt. The universal affirmative is

proved by means of the first figure

only and by this in only one mood; theuniversal negative is proved boththrough the first figure and throughthe second, through the first in one

mood, through the second in two. The





particular, and particular statements by means of universal: but it is not possible to establish universal

statements by means of particular,though it is possible to establish

particular statements by means ofuniversal. At the same time it isevident that it is easier to refutethan to establish.

The manner in which every syllogism is

produced, the number of the terms and premisses through which it proceeds,

the relation of the premisses to oneanother, the character of the problem

proved in each figure, and the numberof the figures appropriate to each

problem, all these matters are clearfrom what has been said.

27

We must now state how we may ourselvesalways have a supply of syllogisms in

reference to the problem proposed and by what road we may reach the principles relative to the problem: for perhaps we ought not only to

investigate the construction of



syllogisms, but also to have the powerof making them.

Of all the things which exist some aresuch that they cannot be predicated ofanything else truly and universally,e.g. Cleon and Callias, i.e. theindividual and sensible, but otherthings may be predicated of them (foreach of these is both man and animal);and some things are themselves

predicated of others, but nothing prioris predicated of them; and some are

predicated of others, and yet others ofthem, e.g. man of Callias and animal of

man. It is clear then that some thingsare naturally not stated of anything:for as a rule each sensible thing issuch that it cannot be predicated ofanything, save incidentally: for wesometimes say that that white object isSocrates, or that that which approachesis Callias. We shall explain in another

place that there is an upward limitalso to the process of predicating: forthe present we must assume this. Of

these ultimate predicates it is not possible to demonstrate another predicate, save as a matter of opinion, but these may be predicated of other

things. Neither can individuals be



predicated of other things, thoughother things can be predicated of them.

Whatever lies between these limits can be spoken of in both ways: they may be

stated of others, and others stated ofthem. And as a rule arguments andinquiries are concerned with thesethings. We must select the premissessuitable to each problem in this

manner: first we must lay down thesubject and the definitions and the

properties of the thing; next we mustlay down those attributes which followthe thing, and again those which thething follows, and those which cannot

belong to it. But those to which itcannot belong need not be selected,

because the negative statement impliedabove is convertible. Of the attributeswhich follow we must distinguish thosewhich fall within the definition, thosewhich are predicated as properties, andthose which are predicated asaccidents, and of the latter thosewhich apparently and those which really

belong. The larger the supply a man has

of these, the more quickly will hereach a conclusion; and in proportionas he apprehends those which are truer,the more cogently will he demonstrate.But he must select not those which



follow some particular but those whichfollow the thing as a whole, e.g. notwhat follows a particular man but whatfollows every man: for the syllogism

proceeds through universal premisses.If the statement is indefinite, it isuncertain whether the premiss isuniversal, but if the statement isdefinite, the matter is clear.Similarly one must select thoseattributes which the subject follows as

wholes, for the reason given. But thatwhich follows one must not suppose tofollow as a whole, e.g. that everyanimal follows man or every science

music, but only that it follows,without qualification, and indeed westate it in a proposition: for theother statement is useless andimpossible, e.g. that every man isevery animal or justice is all good.But that which something followsreceives the mark ‘every’. Whenever thesubject, for which we must obtain theattributes that follow, is contained bysomething else, what follows or does

not follow the highest term universally must not be selected in dealing with

the subordinate term (for theseattributes have been taken in dealingwith the superior term; for what



follows animal also follows man, andwhat does not belong to animal does not

belong to man); but we must choosethose attributes which are peculiar toeach subject. For some things are

peculiar to the species as distinctfrom the genus; for species beingdistinct there must be attributes

peculiar to each. Nor must we take asthings which the superior term follows,those things which the inferior term

follows, e.g. take as subjects of the predicate ‘animal’ what are really

subjects of the predicate ‘man’. It isnecessary indeed, if animal follows

man, that it should follow all thesealso. But these belong more properly tothe choice of what concerns man. One

must apprehend also normal consequentsand normal antecedents-, for

propositions which obtain normally areestablished syllogistically from

premisses which obtain normally, someif not all of them having thischaracter of normality. For theconclusion of each syllogism resembles

its principles. We must not howeverchoose attributes which are consequentupon all the terms: for no syllogismcan be made out of such premisses. The



reason why this is so will be clear inthe sequel.

28

If men wish to establish somethingabout some whole, they must look to thesubjects of that which is beingestablished (the subjects of which ithappens to be asserted), and theattributes which follow that of which

it is to be predicated. For if any ofthese subjects is the same as any ofthese attributes, the attributeoriginally in question must belong tothe subject originally in question. Butif the purpose is to establish not auniversal but a particular proposition,they must look for the terms of whichthe terms in question are predicable:for if any of these are identical, theattribute in question must belong tosome of the subject in question.

Whenever the one term has to belong tonone of the other, one must look to theconsequents of the subject, and to

those attributes which cannot possibly be present in the predicate in

question: or conversely to theattributes which cannot possibly be

present in the subject, and to the



consequents of the predicate. If any members of these groups are identical,

one of the terms in question cannot possibly belong to any of the other.

For sometimes a syllogism in the firstfigure results, sometimes a syllogismin the second. But if the object is toestablish a particular negative

proposition, we must find antecedentsof the subject in question andattributes which cannot possibly belong

to the predicate in question. If any members of these two groups are

identical, it follows that one of theterms in question does not belong tosome of the other. Perhaps each ofthese statements will become clearer inthe following way. Suppose theconsequents of A are designated by B,the antecedents of A by C, attributeswhich cannot possibly belong to A by D.Suppose again that the attributes of Eare designated by F, the antecedents ofE by G, and attributes which cannot

belong to E by H. If then one of the Csshould be identical with one of the Fs,

A must belong to all E: for F belongsto all E, and A to all C, consequently

A belongs to all E. If C and G areidentical, A must belong to some of theEs: for A follows C, and E follows all



G. If F and D are identical, A will belong to none of the Es by a prosyllogism: for since the negative proposition is convertible, and F is

identical with D, A will belong to noneof the Fs, but F belongs to all E.

Again, if B and H are identical, A will belong to none of the Es: for B will belong to all A, but to no E: for it

was assumed to be identical with H, andH belonged to none of the Es. If D and

G are identical, A will not belong tosome of the Es: for it will not belongto G, because it does not belong to D:

but G falls under E: consequently Awill not belong to some of the Es. If Bis identical with G, there will be aconverted syllogism: for E will belongto all A since B belongs to A and E toB (for B was found to be identical withG): but that A should belong to all Eis not necessary, but it must belong tosome E because it is possible toconvert the universal 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:for all syllogisms proceed through



these. But if we are seekingconsequents and antecedents we mustlook for those which are primary and

most universal, e.g. in reference to Ewe must look to KF rather than to Falone, and in reference to A we mustlook to KC rather than to C alone. Forif A belongs to KF, it belongs both toF and to E: but if it does not followKF, it may yet follow F. Similarly we

must consider the antecedents of A

itself: for if a term follows the 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

the two premisses, and that all thesyllogisms proceed through theaforesaid figures. For it is provedthat A belongs to all E, whenever anidentical term is found among the Csand Fs. This will be the middle term; Aand E will be 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 thelast figure: for G becomes the middleterm. And A will belong to no E, when D





belong to E, or if those attributes areidentical which cannot belong to eitherterm: for no syllogism is produced by

means of these. For if the consequentsare identical, e.g. B and F, we havethe middle figure with both premissesaffirmative: if the antecedents of Aare identical with attributes whichcannot belong to E, e.g. C with H, wehave the first figure with its minor

premiss negative. If attributes which

cannot belong to either term areidentical, e.g. C and H, both premissesare negative, either in the first or inthe middle figure. But no syllogism is

possible in this way.

It is evident too that we must find outwhich terms in this inquiry areidentical, not which are different orcontrary, first because the object ofour investigation is the middle term,and the middle term must be not diverse

but identical. Secondly, wherever ithappens that a syllogism results fromtaking contraries or terms which cannot

belong to the same thing, all argumentscan be reduced to the aforesaid moods,e.g. if B and F are contraries orcannot belong to the same thing. For ifthese are taken, a syllogism will be



formed to prove that A belongs to noneof the Es, not however from the

premisses taken but in the aforesaid mood. For B will belong to all A and to

no E. Consequently B must be identicalwith one of the Hs. Again, if B and Gcannot belong to the same thing, itfollows that A will not belong to someof the Es: for then too we shall havethe middle figure: for B will belong toall A and to no G. Consequently B must

be identical with some of the Hs. Forthe fact that B and G cannot belong tothe same thing differs in no way fromthe fact that B is identical with someof the Hs: for that includes everythingwhich cannot belong to E.

It is clear then that from theinquiries taken by themselves nosyllogism results; but if B and F arecontraries B must be identical with oneof the Hs, and the syllogism resultsthrough these terms. It turns out thenthat those who inquire in this mannerare looking gratuitously for some other

way than the necessary way because theyhave failed to observe the identity ofthe Bs with the Hs.



29

Syllogisms which lead to impossibleconclusions are similar to ostensivesyllogisms; they also are formed by

means of the consequents andantecedents of the terms in question.In both cases the same inquiry isinvolved. For what is provedostensively may also be concludedsyllogistically per impossibile by

means of the same terms; and what is proved per impossibile may also be proved ostensively, e.g. that A belongs

to none of the Es. For suppose A to belong to some E: then since B belongs

to all A and A to some of the Es, Bwill belong to some of the Es: but itwas assumed that it belongs to none.

Again we may prove that A belongs tosome E: for if A belonged to none ofthe Es, and E belongs to all G, A will

belong to none of the Gs: but it wasassumed to belong to all. Similarlywith the other propositions requiring

proof. The proof per impossibile will

always and in all cases be from theconsequents and antecedents of theterms in question. Whatever the problemthe same inquiry is necessary whetherone wishes to use an ostensive



syllogism or a reduction toimpossibility. For both thedemonstrations start from the sameterms, e.g. suppose it has been provedthat A belongs to no E, because itturns out that otherwise B belongs tosome of the Es and this is impossible-if now it is assumed that B belongs tono E and to all A, it is clear that Awill belong to no E. Again if it has

been proved by an ostensive syllogism

that A belongs to no E, assume that A belongs to some E and it will be proved per impossibile to belong to no E.

Similarly with the rest. In all casesit is necessary to find some commonterm other than the subjects ofinquiry, to which the syllogismestablishing the false conclusion mayrelate, so that if this premiss isconverted, and the other remains as itis, the syllogism will be ostensive by

means of the same terms. For theostensive syllogism differs from thereductio ad impossibile in this: in theostensive syllogism both remisses are

laid down in accordance with the truth,in the reductio ad impossibile one ofthe premisses is assumed falsely.



These points will be made clearer bythe sequel, when we discuss thereduction to impossibility: at presentthis much must be clear, that we mustlook to terms of the kinds mentionedwhether we wish to use an ostensivesyllogism or a reduction toimpossibility. In the otherhypothetical syllogisms, I mean thosewhich proceed by substitution, or by

positing a certain quality, the inquiry

will be directed to the terms of the problem to be proved-not the terms of

the original problem, but the new termsintroduced; and the method of theinquiry will be the same as before. Butwe must consider and determine in how

many ways hypothetical syllogisms are possible.

Each of the problems then can be provedin the manner described; but it is

possible to establish some of themsyllogistically in another way, e.g.universal problems by the inquiry whichleads up to a particular conclusion,

with the addition of an hypothesis. Forif the Cs and the Gs should beidentical, but E should be assumed to

belong to the Gs only, then A would belong to every E: and again if the Ds



and the Gs should be identical, but Eshould be predicated of the Gs only, itfollows that A will belong to none ofthe Es. Clearly then we must considerthe matter in this way also. The methodis the same whether the relation isnecessary or possible. For the inquirywill be the same, and the syllogismwill proceed through terms arranged inthe same order whether a possible or a

pure proposition is proved. We must

find in the case of possible relations,as well as terms that belong, termswhich can belong though they actuallydo not: for we have proved that thesyllogism which establishes a possiblerelation proceeds through these termsas well. Similarly also with the other

modes of predication.

It is clear then from what has beensaid not only that all syllogisms can

be formed in this way, but also thatthey cannot be formed in any other. Forevery syllogism has been proved to beformed through one of the

aforementioned figures, and thesecannot be composed through other termsthan the consequents and antecedents ofthe terms in question: for from thesewe obtain the premisses and find the



middle term. Consequently a syllogismcannot be formed by means of otherterms.

30

The method is the same in all cases, in philosophy, in any art or study. We must 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 by meansof the three terms, refuting statementsin one way, confirming them in another,in the pursuit of truth starting from

premisses in which the arrangement ofthe terms is in accordance with truth,while if we look for dialecticalsyllogisms we must start from probable

premisses. The principles of syllogismshave been stated in general terms, bothhow they are characterized and how we

must hunt for them, so as not to lookto everything that is said about theterms of the problem or to the same

points whether we are confirming or

refuting, or again whether we areconfirming of all or of some, andwhether we are refuting of all or some.we must look to fewer points and they

must be definite. We have also stated



how we must select with reference toeverything that is, e.g. about good orknowledge. But in each science the

principles which are peculiar are the most numerous. Consequently it is the business of experience to give the principles which belong to each

subject. I mean for example thatastronomical experience supplies the

principles of astronomical science: foronce the phenomena were adequately

apprehended, the demonstrations ofastronomy were discovered. Similarlywith any other art or science.Consequently, if the attributes of thething are apprehended, our businesswill then be to exhibit readily thedemonstrations. For if none of the trueattributes of things had been omittedin the historical survey, we should beable to discover the proof anddemonstrate everything which admittedof proof, and to make that clear, whosenature does not admit of proof.

In general then we have explained

fairly well how we must select premisses: we have discussed the matter

accurately in the treatise concerningdialectic.



31

It is easy to see that division intoclasses is a small part of the methodwe have described: for division is, soto speak, a weak syllogism; for what itought to prove, it begs, and it alwaysestablishes something more general thanthe attribute in question. First, thisvery point had escaped all those whoused the method of division; and they

attempted to persuade men that it was possible to make a demonstration of

substance and essence. Consequentlythey did not understand what it is

possible to prove syllogistically bydivision, nor did they understand thatit was possible to provesyllogistically in the manner we havedescribed. In demonstrations, whenthere is a need to prove a positivestatement, the middle term throughwhich the syllogism is formed mustalways be inferior to and notcomprehend the first of the extremes.But division has a contrary intention:

for it takes the universal as middle.Let animal be the term signified by A,

mortal by B, and immortal 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 immortal: i.e. whatever is A

is all either B or C. Again, alwaysdividing, he lays it down that man isan animal, so he assumes A of D as

belonging to it. Now the trueconclusion is that every D is either Bor C, consequently man must be either

mortal or immortal, but it is notnecessary that man should be a mortalanimal-this is begged: and this is what

ought to have been provedsyllogistically. And again, taking A as

mortal animal, B as footed, C asfootless, and D as man, he assumes inthe same way that A inheres either in Bor in C (for every mortal animal iseither footed or footless), and heassumes A of D (for he assumed man, aswe saw, to be a mortal animal);consequently it is necessary that manshould be either a footed or a footlessanimal; but it is not necessary that

man should be footed: this he assumes:and it is just this again which heought to have demonstrated. Always

dividing then in this way it turns outthat these logicians assume as middlethe universal term, and as extremesthat which ought to have been thesubject of demonstration and the



differentiae. In conclusion, they donot make it clear, and show it to benecessary, that this is man or whateverthe subject of inquiry may be: for they

pursue the other method altogether,never even suspecting the presence ofthe rich supply of evidence which might

be used. It is clear that it is neither possible to refute a statement by this method of division, nor to draw a

conclusion about an accident or

property of a thing, nor about itsgenus, nor in cases in which it isunknown whether it is thus or thus,e.g. whether the diagonal isincommensurate. For if he assumes thatevery length is either commensurate orincommensurate, and the diagonal is alength, he has proved that the diagonalis either incommensurate orcommensurate. But if he should assumethat it is incommensurate, he will haveassumed what he ought to have proved.He cannot then prove it: for this ishis method, but proof is not possible

by this method. Let A stand for

‘incommensurate or commensurate’, B for‘length’, C for ‘diagonal’. It is clearthen that this method of investigationis not suitable for every inquiry, nor



is it useful in those cases in which itis thought to be most suitable.

From what has been said it is clearfrom what elements demonstrations areformed and in what manner, and to what

points we must look in each problem.

32

Our next business is to state how we

can reduce syllogisms to theaforementioned figures: for this partof the inquiry still remains. If weshould investigate the production ofthe syllogisms and had the power ofdiscovering them, and further if wecould resolve the syllogisms producedinto the aforementioned figures, ouroriginal problem would be brought to aconclusion. It will happen at the sametime that what has been already saidwill be confirmed and its truth madeclearer by what we are about to say.For everything that is true must inevery respect agree with itself First

then we must attempt to select the two premisses of the syllogism (for it is

easier to divide into large parts thaninto small, and the composite parts arelarger than the elements out of which



they are made); next we must inquirewhich are universal and which

particular, and if both premisses havenot been stated, we must ourselvesassume the one which is missing. Forsometimes men put forward the universal

premiss, but do not posit the premisswhich is contained in it, either inwriting or in discussion: or men putforward the premisses of the principalsyllogism, but omit those through which

they are inferred, and invite theconcession of others to no purpose. We

must inquire then whether anythingunnecessary has been assumed, oranything necessary has been omitted,and we must posit the one and take awaythe other, until we have reached thetwo premisses: for unless we havethese, we cannot reduce arguments putforward in the way described. In somearguments it is easy to see what iswanting, but some escape us, and appearto be syllogisms, because somethingnecessary results from what has beenlaid down, e.g. if the assumptions were

made that substance is not annihilated by the annihilation of what is not

substance, and that if the elements outof which a thing is made areannihilated, then that which is made





found in both premisses in all thefigures.

If then the middle term is a predicateand a subject of predication, or if itis a predicate, and something else isdenied of it, we shall have the firstfigure: if it both is a predicate andis denied of something, the middlefigure: if other things are predicatedof it, or one is denied, the other

predicated, the last figure. For it wasthus that we found the middle term

placed in each figure. It is placedsimilarly too if the premisses are notuniversal: for the middle term isdetermined in the same way. Clearlythen, if the same term is not stated

more than once in the course of anargument, a syllogism cannot be made:for a middle term has not been taken.Since we know what sort of thesis isestablished in each figure, and inwhich the universal, in what sort the

particular is described, clearly we must not look for all the figures, but

for that which is appropriate to thethesis in hand. If the thesis isestablished in more figures than one,we shall recognize the figure by the

position of the middle term.



33

Men are frequently deceived aboutsyllogisms because the inference isnecessary, as has been said above;sometimes they are deceived by thesimilarity in the positing of theterms; and this ought not to escape our

notice. E.g. if A is stated of B, and Bof C: it would seem that a syllogism is

possible since the terms stand thus: but nothing necessary results, nor does

a syllogism. Let A represent the term‘being eternal’, B ‘Aristomenes as anobject of thought’, C ‘Aristomenes’. Itis true then that A belongs to B. For

Aristomenes as an object of thought iseternal. But B also belongs to C: for

Aristomenes is Aristomenes as an objectof thought. But A does not belong to C:for Aristomenes is perishable. For nosyllogism was made although the termsstood thus: that required that the

premiss AB should be stateduniversally. But this is false, thatevery Aristomenes who is an object ofthought is eternal, since Aristomenesis perishable. Again let C stand for



‘Miccalus’, B for ‘musical Miccalus’, Afor ‘perishing to-morrow’. It is trueto predicate B of C: for Miccalus is

musical Miccalus. Also A can be predicated of B: for musical Miccalus might perish to-morrow. But to state A

of C is false at any rate. Thisargument then is identical with theformer; for it is not true universallythat musical Miccalus perishes to-

morrow: but unless this is assumed, no

syllogism (as we have shown) is possible.

This deception then arises throughignoring a small distinction. For if weaccept the conclusion as though it madeno difference whether we said ‘This

belong to that’ or ‘This belongs to allof that’.

34

Men will frequently fall into fallaciesthrough not setting out the terms ofthe premiss well, e.g. suppose A to be

health, B disease, C man. It is true tosay that A cannot belong to any B (forhealth belongs to no disease) and againthat B belongs to every C (for every

man is capable of disease). It would



seem to follow that health cannot belong to any man. The reason for this

is that the terms are not set out wellin the statement, since if the thingswhich are in the conditions aresubstituted, no syllogism can be made,e.g. if ‘healthy’ is substituted for‘health’ and ‘diseased’ for ‘disease’.For it is not true to say that beinghealthy cannot belong to one who isdiseased. But unless this is assumed no

conclusion results, save in respect of possibility: but such a conclusion is

not impossible: for it is possible thathealth should belong to no man. Againthe fallacy may occur in a similar wayin the middle figure: ‘it is not

possible that health should belong toany disease, but it is possible thathealth should belong to every man,consequently it is not possible thatdisease should belong to any man’. Inthe third figure the fallacy results inreference to possibility. For healthand diseae and knowledge and ignorance,and in general contraries, may possibly

belong to the same thing, but cannot belong 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 thesecases the fallacy arises from thesetting out of the terms: for if thethings that are in the conditions aresubstituted, no fallacy arises. It isclear then that in such premisses what

possesses the condition ought always to be substituted for the condition and

taken as the term.

35

We must not always seek to set out theterms a single word: for we shall oftenhave complexes of words to which asingle name is not given. Hence it isdifficult to reduce syllogisms withsuch terms. Sometimes too fallacieswill result from such a search, e.g.the belief that syllogism can establishthat which has no mean. Let A stand fortwo right angles, B for triangle, C forisosceles triangle. A then belongs to C

because of B: but A belongs to Bwithout the mediation of another term:for the triangle in virtue of its ownnature contains two right angles,consequently there will be no middle



term for the proposition AB, althoughit is demonstrable. For it is clearthat the middle must not always beassumed to be an individual thing, butsometimes a complex of words, ashappens in the case mentioned.

36

That the first term belongs to the middle, and the middle to the extreme,

must not be understood in the sensethat they can always be predicated ofone another or that the first term will

be predicated of the middle in the sameway as the middle is predicated of thelast term. The same holds if the

premisses are negative. But we mustsuppose the verb ‘to belong’ to have as

many meanings as the senses in whichthe verb ‘to be’ is used, and in whichthe assertion that a thing ‘is’ may besaid to be true. Take for example thestatement that there is a singlescience of contraries. Let A stand for‘there being a single science’, and B

for things which are contrary to oneanother. Then A belongs to B, not inthe sense that contraries are the factof there being a single science ofthem, but in the sense that it is true



to say of the contraries that there isa single science of them.

It happens sometimes that the firstterm is stated of the middle, but the

middle is not stated of the third term,e.g. if wisdom is knowledge, and wisdomis of the good, the conclusion is thatthere is knowledge of the good. Thegood then is not knowledge, thoughwisdom is knowledge. Sometimes the

middle term is stated of the third, butthe first is not stated of the middle,e.g. if there is a science ofeverything that has a quality, or is acontrary, and the good both is acontrary and has a quality, theconclusion is that there is a scienceof the good, but the good is notscience, nor is that which has aquality or is a contrary, though thegood is both of these. Sometimesneither the first term is stated of the

middle, nor the middle of the third,while the first is sometimes stated ofthe third, and sometimes not: e.g. if

there is a genus of that of which thereis a science, and if there is a scienceof the good, we conclude that there isa genus of the good. But nothing is

predicated of anything. And if that of



which there is a science is a genus,and if there is a science of the good,we conclude that the good is a genus.The first term then is predicated ofthe extreme, but in the premisses onething is not stated of another.

The same holds good where the relationis negative. For ‘that does not belongto this’ does not always mean that‘this is not that’, but sometimes that

‘this is not of that’ or ‘for that’,e.g. ‘there is not a motion of a motionor a becoming of a becoming, but thereis a becoming of pleasure: so pleasureis not a becoming.’ Or again it may besaid that there is a sign of laughter,

but there is not a sign of a sign,consequently laughter is not a sign.This holds in the other cases too, inwhich the thesis is refuted because thegenus is asserted in a particular way,in relation to the terms of the thesis.

Again take the inference ‘opportunityis not the right time: for opportunity

belongs to God, but the right time does

not, since nothing is useful to God’. We must take as terms opportunity-right

time-God: but the premiss must beunderstood according to the case of thenoun. For we state this universally



without qualification, that the termsought always to be stated in thenominative, e.g. man, good, contraries,not in oblique cases, e.g. of man, of agood, of contraries, but the premissesought to be understood with referenceto the cases of each term-either thedative, e.g. ‘equal to this’, or thegenitive, e.g. ‘double of this’, or theaccusative, e.g. ‘that which strikes orsees this’, or the nominative, e.g.

‘man is an animal’, or in whateverother way the word falls in the

premiss.

37

The expressions ‘this belongs to that’and ‘this holds true of that’ must beunderstood in as many ways as there aredifferent categories, and thesecategories must be taken either with orwithout qualification, and further assimple or compound: the same holds good

of the corresponding negativeexpressions. We must consider these

points and define them better.



38

A term which is repeated in the premisses ought to be joined to the

first extreme, not to the middle. I mean for example that if a syllogism

should be made proving that there isknowledge of justice, that it is good,the expression ‘that it is good’ (or‘qua good’) should be joined to thefirst term. Let A stand for ‘knowledge

that it is good’, B for good, C forjustice. It is true to predicate A ofB. For of the good there is knowledgethat it is good. Also it is true to

predicate B of C. For justice isidentical with a good. In this way ananalysis of the argument can be made.But if the expression ‘that it is good’were added to B, the conclusion willnot follow: for A will be true of B,

but B will not be true of C. For to predicate of justice the term ‘good

that it is good’ is false and notintelligible. Similarly if it should be

proved that the healthy is an object of

knowledge qua good, of goat-stag anobject of knowledge qua not existing,or man perishable qua an object ofsense: in every case in which an



addition is made to the predicate, theaddition must be joined to the extreme.

The position of the terms is not thesame when something is establishedwithout qualification and when it isqualified by some attribute orcondition, e.g. when the good is provedto be an object of knowledge and whenit is proved to be an object ofknowledge that it is good. If it has

been proved to be an object ofknowledge without qualification, we

must put as middle term ‘that whichis’, but if we add the qualification‘that it is good’, the middle term must

be ‘that which is something’. Let Astand for ‘knowledge that it issomething’, B stand for ‘something’,and C stand for ‘good’. It is true to

predicate A of B: for ex hypothesithere is a science of that which issomething, that it is something. B toois true of C: for that which Crepresents is something. Consequently Ais true of C: there will then be

knowledge of the good, that it is good:for ex hypothesi the term ‘something’indicates the thing’s special nature.But if ‘being’ were taken as middle and‘being’ simply were joined to the



extreme, not ‘being something’, weshould not have had a syllogism provingthat there is knowledge of the good,that it is good, but that it is; e.g.let A stand for knowledge that it is, Bfor being, C for good. Clearly then insyllogisms which are thus limited we

must take the terms in the way stated.

39

We ought also to exchange terms whichhave the same value, word for word, and

phrase for phrase, and word and phrase,and always take a word in preference toa phrase: for thus the setting out ofthe terms will be easier. For exampleif it makes no difference whether wesay that the supposable is not thegenus of the opinable or that theopinable is not identical with a

particular kind of supposable (for whatis meant is the same in bothstatements), it is better to take asthe terms the supposable and theopinable in preference to the phrase

suggested.



40

Since the expressions ‘pleasure isgood’ and ‘pleasure is the good’ arenot identical, we must not set out theterms in the same way; but if thesyllogism is to prove that pleasure isthe good, the term must be ‘the good’,

but if the object is to prove that pleasure is good, the term will be

‘good’. Similarly in all other cases.

41

It is not the same, either in fact orin speech, that A belongs to all ofthat to which B belongs, and that A

belongs to all of that to all of whichB belongs: for nothing prevents B from

belonging to C, though not to all C:e.g. let B stand for beautiful, and Cfor white. If beauty belongs tosomething white, it is true to say that

beauty belongs to that which is white; but not perhaps to everything that is

white. If then A belongs to B, but not

to everything of which B is predicated,then whether B belongs to all C or

merely belongs to C, it is notnecessary that A should belong, I donot say to all C, but even to C at all.



But if A belongs to everything of whichB is truly stated, it will follow that

A can be said of all of that of all ofwhich B is said. If however A is saidof that of all of which B may be said,nothing prevents B belonging to C, andyet A not belonging to all C or to anyC at all. If then we take three termsit is clear that the expression ‘A issaid 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 ofall of a third term, so also is A: butif B is not said of all of the thirdterm, there is no necessity that Ashould be said of all of it.

We must not suppose that somethingabsurd results through setting out theterms: for we do not use the existenceof this particular thing, but imitatethe geometrician who says that ‘thisline a foot long’ or ‘this straightline’ or ‘this line without breadth’exists although it does not, but doesnot use the diagrams in the sense that

he reasons from them. For in general,if two things are not related as wholeto part and part to whole, the proverdoes not prove from them, and so nosyllogism a is formed. We (I mean the



learner) use the process of setting outterms like perception by sense, not asthough it were impossible todemonstrate without these illustrativeterms, as it is to demonstrate withoutthe premisses of the syllogism.

42

We should not forget that in the samesyllogism not all conclusions are

reached through one figure, but onethrough one figure, another throughanother. Clearly then we must analysearguments in accordance with this.Since not every problem is proved inevery figure, but certain problems ineach figure, it is clear from theconclusion in what figure the premissesshould be sought.

43

In reference to those arguments aimingat a definition which have beendirected to prove some part of the

definition, we must take as a term the point to which the argument has been

directed, not the whole definition: forso we shall be less likely to bedisturbed by the length of the term:



e.g. if a man proves that water is adrinkable liquid, we must take as termsdrinkable and water.

44

Further we must not try to reducehypothetical syllogisms; for with thegiven premisses it is not possible toreduce them. For they have not been

proved by syllogism, but assented to by

agreement. For instance if a man shouldsuppose that unless there is onefaculty of contraries, there cannot beone science, and should then argue thatnot every faculty is of contraries,e.g. of what is healthy and what issickly: for the same thing will then beat the same time healthy and sickly. Hehas shown that there is not one facultyof all contraries, but he has not

proved that there is not a science. Andyet one must agree. But the agreementdoes not come from a syllogism, butfrom an hypothesis. This argumentcannot be reduced: but the proof that

there is not a single faculty can. Thelatter argument perhaps was asyllogism: but the former was anhypothesis.



The same holds good of arguments whichare brought to a conclusion perimpossibile. These cannot be analysedeither; but the reduction to what isimpossible can be analysed since it is

proved by syllogism, though the rest ofthe argument cannot, because theconclusion is reached from anhypothesis. But these differ from the

previous arguments: for in the former a preliminary 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,then contraries fall under the samescience; whereas in the latter, even ifno preliminary agreement has been made,

men still accept the reasoning, becausethe falsity is patent, e.g. the falsityof what follows from the assumptionthat the diagonal is commensurate, viz.that then odd numbers are equal toevens.

Many other arguments are brought to aconclusion by the help of an

hypothesis; these we ought to considerand mark out clearly. We shall describein the sequel their differences, andthe various ways in which hypotheticalarguments are formed: but at present



this much must be clear, that it is not possible to resolve such arguments into

the figures. And we have explained thereason.

45

Whatever problems are proved in morethan one figure, if they have beenestablished in one figure by syllogism,can be reduced to another figure, e.g.

a negative syllogism in the firstfigure can be reduced to the second,and a syllogism in the middle figure tothe first, not all however but someonly. The point will be clear in thesequel. If A belongs to no B, and B toall C, then A belongs to no C. Thus thefirst figure; but if the negativestatement is converted, we shall havethe middle figure. For B belongs to no

A, and to all C. Similarly if thesyllogism is not universal but

particular, e.g. if A belongs to no B,and B to some C. Convert the negativestatement and you will have the middle

figure.

The universal syllogisms in the secondfigure can be reduced to the first, butonly one of the two particular



syllogisms. Let A belong to no B and toall C. Convert the negative statement,and you will have the first figure. ForB will belong to no A and A to all C.But if the affirmative statementconcerns 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: forthe negative statement is convertible.

But if the syllogism is particular,whenever the negative statementconcerns the major extreme, reductionto the first figure will be possible,e.g. if A belongs to no B and to someC: convert the negative statement andyou will have the first figure. For Bwill belong to no A and A to some C.But when the affirmative statementconcerns the major extreme, noresolution will be possible, e.g. if A

belongs to all B, but not to all C: forthe statement AB does not admit ofconversion, nor would there be asyllogism if it did.

Again syllogisms in the third figurecannot all be resolved into the first,though all syllogisms in the firstfigure can be resolved into the third.



Let A belong to all B and B to some C.Since the particular affirmative isconvertible, C will belong to some B:

but A belonged to all B: so that thethird figure is formed. Similarly ifthe syllogism is negative: for the

particular affirmative is convertible:therefore A will belong to no B, and tosome C.

Of the syllogisms in the last figure

one only cannot be resolved into thefirst, viz. when the negative statementis not universal: all the rest can beresolved. Let A and B be affirmed ofall C: then C can be converted

partially with either A or B: C then belongs to some B. Consequently we

shall get the first figure, if A belongs to all C, and C to some of the

Bs. If A belongs to all C and B to someC, the argument is the same: for B isconvertible in reference to C. But if B

belongs to all C and A to some C, thefirst term must be B: for B belongs toall 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. If the syllogismis negative, when the terms areuniversal we must take them in a



similar way. Let B belong to all C, and A to no C: then C will belong to some

B, and A to no C; and so C will be middle term. Similarly if the negative

statement is universal, the affirmative particular: for A will belong to no C,

and C to some of the Bs. But if thenegative statement is particular, noresolution 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 resolvethe figures into one another the

premiss which concerns the minorextreme must be converted in both thefigures: for when this premiss isaltered, the transition to the otherfigure is made.

One of the syllogisms in the middlefigure can, the other cannot, beresolved into the third figure.

Whenever the universal statement isnegative, resolution is possible. For

if A belongs to no B and to some C, both B and C alike are convertible in

relation to A, so that B belongs to no A and C to some A. A therefore is middle term. But when A belongs to all



B, and not to some C, resolution willnot be possible: for neither of the

premisses is universal afterconversion.

Syllogisms in the third figure can beresolved into the middle figure,whenever the negative statement isuniversal, 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. But if

the negative statement is particular,no resolution will be possible: for the

particular negative does not admit ofconversion.

It is clear then that the samesyllogisms cannot be resolved in thesefigures which could not be resolvedinto the first figure, and that whensyllogisms are reduced to the firstfigure these alone are confirmed byreduction to what is impossible.

It is clear from what we have said howwe ought to reduce syllogisms, and that

the figures may be resolved into oneanother.



46

In establishing or refuting, it makessome difference whether we suppose theexpressions ‘not to be this’ and ‘to benot-this’ are identical or different in

meaning, e.g. ‘not to be white’ and ‘to be not-white’. For they do not mean the

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 therelation of ‘it is white’ to ‘it isnot-white’; so is that of ‘he knowswhat is good’ to ‘he knows what is not-good’. For there is no difference

between the expressions ‘he knows whatis good’ and ‘he is knowing what isgood’, or ‘he can walk’ and ‘he is ableto walk’: therefore there is nodifference between their contraries ‘hecannot walk’-’he is not able to walk’.If then ‘he is not able to walk’ meansthe same as ‘he is able not to walk’,capacity to walk and incapacity to walk

will belong at the same time to thesame person (for the same man can bothwalk and not-walk, and is possessed ofknowledge of what is good and of whatis not-good), but an affirmation and a



denial which are opposed to one anotherdo not belong at the same time to thesame thing. As then ‘not to know whatis good’ is not the same as ‘to knowwhat is not good’, so ‘to be not-good’is not the same as ‘not to be good’.For when two pairs correspond, if theone pair are different from oneanother, the other pair also must bedifferent. Nor is ‘to be not-equal’ thesame as ‘not to be equal’: for there is

something underlying the one, viz. thatwhich is not-equal, and this is theunequal, but there is nothingunderlying the other. Wherefore noteverything is either equal or unequal,

but everything is equal or is notequal. Further the expressions ‘it is anot-white log’ and ‘it is not a whitelog’ 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 whitelog need not be a log at all. Thereforeit is clear that ‘it is not-good’ isnot the denial of ‘it is good’. If thenevery single statement may truly be

said to be either an affirmation or anegation, if it is not a negationclearly it must in a sense be anaffirmation. But every affirmation hasa corresponding negation. The negation



then of ‘it is not-good’ is ‘it is notnot-good’. The relation of thesestatements to one another is asfollows. 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,and let D stand for not to be not-good’and be placed under A. Then either A orB will belong to everything, but theywill never belong to the same thing;and either C or D will belong to

everything, but they will never belongto the same thing. And B must belong toeverything to which C belongs. For ifit is true to say ‘it is a not-white’,it is true also to say ‘it is notwhite’: for it is impossible that athing should simultaneously be whiteand be not-white, or be a not-white logand be a white log; consequently if theaffirmation does not belong, the denial

must belong. But C does not always belong to B: for what is not a log at

all, cannot be a not-white log either.On the other hand D belongs toeverything to which A belongs. For

either C or D belongs to everything towhich A belongs. But since a thingcannot be simultaneously not-white andwhite, D must belong to everything towhich A belongs. For of that which is



white it is true to say that it is notnot-white. But A is not true of all D.For of that which is not a log at allit is not true to say A, viz. that itis a white log. Consequently D is true,

but A is not true, i.e. that it is awhite log. It is clear also that A andC 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

arrangement. Let A stand for ‘equal’, Bfor ‘not equal’, C for ‘unequal’, D for‘not unequal’.

In many things also, to some of whichsomething belongs which does not belongto others, the negation may be true ina similar way, viz. that all are notwhite or that each is not white, whilethat each is not-white or all are not-white is false. Similarly also ‘everyanimal is not-white’ is not thenegation of ‘every animal is white’

(for both are false): the propernegation is ‘every animal is notwhite’. Since it is clear that ‘it isnot-white’ and ‘it is not white’ meandifferent things, and one is an



affirmation, the other a denial, it isevident that the method of proving eachcannot be the same, e.g. that whateveris an animal is not white or may not bewhite, and that it is true to call itnot-white; for this means that it isnot-white. But we may prove that it istrue to call it white or not-white inthe same way for both are provedconstructively by means of the firstfigure. For the expression ‘it is true’

stands on a similar footing to ‘it is’.For the negation of ‘it is true to callit white’ is not ‘it is true to call itnot-white’ but ‘it is not true to callit white’. If then it is to be true tosay that whatever is a man is musicalor is not-musical, we must assume thatwhatever is an animal either is musicalor is not-musical; and the proof has

been made. That whatever is a man isnot musical is proved destructively inthe three ways mentioned.

In general whenever A and B are suchthat they cannot belong at the same

time to the same thing, and one of thetwo necessarily belongs to everything,and again C and D are related in thesame way, and A follows C but therelation cannot be reversed, then D



must follow B and the relation cannot be reversed. And A and D may belong to

the same thing, but B and C cannot.First it is clear from the followingconsideration that D follows B. Forsince either C or D necessarily belongsto everything; and since C cannot

belong to that to which B belongs, because it carries A along with it and A and B cannot belong to the same

thing; it is clear that D must follow

B. Again since C does not reciprocatewith but A, but C or D belongs toeverything, it is possible that A and Dshould belong to the same thing. But Band C cannot belong to the same thing,

because A follows C; and so somethingimpossible results. It is clear thenthat B does not reciprocate with Deither, since it is possible that D and

A should belong at the same time to thesame thing.

It results sometimes even in such anarrangement of terms that one isdeceived through not apprehending the

opposites rightly, one of which must belong to everything, e.g. we may

reason that ‘if A and B cannot belongat the same time to the same thing, butit is necessary that one of them should



belong to whatever the other does not belong to: and again C and D are

related in the same way, and followseverything which C follows: it willresult that B belongs necessarily toeverything to which D belongs’: butthis is false. ‘Assume that F standsfor the negation of A and B, and againthat H stands for the negation of C andD. It is necessary then that either Aor F should belong to everything: for

either the affirmation or the denial must belong. And again either C or H must belong to everything: for they are

related as affirmation and denial. Andex hypothesi A belongs to everythingever thing to which C belongs.Therefore H belongs to everything towhich F belongs. Again since either For B belongs to everything, andsimilarly either H or D, and since Hfollows F, B must follow D: for we knowthis. If then A follows C, B mustfollow D’. But this is false: for as we

proved the sequence is reversed interms so constituted. The fallacy

arises because perhaps it is notnecessary that A or F should belong toeverything, or that F or B should

belong to everything: for F is not thedenial of A. For not good is the



negation of good: and not-good is notidentical with ‘neither good nor not-good’. Similarly also with C and D. Fortwo negations have been assumed inrespect to one term.



Book II

1

We have already explained the number ofthe figures, the character and numberof the premisses, when and how asyllogism is formed; further what we

must look for when a refuting andestablishing propositions, and how weshould investigate a given problem in

any branch of inquiry, also by what means we shall obtain principles

appropriate to each subject. Since somesyllogisms are universal, others

particular, all the universalsyllogisms give more than one result,and of particular syllogisms theaffirmative yield more than one, thenegative yield only the statedconclusion. For all propositions areconvertible save only the particularnegative: and the conclusion states onedefinite thing about another definitething. Consequently all syllogisms savethe particular negative yield more than

one conclusion, e.g. if A has been proved to to all or to some B, then B must belong to some A: and if A has been proved to belong to no B, then B belongs to no A. This is a different



conclusion from the former. But if Adoes not belong to some B, it is notnecessary that B should not belong tosome A: for it may possibly belong toall A.

This then is the reason common to allsyllogisms whether universal or

particular. But it is possible to giveanother reason concerning those whichare universal. For all the things that

are subordinate to the middle term orto the conclusion may be proved by thesame syllogism, if the former are

placed in the middle, the latter in theconclusion; e.g. if the conclusion ABis proved through C, whatever issubordinate to B or C must accept the

predicate A: for if D is included in Bas in a whole, and B is included in A,then D will be included in A. Again ifE is included in C as in a whole, and Cis included in A, then E will beincluded in A. Similarly if thesyllogism is negative. In the secondfigure it will be possible to infer

only that which is subordinate to theconclusion, e.g. if A belongs to no Band to all C; we conclude that B

belongs to no C. If then D issubordinate 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 means of 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, it has been assumed

without proof that B does not belong to A, consequently it does not result

through the syllogism that B does not belong to E.

But in particular syllogisms there will be no necessity of inferring what is

subordinate to the conclusion (for asyllogism does not result when this

premiss is particular), but whatever issubordinate to the middle term may beinferred, not however through thesyllogism, e.g. if A belongs to all Band B to some C. Nothing can beinferred about that which issubordinate to C; something can beinferred about that which issubordinate to B, but not through the

preceding syllogism. Similarly in the

other figures. That which issubordinate to the conclusion cannot be

proved; the other subordinate can be proved, only not through the syllogism,

just as in the universal syllogisms



what is subordinate to the middle termis proved (as we saw) from a premisswhich is not demonstrated: consequentlyeither a conclusion is not possible inthe case of universal syllogisms orelse it is possible also in the case of

particular syllogisms.

2

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 isnot possible to draw a falseconclusion, but a true conclusion may

be drawn from false premisses, truehowever only in respect to the fact,not to the reason. The reason cannot beestablished from false premisses: whythis is so will be explained in thesequel.

First then that it is not possible todraw a false conclusion from true

premisses, is made clear by thisconsideration. If it is necessary thatB should be when A is, it is necessarythat A should not be when B is not. Ifthen A is true, B must be true:



otherwise it will turn out that thesame thing both is and is not at thesame time. But this is impossible. Letit not, because A is laid down as asingle term, be supposed that it is

possible, when a single fact is given,that something should necessarilyresult. For that is not possible. Forwhat results necessarily is theconclusion, and the means by which thiscomes about are at the least three

terms, and two relations of subject and predicate or premisses. If then it is

true that A belongs to all that towhich B belongs, and that B belongs toall that to which C belongs, it isnecessary that A should belong to allthat to which C belongs, and thiscannot be false: for then the samething will belong and not belong at thesame time. So A is posited as onething, being two premisses takentogether. The same holds good ofnegative syllogisms: it is not possibleto prove a false conclusion from true

premisses.

But from what is false a trueconclusion may be drawn, whether boththe premisses are false or only one,

provided that this is not either of the



premisses indifferently, if it is takenas wholly false: but if the premiss isnot taken as wholly false, it does not

matter which of the two is false. (1)Let A belong to the whole of C, but tonone of the Bs, neither let B belong toC. This is possible, e.g. animal

belongs to no stone, nor stone to any man. If then A is taken to belong to

all B and B to all C, A will belong toall C; consequently though both the

premisses are false the conclusion istrue: for every man is an animal.Similarly with the negative. For it is

possible that neither A nor B should belong to any C, although A belongs to

all B, e.g. if the same terms are takenand man is put as middle: for neitheranimal nor man belongs to any stone,

but animal belongs to every man.Consequently if one term is taken to

belong to none of that to which it does belong, and the other term is taken to belong to all of that to which it does

not belong, though both the premissesare false the conclusion will be true.

(2) A similar proof may be given ifeach premiss is partially false.

(3) But if one only of the premisses isfalse, when the first premiss is wholly



false, e.g. AB, the conclusion will not be true, but if the premiss BC is

wholly false, a true conclusion will be possible. I mean by ‘wholly false’ the

contrary of the truth, e.g. if what belongs to none is assumed to belong to

all, or if what belongs to all isassumed to belong to none. Let A belongto no B, and B to all C. If then the

premiss BC which I take is true, andthe 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 towhich B belonged, and B belonged to allC. Similarly there cannot be a trueconclusion if A belongs to all B, and Bto all C, but while the true premiss BCis assumed, the wholly false premiss ABis also assumed, viz. that A belongs tonothing to which B belongs: here theconclusion must be false. For A will

belong to all C, since A belongs toeverything to which B belongs, and B toall C. It is clear then that when the

first premiss is wholly false, whetheraffirmative or negative, and the other

premiss is true, the conclusion cannot be true.



(4) But if the premiss is not whollyfalse, a true conclusion is possible.For if A belongs to all C and to someB, and if B belongs to all C, e.g.animal to every swan and to some whitething, and white to every swan, then ifwe take as premisses that A belongs toall B, and B to all C, A will belong toall C truly: for every swan is ananimal. Similarly if the statement ABis negative. For it is possible that A

should belong to some B and to no C,and that B should belong to all C, e.g.animal to some white thing, but to nosnow, and white to all snow. If thenone should assume that A belongs to noB, and B to all C, then will belong tono C.

(5) But if the premiss AB, which isassumed, is wholly true, and the

premiss BC is wholly false, a truesyllogism will be possible: for nothing

prevents A belonging to all B and toall C, though B belongs to no C, e.g.these being species of the same genus

which are not subordinate one to theother: for animal belongs both to horseand to man, but horse to no man. Ifthen it is assumed that A belongs toall B and B to all C, the conclusion



will be true, although the premiss BCis wholly false. Similarly if the

premiss AB is negative. For it is possible that A should belong neither

to any B nor to any C, and that Bshould not belong to any C, e.g. agenus to species of another genus: foranimal belongs neither to music nor tothe art of healing, nor does music

belong to the art of healing. If thenit is assumed that A belongs to no B,

and B to all C, the conclusion will betrue.

(6) And if the premiss BC is not whollyfalse 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 anddifference: for animal belongs to every

man and to every footed thing, and manto some footed things though not toall. If then it is assumed that A

belongs to all B, and B to all C, Awill belong to all C: and this ex

hypothesi is true. Similarly if the premiss AB is negative. For it is possible that A should neither belong

to any B nor to any C, though B belongsto some C, e.g. a genus to the species



of another genus and its difference:for animal neither belongs to anywisdom nor to any instance of‘speculative’, but wisdom belongs tosome instance of ‘speculative’. If thenit should be assumed that A belongs tono B, and B to all C, will belong to noC: and this ex hypothesi is true.

In particular syllogisms it is possiblewhen the first premiss is wholly false,

and the other true, that the conclusionshould be true; also when the first

premiss is false in part, and the othertrue; and when the first is true, andthe particular is false; and when bothare false. (7) For nothing prevents A

belonging to no B, but to some C, and Bto some C, e.g. animal belongs to nosnow, but to some white thing, and snowto some white thing. If then snow istaken as middle, and animal as firstterm, and it is assumed that A belongsto the whole of B, and B to some C,then the premiss BC is wholly false,the premiss BC true, and the conclusion

true. Similarly if the premiss AB isnegative: for it is possible that Ashould belong to the whole of B, butnot to some C, although B belongs tosome C, e.g. animal belongs to every



man, but does not follow some white, but man belongs to some white;

consequently if man be taken as middleterm and it is assumed that A belongsto no B but B belongs to some C, theconclusion will be true although the

premiss AB is wholly false. (If the premiss AB is false in part, the

conclusion may be true. For nothing prevents A belonging both to B and to

some C, and B belonging to some C, e.g.

animal to something beautiful and tosomething great, and beautiful

belonging to something great. If then Ais assumed to belong to all B, and B tosome C, the a premiss AB will be

partially false, the premiss BC will betrue, and the conclusion true.Similarly if the premiss AB isnegative. For the same terms willserve, and in the same positions, to

prove the point.

(9) Again if the premiss AB is true,and the premiss BC is false, theconclusion 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 some

black things, though swan belongs to no black thing. Consequently if it should



be assumed that A belongs to all B, andB to some C, the conclusion will betrue, although the statement BC isfalse. Similarly if the premiss AB isnegative. For it is possible that Ashould belong to no B, and not to someC, while B belongs to no C, e.g. agenus to the species of another genusand to the accident of its own species:for animal belongs to no number and notto some white things, and number

belongs to nothing white. If thennumber is taken as middle, and it isassumed that A belongs to no B, and Bto some C, then A will not belong tosome C, which ex hypothesi is true. Andthe premiss AB is true, the premiss BCfalse.

(10) Also if the premiss AB is partially false, and the premiss BC is

false too, the conclusion may be true.For nothing prevents A belonging tosome B and to some C, though B belongsto no C, e.g. if B is the contrary ofC, and both are accidents of the same

genus: for animal belongs to some whitethings and to some black things, butwhite belongs to no black thing. Ifthen it is assumed that A belongs toall B, and B to some C, the conclusion



will be true. Similarly if the premiss AB is negative: for the same terms

arranged in the same way will serve forthe proof.

(11) Also though both premisses arefalse the conclusion may be true. Forit is possible that A may belong to noB and to some C, while B belongs to noC, e.g. a genus in relation to thespecies of another genus, and to the

accident of its own species: for animal belongs to no number, but to some white

things, and number to nothing white. Ifthen it is assumed that A belongs toall B and B to some C, the conclusionwill be true, though both premisses arefalse. Similarly also if the premiss ABis negative. For nothing prevents A

belonging to the whole of B, and not tosome C, while B belongs to no C, e.g.animal belongs to every swan, and notto some black things, and swan belongsto nothing black. Consequently if it isassumed that A belongs to no B, and Bto some C, then A does not belong to

some C. The conclusion then is true, but the premisses arc false.



3

In the middle figure it is possible inevery way to reach a true conclusionthrough false premisses, whether thesyllogisms are universal or particular,viz. when both premisses are whollyfalse; when each is partially false;when one is true, the other whollyfalse (it does not matter which of thetwo premisses is false); if both

premisses are partially false; if oneis quite true, the other partiallyfalse; if one is wholly false, theother partially true. For (1) if A

belongs to no B and to all C, e.g.animal to no stone and to every horse,then if the premisses are statedcontrariwise and it is assumed that A

belongs to all B and to no C, thoughthe premisses are wholly false theywill yield a true conclusion. Similarlyif A belongs to all B and to no C: forwe shall have the same syllogism.

(2) Again if one premiss is wholly

false, the other wholly true: fornothing prevents A belonging to all Band to all C, though B belongs to no C,e.g. a genus to its co-ordinatespecies. 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 the one, and none ofthe other, the one premiss will bewholly false, the other wholly true,and the conclusion will be truewhichever term the negative statementconcerns.

(3) Also if one premiss is partiallyfalse, the other wholly true. For it is

possible that A should belong to some Band to all C, though B belongs to no C,e.g. animal to some white things and toevery raven, though white belongs to noraven. If then it is assumed that A

belongs to no B, but to the whole of C,the premiss AB is partially false, the

premiss AC wholly true, and theconclusion true. Similarly if thenegative statement is transposed: the

proof can be made by means of the sameterms. Also if the affirmative premissis partially false, the negative whollytrue, a true conclusion is possible.For nothing prevents A belonging to

some B, but not to C as a whole, whileB belongs to no C, e.g. animal belongsto some white things, but to no pitch,and white belongs to no pitch.Consequently if it is assumed that A





affirmative: for it is possible that Ashould belong to no B, and not to someC, though B does not belong to some C,e.g. animal belongs to nothinglifeless, and does not belong to somewhite things, and lifeless will not

belong to some white things. If then itis stated that A belongs to all B andnot to some C, the premiss AB which isuniversal is wholly false, the premiss

AC is true, and the conclusion is true.

Also a true conclusion is possible whenthe universal premiss is true, and the

particular is false. For nothing prevents A following neither B nor C at

all, while B does not belong to some C,e.g. animal belongs to no number nor toanything lifeless, and number does notfollow some lifeless things. If then itis stated that A belongs to no B and tosome C, the conclusion will be true,and the universal premiss true, but the

particular false. Similarly if the premiss which is stated universally is

affirmative. For it is possible thatshould A belong both to B and to C as

wholes, though B does not follow someC, e.g. a genus in relation to itsspecies and difference: for animalfollows every man and footed things asa whole, but man does not follow every



footed thing. Consequently if it isassumed that A belongs to the whole ofB, but does not belong to some C, theuniversal premiss is true, the

particular false, and the conclusiontrue.

(6) It is clear too that though both premisses are false they may yield a

true conclusion, since it is possiblethat A should belong both to B and to C

as wholes, though B does not followsome C. For if it is assumed that A

belongs to no B and to some C, the premisses are both false, but the

conclusion is true. Similarly if theuniversal premiss is affirmative andthe particular negative. For it is

possible that A should follow no B andall C, though B does not belong to someC, e.g. animal follows no science butevery man, though science does notfollow every man. If then A is assumedto belong to the whole of B, and not tofollow some C, the premisses are false

but the conclusion is true.

4

In the last figure a true conclusion may come through what is false, alike



when both premisses are wholly false,when each is partly false, when one

premiss is wholly true, the otherfalse, when one premiss is partlyfalse, the other wholly true, and viceversa, and in every other way in whichit is possible to alter the premisses.For (1) nothing prevents neither A norB from belonging to any C, while A

belongs to some B, e.g. neither man norfooted follows anything lifeless,

though man belongs to some footedthings. If then it is assumed that Aand B belong to all C, the premisseswill be wholly false, but theconclusion true. Similarly if one

premiss is negative, the otheraffirmative. For it is possible that Bshould belong to no C, but A to all C,and that should not belong to some B,e.g. black belongs to no swan, animalto every swan, and animal not toeverything black. Consequently if it isassumed that B belongs to all C, and Ato 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 partlyfalse, 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 belongto some animals, and white to some

beautiful things. If then it is statedthat A and B belong to all C, the

premisses are partially false, but theconclusion is true. Similarly if the

premiss AC is stated as negative. Fornothing prevents A from not belonging,and B from belonging, to some C, while

A does not belong to all B, e.g. white

does not belong to some animals, beautiful belongs to some animals, and

white does not belong to everything beautiful. Consequently if it is

assumed that A belongs to no C, and Bto all C, both premisses are partlyfalse, but the conclusion is true.

(3) Similarly if one of the premissesassumed is wholly false, the otherwholly true. For it is possible that

both A and B should follow all C,though A does not belong to some B,e.g. animal and white follow everyswan, though animal does not belong to

everything white. Taking these then asterms, if one assumes that B belongs tothe whole of C, but A does not belongto C at all, the premiss BC will bewholly true, the premiss AC wholly



false, and the conclusion true.Similarly if the statement BC is false,the statement AC true, the conclusion

may be true. The same terms will servefor the proof. Also if both the

premisses assumed are affirmative, theconclusion may be true. For nothing

prevents B from following all C, and Afrom not belonging to 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 assumed that Aand B belong to every C, the premiss BCis wholly true, the premiss AC iswholly false, and the conclusion istrue. Similarly if the premiss AC whichis assumed is true: the proof can be

made through the same terms.

(4) Again if one premiss is whollytrue, the other partly false, theconclusion may be true. For it is

possible that B should belong to all C,and A to some C, while A belongs tosome B, e.g. biped belongs to every

man, beautiful not to every man, and beautiful to some bipeds. If then it is

assumed that both A and B belong to thewhole of C, the premiss BC is whollytrue, the premiss AC partly false, the



conclusion true. Similarly if of the premisses assumed AC is true and BC partly false, a true conclusion is possible: this can be proved, if the

same terms as before are transposed. Also the conclusion may be true if one premiss is negative, the other

affirmative. For since it is possiblethat B should belong to the whole of C,and A to some C, and, when they are so,that A should not belong to all B,

therefore it is assumed that B belongsto the whole of C, and A to no C, thenegative premiss is partly false, theother premiss wholly true, and theconclusion is true. Again since it has

been proved that if A belongs to no Cand B to some C, it is possible that Ashould not belong to some C, it isclear that if the premiss AC is whollytrue, and the premiss BC partly false,it is possible that the conclusionshould be true. For if it is assumedthat A belongs to no C, and B to all C,the premiss AC is wholly true, and the

premiss BC is partly false.

(5) It is clear also in the case of particular syllogisms that a true

conclusion may come through what isfalse, in every possible way. For the



same terms must be taken as have beentaken when the premisses are universal,

positive terms in positive syllogisms,negative terms in negative. For it

makes no difference to the setting outof the terms, whether one assumes thatwhat belongs to none belongs to all orthat what belongs to some belongs toall. The same applies to negativestatements.

It is clear then that if the conclusionis false, the premisses of the argument

must be false, either all or some ofthem; but when the conclusion is true,it is not necessary that the premissesshould be true, either one or all, yetit is possible, though no part of thesyllogism is true, that the conclusion

may none the less be true; but it isnot necessitated. The reason is thatwhen two things are so related to oneanother, that if the one is, the othernecessarily is, then if the latter isnot, the former will not be either, butif the latter is, it is not necessary

that the former should be. But it isimpossible that the same thing should

be necessitated by the being and by thenot-being of the same thing. I mean,for example, that it is impossible that



B should necessarily be great since Ais white and that B should necessarily

be great since A is not white. Forwhenever since this, A, is white it isnecessary that that, B, should begreat, and since B is great that Cshould not be white, then it isnecessary if is white that C should not

be white. And whenever it is necessary,since one of two things is, that theother should be, it is necessary, if

the latter is not, that the former(viz. A) should not be. If then B isnot great A cannot be white. But if,when A is not white, it is necessarythat B should be great, it necessarilyresults that if B is not great, Bitself is great. (But this isimpossible.) For if B is not great, Awill necessarily not be white. If thenwhen this is not white B must be great,it results that if B is not great, itis great, just as if it were provedthrough three terms.

5

Circular and reciprocal proof means proof by means of the conclusion, i.e. by converting one of the premisses

simply and inferring the premiss which



was assumed in the original syllogism:e.g. suppose it has been necessary to

prove that A belongs to all C, and ithas been proved through B; suppose that

A should now be proved to belong to B by assuming that A belongs to C, and C

to B-so A belongs to B: but in thefirst syllogism the converse wasassumed, viz. that B belongs to C. Orsuppose it is necessary to prove that B

belongs to C, and A is assumed to

belong to C, which was the conclusionof the first syllogism, and B to belongto A but the converse was assumed inthe earlier syllogism, viz. that A

belongs to B. In no other way isreciprocal proof possible. If anotherterm is taken as middle, the proof isnot circular: for neither of the

propositions assumed is the same as before: if one of the accepted terms is

taken as middle, only one of the premisses of the first syllogism can be

assumed in the second: for if both ofthem are taken the same conclusion as

before will result: but it must be

different. If the terms are notconvertible, one of the premisses fromwhich the syllogism results must beundemonstrated: for it is not possibleto demonstrate through these terms that



the third belongs to the middle or the middle to the first. If the terms are

convertible, it is possible todemonstrate everything reciprocally,e.g. if A and B and C are convertiblewith one another. Suppose the

proposition AC has been demonstratedthrough B as middle term, and again the

proposition AB through the conclusionand the premiss BC converted, andsimilarly the proposition BC through

the conclusion and the premiss ABconverted. But it is necessary to prove

both the premiss CB, and the premissBA: for we have used these alonewithout demonstrating them. If then itis assumed that B belongs to all C, andC to all A, we shall have a syllogismrelating B to A. Again if it is assumedthat C belongs to all A, and A to allB, C must belong to all B. In boththese syllogisms the premiss CA has

been assumed without beingdemonstrated: the other premisses hadex hypothesi been proved. Consequentlyif we succeed in demonstrating this

premiss, all the premisses will have been proved reciprocally. If then it is

assumed that C belongs to all B, and Bto all A, both the premisses assumedhave been proved, and C must belong to



A. It is clear then that only if theterms are convertible is circular andreciprocal demonstration possible (ifthe terms are not convertible, the

matter stands as we said above). But itturns out in these also that we use forthe demonstration the very thing thatis being proved: for C is proved of B,and B of by assuming that C is said ofand C is proved of A through these

premisses, so that we use the

conclusion for the demonstration.

In negative syllogisms reciprocal proofis as follows. Let B belong to all C,and A to none of the Bs: we concludethat A belongs to none of the Cs. Ifagain it is necessary to prove that A

belongs to none of the Bs (which was previously assumed) A must belong to no

C, and C to all B: thus the previous 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’. But we must assume that B belongs to all of

that to none of which longs. Let A belong to none of the Cs (which was the previous conclusion) and assume that B



belongs to all of that to none of which A belongs. It is necessary then that B

should belong to all C. Consequentlyeach of the three propositions has been

made a conclusion, and this is circulardemonstration, to assume the conclusionand the converse of one of the

premisses, and deduce the remaining premiss.

In particular syllogisms it is not

possible to demonstrate the universal premiss through the other propositions, but the particular premiss can be

demonstrated. Clearly it is impossibleto demonstrate the universal premiss:for what is universal is proved through

propositions which are universal, butthe conclusion is not universal, andthe proof must start from theconclusion and the other premiss.Further a syllogism cannot be made atall if the other premiss is converted:for the result is that both premissesare particular. But the particular

premiss may be proved. Suppose that A

has been proved of some C through B. Ifthen it is assumed that B belongs toall A and the conclusion is retained, Bwill belong to some C: for we obtainthe first figure and A is middle. But



if the syllogism is negative, it is not possible to prove the universal premiss, for the reason given above.

But it is possible to prove the particular premiss, if the proposition AB is converted as in the universal

syllogism, i.e ‘B belongs to some ofthat to some of which A does not

belong’: otherwise no syllogism results because the particular premiss is

negative.

6

In the second figure it is not possibleto prove an affirmative proposition inthis way, but a negative proposition

may be proved. An affirmative proposition is not proved because both premisses of the new syllogism are not

affirmative (for the conclusion isnegative) but an affirmative

proposition is (as we saw) proved from premisses which are both affirmative.

The negative is proved as follows. Let A belong to all B, and to no C: we

conclude that B belongs to no C. Ifthen it is assumed that B belongs toall A, it is necessary that A should

belong to no C: for we get the secondfigure, with B as middle. But if the



premiss AB was negative, and the otheraffirmative, we shall have the firstfigure. For C belongs to all A and B tono C, consequently B belongs to no A:neither then does A belong to B.Through the conclusion, therefore, andone premiss, we get no syllogism, butif 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, butthe particular premiss can be provedwhenever the universal statement isaffirmative. Let A belong to all B, andnot to all C: the conclusion is BC. Ifthen it is assumed that B belongs toall A, but not to all C, A will not

belong to some C, B being middle. Butif the universal premiss is negative,the premiss AC will not be demonstrated

by the conversion of AB: for it turnsout that either both or one of the

premisses is negative; consequently asyllogism will not be possible. But the

proof will proceed as in the universal

syllogisms, if it is assumed that A belongs to some of that to some of

which B does not belong.



7

In the third figure, when both premisses are taken universally, it is

not possible to prove themreciprocally: for that which isuniversal is proved through statementswhich are universal, but the conclusionin this figure is always particular, sothat it is clear that it is not

possible at all to prove through thisfigure the universal premiss. But ifone premiss is universal, the other

particular, proof of the latter willsometimes be possible, sometimes not.

When both the premisses assumed areaffirmative, and the universal concernsthe minor extreme, proof will be

possible, but when it concerns theother extreme, impossible. Let A belongto all C and B to some C: theconclusion is the statement AB. If thenit is assumed that C belongs to all A,it has been proved that C belongs tosome B, but that B belongs to some C

has not been proved. And yet it isnecessary, if C belongs to some B, thatB should belong to some C. But it isnot the same that this should belong tothat, and that to this: but we must



assume besides that if this belongs tosome of that, that belongs to some ofthis. But if this is assumed thesyllogism no longer results from theconclusion and the other premiss. Butif B belongs to all C, and A to some C,it will be possible to prove the

proposition AC, when it is assumed thatC belongs to all B, and A to some B.For if C belongs to all B and A to someB, it is necessary that A should belong

to some C, B being middle. And wheneverone premiss is affirmative the othernegative, and the affirmative isuniversal, the other premiss can be

proved. Let B belong to all C, and Anot to some C: the conclusion is that Adoes not belong to some B. If then itis assumed further that C belongs toall B, it is necessary that A shouldnot belong to some C, B being middle.But when the negative premiss isuniversal, the other premiss is notexcept as before, viz. if it is assumedthat that belongs to some of that, tosome of which this does not belong,

e.g. if A belongs to no C, and B tosome C: the conclusion is that A doesnot belong to some B. If then it isassumed that C belongs to some of thatto some of which does not belong, it is



necessary that C should belong to someof the Bs. In no other way is it

possible by converting the universal premiss to prove the other: for in no

other way can a syllogism be formed.

It is clear then that in the firstfigure reciprocal proof is made boththrough the third and through the firstfigure-if the conclusion is affirmativethrough the first; if the conclusion is

negative through the last. For it isassumed that that belongs to all ofthat to none of which this belongs. Inthe middle figure, when the syllogismis universal, proof is possible throughthe second figure and through thefirst, but when particular through thesecond and the last. In the thirdfigure all proofs are made throughitself. It is clear also that in thethird figure and in the middle figurethose syllogisms which are not madethrough those figures themselves eitherare not of the nature of circular proofor are imperfect.

8

To convert a syllogism means to alterthe conclusion and make another



syllogism to prove that either theextreme cannot belong to the middle orthe middle to the last term. For it isnecessary, if the conclusion has beenchanged into its opposite and one ofthe premisses stands, that the other

premiss should be destroyed. For if itshould stand, the conclusion also muststand. It makes a difference whetherthe conclusion is converted into itscontradictory or into its contrary. For

the same syllogism does not resultwhichever form the conversion takes.This will be made clear by the sequel.By contradictory opposition I mean theopposition of ‘to all’ to ‘not to all’,and of ‘to some’ to ‘to none’; bycontrary opposition I mean theopposition of ‘to all’ to ‘to none’,and of ‘to some’ to ‘not to some’.Suppose that A been proved of C,through B as middle term. If then itshould be assumed that A belongs to noC, but to all B, B will belong to no C.

And if A belongs to no C, and B to allC, A will belong, not to no B at all,

but not to all B. For (as we saw) theuniversal is not proved through thelast figure. In a word it is not

possible to refute universally byconversion the premiss which concerns



the major extreme: for the refutationalways proceeds through the third sinceit is necessary to take both premissesin reference to the minor extreme.Similarly if the syllogism is negative.Suppose it has been proved that A

belongs to no C through B. Then if itis assumed that A belongs to all C, andto no B, B will belong to none of theCs. And if A and B belong to all C, Awill belong to some B: but in the

original premiss it belonged to no B.

If the conclusion is converted into itscontradictory, the syllogisms will becontradictory and not universal. Forone premiss is particular, so that theconclusion also will be particular. Letthe syllogism be affirmative, and letit be converted as stated. Then if A

belongs not to all C, but to all B, Bwill belong not to all C. And if A

belongs not to all C, but B belongs toall C, A will belong not to all B.Similarly if the syllogism is negative.For if A belongs to some C, and to no

B, B will belong, not to no C at all, but-not to some C. And if A belongs to

some C, and B to all C, as wasoriginally assumed, A will belong tosome B.



In particular syllogisms when theconclusion is converted into itscontradictory, both premisses may berefuted, but when it is converted intoits contrary, neither. For the resultis no longer, as in the universalsyllogisms, refutation in which theconclusion reached by O, conversionlacks universality, but no refutationat all. Suppose that A has been proved

of some C. If then it is assumed that A belongs to no C, and B to some C, A

will not belong to some B: and if A belongs to no C, but to all B, B will belong to no C. Thus both premisses are

refuted. But neither can be refuted ifthe conclusion is converted into itscontrary. For if A does not belong tosome C, but to all B, 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 to some C. Theuniversal 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. Similarlyif the syllogism is negative: for if itshould be assumed that A belongs to all



C, both premisses are refuted: but ifthe assumption is that A belongs tosome C, neither premiss is refuted. The

proof is the same as before.

9

In the second figure it is not possibleto refute the premiss which concernsthe major extreme by establishingsomething contrary to it, whichever

form the conversion of the conclusion may take. For the conclusion of the

refutation will always be in the thirdfigure, and in this figure (as we saw)there is no universal syllogism. Theother premiss can be refuted in a

manner similar to the conversion: I mean, if the conclusion of the first

syllogism is converted into itscontrary, the conclusion of therefutation will be the contrary of the

minor premiss of the first, if into itscontradictory, the contradictory. Let A

belong to all B and to no C: conclusionBC. If then it is assumed that B

belongs to all C, and the proposition AB stands, A will belong to all C,

since the first figure is produced. IfB belongs to all C, and A to no C, then

A belongs not to all B: the figure is



the last. But if the conclusion BC isconverted into its contradictory, the

premiss AB will be refuted as before,the premiss, AC by its contradictory.For if B belongs to some C, and A to noC, then A will not belong to some B.

Again if B belongs to some C, and A toall B, A will belong to some C, so thatthe syllogism results in thecontradictory of the minor premiss. Asimilar proof can be given if the

premisses are transposed in respect oftheir quality.

If the syllogism is particular, whenthe conclusion is converted into itscontrary neither premiss can berefuted, as also happened in the firstfigure,’ if the conclusion is convertedinto its contradictory, both premissescan be refuted. Suppose that A belongsto no B, and to some C: the conclusionis BC. If then it is assumed that B

belongs to some C, and the statement ABstands, the conclusion will be that Adoes not belong to some C. But the

original statement has not beenrefuted: for it is possible that Ashould belong to some C and also not tosome 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. But ifthe conclusion is converted into itscontradictory, both premisses can berefuted. For if B belongs to all C, and

A to no B, A will belong to no C: butit was assumed to belong to some C.

Again if B belongs to all C and A tosome C, A will belong to some B. Thesame proof can be given if the

universal statement is affirmative.

10

In the third figure when the conclusionis converted into its contrary, neitherof the premisses can be refuted in anyof the syllogisms, but when theconclusion is converted into itscontradictory, both premisses may berefuted and in all the moods. Supposeit has been proved that A belongs tosome B, C being taken as middle, andthe premisses being universal. If thenit is assumed that A does not belong to

some B, but B belongs to all C, nosyllogism is formed about A and C. Norif A does not belong to some B, but

belongs to all C, will a syllogism be possible about B and C. A similar proof



can be given if the premisses are notuniversal. For either both premissesarrived at by the conversion must be

particular, or the universal premiss must refer to the minor extreme. But we

found that no syllogism is possiblethus either in the first or in the

middle figure. But if the conclusion isconverted into its contradictory, boththe 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 tono B, and to all C, B belongs to no C.

And similarly if one of the premissesis not universal. For if A belongs tono B, and B to some C, A will not

belong to some C: if A belongs to no B,and to C, B will belong to no C.

Similarly if the original syllogism isnegative. 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, asyllogism 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 syllogism possible concerningB and C. Therefore the premisses arenot refuted. But when the contradictoryof the conclusion is assumed, they arerefuted. For if A belongs to all B, andB to C, A belongs to all C: but A wassupposed originally to belong to no C.

Again if A belongs to all B, and to noC, then B belongs to no C: but it wassupposed to belong to all C. A similar

proof is possible if the premisses are

not universal. For AC becomes universaland negative, the other premiss

particular and affirmative. If then A belongs to all B, and B to some C, it

results that A belongs to some C: butit was supposed to belong to no C.

Again if A belongs to all B, and to noC, then B belongs to no C: but it wasassumed to belong to some C. If A

belongs to some B and B to some C, nosyllogism results: nor yet if A belongsto some B, and to no C. Thus in one waythe premisses are refuted, in the otherway they are not.

From what has been said it is clear howa syllogism results in each figure whenthe conclusion is converted; when aresult contrary to the premiss, andwhen a result contradictory to the



premiss, is obtained. It is clear thatin the first figure the syllogisms areformed through the middle and the lastfigures, and the premiss which concernsthe minor extreme is alway refutedthrough the middle figure, the premisswhich concerns the major through thelast figure. In the second figuresyllogisms proceed through the firstand the last figures, and the premisswhich concerns the minor extreme is

always refuted through the firstfigure, the premiss which concerns the

major extreme through the last. In thethird figure the refutation proceedsthrough the first and the middlefigures; the premiss which concerns the

major is always refuted through thefirst figure, the premiss whichconcerns the minor through the middlefigure.

11

It is clear then what conversion is,how it is effected in each figure, and

what syllogism results. The syllogism per impossibile is proved when the

contradictory of the conclusion statedand another premiss is assumed; it can

be made in all the figures. For it



resembles conversion, differing only inthis: conversion takes place after asyllogism has been formed and both the

premisses have been taken, but areduction to the impossible takes placenot because the contradictory has beenagreed to already, but because it isclear that it is true. The terms arealike in both, and the premisses of

both are taken in the same way. Forexample if A belongs to all B, C being

middle, then if it is supposed that Adoes not belong to all B or belongs tono B, but to all C (which was admittedto be true), it follows that C belongsto no B or not to all B. But this isimpossible: consequently thesupposition is false: its contradictorythen is true. Similarly in the otherfigures: for whatever moods admit ofconversion admit also of the reduction

per impossibile.

All the problems can be proved perimpossibile in all the figures,excepting the universal affirmative,

which is proved in the middle and thirdfigures, but not in the first. Supposethat A belongs not to all B, or to noB, and take besides another premissconcerning either of the terms, viz.



that C belongs to all A, or that B belongs to all D; thus we get the first

figure. If then it is supposed that Adoes not belong to all B, no syllogismresults whichever term the assumed

premiss concerns; but if it is supposedthat A belongs to no B, when the

premiss BD is assumed as well we shall prove syllogistically what is false, but not the problem proposed. For if A belongs to no B, and B belongs to all

D, A belongs to no D. Let this beimpossible: it is false then A belongsto no B. But the universal affirmativeis not necessarily true if theuniversal negative is false. But if the

premiss CA is assumed as well, nosyllogism results, nor does it do sowhen it is supposed that A does not

belong to all B. Consequently it isclear that the universal affirmativecannot be proved in the first figure

per impossibile.

But the particular affirmative and theuniversal and particular negatives can

all be proved. Suppose that A belongsto no B, and let it have been assumedthat B belongs to all or to some C.Then it is necessary that A should

belong to no C or not to all C. But



this is impossible (for let it be trueand clear that A belongs to all C):consequently if this is false, it isnecessary that A should belong to someB. But if the other premiss assumedrelates to A, no syllogism will be

possible. Nor can a conclusion be drawnwhen the contrary of the conclusion issupposed, e.g. that A does not belongto some B. Clearly then we must supposethe contradictory.

Again suppose that A belongs to some B,and let it have been assumed that C

belongs to all A. It is necessary thenthat C should belong to some B. But letthis be impossible, so that thesupposition is false: in that case itis true that A belongs to no B. We may

proceed in the same way if the proposition CA has been taken as

negative. But if the premiss assumedconcerns B, no syllogism will be

possible. If the contrary is supposed,we shall have a syllogism and animpossible conclusion, but the problem

in hand is not proved. Suppose that A belongs to all B, and let it have been

assumed that C belongs to all A. It isnecessary then that C should belong toall B. But this is impossible, so that



it is false that A belongs to all B.But we have not yet shown it to benecessary that A belongs to no B, if itdoes not belong to all B. Similarly ifthe other premiss taken concerns B; weshall have a syllogism and a conclusionwhich is impossible, but the hypothesisis not refuted. Therefore it is thecontradictory that we must suppose.

To prove that A does not belong to all

B, we must suppose that it belongs toall B: for if A belongs to all B, and Cto all A, then C belongs to all B; sothat if this is impossible, thehypothesis is false. Similarly if theother premiss assumed concerns B. Thesame results if the original

proposition CA was negative: for thusalso we get a syllogism. But if thenegative proposition concerns B,nothing is proved. If the hypothesis isthat A belongs not to all but to someB, it is not proved that A belongs notto all B, but that it belongs to no B.For if A belongs to some B, and C to

all A, then C will belong to some B. Ifthen this is impossible, it is falsethat A belongs to some B; consequentlyit is true that A belongs to no B. Butif this is proved, the truth is refuted



as well; for the original conclusionwas that A belongs to some B, and doesnot belong to some B. Further theimpossible does not result from thehypothesis: for then the hypothesiswould be false, since it is impossibleto draw a false conclusion from true

premisses: but in fact it is true: for A belongs to some B. Consequently we must not suppose that A belongs to some

B, but that it belongs to all B.

Similarly if we should be proving that A does not belong to some B: for if

‘not to belong to some’ and ‘to belongnot to all’ have the same meaning, thedemonstration of both will beidentical.

It is clear then that not the contrary but the contradictory ought to be

supposed in all the syllogisms. Forthus we shall have necessity ofinference, and the claim we make is onethat will be generally accepted. For ifof everything one or other of twocontradictory statements holds good,

then if it is proved that the negationdoes not hold, the affirmation must betrue. Again if it is not admitted thatthe affirmation is true, the claim thatthe negation is true will be generally



accepted. But in neither way does itsuit to maintain the contrary: for itis not necessary that if the universalnegative is false, the universalaffirmative should be true, nor is itgenerally accepted that if the one isfalse the other is true.

12

It is clear then that in the first

figure all problems except theuniversal affirmative are proved perimpossibile. But in the middle and thelast figures this also is proved.Suppose that A does not belong to allB, and let it have been assumed that A

belongs to all C. If then A belongs notto all B, but to all C, C will not

belong to all B. But this is impossible(for suppose it to be clear that C

belongs to all B): consequently thehypothesis is false. It is true thenthat A belongs to all B. But if thecontrary is supposed, we shall have asyllogism and a result which is

impossible: but the problem in hand isnot proved. For if A belongs to no B,and to all C, C will belong to no B.This is impossible; so that it is falsethat A belongs to no B. But though this



is false, it does not follow that it istrue that A belongs to all B.

When A belongs to some B, suppose that A belongs to no B, and let A belong to

all C. It is necessary then that Cshould belong to no B. Consequently, ifthis is impossible, A must belong tosome B. But if it is supposed that Adoes not belong to some B, we shallhave the same results as in the first

figure.

Again suppose that A belongs to some B,and let A belong to no C. It isnecessary then that C should not belongto some B. But originally it belongedto all B, consequently the hypothesisis false: A then will belong to no B.

When A does not belong to an B, supposeit does belong to all B, and to no 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 the syllogisms can be formed in the middle figure.





supposed that A belongs to all B, the problem is not proved.

But this hypothesis must be made if weare prove that A belongs not to all B.For if A belongs to all B and C to someB, then A belongs to some C. But thiswe assumed not to be so, so it is falsethat A belongs to all B. But in thatcase it is true that A belongs not toall B. If however it is assumed that A

belongs to some B, we shall have thesame result as before.

It is clear then that in all thesyllogisms which proceed perimpossibile the contradictory must beassumed. And it is plain that in the

middle figure an affirmativeconclusion, and in the last figure auniversal conclusion, are proved in away.

14

Demonstration per impossibile differs

from ostensive proof in that it positswhat it wishes to refute by reductionto a statement admitted to be false;whereas ostensive proof starts fromadmitted positions. Both, indeed, take



two premisses that are admitted, butthe latter takes the premisses fromwhich the syllogism starts, the formertakes one of these, along with thecontradictory of the originalconclusion. Also in the ostensive proofit is not necessary that the conclusionshould be known, nor that one shouldsuppose beforehand that it is true ornot: in the other it is necessary tosuppose beforehand that it is not true.

It makes no difference whether theconclusion is affirmative or negative;the method is the same in both cases.Everything which is concludedostensively can be proved perimpossibile, and that which is proved

per impossibile can be provedostensively, through the same terms.

Whenever the syllogism is formed in thefirst figure, the truth will be foundin the middle or the last figure, ifnegative in the middle, if affirmativein the last. Whenever the syllogism isformed in the middle figure, the truthwill be found in the first, whatever

the problem may be. Whenever thesyllogism is formed in the last figure,the truth will be found in the firstand middle figures, if affirmative infirst, if negative in the middle.



Suppose that A has been proved to belong to no B, or not to all B,

through the first figure. Then thehypothesis must have been that A

belongs to some B, and the original premisses that C belongs to all A and

to no B. For thus the syllogism was made and the impossible conclusion

reached. But this is the middle figure,if C belongs to all A and to no B. Andit is clear from these premisses that A

belongs to no B. Similarly if has been proved not to belong to all B. For the

hypothesis is that A belongs to all B;and the original premisses are that C

belongs to all A but not to all B.Similarly too, if the premiss CA should

be negative: for thus also we have the middle figure. Again suppose it has been proved that A belongs to some B.

The hypothesis here is that is that A belongs to no B; and the original premisses that B belongs to all C, and A either to all or to some C: for in

this way we shall get what isimpossible. But if A and B belong to

all C, we have the last figure. And itis clear from these premisses that A

must belong to some B. Similarly if Bor A should be assumed to belong tosome C.



Again suppose it has been proved in the middle figure that A belongs to all B.

Then the hypothesis must have been that A belongs not to all B, and the

original premisses that A belongs toall 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 ithas been proved that A belongs to some

B: for the hypothesis then must have been that A belongs to no B, and the

original premisses that A belongs toall C, and C to some B. If thesyllogism is negative, the hypothesis

must have been that A belongs to someB, and the original premisses that A

belongs to no C, and C to all B, sothat the first figure results. If thesyllogism is not universal, but proofhas been given that A does not belongto some B, we may infer in the sameway. The hypothesis is that A belongsto all B, the original premisses that A

belongs to no C, and C belongs to some

B: for thus we get the first figure.

Again suppose it has been proved in thethird figure that A belongs to all B.Then the hypothesis must have been that



A belongs not to all B, and theoriginal premisses that C belongs toall B, and A belongs to all C; for thuswe shall get what is impossible. Andthe original premisses form the firstfigure. Similarly if the demonstrationestablishes a particular proposition:the hypothesis then must have been that

A belongs to no B, and the original premisses that C belongs to some B, and A to all C. If the syllogism is

negative, the hypothesis must have beenthat A belongs to some B, and theoriginal premisses that C belongs to no

A and to all B, and this is the middlefigure. Similarly if the demonstrationis 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 possiblethrough the same terms to prove each ofthe problems ostensively as well.Similarly it will be possible if thesyllogisms are ostensive to reduce them

ad impossibile in the terms which have been taken, whenever the contradictory

of the conclusion of the ostensivesyllogism is taken as a premiss. Forthe syllogisms become identical with



those which are obtained by means ofconversion, so that we obtainimmediately the figures through whicheach problem will be solved. It isclear then that every thesis can be

proved in both ways, i.e. perimpossibile and ostensively, and it isnot possible to separate one methodfrom the other.

15

In what figure it is possible to draw aconclusion from premisses which areopposed, and in what figure this is not

possible, will be made clear in thisway. Verbally four kinds of oppositionare possible, viz. universalaffirmative to universal negative,universal affirmative to particularnegative, particular affirmative touniversal negative, and particularaffirmative to particular negative: butreally there are only three: for the

particular affirmative is only verballyopposed to the particular negative. Of

the genuine opposites I call thosewhich are universal contraries, theuniversal affirmative and the universalnegative, e.g. ‘every science is good’,



‘no science is good’; the others I callcontradictories.

In the first figure no syllogismwhether affirmative or negative can be

made out of opposed premisses: noaffirmative syllogism is possible

because both premisses must beaffirmative, but opposites are, the oneaffirmative, the other negative: nonegative syllogism is possible because

opposites affirm and deny the same predicate of the same subject, and the middle term in the first figure is not predicated of both extremes, but one

thing is denied of it, and it isaffirmed of something else: but such

premisses are not opposed.

In the middle figure a syllogism can be made both oLcontradictories and of

contraries. Let A stand for good, let Band C stand for science. If then oneassumes that every science is good, andno 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 butto no C, so that a particular science



will not be a science. Again, a particular science will not be a

science if A belongs to all C but to noB, and B is science, C medicine, and Asupposition: for after taking ‘noscience is supposition’, one hasassumed that a particular science issupposition. This syllogism differsfrom the preceding because therelations between the terms arereversed: before, the affirmative

statement concerned B, now it concernsC. Similarly if one premiss is notuniversal: for the middle term isalways that which is stated negativelyof one extreme, and affirmatively ofthe other. Consequently it is possiblethat contradictories may lead to aconclusion, though not always or inevery mood, but only if the termssubordinate to the middle are such thatthey are either identical or related aswhole to part. Otherwise it isimpossible: for the premisses cannotanyhow be either contraries orcontradictories.

In the third figure an affirmativesyllogism can never be made out ofopposite premisses, for the reasongiven in reference to the first figure;



but a negative syllogism is possiblewhether the terms are universal or not.Let B and C stand for science, A for

medicine. If then one should assumethat all medicine is science and thatno medicine is science, he has assumedthat B belongs to all A and C to no A,so that a particular science will not

be a science. Similarly if the premissBA 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 aretaken universally; if one is

particular, they are contradictory.

We must recognize that it is possibleto take opposites in the way we said,viz. ‘all science is good’ and ‘noscience is good’ or ‘some science isnot good’. This does not usually escapenotice. But it is possible to establishone part of a contradiction throughother premisses, or to assume it in theway suggested in the Topics. Since

there are three oppositions toaffirmative statements, it follows thatopposite statements may be assumed as

premisses in six ways; we may haveeither universal affirmative and



negative, or universal affirmative and particular negative, or particular

affirmative and universal negative, andthe relations between the terms may bereversed; e.g. A may belong to all Band to no C, or to all C and to no B,or to all of the one, not to all of theother; here too the relation betweenthe terms may be reversed. Similarly inthe third figure. So it is clear in how

many ways and in what figures a

syllogism can be made by means of premisses which are opposed.

It is clear too that from false premisses it is possible to draw a true

conclusion, as has been said before, but it is not possible if the premisses

are opposed. For the syllogism isalways contrary to the fact, e.g. if athing is good, it is proved that it isnot good, if an animal, that it is notan animal because the syllogism springsout of a contradiction and the terms

presupposed are either identical orrelated as whole and part. It is

evident also that in fallaciousreasonings nothing prevents acontradiction to the hypothesis fromresulting, e.g. if something is odd, itis not odd. For the syllogism owed its



contrariety to its contradictory premisses; if we assume such premisses

we shall get a result that contradictsour hypothesis. But we must recognizethat contraries cannot be inferred froma single syllogism in such a way thatwe conclude that what is not good isgood, or anything of that sort unless aself-contradictory premiss is at onceassumed, e.g. ‘every animal is whiteand not white’, and we proceed ‘man is

an animal’. Either we must introducethe contradiction by an additionalassumption, assuming, e.g., that everyscience is supposition, and thenassuming ‘Medicine is a science, butnone of it is supposition’ (which isthe mode in which refutations are

made), or we must argue from twosyllogisms. In no other way than this,as was said before, is it possible thatthe premisses should be reallycontrary.

16

To beg and assume the original questionis a species of failure to demonstratethe problem proposed; but this happensin many ways. A man may not reasonsyllogistically at all, or he may argue



from premisses which are less known orequally unknown, or he may establishthe antecedent by means of itsconsequents; for demonstration proceedsfrom what is more certain and is prior.

Now begging the question is none ofthese: but since we get to know somethings naturally through themselves,and other things by means of somethingelse (the first principles throughthemselves, what is subordinate to them

through something else), whenever a mantries to prove what is not self-evident

by means of itself, then he begs theoriginal question. This may be done byassuming what is in question at once;it is also possible to make atransition to other things which wouldnaturally be proved through the thesis

proposed, and demonstrate it throughthem, e.g. if A should be provedthrough B, and B through C, though itwas natural that C should be provedthrough A: for it turns out that thosewho reason thus are proving A by meansof itself. This is what those persons

do who suppose that they areconstructing parallel straight lines:for they fail to see that they areassuming facts which it is impossibleto demonstrate unless the parallels



exist. So it turns out that those whoreason thus merely say a particularthing is, if it is: in this wayeverything will be self-evident. Butthat is impossible.

If then it is uncertain whether A belongs to C, and also whether A belongs 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 isnot demonstrating: for what is asuncertain as the question to beanswered cannot be a principle of ademonstration. If however B is sorelated to C that they are identical,or if they are plainly convertible, orthe one belongs to the other, theoriginal question is begged. For one

might equally well prove that A belongsto B through those terms if they areconvertible. But if they are notconvertible, it is the fact that theyare not that prevents such ademonstration, not the method of

demonstrating. But if one were to makethe conversion, then he would be doingwhat we have described and effecting areciprocal proof 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, but nodemonstration is made. If however A andB are identical either because they areconvertible or because A follows B,then the question is begged for thesame reason as before. For we haveexplained the meaning of begging the

question, viz. proving that which isnot self-evident by means of itself.

If then begging the question is provingwhat is not self-evident by means ofitself, in other words failing to provewhen the failure is due to the thesisto be proved and the premiss throughwhich it is proved being equallyuncertain, either because predicateswhich are identical belong to the samesubject, or because the same predicate

belongs to subjects which areidentical, the question may be beggedin the middle and third figures in both

ways, though, if the syllogism isaffirmative, only in the third andfirst figures. If the syllogism isnegative, the question is begged whenidentical predicates are denied of the





depend on the assumption laid down. Forwe use the expression ‘false cause’,when the syllogism is concluded inspite of the refutation of this

position; but that is not possible inostensive proofs: since if anassumption is refuted, a syllogism canno longer be drawn in reference to it.It is clear then that the expression‘false cause’ can only be used in thecase of a reductio ad impossibile, and

when the original hypothesis is sorelated to the impossible conclusion,that the conclusion resultsindifferently whether the hypothesis is

made or not. The most obvious case ofthe irrelevance of an assumption to aconclusion which is false is when asyllogism drawn from middle terms to animpossible conclusion is independent ofthe hypothesis, as we have explained inthe Topics. For to put that which isnot the cause as the cause, is justthis: e.g. if a man, wishing to provethat the diagonal of the square isincommensurate with the side, should

try to prove Zeno’s theorem that motionis impossible, and so establish areductio ad impossibile: for Zeno’sfalse theorem has no connexion at allwith the original assumption. Another



case is where the impossible conclusionis connected with the hypothesis, butdoes not result from it. This mayhappen whether one traces the connexionupwards or downwards, e.g. if it islaid down that A belongs to B, B to C,and C to D, and it should be false thatB belongs to D: for if we eliminated Aand assumed all the same that B belongsto C and C to D, the false conclusionwould not depend on the original

hypothesis. Or again trace theconnexion upwards; e.g. suppose that A

belongs to B, E to A and F to E, it being false that F belongs to A. In

this way too the impossible conclusionwould result, though the originalhypothesis were eliminated. But theimpossible conclusion ought to beconnected with the original terms: inthis way it will depend on thehypothesis, e.g. when one traces theconnexion downwards, the impossibleconclusion must be connected with thatterm which is predicate in thehypothesis: for if it is impossible

that A should belong to D, the falseconclusion will no longer result after

A has been eliminated. If one tracesthe connexion upwards, the impossibleconclusion must be connected with that



term which is subject in thehypothesis: for if it is impossiblethat F should belong to B, theimpossible conclusion will disappear ifB is eliminated. Similarly when thesyllogisms are negative.

It is clear then that when theimpossibility is not related to theoriginal terms, the false conclusiondoes not result on account of the

assumption. Or perhaps even so it maysometimes be independent. For if itwere laid down that A belongs not to B

but to K, and that K belongs to C and Cto D, the impossible conclusion wouldstill stand. Similarly if one takes theterms in an ascending series.Consequently since the impossibilityresults whether the first assumption issuppressed or not, it would appear to

be independent of that assumption. Or perhaps we ought not to understand the

statement that the false conclusionresults independently of theassumption, in the sense that if

something else were supposed theimpossibility would result; but ratherwe mean that when the first assumptionis eliminated, the same impossibilityresults through the remaining



premisses; since it is not perhapsabsurd that the same false resultshould follow from several hypotheses,e.g. that parallels meet, both on theassumption that the interior angle isgreater than the exterior and on theassumption that a triangle contains

more than two right angles.

18

A false argument depends on the firstfalse 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 fromtwo premisses. But if the premisses are

more than two, e.g. if C is establishedthrough A and B, and these through D,E, F, and G, one of these higher

propositions must be false, and on thisthe argument depends: for A and B areinferred by means of D, E, F, and G.Therefore the conclusion and the error

results from one of them.



19

In order to avoid having a syllogismdrawn against us we must take care,whenever an opponent asks us to admitthe reason without the conclusions, notto grant him the same term twice overin his premisses, since we know that asyllogism cannot be drawn without a

middle term, and that term which isstated more than once is the middle.

How we ought to watch the middle inreference to each conclusion, isevident from our knowing what kind ofthesis is proved in each figure. Thiswill not escape us since we know how weare maintaining the argument.

That which we urge men to beware of intheir admissions, they ought in attackto try to conceal. This will be

possible first, if, instead of drawingthe conclusions of preliminarysyllogisms, they take the necessary

premisses and leave the conclusions inthe dark; secondly if instead of

inviting assent to propositions whichare closely connected they take as faras possible those that are notconnected by middle terms. For examplesuppose that A is to be inferred to be



true of F, B, C, D, and E being middleterms. One ought then to ask whether A

belongs to B, and next whether D belongs to E, instead of asking whether

B belongs to C; after that he may askwhether B belongs to C, and so on. Ifthe syllogism is drawn through one

middle term, he ought to begin withthat: in this way he will most likelydeceive his opponent.

20

Since we know when a syllogism can beformed and how its terms must berelated, it is clear when refutationwill be possible and when impossible. Arefutation is possible whethereverything is conceded, or the answersalternate (one, I mean, beingaffirmative, the other negative). Foras has been shown a syllogism is

possible whether the terms are relatedin affirmative propositions or one

proposition is affirmative, the othernegative: consequently, if what is laid

down is contrary to the conclusion, arefutation must take place: for arefutation is a syllogism whichestablishes the contradictory. But ifnothing is conceded, a refutation is



impossible: for no syllogism is possible (as we saw) when all the terms

are negative: therefore no refutationis possible. For if a refutation were

possible, a syllogism must be possible;although if a syllogism is possible itdoes not follow that a refutation is

possible. Similarly refutation is not possible if nothing is conceded

universally: since the fields ofrefutation and syllogism are defined in

the same way.

21

It sometimes happens that just as weare deceived in the arrangement of theterms, so error may arise in ourthought about them, e.g. if it is

possible that the same predicate should belong to more than one subject

immediately, but although knowing theone, a man may forget the other andthink the opposite true. Suppose that A

belongs to B and to C in virtue oftheir nature, and that B and C belong

to all D in the same way. If then a manthinks that A belongs to all B, and Bto D, but A to no C, and C to all D, hewill both know and not know the samething in respect of the same thing.



Again if a man were to make a mistakeabout the members of a single series;e.g. suppose A belongs to B, B to C,and C to D, but some one thinks that A

belongs to all B, but to no C: he will both know that A belongs to D, and

think that it does not. Does he then maintain after this simply that what he

knows, he does not think? For he knowsin a way that A belongs to C through B,since the part is included in the

whole; so that what he knows in a way,this he maintains he does not think atall: but that is impossible.

In the former case, where the middleterm does not belong to the sameseries, it is not possible to think

both the premisses with reference toeach of the two middle terms: e.g. that

A belongs to all B, but to no C, and both B and C belong to all D. For it

turns out that the first premiss of theone syllogism is either wholly or

partially contrary to the first premissof the other. For if he thinks that A

belongs to everything to which B belongs, and he knows that B belongs to

D, then he knows that A belongs to D.Consequently if again he thinks that A

belongs to nothing to which C belongs,



he thinks that A does not belong tosome of that to which B belongs; but ifhe thinks that A belongs to everythingto which B belongs, and again thinksthat A does not belong to some of thatto which B belongs, these beliefs arewholly or partially contrary. In thisway then it is not possible to think;

but nothing prevents a man thinking one premiss of each syllogism of both premisses of one of the two syllogisms:

e.g. A belongs to all B, and B to D,and again A belongs to no C. An errorof this kind is similar to the errorinto which we fall concerning

particulars: e.g. if A belongs to allB, and B to all C, A will belong to allC. If then a man knows that A belongsto everything to which B belongs, heknows that A belongs to C. But nothing

prevents his being ignorant that Cexists; e.g. let A stand for two rightangles, B for triangle, C for a

particular diagram of a triangle. A man might think that C did not exist,

though he knew that every triangle

contains two right angles; consequentlyhe will know and not know the samething at the same time. For theexpression ‘to know that every trianglehas its angles equal to two right



angles’ is ambiguous, meaning to havethe knowledge either of the universalor of the particulars. Thus then heknows that C contains two right angleswith a knowledge of the universal, butnot with a knowledge of the

particulars; consequently his knowledgewill not be contrary to his ignorance.The argument in the Meno that learningis recollection may be criticized in asimilar way. For it never happens that

a man starts with a foreknowledge ofthe particular, but along with the

process of being led to see the general principle he receives a knowledge of

the particulars, by an act (as it were)of recognition. For we know some thingsdirectly; e.g. that the angles areequal to two right angles, if we knowthat the figure is a triangle.Similarly in all other cases.

By a knowledge of the universal then wesee the particulars, but we do not knowthem by the kind of knowledge which is

proper to them; consequently it is

possible that we may make mistakesabout them, but not that we should havethe knowledge and error that arecontrary to one another: rather we havethe knowledge of the universal but make



a mistake in apprehending the particular. Similarly in the cases

stated above. The error in respect ofthe middle term is not contrary to theknowledge obtained through thesyllogism, nor is the thought inrespect of one middle term contrary tothat in respect of the other. Nothing

prevents a man who knows both that A belongs to the whole of B, and that B

again belongs to C, thinking that A

does not belong to C, e.g. knowing thatevery mule is sterile and that this isa mule, and thinking that this animalis with foal: for he does not know that

A belongs to C, unless he considers thetwo propositions together. So it isevident that if he knows the one anddoes not know the other, he will fallinto error. And this is the relation ofknowledge of the universal to knowledgeof the particular. For we know nosensible thing, once it has passed

beyond the range of our senses, even ifwe happen to have perceived it, except

by means of the universal and the

possession of the knowledge which is 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 knowledge of



the universal or to have knowledge proper to the matter in hand or to

exercise such knowledge: consequentlythree kinds of error also are possible.

Nothing then prevents a man bothknowing and being mistaken about thesame thing, provided that his knowledgeand his error are not contrary. Andthis happens also to the man whoseknowledge is limited to each of the

premisses and who has not previously

considered the particular question. Forwhen he thinks that the mule is withfoal he has not the knowledge in thesense of its actual exercise, nor onthe other hand has his thought causedan error contrary to his knowledge: forthe error contrary to the knowledge ofthe universal would be a syllogism.

But he who thinks the essence of goodis the essence of bad will think thesame thing to be the essence of goodand the essence of bad. Let A stand forthe essence of good and B for theessence of bad, and again C for the

essence of good. Since then he thinks Band C identical, he will think that Cis B, and similarly that B is A,consequently that C is A. For just aswe saw that if B is true of all of



which C is true, and A is true of allof which B is true, A is true of C,similarly with the word ‘think’.Similarly also with the word ‘is’; forwe saw that if C is the same as B, andB as A, C is the same as A. Similarlytherefore with ‘opine’. Perhaps thenthis is necessary if a man will grantthe first point. But presumably that isfalse, that any one could suppose theessence of good to be the essence of

bad, save incidentally. For it is possible to think this in many

different ways. But we must considerthis matter better.

22

Whenever the extremes are convertibleit is necessary that the middle should

be convertible with both. For if A belongs to C through B, then if A and C

are convertible and C belongseverything to which A belongs, B isconvertible with A, and B belongs toeverything to which A belongs, through

C as middle, and C is convertible withB through A as middle. Similarly if theconclusion is negative, e.g. if B

belongs to C, but A does not belong toB, neither will A belong to C. If then



B is convertible with A, C will beconvertible with A. Suppose B does not

belong to A; neither then will C: forex hypothesi B belonged to all C. Andif C is convertible with B, B isconvertible also with A, for C is saidof that of all of which B is said. Andif C is convertible in relation to Aand to B, B also is convertible inrelation to A. For C belongs to that towhich B belongs: but C does not belong

to that to which A belongs. And thisalone starts from the conclusion; the

preceding moods do not do so as in theaffirmative syllogism. Again if A and Bare convertible, and similarly C and D,and if A or C must belong to anythingwhatever, then B and D will be suchthat one or other belongs to anythingwhatever. For since B belongs to thatto which A belongs, and D belongs tothat to which C belongs, and since A orC belongs to everything, but nottogether, it is clear that B or D

belongs to everything, but nottogether. For example if that which is

uncreated is incorruptible and thatwhich is incorruptible is uncreated, itis necessary that what is createdshould be corruptible and what iscorruptible should have been created.



For two syllogisms have been puttogether. Again if A or B belongs toeverything and if C or D belongs toeverything, but they cannot belongtogether, then when A and C areconvertible B and D are convertible.For if B does not belong to somethingto which D belongs, it is clear that A

belongs to it. But if A then C: forthey are convertible. Therefore C and D

belong together. But this is

impossible. When A belongs to the wholeof B and to C and is affirmed ofnothing else, and B also belongs to allC, it is necessary that A and B should

be convertible: for since A is said ofB and C only, and B is affirmed both ofitself and of C, it is clear that Bwill be said of everything of which Ais said, except A itself. Again when Aand B belong to the whole of C, and Cis convertible with B, it is necessarythat A should belong to all B: forsince A belongs to all C, and C to B byconversion, A will belong to all B.

When, of two opposites A and B, A is preferable to B, and similarly D is preferable to C, then if A and C

together are preferable to B and Dtogether, A must be preferable to D.



For A is an object of desire to thesame extent as B is an object ofaversion, since they are opposites: andC is similarly related to D, since theyalso are opposites. If then A is anobject of desire to the same extent asD, B is an object of aversion to thesame extent as C (since each is to thesame extent as each-the one an objectof aversion, the other an object ofdesire). Therefore both A and C

together, and B and D together, will beequally objects of desire or aversion.But since A and C are preferable to Band D, A cannot be equally desirablewith D; for then B along with D would

be equally desirable with A along withC. But if D is preferable to A, then B

must be less an object of aversion thanC: for the less is opposed to the less.But the greater good and lesser evilare preferable to the lesser good andgreater evil: the whole BD then is

preferable to the whole AC. But exhypothesi this is not so. A then is

preferable to D, and C consequently is

less an object of aversion than B. Ifthen every lover in virtue of his lovewould prefer A, viz. that the belovedshould 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 (represented by B), it is clear that A (being of

such a nature) is preferable togranting the favour. To receiveaffection then is preferable in love tosexual intercourse. Love then is moredependent on friendship than onintercourse. And if it is mostdependent on receiving affection, then

this is its end. Intercourse theneither is not an end at all or is anend relative to the further end, thereceiving of affection. And indeed thesame is true of the other desires andarts.

23

It is clear then how the terms arerelated in conversion, and in respectof being in a higher degree objects ofaversion or of desire. We must nowstate that not only dialectical anddemonstrative syllogisms are formed by

means of the aforesaid figures, butalso rhetorical syllogisms and ingeneral any form of persuasion, howeverit may be presented. For every belief



comes either through syllogism or frominduction.

Now induction, or rather the syllogismwhich springs out of induction,consists in establishingsyllogistically a relation between oneextreme and the middle by means of theother extreme, e.g. if B is the middleterm between A and C, it consists in

proving through C that A belongs to B.

For this is the manner in which we makeinductions. For example let A stand forlong-lived, B for bileless, and C forthe particular long-lived animals, e.g.

man, horse, mule. A then belongs to thewhole of C: for whatever is bileless islong-lived. But B also (’not possessing

bile’) belongs to all C. If then C isconvertible with B, and the middle termis not wider in extension, it isnecessary that A should belong to B.For it has already been proved that iftwo things belong to the same thing,and the extreme is convertible with oneof them, then the other predicate will

belong to the predicate that isconverted. But we must apprehend C as

made up of all the particulars. Forinduction proceeds through anenumeration of all the cases.



Such is the syllogism which establishesthe first and immediate premiss: forwhere there is a middle term thesyllogism proceeds through the middleterm; when there is no middle term,through induction. And in a wayinduction is opposed to syllogism: forthe latter proves the major term to

belong to the third term by means ofthe middle, the former proves the major

to belong to the middle by means of thethird. In the order of nature,syllogism through the middle term is

prior and better known, but syllogismthrough induction is clearer to us.

24

We have an ‘example’ when the majorterm is proved to belong to the middle

by means of a term which resembles thethird. It ought to be known both thatthe middle belongs to the third term,and that the first belongs to thatwhich resembles the third. For example

let A be evil, B making war againstneighbours, C Athenians againstThebans, D Thebans against Phocians. Ifthen we wish to prove that to fightwith the Thebans is an evil, we must



assume that to fight against neighboursis an evil. Evidence of this isobtained from similar cases, e.g. thatthe war against the Phocians was anevil to the Thebans. Since then tofight against neighbours is an evil,and to fight against the Thebans is tofight against neighbours, it is clearthat to fight against the Thebans is anevil. Now it is clear that B belongs toC and to D (for both are cases of

making war upon one’s neighbours) andthat A belongs to D (for the waragainst the Phocians did not turn outwell for the Thebans): but that A

belongs to B will be proved through D.Similarly if the belief in the relationof the middle term to the extremeshould be produced by several similarcases. Clearly then to argue by exampleis neither like reasoning from part towhole, nor like reasoning from whole to

part, but rather reasoning from part to part, when both particulars are

subordinate to the same term, and oneof them is known. It differs from

induction, because induction startingfrom all the particular cases proves(as we saw) that the major term belongsto the middle, and does not apply thesyllogistic conclusion to the minor



term, whereas argument by example does make this application and does not draw

its proof from all the particularcases.

25

By reduction we mean an argument inwhich the first term clearly belongs tothe middle, but the relation of the

middle to the last term is uncertain

though equally or more probable thanthe conclusion; or again an argument inwhich the terms intermediate betweenthe last term and the middle are few.For in any of these cases it turns outthat we approach more nearly toknowledge. For example let A stand forwhat can be taught, B for knowledge, Cfor justice. Now it is clear thatknowledge can be taught: but it isuncertain whether virtue is knowledge.If now the statement BC is equally or

more probable than AC, we have areduction: for we are nearer toknowledge, since we have taken a new

term, being so far without knowledgethat A belongs to C. Or again supposethat the terms intermediate between Band C are few: for thus too we arenearer knowledge. For example let D



stand for squaring, E for rectilinearfigure, F for circle. If there wereonly one term intermediate between Eand F (viz. that the circle is madeequal to a rectilinear figure by thehelp of lunules), we should be near toknowledge. But when BC is not more

probable than AC, and the intermediateterms are not few, I do not call thisreduction: nor again when the statementBC is immediate: for such a statement

is knowledge.

26

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

all or not in universal syllogisms. Anobjection is brought in two ways andthrough two figures; in two ways

because every objection is eitheruniversal or particular, by two figures

because objections are brought inopposition to the premiss, and

opposites can be proved only in thefirst and third figures. If a man

maintains a universal affirmative, wereply with a universal or a particularnegative; the former is proved from the



first figure, the latter from thethird. For example let stand for there

being a single science, B forcontraries. If a man premises thatcontraries are subjects of a singlescience, the objection may be eitherthat opposites are never subjects of asingle science, and contraries areopposites, so that we get the firstfigure, or that the knowable and theunknowable are not subjects of a single

science: this proof is in the thirdfigure: for it is true of C (theknowable and the unknowable) that theyare contraries, and it is false thatthey are the subjects of a singlescience.

Similarly if the premiss objected to isnegative. For if a man maintains thatcontraries are not subjects of a singlescience, we reply either that allopposites or that certain contraries,e.g. what is healthy and what issickly, are subjects of the samescience: the former argument issues

from the first, the latter from thethird figure.

In general if a man urges a universalobjection he must frame his



contradiction with reference to theuniversal of the terms taken by hisopponent, e.g. if a man maintains thatcontraries are not subjects of the samescience, his opponent must reply thatthere is a single science of allopposites. Thus we must have the firstfigure: for the term which embraces theoriginal subject becomes the middleterm.

If the objection is particular, theobjector must frame his contradictionwith reference to a term relatively towhich the subject of his opponent’s

premiss is universal, e.g. he will point out that the knowable and the

unknowable are not subjects of the samescience: ‘contraries’ is universalrelatively to these. And we have thethird figure: for the particular termassumed is middle, e.g. the knowableand the unknowable. Premisses fromwhich it is possible to draw thecontrary conclusion are what we startfrom when we try to make objections.

Consequently we bring objections inthese figures only: for in them onlyare opposite syllogisms possible, sincethe second figure cannot produce anaffirmative conclusion.



Besides, an objection in the middlefigure would require a fuller argument,e.g. if it should not be granted that A

belongs to B, because C does not followB. This can be made clear only by other

premisses. But an objection ought notto turn off into other things, but haveits new premiss quite clearimmediately. For this reason also thisis the only figure from which proof by

signs cannot be obtained.

We must consider later the other kindsof objection, namely the objection fromcontraries, from similars, and fromcommon opinion, and inquire whether a

particular objection cannot be elicitedfrom the first figure or a negativeobjection from the second.

27

A probability and a sign are notidentical, but a probability is agenerally approved proposition: what

men know to happen or not to happen, to be or not to be, for the most part thus

and thus, is a probability, e.g. ‘theenvious hate’, ‘the beloved showaffection’. A sign means a



demonstrative proposition necessary orgenerally approved: for anything suchthat when it is another thing is, orwhen it has come into being the otherhas come into being before or after, isa sign of the other’s being or havingcome into being. Now an enthymeme is asyllogism starting from probabilitiesor signs, and a sign may be taken inthree ways, corresponding to the

position of the middle term in the

figures. For it may be taken as in thefirst figure or the second or thethird. For example the proof that awoman is with child because she has

milk is in the first figure: for tohave milk is the middle term. Let Arepresent to be with child, B to have

milk, C woman. The proof that wise menare good, since Pittacus is good, comesthrough the last figure. Let A standfor good, B for wise men, C forPittacus. It is true then to affirm

both A and B of C: only men do not saythe latter, because they know it,though they state the former. The proof

that a woman is with child because sheis pale is meant to come through the

middle figure: for since palenessfollows women with child and is aconcomitant of this woman, people



suppose it has been proved that she iswith child. Let A stand for paleness, Bfor being with child, C for woman. Nowif the one proposition is stated, wehave only a sign, but if the other isstated as well, a syllogism, e.g.‘Pittacus is generous, since ambitious

men are generous and Pittacus isambitious.’ Or again ‘Wise men aregood, since Pittacus is not only good

but wise.’ In this way then syllogisms

are formed, only that which proceedsthrough the first figure is irrefutableif it is true (for it is universal),that which proceeds through the lastfigure is refutable even if theconclusion is true, since the syllogismis not universal nor correlative to the

matter in question: for though Pittacusis good, it is not therefore necessarythat all other wise men should be good.But the syllogism which proceedsthrough the middle figure is alwaysrefutable in any case: for a syllogismcan never be formed when the terms arerelated in this way: for though a woman

with child is pale, and this woman alsois pale, it is not necessary that sheshould be with child. Truth then may befound in signs whatever their kind, but



they have the differences we havestated.

We must either divide signs in the waystated, and among them designate the

middle term as the index (for peoplecall that the index which makes usknow, and the middle term above all hasthis character), or else we must callthe arguments derived from the extremessigns, that derived from the middle

term the index: for that which is proved through the first figure is most

generally accepted and most true.

It is possible to infer character fromfeatures, if it is granted that the

body and the soul are changed together by the natural affections: I say

‘natural’, for though perhaps bylearning music a man has made somechange in his soul, this is not one ofthose affections which are natural tous; rather I refer to passions anddesires when I speak of naturalemotions. If then this were granted and

also that for each change there is acorresponding sign, and we could statethe affection and sign proper to eachkind of animal, we shall be able toinfer character from features. For if



there is an affection which belongs properly to an individual kind, e.g.

courage to lions, it is necessary thatthere should be a sign of it: for exhypothesi body and soul are affectedtogether. Suppose this sign is the

possession of large extremities: this may belong to other kinds also though

not universally. For the sign is properin the sense stated, because theaffection is proper to the whole kind,

though not proper to it alone,according to our usual manner ofspeaking. The same thing then will befound in another kind, and man may be

brave, and some other kinds of animalas well. They will then have the sign:for ex hypothesi there is one signcorresponding to each affection. Ifthen this is so, and we can collectsigns of this sort in these animalswhich have only one affection proper tothem-but each affection has its sign,since it is necessary that it shouldhave a single sign-we shall then beable to infer character from features.

But if the kind as a whole has two properties, e.g. if the lion is both brave and generous, how shall we know

which of the signs which are its properconcomitants is the sign of a



particular affection? Perhaps if both belong to some other kind though not to

the whole of it, and if, in those kindsin which each is found though not inthe whole of their members, some

members possess one of the affectionsand not the other: e.g. if a man is

brave but not generous, but possesses,of the two signs, large extremities, itis clear that this is the sign ofcourage in the lion also. To judge

character from features, then, is possible in the first figure if the middle term is convertible with the

first extreme, but is wider than thethird term and not convertible with it:e.g. let A stand for courage, B forlarge extremities, and C for lion. Bthen belongs to everything to which C

belongs, but also to others. But A belongs to everything to which B belongs, and to nothing besides, but is

convertible with B: otherwise, therewould not be a single sign correlativewith each affection.



Posterior Analytics

Book I

1

ALL instruction given or received byway of argument proceeds from pre-existent knowledge. This becomesevident upon a survey of all the

species of such instruction. The mathematical sciences and all other

speculative disciplines are acquired inthis way, and so are the two forms ofdialectical reasoning, syllogistic andinductive; for each of these latter

make use of old knowledge to impartnew, the syllogism assuming an audiencethat accepts its premisses, inductionexhibiting the universal as implicit inthe clearly known particular. Again,the persuasion exerted by rhetoricalarguments is in principle the same,since they use either example, a kindof induction, or enthymeme, a form of

syllogism.

The pre-existent knowledge required isof two kinds. In some cases admissionof the fact must be assumed, in others



comprehension of the meaning of theterm used, and sometimes bothassumptions are essential. Thus, weassume that every predicate can beeither truly affirmed or truly deniedof any subject, and that ‘triangle’

means so and so; as regards ‘unit’ wehave to make the double assumption ofthe meaning of the word and theexistence of the thing. The reason isthat these several objects are not

equally obvious to us. Recognition of atruth may in some cases contain asfactors both previous knowledge andalso knowledge acquired simultaneouslywith that recognition-knowledge, thislatter, of the particulars actuallyfalling under the universal and thereinalready virtually known. For example,the student knew beforehand that theangles of every triangle are equal totwo right angles; but it was only atthe actual moment at which he was beingled on to recognize this as true in theinstance before him that he came toknow ‘this figure inscribed in the

semicircle’ to be a triangle. For somethings (viz. the singulars finallyreached which are not predicable ofanything else as subject) are onlylearnt in this way, i.e. there is here



no recognition through a middle of a minor term as subject to a major.

Before he was led on to recognition or before he actually drew a conclusion,

we should perhaps say that in a mannerhe knew, in a manner not.

If he did not in an unqualified senseof the term know the existence of thistriangle, how could he know withoutqualification that its angles were

equal to two right angles? No: clearlyhe knows not without qualification butonly in the sense that he knowsuniversally. If this distinction is notdrawn, we are faced with the dilemma inthe Meno: either a man will learnnothing or what he already knows; forwe cannot accept the solution whichsome people offer. A man is asked, ‘Doyou, or do you not, know that every

pair is even?’ He says he does know it.The questioner then produces a

particular pair, of the existence, andso a fortiori of the evenness, of whichhe was unaware. The solution which some

people offer is to assert that they donot know that every pair is even, butonly that everything which they know to

be a pair is even: yet what they knowto be even is that of which they have



demonstrated evenness, i.e. what they made the subject of their premiss, viz.

not merely every triangle or numberwhich they know to be such, but any andevery number or triangle withoutreservation. For no premiss is evercouched in the form ‘every number whichyou know to be such’, or ‘everyrectilinear figure which you know to besuch’: the predicate is alwaysconstrued as applicable to any and

every instance of the thing. On theother hand, I imagine there is nothingto prevent a man in one sense knowingwhat he is learning, in another notknowing it. The strange thing would be,not if in some sense he knew what hewas learning, but if he were to know itin that precise sense and manner inwhich he was learning it.

2

We suppose ourselves to possessunqualified scientific knowledge of a

thing, as opposed to knowing it in theaccidental way in which the sophistknows, when we think that we know thecause on which the fact depends, as thecause of that fact and of no other,



and, further, that the fact could not be other than it is. Now that

scientific knowing is something of thissort is evident-witness both those whofalsely claim it and those who actually

possess it, since the former merelyimagine themselves to be, while thelatter are also actually, in thecondition described. Consequently the

proper object of unqualified scientificknowledge is something which cannot be

other than it is.

There may be another manner of knowingas well-that will be discussed later.

What I now assert is that at all eventswe do know by demonstration. Bydemonstration I mean a syllogism

productive of scientific knowledge, asyllogism, that is, the grasp of whichis eo ipso such knowledge. Assumingthen that my thesis as to the nature ofscientific knowing is correct, the

premisses of demonstrated knowledge must be true, primary, immediate, better known than and prior to the

conclusion, which is further related tothem as effect to cause. Unless theseconditions are satisfied, the basictruths will not be ‘appropriate’ to theconclusion. Syllogism there may indeed



be without these conditions, but suchsyllogism, not being productive ofscientific knowledge, will not bedemonstration. The premisses must betrue: for that which is non-existentcannot be known-we cannot know, e.g.that the diagonal of a square iscommensurate with its side. The

premisses must be primary andindemonstrable; otherwise they willrequire demonstration in order to be

known, since to have knowledge, if it be not accidental knowledge, of things

which are demonstrable, means preciselyto have a demonstration of them. The

premisses must be the causes of theconclusion, better known than it, and

prior to it; its causes, since we possess scientific knowledge of a thing

only when we know its cause; prior, inorder to be causes; antecedently known,this antecedent knowledge being not our

mere understanding of the meaning, butknowledge of the fact as well. Now‘prior’ and ‘better known’ areambiguous terms, for there is a

difference between what is prior and better known in the order of being and

what is prior and better known to man.I mean that objects nearer to sense are

prior and better known to man; objects



without qualification prior and betterknown are those further from sense. Nowthe most universal causes are furthestfrom sense and particular causes arenearest to sense, and they are thusexactly opposed to one another. Insaying that the premisses ofdemonstrated knowledge must be primary,I mean that they must be the‘appropriate’ basic truths, for Iidentify primary premiss and basic

truth. A ‘basic truth’ in ademonstration is an immediate

proposition. An immediate propositionis one which has no other 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 isdialectical, it assumes either partindifferently; if it is demonstrative,it lays down one part to the definiteexclusion of the other because that

part is true. The term ‘enunciation’denotes either part of a contradictionindifferently. A contradiction is an

opposition which of its own natureexcludes a middle. The part of acontradiction which conjoins a

predicate with a subject is anaffirmation; the part disjoining them



is a negation. I call an immediate basic truth of syllogism a ‘thesis’

when, though it is not susceptible of proof by the teacher, yet ignorance of

it does not constitute a total bar to progress on the part of the pupil: one

which the pupil must know if he is tolearn anything whatever is an axiom. Icall it an axiom because there are suchtruths and we give them the name ofaxioms par excellence. If a thesis

assumes one part or the other of anenunciation, i.e. asserts either theexistence or the non-existence of asubject, it is a hypothesis; if it doesnot so assert, it is a definition.Definition is a ‘thesis’ or a ‘layingsomething down’, since thearithmetician lays it down that to be aunit is to be quantitativelyindivisible; but it is not ahypothesis, for to define what a unitis is not the same as to affirm itsexistence.

Now since the required ground of our

knowledge-i.e. of our conviction-of afact is the possession of such asyllogism as we call demonstration, andthe ground of the syllogism is thefacts constituting its premisses, we



must not only know the primary premisses-some if not all of them- beforehand, but know them better than

the conclusion: for the cause of anattribute’s inherence in a subjectalways itself inheres in the subject

more firmly than that attribute; e.g.the cause of our loving anything isdearer to us than the object of ourlove. So since the primary premissesare the cause of our knowledge-i.e. of

our conviction-it follows that we knowthem better-that is, are more convincedof them-than their consequences,

precisely because of our knowledge ofthe latter is the effect of ourknowledge of the premisses. Now a mancannot believe in anything more than inthe things he knows, unless he haseither actual knowledge of it orsomething better than actual knowledge.But we are faced with this paradox if astudent whose belief rests ondemonstration has not prior knowledge;a man must believe in some, if not inall, of the basic truths more than in

the conclusion. Moreover, if a man setsout to acquire the scientific knowledgethat comes through demonstration, he

must not only have a better knowledgeof the basic truths and a firmer



conviction of them than of theconnexion which is being demonstrated:

more than this, nothing must be morecertain or better known to him thanthese basic truths in their characteras contradicting the fundamental

premisses which lead to the opposed anderroneous conclusion. For indeed theconviction of pure science must beunshakable.

3

Some hold that, owing to the necessityof knowing the primary premisses, thereis no scientific knowledge. Othersthink there is, but that all truths aredemonstrable. Neither doctrine iseither true or a necessary deductionfrom the premisses. The first school,assuming that there is no way ofknowing other than by demonstration,

maintain that an infinite regress isinvolved, on the ground that if behind

the prior stands no primary, we couldnot know the posterior through the

prior (wherein they are right, for onecannot traverse an infinite series): ifon the other hand-they say-the series



terminates and there are primary premisses, yet these are unknowable because incapable of demonstration,

which according to them is the onlyform of knowledge. And since thus onecannot know the primary premisses,knowledge of the conclusions whichfollow from them is not pure scientificknowledge nor properly knowing at all,

but rests on the mere supposition thatthe premisses are true. The other party

agree with them as regards knowing,holding that it is only possible bydemonstration, but they see nodifficulty in holding that all truthsare demonstrated, on the ground thatdemonstration may be circular andreciprocal.

Our own doctrine is that not allknowledge is demonstrative: on thecontrary, knowledge of the immediate

premisses is independent ofdemonstration. (The necessity of thisis obvious; for since we must know the

prior premisses from which the

demonstration is drawn, and since theregress must end in immediate truths,those truths must be indemonstrable.)Such, then, is our doctrine, and inaddition we maintain that besides



scientific knowledge there is itsoriginative source which enables us torecognize the definitions.

Now demonstration must be based on premisses prior to and better known

than the conclusion; and the samethings cannot simultaneously be both

prior and posterior to one another: socircular demonstration is clearly not

possible in the unqualified sense of

‘demonstration’, but only possible if‘demonstration’ be extended to includethat other method of argument whichrests on a distinction between truths

prior to us and truths withoutqualification prior, i.e. the method bywhich induction produces knowledge. Butif we accept this extension of its

meaning, our definition of unqualifiedknowledge will prove faulty; for thereseem to be two kinds of it. Perhaps,however, the second form ofdemonstration, that which proceeds fromtruths better known to us, is notdemonstration in the unqualified sense

of the term.

The advocates of circular demonstrationare not only faced with the difficultywe have just stated: in addition their



theory reduces to the mere statementthat if a thing exists, then it doesexist-an easy way of proving anything.That this is so can be clearly shown bytaking three terms, for to constitutethe circle it makes no differencewhether many terms or few or even onlytwo are taken. Thus by direct proof, if

A is, B must be; if B is, C must be;therefore if A is, C must be. Sincethen-by the circular proof-if A is, 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 ‘if Ais, C must be’: but C and A have beenidentified. Consequently the upholdersof circular demonstration are in the

position of saying that if A is, A must be-a simple way of proving anything. Moreover, even such circular

demonstration is impossible except inthe case of attributes that imply oneanother, viz. ‘peculiar’ properties.

Now, it has been shown that the

positing of one thing-be it one term orone premiss-never involves a necessaryconsequent: two premisses constitutethe first and smallest foundation fordrawing a conclusion at all and



therefore a fortiori for thedemonstrative syllogism of science. If,then, A is implied in B and C, and Band C are reciprocally implied in oneanother and in A, it is possible, ashas been shown in my writings on thesyllogism, to prove all the assumptionson which the original conclusionrested, by circular demonstration inthe first figure. But it has also beenshown that in the other figures either

no conclusion is possible, or at leastnone which proves both the original

premisses. Propositions the terms ofwhich are not convertible cannot becircularly demonstrated at all, andsince convertible terms occur rarely inactual demonstrations, it is clearlyfrivolous and impossible to say thatdemonstration is reciprocal and thattherefore everything can bedemonstrated.

4

Since the object of pure scientificknowledge cannot be other than it is,the truth obtained by demonstrativeknowledge will be necessary. And sincedemonstrative knowledge is only present



when we have a demonstration, itfollows that demonstration is aninference from necessary premisses. Sowe must consider what are the premissesof demonstration-i.e. what is theircharacter: and as a preliminary, let usdefine what we mean by an attribute‘true in every instance of itssubject’, an ‘essential’ attribute, anda ‘commensurate and universal’attribute. I call ‘true in every

instance’ what is truly predicable ofall instances-not of one to theexclusion of others-and at all times,not at this or that time only; e.g. ifanimal is truly predicable of everyinstance of man, then if it be true tosay ‘this is a man’, ‘this is ananimal’ is also true, and if the one betrue now the other is true now. Acorresponding account holds if point isin every instance predicable ascontained in line. There is evidencefor this in the fact that the objectionwe raise against a proposition put tous as true in every instance is either

an instance in which, or an occasion onwhich, it is not true. Essentialattributes are (1) such as belong totheir subject as elements in itsessential nature (e.g. line thus



belongs to triangle, point to line; forthe very being or ‘substance’ oftriangle and line is composed of theseelements, which are contained in theformulae defining triangle and line):(2) such that, while they belong tocertain subjects, the subjects to whichthey belong are contained in theattribute’s own defining formula. Thusstraight and curved belong to line, oddand even, prime and compound, square

and oblong, to number; and also theformula defining any one of theseattributes contains its subject-e.g.line or number as the case may be.

Extending this classification to allother attributes, I distinguish thosethat answer the above description as

belonging essentially to theirrespective subjects; whereas attributesrelated in neither of these two ways totheir subjects I call accidents or‘coincidents’; e.g. musical or white isa ‘coincident’ of animal.

Further (a) that is essential which isnot predicated of a subject other thanitself: e.g. ‘the walking [thing]’walks and is white in virtue of beingsomething else besides; whereas



substance, in the sense of whateversignifies a ‘this somewhat’, is notwhat it is in virtue of being somethingelse besides. Things, then, not

predicated of a subject I callessential; things predicated of asubject I call accidental or‘coincidental’.

In another sense again (b) a thingconsequentially connected with anything

is essential; one not so connected is‘coincidental’. An example of thelatter is ‘While he was walking itlightened’: the lightning was not dueto his walking; it was, we should say,a coincidence. If, on the other hand,there is a consequential connexion, the

predication is essential; e.g. if a beast dies when its throat is being

cut, then its death is also essentiallyconnected with the cutting, because thecutting was the cause of death, notdeath a ‘coincident’ of the cutting.

So far then as concerns the sphere of

connexions scientifically known in theunqualified sense of that term, allattributes which (within that sphere)are essential either in the sense thattheir subjects are contained in them,



or in the sense that they are containedin their subjects, are necessary aswell as consequentially connected withtheir subjects. For it is impossiblefor them not to inhere in theirsubjects either simply or in thequalified sense that one or other of a

pair of opposites must inhere in thesubject; e.g. in line must be eitherstraightness or curvature, in numbereither oddness or evenness. For within

a single identical genus the contraryof a given attribute is either its

privative or its contradictory; e.g.within number what is not odd is even,inasmuch as within this sphere even isa necessary consequent of not-odd. So,since any given predicate must beeither affirmed or denied of anysubject, essential attributes mustinhere in their subjects of necessity.

Thus, then, we have established thedistinction between the attribute whichis ‘true in every instance’ and the‘essential’ attribute.

I term ‘commensurately universal’ anattribute which belongs to everyinstance of its subject, and to everyinstance essentially and as such; from



which it clearly follows that allcommensurate universals inherenecessarily in their subjects. Theessential attribute, and the attributethat belongs to its subject as such,are identical. E.g. point and straight

belong to line essentially, for they belong to line as such; and triangle as

such has two right angles, for it isessentially equal to two right angles.

An attribute belongs commensurately anduniversally to a subject when it can beshown to belong to any random instanceof that subject and when the subject isthe first thing to which it can beshown to belong. Thus, e.g. (1) theequality of its angles to two rightangles is not a commensuratelyuniversal attribute of figure. Forthough it is possible to show that afigure has its angles equal to tworight angles, this attribute cannot bedemonstrated of any figure selected athaphazard, nor in demonstrating doesone take a figure at random-a square is

a figure but its angles are not equalto two right angles. On the other hand,any isosceles triangle has its anglesequal to two right angles, yetisosceles triangle is not the primary



subject of this attribute but triangleis prior. So whatever can be shown tohave its angles equal to two rightangles, or to possess any otherattribute, in any random instance ofitself and primarily-that is the firstsubject to which the predicate inquestion belongs commensurately anduniversally, and the demonstration, inthe essential sense, of any predicateis the proof of it as belonging to this

first subject commensurately anduniversally: while the proof of it as

belonging to the other subjects towhich it attaches is demonstration onlyin a secondary and unessential sense.

Nor again (2) is equality to two rightangles a commensurately universalattribute of isosceles; it is of widerapplication.

5

We must not fail to observe that weoften fall into error because ourconclusion is not in fact primary and

commensurately universal in the sensein which we think we prove it so. We

make this mistake (1) when the subjectis an individual or individuals abovewhich there is no universal to be



found: (2) when the subjects belong todifferent species and there is a higheruniversal, but it has no name: (3) whenthe subject which the demonstratortakes as a whole is really only a partof a larger whole; for then thedemonstration will be true of theindividual instances within the partand will hold in every instance of it,yet the demonstration will not be trueof this subject primarily and

commensurately and universally. When ademonstration is true of a subject

primarily and commensurately anduniversally, that is to be taken to

mean that it is true of a given subject primarily and as such. Case (3) may be

thus exemplified. If a proof were giventhat perpendiculars to the same lineare parallel, it might be supposed thatlines thus perpendicular were the

proper subject of the demonstration because being parallel is true of every

instance of them. But it is not so, forthe parallelism depends not on theseangles being equal to one another

because each is a right angle, butsimply on their being equal to oneanother. An example of (1) would be asfollows: if isosceles were the onlytriangle, it would be thought to have



its angles equal to two right anglesqua isosceles. An instance of (2) would

be the law that proportionalsalternate. Alternation used to bedemonstrated separately of numbers,lines, solids, and durations, though itcould have been proved of them all by asingle demonstration. Because there wasno single name to denote that in whichnumbers, lengths, durations, and solidsare identical, and because they

differed specifically from one another,this property was proved of each ofthem separately. To-day, however, the

proof is commensurately universal, forthey do not possess this attribute qualines or qua numbers, but qua

manifesting this generic characterwhich they are postulated as possessinguniversally. Hence, even if one proveof each kind of triangle that itsangles are equal to two right angles,whether by means of the same ordifferent proofs; still, as long as onetreats separately equilateral, scalene,and isosceles, one does not yet know,

except sophistically, that triangle hasits angles equal to two right angles,nor does one yet know that triangle hasthis property commensurately anduniversally, even if there is no other



species of triangle but these. For onedoes not know that triangle as such hasthis property, nor even that ‘all’triangles have it-unless ‘all’ means‘each taken singly’: if ‘all’ means ‘asa whole class’, then, though there benone in which one does not recognizethis property, one does not know it of‘all triangles’.

When, then, does our knowledge fail of

commensurate universality, and when itis unqualified knowledge? If triangle

be identical in essence withequilateral, i.e. with each or allequilaterals, then clearly we haveunqualified knowledge: if on the otherhand it be not, and the attribute

belongs to equilateral qua triangle;then our knowledge fails ofcommensurate universality. ‘But’, itwill be asked, ‘does this attribute

belong to the subject of which it has been demonstrated qua triangle or qua

isosceles? What is the point at whichthe subject. to which it belongs is

primary? (i.e. to what subject can it be demonstrated as belonging

commensurately and universally?)’Clearly this point is the first term inwhich it is found to inhere as the



elimination of inferior differentiae proceeds. Thus the angles of a brazen

isosceles triangle are equal to tworight angles: but eliminate brazen andisosceles and the attribute remains.‘But’-you may say-’eliminate figure orlimit, and the attribute vanishes.’True, but figure and limit are not thefirst differentiae whose eliminationdestroys the attribute. ‘Then what isthe first?’ If it is triangle, it will

be in virtue of triangle that theattribute belongs to all the othersubjects of which it is predicable, andtriangle is the subject to which it can

be demonstrated as belongingcommensurately and universally.

6

Demonstrative knowledge must rest onnecessary basic truths; for the objectof scientific knowledge cannot be otherthan it is. Now attributes attachingessentially to their subjects attach

necessarily to them: for essentialattributes are either elements in theessential nature of their subjects, orcontain their subjects as elements intheir own essential nature. (The pairs



of opposites which the latter classincludes are necessary because one

member or the other necessarilyinheres.) It follows from this that

premisses of the demonstrativesyllogism must be connexions essentialin the sense explained: for allattributes must inhere essentially orelse be accidental, and accidentalattributes are not necessary to theirsubjects.

We must either state the case thus, orelse premise that the conclusion ofdemonstration is necessary and that ademonstrated conclusion cannot be otherthan it is, and then infer that theconclusion must be developed fromnecessary premisses. For though you mayreason from true premisses withoutdemonstrating, yet if your premissesare necessary you will assuredlydemonstrate-in such necessity you haveat once a distinctive character ofdemonstration. That demonstration

proceeds from necessary premisses is

also indicated by the fact that theobjection we raise against a professeddemonstration is that a premiss of itis not a necessary truth-whether wethink it altogether devoid of



necessity, or at any rate so far as ouropponent’s previous argument goes. Thisshows how naive it is to suppose one’s

basic truths rightly chosen if onestarts with a proposition which is (1)

popularly accepted and (2) true, suchas the sophists’ assumption that toknow is the same as to possessknowledge. For (1) popular acceptanceor rejection is no criterion of a basictruth, which can only be the primary

law of the genus constituting thesubject matter of the demonstration;and (2) not all truth is ‘appropriate’.

A further proof that the conclusion must be the development of necessary premisses is as follows. Where

demonstration is possible, one who cangive no account which includes thecause has no scientific knowledge. If,then, we suppose a syllogism in which,though A necessarily inheres in C, yetB, the middle term of thedemonstration, is not necessarilyconnected with A and C, then the man

who argues thus has no reasonedknowledge of the conclusion, since thisconclusion does not owe its necessityto the middle term; for though theconclusion is necessary, the mediating



link is a contingent fact. Or again, ifa man is without knowledge now, thoughhe still retains the steps of theargument, though there is no change inhimself or in the fact and no lapse of

memory on his part; then neither had heknowledge previously. But the mediatinglink, not being necessary, may have

perished in the interval; and if so,though there be no change in him nor inthe fact, and though he will still

retain the steps of the argument, yethe has not knowledge, and therefore hadnot knowledge before. Even if the linkhas not actually perished but is liableto perish, this situation is possibleand might occur. But such a conditioncannot be knowledge.

When the conclusion is necessary, the middle through which it was proved may

yet quite easily be non-necessary. Youcan in fact infer the necessary evenfrom a non-necessary premiss, just asyou can infer the true from the nottrue. On the other hand, when the

middle is necessary the conclusion 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 necessarily predicated



of C. But when the conclusion isnonnecessary the middle cannot benecessary either. Thus: let A be

predicated non-necessarily of C butnecessarily of B, and let B be anecessary predicate of C; then A toowill be a necessary predicate of C,which by hypothesis it is not.

To sum up, then: demonstrativeknowledge must be knowledge of a

necessary nexus, and therefore mustclearly be obtained through a necessary

middle term; otherwise its possessorwill know neither the cause nor thefact that his conclusion is a necessaryconnexion. Either he will mistake thenon-necessary for the necessary and

believe the necessity of the conclusionwithout knowing it, or else he will noteven believe it-in which case he will

be equally ignorant, whether heactually infers the mere fact through

middle terms or the reasoned fact andfrom immediate premisses.

Of accidents that are not essentialaccording to our definition ofessential there is no demonstrativeknowledge; for since an accident, inthe sense in which I here speak of it,



may also not inhere, it is impossibleto prove its inherence as a necessaryconclusion. A difficulty, however,

might be raised as to why in dialectic,if the conclusion is not a necessaryconnexion, such and such determinate

premisses should be proposed in orderto deal with such and such determinate

problems. Would not the result be thesame if one asked any questionswhatever and then merely stated one’s

conclusion? The solution is thatdeterminate questions have to be put,not because the replies to them affirmfacts which necessitate facts affirmed

by the conclusion, but because theseanswers are propositions which if theanswerer affirm, he must affirm theconclusion and affirm it with truth ifthey are true.

Since it is just those attributeswithin every genus which are essentialand possessed by their respectivesubjects as such that are necessary itis clear that both the conclusions and

the premisses of demonstrations which produce scientific knowledge are

essential. For accidents are notnecessary: and, further, sinceaccidents are not necessary one does



not necessarily have reasoned knowledgeof a conclusion drawn from them (thisis so even if the accidental premissesare invariable but not essential, as in

proofs through signs; for though theconclusion be actually essential, onewill not know it as essential nor knowits reason); but to have reasonedknowledge of a conclusion is to know itthrough its cause. We may conclude thatthe middle must be consequentially

connected with the minor, and the majorwith the middle.

7

It follows that we cannot indemonstrating pass from one genus toanother. We cannot, for instance, provegeometrical truths by arithmetic. Forthere are three elements indemonstration: (1) what is proved, theconclusion-an attribute inheringessentially in a genus; (2) the axioms,i.e. axioms which are premisses of

demonstration; (3) the subject-genuswhose attributes, i.e. essential

properties, are revealed by thedemonstration. The axioms which are

premisses of demonstration may be



identical in two or more sciences: butin the case of two different generasuch as arithmetic and geometry youcannot apply arithmetical demonstrationto the properties of magnitudes unlessthe magnitudes in question are numbers.How in certain cases transference is

possible I will explain later.

Arithmetical demonstration and theother sciences likewise possess, each

of them, their own genera; so that ifthe demonstration is to pass from onesphere to another, the genus must beeither absolutely or to some extent thesame. If this is not so, transferenceis clearly impossible, because theextreme and the middle terms must bedrawn from the same genus: otherwise,as predicated, they will not beessential and will thus be accidents.That is why it cannot be proved bygeometry that opposites fall under onescience, nor even that the product oftwo cubes is a cube. Nor can thetheorem of any one science be

demonstrated by means of anotherscience, unless these theorems arerelated 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 possessqua lines, i.e. in virtue of thefundamental truths of their peculiargenus: it cannot show, for example,that the straight line is the most

beautiful of lines or the contrary ofthe circle; for these qualities do not

belong to lines in virtue of their peculiar genus, but through some property which it shares with other

genera.

8

It is also clear that if the premissesfrom which the syllogism proceeds arecommensurately universal, theconclusion of such i.e. in theunqualified sense-must also be eternal.Therefore no attribute can bedemonstrated nor known by strictlyscientific knowledge to inhere in

perishable things. The proof can only be accidental, because the attribute’s

connexion with its perishable subjectis not commensurately universal buttemporary and special. If such ademonstration is made, one premiss must

be perishable and not commensurately



universal (perishable because only ifit is perishable will the conclusion be

perishable; not commensuratelyuniversal, because the predicate will

be predicable of some instances of thesubject and not of others); so that theconclusion can only be that a fact istrue at the moment-not commensuratelyand universally. The same is true ofdefinitions, since a definition iseither a primary premiss or a

conclusion of a demonstration, or elseonly differs from a demonstration inthe order of its terms. Demonstrationand science of merely frequentoccurrences-e.g. of eclipse ashappening to the moon-are, as such,clearly eternal: whereas so far as theyare not eternal they are not fullycommensurate. Other subjects too have

properties attaching to them in thesame way as eclipse attaches to the

moon.

9

It is clear that if the conclusion isto show an attribute inhering as such,nothing can be demonstrated except from



its ‘appropriate’ basic truths.Consequently 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, whichthe subject may share with another-andconsequently they apply equally tosubjects different in kind. They

therefore afford knowledge of anattribute only as inheringaccidentally, not as belonging to itssubject as such: otherwise they wouldnot have been applicable to anothergenus.

Our knowledge of any attribute’sconnexion with a subject is accidentalunless we know that connexion throughthe middle term in virtue of which itinheres, and as an inference from basic

premisses essential and ‘appropriate’to the subject-unless we know, e.g. the

property of possessing angles equal to

two right angles as belonging to thatsubject in which it inheresessentially, and as inferred from basic

premisses essential and ‘appropriate’to that subject: so that if that middle



term also belongs essentially to the minor, the middle must belong to the

same kind as the major and minor terms.The only exceptions to this rule aresuch cases as theorems in harmonicswhich are demonstrable by arithmetic.Such theorems are proved by the same

middle terms as arithmetical properties, but with a qualification-

the fact falls under a separate science(for the subject genus is separate),

but the reasoned fact concerns thesuperior science, to which theattributes essentially belong. Thus,even these apparent exceptions showthat no attribute is strictlydemonstrable except from its‘appropriate’ basic truths, which,however, in the case of these scienceshave the requisite identity ofcharacter.

It is no less evident that the peculiar basic truths of each inhering attribute

are indemonstrable; for basic truthsfrom which they might be deduced would

be basic truths of all that is, and thescience to which they belonged would

possess universal sovereignty. This isso because he knows better whoseknowledge is deduced from higher



causes, for his knowledge is from prior premisses when it derives from causes

themselves uncaused: hence, if he knows better than others or best of all, his

knowledge would be science in a higheror the highest degree. But, as thingsare, demonstration is not transferableto another genus, with such exceptionsas we have mentioned of the applicationof geometrical demonstrations totheorems in mechanics or optics, or of

arithmetical demonstrations to those ofharmonics.

It is hard to be sure whether one knowsor not; for it is hard to be surewhether one’s knowledge is based on the

basic truths appropriate to eachattribute-the differentia of trueknowledge. We think we have scientificknowledge if we have reasoned from trueand primary premisses. But that is notso: the conclusion must be homogeneouswith the basic facts of the science.

10

I call the basic truths of every genusthose clements in it the existence ofwhich cannot be proved. As regards both



these primary truths and the attributesdependent on them the meaning of thename is assumed. The fact of theirexistence as regards the primary truths

must be assumed; but it has to be proved of the remainder, the

attributes. Thus we assume the meaningalike of unity, straight, andtriangular; but while as regards unityand magnitude we assume also the factof their existence, in the case of the

remainder proof is required.

Of the basic truths used in thedemonstrative sciences some are

peculiar to each science, and some arecommon, but common only in the sense ofanalogous, being of use only in so faras they fall within the genusconstituting the province of thescience in question.

Peculiar truths are, e.g. thedefinitions of line and straight;common truths are such as ‘take equalsfrom equals and equals remain’. Only so

much of these common truths is requiredas falls within the genus in question:for a truth of this kind will have thesame force even if not used generally

but applied by the geometer only to



magnitudes, or by the arithmeticianonly to numbers. Also peculiar to ascience are the subjects the existenceas well as the meaning of which itassumes, and the essential attributesof which it investigates, e.g. inarithmetic units, in geometry pointsand lines. Both the existence and the

meaning of the subjects are assumed bythese sciences; but of their essentialattributes only the meaning is assumed.

For example arithmetic assumes the meaning of odd and even, square and

cube, geometry that of incommensurable,or of deflection or verging of lines,whereas the existence of theseattributes is demonstrated by means ofthe axioms and from previousconclusions as premisses. Astronomy too

proceeds in the same way. For indeedevery demonstrative science has threeelements: (1) that which it posits, thesubject genus whose essentialattributes it examines; (2) the so-called axioms, which are primary

premisses of its demonstration; (3) the

attributes, the meaning of which itassumes. Yet some sciences may verywell pass over some of these elements;e.g. we might not expressly posit theexistence of the genus if its existence



were obvious (for instance, theexistence of hot and cold is moreevident than that of number); or we

might omit to assume expressly the meaning of the attributes if it were

well understood. In the way the meaningof axioms, such as ‘Take equals fromequals and equals remain’, is wellknown and so not expressly assumed.

Nevertheless in the nature of the casethe essential elements of demonstration

are three: the subject, the attributes,and the basic premisses.

That which expresses necessary self-grounded fact, and which we mustnecessarily believe, is distinct bothfrom the hypotheses of a science andfrom illegitimate postulate-I say ‘must

believe’, because all syllogism, andtherefore a fortiori demonstration, isaddressed not to the spoken word, butto the discourse within the soul, andthough we can always raise objectionsto the spoken word, to the inwarddiscourse we cannot always object. That

which is capable of proof but assumed by the teacher without proof is, if the pupil believes and accepts it,

hypothesis, though only in a limitedsense hypothesis-that is, relatively to



the pupil; if the pupil has no opinionor a contrary opinion on the matter,the same assumption is an illegitimate

postulate. Therein lies the distinction between hypothesis and illegitimate postulate: the latter is the contrary

of the pupil’s opinion, demonstrable, but assumed and used without

demonstration.

The definition-viz. those which are not

expressed as statements that anythingis or is not-are not hypotheses: but itis in the premisses of a science thatits hypotheses are contained.Definitions require only to beunderstood, 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 beingof which depends the being of the factinferred. Nor are the geometer’shypotheses false, as some have held,urging that one must not employfalsehood and that the geometer is

uttering falsehood in stating that theline which he draws is a foot long orstraight, when it is actually neither.The truth is that the geometer does notdraw any conclusion from the being of



the particular line of which he speaks, but from what his diagrams symbolize. A

further distinction is that allhypotheses and illegitimate postulatesare either universal or particular,whereas a definition is neither.

11

So demonstration does not necessarily

imply the being of Forms nor a One beside a Many, but it does necessarily

imply the possibility of truly predicating one of many; since without

this possibility we cannot save theuniversal, and if the universal goes,the middle term goes witb. it, and sodemonstration becomes impossible. Weconclude, then, that there must be asingle identical term unequivocally

predicable of a number of individuals.

The law that it is impossible to affirmand deny simultaneously the same

predicate 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



affirmed of the middle but falselydenied. It makes no difference,however, if we add to the middle, oragain to the minor term, thecorresponding negative. For grant a

minor term of which it is true to predicate man-even if it be also true

to predicate not-man of it—still grantsimply that man is animal and not not-animal, and the conclusion follows: forit will still be true to say that

Callias—even if it be also true to saythat not-Callias—is animal and not not-animal. The reason is that the majorterm is predicable not only of the

middle, but of something other than the middle as well, being of wider

application; so that the conclusion isnot affected even if the middle isextended to cover the original middleterm and also what is not the original

middle term.

The law that every predicate can beeither truly affirmed or truly deniedof every subject is posited by such

demonstration as uses reductio adimpossibile, and then not alwaysuniversally, but so far as it isrequisite; within the limits, that is,of the genus-the genus, I mean (as I



have already explained), to which the man of science applies his

demonstrations. In virtue of the commonelements of demonstration-I mean thecommon axioms which are used as

premisses of demonstration, not thesubjects nor the attributesdemonstrated as belonging to them-allthe sciences have communion with oneanother, and in communion with them allis dialectic and any science which

might attempt a universal proof ofaxioms such as the law of excluded

middle, the law that the subtraction ofequals from equals leaves equalremainders, or other axioms of the samekind. Dialectic has no definite sphereof this kind, not being confined to asingle genus. Otherwise its methodwould not be interrogative; for theinterrogative method is barred to thedemonstrator, who cannot use theopposite facts to prove the same nexus.This was shown in my work on thesyllogism.

12

If a syllogistic question is equivalentto a proposition embodying one of the



two sides of a contradiction, and ifeach science has its peculiar

propositions from which its peculiarconclusion is developed, then there issuch a thing as a distinctivelyscientific question, and it is theinterrogative form of the premissesfrom which the ‘appropriate’ conclusionof each science is developed. Hence itis clear that not every question will

be relevant to geometry, nor to

medicine, nor to any other science:only those questions will begeometrical which form premisses forthe proof of the theorems of geometryor of any other science, such asoptics, which uses the same basictruths as geometry. Of the othersciences the like is true. Of thesequestions the geometer is bound to givehis account, using the basic truths ofgeometry in conjunction with his

previous conclusions; of the basictruths the geometer, as such, is not

bound to give any account. The like istrue of the other sciences. There is a

limit, then, to the questions which we may put to each man of science; nor is

each man of science bound to answer allinquiries on each several subject, butonly such as fall within the defined



field of his own science. If, then, incontroversy with a geometer quageometer the disputant confines himselfto geometry and proves anything fromgeometrical premisses, he is clearly to

be applauded; if he goes outside thesehe will be at fault, and obviouslycannot even refute the geometer exceptaccidentally. One should therefore notdiscuss geometry among those who arenot geometers, for in such a company an

unsound argument will pass unnoticed.This is correspondingly true in theother sciences.

Since there are ‘geometrical’questions, does it follow that thereare also distinctively ‘ungeometrical’questions? Further, in each specialscience-geometry for instance-what kindof error is it that may vitiatequestions, and yet not exclude themfrom that science? Again, is theerroneous conclusion one constructedfrom premisses opposite to the true

premisses, or is it formal fallacy

though drawn from geometrical premisses? Or, perhaps, the erroneous

conclusion is due to the drawing of premisses from another science; e.g. in

a geometrical controversy a musical



question is distinctivelyungeometrical, whereas the notion that

parallels meet is in one sensegeometrical, being ungeometrical in adifferent fashion: the reason beingthat ‘ungeometrical’, like‘unrhythmical’, is equivocal, meaningin the one case not geometry at all, inthe other bad geometry? It is thiserror, i.e. error based on premisses ofthis kind-’of’ the science but false-

that is the contrary of science. In mathematics the formal fallacy is not

so common, because it is the middleterm in which the ambiguity lies, sincethe major is predicated of the whole ofthe middle and the middle of the wholeof the minor (the predicate of coursenever has the prefix ‘all’); and in

mathematics one can, so to speak, seethese middle terms with an intellectualvision, while in dialectic theambiguity may escape detection. E.g.‘Is every circle a figure?’ A diagramshows that this is so, but the minor

premiss ‘Are epics circles?’ is shown

by the diagram to be false.

If a proof has an inductive minor premiss, one should not bring an

‘objection’ against it. For since every



premiss must be applicable to a numberof cases (otherwise it will not be truein every instance, which, since thesyllogism proceeds from universals, it

must be), then assuredly the same istrue of an ‘objection’; since premissesand ‘objections’ are so far the samethat anything which can be validlyadvanced as an ‘objection’ must be suchthat it could take the form of a

premiss, either demonstrative or

dialectical. On the other hand,arguments formally illogical dosometimes occur through taking as

middles mere attributes of the majorand minor terms. An instance of this isCaeneus’ proof that fire increases ingeometrical proportion: ‘Fire’, heargues, ‘increases rapidly, and so doesgeometrical proportion’. There is nosyllogism so, but there is a syllogismif the most rapidly increasing

proportion is geometrical and the mostrapidly increasing proportion isattributable to fire in its motion.Sometimes, no doubt, it is impossible

to reason from premisses predicating mere attributes: but sometimes it is possible, though the possibility is

overlooked. If false premisses couldnever give true conclusions



‘resolution’ would be easy, for premisses and conclusion would in that

case inevitably reciprocate. I mightthen argue thus: let A be an existingfact; let the existence of A imply suchand such facts actually known to me toexist, which we may call B. I can now,since they reciprocate, infer A from B.

Reciprocation of premisses andconclusion is more frequent in

mathematics, because mathematics takesdefinitions, but never an accident, forits premisses-a second characteristicdistinguishing mathematical reasoningfrom dialectical disputations.

A science expands not by theinterposition of fresh middle terms,

but by the apposition of fresh extremeterms. E.g. A is predicated of B, B ofC, C of D, and so indefinitely. Or theexpansion may be lateral: e.g. one

major A, may be proved of two minors, Cand E. Thus let A represent number-anumber or number taken indeterminately;

B determinate odd number; C any particular odd number. We can then predicate A of C. Next let D represent

determinate even number, and E evennumber. Then A is predicable of E.



13

Knowledge of the fact differs fromknowledge of the reasoned fact. To

begin with, they differ within the samescience and in two ways: (1) when the

premisses of the syllogism are notimmediate (for then the proximate causeis not contained in them-a necessary

condition of knowledge of the reasonedfact): (2) when the premisses areimmediate, but instead of the cause the

better known of the two reciprocals istaken as the middle; for of tworeciprocally predicable terms the onewhich is not the cause may quite easily

be the better known and so become the middle term of the demonstration. Thus

(2) (a) you might prove as follows thatthe planets are near because they donot twinkle: let C be the planets, Bnot twinkling, A proximity. Then B is

predicable of C; for the planets do nottwinkle. But A is also predicable of B,

since that which does not twinkle isnear—we must take this truth as having

been reached by induction or sense- perception. Therefore A is a necessary predicate of C; so that we have



demonstrated that the planets are near.This syllogism, then, proves not thereasoned fact but only the fact; sincethey are not near because they do nottwinkle, but, because they are near, donot twinkle. The major and middle ofthe proof, however, may be reversed,and then the demonstration will be ofthe reasoned fact. Thus: let C 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 syllogism proves the reasoned fact, since its middle term is the proximate cause. Another example is the inference that

the moon is spherical from its mannerof waxing. Thus: since that which sowaxes is spherical, and since the moonso waxes, clearly the moon isspherical. Put in this form, thesyllogism turns out to be proof of thefact, but if the middle and major bereversed it is proof of the reasonedfact; since the moon is not spherical

because it waxes in a certain manner,

but waxes in such a manner because itis spherical. (Let C be the moon, Bspherical, and A waxing.) Again (b), incases where the cause and the effectare not reciprocal and the effect is



the better known, the fact isdemonstrated but not the reasoned fact.This also occurs (1) when the middlefalls outside the major and minor, forhere too the strict cause is not given,and so the demonstration is of thefact, not of the reasoned fact. Forexample, the question ‘Why does not awall breathe?’ might be answered,‘Because it is not an animal’; but thatanswer would not give the strict cause,

because if not being an animal causesthe absence of respiration, then beingan animal should be the cause ofrespiration, according to the rule thatif the negation of causes the non-inherence of y, the affirmation of xcauses the inherence of y; e.g. if thedisproportion of the hot and coldelements is the cause of ill health,their proportion is the cause ofhealth; and conversely, if theassertion of x causes the inherence ofy, the negation of x must cause y’snon-inherence. But in the case giventhis consequence does not result; for

not every animal breathes. A syllogismwith this kind of cause takes place inthe second figure. Thus: let A beanimal, B respiration, C wall. Then Ais predicable of all B (for all that



breathes is animal), but of no C; andconsequently B is predicable of no C;that is, the wall does not breathe.Such causes are like far-fetchedexplanations, which precisely consistin making the cause too remote, as in

Anacharsis’ account of why theScythians have no 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 andaccording to the position of the middleterms. But there is another way too inwhich the fact and the reasoned factdiffer, and that is when they areinvestigated respectively by differentsciences. This occurs in the case of

problems related to one another assubordinate and superior, as whenoptical problems are subordinated togeometry, mechanical problems tostereometry, harmonic problems toarithmetic, the data of observation toastronomy. (Some of these sciences bear

almost the same name; e.g. mathematicaland nautical astronomy, mathematicaland acoustical harmonics.) Here it isthe business of the empirical observersto know the fact, of the mathematicians



to know the reasoned fact; for thelatter are in possession of thedemonstrations giving the causes, andare often ignorant of the fact: just aswe have often a clear insight into auniversal, but through lack ofobservation are ignorant of some of its

particular instances. These connexionshave a perceptible existence thoughthey are manifestations of forms. Forthe mathematical sciences concern

forms: they do not demonstrate properties of a substratum, since, even

though the geometrical subjects are predicable as properties of a perceptible substratum, it is not as

thus predicable that the mathematiciandemonstrates properties of them. Asoptics is related to geometry, soanother science is related to optics,namely the theory of the rainbow. Hereknowledge of the fact is within the

province of the natural philosopher,knowledge of the reasoned fact withinthat of the optician, either quaoptician or qua mathematical optician.

Many sciences not standing in this mutual relation enter into it at points; e.g. medicine and geometry: it

is the physician’s business to know



that circular wounds heal more slowly,the geometer’s to know the reason why.

14

Of all the figures the most scientificis the first. Thus, it is the vehicleof the demonstrations of all the

mathematical sciences, such asarithmetic, geometry, and optics, and

practically all of all sciences thatinvestigate causes: for the syllogismof the reasoned fact is eitherexclusively or generally speaking andin most cases in this figure-a second

proof that this figure is the mostscientific; for grasp of a reasonedconclusion is the primary condition ofknowledge. Thirdly, the first is theonly figure which enables us to pursueknowledge of the essence of a thing. Inthe second figure no affirmativeconclusion is possible, and knowledgeof a thing’s essence must beaffirmative; while in the third figure

the conclusion can be affirmative, butcannot be universal, and essence musthave a universal character: e.g. man isnot two-footed animal in any qualifiedsense, but universally. Finally, the



first figure has no need of the others,while it is by means of the first thatthe other two figures are developed,and have their intervals closepackeduntil immediate premisses are reached.

Clearly, therefore, the first figure isthe primary condition of knowledge.

15

Just as an attribute A may (as we saw) be atomically connected with a subject

B, so its disconnexion may be atomic. Icall ‘atomic’ connexions ordisconnexions which involve nointermediate term; since in that casethe connexion or disconnexion will not

be mediated by something other than theterms themselves. It follows that ifeither A or B, or both A and B, have agenus, their disconnexion cannot be

primary. Thus: let C be the genus of A.Then, if C is not the genus of B-for A

may well have a genus which is not the

genus of 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, wehave

all B is D,no D is A,therefore no B is A, by syllogism;

and the proof will be similar if both Aand B have a genus. That the genus of Aneed not be the genus of B and viceversa, is shown by the existence of

mutually exclusive coordinate series of predication. If no term in the series ACD...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, if it were, the series would not

be mutually exclusive. So also if B hasa genus, it will not be the genus of A.If, on the other hand, neither A nor Bhas a genus and A does not inhere in B,

this disconnexion must be atomic. Ifthere be a middle term, one or other ofthem is bound to have a genus, for thesyllogism will be either in the firstor the second figure. If it is in the



first, B will have a genus-for the premiss containing it must be

affirmative: if in the second, either Aor B indifferently, since syllogism is

possible if either is contained in anegative premiss, but not if both

premisses are negative.

Hence it is clear that one thing may beatomically disconnected from another,and we have stated when and how this is

possible.

16

Ignorance-defined not as the negationof knowledge but as a positive state of

mind-is error produced by inference.

(1) Let us first consider propositionsasserting a predicate’s immediateconnexion with or disconnexion from asubject. Here, it is true, positiveerror may befall one in alternativeways; for it may arise where one

directly believes a connexion ordisconnexion as well as where one’s

belief is acquired by inference. Theerror, however, that consists in adirect belief is without complication;





neither of those terms will belong tothe other. It is, of course, equallythe case if A-C is not atomic.

Error of attribution, then, occursthrough these causes and in this formonly-for we found that no syllogism ofuniversal attribution was possible inany figure but the first. On the otherhand, an error of non-attribution mayoccur either in the first or in the

second figure. Let us therefore firstexplain the various forms it takes inthe first figure and the character ofthe premisses in each case.

(c) It may occur when both premissesare false; e.g. supposing A atomicallyconnected with both C and B, if it bethen assumed that no C is and all B isC, both premisses are false.

(d) It is also possible when one isfalse. This may be either premissindifferently. A-C may be true, C-Bfalse-A-C true because A is not an

attribute of all things, C-B false because C, which never has the

attribute A, cannot be an attribute ofB; for if C-B were true, the premiss A-C would no longer be true, and besides



if both premisses were true, theconclusion would be true. Or again, C-B

may be true and A-C false; e.g. if bothC and A contain B as genera, one ofthem must be subordinate to the other,so that if the premiss takes the form

No C is A, it will be false. This makesit clear that whether either or both

premisses are false, the conclusionwill equally be false.

In the second figure the premissescannot both be wholly false; for if allB is A, no middle term can be withtruth universally affirmed of oneextreme and universally denied of theother: but premisses in which the

middle is affirmed of one extreme anddenied of the other are the necessarycondition if one is to get a validinference at all. Therefore if, takenin this way, they are wholly false,their contraries conversely should bewholly true. But this is impossible. Onthe other hand, there is nothing to

prevent both premisses being partially

false; e.g. if actually some A is C andsome B is C, then if it is premisedthat all A is C and no B is C, both

premisses are false, yet partially, notwholly, false. The same is true if the



major is made negative instead of the minor. Or one premiss may be wholly

false, and it may be either of them.Thus, supposing that actually anattribute of all A must also be anattribute of all B, then if C is yettaken to be a universal attribute ofall but universally non-attributable toB, C-A will be true but C-B false.

Again, actually that which is anattribute of no B will not be an

attribute of all A either; for if it bean attribute of all A, it will also bean attribute of all B, which iscontrary to supposition; but if C benevertheless assumed to be a universalattribute of A, but an attribute of noB, then the premiss C-B is true but the

major is false. The case is similar ifthe major is made the negative premiss.For in fact what is an attribute of no

A will not be an attribute of any Beither; and if it be yet assumed that Cis universally non-attributable to A,

but a universal attribute of B, the premiss C-A is true but the minor

wholly false. Again, in fact it isfalse to assume that that which is anattribute of all B is an attribute ofno A, for if it be an attribute of allB, it must be an attribute of some A.



If then C is nevertheless assumed to bean attribute of all B but of no A, C-Bwill be true but C-A false.

It is thus clear that in the case ofatomic propositions erroneous inferencewill be possible not only when both

premisses are false but also when onlyone is false.

17

In the case of attributes notatomically connected with ordisconnected from their subjects, (a)(i) as long as the false conclusion isinferred through the ‘appropriate’

middle, only the major and not both premisses can be false. By ‘appropriate middle’ I mean the middle term through

which the contradictory-i.e. the true-conclusion is inferrible. Thus, let A

be attributable to B through a middleterm C: then, since to produce aconclusion the premiss C-B must be

taken affirmatively, it is clear thatthis premiss must always be true, forits 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 middleis taken from another series of

predication; e.g. suppose D to be notonly contained within A as a partwithin its whole but also predicable ofall B. Then the premiss D-B must remainunchanged, but the quality of A-D must

be changed; so that D-B is always true, A-D always false. Such error is practically identical with that which

is inferred through the ‘appropriate’ middle. On the other hand, (b) if the

conclusion is not inferred through the‘appropriate’ middle-(i) when the

middle is subordinate to A but is predicable of no B, both premisses must be false, because if there is to be a

conclusion both must be posited asasserting the contrary of what isactually the fact, and so posited both

become false: e.g. suppose thatactually all D is A but no B is D; thenif these premisses are changed inquality, a conclusion will follow and

both of the new premisses will be

false. When, however, (ii) the middle Dis not subordinate to A, A-D will betrue, D-B false-A-D true because A wasnot subordinate to D, D-B false becauseif it had been true, the conclusion too



would have been true; but it is exhypothesi false.

When the erroneous inference is in thesecond figure, both premisses cannot beentirely false; since if B issubordinate to A, there can be no

middle predicable of all of one extremeand of none of the other, as was stated

before. One premiss, however, may befalse, and it may be either of them.

Thus, if C is actually an attribute of both A and B, but is assumed to be an

attribute of A only and not of B, C-Awill be true, C-B false: or again if C

be assumed to be attributable to B butto no A, C-B will be true, C-A false.

We have stated when and through whatkinds of premisses error will result incases where the erroneous conclusion isnegative. If the conclusion isaffirmative, (a) (i) it may be inferredthrough the ‘appropriate’ middle term.In this case both premisses cannot befalse since, as we said before, C-B

must remain unchanged if there is to bea conclusion, and consequently A-C, thequality of which is changed, willalways be false. This is equally trueif (ii) the middle is taken from



another series of predication, as wasstated to be the case also with regardto negative error; for D-B must remainunchanged, while the quality of A-D

must be converted, and the type oferror is the same as before.

(b) The middle may be inappropriate.Then (i) if D is subordinate to A, A-Dwill be true, but D-B false; since A

may quite well be predicable of several

terms no one of which can besubordinated to another. If, however,(ii) D is not subordinate to A,obviously A-D, since it is affirmed,will always be false, while D-B may beeither true or false; for A may verywell be an attribute of no D, whereasall B is D, e.g. no science is animal,all music is science. Equally well A

may be an attribute of no D, and D ofno B. It emerges, then, that if the

middle term is not subordinate to the major, not only both premisses but

either singly may be false.

Thus we have made it clear how manyvarieties of erroneous inference areliable to happen and through what kindsof premisses they occur, in the case



both of immediate and of demonstrabletruths.

18

It is also clear that the loss of anyone of the senses entails the loss of acorresponding portion of knowledge, andthat, since we learn either byinduction or by demonstration, this

knowledge cannot be acquired. Thusdemonstration develops from universals,induction from particulars; but sinceit is possible to familiarize the pupilwith even the so-called mathematicalabstractions only through induction-i.e. only because each subject genus

possesses, in virtue of a determinate mathematical character, certain properties which can be treated as

separate even though they do not existin isolation-it is consequentlyimpossible to come to grasp universalsexcept through induction. But inductionis impossible for those who have not

sense-perception. For it is sense- perception alone which is adequate for

grasping the particulars: they cannot be objects of scientific knowledge, because neither can universals give us



knowledge of them without induction,nor can we get it through inductionwithout sense-perception.

19

Every syllogism is effected by means ofthree terms. One kind of syllogismserves to prove that A inheres in C byshowing that A inheres in B and B in C;

the other is negative and one of its premisses asserts one term of another,

while the other denies one term ofanother. It is clear, then, that theseare the fundamentals and so-calledhypotheses of syllogism. Assume them asthey have been stated, and proof is

bound to follow-proof that A inheres inC through B, and again that A inheresin B through some other middle term,and similarly that B inheres in C. Ifour reasoning aims at gaining credenceand so is merely dialectical, it isobvious that we have only to see thatour inference is based on premisses as

credible as possible: so that if a middle term between A and B is credible

though not real, one can reason throughit and complete a dialecticalsyllogism. If, however, one is aiming



at truth, one must be guided by thereal connexions of subjects andattributes. Thus: since there areattributes which are predicated of asubject essentially or naturally andnot coincidentally-not, that is, in thesense in which we say ‘That white(thing) is a man’, which is not thesame mode of predication as when we say‘The man is white’: the man is whitenot because he is something else but

because he is man, but the white is man because ‘being white’ coincides with

‘humanity’ within one substratum-therefore there are terms such as arenaturally subjects of predicates.Suppose, then, C such a term not itselfattributable to anything else as to asubject, but the proximate subject ofthe attribute B—i.e. so that B-C isimmediate; suppose further E relatedimmediately to F, and F to B. The firstquestion is, must this seriesterminate, or can it proceed toinfinity? The second question is asfollows: Suppose nothing is essentially

predicated of A, but A is predicated primarily of H and of no intermediate prior term, and suppose H similarly

related to G and G to B; then must thisseries also terminate, or can it too



proceed to infinity? There is this muchdifference between the questions: thefirst is, is it possible to start fromthat which is not itself attributableto anything else but is the subject ofattributes, and ascend to infinity? Thesecond is the problem whether one canstart from that which is a predicate

but not itself a subject of predicates,and descend to infinity? A thirdquestion is, if the extreme terms are

fixed, can there be an infinity of middles? I mean this: suppose for

example that A inheres in C and B isintermediate between them, but betweenB and A there are other middles, and

between these again fresh middles; canthese proceed to infinity or can theynot? This is the equivalent ofinquiring, do demonstrations proceed toinfinity, i.e. is everythingdemonstrable? Or do ultimate subjectand primary attribute limit oneanother?

I hold that the same questions arise

with regard to negative conclusions and premisses: viz. if A is attributable to

no B, then either this predication will be primary, or there will be an

intermediate term prior to B to which a



is not attributable-G, let us say,which is attributable to all B-andthere may still be another term H priorto G, which is attributable to all G.The same questions arise, I say,

because in these cases too either theseries of prior terms to which a is notattributable is infinite or itterminates.

One cannot ask the same questions in

the case of reciprocating terms, sincewhen subject and predicate areconvertible there is neither primarynor ultimate subject, seeing that allthe reciprocals qua subjects stand inthe same relation to one another,whether we say that the subject has aninfinity of attributes or that bothsubjects and attributes-and we raisedthe question in both cases-are infinitein number. These questions then cannot

be asked-unless, indeed, the terms canreciprocate by two different modes, byaccidental predication in one relationand natural predication in the other.



20

Now, it is clear that if the predications terminate in both the

upward and the downward direction (by‘upward’ I mean the ascent to the moreuniversal, by ‘downward’ the descent tothe more particular), the middle termscannot be infinite in number. Forsuppose that A is predicated of F, andthat the intermediates-call them

BB’B”...-are infinite, then clearly you might descend from and find one term predicated of another ad infinitum,

since you have an 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 processes are impossible therecannot be an infinity of intermediates

between A and F. Nor is it of anyeffect to urge that some terms of theseries AB...F are contiguous so as toexclude intermediates, while otherscannot be taken into the argument atall: whichever terms of the series

B...I take, the number of intermediatesin the direction either of A or of F

must be finite or infinite: where theinfinite series starts, whether fromthe first term or from a later one, is



of no moment, for the succeeding termsin any case are infinite in number.

21

Further, if in affirmativedemonstration the series terminates in

both directions, clearly it willterminate too in negativedemonstration. Let us assume that we

cannot proceed to infinity either byascending from the ultimate term (by‘ultimate term’ I mean a term such aswas, not itself attributable to asubject but itself the subject ofattributes), or by descending towardsan ultimate from the primary term (by‘primary term’ I mean a term predicableof a subject but not itself a subject).If this assumption is justified, theseries will also terminate in the caseof negation. For a negative conclusioncan be proved in all three figures. Inthe first figure it is proved thus: noB is A, all C is B. In packing the

interval B-C we must reach immediate propositions—as is always the case with

the minor premiss—since B-C isaffirmative. As regards the other

premiss it is plain that if the major



term is denied of a term D prior to 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 andthere will be a subject of which A is

primarily non-predicable. In the secondfigure the syllogism is, all A is B, noC is B,..no C is A. If proof of this is

required, plainly it may be showneither in the first figure as above, inthe second as here, or in the third.The first figure has been discussed,and we will proceed to display thesecond, proof by which will be asfollows: all B is D, no C is D...,since it is required that B should be asubject of which a predicate isaffirmed. Next, since D is to be provednot to belong to C, then D has afurther predicate which is denied of C.Therefore, since the succession of

predicates affirmed of an ever higheruniversal terminates, the succession of

predicates denied 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 figuresdiscussed above. In the first andsecond figures the series terminates.If we use the third figure, we shalltake as premisses, all E is B, some Eis not C, and this premiss again will

be proved by a similar prosyllogism.But since it is assumed that the seriesof descending subjects also terminates,

plainly the series of more universal

non-predicables will terminate also.Even supposing that the proof is notconfined to one method, but employsthem all and is now in the firstfigure, now in the second or third-evenso the regress will terminate, for the

methods are finite in number, and iffinite things are combined in a finitenumber of ways, the result must befinite.

Thus it is plain that the regress of middles terminates in the case of

negative demonstration, if it does soalso in the case of affirmative

demonstration. That in fact the regressterminates in both these cases may be

made clear by the following dialecticalconsiderations.



22

In the case of predicates constitutingthe essential nature of a thing, itclearly terminates, seeing that ifdefinition is possible, or in otherwords, if essential form is knowable,and an infinite series cannot betraversed, predicates constituting athing’s essential nature must be finite

in number. But as regards predicatesgenerally we have the following

prefatory remarks to make. (1) We canaffirm without falsehood ‘the white(thing) is walking’, and that big(thing) is a log’; or again, ‘the logis big’, and ‘the man walks’. But theaffirmation differs in the two cases.

When I affirm ‘the white is a log’, I mean that something which happens to be

white is a log-not that white is thesubstratum in which log inheres, for itwas not qua white or qua a species ofwhite that the white (thing) came to bea log, and the white (thing) is

consequently not a log exceptincidentally. On the other hand, when Iaffirm ‘the log is white’, I do not

mean that something else, which happensalso to be a log, is white (as I should



if I said ‘the musician is white,’which would mean ‘the man who happensalso to be a musician is white’); onthe contrary, log is here thesubstratum-the substratum whichactually came to be white, and did soqua wood or qua a species of wood andqua nothing else.

If we must lay down a rule, let usentitle the latter kind of statement

predication, and the former not predication at all, or not strict but

accidental predication. ‘White’ and‘log’ will thus serve as typesrespectively of predicate and subject.

We shall assume, then, that the predicate is invariably predicated

strictly and not accidentally of thesubject, for on such predicationdemonstrations depend for their force.It follows from this that when a singleattribute is predicated of a singlesubject, the predicate must affirm ofthe subject either some element

constituting its essential nature, orthat it is in some way qualified,quantified, essentially related,active, passive, placed, or dated.



(2) Predicates which signify substancesignify that the subject is identicalwith the predicate or with a species ofthe predicate. Predicates notsignifying substance which are

predicated of a subject not identicalwith themselves or with a species ofthemselves are accidental orcoincidental; e.g. white is acoincident of man, seeing that man isnot identical with white or a species

of white, but rather with animal, since man is identical with a species of

animal. These predicates which do notsignify substance must be predicates ofsome other subject, and nothing can bewhite which is not also other thanwhite. The Forms we can dispense with,for they are mere sound without sense;and even if there are such things, theyare not relevant to our discussion,since demonstrations are concerned with

predicates such as we have defined.

(3) If A is a quality of B, B cannot bea quality of A-a quality of a quality.

Therefore A and B cannot be predicatedreciprocally of one another in strict

predication: they can be affirmedwithout falsehood of one another, butnot genuinely predicated of each other.



For one alternative is that they should be substantially predicated of one

another, i.e. B would become the genusor differentia of A-the predicate now

become subject. But it has been shownthat in these substantial predicationsneither the ascending predicates northe descending subjects form aninfinite series; e.g. neither theseries, man is biped, biped is animal,&c., nor the series predicating animal

of man, man of Callias, Callias of afurther. subject as an element of itsessential nature, is infinite. For allsuch substance is definable, and aninfinite series cannot be traversed inthought: consequently neither theascent nor the descent is infinite,since a substance whose predicates wereinfinite would not be definable. Hencethey will not be predicated each as thegenus of the other; for this wouldequate a genus with one of its ownspecies. Nor (the other alternative)can a quale be reciprocally predicatedof a quale, nor any term belonging to

an adjectival category of another suchterm, except by accidental predication;for all such predicates are coincidentsand are predicated of substances. Onthe other hand-in proof of the



impossibility of an infinite ascendingseries-every predication displays thesubject as somehow qualified orquantified or as characterized underone of the other adjectival categories,or else is an element in itssubstantial nature: these latter arelimited in number, and the number ofthe widest kinds under which

predications fall is also limited, forevery predication must exhibit its

subject as somehow qualified,quantified, essentially related, actingor suffering, or in some place or atsome time.

I assume first that predication impliesa single subject and a singleattribute, and secondly that predicateswhich are not substantial are not

predicated of one another. We assumethis because such predicates are allcoincidents, and though some areessential coincidents, others of adifferent type, yet we maintain thatall of them alike are predicated of

some substratum and that a coincidentis never a substratum-since we do notclass as a coincident anything whichdoes not owe its designation to its

being something other than itself, but



always hold that any coincident is predicated of some substratum other

than itself, and that another group ofcoincidents may have a differentsubstratum. Subject to theseassumptions then, neither the ascendingnor the descending series of

predication in which a single attributeis predicated of a single subject isinfinite. For the subjects of whichcoincidents are predicated are as many

as the constitutive elements of eachindividual substance, and these we haveseen are not infinite in number, whilein the ascending series are containedthose constitutive elements with theircoincidents-both of which are finite.

We conclude that there is a givensubject (D) of which some attribute (C)is primarily predicable; that there

must be an attribute (B) primarily predicable of the first attribute, and

that the series must end with a term(A) not predicable of any term prior tothe last subject of which it was

predicated (B), and of which no term

prior to it is predicable.

The argument we have given is one ofthe so-called proofs; an alternative

proof follows. Predicates so related to



their subjects that there are other predicates prior to them predicable of

those subjects are demonstrable; but ofdemonstrable propositions one cannothave something better than knowledge,nor can one know them withoutdemonstration. Secondly, if aconsequent is only known through anantecedent (viz. premisses prior to it)and we neither know this antecedent norhave something better than knowledge of

it, then we shall not have scientificknowledge of the consequent. Therefore,if it is possible through demonstrationto know anything without qualificationand not merely as dependent on theacceptance of certain premisses-i.e.hypothetically-the series ofintermediate predications mustterminate. If it does not terminate,and beyond any predicate taken ashigher than another there remainsanother still higher, then every

predicate is demonstrable.Consequently, since these demonstrable

predicates are infinite in number and

therefore cannot be traversed, we shallnot know them by demonstration. If,therefore, we have not something betterthan knowledge of them, we cannotthrough demonstration have unqualified



but only hypothetical science ofanything.

As dialectical proofs of our contentionthese may carry conviction, but ananalytic process will show more brieflythat neither the ascent nor the descentof predication can be infinite in thedemonstrative sciences which are theobject of our investigation.Demonstration proves the inherence of

essential attributes in things. Nowattributes may be essential for tworeasons: either because they areelements in the essential nature oftheir subjects, or because theirsubjects are elements in theiressential nature. An example of thelatter is odd as an attribute ofnumber-though it is number’s attribute,yet number itself is an element in thedefinition of odd; of the former,

multiplicity or the indivisible, whichare elements in the definition ofnumber. In neither kind of attributioncan the terms be infinite. They are not

infinite where each is related to theterm below it as odd is to number, forthis would mean the inherence in odd ofanother attribute of odd in whosenature odd was an essential element:



but then number will be an ultimatesubject of the whole infinite chain ofattributes, and be an element in thedefinition of each of them. Hence,since an infinity of attributes such ascontain their subject in theirdefinition cannot inhere in a singlething, the ascending series is equallyfinite. Note, moreover, that all suchattributes must so inhere in theultimate subject-e.g. its attributes in

number and number in them-as to becommensurate with the subject and notof wider extent. Attributes which areessential elements in the nature oftheir subjects are equally finite:otherwise definition would beimpossible. Hence, if all theattributes predicated are essential andthese cannot be infinite, the ascendingseries will terminate, and consequentlythe descending series too.

If this is so, it follows that theintermediates between any two terms arealso always limited in number. An

immediately obvious consequence of thisis that demonstrations necessarilyinvolve basic truths, and that thecontention of some-referred to at theoutset-that all truths are demonstrable



is mistaken. For if there are basictruths, (a) not all truths aredemonstrable, and (b) an infiniteregress is impossible; since if either(a) or (b) were not a fact, it would

mean that no interval was immediate andindivisible, but that all intervalswere divisible. This is true because aconclusion is demonstrated by theinterposition, not the apposition, of afresh term. If such interposition could

continue to infinity there might be aninfinite number of terms between anytwo terms; but this is impossible if

both the ascending and descendingseries of predication terminate; and ofthis fact, which before was showndialectically, analytic proof has now

been given.

23

It is an evident corollary of theseconclusions that if the same attribute

A inheres in two terms C and D

predicable either not at all, or not ofall instances, of one another, it doesnot always belong to them in virtue ofa common middle term. Isosceles andscalene possess the attribute of having



their angles equal to two right anglesin virtue of a common middle; for they

possess it in so far as they are both acertain kind of figure, and not in sofar as they differ from one another.But this is not always the case: for,were it so, if we take B as the common

middle in virtue of which A inheres inC and D, clearly B would inhere in Cand D through a second common middle,and this in turn would inhere in C and

D through a third, so that between twoterms an infinity of intermediateswould fall-an impossibility. Thus itneed not always be in virtue of acommon middle term that a singleattribute inheres in several subjects,since there must be immediateintervals. Yet if the attribute to be

proved common to two subjects is to beone of their essential attributes, the

middle terms involved must be withinone subject genus and be derived fromthe same group of immediate premisses;for we have seen that processes of

proof cannot pass from one genus to

another.

It is also clear that when A inheres inB, this can be demonstrated if there isa middle term. Further, the ‘elements’



of such a conclusion are the premissescontaining the middle in question, andthey are identical in number with the

middle terms, seeing that the immediate propositions-or at least such immediate propositions as are universal-are the

‘elements’. If, on the other hand,there is no middle term, demonstrationceases to be possible: we are on theway to the basic truths. Similarly if Adoes not inhere in B, this can be

demonstrated if there is a middle termor a term prior to B in which A doesnot inhere: otherwise there is nodemonstration and a basic truth isreached. There are, moreover, as many‘elements’ of the demonstratedconclusion as there are middle terms,since it is propositions containingthese middle terms that are the basic

premisses on which the demonstrationrests; and as there are someindemonstrable basic truths assertingthat ‘this is that’ or that ‘thisinheres in that’, so there are othersdenying that ‘this is that’ or that

‘this inheres in that’-in fact some basic truths will affirm and some will

deny being.



When we are to prove a conclusion, we must take a primary essential predicate-suppose it C-of the subject

B, and then suppose A similarly predicable of C. If we proceed in this manner, no proposition or attribute

which falls beyond A is admitted in the proof: the interval is constantly

condensed until subject and predicate become indivisible, i.e. one. We have

our unit when the premiss becomes

immediate, since the immediate premissalone is a single premiss in theunqualified sense of ‘single’. And asin other spheres the basic element issimple but not identical in all-in asystem of weight it is the mina, in

music the quarter-tone, and so on—so insyllogism the unit is an immediate

premiss, and in the knowledge thatdemonstration gives it is an intuition.In syllogisms, then, which prove theinherence of an attribute, nothingfalls outside the major term. In thecase of negative syllogisms on theother hand,

in the first figure nothing fallsoutside the major term whose inherenceis in question; e.g. to prove through a

middle C that A does not inhere in B



the premisses required are, all B is C,no C is A. Then if it has to be provedthat no C is A, a middle must be found

between and C; and this procedure willnever vary.

If we have to show that E is not D by means of the premisses, all D is C; no

E, or not all E, is C; then the middlewill never fall beyond E, and E is thesubject of which D is to be denied in

the conclusion.

In the third figure the middle willnever fall beyond the limits of thesubject and the attribute denied of it.

24

Since demonstrations may be eithercommensurately universal or particular,and either affirmative or negative; thequestion arises, which form is the

better? And the same question may be put in regard to so-called ‘direct’

demonstration and reductio adimpossibile. Let us first examine thecommensurately universal and the



particular forms, and when we havecleared up this problem proceed todiscuss ‘direct’ demonstration andreductio ad impossibile.

The following considerations might leadsome minds to prefer particulardemonstration.

(1) The superior demonstration is thedemonstration which gives us greater

knowledge (for this is the ideal ofdemonstration), and we have greaterknowledge of a particular individualwhen we know it in itself than when weknow it through something else; e.g. weknow Coriscus the musician better whenwe know that Coriscus is musical thanwhen we know only that man is musical,and a like argument holds in all othercases. But commensurately universaldemonstration, instead of proving thatthe subject itself actually is x,

proves only that something else is x— e.g. in attempting to prove thatisosceles is x, it proves not that

isosceles but only that triangle is x— whereas particular demonstration provesthat the subject itself is x. Thedemonstration, then, that a subject, assuch, possesses an attribute is



superior. If this is so, and if the particular rather than the

commensurately universal formsdemonstrates, particular demonstrationis superior.

(2) The universal has not a separate being over against groups of singulars.

Demonstration nevertheless creates theopinion that its function isconditioned by something like this-some

separate entity belonging to the realworld; that, for instance, of triangleor of figure or number, over against

particular triangles, figures, andnumbers. But demonstration whichtouches the real and will not misleadis superior to that which moves amongunrealities and is delusory. Nowcommensurately universal demonstrationis of the latter kind: if we engage init we find ourselves reasoning after afashion well illustrated by theargument that the proportionate is whatanswers to the definition of someentity which is neither line, number,

solid, nor plane, but a proportionateapart from all these. Since, then, sucha proof is characteristicallycommensurate and universal, and lesstouches reality than does particular



demonstration, and creates a falseopinion, it will follow thatcommensurate and universal is inferiorto particular demonstration.

We may retort thus.

(1) The first argument applies no moreto commensurate and universal than to

particular demonstration. If equalityto two right angles is attributable to

its subject not qua isosceles but quatriangle, he who knows that isosceles

possesses that attribute knows thesubject as qua itself possessing theattribute, to a less degree than he whoknows that triangle has that attribute.To sum up the whole matter: if asubject is proved to possess quatriangle an attribute which it does notin fact possess qua triangle, that isnot demonstration: but if it does

possess it qua triangle the ruleapplies that the greater knowledge ishis who knows the subject as possessingits attribute qua that in virtue of

which it actually does possess it.Since, then, triangle is the widerterm, and there is one identicaldefinition of triangle-i.e. the term isnot equivocal-and since equality to two



right angles belongs to all triangles,it is isosceles qua triangle and nottriangle qua isosceles which has itsangles so related. It follows that hewho knows a connexion universally hasgreater knowledge of it as it in factis than he who knows the particular;and the inference is that commensurateand universal is superior to particulardemonstration.

(2) If there is a single identicaldefinition i.e. if the commensurateuniversal is unequivocal-then theuniversal will possess being not less

but more than some of the particulars,inasmuch as it is universals whichcomprise the imperishable, particularsthat tend to perish.

(3) Because the universal has a single meaning, we are not therefore compelled

to suppose that in these examples ithas being as a substance apart from its

particulars-any more than we need makea similar supposition in the other

cases of unequivocal universal predication, viz. where the predicate

signifies not substance but quality,essential relatedness, or action. Ifsuch a supposition is entertained, the



blame rests not with the demonstration but with the hearer.

(4) Demonstration is syllogism that proves the cause, i.e. the reasoned

fact, and it is rather the commensurateuniversal than the particular which iscausative (as may be shown thus: thatwhich possesses an attribute throughits own essential nature is itself thecause of the inherence, and the

commensurate universal is primary;hence the commensurate universal is thecause). Consequently commensuratelyuniversal demonstration is superior as

more especially proving the cause, thatis the reasoned fact.

(5) Our search for the reason ceases,and we think that we know, when thecoming to be or existence of the fact

before us is not due to the coming to be or existence of some other fact, for

the last step of a search thusconducted is eo ipso the end and limitof the problem. Thus: ‘Why did he

come?’ ‘To get the money-wherewith to pay a debt-that he might thereby do

what was right.’ When in this regresswe can no longer find an efficient orfinal cause, we regard the last step of



it as the end of the coming-or being orcoming to be-and we regard ourselves asthen only having full knowledge of thereason why he came.

If, then, all causes and reasons arealike in this respect, and if this isthe means to full knowledge in the caseof final causes such as we haveexemplified, it follows that in thecase of the other causes also full

knowledge is attained when an attributeno longer inheres because of somethingelse. Thus, when we learn that exteriorangles are equal to four right angles

because they are the exterior angles ofan isosceles, there still remains thequestion ‘Why has isosceles thisattribute?’ and its answer ‘Because itis a triangle, and a triangle has it

because a triangle is a rectilinearfigure.’ If rectilinear figure

possesses the property for no furtherreason, at this point we have fullknowledge-but at this point ourknowledge has become commensurately

universal, and so we conclude thatcommensurately universal demonstrationis superior.



(6) The more demonstration becomes particular the more it sinks into an

indeterminate manifold, while universaldemonstration tends to the simple anddeterminate. But objects so far as theyare an indeterminate manifold areunintelligible, so far as they aredeterminate, intelligible: they aretherefore intelligible rather in so faras they are universal than in so far asthey are particular. From this it

follows that universals are moredemonstrable: but since relative andcorrelative increase concomitantly, ofthe more demonstrable there will befuller demonstration. Hence thecommensurate and universal form, being

more truly demonstration, is thesuperior.

(7) Demonstration which teaches twothings is preferable to demonstrationwhich teaches only one. He who

possesses commensurately universaldemonstration knows the particular aswell, but he who possesses particular

demonstration does not know theuniversal. So that this is anadditional reason for preferringcommensurately universal demonstration.

And there is yet this further argument:



(8) Proof becomes more and more proofof the commensurate universal as its

middle term approaches nearer to the basic truth, and nothing is so near as

the immediate premiss which is itselfthe basic truth. If, then, proof fromthe basic truth is more accurate than

proof not so derived, demonstrationwhich depends more closely on it is

more accurate than demonstration which

is less closely dependent. Butcommensurately universal demonstrationis characterized by this closerdependence, and is therefore superior.Thus, if A had to be proved to inherein D, and the middles were B and C, B

being the higher term would render thedemonstration which it mediated the

more universal.

Some of these arguments, however, aredialectical. The clearest indication ofthe precedence of commensuratelyuniversal demonstration is as follows:if of two propositions, a prior and a

posterior, we have a grasp of the prior, we have a kind of knowledge-a potential grasp-of the posterior as

well. For example, if one knows thatthe angles of all triangles are equal



to two right angles, one knows in asense-potentially-that the isosceles’angles also are equal to two rightangles, even if one does not know thatthe isosceles is a triangle; but tograsp this posterior proposition is byno means to know the commensurateuniversal either potentially oractually. Moreover, commensuratelyuniversal demonstration is through andthrough intelligible; particular

demonstration issues in sense- perception.

25

The preceding arguments constitute ourdefence of the superiority ofcommensurately universal to particulardemonstration. That affirmativedemonstration excels negative may beshown as follows.

(1) We may assume the superiorityceteris paribus of the demonstrationwhich derives from fewer postulates orhypotheses-in short from fewer



premisses; for, given that all theseare equally well known, where they arefewer knowledge will be more speedilyacquired, and that is a desideratum.The argument implied in our contentionthat demonstration from fewerassumptions is superior may be set outin universal form as follows. Assumingthat in both cases alike the middleterms are known, and that middles whichare prior are better known than such as

are posterior, we may suppose twodemonstrations of the inherence of A inE, the one proving it through the

middles B, C and D, the other through Fand G. Then A-D is known to the samedegree as A-E (in the second proof),

but A-D is better known than and priorto A-E (in the first proof); since A-Eis proved through A-D, and the groundis more certain than the conclusion.

Hence demonstration by fewer premissesis ceteris paribus superior. Now bothaffirmative and negative demonstrationoperate through three terms and two

premisses, but whereas the formerassumes only that something is, thelatter assumes both that something isand that something else is not, and



thus operating through more kinds of premiss is inferior.

(2) It has been proved that noconclusion follows if both premissesare negative, but that one must benegative, the other affirmative. So weare compelled to lay down the followingadditional rule: as the demonstrationexpands, the affirmative premisses mustincrease in number, but there cannot be

more than one negative premiss in eachcomplete proof. Thus, suppose no B is

A, and all C is B. Then if both the premisses are to be again expanded, a middle must be interposed. Let us

interpose D between A and B, and E between B and C. Then clearly E is

affirmatively related to B and C, whileD is affirmatively related to B butnegatively to A; for all B is D, butthere must be no D which is A. Thusthere proves to be a single negative

premiss, A-D. In the further prosyllogisms too it is the same, because in the terms of an affirmative

syllogism the middle is always relatedaffirmatively to both extremes; in anegative syllogism it must benegatively related only to one of them,and so this negation comes to be a



single negative premiss, the other premisses being affirmative. If, then,

that through which a truth is proved isa better known and more certain truth,and if the negative proposition is

proved through the affirmative and notvice versa, affirmative demonstration,

being prior and better known and morecertain, will be superior.

(3) The basic truth of demonstrative

syllogism is the universal immediate premiss, and the universal premiss

asserts in affirmative demonstrationand in negative denies: and theaffirmative proposition is prior to and

better known than the negative (sinceaffirmation explains denial and is

prior to denial, just as being is priorto not-being). It follows that the

basic premiss of affirmativedemonstration is superior to that ofnegative demonstration, and thedemonstration which uses superior basic

premisses is superior.

(4) Affirmative demonstration is moreof the nature of a basic form of proof,

because it is a sine qua non ofnegative demonstration.



26

Since affirmative demonstration issuperior to negative, it is clearlysuperior also to reductio adimpossibile. We must first make certainwhat is the difference between negativedemonstration and reductio adimpossibile. Let us suppose that no Bis A, and that all C is B: the

conclusion necessarily follows that noC is A. If these premisses are assumed,therefore, the negative demonstrationthat no C is A is direct. Reductio adimpossibile, on the other hand,

proceeds as follows. Supposing we areto prove that does not inhere in B, wehave to assume that it does inhere, andfurther that B inheres in C, with theresulting inference that A inheres inC. This we have to suppose a known andadmitted impossibility; and we theninfer that A cannot inhere in B. Thusif the inherence of B in C is notquestioned, A’s inherence in B is

impossible.

The order of the terms is the same in both proofs: they differ according to

which of the negative propositions is



the better known, the one denying A ofB or the one denying A of C. When thefalsity of the conclusion is the betterknown, we use reductio ad impossible;when the major premiss of the syllogismis the more obvious, we use directdemonstration. All the same the

proposition denying A of B is, in theorder of being, prior to that denying Aof C; for premisses are prior to theconclusion which follows from them, and

‘no C is A’ is the conclusion, ‘no B is A’ one of its premisses. For the

destructive result of reductio adimpossibile is not a proper conclusion,nor are its antecedents proper

premisses. On the contrary: theconstituents of syllogism are premissesrelated to one another as whole to partor part to whole, whereas the premisses

A-C and A-B are not thus related to oneanother. Now the superior demonstrationis that which proceeds from betterknown and prior premisses, and while

both these forms depend for credence onthe not-being of something, yet the

source of the one is prior to that ofthe other. Therefore negativedemonstration will have an unqualifiedsuperiority to reductio ad impossibile,and affirmative demonstration, being



superior to negative, will consequently be superior also to reductio ad

impossibile.

27

The science which is knowledge at onceof the fact and of the reasoned fact,not of the fact by itself without thereasoned fact, is the more exact and

the prior science.

A science such as arithmetic, which isnot a science of properties quainhering in a substratum, is more exactthan and prior to a science likeharmonics, which is a science of

pr,operties inhering in a substratum;and similarly a science likearithmetic, which is constituted offewer basic elements, is more exactthan and prior to geometry, whichrequires additional elements. What I

mean by ‘additional elements’ is this:a unit is substance without position,

while a point is substance with position; the latter contains an

additional element.



28

A single science is one whose domain isa single genus, viz. all the subjectsconstituted out of the primary entitiesof the genus-i.e. the parts of thistotal subject-and their essential

properties.

One science differs from another when

their basic truths have neither acommon source nor are derived those ofthe one science from those the other.This is verified when we reach theindemonstrable premisses of a science,for they must be within one genus withits conclusions: and this again isverified if the conclusions proved by

means of them fall within one genus-i.e. are homogeneous.

29

One can have several demonstrations of

the same connexion not only by takingfrom the same series of predication

middles which are other than theimmediately cohering term e.g. bytaking C, D, and F severally to prove



A-B—but also by taking a middle fromanother 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 thatwhich alters a property changes. Again,we can predicate A of G withoutfalsehood, and G of B; for to feel

pleasure is to relax, and to relax is

to change. So the conclusion can bedrawn through middles which aredifferent, i.e. not in the same series-yet not so that neither of these

middles is predicable of the other, forthey must both be attributable to someone subject.

A further point worth investigating ishow many ways of proving the sameconclusion can be obtained by varyingthe figure,

30

There is no knowledge by demonstrationof chance conjunctions; for chanceconjunctions exist neither by necessitynor as general connexions but comprise



what comes to be as something distinctfrom these. Now demonstration isconcerned only with one or other ofthese two; for all reasoning proceedsfrom necessary or general premisses,the conclusion being necessary if the

premisses are necessary and general ifthe premisses are general.Consequently, if chance conjunctionsare neither general nor necessary, theyare not demonstrable.

31

Scientific knowledge is not possiblethrough the act of perception. Even if

perception as a faculty is of ‘thesuch’ and not merely of a ‘thissomewhat’, yet one must at any rateactually perceive a ‘this somewhat’,and at a definite present place andtime: but that which is commensuratelyuniversal and true in all cases onecannot perceive, since it is not ‘this’and it is not ‘now’; if it were, it

would not be commensurately universal-the term we apply to what is always andeverywhere. Seeing, therefore, thatdemonstrations are commensuratelyuniversal and universals imperceptible,



we clearly cannot obtain scientificknowledge by the act of perception:nay, it is obvious that even if it were

possible to perceive that a trianglehas its angles equal to two rightangles, we should still be looking fora demonstration-we should not (as somesay) possess knowledge of it; for

perception must be of a particular,whereas scientific knowledge involvesthe recognition of the commensurate

universal. So if we were on the moon,and saw the earth shutting out thesun’s light, we should not know thecause of the eclipse: we should

perceive the present fact of theeclipse, but not the reasoned fact atall, since the act of perception is notof the commensurate universal. I donot, of course, deny that by watchingthe frequent recurrence of this eventwe might, after tracking thecommensurate universal, possess ademonstration, for the commensurateuniversal is elicited from the severalgroups of singulars.

The commensurate universal is precious because it makes clear the cause; so

that in the case of facts like thesewhich have a cause other than



themselves universal knowledge is more precious than sense-perceptions and

than intuition. (As regards primarytruths there is of course a differentaccount to be given.) Hence it is clearthat knowledge of things demonstrablecannot be acquired by perception,unless the term perception is appliedto the possession of scientificknowledge through demonstration.

Nevertheless certain points do arise

with regard to connexions to be provedwhich are referred for theirexplanation to a failure in sense-

perception: there are cases when an actof vision would terminate our inquiry,not because in seeing we should beknowing, but because we should haveelicited the universal from seeing; if,for example, we saw the pores in theglass and the light passing through,the reason of the kindling would beclear to us because we should at thesame time see it in each instance andintuit that it must be so in allinstances.



32

All syllogisms cannot have the same basic truths. This may be shown first

of all by the following dialecticalconsiderations. (1) Some syllogisms aretrue and some false: for though a trueinference is possible from false

premisses, yet this occurs once only-I mean if A for instance, is truly predicable of C, but B, the middle, is

false, both A-B and B-C being false;nevertheless, if middles are taken to

prove these premisses, they will befalse because every conclusion which isa falsehood has false premisses, whiletrue conclusions have true premisses,and false and true differ in kind. Thenagain, (2) falsehoods are not allderived from a single identical set of

principles: there are falsehoods whichare the contraries of one another andcannot coexist, e.g. ‘justice isinjustice’, and ‘justice is cowardice’;‘man is horse’, and ‘man is ox’; ‘theequal is greater’, and ‘the equal is

less.’ From established principles we may argue the case as follows,

confining-ourselves therefore to trueconclusions. Not even all these areinferred from the same basic truths;



many of them in fact have basic truthswhich differ generically and are nottransferable; units, for instance,which are without position, cannot takethe place of points, which have

position. The transferred terms couldonly fit in as middle terms or as majoror minor terms, or else have some ofthe other terms between them, othersoutside them.

Nor can any of the common axioms-such,I mean, as the law of excluded middle-serve as premisses for the proof of allconclusions. For the kinds of being aredifferent, and some attributes attachto quanta and some to qualia only; and

proof is achieved by means of thecommon axioms taken in conjunction withthese several kinds and theirattributes.

Again, it is not true that the basictruths are much fewer than theconclusions, for the basic truths arethe premisses, and the premisses are

formed by the apposition of a freshextreme term or the interposition of afresh middle. Moreover, the number ofconclusions is indefinite, though thenumber of middle terms is finite; and



lastly some of the basic truths arenecessary, others variable.

Looking at it in this way we see that,since the number of conclusions isindefinite, the basic truths cannot beidentical or limited in number. If, onthe other hand, identity is used inanother sense, and it is said, e.g.‘these and no other are the fundamentaltruths of geometry, these the

fundamentals of calculation, theseagain of medicine’; would the statement

mean anything except that the scienceshave basic truths? To call themidentical because they are self-identical is absurd, since everythingcan be identified with everything inthat sense of identity. Nor again canthe contention that all conclusionshave the same basic truths mean thatfrom the mass of all possible premissesany conclusion may be drawn. That would

be exceedingly naive, for it is not thecase in the clearly evident

mathematical sciences, nor is it

possible in analysis, since it is theimmediate premisses which are the basictruths, and a fresh conclusion is onlyformed by the addition of a newimmediate premiss: but if it be



admitted that it is these primaryimmediate premisses which are basictruths, each subject-genus will provideone basic truth. If, however, it is notargued that from the mass of all

possible premisses any conclusion may be proved, nor yet admitted that basic

truths differ so as to be genericallydifferent for each science, it remainsto consider the possibility that, whilethe basic truths of all knowledge are

within one genus, special premisses arerequired to prove special conclusions.But that this cannot be the case has

been shown by our proof that the basictruths of things generically differentthemselves differ generically. Forfundamental truths are of two kinds,those which are premisses ofdemonstration and the subject-genus;and though the former are common, thelatter-number, for instance, and

magnitude-are peculiar.

33

Scientific knowledge and its objectdiffer from opinion and the object ofopinion in that scientific knowledge iscommensurately universal and proceeds



by necessary connexions, and that whichis necessary cannot be otherwise. Sothough there are things which are trueand real and yet can be otherwise,scientific knowledge clearly does notconcern them: if it did, things whichcan be otherwise would be incapable of

being otherwise. Nor are they anyconcern of rational intuition-byrational intuition I mean anoriginative source of scientific

knowledge-nor of indemonstrableknowledge, which is the grasping of theimmediate premiss. Since then rationalintuition, science, and opinion, andwhat is revealed by these terms, arethe only things that can be ‘true’, itfollows that it is opinion that isconcerned with that which may be trueor false, and can be otherwise: opinionin fact is the grasp of a premiss whichis immediate but not necessary. Thisview also fits the observed facts, foropinion is unstable, and so is the kindof being we have described as itsobject. Besides, when a man thinks a

truth incapable of being otherwise healways thinks that he knows it, neverthat he opines it. He thinks that heopines when he thinks that a connexion,though actually so, may quite easily be



otherwise; for he believes that such isthe proper object of opinion, while thenecessary is the object of knowledge.

In what sense, then, can the same thing be the object of both opinion and

knowledge? And if any one chooses to maintain that all that he knows he can

also opine, why should not opinion beknowledge? For he that knows and hethat opines will follow the same train

of thought through the same middleterms until the immediate premisses arereached; because it is possible toopine not only the fact but also thereasoned fact, and the reason is the

middle term; so that, since the formerknows, he that opines also hasknowledge.

The truth perhaps is that if a mangrasp truths that cannot be other thanthey are, in the way in which he graspsthe definitions through whichdemonstrations take place, he will havenot opinion but knowledge: if on the

other hand he apprehends theseattributes as inhering in theirsubjects, but not in virtue of thesubjects’ substance and essentialnature possesses opinion and not



genuine knowledge; and his opinion, ifobtained through immediate premisses,will be both of the fact and of thereasoned fact; if not so obtained, ofthe fact alone. The object of opinionand knowledge is not quite identical;it is only in a sense identical, justas the object of true and false opinionis in a sense identical. The sense inwhich some maintain that true and falseopinion can have the same object leads

them to embrace many strange doctrines, particularly the doctrine that what a man opines falsely he does not opine at

all. There are really many senses of‘identical’, and in one sense theobject of true and false opinion can bethe same, in another it cannot. Thus,to have a true opinion that thediagonal is commensurate with the sidewould be absurd: but because thediagonal with which they are bothconcerned is the same, the two opinionshave objects so far the same: on theother hand, as regards their essentialdefinable nature these objects differ.

The identity of the objects ofknowledge and opinion is similar.Knowledge is the apprehension of, e.g.the attribute ‘animal’ as incapable of

being otherwise, opinion the



apprehension of ‘animal’ as capable of being otherwise-e.g. the apprehension

that animal is an element in theessential nature of man is knowledge;the apprehension of animal as

predicable of man but not as an elementin man’s essential nature is opinion:

man is the subject in both judgements, but the mode of inherence differs.

This also shows that one cannot opine

and know the same thing simultaneously;for then one would apprehend the samething as both capable and incapable of

being otherwise-an impossibility.Knowledge and opinion of the same thingcan co-exist in two different people inthe sense we have explained, but notsimultaneously in the same person. Thatwould involve a man’s simultaneouslyapprehending, e.g. (1) that man isessentially animal-i.e. cannot be otherthan animal-and (2) that man is notessentially animal, that is, we mayassume, may be other than animal.

Further consideration of modes ofthinking and their distribution underthe heads of discursive thought,intuition, science, art, practicalwisdom, and metaphysical thinking,



belongs rather partly to naturalscience, partly to moral philosophy.

34

Quick wit is a faculty of hitting uponthe middle term instantaneously. Itwould be exemplified by a man who sawthat the moon has her bright sidealways turned towards the sun, and

quickly grasped the cause of this,namely that she borrows her light fromhim; or observed somebody inconversation with a man of wealth anddivined that he was borrowing money, orthat the friendship of these peoplesprang from a common enmity. In allthese instances he has seen the majorand minor terms and then grasped thecauses, the middle terms.

Let A represent ‘bright side turnedsunward’, B ‘lighted from the sun’, Cthe moon. Then B, ‘lighted from thesun’ is predicable of C, the moon, and

A, ‘having her bright side towards thesource of her light’, is predicable ofB. So A is predicable of C through B.



Book II

1

THE kinds of question we ask are as many as the kinds of things which we

know. They are in fact four:-(1)whether the connexion of an attributewith a thing is a fact, (2) what is thereason of the connexion, (3) whether a

thing exists, (4) What is the nature ofthe thing. Thus, when our questionconcerns a complex of thing andattribute and we ask whether the thingis thus or otherwise qualified-whether,e.g. the sun suffers eclipse or not-then we are asking as to the fact of aconnexion. That our inquiry ceases withthe discovery that the sun does suffereclipse is an indication of this; andif we know from the start that the sunsuffers eclipse, we do not inquirewhether it does so or not. On the otherhand, when we know the fact we ask thereason; as, for example, when we know

that the sun is being eclipsed and thatan earthquake is in progress, it is thereason of eclipse or earthquake intowhich we inquire.



Where a complex is concerned, then,those are the two questions we ask; butfor some objects of inquiry we have adifferent kind of question to ask, suchas whether there is or is not a centauror a God. (By ‘is or is not’ I mean ‘isor is not, without furtherqualification’; as opposed to ‘is or isnot [e.g.] white’.) On the other hand,when we have ascertained the thing’sexistence, we inquire as to its nature,

asking, for instance, ‘what, then, isGod?’ or ‘what is man?’.

2

These, then, are the four kinds ofquestion we ask, and it is in theanswers to these questions that ourknowledge consists.

Now when we ask whether a connexion isa fact, or whether a thing without

qualification is, we are really askingwhether the connexion or the thing hasa ‘middle’; and when we haveascertained either that the connexionis a fact or that the thing is-i.e.



ascertained either the partial or theunqualified being of the thing-and are

proceeding to ask the reason of theconnexion or the nature of the thing,then we are asking what the ‘middle’is.

(By distinguishing the fact of theconnexion and the existence of thething as respectively the partial andthe unqualified being of the thing, I

mean that if we ask ‘does the moonsuffer eclipse?’, or ‘does the moonwax?’, the question concerns a part ofthe thing’s being; for what we areasking in such questions is whether athing is this or that, i.e. has or hasnot this or that attribute: whereas, ifwe ask whether the moon or nightexists, the question concerns theunqualified being of a thing.)

We conclude that in all our inquirieswe are asking either whether there is a‘middle’ or what the ‘middle’ is: forthe ‘middle’ here is precisely the

cause, and it is the cause that we seekin all our inquiries. Thus, ‘Does the

moon suffer eclipse?’ means ‘Is thereor is there not a cause producingeclipse of the moon?’, and when we have



learnt that there is, our next questionis, ‘What, then, is this cause? for thecause through which a thing is-not isthis or that, i.e. has this or thatattribute, but without qualificationis-and the cause through which it is-not is without qualification, but isthis or that as having some essentialattribute or some accident-are bothalike the middle’. By that which iswithout qualification I mean the

subject, e.g. moon or earth or sun ortriangle; by that which a subject is(in the partial sense) I mean a

property, e.g. eclipse, equality orinequality, interposition or non-interposition. For in all theseexamples it is clear that the nature ofthe thing and the reason of the factare identical: the question ‘What iseclipse?’ and its answer ‘The privationof the moon’s light by theinterposition of the earth’ areidentical with the question ‘What isthe reason of eclipse?’ or ‘Why doesthe moon suffer eclipse?’ and the reply

‘Because of the failure of lightthrough the earth’s shutting it out’.

Again, for ‘What is a concord? Acommensurate numerical ratio of a highand a low note’, we may substitute



‘What ratio makes a high and a low noteconcordant? Their relation according toa commensurate numerical ratio.’ ‘Arethe high and the low note concordant?’is equivalent to ‘Is their ratiocommensurate?’; and when we find thatit is commensurate, we ask ‘What, then,is their ratio?’.

Cases in which the ‘middle’ is sensibleshow that the object of our inquiry 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 shouldnot be inquiring either as to the factor the reason, but both fact and reasonwould be obvious simultaneously. Forthe act of perception would haveenabled 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 factof the earth’s screening the sun’slight, and from this would arise the

universal.

Thus, as we maintain, to know a thing’snature is to know the reason why 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 in sofar as they are said to be possessed ofsome attribute such as equal to rightangles, or greater or less.

3

It is clear, then, that all questionsare a search for a ‘middle’. Let us now

state how essential nature is revealedand in what way it can be reduced todemonstration; what definition is, andwhat things are definable. And let usfirst discuss certain difficultieswhich these questions raise, beginningwhat we have to say with a point mostintimately connected with ourimmediately preceding remarks, namelythe doubt that might be felt as towhether or not it is possible to knowthe same thing in the same relation,

both by definition and bydemonstration. It might, I mean, beurged that definition is held to

concern essential nature and is inevery case universal and affirmative;whereas, on the other hand, someconclusions are negative and some arenot universal; e.g. all in the second



figure are negative, none in the thirdare universal. And again, not even allaffirmative conclusions in the firstfigure are definable, e.g. ‘everytriangle has its angles equal to tworight angles’. An argument proving thisdifference between demonstration anddefinition is that to have scientificknowledge of the demonstrable isidentical with possessing ademonstration of it: hence if

demonstration of such conclusions asthese is possible, there clearly cannotalso be definition of them. If therecould, one might know such a conclusionalso in virtue of its definitionwithout possessing the demonstration ofit; for there is nothing to stop ourhaving the one without the other.

Induction too will sufficientlyconvince us of this difference; fornever yet by defining anything-essential attribute or accident-did weget knowledge of it. Again, if todefine is to acquire knowledge of a

substance, at any rate such attributesare not substances.

It is evident, then, that noteverything demonstrable can be defined.



What then? Can everything definable bedemonstrated, or not? There is one ofour previous arguments which coversthis too. Of a single thing qua singlethere is a single scientific knowledge.Hence, since to know the demonstrablescientifically is to possess thedemonstration of it, an impossibleconsequence will follow:-possession ofits definition without itsdemonstration will give knowledge of

the demonstrable.

Moreover, the basic premisses ofdemonstrations are definitions, and ithas already been shown that these will

be found indemonstrable; either the basic premisses will be demonstrable

and will depend on prior premisses, andthe regress will be endless; or the

primary truths will be indemonstrabledefinitions.

But if the definable and thedemonstrable are not wholly the same,

may they yet be partially the same? Or

is that impossible, because there can be no demonstration of the definable?

There can be none, because definitionis of the essential nature or being ofsomething, and all demonstrations



evidently posit and assume theessential nature-mathematicaldemonstrations, for example, the natureof unity and the odd, and all the othersciences likewise. Moreover, everydemonstration proves a predicate of asubject as attaching or as notattaching to it, but in definition onething is not predicated of another; wedo not, e.g. predicate animal of bipednor biped of animal, nor yet figure of

plane-plane not being figure nor figure plane. Again, to prove essential nature

is not the same as to prove the fact ofa connexion. Now definition revealsessential nature, demonstration revealsthat a given attribute attaches or doesnot attach to a given subject; butdifferent things require differentdemonstrations-unless the onedemonstration is related to the otheras part to whole. I add this because ifall triangles have been proved to

possess angles equal to two rightangles, then this attribute has been

proved to attach to isosceles; for

isosceles is a part of which alltriangles constitute the whole. But inthe case before us the fact and theessential nature are not so related to



one another, since the one is not a part of the other.

So it emerges that not all thedefinable is demonstrable nor all thedemonstrable definable; and we may drawthe general conclusion that there is noidentical object of which it is

possible to possess both a definitionand a demonstration. It followsobviously that definition and

demonstration are neither identical norcontained either within the other: ifthey were, their objects would berelated either as identical or as wholeand part.

4

So much, then, for the first stage ofour problem. The next step is to raisethe question whether syllogism-i.e.demonstration-of the definable natureis possible or, as our recent argumentassumed, impossible.

We might argue it impossible on thefollowing grounds:-(a) syllogism provesan attribute of a subject through the

middle term; on the other hand (b) itsdefinable nature is both ‘peculiar’ to



a subject and predicated of it as 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 Ais ‘peculiar’ to B and B to C-in factall three terms are ‘peculiar’ to oneanother: and further (2) if A inheresin the essence of all B and B is

predicated universally of all C as

belonging to C’s essence, A also must be predicated of C as belonging to its

essence.

If one does not take this relation asthus duplicated-if, that is, A is

predicated as being of the essence ofB, but B is not of the essence of thesubjects of which it is predicated-Awill not necessarily be predicated of Cas belonging to its essence. So both

premisses will predicate essence, andconsequently B also will be predicatedof C as its essence. Since, therefore,

both premisses do predicate essence-

i.e. definable form-C’s definable formwill appear in the middle term beforethe conclusion is drawn.



We may generalize by supposing that itis possible to prove the essentialnature of man. Let C be man, A man’sessential nature—two-footed animal, oraught else it may be. Then, if we areto syllogize, A must be predicated ofall B. But this premiss will be

mediated by a fresh definition, whichconsequently will also be the essentialnature of man. Therefore the argumentassumes what it has to prove, since B

too is the essential nature of man. Itis, however, the case in which thereare only the two premisses-i.e. inwhich the premisses are primary andimmediate-which we ought toinvestigate, because it bestillustrates the point under discussion.

Thus they who prove the essentialnature of soul or man or anything elsethrough reciprocating terms beg thequestion. It would be begging thequestion, for example, to contend thatthe 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 aself-moving number in the sense of

being identical with it. For if A is predicable as a mere consequent of B



and B of C, A will not on that account be the definable form of C: A will merely be what it was true to say of C.

Even if A is predicated of all Binasmuch as B is identical with aspecies of A, still it will not follow:

being an animal is predicated of beinga man-since it is true that in allinstances to be human is to be animal,just as it is also true that every manis an animal-but not as identical with

being man.

We conclude, then, that unless onetakes both the premisses as predicatingessence, one cannot infer that A is thedefinable form and essence of C: but ifone does so take them, in assuming Bone will have assumed, before drawingthe conclusion, what the definable formof C is; so that there has been noinference, for one has begged thequestion.

5

Nor, as was said in my formal logic, isthe method of division a process ofinference at all, since at no pointdoes the characterization of thesubject follow necessarily from the



premising of certain other facts:division demonstrates as little as doesinduction. For in a genuinedemonstration the conclusion must not

be put as a question nor depend on aconcession, but must follow necessarilyfrom its premisses, even if therespondent deny it. The definer asks‘Is man animal or inanimate?’ and thenassumes-he has not inferred-that man isanimal. Next, when presented with an

exhaustive division of animal intoterrestrial and aquatic, he assumesthat man is terrestrial. Moreover, that

man is the complete formula,terrestrial-animal, does not follownecessarily from the premisses: thistoo is an assumption, and equally anassumption whether the divisioncomprises many differentiae or few.(Indeed as this method of division isused by those who proceed by it, eventruths that can be inferred actuallyfail to appear as such.) For why shouldnot the whole of this formula be trueof man, and yet not exhibit his

essential nature or definable form? Again, what guarantee is there against

an unessential addition, or against theomission of the final or of an



intermediate determinant of thesubstantial being?

The champion of division might hereurge that though these lapses do occur,yet we can solve that difficulty if allthe attributes we assume areconstituents of the definable form, andif, postulating the genus, we produce

by division the requisite uninterruptedsequence of terms, and omit nothing;

and that indeed we cannot fail tofulfil these conditions if what is to

be divided falls whole into thedivision at each stage, and none of itis omitted; and that this-thedividendum-must without furtherquestion be (ultimately) incapable offresh specific division. Nevertheless,we reply, division does not involveinference; if it gives knowledge, itgives it in another way. Nor is thereany absurdity in this: induction,

perhaps, is not demonstration any morethan is division, et it does makeevident some truth. Yet to state a

definition reached by division is notto state a conclusion: as, whenconclusions are drawn without theirappropriate middles, the allegednecessity by which the inference



follows from the premisses is open to aquestion as to the reason for it, sodefinitions reached by division invitethe same question.

Thus to the question ‘What is theessential nature of man?’ the dividerreplies ‘Animal, mortal, footed, biped,wingless’; and when at each step he isasked ‘Why?’, he will say, and, as hethinks, proves by division, that all

animal is mortal or immortal: but sucha formula taken in its entirety is notdefinition; so that even if divisiondoes demonstrate its formula,definition at any rate does not turnout to be a conclusion of inference.

6

Can we nevertheless actuallydemonstrate what a thing essentiallyand substantially is, buthypothetically, i.e. by premising (1)that its definable form is constituted

by the ‘peculiar’ attributes of its

essential nature; (2) that such andsuch are the only attributes of itsessential nature, and that the completesynthesis of them is peculiar to thething; and thus-since in this synthesis



consists the being of the thing-obtaining our conclusion? Or is thetruth that, since proof must be throughthe middle term, the definable form isonce more assumed in this minor premisstoo?

Further, just as in syllogizing we donot premise what syllogistic inferenceis (since the premisses from which weconclude must be related as whole and

part), so the definable form must notfall within the syllogism but remainoutside the premisses posited. It isonly against a doubt as to its having

been a syllogistic inference at allthat we have to defend our argument asconforming to the definition ofsyllogism. It is only when some onedoubts whether the conclusion proved isthe definable form that we have todefend it as conforming to thedefinition of definable form which weassumed. 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

is definable as the divisible, and the



definition of a thing’s contrary-if ithas one the contrary of the thing’sdefinition; then, if good is thecontrary of evil and the indivisible ofthe divisible, we conclude that to begood is essentially to be indivisible.The question is begged becausedefinable form is assumed as a premiss,and as a premiss which is to provedefinable form. ‘But not the samedefinable form’, you may object. That I

admit, for in demonstrations also we premise that ‘this’ is predicable of

‘that’; but in this premiss the term weassert of the minor is neither the

major itself nor a term identical indefinition, or convertible, with the

major.

Again, both proof by division and thesyllogism just described are open tothe question why man should be animal-

biped-terrestrial and not merely animaland terrestrial, since what they

premise does not ensure that the predicates shall constitute a genuine

unity and not merely belong to a singlesubject as do musical and grammaticalwhen predicated of the same man.

7



How then by definition shall we provesubstance or essential nature? Wecannot show it as a fresh factnecessarily following from theassumption of premisses admitted to befacts-the method of demonstration: we

may not proceed as by induction toestablish a universal on the evidenceof groups of particulars which offer noexception, because induction proves not

what the essential nature of a thing is but that it has or has not some

attribute. Therefore, since presumablyone cannot prove essential nature by anappeal to sense perception or by

pointing with the finger, what other method remains?

To put it another way: how shall we bydefinition prove essential nature? Hewho knows what human-or any other-nature is, must know also that manexists; for no one knows the nature ofwhat does not exist-one can know the

meaning of the phrase or name ‘goat-

stag’ but not what the essential natureof a goat-stag is. But further, ifdefinition can prove what is theessential nature of a thing, can italso prove that it exists? And how will



it prove them both by the same process,since definition exhibits one singlething and demonstration another singlething, and what human nature is and thefact that man exists are not the samething? Then too we hold that it is bydemonstration that the being ofeverything must be proved-unless indeedto be were its essence; and, since

being is not a genus, it is not theessence of anything. Hence the being of

anything as fact is matter fordemonstration; and this is the actual

procedure of the sciences, for thegeometer assumes the meaning of theword triangle, but that it is possessedof some attribute he proves. What isit, then, that we shall prove indefining essential nature? Triangle? Inthat case a man will know by definitionwhat a thing’s nature is withoutknowing whether it exists. But that isimpossible.

Moreover it is clear, if we considerthe methods of defining actually in

use, that definition does not provethat the thing defined exists: sinceeven if there does actually existsomething which is equidistant from acentre, yet why should the thing named



in the definition exist? Why, in otherwords, should this be the formuladefining circle? One might equally wellcall it the definition of mountaincopper. For definitions do not carry afurther guarantee that the thingdefined can exist or that it is whatthey claim to define: one can alwaysask why.

Since, therefore, to define is to prove

either a thing’s essential nature orthe meaning of its name, we mayconclude that definition, if it in nosense proves essential nature, is a setof words signifying precisely what aname signifies. But that were a strangeconsequence; for (1) both what is notsubstance and what does not exist atall would be definable, since even non-existents can be signified by a name:(2) all sets of words or sentenceswould be definitions, since any kind ofsentence could be given a name; so thatwe should all be talking indefinitions, and even the Iliad would

be a definition: (3) no demonstrationcan prove that any particular name

means any particular thing: neither,therefore, do definitions, in additionto revealing the meaning of a name,



also reveal that the name has this meaning. It appears then from these

considerations that neither definitionand syllogism nor their objects areidentical, and further that definitionneither demonstrates nor provesanything, and that knowledge ofessential nature is not to be obtainedeither by definition or bydemonstration.

8

We must now start afresh and considerwhich of these conclusions are soundand which are not, and what is thenature of definition, and whetheressential nature is in any sensedemonstrable and definable or in none.

Now to know its essential nature is, aswe said, the same as to know the causeof a thing’s existence, and the proofof this depends on the fact that athing must have a cause. Moreover, thiscause is either identical with the

essential nature of the thing ordistinct from it; and if its cause isdistinct from it, the essential natureof the thing is either demonstrable orindemonstrable. Consequently, if the



cause is distinct from the thing’sessential nature and demonstration is

possible, the cause must be the middleterm, and, the conclusion proved beinguniversal and affirmative, the proof isin the first figure. So the method justexamined of proving it through anotheressential nature would be one way of

proving essential nature, because aconclusion containing essential nature

must be inferred through a middle which

is an essential nature just as a‘peculiar’ property must be inferredthrough a middle which is a ‘peculiar’

property; so that of the two definablenatures of a single thing this methodwill prove one and not the other.

Now it was said before that this methodcould not amount to demonstration ofessential nature-it is actually adialectical proof of it-so let us beginagain and explain by what method it can

be demonstrated. When we are aware of afact we seek its reason, and thoughsometimes the fact and the reason dawn

on us simultaneously, yet we cannotapprehend the reason a moment soonerthan the fact; and clearly in just thesame way we cannot apprehend a thing’sdefinable form without apprehending



that it exists, since while we areignorant whether it exists we cannotknow its essential nature. Moreover weare aware whether a thing exists or notsometimes through apprehending anelement in its character, and sometimesaccidentally, as, for example, when weare aware of thunder as a noise in theclouds, of eclipse as a privation oflight, or of man as some species ofanimal, or of the soul as a self-moving

thing. As often as we have accidentalknowledge that the thing exists, we

must be in a wholly negative state asregards awareness of its essentialnature; for we have not got genuineknowledge even of its existence, and tosearch for a thing’s essential naturewhen we are unaware that it exists isto search for nothing. On the otherhand, whenever we apprehend an elementin the thing’s character there is lessdifficulty. Thus it follows that thedegree of our knowledge of a thing’sessential nature is determined by thesense in which we are aware that it

exists. Let us then take the followingas our first instance of being aware ofan element in the essential nature. Let

A be eclipse, C the moon, B the earth’sacting as a screen. Now to ask whether



the moon is eclipsed or not is to askwhether or not B has occurred. But thatis precisely the same as asking whether

A has a defining condition; and if thiscondition actually exists, we assertthat A also actually exists. Or againwe may ask which side of acontradiction the defining conditionnecessitates: does it make the anglesof a triangle equal or not equal to tworight angles? When we have found the

answer, if the premisses are immediate,we know fact and reason together; ifthey are not immediate, we know thefact without the reason, as in thefollowing example: let C be the moon, Aeclipse, B the fact that the moon failsto produce shadows though she is fulland though no visible body intervenes

between us and her. Then if B, failureto produce shadows in spite of theabsence of an intervening body, isattributable A to C, and eclipse, isattributable to B, it is clear that the

moon is eclipsed, but the reason why isnot yet clear, and we know that eclipse

exists, but we do not know what itsessential nature is. But when it isclear that A is attributable to C andwe proceed to ask the reason of thisfact, we are inquiring what is the



nature of B: is it the earth’s actingas a screen, or the moon’s rotation orher extinction? But B is the definitionof the other term, viz. in theseexamples, of the major term A; foreclipse is constituted by the earthacting as a screen. Thus, (1) ‘What isthunder?’ ‘The quenching of fire incloud’, 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 isassuredly the definition of the majorterm A. If there be a further mediatingcause of B, it will be one of theremaining partial definitions of A.

We have stated then how essentialnature is discovered and becomes known,and we see that, while there is nosyllogism-i.e. no demonstrativesyllogism-of essential nature, yet itis through syllogism, viz.

demonstrative syllogism, that essentialnature is exhibited. So we concludethat neither can the essential natureof anything which has a cause distinctfrom itself be known without



demonstration, nor can it bedemonstrated; and this is what wecontended in our preliminarydiscussions.

9

Now while some things have a causedistinct from themselves, others havenot. Hence it is evident that there areessential natures which are immediate,

that is are basic premisses; and ofthese not only that they are but alsowhat they are must be assumed orrevealed in some other way. This too isthe actual procedure of thearithmetician, who assumes both thenature and the existence of unit. Onthe other hand, it is possible (in the

manner explained) to exhibit throughdemonstration the essential nature ofthings which have a ‘middle’, i.e. acause of their substantial being otherthan that being itself; but we do notthereby demonstrate it.

10

Since definition is said to be thestatement of a thing’s nature,obviously one kind of definition will



be a statement of the meaning of thename, or of an equivalent nominalformula. A definition in this sensetells you, e.g. the meaning of the

phrase ‘triangular character’. When weare aware that triangle exists, weinquire the reason why it exists. Butit is difficult thus to learn thedefinition of things the existence ofwhich we do not genuinely know-thecause of this difficulty being, as we

said before, that we only knowaccidentally whether or not the thingexists. Moreover, a statement may be aunity in either of two ways, byconjunction, like the Iliad, or becauseit exhibits a single predicate asinhering not accidentally in a singlesubject.

That then is one way of definingdefinition. Another kind of definitionis a formula exhibiting the cause of athing’s existence. Thus the formersignifies without proving, but thelatter will clearly be a quasi-

demonstration of essential nature,differing from demonstration in thearrangement of its terms. For there isa difference between stating why itthunders, and stating what is the



essential nature of thunder; since thefirst statement will be ‘Because fireis quenched in the clouds’, while thestatement of what the nature of thunderis will be ‘The noise of fire beingquenched in the clouds’. Thus the samestatement takes a different form: inone form it is continuousdemonstration, in the other definition.

Again, thunder can be defined as noisein the clouds, which is the conclusion

of the demonstration embodyingessential nature. On the other hand thedefinition of immediates is anindemonstrable positing of essentialnature.

We conclude then that definition is (a)an indemonstrable statement ofessential nature, or (b) a syllogism ofessential nature differing fromdemonstration in grammatical form, or(c) the conclusion of a demonstrationgiving essential nature.

Our discussion has therefore made plain

(1) in what sense and of what thingsthe essential nature is demonstrable,and in what sense and of what things itis not; (2) what are the various

meanings of the term definition, and in



what sense and of what things it provesthe essential nature, and in what senseand of what things it does not; (3)what is the relation of definition todemonstration, and how far the samething is both definable anddemonstrable and how far it is not.

11

We think we have scientific knowledge

when we know the cause, and there arefour causes: (1) the definable form,(2) an antecedent which necessitates aconsequent, (3) the efficient cause,(4) the final cause. Hence each ofthese can be the middle term of a

proof, for (a) though the inferencefrom antecedent to necessary consequentdoes not hold if only one premiss isassumed-two is the minimum-still whenthere are two it holds on conditionthat they have a single common middleterm. So it is from the assumption ofthis single middle term that theconclusion follows necessarily. The

following example will also show this. Why is the angle in a semicircle a

right angle?-or from what assumptiondoes it follow that it is a rightangle? Thus, let A be right angle, B



the half of two right angles, C theangle in a semicircle. Then B is thecause in virtue of which A, rightangle, is attributable to C, the anglein a semicircle, since B=A and theother, viz. C,=B, for C is half of tworight angles. Therefore it is theassumption of B, the half of two rightangles, from which it follows that A isattributable to C, i.e. that the anglein a semicircle is a right angle.

Moreover, B is identical with (b) thedefining form of A, since it is what

A’s definition signifies. Moreover, theformal cause has already been shown to

be the middle. (c) ‘Why did the Athenians become involved in the

Persian war?’ means ‘What causeoriginated the waging of war againstthe Athenians?’ and the answer is,‘Because they raided Sardis with theEretrians’, since this originated thewar. Let A be war, B unprovokedraiding, 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 aggressor.So A, having war waged upon them, istrue of B, the initial aggressors, andB is true of C, the Athenians, who werethe aggressors. Hence here too the



cause-in this case the efficient cause-is the middle term. (d) This is no lesstrue where the cause is the finalcause. E.g. why does one take a walkafter supper? For the sake of one’shealth. Why does a house exist? For the

preservation of one’s goods. The end inview is in the one case health, in theother preservation. To ask the reasonwhy one must walk after supper is

precisely to ask to what end one must

do it. Let C be walking after supper, Bthe non-regurgitation of food, Ahealth. Then let walking after supper

possess the property of preventing foodfrom rising to the orifice of thestomach, and let this condition behealthy; since it seems that B, thenon-regurgitation of food, isattributable to C, taking a walk, andthat A, health, is attributable to B.

What, then, is the cause through which A, the final cause, inheres in C? It is

B, the non-regurgitation of food; but Bis a kind of definition of A, for Awill be explained by it. Why is B the

cause of A’s belonging to C? Because to be in a condition such as B is to be in

health. The definitions must betransposed, and then the detail will

become clearer. Incidentally, here the



order of coming to be is the reverse ofwhat it is in proof through theefficient cause: in the efficient orderthe middle term must come to be first,whereas in the teleological order the

minor, C, must first take place, andthe end in view comes last in time.

The same thing may exist for an end and be necessitated as well. For example,

light shines through a lantern (1)

because that which consists ofrelatively small particles necessarily

passes through pores larger than those particles-assuming that light does

issue by penetrationand (2) for an end,namely to save us from stumbling. Ifthen, a thing can exist through twocauses, can it come to be through twocauses-as for instance if thunder be ahiss and a roar necessarily produced bythe quenching of fire, and alsodesigned, as the Pythagoreans say, fora threat to terrify those that lie inTartarus? Indeed, there are very manysuch cases, mostly among the processes

and products of the natural world; fornature, in different senses of the term‘nature’, produces now for an end, now

by necessity.



Necessity too is of two kinds. It maywork in accordance with a thing’snatural tendency, or by constraint andin opposition to it; as, for instance,

by necessity a stone is borne bothupwards and downwards, but not by thesame necessity.

Of the products of man’s intelligencesome 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 resultfrom chance as well.

It is mostly in cases where the issueis indeterminate (though only where the

production does not originate inchance, and the end is consequentlygood), that a result is due to an end,and this is true alike in nature or inart. By chance, on the other hand,nothing comes to be for an end.

12

The effect may be still coming to be,or its occurrence may be past orfuture, yet the cause will be the sameas when it is actually existent-for itis the middle which is the cause-except



that if the effect actually exists thecause is actually existent, if it iscoming to be so is the cause, if itsoccurrence is past the cause is past,if future the cause is future. Forexample, the moon was eclipsed becausethe earth intervened, is becomingeclipsed because the earth is in

process of intervening, will beeclipsed because the earth willintervene, is eclipsed because the

earth intervenes.

To take a second example: assuming thatthe definition of ice is solidifiedwater, let C be water, A solidified, Bthe middle, which is the cause, namelytotal failure of heat. Then B isattributed to C, and A, solidification,to B: ice when B is occurring, hasformed when B has occurred, and willform when B shall occur.

This sort of cause, then, and itseffect come to be simultaneously whenthey are in process of becoming, and

exist simultaneously when they actuallyexist; and the same holds good whenthey are past and when they are future.But what of cases where they are notsimultaneous? Can causes and effects



different from one another form, asthey seem to us to form, a continuoussuccession, a past effect resultingfrom a past cause different fromitself, a future effect from a futurecause different from it, and an effectwhich is coming-to-be from a causedifferent from and prior to it? Now onthis theory it is from the posteriorevent that we reason (and this thoughthese later events actually have their

source of origin in previous events—afact which shows that also when theeffect is coming-to-be we still reasonfrom the posterior event), and from theevent we cannot reason (we cannot arguethat because an event A has occurred,therefore an event B has occurredsubsequently to A but still in the

past-and the same holds good if theoccurrence is future)-cannot reason

because, be the time interval definiteor indefinite, it will never be

possible to infer that because it istrue to say that A occurred, thereforeit is true to say that B, the

subsequent event, occurred; for in theinterval between the events, though Ahas already occurred, the latterstatement will be false. And the sameargument applies also to future events;



i.e. one cannot infer from an eventwhich occurred in the past that afuture event will occur. The reason ofthis is that the middle must behomogeneous, past when the extremes are

past, future when they are future,coming to be when they are coming-to-

be, actually existent when they areactually existent; and there cannot bea middle term homogeneous with extremesrespectively past and future. And it is

a further difficulty in this theorythat the time interval can be neitherindefinite nor definite, since duringit the inference will be false. We havealso to inquire what it is that holdsevents together so that the coming-to-

be now occurring in actual thingsfollows upon a past event. It isevident, we may suggest, that a pastevent and a present process cannot be‘contiguous’, for not even two pastevents can be ‘contiguous’. For pastevents are limits and atomic; so justas points are not ‘contiguous’ neitherare past events, since both are

indivisible. For the same reason a pastevent and a present process cannot be‘contiguous’, for the process isdivisible, the event indivisible. Thusthe relation of present process to past



event is analogous to that of line to point, since a process contains an

infinity of past events. Thesequestions, however, must receive a moreexplicit treatment in our generaltheory of change.

The following must suffice as anaccount of the manner in which the

middle would be identical with thecause on the supposition that coming-

to-be is a series of consecutiveevents: for in the terms of such aseries too the middle and major terms

must form an immediate premiss; e.g. weargue that, since C has occurred,therefore A occurred: and C’soccurrence was posterior, A’s prior;

but C is the source of the inference because it is nearer to the present moment, and the starting-point of time

is the present. We next argue that,since D has occurred, therefore Coccurred. Then we conclude that, sinceD has occurred, therefore A must haveoccurred; and the cause is C, for since

D has occurred C must have occurred,and since C has occurred A must

previously have occurred.



If we get our middle term in this way,will the series terminate in animmediate premiss, or since, as wesaid, no two events are ‘contiguous’,will a fresh middle term alwaysintervene because there is an infinityof middles? No: though no two eventsare ‘contiguous’, yet we must startfrom a premiss consisting of a middleand the present event as major. Thelike is true of future events too,

since if it is true to say that D willexist, it must be a prior truth to saythat A will exist, and the cause ofthis conclusion is C; for if D willexist, C will exist prior to D, and ifC will exist, A will exist prior to it.

And here too the same infinitedivisibility might be urged, sincefuture events are not ‘contiguous’. Buthere too an immediate basic premiss

must be assumed. And in the world offact this is so: if a house has been

built, then blocks must have beenquarried and shaped. The reason is thata house having been built necessitates

a foundation having been laid, and if afoundation has been laid blocks musthave been shaped beforehand. Again, ifa house will be built, blocks willsimilarly be shaped beforehand; and



proof is through the middle in the sameway, for the foundation will exist

before the house.

Now we observe in Nature a certain kindof circular process of coming-to-be;and this is possible only if the middleand extreme terms are reciprocal, sinceconversion is conditioned byreciprocity in the terms of the proof.This-the convertibility of conclusions

and premisses-has been proved in ourearly chapters, and the circular

process is an instance of this. Inactual fact it is exemplified thus:when the earth had been moistened anexhalation was bound to rise, and whenan exhalation had risen cloud was boundto form, and from the formation ofcloud rain necessarily resulted and bythe fall of rain the earth wasnecessarily moistened: but this was thestarting-point, so that a circle iscompleted; for posit any one of theterms and another follows from it, andfrom that another, and from that again

the first.

Some occurrences are universal (forthey are, or come-to-be what they are,always and in ever case); others again



are not always what they are but onlyas a general rule: for instance, notevery man can grow a beard, but it isthe general rule. In the case of suchconnexions the middle term too must bea general rule. For if A is predicateduniversally of B and B of C, A too must

be predicated always and in everyinstance of C, since to hold in everyinstance and always is of the nature ofthe universal. But we have assumed a

connexion which is a general rule;consequently the middle term B mustalso be a general rule. So connexionswhich embody a general rule-i.e. whichexist or come to be as a general rule-will also derive from immediate basic

premisses.

13

We have already explained how essentialnature is set out in the terms of ademonstration, and the sense in whichit is or is not demonstrable ordefinable; so let us now discuss the

method to be adopted in tracing theelements predicated as constituting thedefinable form.



Now of the attributes which inherealways in each several thing there aresome which are wider in extent than it

but not wider than its genus (byattributes of wider extent mean allsuch as are universal attributes ofeach several subject, but in theirapplication are not confined to thatsubject). while an attribute may inherein every triad, yet also in a subjectnot a triad-as being inheres in triad

but also in subjects not numbers atall-odd on the other hand is anattribute inhering in every triad andof wider application (inhering as itdoes also in pentad), but which doesnot extend beyond the genus of triad;for pentad is a number, but nothingoutside number is odd. It is suchattributes which we have to select, upto the exact point at which they areseverally of wider extent than thesubject but collectively coextensivewith it; for this synthesis must be thesubstance of the thing. For exampleevery triad possesses the attributes

number, odd, and prime in both senses,i.e. not only as possessing nodivisors, but also as not being a sumof numbers. This, then, is preciselywhat triad is, viz. a number, odd, and



prime in the former and also the lattersense of the term: for these attributestaken severally apply, the first two toall odd numbers, the last to the dyadalso as well as to the triad, but,taken collectively, to no othersubject. Now since we have shown above’that attributes predicated as belongingto the essential nature are necessaryand that universals are necessary, andsince the attributes which we select as

inhering in triad, or in any othersubject whose attributes we select inthis way, are predicated as belongingto its essential nature, triad willthus possess these attributesnecessarily. Further, that thesynthesis of them constitutes thesubstance of triad is shown by thefollowing argument. If it is notidentical with the being of triad, it

must be related to triad as a genusnamed or nameless. It will then be ofwider extent than triad-assuming thatwider potential extent is the characterof a genus. If on the other hand this

synthesis is applicable to no subjectother than the individual triads, itwill be identical with the being oftriad, because we make the furtherassumption that the substance of each



subject is the predication of elementsin its essential nature down to thelast differentia characterizing theindividuals. It follows that any othersynthesis thus exhibited will likewise

be identical with the being of thesubject.

The author of a hand-book on a subjectthat is a generic whole should dividethe genus into its first infimae

species-number e.g. into triad anddyad-and then endeavour to seize theirdefinitions by the method we havedescribed-the definition, for example,of straight line or circle or rightangle. After that, having establishedwhat the category is to which thesubaltern genus belongs-quantity orquality, for instance-he should examinethe properties ‘peculiar’ to thespecies, working through the proximatecommon differentiae. He should proceedthus because the attributes of thegenera compounded of the infimaespecies will be clearly given by the

definitions of the species; since the basic element of them all is the

definition, i.e. the simple infirmaspecies, and the attributes inhereessentially in the simple infimae



species, in the genera only in virtueof these.

Divisions according to differentiae area useful accessory to this method. Whatforce they have as proofs we did,indeed, explain above, but that merelytowards collecting the essential naturethey may be of use we will proceed toshow. They might, indeed, seem to be ofno use at all, but rather to assume

everything at the start and to be no better than an initial assumption made

without division. But, in fact, theorder in which the attributes are

predicated does make a difference—it matters whether we say animal-tame- biped, or biped-animal-tame. For if

every definable thing consists of twoelements and ‘animal-tame’ forms aunity, and again out of this and thefurther differentia man (or whateverelse is the unity under construction)is constituted, then the elements weassume have necessarily been reached bydivision. Again, division is the only

possible method of avoiding theomission of any element of theessential nature. Thus, if the primarygenus is assumed and we then take oneof the lower divisions, the dividendum



will not fall whole into this division:e.g. it is not all animal which iseither whole-winged or split-winged butall winged animal, for it is wingedanimal to which this differentiation

belongs. The primary differentiation ofanimal is that within which all animalfalls. The like is true of every othergenus, whether outside animal or asubaltern genus of animal; e.g. the

primary differentiation of bird is that

within which falls every bird, of fishthat within which falls every fish. So,if we proceed in this way, we can besure that nothing has been omitted: byany other method one is bound to omitsomething without knowing it.

To define and divide one need not knowthe whole of existence. Yet some holdit impossible to know the differentiaedistinguishing each thing from everysingle other thing without knowingevery single other thing; and onecannot, they say, know each thingwithout knowing its differentiae, since

everything is identical with that fromwhich it does not differ, and otherthan that from which it differs. Nowfirst of all this is a fallacy: notevery differentia precludes identity,



since many differentiae inhere inthings specifically identical, thoughnot in the substance of these noressentially. Secondly, when one hastaken one’s differing pair of oppositesand assumed that the two sides exhaustthe genus, and that the subject oneseeks to define is present in one orother of them, and one has furtherverified its presence in one of them;then it does not matter whether or not

one knows all the other subjects ofwhich the differentiae are also

predicated. For it is obvious that when by this process one reaches subjects

incapable of further differentiationone will possess the formula definingthe substance. Moreover, to postulatethat the division exhausts the genus isnot illegitimate if the oppositesexclude a middle; since if it is thedifferentia of that genus, anythingcontained in the genus must lie on oneof the two sides.

In establishing a definition by

division one should keep three objectsin view: (1) the admission only ofelements in the definable form, (2) thearrangement of these in the rightorder, (3) the omission of no such



elements. The first is feasible becauseone can establish genus and differentiathrough the topic of the genus, just asone can conclude the inherence of anaccident through the topic of theaccident. The right order will beachieved if the right term is assumedas primary, and this will be ensured ifthe term selected is predicable of allthe others but not all they of it;since there must be one such term.

Having assumed this we at once proceedin the same way with the lower terms;for our second term will be the firstof the remainder, our third the firstof those which follow the second in a‘contiguous’ series, since when thehigher term is excluded, that term ofthe remainder which is ‘contiguous’ toit will be primary, and so on. Our

procedure makes it clear that noelements in the definable form have

been omitted: we have taken thedifferentia that comes first in theorder of division, pointing out thatanimal, e.g. is divisible exhaustively

into A and B, and that the subjectaccepts one of the two as its

predicate. Next we have taken thedifferentia of the whole thus reached,and shown that the whole we finally



reach is not further divisible-i.e.that as soon as we have taken the lastdifferentia to form the concretetotality, this totality admits of nodivision into species. For it is clearthat there is no superfluous addition,since all these terms we have selectedare elements in the definable form; andnothing lacking, since any omissionwould have to be a genus or adifferentia. Now the primary term is a

genus, and this term taken inconjunction with its differentiae is agenus: moreover the differentiae areall included, because there is now nofurther differentia; if there were, thefinal concrete would admit of divisioninto species, which, we said, is notthe case.

To resume our account of the right method of investigation: We must start by observing a set of similar-i.e.

specifically identical-individuals, andconsider what element they have incommon. We must then apply the same

process to another set of individualswhich belong to one species and aregenerically but not specificallyidentical with the former set. When wehave established what the common



element is in all members of thissecond species, and likewise in membersof further species, we should againconsider whether the resultsestablished possess any identity, and

persevere until we reach a singleformula, since this will be thedefinition of the thing. But if wereach not one formula but two or more,evidently the definiendum cannot be onething but must be more than one. I may

illustrate my meaning as follows. If wewere inquiring what the essentialnature of pride is, we should examineinstances of proud men we know of tosee what, as such, they have in common;e.g. if Alcibiades was proud, or

Achilles and Ajax were proud, we shouldfind on inquiring what they all had incommon, that it was intolerance ofinsult; it was this which drove

Alcibiades to war, Achilles wrath, and Ajax to suicide. We should next examine

other cases, Lysander, for example, orSocrates, and then if these have incommon indifference alike to good and

ill fortune, I take these two resultsand inquire what common element haveequanimity amid the vicissitudes oflife and impatience of dishonour. Ifthey have none, there will be two



genera of pride. Besides, everydefinition is always universal andcommensurate: the physician does not

prescribe what is healthy for a singleeye, but for all eyes or for adeterminate species of eye. It is alsoeasier by this method to define thesingle species than the universal, andthat is why our procedure should befrom the several species to theuniversal genera-this for the further

reason too that equivocation is lessreadily detected in genera than ininfimae species. Indeed, perspicuity isessential in definitions, just asinferential movement is the minimumrequired in demonstrations; and weshall attain perspicuity if we cancollect separately the definition ofeach species through the group ofsingulars which we have establishede.g. the definition of similarity notunqualified but restricted to coloursand to figures; the definition ofacuteness, but only of sound-and so

proceed to the common universal with a

careful avoidance of equivocation. We may add that if dialectical disputation must not employ metaphors, clearly metaphors and metaphorical expressions



are precluded in definition: otherwisedialectic would involve metaphors.

14

In order to formulate the connexions wewish to prove we have to select ouranalyses and divisions. The method ofselection consists in laying down thecommon genus of all our subjects ofinvestigation-if e.g. they are animals,

we lay down what the properties arewhich inhere in every animal. Theseestablished, we next lay down the

properties essentially connected withthe first of the remaining classes-e.g.if this first subgenus is bird, theessential properties of every bird-andso on, always characterizing the

proximate subgenus. This will clearlyat once enable us to say in virtue ofwhat character the subgenera-man, e.g.or horse-possess their properties. Let

A be animal, B the properties of everyanimal, C D E various species ofanimal. Then it is clear in virtue of

what character B inheres in D-namely A-and that it inheres in C and E for thesame reason: and throughout theremaining subgenera always the samerule applies.



We are now taking our examples from the

traditional class-names, but we mustnot confine ourselves to consideringthese. We must collect any other commoncharacter which we observe, and thenconsider with what species it isconnected and what.properties belong toit. For example, as the common

properties of horned animals we collectthe possession of a third stomach and

only one row of teeth. Then since it isclear in virtue of what character they

possess these attributes-namely theirhorned character-the next question is,to what species does the possession ofhorns attach?

Yet a further method of selection is byanalogy: for we cannot find a singleidentical name to give to a squid’s

pounce, a fish’s spine, and an animal’s bone, although these too possess common properties as if there were a single

osseous nature.

15

Some connexions that require proof areidentical in that they possess anidentical ‘middle’ e.g. a whole group



might be proved through ‘reciprocalreplacement’-and of these one class areidentical in genus, namely all thosewhose difference consists in theirconcerning different subjects or intheir mode of manifestation. Thislatter class may be exemplified by thequestions as to the causes respectivelyof echo, of reflection, and of therainbow: the connexions to be provedwhich these questions embody are

identical generically, because allthree are forms of repercussion; butspecifically they are different.

Other connexions that require proofonly differ in that the ‘middle’ of theone is subordinate to the ‘middle’ ofthe other. For example: Why does the

Nile rise towards the end of the month?Because towards its close the month is

more stormy. Why is the month morestormy towards its close? Because the

moon is waning. Here the one cause issubordinate to the other.

16

The question might be raised withregard to cause and effect whether whenthe effect is present the cause also is



present; whether, for instance, if a plant sheds its leaves or the moon is

eclipsed, there is present also thecause of the eclipse or of the fall ofthe leaves-the possession of broadleaves, let us say, in the latter case,in the former the earth’sinterposition. For, one might argue, ifthis cause is not present, these

phenomena will have some other cause:if it is present, its effect will be at

once implied by it-the eclipse by theearth’s interposition, the fall of theleaves by the possession of broadleaves; but if so, they will belogically coincident and each capableof proof through the other. Let meillustrate: Let A be deciduouscharacter, B the possession of broadleaves, C vine. Now if A inheres in B(for every broad-leaved plant isdeciduous), and B in C (every vine

possessing broad leaves); then Ainheres in C (every vine is deciduous),and the middle term B is the cause. Butwe can also demonstrate that the vine

has broad leaves because it isdeciduous. Thus, let D be broad-leaved,E deciduous, F vine. Then E inheres inF (since every vine is deciduous), andD in E (for every deciduous plant has



broad leaves): therefore every vine has broad leaves, and the cause is its

deciduous character. If, however, theycannot each be the cause of the other(for cause is prior to effect, and theearth’s interposition is the cause ofthe moon’s eclipse and not the eclipseof the interposition)-if, then,demonstration through the cause is ofthe reasoned fact and demonstration notthrough the cause is of the bare fact,

one who knows it through the eclipseknows the fact of the earth’sinterposition but not the reasonedfact. Moreover, that the eclipse is notthe cause of the interposition, but theinterposition of the eclipse, isobvious because the interposition is anelement in the definition of eclipse,which shows that the eclipse is knownthrough the interposition and not viceversa.

On the other hand, can a single effecthave more than one cause? One mightargue as follows: if the same attribute

is predicable of more than one thing asits primary subject, let B be a primarysubject in which A inheres, and Canother primary subject of A, and D andE primary subjects of B and C



respectively. A will then inhere in Dand E, and B will be the cause of A’sinherence in D, C of A’s inherence inE. The presence of the cause thusnecessitates that of the effect, butthe presence of the effect necessitatesthe presence not of all that may causeit but only of a cause which yet neednot be the whole cause. We may,however, suggest that if the connexionto be proved is always universal and

commensurate, not only will the cause be a whole but also the effect will be

universal and commensurate. Forinstance, deciduous character will

belong exclusively to a subject whichis a whole, and, if this whole hasspecies, universally and commensuratelyto those species-i.e. either to allspecies of plant or to a singlespecies. So in these universal andcommensurate connexions the ‘middle’and its effect must reciprocate, i.e.

be convertible. Supposing, for example,that the reason why trees are deciduousis the coagulation of sap, then if a

tree is deciduous, coagulation must be present, and if coagulation is present-

not in any subject but in a tree-thenthat tree must be deciduous.



17

Can the cause of an identical effect benot identical in every instance of theeffect but different? Or is thatimpossible? Perhaps it is impossible ifthe effect is demonstrated as essentialand not as inhering in virtue of asymptom or an accident-because the

middle is then the definition of the major term-though possible if the

demonstration is not essential. Now itis possible to consider the effect andits subject as an accidentalconjunction, though such conjunctionswould not be regarded as connexionsdemanding scientific proof. But if theyare accepted as such, the middle willcorrespond to the extremes, and beequivocal if they are equivocal,generically one if they are genericallyone. Take the question why

proportionals alternate. The cause whenthey are lines, and when they arenumbers, is both different andidentical; different in so far as lines

are lines and not numbers, identical asinvolving a given determinateincrement. In all proportionals this isso. Again, the cause of likeness

between colour and colour is other than



that between figure and figure; forlikeness here is equivocal, meaning

perhaps in the latter case equality ofthe ratios of the sides and equality ofthe angles, in the case of coloursidentity of the act of perceiving them,or something else of the sort. Again,connexions requiring proof which areidentical by analogy middles alsoanalogous.

The truth is that cause, effect, andsubject are reciprocally predicable inthe following way. If the species aretaken severally, the effect is widerthan the subject (e.g. the possessionof external angles equal to four rightangles is an attribute wider thantriangle or are), but it is coextensivewith the species taken collectively (inthis instance with all figures whoseexternal angles are equal to four rightangles). And the middle likewisereciprocates, for the middle is adefinition of the major; which isincidentally the reason why all the

sciences are built up throughdefinition.

We may illustrate as follows. Deciduousis a universal attribute of vine, and



is at the same time of wider extentthan vine; and of fig, and is of widerextent than fig: but it is not widerthan but coextensive with the totalityof the species. Then if you take the

middle which is proximate, it is adefinition of deciduous. I say that,

because you will first reach a middlenext the subject, and a premissasserting it of the whole subject, andafter that a middle-the coagulation of

sap or something of the sort-provingthe connexion of the first middle withthe major: but it is the coagulation ofsap at the junction of leaf-stalk andstem which defines deciduous.

If an explanation in formal terms ofthe inter-relation of cause and effectis demanded, we shall offer thefollowing. Let A be an attribute of allB, and B of every species of D, but sothat both A and B are wider than theirrespective subjects. Then B will be auniversal attribute of each species ofD (since I call such an attribute

universal even if it is notcommensurate, and I call an attribute

primary universal if it iscommensurate, not with each speciesseverally but with their totality), and



it extends beyond each of them takenseparately.

Thus, B is the cause of A’s inherencein the species of D: consequently A

must be of wider extent than B;otherwise why should B be the cause of

A’s inherence in D any more than A thecause of B’s inherence in D? Now if Ais an attribute of all the species ofE, all the species of E will be united

by possessing some common cause otherthan B: otherwise how shall we be ableto say that A is predicable of all ofwhich E is predicable, while E is not

predicable of all of which A can be predicated? I mean how can there fail

to be some special cause of A’sinherence in E, as there was of A’sinherence in all the species of D? Thenare the species of E, too, united by

possessing some common cause? Thiscause we must look for. Let us call itC.

We conclude, then, that the same effect

may have more than one cause, but notin subjects specifically identical. Forinstance, the cause of longevity inquadrupeds is lack of bile, in birds a



dry constitution-or certainly somethingdifferent.

18

If immediate premisses are not reachedat once, and there is not merely one

middle but several middles, i.e.several causes; is the cause of the

property’s inherence in the severalspecies the middle which is proximateto the primary universal, or the middlewhich is proximate to the species?Clearly the cause is that nearest toeach species severally in which it is

manifested, for that is the cause ofthe subject’s falling under theuniversal. To illustrate formally: C isthe cause of B’s inherence in D; henceC is the cause of A’s inherence in D, Bof A’s inherence in C, while the causeof A’s inherence in B is B itself.

19

As regards syllogism and demonstration,the definition of, and the conditionsrequired to produce each of them, arenow clear, and with that also the



definition of, and the conditionsrequired to produce, demonstrativeknowledge, since it is the same asdemonstration. As to the basic

premisses, how they become known andwhat is the developed state ofknowledge of them is made clear byraising some preliminary problems.

We have already said that scientificknowledge through demonstration is

impossible unless a man knows the primary immediate premisses. But there

are questions which might be raised inrespect of the apprehension of theseimmediate premisses: one might not onlyask whether it is of the same kind asthe apprehension of the conclusions,

but also whether there is or is notscientific knowledge of both; orscientific knowledge of the latter, andof the former a different kind ofknowledge; and, further, whether thedeveloped states of knowledge are notinnate but come to be in us, or areinnate but at first unnoticed. Now it

is strange if we possess them from birth; for it means that we possess

apprehensions more accurate thandemonstration and fail to notice them.If on the other hand we acquire them



and do not previously possess them, howcould we apprehend and learn without a

basis of pre-existent knowledge? Forthat is impossible, as we used to findin the case of demonstration. So itemerges that neither can we possessthem from birth, nor can they come to

be in us if we are without knowledge ofthem to the extent of having no suchdeveloped state at all. Therefore we

must possess a capacity of some sort,

but not such as to rank higher inaccuracy than these developed states.

And this at least is an obviouscharacteristic of all animals, for they

possess a congenital discriminativecapacity which is called sense-

perception. But though sense-perceptionis innate in all animals, in some thesense-impression comes to persist, inothers it does not. So animals in whichthis persistence does not come to behave either no knowledge at all outsidethe act of perceiving, or no knowledgeof objects of which no impression

persists; animals in which it does come

into being have perception and cancontinue to retain the sense-impressionin the soul: and when such persistenceis frequently repeated a furtherdistinction at once arises between



those which out of the persistence ofsuch sense-impressions develop a powerof systematizing them and those whichdo not. So out of sense-perceptioncomes to be what we call memory, andout of frequently repeated memories ofthe same thing develops experience; fora number of memories constitute asingle experience. From experienceagain-i.e. from the universal nowstabilized in its entirety within the

soul, the one beside the many which isa single identity within them all-originate the skill of the craftsmanand the knowledge of the man ofscience, skill in the sphere of comingto be and science in the sphere of

being.

We conclude that these states ofknowledge are neither innate in adeterminate form, nor developed fromother higher states of knowledge, butfrom sense-perception. It is like arout in battle stopped by first one man

making a stand and then another, until

the original formation has beenrestored. The soul is so constituted asto be capable of this process.



Let us now restate the account givenalready, though with insufficientclearness. When one of a number oflogically indiscriminable particularshas made a stand, the earliestuniversal is present in the soul: forthough the act of sense-perception isof the particular, its content isuniversal-is man, for example, not the

man Callias. A fresh stand is madeamong these rudimentary universals, and

the process does not cease until theindivisible concepts, the trueuniversals, are established: e.g. suchand such a species of animal is a steptowards the genus animal, which by thesame process is a step towards afurther generalization.

Thus it is clear that we must get toknow the primary premisses byinduction; for the method by which evensense-perception implants the universalis inductive. Now of the thinkingstates by which we grasp truth, someare unfailingly true, others admit of

error-opinion, for instance, andcalculation, whereas scientific knowingand intuition are always true: further,no other kind of thought exceptintuition is more accurate than



scientific knowledge, whereas primary premisses are more knowable than

demonstrations, and all scientificknowledge is discursive. From theseconsiderations it follows that therewill be no scientific knowledge of the

primary premisses, and since exceptintuition nothing can be truer thanscientific knowledge, it will beintuition that apprehends the primary

premisses-a result which also follows

from the fact that demonstration cannot be the originative source of

demonstration, nor, consequently,scientific knowledge of scientificknowledge.If, therefore, it is the onlyother kind of true thinking exceptscientific knowing, intuition will bethe originative source of scientificknowledge. And the originative sourceof science grasps the original basic

premiss, while science as a whole issimilarly related as originative sourceto the whole body of fact.



Topics

Book I

1

Our treatise proposes to find a line ofinquiry whereby we shall be able toreason from opinions that are generallyaccepted about every problem propoundedto us, and also shall ourselves, when



standing up to an argument, avoidsaying anything that will obstruct us.First, then, we must say what reasoningis, and what its varieties are, inorder to grasp dialectical reasoning:for this is the object of our search inthe 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 premissesfrom which the reasoning starts aretrue and primary, or are such that ourknowledge of them has originally comethrough premisses which are primary andtrue: (b) reasoning, on the other hand,is ‘dialectical’, if it reasons fromopinions that are generally accepted.Things are ‘true’ and ‘primary’ whichare believed on the strength not ofanything else but of themselves: for inregard to the first principles ofscience it is improper to ask anyfurther for the why and wherefore of

them; each of the first principlesshould command belief in 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 startsfrom opinions that seem to be generallyaccepted, but are not really such, oragain if it merely seems to reason fromopinions that are or seem to begenerally accepted. For not everyopinion that seems to be generallyaccepted actually is generally

accepted. For in none of the opinionswhich we call generally accepted is theillusion entirely on the surface, ashappens in the case of the principlesof contentious arguments; for thenature of the fallacy in these isobvious immediately, and as a rule evento persons with little power ofcomprehension. So then, of thecontentious reasonings mentioned, theformer really deserves to be called‘reasoning’ as well, but the othershould be called ‘contentiousreasoning’, but not ‘reasoning’, sinceit appears to reason, but does not

really do so. Further (d), besides allthe reasonings we have mentioned thereare the mis-reasonings that start fromthe premisses peculiar to the specialsciences, as happens (for example) in



the case of geometry and her sistersciences. For this form of reasoningappears to differ from the reasonings

mentioned above; the man who draws afalse figure reasons from things thatare neither true and primary, nor yetgenerally accepted. For he does notfall within the definition; he does notassume opinions that are receivedeither by every one or by the majorityor by philosophers-that is to say, by

all, or by most, or by the mostillustrious of them-but he conducts hisreasoning upon assumptions which,though appropriate to the science inquestion, are not true; for he effectshis mis-reasoning either by describingthe semicircles wrongly or by drawingcertain lines in a way in which theycould not be drawn.

The foregoing must stand for an outlinesurvey of the species of reasoning. Ingeneral, in regard both to all that wehave already discussed and to thosewhich we shall discuss later, we may

remark that that amount of distinction between them may serve, because it is

not our purpose to give the exactdefinition of any of them; we merelywant to describe them in outline; we



consider it quite enough from the pointof view of the line of inquiry beforeus to be able to recognize each of themin some sort of way.

2

Next in order after the foregoing, we must say for how many and for what purposes the treatise is useful. They

are three-intellectual training, casual

encounters, and the philosophicalsciences. That it is useful as atraining is obvious on the face of it.The possession of a plan of inquirywill enable us more easily to argueabout the subject proposed. For

purposes of casual encounters, it isuseful because when we have counted upthe opinions held by most people, weshall meet them on the ground not ofother people’s convictions but of theirown, while we shift the ground of anyargument that they appear to us tostate unsoundly. For the study of the

philosophical sciences it is useful,

because the ability to raise searchingdifficulties on both sides of a subjectwill make us detect more easily thetruth and error about the several

points that arise. It has a further use



in relation to the ultimate bases ofthe principles used in the severalsciences. For it is impossible todiscuss them at all from the principles

proper to the particular science inhand, seeing that the principles arethe prius of everything else: it isthrough the opinions generally held onthe particular points that these haveto be discussed, and this task belongs

properly, or most appropriately, to

dialectic: for dialectic is a processof criticism wherein lies the path tothe principles of all inquiries.

3

We shall be in perfect possession ofthe way to proceed when we are in a

position like that which we occupy inregard to rhetoric and medicine andfaculties of that kind: this means thedoing of that which we choose with the

materials that are available. For it isnot 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 hisgrasp of the science is adequate.

4



First, then, we must see of what partsour inquiry consists. Now if we were tograsp (a) with reference to how many,and what kind of, things arguments take

place, and with what materials theystart, and (h) how we are to becomewell supplied with these, we shouldhave sufficiently won our goal. Now the

materials with which arguments startare equal in number, and are identical,

with the subjects on which reasoningstake place. For arguments start with‘propositions’, while the subjects onwhich reasonings take place are‘problems’. Now every proposition andevery problem indicates either a genusor a peculiarity or an accident-for thedifferentia too, applying as it does toa class (or genus), should be rankedtogether with the genus. Since,however, of what is peculiar toanything part signifies its essence,while part does not, let us divide the‘peculiar’ into both the aforesaid

parts, and call that part which

indicates the essence a ‘definition’,while of the remainder let us adopt theterminology which is generally currentabout these things, and speak of it asa ‘property’. What we have said, then,



makes it clear that according 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 any one suppose usto mean that each of these enunciated

by itself constitutes a proposition or problem, but only that it is from these

that both problems and propositions areformed. The difference between a

problem and a proposition is a

difference in the turn of the phrase.For if it be put in this way, “’Ananimal that walks on two feet” is thedefinition of man, is it not?’ or‘”Animal” is the genus of man, is itnot?’ the result is a proposition: butif thus, ‘Is “an animal that walks ontwo feet” a definition of man or no?’[or ‘Is “animal” his genus or no?’] theresult is a problem. Similarly too inother cases. Naturally, then, problemsand propositions are equal in number:for out of every proposition you will

make a problem if you change the turnof the phrase.

5

We must now say what are ‘definition’,‘property’, ‘genus’, and ‘accident’. A



‘definition’ is a phrase signifying athing’s essence. It is rendered in theform either of a phrase in lieu of aterm, or of a phrase in lieu of another

phrase; for it is sometimes possible todefine the meaning of a phrase as well.People whose rendering consists of aterm only, try it as they may, clearlydo not render the definition of thething in question, because a definitionis always a phrase of a certain kind.

One may, however, use the word‘definitory’ also of such a remark as‘The “becoming” is “beautiful”’, andlikewise also of the question, ‘Aresensation and knowledge the same ordifferent?’, for argument aboutdefinitions is mostly concerned withquestions of sameness and difference.In a word we may call ‘definitory’everything that falls under the same

branch of inquiry as definitions; andthat all the above-mentioned examplesare of this character is clear on theface of them. For if we are able toargue that two things are the same or

are different, we shall be wellsupplied by the same turn of argumentwith lines of attack upon theirdefinitions as well: for when we haveshown that they are not the same we



shall have demolished the definition.Observe, please, that the converse ofthis last statement does not hold: forto show that they are the same is notenough to establish a definition. Toshow, however, that they are not thesame is enough of itself to overthrowit.

A ‘property’ is a predicate which doesnot indicate the essence of a thing,

but yet belongs to that thing alone,and is predicated convertibly of it.Thus it is a property of man to-be-capable of learning grammar: for if A

be a man, then he is capable oflearning grammar, and if he be capableof learning grammar, he is a man. Forno one calls anything a ‘property’which may possibly belong to somethingelse, e.g. ‘sleep’ in the case of man,even though at a certain time it mayhappen to belong to him alone. That isto say, if any such thing were actuallyto be called a property, it will becalled not a ‘property’ absolutely, but

a ‘temporary’ or a ‘relative’ property:for ‘being on the right hand side’ is atemporary property, while ‘two-footed’is in point of fact ascribed as a

property in certain relations; e.g. it



is a property of man relatively to ahorse and a dog. That nothing which may

belong to anything else than A is aconvertible predicate of A is clear:for it does not necessarily follow thatif something is asleep it is a man.

A ‘genus’ is what is predicated in thecategory of essence of a number ofthings exhibiting differences in kind.

We should treat as predicates in the

category of essence all such things asit would be appropriate to mention inreply to the question, ‘What is theobject before you?’; as, for example,in the case of man, if asked thatquestion, it is appropriate to say ‘Heis an animal’. The question, ‘Is onething in the same genus as another orin a different one?’ is also a‘generic’ question; for a question ofthat kind as well falls under the same

branch of inquiry as the genus: forhaving argued that ‘animal’ is thegenus of man, and likewise also of ox,we shall have argued that they are in

the same genus; whereas if we show thatit is the genus of the one but not ofthe other, we shall have argued thatthese things are not in the same genus.



An ‘accident’ is (i) something which,though it is none of the foregoing-i.e.neither a definition nor a property nora genus yet belongs to the thing:(something which may possibly either

belong or not belong to any one and theself-same thing, as (e.g.) the ‘sitting

posture’ may belong or not belong tosome self-same thing. Likewise also‘whiteness’, for there is nothing to

prevent the same thing being at one

time white, and at another not white.Of the definitions of accident thesecond is the better: for if he adoptsthe first, any one is bound, if he isto understand it, to know already what‘definition’ and ‘genus’ and ‘property’are, whereas the second is sufficientof itself to tell us the essential

meaning of the term in question. To Accident are to be attached also all

comparisons of things together, whenexpressed in language that is drawn inany kind of way from what happens(accidit) to be true of them; such as,for example, the question, ‘Is the

honourable or the expedient preferable?’ and ‘Is the life of virtue

or the life of self-indulgence the pleasanter?’, and any other problem

which may happen to be phrased in terms



like these. For in all such cases thequestion is ‘to which of the two doesthe predicate in question happen(accidit) to belong more closely?’ Itis clear on the face of it that thereis nothing to prevent an accident from

becoming 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 those who are

not sitting. So then, there is nothingto prevent an accident from becoming

both a relative and a temporary property; but a property absolutely it

will never be.

6

We must not fail to observe that allremarks made in criticism of a‘property’ and ‘genus’ and ‘accident’will be applicable to ‘definitions’ aswell. For when we have shown that the

attribute in question fails to belongonly to the term defined, as we do alsoin the case of a property, or that thegenus rendered in the definition is notthe true genus, or that any of the



things mentioned in the phrase useddoes not belong, as would be remarkedalso in the case of an accident, weshall have demolished the definition;so that, to use the phrase previouslyemployed,’ all the points we haveenumerated might in a certain sense becalled ‘definitory’. But we must not onthis account expect to find a singleline of inquiry which will applyuniversally to them all: for this is

not an easy thing to find, and, evenwere one found, it would be veryobscure indeed, and of little servicefor the treatise before us. Rather, aspecial plan of inquiry must be laiddown for each of the classes we havedistinguished, and then, starting fromthe rules that are appropriate in eachcase, it will probably be easier to

make our way right through the task before us. So then, as was said before,’ we must outline a division of

our subject, and other questions we must relegate each to the particular branch to which it most naturally

belongs, speaking of them as‘definitory’ and ‘generic’ questions.The questions I mean have practically

been already assigned to their several branches.



7

First of all we must define the numberof senses borne by the term ‘Sameness’.Sameness would be generally regarded asfalling, roughly speaking, into threedivisions. We generally apply the term

numerically or specifically orgenerically-numerically in cases wherethere is more than one name but onlyone thing, e.g. ‘doublet’ and ‘cloak’;specifically, where there is more thanone thing, but they present nodifferences in respect of theirspecies, as one man and another, or onehorse and another: for things like thisthat fall under the same species aresaid to be ‘specifically the same’.Similarly, too, those things are calledgenerically the same which fall underthe same genus, such as a horse and a

man. It might appear that the sense in

which water from the same spring iscalled ‘the same water’ is somehowdifferent and unlike the senses

mentioned above: but really such a caseas this ought to be ranked in the same



class with the things that in one wayor another are called ‘the same’ inview of unity of species. For all suchthings seem to be of one family and toresemble one another. For the reaon whyall water is said to be specificallythe same as all other water is becauseof a certain likeness it bears to it,and the only difference in the case ofwater drawn from the same spring isthis, that the likeness is more

emphatic: that is why we do notdistinguish it from the things that inone way or another are called ‘thesame’ in view of unity of species. Itis generally supposed that the term‘the same’ is most used in a senseagreed 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 primaryuse is found whenever the sameness isrendered in reference to an alternativename or definition, as when a cloak issaid to be the same as a doublet, or ananimal that walks on two feet is said

to be the same as a man: a second senseis when it is rendered in reference toa property, as when what can acquireknowledge is called the same as a man,and what naturally travels upward the



same as fire: while a third use isfound when it is rendered in referenceto some term drawn from Accident, aswhen the creature who is sitting, orwho is musical, is called the same asSocrates. For all these uses mean tosignify numerical unity. That what Ihave just said is true may be best seenwhere one form of appellation issubstituted for another. For often whenwe give the order to call one of the

people who are sitting down, indicatinghim by name, we change our description,whenever the person to whom we give theorder happens not to understand us; hewill, we think, understand better fromsome accidental feature; so we bid himcall to us ‘the man who is sitting’ or‘who is conversing over there’-clearlysupposing ourselves to be indicatingthe same object by its name and by itsaccident.

8

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 outof which and through which and to whicharguments proceed, is by induction: for



if any one were to survey propositionsand problems one by one, it would beseen that each was formed either fromthe definition of something or from its

property or from its genus or from itsaccident. Another way to confirm it isthrough reasoning. For every predicateof a subject must of necessity beeither convertible with its subject ornot: 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.what is predicated convertibly, butdoes not signify the essence. If, onthe other hand, it is not predicatedconvertibly of the thing, it either isor is not one of the terms contained inthe definition of the subject: and ifit be one of those terms, then it will

be the genus or the differentia,inasmuch as the definition consists ofgenus and differentiae; whereas, if it

be not one of those terms, clearly itwould be an accident, for accident was

said’ to be what belongs as anattribute to a subject without beingeither its definition or its genus or a

property.



9

Next, then, we must distinguish betweenthe classes of predicates in which thefour orders in question are found.These are ten in number: Essence,Quantity, Quality, Relation, Place,Time, Position, State, Activity,Passivity. For the accident and genusand property and definition of anythingwill always be in one of these

categories: for all the propositionsfound through these signify eithersomething’s essence or its quality orquantity or some one of the other typesof predicate. It is clear, too, on theface of it that the man who signifiessomething’s essence signifies sometimesa substance, sometimes a quality,sometimes some one of the other typesof predicate. For when man is set

before him and he says that what is setthere is ‘a man’ or ‘an animal’, hestates its essence and signifies asubstance; but when a white colour isset before him and he says that what is

set there is ‘white’ or is ‘a colour’,he states its essence and signifies aquality. Likewise, also, if a magnitudeof a cubit be set before him and hesays that what is set there is a



magnitude of a cubit, he will bedescribing its essence and signifying aquantity. Likewise, also, in the othercases: for each of these kinds of

predicate, if either it be asserted ofitself, or its genus be asserted of it,signifies an essence: if, on the otherhand, one kind of predicate is assertedof another kind, it does not signify anessence, but a quantity or a quality orone of the other kinds of predicate.

Such, then, and so many, are thesubjects on which arguments take place,and the materials with which theystart. How we are to acquire them, and

by what means we are to become wellsupplied with them, falls next to betold.

10

First, then, a definition must be givenof a ‘dialectical proposition’ and a‘dialectical problem’. For it is notevery proposition nor yet every problemthat is to be set down as dialectical:

for no one in his senses would make a proposition of what no one holds, nor

yet make a problem of what is obviousto everybody or to most people: for thelatter admits of no doubt, while to the



former no one would assent. Now adialectical proposition consists inasking 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 be not contrary to the

general opinion; for a man would probably assent to the view of the philosophers, if it be not contrary to

the opinions of most men. Dialectical

propositions also include views whichare like those generally accepted; also

propositions which contradict thecontraries of opinions that are takento be generally accepted, and also allopinions that are in accordance withthe recognized arts. Thus, supposing itto be a general opinion that theknowledge of contraries is the same, it

might probably pass for a generalopinion also that the perception ofcontraries is the same: also, supposingit to be a general opinion that thereis but one single science of grammar,it might pass for a general opinion

that there is but one science of flute- playing as well, whereas, if it be a

general opinion that there is more thanone science of grammar, it might passfor a general opinion that there is



more than one science of flute-playingas well: for all these seem to be alikeand akin. Likewise, also, propositionscontradicting the contraries of generalopinions will pass as general opinions:for if it be a general opinion that oneought to do good to one’s friends, itwill also be a general opinion that oneought not to do them harm. Here, thatone ought to do harm to one’s friendsis contrary to the general view, and

that one ought not to do them harm isthe contradictory of that contrary.Likewise also, if one ought to do goodto one’s friends, one ought not to dogood to one’s enemies: this too is thecontradictory of the view contrary tothe general view; the contrary beingthat one ought to do good to one’senemies. Likewise, also, in othercases. Also, on comparison, it willlook like a general opinion that thecontrary predicate belongs to thecontrary subject: e.g. if one ought todo good to one’s friends, one oughtalso to do evil to one’s enemies. it

might appear also as if doing good toone’s friends were a contrary to doingevil to one’s enemies: but whether thisis or is not so in reality as well will

be stated in the course of the



discussion upon contraries. Clearlyalso, all opinions that are inaccordance with the arts aredialectical propositions; for peopleare likely to assent to the views held

by those who have made a study of thesethings, e.g. on a question of medicinethey will agree with the doctor, and ona question of geometry with thegeometrician; and likewise also inother cases.

11

A dialectical problem is a subject ofinquiry that contributes either tochoice and avoidance, or to truth andknowledge, and that either by itself,or as a help to the solution of someother such problem. It must, moreover,

be something on which either peoplehold no opinion either way, or the

masses hold a contrary opinion to the philosophers, or the philosophers to

the masses, or each of them amongthemselves. For some problems it is

useful to know with a view to choice oravoidance, e.g. whether pleasure is to

be chosen or not, while some it isuseful to know merely with a view toknowledge, e.g. whether the universe is



eternal or not: others, again, are notuseful in and by themselves for eitherof these purposes, but yet help us inregard to some such problems; for thereare many things which we do not wish toknow in and by themselves, but for thesake of other things, in order thatthrough them we may come to knowsomething else. Problems also includequestions in regard to which reasoningsconflict (the difficulty then being

whether so-and so is so or not, there being convincing arguments for both

views); others also in regard to whichwe have no argument because they are sovast, and we find it difficult to giveour reasons, e.g. the question whetherthe universe is eternal or no: for intoquestions of that kind too it is

possible to inquire.

Problems, then, and propositions are to be defined as aforesaid. A ‘thesis’ is

a supposition of some eminent philosopher that conflicts with the

general opinion; 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, as Melissus 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 theorycontrary to men’s usual opinions, e.g.the view maintained by the sophiststhat what is need not in every caseeither have come to be or be eternal:for a musician who is a grammarian ‘is’so without ever having ‘come to be’ so,or being so eternally. For even if a

man does not accept this view, he mightdo so on the ground that it isreasonable.

Now a ‘thesis’ also is a problem,though a problem is not always athesis, inasmuch as some problems aresuch 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 beensaid that either the mass of mendisagree with the philosophers aboutthe thesis, or that the one or theother class disagree among themselves,

seeing that the thesis is a suppositionin conflict with general opinion.Practically all dialectical problemsindeed are now called ‘theses’. But itshould make no difference whichever



description is used; for our object inthus distinguishing them has not beento create a terminology, but torecognize what differences happen to befound between them.

Not every problem, nor every thesis,should be examined, but only one which

might puzzle one of those who needargument, not punishment or perception.For people who are puzzled to know

whether one ought to honour the godsand love one’s parents or not need

punishment, while those who are puzzledto know whether snow is white or notneed perception. The subjects shouldnot border too closely upon the sphereof demonstration, nor yet be too farremoved from it: for the former casesadmit of no doubt, while the latterinvolve difficulties too great for theart of the trainer.

12

Having drawn these definitions, we must

distinguish how many species there areof dialectical arguments. There is onthe one hand Induction, on the otherReasoning. Now what reasoning is has

been said before: induction is a



passage from individuals to universals,e.g. the argument that supposing theskilled 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 tothe mass of men, though reasoning is

more forcible and effective against

contradictious people.

13

The classes, then, of things aboutwhich, and of things out of which,arguments are constructed, are to bedistinguished in the way we have said

before. The means whereby we are to become well supplied with reasonings

are 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. Thelast three, as well, are in a certainsense propositions: for it is possibleto make a proposition corresponding toeach of them, e.g. (1) ‘The desirable



may mean either the honourable or the pleasant or the expedient’; and (2)

Sensation differs from knowledge inthat the latter may be recovered againafter it has been lost, while theformer cannot’; and (3) The relation ofthe healthy to health is like that ofthe vigorous to vigour’. The first

proposition depends upon the use of oneterm in several senses, the second uponthe differences of things, the third

upon their likenesses.

14

Propositions should be selected in anumber of ways corresponding to thenumber of distinctions drawn in regardto the proposition: thus one may firsttake in hand the opinions held by allor by most men or by the philosophers,i.e. by all, or most, or the mostnotable of them; or opinions contraryto those that seem to be generallyheld; and, again, all opinions that arein accordance with the arts. We must

make propositions also of thecontradictories of opinions contrary tothose that seem to be generally held,as was laid down before. It is usefulalso to make them by selecting not only



those opinions that actually areaccepted, but also those that are likethese, e.g. ‘The perception ofcontraries is the same’-the knowledgeof them being so-and ‘we see byadmission of something into ourselves,not by an emission’; for so it is, too,in the case of the other senses; for inhearing we admit something intoourselves; we do not emit; and we tastein the same way. Likewise also in the

other cases. Moreover, all statementsthat seem to be true in all or in mostcases, should be taken as a principleor accepted position; for they are

posited by those who do not also seewhat exception there may be. We shouldselect also from the written handbooksof argument, and should draw up sketch-lists of them upon each several kind ofsubject, putting them down underseparate headings, e.g. ‘On Good’, or‘On Life’-and that ‘On Good’ shoulddeal with every form of good, beginningwith the category of essence. In the

margin, too, one should indicate also

the opinions of individual thinkers,e.g. ‘Empedocles said that the elementsof bodies were four’: for any one mightassent to the saying of some generallyaccepted authority.



Of propositions and problems there are-to comprehend the matter in outline-three divisions: for some are ethical

propositions, some are on natural philosophy, while some are logical.

Propositions such as the following areethical, e.g. ‘Ought one rather to obeyone’s parents or the laws, if theydisagree?’; such as this are logical,e.g. ‘Is the knowledge of opposites the

same or not?’; while such as this areon natural philosophy, e.g. ‘Is theuniverse eternal or not?’ Likewise alsowith problems. The nature of each ofthe aforesaid kinds of proposition isnot easily rendered in a definition,

but we have to try to recognize each ofthem by means of the familiarityattained through induction, examiningthem in the light of the illustrationsgiven above.

For purposes of philosophy we musttreat of these things according totheir truth, but for dialectic only

with an eye to general opinion. All propositions should be taken in their most universal form; then, the one

should be made into many. E.g. ‘Theknowledge of opposites is the same’;



next, ‘The knowledge of contraries isthe same’, and that ‘of relativeterms’. In the same way these twoshould again be divided, as long asdivision is possible, e.g. theknowledge of ‘good and evil’, of ‘whiteand black’, or ‘cold and hot’. Likewisealso in other cases.

15

On the formation, then, of propositions, the above remarks are

enough. As regards the number of sensesa term bears, we must not only treat ofthose terms which bear differentsenses, but we must also try to rendertheir definitions; e.g. we must not

merely say that justice and courage arecalled ‘good’ in one sense, and thatwhat conduces to vigour and whatconduces to health are called so inanother, but also that the former areso called because of a certainintrinsic quality they themselves have,the latter because they are productive

of a certain result and not because ofany intrinsic quality in themselves.Similarly also in other cases.



Whether a term bears a number ofspecific meanings or one only, may beconsidered by the following means.First, look and see if its contrary

bears a number of meanings, whether thediscrepancy between them be one of kindor one of names. For in some cases adifference is at once displayed even inthe names; e.g. the contrary of ‘sharp’in the case of a note is ‘flat’, whilein the case of a solid edge it is

‘dull’. Clearly, then, the contrary of‘sharp’ bears several meanings, and ifso, also does ‘sharp’; forcorresponding to each of the formerterms the meaning of its contrary will

be different. For ‘sharp’ will not bethe same when contrary to ‘dull’ and to‘flat’, though ‘sharp’ is the contraryof each. Again Barhu (’flat’, ‘heavy’)in the case of a note has ‘sharp’ asits contrary, but in the case of asolid mass ‘light’, so that Barhu isused with a number of meanings,inasmuch as its contrary also is soused. Likewise, also, ‘fine’ as applied

to a picture has ‘ugly’ as itscontrary, but, as applied to a house,‘ramshackle’; so that ‘fine’ is anambiguous term.



In some cases there is no discrepancyof any sort in the names used, but adifference of kind between the meaningsis at once obvious: e.g. in the case of‘clear’ and ‘obscure’: for sound iscalled ‘clear’ and ‘obscure’, just as‘colour’ is too. As regards the names,then, there is no discrepancy, but thedifference in kind between the meaningsis at once obvious: for colour is notcalled ‘clear’ in a like sense to

sound. This is plain also throughsensation: for of things that are thesame in kind we have the samesensation, whereas we do not judgeclearness by the same sensation in thecase of sound and of colour, but in thelatter case we judge by sight, in theformer by hearing. Likewise also with‘sharp’ and ‘dull’ in regard toflavours and solid edges: here in thelatter case we judge by touch, but inthe former by taste. For here againthere is no discrepancy in the namesused, in the case either of theoriginal terms or of their contraries:

for the contrary also of sharp ineither sense is ‘dull’.

Moreover, see if one sense of a termhas a contrary, while another has



absolutely none; e.g. the pleasure ofdrinking has a contrary in the pain ofthirst, whereas the pleasure of seeingthat the diagonal is incommensuratewith the side has none, so that‘pleasure’ is used in more than onesense. To ‘love’ also, used of theframe of mind, has to ‘hate’ as itscontrary, while as used of the physicalactivity (kissing) it has none:clearly, therefore, to ‘love’ is an

ambiguous term. Further, see in regardto their intermediates, if some

meanings and their contraries have anintermediate, others have none, or if

both have one but not the same one,e.g. ‘clear’ and ‘obscure’ in the caseof colours have ‘grey’ as anintermediate, whereas in the case ofsound they have none, or, if they have,it is ‘harsh’, as some people say thata harsh sound is intermediate. ‘Clear’,then, is an ambiguous term, andlikewise also ‘obscure’. See, moreover,if some of them have more than oneintermediate, while others have but

one, as is the case with ‘clear’ and‘obscure’, for in the case of coloursthere are numbers of intermediates,whereas in regard to sound there is butone, viz. ‘harsh’.



Again, in the case of the contradictory

opposite, look and see if it bears morethan 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 tosee’ a phrase with more than one

meaning, viz. (1) to fail to possessthe power of sight, (2) to fail to putthat power to active use. But if this

has more than one meaning, it followsnecessarily that ‘to see’ also has morethan one meaning: for there will be anopposite to each sense of ‘to fail tosee’; e.g. the opposite of ‘not to

possess the power of sight’ is to possess it, while of ‘not to put the power of sight to active use’, the

opposite is to put it to active use.

Moreover, examine the case of termsthat denote the privation or presenceof a certain state: for if the one term

bears more than one meaning, then sowill the remaining term: e.g. if ‘to

have sense’ be used with more than one meaning, 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 to



the body. That the opposition betweenthe terms now in question depends uponthe privation or presence of a certainstate is clear, since animals naturally

possess each kind of ‘sense’, both asapplied to the soul and as applied tothe body.

Moreover, examine the inflected forms.For if ‘justly’ has more than one

meaning, then ‘just’, also, will be

used with more than one meaning; forthere will be a meaning of ‘just’ toeach of the meanings of ‘justly’; e.g.if the word ‘justly’ be used of judgingaccording to one’s own opinion, andalso of judging as one ought, then‘just’ also will be used in like

manner. In the same way also, if‘healthy’ has more than one meaning,then ‘healthily’ also will be used with

more than one meaning: e.g. if‘healthy’ describes both what produceshealth and what preserves health andwhat betokens health, then ‘healthily’also will be used to mean ‘in such a

way as to produce’ or ‘preserve’ or‘betoken’ health. Likewise also inother cases, whenever the original term

bears more than one meaning, theinflexion also that is formed from 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

see if they are the same in all cases.For if they are not the same, thenclearly the term is ambiguous: e.g.‘good’ in the case of food means‘productive of pleasure’, and in thecase of medicine ‘productive of

health’, whereas as applied to the soulit means to be of a certain quality,e.g. temperate or courageous or just:and likewise also, as applied to ‘man’.Sometimes it signifies what happens ata certain time, as (e.g.) the good thathappens at the right time: for whathappens at the right time is calledgood. Often it signifies what is ofcertain quantity, e.g. as applied tothe proper amount: for the properamount too is called good. So then theterm ‘good’ is ambiguous. In the sameway also ‘clear’, as applied to a body,signifies a colour, but in regard to a

note it denotes what is ‘easy to hear’.‘Sharp’, too, is in a closely similarcase: for the same term does not bearthe same meaning in all itsapplications: for a sharp note is a



swift note, as the mathematicaltheorists of harmony tell us, whereas asharp (acute) angle is one that is lessthan a right angle, while a sharpdagger is one containing a sharp angle(point).

Look also at the genera of the objectsdenoted by the same term, and see ifthey are different without beingsubaltern, as (e.g.) ‘donkey’, which

denotes 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 otherto be an engine of a certain kind. If,however, the genera be subaltern, thereis no necessity for the definitions to

be different. Thus (e.g.) ‘animal’ isthe genus of ‘raven’, and so is ‘bird’.

Whenever therefore we say that theraven is a bird, we also say that it isa certain kind of animal, so that boththe genera are predicated of it.Likewise also whenever we call the

raven a ‘flying biped animal’, wedeclare it to be a bird: in this way,then, as well, both the genera are

predicated of raven, and also theirdefinition. But in the case of genera



that are not subaltern this does nothappen, for whenever we call a thing an‘engine’, we do not call it an animal,nor vice versa.

Look also and see not only if thegenera of the term before you aredifferent without being subaltern, butalso in the case of its contrary: forif its contrary bears several senses,clearly the term before you does so as

well.

It is useful also to look at thedefinition that arises from the use ofthe term in combination, e.g. of a‘clear (lit. white) body’ of a ‘clearnote’. For then if what is peculiar ineach case be abstracted, the sameexpression ought to remain over. Thisdoes not happen in the case ofambiguous terms, e.g. in the cases just

mentioned. For the former will be body possessing such and such a colour’,

while the latter will be ‘a note easyto hear’. Abstract, then, ‘a body ‘and’

a note’, and the remainder in each caseis not the same. It should, however,have been had the meaning of ‘clear’ ineach case been synonymous.



Often in the actual definitions as wellambiguity creeps in unawares, and forthis reason the definitions also should

be examined. If (e.g.) any onedescribes what betokens and what

produces health as ‘relatedcommensurably to health’, we must notdesist but go on to examine in whatsense he has used the term‘commensurably’ in each case, e.g. ifin the latter case it means that ‘it is

of the right amount to produce health’,whereas in the for it means that ‘it issuch as to betoken what kind of state

prevails’.

Moreover, see if the terms cannot becompared as ‘more or less’ or as ‘inlike manner’, as is the case (e.g.)with a ‘clear’ (lit. white) sound and a‘clear’ garment, and a ‘sharp’ flavourand 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 theother. ‘Clear’, then, and ‘sharp’ are

ambiguous. For synonyms are alwayscomparable; for they will always beused either in like manner, or else ina greater degree in one case.



Now since of genera that are differentwithout being subaltern thedifferentiae also are different inkind, e.g. those of ‘animal’ and‘knowledge’ (for the differentiae ofthese are different), look and see ifthe meanings comprised under the sameterm are differentiae of genera thatare different without being subaltern,as e.g. ‘sharp’ is of a ‘note’ and a‘solid’. For being ‘sharp’

differentiates note from note, andlikewise also one solid from another.‘Sharp’, then, is an ambiguous term:for it forms differentiae of generathat are different without beingsubaltern.

Again, see if the actual meaningsincluded under the same term themselveshave different differentiae, e.g.‘colour’ in bodies and ‘colour’ intunes: for the differentiae of ‘colour’in bodies are ‘sight-piercing’ and‘sight compressing’, whereas ‘colour’in melodies has not the same

differentiae. Colour, then, is anambiguous term; for things that are thesame have the same differentiae.



Moreover, since the species is neverthe differentia of anything, look andsee if one of the meanings includedunder 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 caseof a note it is a differentia; for onenote is differentiated from another by

being ‘clear’.

16

The presence, then, of a number of meanings in a term may be investigated by these and like means. The

differences which things present toeach other should be examined withinthe same genera, e.g. ‘Wherein doesjustice differ from courage, and wisdomfrom temperance?’-for all these belongto the same genus; and also from onegenus to another, provided they be notvery much too far apart, e.g. ‘Whereindoes sensation differ from knowledge?:for in the case of genera that are very

far apart, the differences are entirelyobvious.

17



Likeness should be studied, first, inthe case of things belonging todifferent genera, the formulae being‘A:B = C:D’ (e.g. as knowledge standsto the object of knowledge, so issensation related to the object ofsensation), and ‘As A is in B, so is Cin D’ (e.g. as sight is in the eye, sois reason in the soul, and as is a calmin the sea, so is windlessness in theair). Practice is more especially

needed in regard to terms that are farapart; for in the case of the rest, weshall be more easily able to see in oneglance the points of likeness. Weshould also look at things which belongto the same genus, to see if anyidentical attribute belongs to themall, e.g. to a man and a horse and adog; for in so far as they have anyidentical attribute, in so far they arealike.

18

It is useful to have examined the

number of meanings of a term both forclearness’ sake (for a man is morelikely to know what it is he asserts,if it bas been made clear to him how

many meanings it may have), and also



with a view to ensuring that ourreasonings shall be in accordance withthe actual facts and not addressed

merely to the term used. For as long asit is not clear in how many senses aterm is used, it is possible that theanswerer and the questioner are notdirecting their minds upon the samething: whereas when once it has been

made clear how many meanings there are,and also upon which of them the former

directs his mind when he makes hisassertion, the questioner would thenlook ridiculous if he failed to addresshis argument to this. It helps us also

both to avoid being misled and to mislead by false reasoning: for if we

know the number of meanings of a term,we shall certainly never be misled byfalse reasoning, but shall know if thequestioner fails to address hisargument to the same point; and when weourselves put the questions we shall beable to mislead him, if our answererhappens not to know the number of

meanings of our terms. This, however,

is not possible in all cases, but onlywhen of the many senses some are trueand others are false. This manner ofargument, however, does not belong

properly to dialectic; dialecticians



should therefore by all means beware ofthis kind of verbal discussion, unlessany one is absolutely unable to discussthe subject before him in any otherway.

The discovery of the differences ofthings helps us both in reasoningsabout sameness and difference, and alsoin recognizing what any particularthing is. That it helps us in reasoning

about sameness and difference is clear:for when we have discovered adifference of any kind whatever betweenthe objects before us, we shall alreadyhave shown that they are not the same:while it helps us in recognizing what athing is, because we usuallydistinguish the expression that is

proper to the essence of each particular thing by means of the

differentiae that are proper to it.

The examination of likeness is usefulwith a view both to inductive argumentsand to hypothetical reasonings, and

also with a view to the rendering ofdefinitions. It is useful for inductivearguments, because it is by means of aninduction of individuals in cases thatare alike that we claim to bring the



universal in evidence: for it is noteasy to do this if we do not know the

points of likeness. It is useful forhypothetical reasonings because it is ageneral opinion that among similarswhat is true of one is true also of therest. If, then, with regard to any ofthem we are well supplied with matterfor a discussion, we shall secure a

preliminary admission that however itis in these cases, so it is also in the

case before us: then when we have shownthe former we shall have shown, on thestrength of the hypothesis, the matter

before us as well: for we have first made the hypothesis that however it is

in these cases, so it is also in thecase before us, and have then provedthe point as regards these cases. It isuseful for the rendering of definitions

because, if we are able to see in oneglance what is the same in eachindividual case of it, we shall be atno loss into what genus we ought to putthe object before us when we define it:for of the common predicates that which

is most definitely in the category ofessence is likely to be the genus.Likewise, also, in the case of objectswidely divergent, the examination oflikeness is useful for purposes of



definition, e.g. the sameness of a calmat sea, and windlessness in the air(each being a form of rest), and of a

point on a line and the unit in number-each being a starting point. If, then,we render as the genus what is commonto all the cases, we shall get thecredit of defining not inappropriately.Definition-mongers too nearly alwaysrender them in this way: they declarethe unit to be the startingpoint of

number, and the point the startingpointof a line. It is clear, then, that they

place them in that which is common to both as their genus.

The means, then, whereby reasonings areeffected, are these: the commonplacerules, for the observance of which theaforesaid means are useful, are asfollows.

Book II

1

Of problems some are universal, others particular. Universal problems are such

as ‘Every pleasure is good’ and ‘No pleasure is good’; particular problems

are such as ‘Some pleasure is good’ and



‘Some pleasure is not good’. The methods of establishing and

overthrowing a view universally arecommon to both kinds of problems; forwhen we have shown that a predicate

belongs in every case, we shall alsohave shown that it belongs in somecases. Likewise, also, if we show thatit does not belong in any case, weshall also have shown that it does not

belong in every case. First, then, we

must speak of the methods ofoverthrowing a view universally,

because such are common to bothuniversal and particular problems, and

because people more usually introducetheses asserting a predicate thandenying it, while those who argue withthem overthrow it. The conversion of anappropriate name which is drawn fromthe element ‘accident’ is an extremely

precarious thing; for in the case ofaccidents and in no other it is

possible for something to be trueconditionally and not universally.

Names drawn from the elements

‘definition’ and ‘property’ and ‘genus’are bound to be convertible; e.g. if‘to be an animal that walks on two feetis an attribute of S’, then it will betrue by conversion to say that ‘S is an



animal that walks on two feet’.Likewise, also, if drawn from thegenus; for if ‘to be an animal is anattribute of S’, then ‘S is an animal’.The same is true also in the case of a

property; for if ‘to be capable oflearning grammar is an attribute of S’,then ‘S will be capable of learninggrammar’. For none of these attributescan possibly belong or not belong in

part; they must either belong or not

belong absolutely. In the case ofaccidents, on the other hand, there isnothing to prevent an attribute (e.g.whiteness or justice) belonging in

part, so that it is not enough to showthat whiteness or justice is anattribute of a man in order to showthat he is white or just; for it isopen to dispute it and say that he iswhite or just in part only. Conversion,then, is not a necessary process in thecase of accidents.

We must also define the errors thatoccur in problems. They are of two

kinds, caused either by false statementor by transgression of the establisheddiction. For those who make falsestatements, and say that an attribute

belongs to thing which does not belong



to it, commit error; and those who callobjects by the names of other objects(e.g. calling a planetree a ‘man’)transgress the established terminology.

2

Now one commonplace rule is to look andsee if a man has ascribed as anaccident what belongs in some otherway. This mistake is most commonly made

in regard to the genera of things, e.g.if one were to say that white happens(accidit) to be a colour-for being acolour does not happen by accident towhite, but colour is its genus. Theassertor may of course define it so inso many words, saying (e.g.) that‘Justice happens (accidit) to be avirtue’; but often even without suchdefinition it is obvious that he hasrendered the genus as an accident; e.g.suppose that one were to say thatwhiteness is coloured or that walkingis in motion. For a predicate drawnfrom the genus is never ascribed to the

species in an inflected form, butalways the genera are predicated oftheir species literally; for thespecies take on both the name and thedefinition 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 thedefinition and property of a thing

belong to it and to nothing else,whereas many things besides white arecoloured, e.g. a log, a stone, a man,and a horse. Clearly then he renders itas an accident.

Another rule is to examine all caseswhere a predicate has been eitherasserted or denied universally to

belong to something. Look at themspecies by species, and not in theirinfinite multitude: for then theinquiry will proceed more directly andin fewer steps. You should look and

begin with the most primary groups, andthen proceed in order down to thosethat are not further divisible: e.g. ifa man has said that the knowledge ofopposites is the same, you should lookand see whether it be so of relative

opposites and of contraries and ofterms signifying the privation or

presence of certain states, and ofcontradictory terms. Then, if no clearresult be reached so far in these



cases, you should again divide theseuntil you come to those that are notfurther 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 beshown that the knowledge of them is notthe same we shall have demolished the

problem. Likewise, also, if the predicate belongs in no case. This rule

is convertible for both destructive andconstructive purposes: for if, when wehave suggested a division, the

predicate appears to hold in all or ina large number of cases, we may thenclaim that the other should actuallyassert it universally, or else bring anegative instance to show in what caseit is not so: for if he does neither ofthese things, a refusal to assert itwill 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 ifanything untrue has been assumed astrue in the definitions. Thus (e.g.) tosee if it is possible to wrong a god,ask what is ‘to wrong’? For if it be



‘to injure deliberately’, clearly it isnot possible for a god to be wronged:for it is impossible that God should beinjured. Again, to see if the good manis jealous, ask who is the ‘jealous’

man and what is ‘jealousy’. For if‘jealousy’ is pain at the apparentsuccess of some well-behaved person,clearly the good man is not jealous:for then he would be bad. Again, to seeif the indignant man is jealous, ask

who each of them is: for then it will be obvious whether the statement is

true or false; e.g. if he is ‘jealous’who grieves at the successes of thegood, and he is ‘indignant’ who grievesat the successes of the evil, thenclearly the indignant man would not bejealous. A man should substitutedefinitions also for the termscontained in his definitions, and notstop until he comes to a familiar term:for often if the definition be renderedwhole, the point at issue is notcleared up, whereas if for one of theterms used in the definition a

definition be stated, it becomesobvious.

Moreover, a man should make the probleminto a proposition for himself, and



then bring a negative instance againstit: for the negative instance will be aground of attack upon the assertion.This rule is very nearly the same asthe rule to look into cases where a

predicate has been attributed or denieduniversally: but it differs in the turnof the argument.

Moreover, you should define what kindof things should be called as most men

call them, and what should not. Forthis is useful both for establishingand for overthrowing a view: e.g. youshould say that we ought to use ourterms to mean the same things as most

people mean by them, but when we askwhat kind of things are or are not ofsuch and such a kind, we should nothere go with the multitude: e.g. it isright to call ‘healthy’ whatever tendsto produce health, as do most men: butin saying whether the object before ustends to produce health or not, weshould adopt the language no longer ofthe multitude but of the doctor.

3

Moreover, if a term be used in severalsenses, and it has been laid down that



it is or that it is not an attribute ofS, you should show your case of one ofits several senses, if you cannot showit of both. This rule is to be observedin cases where the difference of

meaning is undetected; for supposingthis to be obvious, then the other manwill object that the point which hehimself questioned has not beendiscussed, but only the other point.This commonplace rule is convertible

for purposes both of establishing andof overthrowing a view. For if we wantto establish a statement, we shall showthat in one sense the attribute

belongs, if we cannot show it of bothsenses: whereas if we are overthrowinga statement, we shall show that in onesense the attribute does not belong, ifwe cannot show it of both senses. Ofcourse, in overthrowing a statementthere is no need to start thediscussion by securing any admission,either when the statement asserts orwhen it denies the attributeuniversally: for if we show that in any

case whatever the attribute does not belong, we shall have demolished the

universal assertion of it, and likewisealso if we show that it belongs in asingle case, we shall demolish the



universal denial of it. Whereas inestablishing a statement we ought tosecure a preliminary admission that ifit belongs in any case whatever, it

belongs universally, supposing thisclaim to be a plausible one. For it isnot enough to discuss a single instancein order to show that an attribute

belongs universally; e.g. to argue thatif the soul of man be immortal, thenevery soul is immortal, so that a

previous admission must be secured thatif any soul whatever be immortal, thenevery soul is immortal. This is not to

be done in every case, but onlywhenever we are not easily able toquote any single argument applying toall cases in common, as (e.g.) thegeometrician can argue that thetriangle has its angles equal to tworight angles.

If, again, the variety of meanings of aterm be obvious, distinguish how many

meanings it has before proceedingeither to demolish or to establish it:

e.g. supposing ‘the right’ to mean ‘theexpedient’ or ‘the honourable’, youshould try either to establish or todemolish both descriptions of thesubject in question; e.g. by showing



that it is honourable and expedient, orthat it is neither honourable norexpedient. Supposing, however, that itis impossible to show both, you shouldshow the one, adding an indication thatit is true in the one sense and not inthe other. The same rule applies alsowhen the number of senses into which itis divided is more than two.

Again, consider those expressions whose

meanings are many, but differ not byway of ambiguity of a term, but in someother way: e.g. ‘The science of manythings is one’: here ‘many things’ may

mean the end and the means to that end,as (e.g.) medicine is the science bothof producing health and of dieting; orthey may be both of them ends, as thescience of contraries is said to be thesame (for of contraries the one is no

more an end than the other); or againthey may be an essential and anaccidental attribute, as (e.g.) theessential fact that the triangle hasits angles equal to two right angles,

and the accidental fact that theequilateral figure has them so: for itis because of the accident of theequilateral triangle happening to be atriangle that we know that it has its



angles equal to two right angles. If,then, it is not possible in any senseof the term that the science of manythings should be the same, it clearlyis altogether impossible that it should

be so; or, if it is possible in somesense, then clearly it is possible.Distinguish as many meanings as arerequired: e.g. if we want to establisha view, we should bring forward allsuch meanings as admit that view and

should divide them only into those meanings which also are required for

the establishment of our case: whereasif we want to overthrow a view, weshould bring forward all that do notadmit that view, and leave the restaside. We must deal also in these casesas well with any uncertainty about thenumber of meanings involved. Further,that one thing is, or is not, ‘of’another should be established by meansof the same commonplace rules; e.g.that a particular science is of a

particular thing, treated either as anend or as a means to its end, or as

accidentally connected with it; oragain that it is not ‘of’ it in any ofthe aforesaid ways. The same rule holdstrue also of desire and all other termsthat have more than one object. For the



‘desire of X’ may mean the desire of itas an end (e.g. the desire of health)or as a means to an end (e.g. thedesire of being doctored), or as athing desired accidentally, as, in thecase of wine, the sweet-toothed persondesires it not because it is wine but

because it is sweet. For essentially hedesires the sweet, and onlyaccidentally the wine: for if it bedry, he no longer desires it. His

desire for it is therefore accidental.This rule is useful in dealing withrelative terms: for cases of this kindare generally cases of relative terms.

4

Moreover, it is well to alter a terminto one more familiar, e.g. tosubstitute ‘clear’ for ‘exact’ indescribing a conception, and ‘beingfussy’ for ‘being busy’: for when theexpression is made more familiar, thethesis becomes easier to attack. Thiscommonplace rule also is available for

both purposes alike, both forestablishing and for overthrowing aview.



In order to show that contraryattributes belong to the same thing,look at its genus; e.g. if we want toshow that rightness and wrongness are

possible in regard to perception, andto perceive is to judge, while it is

possible to judge rightly or wrongly,then in regard to perception as wellrightness and wrongness must be

possible. In the present instance the proof proceeds from the genus and

relates to the species: for ‘to judge’is the genus of ‘to —perceive’; for the

man who perceives judges in a certainway. But per contra it may proceed fromthe species to the genus: for all theattributes that belong to the species

belong to the genus as well; e.g. ifthere is a bad and a good knowledgethere is also a bad and a gooddisposition: for ‘disposition’ is thegenus of knowledge. Now the formercommonplace argument is fallacious for

purposes of establishing a view, whilethe second is true. For there is nonecessity that all the attributes that

belong to the genus should belong alsoto the species; for ‘animal’ is flyingand quadruped, but not so ‘man’. Allthe attributes, on the other hand, that

belong to the species must of necessity



belong also to the genus; for if ‘man’is good, then animal also is good. Onthe other hand, for purposes ofoverthrowing a view, the formerargument is true while the latter isfallacious; for all the attributeswhich do not belong to the genus do not

belong to the species either; whereasall those that are wanting to thespecies are not of necessity wanting tothe genus.

Since those things of which the genusis predicated must also of necessityhave one of its species predicated ofthem, and since those things that are

possessed of the genus in question, orare described by terms derived fromthat genus, must also of necessity be

possessed of one of its species or bedescribed by terms derived from one ofits 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 the

other sciences; and if any one possesses scientific knowledge or is

described by a term derived from‘science’, then he will also possessgrammatical or musical knowledge or



knowledge of one of the other sciences,or will be described by a term derivedfrom one of them, e.g. as a‘grammarian’ or a ‘musician’)-thereforeif any expression be asserted that isin any way derived from the genus (e.g.that the soul is in motion), look andsee whether it be possible for the soulto 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 with all the other species of motion. For if it be not moved in any

of these ways, clearly it does not moveat all. This commonplace rule is commonfor both purposes, both foroverthrowing and for establishing aview: for if the soul moves with one ofthe species of motion, clearly it does

move; while if it does not move withany of the species of motion, clearlyit does not move.

If you are not well equipped with anargument against the assertion, lookamong the definitions, real or

apparent, of the thing before you, andif one is not enough, draw uponseveral. For it will be easier toattack people when committed to a



definition: for an attack is always more easily made on definitions.

Moreover, look and see in regard to thething in question, what it is whosereality conditions the reality of thething in question, or what it is whosereality necessarily follows if thething in question be real: if you wishto establish a view inquire what thereis on whose reality the reality of the

thing in question will follow (for ifthe former be shown to be real, thenthe thing in question will also have

been shown to be real); while if youwant to overthrow a view, ask what itis that is real if the thing inquestion be real, for if we show thatwhat follows from the thing in questionis unreal, we shall have demolished thething in question.

Moreover, look at the time involved, tosee if there be any discrepancyanywhere: e.g. suppose a man to havestated that what is being nourished of

necessity grows: for animals are alwaysof necessity being nourished, but theydo not always grow. Likewise, also, ifhe has said that knowing isremembering: for the one is concerned



with past time, whereas the other hasto do also with the present and thefuture. For we are said to know things

present and future (e.g. that therewill be an eclipse), whereas it isimpossible to remember anything savewhat is in the past.

5

Moreover, there is the sophistic turn

of argument, whereby we draw ouropponent into the kind of statementagainst which we shall be well suppliedwith lines of argument. This process issometimes a real necessity, sometimesan apparent necessity, sometimesneither an apparent nor a realnecessity. It is really necessarywhenever the answerer has denied anyview that would be useful in attackingthe thesis, and the questionerthereupon addresses his arguments tothe support of this view, and when

moreover the view in question happensto be one of a kind on which he has a

good stock of lines of argument.Likewise, also, it is really necessarywhenever he (the questioner) first, byan induction made by means of the viewlaid down, arrives at a certain



statement and then tries to demolishthat statement: for when once this has

been demolished, the view originallylaid down is demolished as well. It isan apparent necessity, when the pointto which the discussion comes to bedirected appears to be useful, andrelevant to the thesis, without beingreally so; whether it be that the manwho is standing up to the argument hasrefused to concede something, or

whether he (the questioner) has firstreached it by a plausible induction

based upon the thesis and then tries todemolish it. The remaining case is whenthe point to which the discussion comesto be directed is neither really norapparently necessary, and it is theanswerer’s luck to be confuted on a

mere side issue You should beware ofthe last of the aforesaid methods; forit appears to be wholly disconnectedfrom, and foreign to, the art ofdialectic. For this reason, moreover,the answerer should not lose histemper, but assent to those statements

that are of no use in attacking thethesis, adding an indication wheneverhe assents although he does not agreewith the view. For, as a rule, itincreases the confusion of questioners



if, after all propositions of this kindhave been granted them, they can thendraw no conclusion.

Moreover, any one who has made anystatement whatever has in a certainsense made several statements, inasmuchas each statement has a number ofnecessary consequences: e.g. the manwho said ‘X is a man’ has also saidthat it is an animal and that it is

animate and a biped and capable ofacquiring reason and knowledge, so that

by the demolition of any single one ofthese consequences, of whatever kind,the original statement is demolished aswell. But you should beware here too of

making a change to a more difficultsubject: for sometimes the consequence,and sometimes the original thesis, isthe easier to demolish.

6

In regard to subjects which must haveone and one only of two predicates, as

(e.g.) a man must have either a diseaseor health, supposing we are wellsupplied as regards the one for arguingits presence or absence, we shall bewell equipped as regards the remaining



one as well. This rule is convertiblefor both purposes: for when we haveshown that the one attribute belongs,we shall have shown that the remainingone does not belong; while if we showthat the one does not belong, we shallhave shown that the remaining one does

belong. Clearly then the rule is usefulfor both purposes.

Moreover, you may devise a line of

attack by reinterpreting a term in itsliteral meaning, with the implicationthat 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 isstrong; just as also the expression ‘ofa good hope’ may be taken to mean the

man who hopes for good things. Likewisealso ‘well-starred’ may be taken to

mean the man whose star is good, asXenocrates says ‘well-starred is he whohas a noble soul’.’ For a man’s star is

his soul.

Some things occur of necessity, othersusually, others however it may chance;if therefore a necessary event has been



asserted to occur usually, or if ausual event (or, failing such an eventitself, its contrary) has been statedto occur of necessity, it always givesan opportunity for attack. For if anecessary event has been asserted tooccur usually, clearly the speaker hasdenied an attribute to be universalwhich is universal, and so has made a

mistake: and so he has if he hasdeclared the usual attribute to be

necessary: for then he declares it to belong universally when it does not so belong. Likewise also if he has

declared the contrary of what is usualto be necessary. For the contrary of ausual attribute is always acomparatively rare attribute: e.g. if

men are usually bad, they arecomparatively seldom good, so that his

mistake is even worse if he hasdeclared them to be good of necessity.The same is true also if he hasdeclared a mere matter of chance tohappen of necessity or usually; for achance event happens neither of

necessity nor usually. If the thinghappens usually, then even supposinghis statement does not distinguishwhether he meant that it happensusually or that it happens necessarily,



it is open to you to discuss it on theassumption that he meant that ithappens necessarily: e.g. if he hasstated without any distinction thatdisinherited persons are bad, you mayassume in discussing it that he meansthat they are so necessarily.

Moreover, look and see also if he hasstated a thing to be an accident ofitself, taking it to be a different

thing because it has a different name,as Prodicus used to divide pleasuresinto joy and delight and good cheer:for all these are names of the samething, to wit, Pleasure. If then anyone says that joyfulness is anaccidental attribute of cheerfulness,he would be declaring it to be anaccidental attribute of itself.

7

Inasmuch as contraries can be conjoinedwith each other in six ways, and fourof these conjunctions constitute a

contrariety, we must grasp the subjectof contraries, in order that it mayhelp us both in demolishing and inestablishing a view. Well then, thatthe modes of conjunction are six is



clear: for either (1) each of thecontrary verbs will be conjoined toeach of the contrary objects; and thisgives two modes: e.g. to do good tofriends and to do evil to enemies, or

per contra to do evil to friends and todo good to enemies. Or else (2) bothverbs may be attached to one object;and this too gives two modes, e.g. todo good to friends and to do evil tofriends, or to do good to enemies and

to do evil to enemies. Or (3) a singleverb may be attached to both objects:and this also gives two modes; e.g. todo good to friends and to do good toenemies, or to do evil to friends andevil to enemies.

The first two then of the aforesaidconjunctions do not constitute anycontrariety; for the doing of good tofriends is not contrary to the doing ofevil to enemies: for both courses aredesirable and belong to the samedisposition. Nor is the doing of evilto friends contrary to the doing of

good to enemies: for both of these areobjectionable and belong to the samedisposition: and one objectionablething is not generally thought to bethe contrary of another, unless the one



be an expression denoting an excess,and the other an expression denoting adefect: for an excess is generallythought to belong to the class ofobjectionable things, and likewise alsoa defect. But the other four allconstitute a contrariety. For to dogood to friends is contrary to thedoing of evil to friends: for it

proceeds from the contrary disposition,and the one is desirable, and the other

objectionable. The case is the samealso in regard to the otherconjunctions: for in each combinationthe one course is desirable, and theother objectionable, and the one

belongs to a reasonable disposition andthe other to a bad. Clearly, then, fromwhat has been said, the same course has

more than one contrary. For the doingof good to friends has as its contrary

both the doing of good to enemies andthe doing of evil to friends. Likewise,if we examine them in the same way, weshall find that the contraries of eachof the others also are two in number.

Select therefore whichever of the twocontraries is useful in attacking thethesis.



Moreover, if the accident of a thinghave a contrary, see whether it belongsto the subject to which the accident inquestion has been declared to belong:for if the latter belongs the formercould not belong; for it is impossiblethat contrary predicates should belongat the same time to the same thing.

Or again, look and see if anything has been said about something, of such a

kind that if it be true, contrary predicates must necessarily belong to

the thing: e.g. if he has said that the‘Ideas’ exist in us. For then theresult will be that they are both in

motion and at rest, and moreover thatthey are objects both of sensation andof thought. For according to the viewsof those who posit the existence ofIdeas, those Ideas are at rest and areobjects of thought; while if they existin us, it is impossible that theyshould be unmoved: for when we move, itfollows necessarily that all that is inus moves with us as well. Clearly also

they are objects of sensation, if theyexist in us: for it is through thesensation of sight that we recognizethe Form present in each individual.



Again, if there be posited an accidentwhich has a contrary, look and see ifthat which admits of the accident willadmit of its contrary as well: for thesame thing admits of contraries. Thus(e.g.) if he has asserted that hatredfollows anger, hatred would in thatcase be in the ‘spirited faculty’: forthat is where anger is. You shouldtherefore look and see if its contrary,to wit, friendship, be also in the

‘spirited faculty’: for if not-iffriendship is in the faculty of desire-then hatred could not follow anger.Likewise also if he has asserted thatthe faculty of desire is ignorant. Forif it were capable of ignorance, itwould be capable of knowledge as well:and this is not generally held-I meanthat the faculty of desire is capableof knowledge. For purposes, then, ofoverthrowing a view, as has been said,this rule should be observed: but for

purposes of establishing one, thoughthe rule will not help you to assertthat the accident actually belongs, it

will help you to assert that it may possibly belong. For having shown that

the thing in question will not admit ofthe contrary of the accident asserted,we shall have shown that the accident



neither belongs nor can possibly belong; while on the other hand, if we

show that the contrary belongs, or thatthe thing is capable of the contrary,we shall not indeed as yet have shownthat the accident asserted does belongas well; our proof will merely havegone to this point, that it is possiblefor it to belong.

8

Seeing that the modes of opposition arefour in number, you should look forarguments among the contradictories ofyour terms, converting the order oftheir sequence, both when demolishingand when establishing a view, and youshould secure them by means ofinduction-such arguments (e.g.) as that

man be an animal, what is not an animalis not a man’: and likewise also inother instances of contradictories. Forin those cases the sequence isconverse: for ‘animal’ follows upon‘man but ‘not-animal’ does not follow

upon ‘not-man’, but conversely ‘not- man’ upon ‘not-animal’. In all cases,

therefore, a postulate of this sortshould be made, (e.g.) that ‘If thehonourable is pleasant, what is not



pleasant is not honourable, while ifthe latter be untrue, so is theformer’. Likewise, also, ‘If what isnot pleasant be not honourable, thenwhat is honourable is pleasant’.Clearly, then, the conversion of thesequence formed by contradiction of theterms of the thesis is a methodconvertible for both purposes.

Then look also at the case of the

contraries of S and P in the thesis,and see if the contrary of the onefollows upon the contrary of the other,either directly or conversely, bothwhen you are demolishing and when youare establishing a view: securearguments of this kind as well by meansof induction, so far as may berequired. Now the sequence is direct ina case such as that of courage andcowardice: for upon the one of themvirtue follows, and vice upon theother; and upon the one it follows thatit is desirable, while upon the otherit follows that it is objectionable.

The sequence, therefore, in the lattercase also is direct; for the desirableis the contrary of the objectionable.Likewise also in other cases. Thesequence is, on the other hand,



converse in such a case as this: Healthfollows upon vigour, but disease doesnot follow upon debility; ratherdebility follows upon disease. In thiscase, then, clearly the sequence isconverse. Converse sequence is,however, rare in the case ofcontraries; usually the sequence isdirect. If, therefore, the contrary ofthe one term does not follow upon thecontrary of the other either directly

or conversely, clearly neither does theone term follow upon the other in thestatement made: whereas if the onefollowed the other in the case of thecontraries, it must of necessity do soas well in the original statement.

You should look also into cases of the privation or presence of a state in

like manner to the case of contraries.Only, in the case of such privationsthe converse sequence does not occur:the sequence is always bound to bedirect: e.g. as sensation followssight, while absence of sensation

follows blindness. For the oppositionof sensation to absence of sensation isan opposition of the presence to the

privation of a state: for the one of



them is a state, and the other the privation of it.

The case of relative terms should also be studied in like manner to that of a

state and its privation: for thesequence of these as well is direct;e.g. if 3/1 is a multiple, then 1/3 isa fraction: for 3/1 is relative to 1/3,and so is a multiple to a fraction.

Again, if knowledge be a conceiving,

then also the object of knowledge is anobject of conception; and if sight be asensation, then also the object ofsight is an object of sensation. Anobjection may be made that there is nonecessity for the sequence to take

place, in the case of relative terms,in the way described: for the object ofsensation is an object of knowledge,whereas sensation is not knowledge. Theobjection is, however, not generallyreceived as really true; for many

people deny that there is knowledge ofobjects of sensation. Moreover, the

principle stated is just as useful for

the contrary purpose, e.g. to show thatthe object of sensation is not anobject of knowledge, on the ground thatneither is sensation knowledge.



9

Again look at the case of the co-ordinates and inflected forms of theterms in the thesis, both indemolishing and in establishing it. Byco-ordinates’ are meant terms such asthe following: ‘Just deeds’ and the‘just man’ are coordinates of‘justice’, and ‘courageous deeds’ andthe ‘courageous man’ are co-ordinates

of courage. Likewise also things thattend to produce and to preserveanything are called co-ordinates ofthat which they tend to produce and to

preserve, as e.g. ‘healthy habits’ areco-ordinates of ‘health’ and a‘vigorous constitutional’ of a‘vigorous constitution’ and so forthalso in other cases. ‘Co-ordinate’,then, usually describes cases such asthese, whereas ‘inflected forms’ aresuch as the following: ‘justly’,‘courageously’, ‘healthily’, and suchas are formed in this way. It isusually held that words when used in

their inflected forms as well are co-ordinates, as (e.g.) ‘justly’ inrelation 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 itskind, of the same kindred series isshown to be good or praiseworthy, thenall the rest as well come to be shownto be so: e.g. if ‘justice’ besomething praiseworthy, then so will‘just’, of a man or thing, and ‘justly’connote something praiseworthy. Then‘justly’ will be rendered also

‘praiseworthily’, derived will by thesame inflexion from ‘the praiseworthy’whereby ‘justly’ is derived from‘justice’.

Look not only in the case of thesubject mentioned, but also in the caseof its contrary, for the contrary

predicate: e.g. argue that good is notnecessarily pleasant; for neither isevil painful: or that, if the latter bethe case, so is the former. Also, ifjustice be knowledge, then injustice isignorance: and if ‘justly’ means‘knowingly’ and ‘skilfully’, then

‘unjustly’ means ‘ignorantly’ and‘unskilfully’: whereas if the latter benot true, neither is the former, as inthe instance given just now: for‘unjustly’ is more likely to seem



equivalent to ‘skilfully’ than to‘unskilfully’. This commonplace rulehas been stated before in dealing withthe sequence of contraries; for all weare claiming now is that the contraryof P shall follow the contrary of S.

Moreover, look at the modes ofgeneration and destruction of a thing,and at the things which tend to produceor to destroy it, both in demolishing

and in establishing a view. For thosethings whose modes of generation rankamong good things, are themselves alsogood; and if they themselves be good,so also are their modes of generation.If, on the other hand, their modes ofgeneration be evil, then theythemselves also are evil. In regard to

modes of destruction the converse istrue: for if the modes of destructionrank as good things, then theythemselves rank as evil things; whereasif the modes of destruction count asevil, they themselves count as good.The same argument applies also to

things tending to produce and destroy:for things whose productive causes aregood, themselves also rank as good;whereas if causes destructive of themare good, they themselves rank as evil.



10

Again, look at things which are likethe subject in question, and see ifthey are in like case; e.g. if one

branch of knowledge has more than oneobject, so also will one opinion; andif to possess sight be to see, thenalso to possess hearing will be tohear. Likewise also in the case of

other things, both those which are andthose which are generally held to belike. The rule in question is usefulfor both purposes; for if it be asstated in the case of some one likething, it is so with the other likethings as well, whereas if it be not soin the case of some one of them,neither is it so in the case of theothers. Look and see also whether thecases are alike as regards a singlething and a number of things: forsometimes there is a discrepancy. Thus,if to ‘know’ a thing be to ‘think of’it, then also to ‘know many things’ is

to ‘be thinking of many things’;whereas this is not true; for it is

possible to know many things but not to be thinking of them. If, then, the

latter proposition be not true, neither



was the former that dealt with a singlething, viz. that to ‘know’ a thing isto ‘think of’ it.

Moreover, argue from greater and lessdegrees. In regard to greater degreesthere are four commonplace rules. Oneis: See whether a greater degree of the

predicate follows a greater degree ofthe subject: e.g. if pleasure be good,see whether also a greater pleasure be

a greater good: and if to do a wrong beevil, see whether also to do a greaterwrong is a greater evil. Now this ruleis of use for both purposes: for if anincrease of the accident follows anincrease of the subject, as we havesaid, clearly the accident belongs;while if it does not follow, theaccident does not belong. You shouldestablish this by induction. Anotherrule is: If one predicate be attributedto two subjects; then supposing it doesnot belong to the subject to which itis the more likely to belong, neitherdoes it belong where it is less likely

to belong; while if it does belongwhere it is less likely to belong, thenit belongs as well where it is morelikely. Again: If two predicates beattributed to one subject, then if the



one which is more generally thought to belong does not belong, neither does

the one that is less generally thoughtto 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 theone which is more usually thought to

belong to the one subject does not belong, neither does the remaining

predicate belong to the remainingsubject; or, if the one which is lessusually thought to belong to the onesubject does belong, so too does theremaining predicate to the remainingsubject.

Moreover, you can argue from the factthat an attribute belongs, or isgenerally supposed to belong, in a likedegree, in three ways, viz. thosedescribed in the last three rules givenin regard to a greater degree.’ Forsupposing that one predicate belongs,or is supposed to belong, to two

subjects in a like degree, then if itdoes not belong to the one, neitherdoes it belong to the other; while ifit belongs to the one, it belongs tothe remaining one as well. Or,



supposing two predicates to belong in alike degree to the same subject, then,if the one does not belong, neitherdoes the remaining one; while if theone does belong, the remaining one

belongs as well. The case is the samealso if two predicates belong in a likedegree to two subjects; for if the one

predicate does not belong to the onesubject, neither does the remaining

predicate belong to the remaining

subject, while if the one predicatedoes belong to the one subject, theremaining predicate belongs to theremaining subject as well.

11

You can argue, then, from greater orless or like degrees of truth in theaforesaid number of ways. Moreover, youshould argue from the addition of onething to another. If the addition ofone thing to another makes that othergood or white, whereas formerly it wasnot white or good, then the thing added

will be white or good-it will possessthe character it imparts to the wholeas well. Moreover, if an addition ofsomething to a given object intensifiesthe character which it had as given,



then the thing added will itself aswell be of that character. Likewise,also, in the case of other attributes.The rule is not applicable in allcases, but only in those in which theexcess described as an ‘increasedintensity’ is found to take place. Theabove rule is, however, not convertiblefor overthrowing a view. For if thething added does not make the othergood, it is not thereby made clear

whether in itself it may not be good:for the addition of good to evil doesnot necessarily make the whole good,any more than the addition of white to

black makes the whole white.

Again, any predicate of which we canspeak of greater or less degrees

belongs also absolutely: for greater orless degrees of good or of white willnot be attributed to what is not goodor white: for a bad thing will never besaid to have a greater or less degreeof goodness than another, but always of

badness. This rule is not convertible,

either, for the purpose of overthrowinga predication: for several predicatesof which we cannot speak of a greaterdegree belong absolutely: for the term‘man’ is not attributed in greater and



less degrees, but a man is a man forall that.

You should examine in the same way predicates attributed in a given

respect, and at a given time and place:for if the predicate be possible insome respect, it is possible alsoabsolutely. Likewise, also, is what is

predicated at a given time or place:for what is absolutely impossible is

not possible either in any respect orat any place or time. An objection may

be raised that in a given respect people may be good by nature, e.g. they may be generous or temperately

inclined, while absolutely they are notgood by nature, because no one is

prudent by nature. Likewise, also, itis possible for a destructible thing toescape destruction at a given time,whereas it is not possible for it toescape absolutely. In the same way alsoit is a good thing at certain places tofollow see and such a diet, e.g. ininfected areas, though it is not a good

thing absolutely. 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 way also it is in certain



places honourable to sacrifice one’sfather, e.g. among the Triballi,whereas, absolutely, it is nothonourable. Or possibly this mayindicate a relativity not to places butto persons: for it is all the samewherever they may be: for everywhere itwill be held honourable among theTriballi themselves, just because theyare Triballi. Again, at certain timesit is a good thing to take medicines,

e.g. when one is ill, but it is not soabsolutely. Or possibly this again mayindicate a relativity not to a certaintime, but to a certain state of health:for it is all the same whenever itoccurs, if only one be in that state. Athing is ‘absolutely’ so which withoutany addition you are prepared to say ishonourable or the contrary. Thus (e.g.)you will deny that to sacrifice one’sfather is honourable: it is honourableonly to certain persons: it is nottherefore honourable absolutely. On theother hand, to honour the gods you willdeclare to be honourable without adding

anything, because that is honourableabsolutely. So that whatever withoutany addition is generally accounted to

be honourable or dishonourable or



anything else of that kind, will besaid to be so ‘absolutely’.

Book III

1

THE question which is the moredesirable, or the better, of two or

more things, should be examined uponthe following lines: only first of all

it must be clearly laid down that theinquiry we are making concerns notthings that are widely divergent andthat exhibit great differences from oneanother (for nobody raises any doubtwhether happiness or wealth is moredesirable), but things that are nearlyrelated and about which we commonlydiscuss for which of the two we oughtrather to vote, because we do not seeany advantage on either side ascompared with the other. Clearly, insuch cases if we can show a singleadvantage, or more than one, ourjudgement will record our assent that

whichever side happens to have theadvantage is the more desirable.

First, then, that which is more lastingor secure is more desirable than that



which is less so: and so is that whichis more likely to be chosen by the

prudent or by the good man or by theright law, or by men who are good inany particular line, when they maketheir choice as such, or by the expertsin regard to any particular class ofthings; i.e. either whatever most ofthem or what all of them would choose;e.g. in medicine or in carpentry thosethings are more desirable which most,

or all, doctors would choose; or, ingeneral, whatever most men or all menor all things would choose, e.g. thegood: for everything aims at the good.You should direct the argument youintend to employ to whatever purposeyou require. Of what is ‘better’ or‘more desirable’ the absolute standardis the verdict of the better science,though relatively to a given individualthe standard may be his own particularscience.

In the second place, that which isknown as ‘an x’ is more desirable than

that which does not come within thegenus ‘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 genusin question is called by the genericname; e.g. a ‘white man’ is not ‘acolour’. Likewise also in other cases.

Also, that which is desired for itselfis more desirable than that which isdesired for something else; e.g. healthis more desirable than gymnastics: forthe former is desired for itself, the

latter for something else. Also, thatwhich is desirable in itself is moredesirable than what is desirable peraccidens; e.g. justice in our friendsthan justice in our enemies: for theformer is desirable in itself, thelatter per accidens: for we desire thatour enemies should be just peraccidens, in order that they may do usno harm. This last principle is thesame as the one that precedes it, with,however, a different turn ofexpression. For we desire justice inour friends for itself, even though itwill make no difference to us, and even

though they be in India; whereas in ourenemies we desire it for somethingelse, in order that they may do us noharm.



Also, that which is in itself the causeof good is more desirable than what isso per accidens, e.g. virtue than luck(for the former in itself, and thelatter per accidens, the cause of goodthings), and so in other cases of thesame kind. Likewise also in the case ofthe contrary; for what is in itself thecause of evil is more objectionablethan what is so per accidens, e.g. viceand chance: for the one is bad in

itself, whereas chance is so peraccidens.

Also, what is good absolutely is moredesirable than what is good for a

particular person, e.g. recovery ofhealth than a surgical operation; forthe former is good absolutely, thelatter only for a particular person,viz. the man who needs an operation. Sotoo what is good by nature is moredesirable 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 acquired. Also the attribute is moredesirable which belongs to the betterand more honourable subject, e.g. to agod rather than to a man, and to thesoul rather than to the body. So too



the property of the better thing is better than the 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 theydo not differ at all from each other,in respect of their properties the onesurpasses the other. Also that is

better which is inherent in things better or prior or more honourable:

thus (e.g.) health is better than

strength and beauty: for the former isinherent in the moist and the dry, andthe hot and the cold, in fact in allthe primary constituents of an animal,whereas the others are inherent in whatis secondary, strength being a featureof the sinews and bones, while beautyis generally supposed to consist in acertain symmetry of the limbs. Also theend is generally supposed to be moredesirable than the means, and of two

means, that which lies nearer the end.In general, too, a means directedtowards the end of life is moredesirable than a means to anything

else, e.g. that which contributes tohappiness than that which contributesto prudence. Also the competent is moredesirable than the incompetent.

Moreover, of two productive agents that



one is more desirable whose end is better; while between a productive

agent and an end we can decide by a proportional sum whenever the excess of

the one end over the other is greaterthan that of the latter over its own

productive means: e.g. supposing theexcess of happiness over health to begreater than that of health over what

produces health, then what produceshappiness is better than health. For

what produces happiness exceeds what produces health just as much as

happiness exceeds health. But healthexceeds what produces health by asmaller amount; ergo, the excess ofwhat produces happiness over what

produces health is greater than that ofhealth over what produces health.Clearly, therefore, what produceshappiness is more desirable thanhealth: for it exceeds the samestandard by a greater amount. Moreover,what is in itself nobler and more

precious and praiseworthy is moredesirable than what is less so, e.g.

friendship than wealth, and justicethan strength. For the former belong inthemselves to the class of things

precious and praiseworthy, while thelatter do so not in themselves but for



something else: for no one prizeswealth for itself but always forsomething else, whereas we prizefriendship for itself, even thoughnothing else is likely to come to usfrom it.

2

Moreover, whenever two things are very much like one another, and we cannot

see any superiority in the one over theother of them, we should look at themfrom the standpoint of theirconsequences. For the one which isfollowed by the greater good is the

more desirable: or, if the consequences be evil, that is more desirable which

is followed by the less evil. Forthough both may be desirable, yet there

may possibly be some unpleasantconsequence 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 before 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 goodthings is more desirable than asmaller, either absolutely or when theone is included in the other, viz. thesmaller number in the greater. Anobjection may be raised suppose in some

particular case the one is valued forthe sake of the other; for then the two

together are not more desirable thanthe one; e.g. recovery of health andhealth, than health alone, inasmuch aswe desire recovery of health for thesake of health. Also it is quite

possible for what is not good, togetherwith what is, to be more desirable thana greater number of good things, e.g.the combination of happiness andsomething else which is not good may be

more desirable than the combination ofjustice and courage. Also, the samethings are more valuable if accompaniedthan if unaccompanied by pleasure, andlikewise when free from pain than when

attended with pain.

Also, everything is more desirable atthe season when it is of greaterconsequence; e.g. freedom from pain in



old age more than in youth: for it isof greater consequence in old age. Onthe same principle also, prudence is

more desirable in old age; for no manchooses the young to guide him, becausehe does not expect them to be prudent.

With courage, the converse is the case,for it is in youth that the activeexercise of courage is moreimperatively required. Likewise alsowith temperance; for the young are more

troubled by their passions than aretheir elders.

Also, that is more desirable which is more useful at every season or at most

seasons, e.g. justice and temperancerather than courage: for they arealways useful, while courage is onlyuseful at times. Also, that one of twothings which if all possess, we do notneed the other thing, is more desirablethan that which all may possess andstill we want the other one as well.Take the case of justice and courage;if everybody were just, there would be

no use for courage, whereas all might be courageous, and still justice would be of use.



Moreover, judge by the destructions andlosses and generations and acquisitionsand contraries of things: for thingswhose destruction is more objectionableare themselves more desirable. Likewisealso with the losses and contraries ofthings; for a thing whose loss or whosecontrary is more objectionable isitself more desirable. With thegenerations or acquisitions of thingsthe opposite is the case: for things

whose acquisition or generation is moredesirable are themselves alsodesirable. Another commonplace rule isthat 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 just man. Also, that which is more like than

another thing to something better thanitself, as e.g. some say that Ajax wasa better man than Odysseus because hewas more like Achilles. An objection

may be raised to this that it is nottrue: for it is quite possible that

Ajax did not resemble Achilles more

nearly than Odysseus in the pointswhich 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 a monkey to a man, whereas a horse bears

none: for the monkey is not the morehandsome creature, despite its nearerresemblance to a man. Again, in thecase of two things, if one is more likethe better thing while another is morelike the worse, then that is likely to

be better which is more like the better. This too, however, admits of an

objection: for quite possibly the one

only slightly resembles the better,while the other strongly resembles theworse, e.g. supposing the resemblanceof Ajax to Achilles to be slight, whilethat of Odysseus to Nestor is strong.

Also it may be that the one which islike the better type shows a degradinglikeness, whereas the one which is likethe worse type improves upon it:witness the likeness of a horse to adonkey, and that of a monkey to a man.

Another rule is that the moreconspicuous good is more desirable thanthe less conspicuous, and the more

difficult than the easier: for weappreciate better the possession ofthings that cannot be easily acquired.

Also the more personal possession is more desirable than the more widely



shared. Also, that which is more freefrom connexion with evil: for what isnot attended by any unpleasantness is

more desirable than what is soattended.

Moreover, if A be without qualification better than B, then also the best of

the members of A is better than the best of the members of B; e.g. if Man be 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 betterthan B without qualification; e.g. ifthe best man be better than the besthorse, then also Man is better thanHorse without qualification.

Moreover, things which our friends canshare are more desirable than thosethey cannot. Also, things which we likerather to do to our friend are moredesirable than those we like to do tothe man in the street, e.g. justdealing and the doing of good rather

than the semblance of them: for wewould rather really do good to ourfriends than seem to do so, whereastowards the man in the street theconverse 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 isa superfluity, whereas mere life itselfis a necessity. Sometimes, though, whatis better is not also more desirable:for there is no necessity that becauseit is better it should also be moredesirable: at least to be a philosopher

is better than to make money, but it isnot more desirable for a man who lacksthe necessities of life. The expression‘superfluity’ applies whenever a man

possesses the necessities of life andsets to work to secure as well othernoble acquisitions. Roughly speaking,

perhaps, necessities are moredesirable, while superfluities are

better.

Also, what cannot be got from anotheris more desirable than what can be gotfrom another as well, as (e.g.) is thecase of justice compared with courage.

Also, A is more desirable if A isdesirable without B, but not B without

A: power (e.g.) is not desirablewithout prudence, but prudence isdesirable without power. Also, if of



two things we repudiate the one inorder to be thought to possess theother, then that one is more desirablewhich we wish to be thought to possess;thus (e.g.) we repudiate the love ofhard work in order that people maythink us geniuses.

Moreover, that is more desirable inwhose absence it is less blameworthyfor people to be vexed; and that is

more desirable in whose absence it is more blameworthy for a man not to be

vexed.

3

Moreover, of things that belong to thesame species one which possesses the

peculiar virtue of the species is moredesirable than one which does not. If

both possess it, then the one which possesses it in a greater degree is more desirable.

Moreover, if one thing makes good

whatever it touches, while another doesnot, the former is more desirable, justas also what makes things warm iswarmer than what does not. If both doso, then that one is more desirable



which does so in a greater degree, orif it render good the better and moreimportant object-if (e.g.), the one

makes good the soul, and the other the body.

Moreover, judge things by theirinflexions and uses and actions andworks, and judge these by them: forthey go with each other: e.g. if‘justly’ means something more desirable

than ‘courageously’, then also justice means something more desirable than

courage; and if justice be moredesirable than courage, then also‘justly’ means something more desirablethan ‘courageously’. Similarly also inthe other cases.

Moreover, if one thing exceeds whilethe other falls short of the samestandard of good, the one which exceedsis the more desirable; or if the oneexceeds an even higher standard. Nay

more, if there be two things both preferable to something, the one which

is more highly preferable to it is moredesirable than the less highly

preferable. Moreover, when the excessof a thing is more desirable than theexcess of something else, that thing is



itself also more desirable than theother, as (e.g.) friendship than money:for an excess of friendship is moredesirable than an excess of money. Soalso that of which a man would ratherthat it were his by his own doing is

more desirable than what he wouldrather get by another’s doing, e.g.friends than money. Moreover, judge by

means of an addition, and see if theaddition of A to the same thing as B

makes the whole more desirable thandoes the addition of B. You must,however, beware of adducing a case inwhich the common term uses, or in someother way helps the case of, one of thethings added to it, but not the other,as (e.g.) if you took a saw and asickle in combination with the art ofcarpentry: for in the combination thesaw is a more desirable thing, but itis not a more desirable thing withoutqualification. Again, a thing is moredesirable if, when added to a lessergood, it makes the whole greater good.Likewise, also, you should judge by

means of subtraction: for the thingupon whose subtraction the remainder isa lesser good may be taken to be agreater good, whichever it be whose



subtraction makes the remainder alesser good.

Also, if one thing be desirable foritself, and the other for the look ofit, the former is more desirable, as(e.g.) health than beauty. A thing isdefined as being desired for the lookof it if, supposing no one knew of it,you would not care to have it. Also, itis more desirable both for itself and

for the look of it, while the otherthing is desirable on the one groundalone. Also, whichever is the more

precious for itself, is also better and more desirable. A thing may be taken to be more precious in itself which we

choose rather for itself, withoutanything else being likely to come ofit.

Moreover, you should distinguish in how many senses ‘desirable’ is used, and

with a view to what ends, e.g.expediency or honour or pleasure. Forwhat is useful for all or most of them

may be taken to be more desirable thanwhat is not useful in like manner. Ifthe same characters belong to boththings you should look and see which

possesses them more markedly, i.e.



which of the two is the more pleasantor more honourable or more expedient.

Again, that is more desirable whichserves the better purpose, e.g. thatwhich serves to promote virtue morethan that which serves to promote

pleasure. Likewise also in the case ofobjectionable things; for that is moreobjectionable which stands more in theway of what is desirable, e.g. disease

more than ugliness: for disease is a

greater hindrance both to pleasure andto being good.

Moreover, argue by showing that thething in question is in like measureobjectionable and desirable: for athing of such a character that a man

might well desire and object to italike is less desirable than the otherwhich is desirable only.

4

Comparisons of things together shouldtherefore be conducted in the manner

prescribed. The same commonplace rulesare useful also for showing thatanything is simply desirable orobjectionable: for we have only tosubtract the excess of one thing over



another. For if what is more precious be more desirable, then also what is precious is desirable; and if what is more useful be more desirable, then

also what is useful is desirable.Likewise, also, in the case of otherthings which admit of comparisons ofthat kind. For in some cases in thevery course of comparing the thingstogether we at once assert also thateach of them, or the one of them, is

desirable, e.g. whenever we call theone good ‘by nature’ and the other ‘not

by nature’: for dearly what is good bynature is desirable.

5

The commonplace rules relating tocomparative degrees and amounts oughtto be taken in the most general

possible form: for when so taken theyare likely to be useful in a largernumber of instances. It is possible torender some of the actual rules givenabove more universal by a slight

alteration of the expression, e.g. thatwhat by nature exhibits such and such aquality exhibits that quality in agreater degree than what exhibits itnot by nature. Also, if one thing does,



and another does not, impart such andsuch a quality to that which possessesit, or to which it belongs, thenwhichever does impart it is of thatquality in greater degree than the onewhich does not impart it; and if bothimpart it, then that one exhibits it ina greater degree which imparts it in agreater degree.

Moreover, if in any character one thing

exceeds and another falls short of thesame standard; also, if the one exceedssomething which exceeds a givenstandard, while the other does notreach that standard, then clearly thefirst-named thing exhibits thatcharacter in a greater degree.

Moreover, you should judge by means ofaddition, and see if A when added tothe same thing as B imparts to thewhole such and such a character in a

more marked degree than B, or if, whenadded to a thing which exhibits thatcharacter in a less degree, it impartsthat character to the whole in a

greater degree. Likewise, also, you mayjudge by means of subtraction: for athing upon whose subtraction theremainder exhibits such and such acharacter in a less degree, itself



exhibits that character in a greaterdegree. Also, things exhibit such andsuch a character in a greater degree if

more free from admixture with theircontraries; e.g. that is whiter whichis more free from admixture with black.

Moreover, apart from the rules givenabove, that has such and such acharacter in greater degree whichadmits in a greater degree of thedefinition proper to the given

character; e.g. if the definition of‘white’ be ‘a colour which pierces thevision’, then that is whiter which isin a greater degree a colour that

pierces the vision.

6

If the question be put in a particularand not in a universal form, in thefirst place the universal constructiveor destructive commonplace rules thathave been given may all be brought intouse. For in demolishing or establishinga thing universally we also show it in

particular: for if it be true of all,it is true also of some, and if untrueof all, it is untrue of some.Especially handy and of generalapplication are the commonplace rules



that are drawn from the opposites andco-ordinates and inflexions of a thing:for public opinion grants alike theclaim that if all pleasure be good,then also all pain is evil, and theclaim that if some pleasure be good,then also some pain is evil. Moreover,if some form of sensation be not acapacity, then also some form offailure of sensation is not a failureof capacity. Also, if the object of

conception is in some cases an objectof knowledge, then also some form ofconceiving is knowledge. Again, if whatis unjust be in some cases good, thenalso what is just is in some casesevil; and if what happens justly is insome cases evil, then also what happensunjustly is in some cases good. Also,if what is pleasant is in some casesobjectionable, then pleasure is in somecases an objectionable thing. On thesame principle, also, if what is

pleasant is in some cases beneficial,then pleasure is in some cases a

beneficial thing. The case is the same

also as regards the things thatdestroy, and the processes ofgeneration and destruction. For ifanything that destroys pleasure orknowledge be in some cases good, then



we may take it that pleasure orknowledge is in some cases an evilthing. Likewise, also, if thedestruction of knowledge be in somecases a good thing or its production anevil thing, then knowledge will be insome cases an evil thing; e.g. if for a

man to forget his disgraceful conduct be a good thing, and to remember it be

an evil thing, then the knowledge ofhis disgraceful conduct may be taken to

be an evil thing. The same holds alsoin other cases: in all such cases the

premiss and the conclusion are equallylikely to be accepted.

Moreover you should judge by means ofgreater or smaller or like degrees: forif some member of another genus exhibitsuch and such a character in a more

marked degree than your object, whileno member of that genus exhibits thatcharacter at all, then you may take itthat neither does the object inquestion exhibit it; e.g. if some formof knowledge be good in a greater

degree than pleasure, while no form ofknowledge is good, then you may take itthat pleasure is not good either. Also,you should judge by a smaller or likedegree in the same way: for so you will



find it possible both to demolish andto establish a view, except thatwhereas both are possible by means oflike degrees, by means of a smallerdegree it is possible only toestablish, not to overthrow. For if acertain form of capacity be good in alike degree to knowledge, and a certainform of capacity be good, then so alsois knowledge; while if no form ofcapacity be good, then neither is

knowledge. If, too, a certain form ofcapacity be good in a less degree thanknowledge, and a certain form ofcapacity be good, then so also isknowledge; but if no form of capacity

be good, there is no necessity that noform of knowledge either should begood. Clearly, then, it is only

possible to establish a view by meansof a less degree.

Not only by means of another genus canyou overthrow a view, but also by meansof the same, if you take the most

marked instance of the character in

question; e.g. if it be maintained thatsome form of knowledge is good, then,suppose it to be shown that prudence isnot good, neither will any other kind

be good, seeing that not even the kind



upon which there is most generalagreement is so. Moreover, you shouldgo to work by means of an hypothesis;you should claim that the attribute, ifit belongs or does not belong in onecase, does so in a like degree in all,e.g. that if the soul of man beimmortal, so are other souls as well,while if this one be not so, neitherare the others. If, then, it be

maintained that in some instance the

attribute belongs, you must show thatin some instance it does not belong:for then it will follow, by reason ofthe hypothesis, that it does not belongto any instance at all. If, on theother hand, it be maintained that itdoes not belong in some instance, you

must show that it does belong in someinstance, for in this way it willfollow that it belongs to allinstances. It is clear that the makerof the hypothesis universalizes thequestion, whereas it was stated in a

particular form: for he claims that the maker of a particular admission should

make a universal admission, inasmuch ashe claims that if the attribute belongsin one instance, it belongs also in allinstances alike.



If the problem be indefinite, it is possible to overthrow a statement in

only one way; e.g. if a man hasasserted that pleasure is good or isnot good, without any furtherdefinition. For if he meant that a

particular pleasure is good, you mustshow universally that no pleasure isgood, if the proposition in question isto be demolished. And likewise, also,if he meant that some particular

pleasure is not good you must showuniversally that all pleasure is good:it is impossible to demolish it in anyother way. For if we show that some

particular pleasure is not good or isgood, the proposition in question isnot 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 universallythat all pleasure is good, or whetherwe show that a particular pleasure isgood, 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 good orthat a particular pleasure is not good,we shall have produced an argument in



both ways, both universally and in particular, to show that some particular pleasure is not good. If, on

the other hand, the statement made bedefinite, it will be possible todemolish it in two ways; e.g. if it be

maintained that it is an attribute ofsome particular pleasure to be good,while of some 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 onesingle pleasure is good, it is possibleto demolish it in three ways: for byshowing that all pleasure, or that no

pleasure, or that more than one pleasure, is good, we shall have

demolished the statement in question.If the statement be made still moredefinite, e.g. that prudence alone ofthe virtues is knowledge, there arefour ways of demolishing it: for if 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,the proposition in question will have

been demolished.



It is useful also to take a look atindividual instances, in cases wheresome attribute has been said to belongor not to belong, as in the case ofuniversal questions. Moreover, youshould take a glance among genera,dividing them by their species untilyou come to those that are not furtherdivisible, as has been said before:’for whether the attribute is found to

belong in all cases or in none, you

should, after adducing severalinstances, claim that he should eitheradmit your point universally, or else

bring an objection showing in what caseit does not hold. Moreover, in caseswhere it is possible to make theaccident definite either specificallyor numerically, you should look and seewhether perhaps none of them belongs,showing e.g. that time is not moved,nor yet a movement, by enumerating how

many species there are of movement: forif 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 a number, bydividing all numbers into either odd oreven: for then, if the soul be neitherodd nor even, clearly it is not anumber.



In regard then to Accident, you shouldset to work by means like these, and inthis manner.

Book IV

1

NEXT we must go on to examine questionsrelating to Genus and Property. Theseare elements in the questions thatrelate to definitions, butdialecticians seldom address theirinquiries to these by themselves. If,then, a genus be suggested forsomething that is, first take a look atall objects which belong to the samegenus as the thing mentioned, and seewhether the genus suggested is not

predicated of one of them, as happensin the case of an accident: e.g. if‘good’ be laid down to be the genus of

‘pleasure’, see whether some particular pleasure be not good: for, if so,

clearly good’ is not the genus of pleasure: for the genus is predicated

of all the members of the same species.



Secondly, see whether it be predicatednot in the category of essence, but asan accident, as ‘white’ is predicatedof ‘snow’, or ‘self-moved’ of the 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 anaccident of it, as it often is of ananimal to walk or to be walking.

Moreover, ‘moving’ does not seem to

indicate the essence, but rather astate of doing or of having somethingdone to it. Likewise, also, ‘white’:for it indicates not the essence ofsnow, but a certain quality of it. Sothat neither of them is predicated inthe category of ‘essence’.

Especially you should take a look atthe definition of Accident, and seewhether it fits the genus mentioned, as(e.g.) is also the case in theinstances just given. For it is

possible for a thing to be and not to be self-moved, and likewise, also, for

it to be and not to be white. So thatneither of these attributes is thegenus but an accident, since we weresaying that an accident is an attribute



which can belong to a thing and alsonot belong.

Moreover, see whether the genus and thespecies be not found in the samedivision, but the one be a substancewhile the other is a quality, or theone be a relative while the other is aquality, as (e.g.) ‘slow’ and ‘swan’are each a substance, while ‘white’ isnot a substance but a quality, so that

‘white’ is not the genus either of‘snow’ or of ‘swan’. Again, knowledge’is a relative, while ‘good’ and ‘noble’are each a quality, so that good, ornoble, is not the genus of knowledge.For the genera of relatives oughtthemselves also to be relatives, as isthe case with ‘double’: for multiple’,which is the genus of ‘double’, isitself also a relative. To speakgenerally, the genus ought to fallunder the same division as the species:for if the species be a substance, sotoo should be the genus, and if thespecies be a quality, so too the genus

should be a quality; e.g. if white be aquality, so too should colour be.Likewise, also, in other cases.



Again, see whether it be necessary or possible for the genus to partake of

the object which has been placed in thegenus. ‘To partake’ is defined as ‘toadmit the definition of that which is

partaken. Clearly, therefore, thespecies partake of the genera, but notthe genera of the species: for thespecies admits the definition of thegenus, whereas the genus does not admitthat of the species. You must look,

therefore, and see whether the genusrendered partakes or can possibly

partake of the species, e.g. if any onewere to render anything as genus of‘being’ or of ‘unity’: for then theresult will be that the genus partakesof the species: for of everything thatis, ‘being’ and ‘unity’ are predicated,and therefore their definition as well.

Moreover, see if there be anything ofwhich the species rendered is true,while the genus is not so, e.g.supposing ‘being’ or ‘object ofknowledge’ were stated to be the genus

of ‘object of opinion’. For ‘object ofopinion’ will be a predicate of whatdoes not exist; for many things whichdo not exist are objects of opinion;whereas that ‘being’ or ‘object of



knowledge’ is not predicated of whatdoes not exist is clear. So thatneither ‘being’ nor ‘object ofknowledge’ is the genus of ‘object ofopinion’: for of the objects of whichthe species is predicated, the genusought to be predicated as well.

Again, see whether the object placed inthe genus be quite unable to partake ofany of its species: for it is

impossible that it should partake ofthe genus if it do not partake of anyof its species, except it be one of thespecies reached by the first division:these do partake of the genus alone.If, therefore, ‘Motion’ be stated asthe genus of pleasure, you should lookand see if pleasure be neitherlocomotion nor alteration, nor any ofthe rest of the given modes of motion:for clearly you may then take it thatit does not partake of any of thespecies, and therefore not of the genuseither, since what partakes of thegenus must necessarily partake of one

of the species as well: so that pleasure could not be a species of Motion, nor yet be one of the

individual phenomena comprised underthe term ‘motion’. For individuals as



well partake in the genus and thespecies, as (e.g.) an individual man

partakes of both ‘man’ and ‘animal’.

Moreover, see if the term placed in thegenus has a wider denotation than thegenus, as (e.g.) ‘object of opinion’has, as compared with ‘being’: for bothwhat is and what is not are objects ofopinion, so that ‘object of opinion’could not be a species of being: for

the genus is always of wider denotationthan the species. Again, see if thespecies and its genus have an equaldenotation; suppose, for instance, thatof the attributes which go witheverything, one were to be stated as aspecies and the other as its genus, asfor example Being and Unity: foreverything has being and unity, so thatneither is the genus of the other,since their denotation is equal.Likewise, also, if the ‘first’ of aseries and the ‘beginning’ were to be

placed one under the other: for the beginning is first and the first is the

beginning, so that either bothexpressions are identical or at anyrate neither is the genus of the other.The elementary principle in regard toall such cases is that the genus has a



wider denotation than the species andits differentia: for the differentia aswell has a narrower denotation than thegenus.

See also whether the genus mentionedfails, or might be generally thought tofail, to apply to some object which isnot specifically different from thething in question; or, if your argument

be constructive, whether it does so

apply. For all things that are notspecifically different have the samegenus. If, therefore, it be shown toapply to one, then clearly it appliesto all, and if it fails to apply toone, clearly it fails to apply to any;e.g. if any one who assumes‘indivisible lines’ were to say thatthe ‘indivisible’ is their genus. Forthe aforesaid term is not the genus ofdivisible lines, and these do notdiffer as regards their species fromindivisible: for straight lines arenever different from each other asregards their species.

2

Look and see, also, if there be anyother genus of the given species which



neither embraces the genus rendered noryet 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 thesegenera embraces the remaining one, sothat knowledge could not be the genusof justice: for it is generallyaccepted that whenever one speciesfalls under two genera, the one isembraced by the other. Yet a principle

of this kind gives rise to a difficultyin some cases. For some people holdthat prudence is both virtue andknowledge, and that neither of itsgenera is embraced by the other:although certainly not everybody admitsthat prudence is knowledge. If,however, any one were to admit thetruth of this assertion, yet it wouldstill be generally agreed to benecessary that the genera of the sameobject must at any rate be subordinateeither the one to the other or both tothe 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. Youshould look, therefore, and see whetherneither of these things is true of thegenus rendered; for if the genera be



subordinate neither the one to theother nor both to the same, then whatis rendered could not be the truegenus.

Look, also, at the genus of the genusrendered, and so continually at thenext higher genus, and see whether allare predicated of the species, and

predicated in the category of essence:for all the higher genera should be

predicated of the species in thecategory of essence. If, then, there beanywhere a discrepancy, clearly what isrendered is not the true genus. [Again,see whether either the genus itself, orone of its higher genera, partakes ofthe species: for the higher genus doesnot partake of any of the lower.] If,then, you are overthrowing a view,follow the rule as given: ifestablishing one, then-suppose thatwhat has been named as genus beadmitted to belong to the species, onlyit be disputed whether it belongs asgenus-it is enough to show that one of

its higher genera is predicated of thespecies in the category of essence. Forif one of them be predicated in thecategory of essence, all of them, bothhigher and lower than this one, if



predicated at all of the species, will be predicated of it in the category of

essence: so that what has been renderedas genus is also predicated in thecategory of essence. The premiss thatwhen one genus is predicated in thecategory of essence, all the rest, if

predicated at all, will be predicatedin the category of essence, should besecured by induction. Supposing,however, that it be disputed whether

what has been rendered as genus belongsat all, it is not enough to show thatone of the higher genera is predicatedof the species in the category ofessence: e.g. if any one has rendered‘locomotion’ as the genus of walking,it is not enough to show that walkingis ‘motion’ in order to show that it is‘locomotion’, seeing that there areother forms of motion as well; but one

must show in addition that walking doesnot partake of any of the species of

motion produced by the same divisionexcept locomotion. For of necessitywhat partakes of the genus partakes

also of one of the species produced bythe first division of the genus. If,therefore, walking does not partakeeither of increase or decrease or ofthe other kinds of motion, clearly it



would partake of locomotion, so thatlocomotion would be the genus ofwalking.

Again, look among the things of whichthe given species is predicated asgenus, and see if what is rendered asits genus be also predicated in thecategory of essence of the very thingsof which the species is so predicated,and likewise if all the genera higher

than this genus are so predicated aswell. For if there be anywhere adiscrepancy, clearly what has beenrendered is not the true genus: for hadit been the genus, then both the generahigher than it, and it itself, wouldall have been predicated in thecategory of essence of those objects ofwhich the species too is predicated inthe category of essence. If, then, youare overthrowing a view, it is usefulto see whether the genus fails to be

predicated in the category of essenceof those things of which the speciestoo is predicated. If establishing a

view, it is useful to see whether it is 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



category of essence, so that the sameobject falls under two genera: thegenera must therefore of necessity besubordinate one to the other, andtherefore if it be shown that the onewe wish to establish as genus is notsubordinate to the species, clearly thespecies would be subordinate to it, sothat you may take it as shown that itis the genus.

Look, also, at the definitions of thegenera, and see whether they apply bothto the given species and to the objectswhich partake of the species. For ofnecessity the definitions of its genera

must be predicated of the species andof the objects which partake of thespecies: if, then, there be anywhere adiscrepancy, clearly what has beenrendered is not the genus.

Again, see if he has rendered thedifferentia as the genus, e.g.‘immortal’ as the genus of ‘God’. For‘immortal’ is a differentia of ‘living

being’, seeing that of living beingssome are mortal and others immortal.Clearly, then, a bad mistake has been

made; for the differentia of a thing isnever its genus. And that this is true



is clear: for a thing’s differentianever signifies its essence, but rathersome quality, as do ‘walking’ and‘biped’.

Also, see whether he has placed thedifferentia inside the genus, e.g. bytaking ‘odd’ as a number’. For ‘odd’ isa differentia of number, not a species.

Nor is the differentia generallythought to partake of the genus: for

what partakes of the genus is alwayseither a species or an individual,whereas the differentia is neither aspecies nor an individual. Clearly,therefore, the differentia does not

partake of the genus, so that ‘odd’ toois no species but a differentia, seeingthat it does not partake of the genus.

Moreover, see whether he has placed thegenus inside the species, e.g. bytaking ‘contact’ to be a ‘juncture’, or‘mixture’ a ‘fusion’, or, as in Plato’sdefinition,’ ‘locomotion’ to be thesame as ‘carriage’. For there is no

necessity that contact should bejuncture: rather, conversely, juncture

must be contact: for what is in contactis not always joined, though what isjoined is always in contact. Likewise,



also, in the remaining instances: for mixture is not always a ‘fusion’ (for

to mix dry things does not fuse them),nor is locomotion always ‘carriage’.For walking is not generally thought to

be carriage: for ‘carriage’ is mostlyused of things that change one placefor another involuntarily, as happensin the case of inanimate things.Clearly, also, the species, in theinstances given, has a wider denotation

than the genus, whereas it ought to bevice versa.

Again, see whether he has placed thedifferentia inside the species, bytaking (e.g.) ‘immortal’ to be ‘a god’.For the result will be that the specieshas an equal or wider denotation: andthis cannot be, for always thedifferentia has an equal or a widerdenotation than the species. Moreover,see whether he has placed the genusinside the differentia, by making‘colour’ (e.g.) to be a thing that‘pierces’, or ‘number’ a thing that is

‘odd’. Also, see if he has mentionedthe genus as differentia: for it is

possible for a man to bring forward astatement of this kind as well, e.g.that ‘mixture’ is the differentia of



‘fusion’, or that change of place’ isthe differentia of ‘carriage’. All suchcases should be examined by means ofthe same principles: for they dependupon common rules: for the genus shouldhave a wider denotation that itsdifferentia, and also should not

partake of its differentia; whereas, ifit be rendered in this manner, neitherof the aforesaid requirements can besatisfied: for the genus will both have

a narrower denotation than itsdifferentia, and will partake of it.

Again, if no differentia belonging tothe 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, see whether the species isnaturally prior and abolishes the genusalong with itself: for the contrary isthe general view. Moreover, if it be

possible for the genus stated, or forits differentia, to be absent from the

alleged species, e.g. for ‘movement’ to be absent from the ‘soul’, or ‘truth

and falsehood’ from ‘opinion’, thenneither of the terms stated could beits genus or its differentia: for the



general view is that the genus and thedifferentia accompany the species, aslong as it exists.

3

Look and see, also, if what is placedin the genus partakes or could possibly

partake of any contrary of the genus:for in that case the same thing will atthe same time partake of contrary

things, seeing that the genus is neverabsent from it, while it partakes, orcan possibly partake, of the contrarygenus as well. Moreover, see whetherthe 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 numberto live, then the soul could not be aspecies of number.

You should look and see, also, if thespecies be a homonym of the genus, andemploy as your elementary principles

those already stated for dealing withhomonymity: for the genus and thespecies are synonymous.



Seeing that of every genus there is more than one species, look and see if

it be impossible that there should beanother species than the given one

belonging to the genus stated: for ifthere should be none, then clearly whathas been stated could not be a genus atall.

Look and see, also, if he has renderedas genus a metaphorical expression,

describing (e.g. ‘temperance’ as a‘harmony’: a ‘harmony’: for a genus isalways predicated of its species in itsliteral sense, whereas ‘harmony’ is

predicated of temperance not in aliteral sense but metaphorically: for aharmony always consists in notes.

Moreover, if there be any contrary ofthe species, examine it. Theexamination may take different forms;first of all see if the contrary aswell be found in the same genus as thespecies, supposing the genus to have nocontrary; for contraries ought to be

found in the same genus, if there be nocontrary to the genus. Supposing, onthe other hand, that there is acontrary to the genus, see if thecontrary of the species be found in the



contrary genus: for of necessity thecontrary species must be in thecontrary genus, if there be anycontrary to the genus. Each of these

points is made plain by means ofinduction. Again, see whether thecontrary of the species be not found inany genus at all, but be itself agenus, e.g. ‘good’: for if this be notfound in any genus, neither will itscontrary be found in any genus, but

will itself be a genus, as happens inthe case of ‘good’ and ‘evil’: forneither of these is found in a genus,

but each of them is a genus. Moreover,see if both genus and species becontrary to something, and one pair ofcontraries have an intermediary, butnot the other. For if the genera havean intermediary, so should theirspecies as well, and if the specieshave, so should their genera as well,as is the case with (1) virtue and viceand (2) justice and injustice: for each

pair has an intermediary. An objectionto this is that there is no

intermediary between health anddisease, although there is one betweenevil and good. Or see whether, thoughthere be indeed an intermediary between

both pairs, i.e. both between the



species and between the genera, yet it be not similarly related, but in one

case be a mere negation of theextremes, whereas in the other case itis a subject. For the general view isthat the relation should be similar in

both cases, as it is in the cases ofvirtue and vice and of justice andinjustice: for the intermediaries

between both are mere negations. Moreover, whenever the genus has no

contrary, look and see not merelywhether the contrary of the species befound in the same genus, but theintermediate as well: for the genuscontaining the extremes contains theintermediates as well, as (e.g.) in thecase of white and black: for ‘colour’is the genus both of these and of allthe intermediate colours as well. Anobjection may be raised that ‘defect’and ‘excess’ are found in the samegenus (for both are in the genus‘evil’), whereas moderate amount’, theintermediate between them, is found notin ‘evil’ but in ‘good’. Look and see

also whether, while the genus has acontrary, the species has none; for ifthe genus be contrary to anything, sotoo is the species, as virtue to viceand justice to injustice.



Likewise. also, if one were to look atother instances, one would come to seeclearly a fact like this. An objection

may be raised in the case of health anddisease: for health in general is thecontrary of disease, whereas a

particular disease, being a species ofdisease, e.g. fever and ophthalmia andany other particular disease, has nocontrary.

If, therefore, you are demolishing aview, there are all these ways in whichyou should make your examination: forif the aforesaid characters do not

belong to it, clearly what has beenrendered is not the genus. If, on theother hand, you are establishing aview, there are three ways: in thefirst place, see whether the contraryof the species be found in the genusstated, suppose the genus have nocontrary: for if the contrary be foundin it, clearly the species in questionis found in it as well. Moreover, see

if the intermediate species is found inthe genus stated: for whatever genuscontains the intermediate contains theextremes as well. Again, if the genushave a contrary, look and see whether



also the contrary species is found inthe contrary genus: for if so, clearlyalso the species in question is foundin the genus in question.

Again, consider in the case of theinflexions and the co-ordinates ofspecies and genus, and see whether theyfollow likewise, both in demolishingand in establishing a view. Forwhatever attribute belongs or does not

belong to one belongs or does not belong at the same time to all; e.g. if

justice be a particular form ofknowledge, then also ‘justly’ is‘knowingly’ and the just man is a manof knowledge: whereas if any of thesethings be not so, then neither is anyof the rest of them.

4

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 to the good: for in eachcase the one produces the other. Iftherefore pleasure be a kind of ‘good’,then also the pleasant will be a kindof ‘useful’: for clearly it may be



taken to be productive of good, seeingthat pleasure is good. In the same wayalso consider the case of processes ofgeneration and destruction; if (e.g.)to build be to be active, then to have

built is to have been active, and if tolearn be to recollect, then also tohave learnt is to have recollected, andif to be decomposed be to be destroyed,then to have been decomposed is to have

been destroyed, and decomposition is a

kind of destruction. Consider also inthe same way the case of things thatgenerate or destroy, and of thecapacities and uses of things; and ingeneral, both in demolishing and inestablishing an argument, you shouldexamine things in the light of anyresemblance of whatever description, aswe were saying in the case ofgeneration and destruction. For if whattends to destroy tends to decompose,then also to be destroyed is to bedecomposed: and if what tends togenerate tends to produce, then to begenerated is to be produced, and

generation is production. Likewise,also, in the case of the capacities anduses of things: for if a capacity be adisposition, then also to be capable ofsomething is to be disposed to it, and



if the use of anything be an activity,then to use it is to be active, and tohave used it is to have been active.

If the opposite of the species be a privation, there are two ways of

demolishing an argument, first of all by looking to see if the opposite be

found in the genus rendered: for eitherthe 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 besensation, then blindness will not be asensation. Secondly, if there be asensation. Secondly, if there be a

privation opposed to both genus andspecies, but the opposite of thespecies be not found in the opposite ofthe genus, then neither could thespecies rendered be in the genusrendered. If, then, you are demolishinga view, you should follow the rule asstated; but if establishing one thereis but one way: for if the oppositespecies be found in the opposite genus,

then also the species in question would be found in the genus in question: e.g.

if ‘blindness’ be a form of‘insensibility’, then ‘sight’ is a formof ‘sensation’.



Again, look at the negations of the

genus and species and convert the orderof terms, according to the methoddescribed in the case of Accident: e.g.if the pleasant be a kind of good, whatis not good is not pleasant. For werethis no something not good as wellwould then be pleasant. That, however,cannot be, for it is impossible, if‘good’ be the genus of pleasant, that

anything not good should be pleasant:for of things of which the genus is not

predicated, none of the species is predicated either. Also, in

establishing a view, you should adoptthe same method of examination: for ifwhat is not good be not pleasant, thenwhat is pleasant is good, so that‘good’ is the genus of ‘pleasant’.

If the species be a relative term, seewhether the genus be a relative term aswell: for if the species be a relativeterm, so too is the genus, as is thecase with ‘double’ and ‘multiple’: for

each is a relative term. If, on theother hand, the genus be a relativeterm, there is no necessity that thespecies should be so as well: for‘knowledge’is a relative term, but not



so ‘grammar’. Or possibly not even thefirst statement would be generallyconsidered true: for virtue is a kindof ‘noble’ and a kind of ‘good’ thing,and yet, while ‘virtue’ is a relativeterm, ‘good’ and ‘noble’ are notrelatives but qualities. Again, seewhether the species fails to be used inthe same relation when called by itsown name, and when called by the nameof 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 not be thegenus of ‘double’.

Moreover, see whether the term fail to be used in the same relation both when

called by the name of its genus, andalso when called by those of all thegenera of its genus. For if the double

be a multiple of a half, then ‘inexcess of ‘will also be used inrelation to a ‘half’: and, in general,the double will be called by the names

of all the higher genera in relation toa ‘half’. An objection may be raisedthat there is no necessity for a termto be used in the same relation whencalled by its own name and when called



by that of its genus: for ‘knowledge’is called knowledge ‘of an object’,whereas it is called a ‘state’ and‘disposition’ not of an ‘object’ but ofthe ‘soul’.

Again, see whether the genus and thespecies be used in the same way inrespect of the inflexions they take,e.g. datives and genitives and all therest. For as the species is used, so

should the genus be as well, as in thecase 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 bothknowledge’ itself and its genera, e.g.‘disposition’ and ‘state’, are said to

be ‘of’ something. An objection may beraised that in some cases it is not so:for we say ‘superior to’ and ‘contraryto’ so and so, whereas ‘other’, whichis the genus of these terms, demandsnot ‘to’ but ‘than’: for the expressionis ‘other than’ so and so.

Again, see whether terms used in likecase relationships fail to yield a likeconstruction when converted, as do‘double’ and ‘multiple’. For each ofthese terms takes a genitive both in



itself and in its converted form: forwe say both a half of’ and ‘a fractionof’ something. The case is the samealso as regards both ‘knowledge’ and‘conception’: for these take agenitive, and by conversion an ‘objectof knowledge’ and an ‘object ofconception’ are both alike used with adative. If, then, in any cases theconstructions after conversion be notalike, clearly the one term is not the

genus of the other.

Again, see whether the species and thegenus fail to be used in relation to anequal number of things: for the generalview is that the uses of both are alikeand equal in number, as is the casewith ‘present’ and ‘grant’. For a

present’ is of something or to someone, and also a ‘grant’ is of somethingand to some one: and ‘grant’ is thegenus of ‘present’, for a ‘present’ isa ‘grant that need not be returned’. Insome cases, however, the number ofrelations in which the terms are used

happens not to be equal, for while‘double’ is double of something, wespeak of ‘in excess’ or ‘greater’ insomething, as well as of or thansomething: for what is in excess or



greater is always in excess insomething, as well as in excess ofsomething. Hence the terms in questionare not the genera of ‘double’,inasmuch as they are not used inrelation to an equal number of thingswith the species. Or possibly it is notuniversally true that species and genusare used in relation to an equal numberof things.

See, also, if the opposite of thespecies have the opposite of the genusas its genus, e.g. whether, if‘multiple’ be the genus of ‘double’,‘fraction’ be also the genus of ‘half’.For the opposite of the genus shouldalways be the genus of the oppositespecies. If, then, any one were toassert that knowledge is a kind ofsensation, then also the object ofknowledge will have to be a kind ofobject of sensation, whereas it is not:for an object of knowledge is notalways an object of sensation: forobjects of knowledge include some of

the 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 genusof ‘knowledge’.



Seeing that of relative terms some areof necessity found in, or used of, thethings in relation to which they happenat any time to be used (e.g.‘disposition’ and ‘state’ and‘balance’; for in nothing else can theaforesaid terms possibly be foundexcept in the things in relation towhich they are used), while others neednot be found in the things in relation

to which they are used at any time,though they still may be (e.g. if theterm ‘object of knowledge’ be appliedto the soul: for it is quite possiblethat the knowledge of itself should be

possessed by the soul itself, but it isnot necessary, for it is possible forthis same knowledge to be found in someone else), while for others, again, itis absolutely impossible that theyshould be found in the things inrelation to which they happen at anytime to be used (as e.g. that thecontrary should be found in thecontrary or knowledge in the object of

knowledge, unless the object ofknowledge happen to be a soul or a

man)-you should look, therefore, andsee whether he places a term of onekind inside 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 thatwhich abides, and is used of that, sothat the abiding of knowledge also will

be found in knowledge. Memory, then, isfound in knowledge, seeing that it isthe abiding of knowledge. But this isimpossible, for memory is always foundin the soul. The aforesaid commonplacerule is common to the subject of

Accident as well: for it is all thesame to say that ‘abiding’ is the genusof memory, or to allege that it is anaccident of it. For if in any waywhatever memory be the abiding ofknowledge, the same argument in regardto it will apply.

5

Again, see if he has placed what is a‘state’ inside the genus ‘activity’, oran activity inside the genus ‘state’,e.g. by defining ‘sensation’ as‘movement communicated through the

body’: for sensation is a ‘state’,whereas movement is an ‘activity’.Likewise, also, if he has said that

memory is a ‘state that is retentive of



a conception’, for memory is never astate, but rather an activity.

They also make a bad mistake who rank a‘state’ within the ‘capacity’ thatattends it, e.g. by defining ‘goodtemper’ as the ‘control of anger’, and‘courage’ and ‘justice’ as ‘control offears’ and of ‘gains’: for the terms‘courageous’ and ‘good-tempered’ areapplied to a man who is immune from

passion, whereas ‘self-controlled’describes the man who is exposed to

passion and not led by it. Quite possibly, indeed, each of the former is

attended by a capacity such that, if hewere exposed to passion, he wouldcontrol it and not be led by it: but,for all that, this is not what is meant

by being ‘courageous’ in the one case,and ‘good tempered’ in the other; whatis meant is an absolute immunity fromany passions of that kind at all.

Sometimes, also, people state any kindof 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 questionfollow in a certain sense upon thegiven species, but neither of them is



genus to it. For when the angry manfeels pain, the pain bas appeared inhim earlier than the anger: for hisanger is not the cause of his pain, buthis pain of his anger, so that angeremphatically is not pain. By the samereasoning, neither is convictionconception: for it is possible to havethe same conception even without beingconvinced of it, whereas this isimpossible if conviction be a species

of conception: for it is impossible fora thing still to remain the same if it

be entirely transferred out of itsspecies, just as neither could the sameanimal at one time be, and at anothernot be, a man. If, on the other hand,any one says that a man who has aconception must of necessity be alsoconvinced of it, then ‘conception’ and‘conviction’ will be used with an equaldenotation, so that not even so couldthe former be the genus of the latter:for the denotation of the genus should

be wider.

See, also, whether both naturally cometo be anywhere in the same thing: forwhat contains the species contains thegenus as well: e.g. what contains‘white’ contains ‘colour’ as well, and



what contains ‘knowledge of grammar’contains ‘knowledge’ as well. If,therefore, any one says that ‘shame’ is‘fear’, or that ‘anger’ is ‘pain’, theresult will be that genus and speciesare not found in the same thing: forshame is found in the ‘reasoning’faculty, whereas fear is in the‘spirited’ faculty, and ‘pain’ is foundin the faculty of ‘desires’. (for inthis pleasure also is found), whereas

‘anger’ is found in the ‘spirited’faculty. Hence the terms rendered arenot the genera, seeing that they do notnaturally come to be in the samefaculty as the species. Likewise, also,if ‘friendship’ be found in the facultyof desires, you may take it that it isnot a form of ‘wishing’: for wishing isalways found in the ‘reasoning’faculty. This commonplace rule isuseful also in dealing with Accident:for the accident and that of which itis an accident are both found in thesame thing, so that if they do notappear in the same thing, clearly it is

not an accident.

Again, see if the species partakes ofthe genus attributed only in some

particular respect: for it is the



general view that the genus is not thusimparted only in some particularrespect: for a man is not an animal ina particular respect, nor is grammarknowledge in a particular respect only.Likewise also in other instances. Look,therefore, and see if in the case ofany of its species the genus beimparted only in a certain respect;e.g. if ‘animal’ has been described asan ‘object of perception’ or of

‘sight’. For an animal is an object of perception or of sight in a particular

respect only; for it is in respect ofits 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 wholeinside the part without detection,defining (e.g.) ‘animal’ as an ‘animate

body’; whereas the part is not predicated in any sense of the whole,

so that ‘body’ could not be the genus

of animal, seeing that it is a part.

See also if he has put anything that is blameworthy or objectionable into the

class ‘capacity’ or ‘capable’, e.g. by



defining a ‘sophist’ or a ‘slanderer’,or a ‘thief’ as ‘one who is capable ofsecretly thieving other people’s

property’. For none of the aforesaidcharacters is so called because he is‘capable’ in one of these respects: foreven God and the good man are capableof doing bad things, but that is nottheir character: for it is always inrespect of their choice that bad menare so called. Moreover, a capacity is

always a desirable thing: for even thecapacities for doing bad things aredesirable, and therefore it is we saythat even God and the good man possessthem; for they are capable (we say) ofdoing evil. So then ‘capacity’ cannever be the genus of anything

blameworthy. Else, the result will bethat what is blameworthy is sometimesdesirable: for there will be a certainform of capacity that is blameworthy.

Also, see if he has put anything thatis precious or desirable for its ownsake into the class ‘capacity’ or

‘capable’ or ‘productive’ of anything.For capacity, and what is capable or

productive of anything, is alwaysdesirable for the sake of somethingelse.



Or see if he has put anything thatexists in two genera or more into oneof them only. For some things it isimpossible 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 thecapacity without the will, is aslanderer or cheat, but he who has bothof them. Hence he must be put not into

one genus, but into both the aforesaidgenera.

Moreover, people sometimes in converseorder render genus as differentia, anddifferentia as genus, defining (e.g.)astonishment as ‘excess of wonderment’and conviction as ‘vehemence ofconception’. For neither ‘excess’ nor‘vehemence’ is the genus, but thedifferentia: for astonishment isusually taken to be an ‘excessivewonderment’, and conviction to be a‘vehement conception’, so that‘wonderment’ and ‘conception’ are the

genus, while ‘excess’ and ‘vehemence’are the differentia. Moreover, if anyone renders ‘excess’ and ‘vehemence’ asgenera, then inanimate things will beconvinced and astonished. For



‘vehemence’ and ‘excess’ of a thing arefound in a thing which is thus vehementand in excess. If, therefore,astonishment be excess of wondermentthe astonishment will be found in thewonderment, so that ‘wonderment’ will

be astonished! Likewise, also,conviction will be found in theconception, if it be ‘vehemence ofconception’, so that the conceptionwill be convinced. Moreover, a man who

renders an answer in this style will inconsequence find himself callingvehemence vehement and excessexcessive: for there is such a thing asa vehement conviction: if thenconviction be ‘vehemence’, there would

be a ‘vehement vehemence’. Likewise,also, there is such a thing asexcessive astonishment: if thenastonishment be an excess, there would

be an ‘excessive excess’. Whereasneither of these things is generally

believed, any more than that knowledgeis a knower or motion a moving thing.

Sometimes, too, people make the bad mistake of putting an affection into

that 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 istrue would appear clear if any one wereto admit that a man can pass from being

mortal and become immortal: for no onewill assert that he takes another life,

but that a certain accidental featureor affection enters into this one as itis. So then ‘life’ is not the genus ofimmortality.

Again, see if to an affection he hasascribed 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 sameair persists both when it is in motionand 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 air whichformed the wind persists. Likewise,also, in other cases of the kind. Even,then, if we ought in this instance toadmit the point that wind is ‘air in

motion’, yet we should accept a

definition of the kind, not about allthose things of which the genus is nottrue, but only in cases where the genusrendered is a true predicate. For insome cases, e.g. ‘mud’ or ‘snow’, it is



not 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 mud earth, so that neither of theterms rendered could be the genus: forthe genus should be true of all itsspecies. Likewise neither is wine‘fermented water’, as Empedocles speaksof ‘water fermented in wood’;’ for itsimply is not water at all.

6

Moreover, see whether the term renderedfail to be the genus of anything atall; for then clearly it also fails to

be the genus of the species mentioned.Examine the point by seeing whether theobjects that partake of the genus failto be specifically different from oneanother, e.g. white objects: for thesedo not differ specifically from oneanother, whereas of a genus the speciesare always different, so that ‘white’could not be the genus of anything.

Again, see whether he has named asgenus or differentia some feature thatgoes with everything: for the number ofattributes that follow everything is



comparatively large: thus (e.g.)‘Being’ and ‘Unity’ are among thenumber of attributes that followeverything. If, therefore, he hasrendered ‘Being’ as a genus, clearly itwould be the genus of everything,seeing that it is predicated ofeverything; for the genus is never

predicated of anything except of itsspecies. Hence Unity, inter alia, will

be a species of Being. The result,

therefore, is that of all things ofwhich the genus is predicated, thespecies is predicated as well, seeingthat Being and Unity are predicates ofabsolutely everything, whereas the

predication of the species ought to beof narrower range. If, on the otherhand, he has named as differentia someattribute that follows everything,clearly the denotation of thedifferentia will be equal to, or widerthan, that of the genus. For if thegenus, too, be some attribute thatfollows everything, the denotation ofthe differentia will be equal to its

denotation, while if the genus do notfollow everything, it will be stillwider.



Moreover, see if the description‘inherent in S’ be used of the genusrendered in relation to its species, asit is used of ‘white’ in the case ofsnow, thus showing clearly that itcould not be the genus: for ‘true of S’is the only description used of thegenus in relation to its species. Lookand see also if the genus fails to besynonymous with its species. For thegenus is always predicated of its

species synonymously.

Moreover, beware, whenever both speciesand genus have a contrary, and he

places the better of the contrariesinside the worse genus: for the resultwill be that the remaining species will

be found in the remaining genus, seeingthat contraries are found in contrarygenera, so that the better species will

be found in the worse genus and theworse in the better: whereas the usualview is that of the better species thegenus too is better. Also see if he has

placed the species inside the worse and

not inside the better genus, when it isat the same time related in like mannerto both, as (e.g.) if he has definedthe ‘soul’ as a ‘form of motion’ or ‘aform of moving thing’. For the same



soul is usually thought to be a principle alike of rest and of motion,

so that, if rest is the better of thetwo, this is the genus into which thesoul should have been put.

Moreover, judge by means of greater andless degrees: if overthrowing a view,see whether the genus admits of agreater degree, whereas neither thespecies itself does so, nor any term

that is called after it: e.g. if virtueadmits of a greater degree, so too doesjustice and the just man: for one manis called ‘more just than another’. If,therefore, the genus rendered admits ofa greater degree, whereas neither thespecies does so itself nor yet any termcalled after it, then what has beenrendered could not be the genus.

Again, if what is more generally, or asgenerally, thought to be the genus benot so, clearly neither is the genusrendered. The commonplace rule inquestion is useful especially in cases

where the species appears to haveseveral predicates in the category ofessence, and where no distinction has

been drawn between them, and we cannotsay which of them is genus; e.g. both



‘pain’ and the ‘conception of a slight’are usually thought to be predicates of‘anger in the category of essence: forthe angry man is both in pain and alsoconceives that he is slighted. The same

mode of inquiry may be applied also tothe case of the species, by comparingit with some other species: for if theone which is more generally, or asgenerally, 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, youshould follow the rule as stated. Inestablishing one, on the other hand,the commonplace rule that you shouldsee if both the genus rendered and thespecies admit of a greater degree willnot serve: for even though both admitit, it is still possible for one not to

be the genus of the other. For both‘beautiful’ and ‘white’ admit of agreater degree, and neither is thegenus of the other. On the other hand,

the comparison of the genera and of thespecies one with another is of use:e.g. supposing A and B to have a likeclaim to be genus, then if one be agenus, so also is the other. Likewise,



also, if what has less claim be agenus, so also is what has more claim:e.g. if ‘capacity’ have more claim than‘virtue’ to be the genus of self-control, and virtue be the genus, soalso is capacity. The same observationswill apply also in the case of thespecies. For instance, supposing A andB to have a like claim to be a speciesof the genus in question, then if theone be a species, so also is the other:

and if that which is less generallythought to be so be a species, so alsois that which is more generally thoughtto be so.

Moreover, to establish a view, youshould look and see if the genus is

predicated in the category of essenceof those things of which it has beenrendered as the genus, supposing thespecies rendered to be not one singlespecies but several different ones: forthen clearly it will be the genus. If,on the other, the species rendered besingle, look and see whether the genus

be predicated in the category ofessence of other species as well: forthen, again, the result will be that itis predicated of several differentspecies.



Since some people think that thedifferentia, too, is a predicate of thevarious species in the category ofessence, you should distinguish thegenus from the differentia by employingthe aforesaid elementary principles-(a)that the genus has a wider denotationthan the differentia; (b) that inrendering the essence of a thing it is

more fitting to state the genus than

the differentia: for any one who saysthat ‘man’ is an ‘animal’ shows what

man is better than he who describes himas ‘walking’; also (c) that thedifferentia always signifies a qualityof the genus, whereas the genus doesnot do this of the differentia: for hewho says ‘walking’ describes an animalof a certain quality, whereas he whosays ‘animal’ describes an animal of acertain quality, whereas he who says‘animal’ does not describe a walkingthing of a certain quality.

The differentia, then, should be

distinguished from the genus in this manner. Now seeing it is generally held

that if what is musical, in being musical, possesses knowledge in some

respect, then also ‘music’ is a



particular kind of ‘knowledge’; andalso that if what walks is moved inwalking, then ‘walking’ is a particularkind of ‘movement’; you shouldtherefore examine in the aforesaid

manner any genus in which you want toestablish the existence of something;e.g. if you wish to prove that‘knowledge’ is a form of ‘conviction’,see whether the knower in knowing isconvinced: for then clearly knowledge

would be a particular kind ofconviction. You should proceed in thesame way also in regard to the othercases of this kind.

Moreover, seeing that it is difficultto distinguish whatever always followsalong with a thing, and is notconvertible with it, from its genus, if

A follows B universally, whereas B doesnot follow A universally-as e.g. ‘rest’always follows a ‘calm’ and‘divisibility’ follows ‘number’, butnot conversely (for the divisible isnot always a number, nor rest a calm)-

you may yourself assume in yourtreatment of them that the one whichalways follows is the genus, wheneverthe other is not convertible with it:if, on the other hand, some one else



puts forward the proposition, do notaccept it universally. An objection toit is that ‘not-being’ always followswhat is ‘coming to be’ (for what iscoming to be is not) and is notconvertible with it (for what is not isnot always coming to be), and thatstill ‘not-being’ is not the genus of‘coming to be’: for ‘not-being’ has notany species at all. Questions, then, inregard to Genus should be investigated

in the ways described.

Book V

1

THE question whether the attributestated is or is not a property, should

be examined by the following methods:

Any ‘property’ rendered is alwayseither essential and permanent or

relative and temporary: e.g. it is an‘essential property’ of man to be ‘bynature a civilized animal’: a ‘relative

property’ is one like that of the soulin relation to the body, viz. that the



one is fitted to command, and the otherto obey: a ‘permanent property’ is onelike the property which belongs to God,of being an ‘immortal living being’: a‘temporary property’ is one like the

property which belongs to any particular man of walking in the

gymnasium.

[The rendering of a property‘relatively’ gives rise either to two

problems or to four. For if he at thesame time render this property of onething and deny it of another, only two

problems arise, as in the case of astatement that it is a property of a

man, in relation to a horse, to be a biped. For one might try both to show

that a man is not a biped, and alsothat a horse is a biped: in both waysthe property would be upset. If on theother hand he render one apiece of twoattributes to each of two things, anddeny it in each case of the other,there will then be four problems; as inthe case of a statement that it is a

property of a man in relation to ahorse 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 horse both is a biped, and is not a

quadruped. If you show any of these atall, the intended attribute isdemolished.]

An ‘essential’ property is one which isrendered of a thing in comparison witheverything else and distinguishes thesaid thing from everything else, asdoes ‘a mortal living being capable of

receiving knowledge’ in the case of man. A ‘relative’ property is one which

separates its subject off not fromeverything else but only from a

particular definite thing, as does the property which virtue possesses, in

comparison with knowledge, viz. thatthe former is naturally produced in

more than one faculty, whereas thelatter is produced in that of reasonalone, and in those who have areasoning faculty. A ‘permanent’

property is one which is true at everytime, and never fails, like being’compounded of soul and body’, in the

case of a living creature. A‘temporary’ property is one which istrue 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’ tosomething else means to state thedifference between them as it is foundeither universally and always, orgenerally and in most cases: thus adifference that is found universallyand always, is one such as man

possesses in comparison with a horse,

viz. being a biped: for a man is alwaysand in every case a biped, whereas ahorse is never a biped at any time. Onthe other hand, a difference that isfound generally and in most cases, isone such as the faculty of reason

possesses in comparison with that ofdesire and spirit, in that the formercommands, while the latter obeys: forthe reasoning faculty does not alwayscommand, but sometimes also is undercommand, nor is that of desire andspirit always under command, but alsoon occasion assumes the command,whenever the soul of a man is vicious.

Of ‘properties’ the most ‘arguable’ arethe essential and permanent and therelative. For a relative property givesrise, as we said before, to several



questions: for of necessity thequestions arising are either two orfour, or that arguments in regard tothese are several. An essential and a

permanent property you can discuss inrelation to many things, or can observein relation to many periods of time: ifessential’, discuss it in comparisonwith many things: for the propertyought to belong to its subject incomparison with every single thing that

is, so that if the subject be notdistinguished by it in comparison witheverything else, the property could nothave been rendered correctly. So a

permanent property you should observein relation to many periods of time;for if it does not or did not, or isnot going to, belong, it will not be a

property. On the other hand, about atemporary property we do not inquirefurther than in regard to the timecalled ‘the present’; and so argumentsin regard to it are not many; whereasan arguable’ question is one in regardto which it is possible for arguments

both numerous and good to arise.

The so-called ‘relative’ property,then, should be examined by means ofthe commonplace arguments relating to



Accident, to see whether it belongs tothe one thing and not to the other: onthe other hand, permanent and essential

properties should be considered by thefollowing methods.

2

First, see whether the property has orhas not been rendered correctly. Of arendering being incorrect or correct,

one test is to see whether the terms inwhich the property is stated are not orare more intelligible-for destructive

purposes, whether they are not so, andfor constructive purposes, whether theyare so. Of the terms not being moreintelligible, one test is to seewhether the property which he rendersis altogether more unintelligible thanthe subject whose property he hasstated: for, if so, the property willnot have been stated correctly. For theobject of getting a propertyconstituted is to be intelligible: theterms therefore in which it is rendered

should be more intelligible: for inthat case it will be possible toconceive it more adequately, e.g. anyone who has stated that it is a

property of ‘fire’ to ‘bear a very



close resemblance to the soul’, usesthe term ‘soul’, which is lessintelligible than ‘fire’-for we know

better what fire is than what soul is-,and therefore a ‘very close resemblanceto the soul’ could not be correctlystated to be a property of fire.

Another test is to see whether theattribution of A (property) to B(subject) fails to be moreintelligible. For not only should the

property be more intelligible than itssubject, but also it should besomething whose attribution to the

particular subject is a moreintelligible attribution. For he whodoes not know whether it is anattribute of the particular subject atall, will not know either whether it

belongs to it alone, so that whicheverof these results happens, its characteras a property becomes obscure. Thus(e.g.) a man who has stated that it isa property of fire to be ‘the primaryelement wherein the soul is naturallyfound’, has introduced a subject which

is less intelligible than ‘fire’, viz.whether the soul is found in it, andwhether it is found there primarily;and therefore to be ‘the primaryelement in which the soul is naturally



found’ could not be correctly stated to be a property of ‘fire’. On the other

hand, for constructive purposes, seewhether the terms in which the propertyis stated are more intelligible, and ifthey are more intelligible in each ofthe aforesaid ways. For then the

property will have been correctlystated in this respect: for ofconstructive arguments, showing thecorrectness of a rendering, some will

show the correctness merely in thisrespect, while others will show itwithout qualification. Thus (e.g.) a

man who has said that the ‘possessionof sensation’ is a property of ‘animal’has both used more intelligible termsand has rendered the property moreintelligible in each of the aforesaidsenses; so that to ‘possess sensation’would in this respect have beencorrectly rendered as a property of‘animal’.

Next, for destructive purposes, seewhether any of the terms rendered in

the property is used in more than onesense, or whether the whole expressiontoo signifies more than one thing. Forthen the property will not have beencorrectly stated. Thus (e.g.) seeing



that to ‘being natural sentient’signifies more than one thing, viz. (1)to possess sensation, (2) to use one’ssensation, being naturally sentient’could not be a correct statement of a

property of ‘animal’. The reason whythe term you use, or the wholeexpression signifying the property,should not bear more than one meaningis this, that an expression bearing

more than one meaning makes the object

described obscure, because the man whois about to attempt an argument is indoubt which of the various senses theexpression bears: and this will not do,for the 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 this fashion should be

somehow refuted whenever any oneaddresses his syllogism to that one ofthe term’s several meanings which doesnot agree. For constructive purposes,on the other hand, see whether both allthe terms and also the expression as a

whole avoid bearing more than onesense: for then the property will have

been correctly stated in this respect.Thus (e.g.) seeing that ‘body’ does not

bear several meanings, nor quickest to



move upwards in space’, nor yet thewhole expression made by putting themtogether, it would be correct in thisrespect to say that it is a property offire to be the ‘body quickest to moveupwards in space’.

Next, for destructive purposes, see ifthe term of which he renders the

property is used in more than onesense, and no distinction has been

drawn as to which of them it is whose property he is stating: for then the property will not have been correctly

rendered. The reasons why this is soare quite clear from what has been saidabove: for the same results are boundto follow. Thus (e.g.) seeing that ‘theknowledge of this’ signifies manythings for it means (1) the possessionof knowledge by it, (2) the use of itsknowledge by it, (3) the existence ofknowledge about it, (4) the use ofknowledge about it-no property of the‘knowledge of this’ could be renderedcorrectly unless he draw a distinction

as to which of these it is whose property he is rendering. For

constructive purposes, a man should seeif the term of which he is renderingthe property avoids bearing many senses



and is one and simple: for then the property will have been correctly

stated in this respect. Thus (e.g.)seeing that ‘man’ is used in a singlesense, ‘naturally civilized animal’would be correctly stated as a propertyof man.

Next, for destructive purposes, seewhether the same term has been repeatedin the property. For people often do

this undetected in rendering‘properties’ also, just as they do intheir ‘definitions’ as well: but a

property to which this has happenedwill not have been correctly stated:for the repetition of it confuses thehearer; thus inevitably the meaning

becomes obscure, and further, such people are thought to babble.

Repetition of the same term is likelyto happen in two ways; one is, when a

man repeatedly uses the same word, aswould happen if any one were to render,as a property of fire, ‘the body whichis the most rarefied of bodies’ (for he

has repeated the word ‘body’); thesecond is, if a man replaces words bytheir definitions, as would happen ifany one were to render, as a propertyof earth, ‘the substance which is by



its nature most easily of all bodies borne downwards in space’, and were

then to substitute ‘substances of suchand such a kind’ for the word ‘bodies’:for ‘body’ and ‘a substance of such andsuch a kind’ mean one and the samething. For he will have repeated theword ‘substance’, and accordinglyneither of the properties would becorrectly stated. For constructive

purposes, on the other hand, see

whether he avoids ever repeating thesame term; for then the property willin this respect have been correctlyrendered. Thus (e.g.) seeing that hewho has stated ‘animal capable ofacquiring knowledge’ as a property of

man has avoided repeating the same termseveral times, the property would inthis respect have been correctlyrendered of man.

Next, for destructive purposes, seewhether he has rendered in the propertyany such term as is a universalattribute. For one which does not

distinguish its subject from otherthings is useless, and it is the

business of the language Of‘properties’, as also of the languageof definitions, to distinguish. In the



case contemplated, therefore, the property will not have been correctly

rendered. Thus (e.g.) a man who hasstated that it is a property ofknowledge to be a ‘conceptionincontrovertible by argument, becauseof its unity’, has used in the propertya term of that kind, viz. ‘unity’,which is a universal attribute; andtherefore the property of knowledgecould not have been correctly stated.

For constructive purposes, on the otherhand, see whether he has avoided allterms that are common to everything andused a term that distinguishes thesubject from something: for then the

property will in this respect have beencorrectly stated. Thus (e.g.) inasmuchas he who has said that it is a

property of a ‘living creature’ to‘have a soul’ has used no term that iscommon to everything, it would in thisrespect have been correctly stated to

be a property of a ‘living creature’ to‘have a soul’.

Next, for destructive purposes seewhether he renders more than one

property of the same thing, without adefinite proviso that he is stating

more than one: for then the property



will not have been correctly stated.For just as in the case of definitionstoo there should be no further addition

beside the expression which shows theessence, so too in the case of

properties nothing further should berendered beside the expression thatconstitutes the property mentioned: forsuch an addition is made to no purpose.Thus (e.g.) a man who has said that itis a property of fire to be ‘the most

rarefied and lightest body’ hasrendered more than one property (foreach term is a true predicate of firealone); and so it could not be acorrectly stated property of fire to be‘the most rarefied and lightest body’.On the other hand, for constructive

purposes, see whether he has avoidedrendering more than one property of thesame thing, and has rendered one only:for then the property will in thisrespect have been correctly stated.Thus (e.g.) a man who has said that itis a property of a liquid to be a ‘bodyadaptable to every shape’ has rendered

as its property a single character andnot several, and so the property of‘liquid’ would in this respect have

been correctly stated.



3

Next, for destructive purposes, seewhether he has employed either theactual subject whose property he isrendering, or any of its species: forthen the property will not have beencorrectly stated. For the object ofrendering the property is that people

may understand: now the subject itselfis just as unintelligible as it was to

start with, while any one of itsspecies is posterior to it, and so isno more intelligible. Accordingly it isimpossible to understand anythingfurther by the use of these terms. Thus(e.g.) any one who has said that it is

property of ‘animal’ to be ‘thesubstance to which “man” belongs as aspecies’ has employed one of itsspecies, and therefore the propertycould not have been correctly stated.For constructive purposes, on the otherhand, see whether he avoids introducingeither the subject itself or any of itsspecies: for then the property will in

this respect have been correctlystated. Thus (e.g.) a man who hasstated that it is a property of aliving creature to be ‘compounded ofsoul and body’ has avoided introducing



among the rest either the subjectitself or any of its species, andtherefore in this respect the propertyof a ‘living creature’ would have beencorrectly rendered.

You should inquire in the same way alsoin the case of other terms that do ordo not make the subject moreintelligible: thus, for destructive

purposes, see whether he has employed

anything either opposite to the subjector, in general, anything simultaneous

by nature with it or posterior to it:for then the property will not have

been correctly stated. For an oppositeis simultaneous by nature with itsopposite, and what is simultaneous bynature or is posterior to it does not

make its subject more intelligible.Thus (e.g.) any one who has said thatit is a property of good to be ‘the

most direct opposite of evil’, hasemployed the opposite of good, and sothe property of good could not have

been correctly rendered. For

constructive purposes, on the otherhand, see whether he has avoidedemploying anything either opposite to,or, in general, simultaneous by naturewith the subject, or posterior to it:



for then the property will in thisrespect have been correctly rendered.Thus (e.g.) a man who has stated thatit is a property of knowledge to be‘the most convincing conception’ hasavoided employing anything eitheropposite to, or simultaneous by naturewith, or posterior to, the subject; andso the property of knowledge would inthis respect have been correctlystated.

Next, for destructive purposes, seewhether he has rendered as propertysomething that does not always followthe subject but sometimes ceases to beits property: for then the propertywill not have been correctly described.For there is no necessity either thatthe name of the subject must also betrue of anything to which we find suchan attribute belonging; nor yet thatthe name of the subject will be untrueof anything to which such an attributeis found not to belong. Moreover, inaddition to this, even after he has

rendered the property it will not beclear whether it belongs, seeing thatit is the kind of attribute that mayfall: and so the property will not beclear. Thus (e.g.) a man who has stated



that it is a property of animal‘sometimes to move and sometimes tostand still’ rendered the kind of

property which sometimes is not a property, and so the property could not

have been correctly stated. Forconstructive purposes, on the otherhand, see whether he has renderedsomething that of necessity must always

be a property: for then the propertywill have been in this respect

correctly stated. Thus (e.g.) a man whohas stated that it is a property ofvirtue to be ‘what makes its possessorgood’ has rendered as propertysomething that always follows, and sothe property of virtue would in thisrespect have been correctly rendered.

Next, for destructive purposes, seewhether in rendering the property ofthe present time he has omitted to makea definite proviso that it is the

property of the present time which heis rendering: for else the propertywill not have been correctly stated.

For in the first place, any unusual procedure always needs a definite proviso: and it is the usual procedure

for everybody to render as propertysome attribute that always follows. In



the second place, a man who omits to provide definitely whether it was the property of the present time which he

intended to state, is obscure: and oneshould not give any occasion foradverse criticism. Thus (e.g.) a manwho has stated it as the property of a

particular man ‘to be sitting with a particular man’, states the property of

the present time, and so he cannot haverendered the property correctly, seeing

that he has described it without anydefinite proviso. For constructive

purposes, on the other hand, seewhether, in rendering the property ofthe present time, he has, in statingit, made a definite proviso that it isthe property of the present time thathe is stating: for then the propertywill in this respect have beencorrectly stated. Thus (e.g.) a man whohas said that it is the property of a

particular man ‘to be walking now’, has made this distinction in his statement,

and so the property would have beencorrectly stated.

Next, for destructive purposes, seewhether he has rendered a property ofthe kind whose appropriateness is notobvious except by sensation: for then



the property will not have beencorrectly stated. For every sensibleattribute, once it is taken beyond thesphere of sensation, becomes uncertain.For it is not clear whether it still

belongs, because it is evidenced only by sensation. This principle will be

true in the case of any attributes thatdo not always and necessarily follow.Thus (e.g.) any one who has stated thatit is a property of the sun to be ‘the

brightest star that moves over theearth’, has used in describing the

property an expression of that kind,viz. ‘to move over the earth’, which isevidenced by sensation; and so thesun’s property could not have beencorrectly rendered: for it will beuncertain, whenever the sun sets,whether it continues to move over theearth, because sensation then fails us.For constructive purposes, on the otherhand, see whether he has rendered the

property of a kind that is not obviousto sensation, or, if it be sensible,

must clearly belong of necessity: for

then the property will in this respecthave been correctly stated. Thus (e.g.)a man who has stated that it is a

property of a surface to be ‘the primary thing that is coloured’, has



introduced amongst the rest a sensiblequality, ‘to be coloured’, but still aquality such as manifestly always

belongs, and so the property of‘surface’ would in this respect have

been correctly rendered.

Next, for destructive purposes, seewhether he has rendered the definitionas a property: for then the propertywill not have been correctly stated:

for the property of a thing ought notto show its essence. Thus (e.g.) a manwho has said that it is the property of

man to be ‘a walking, biped animal’ hasrendered a property of man so as tosignify his essence, and so the

property of man could not have beencorrectly rendered. For constructive

purposes, on the other hand, seewhether the property which he hasrendered forms a predicate convertiblewith its subject, without, however,signifying its essence: for then the

property will in this respect have beencorrectly rendered. Thus (e.g.) he who

has stated that it is a property of manto be a ‘naturally civilized animal’has rendered the property so as to beconvertible with its subject, without,however, showing its essence, and so



the property of man’ would in thisrespect have been correctly rendered.

Next, for destructive purposes, seewhether he has rendered the propertywithout having placed the subjectwithin its essence. For of properties,as also of definitions, the first termto be rendered should be the genus, andthen the rest of it should be appendedimmediately afterwards, and should

distinguish its subject from otherthings. Hence a property which is notstated in this way could not have beencorrectly rendered. Thus (e.g.) a manwho has said that it is a property of aliving creature to ‘have a soul’ hasnot placed ‘living creature’ within itsessence, and so the property of aliving creature could not have beencorrectly stated. For constructive

purposes, on the other hand, seewhether a man first places within itsessence the subject whose property heis rendering, and then appends therest: for then the property will in

this respect have been correctlyrendered. Thus (e.g.) he who has statedthat is a property of man to be an‘animal capable of receivingknowledge’, has rendered the property



after placing the subject within itsessence, and so the property of ‘man’would in this respect have beencorrectly rendered.

4

The inquiry, then, whether the propertyhas been correctly rendered or no,should be made by these means. Thequestion, on the other hand, whether

what is stated is or is not a propertyat all, you should examine from thefollowing points of view. For thecommonplace arguments which establishabsolutely that the property isaccurately stated will be the same asthose that constitute it a property atall: accordingly they will be describedin the course of them.

Firstly, then, for destructive purposes, take a look at each subject

of which he has rendered the property,and see (e.g.) if it fails to belong toany of them at all, or to be true of

them in that particular respect, or to be a property of each of them in

respect of that character of which hehas rendered the property: for thenwhat is stated to be a property will



not be a property. Thus, for example,inasmuch as it is not true of thegeometrician that he ‘cannot bedeceived by an argument’ (for ageometrician is deceived when hisfigure is misdrawn), it could not be a

property of the man of science that heis not deceived by an argument. Forconstructive purposes, on the otherhand, see whether the property rendered

be true of every instance, and true in

that particular respect: for then whatis stated not to be a property will bea property. Thus, for example, in as

much as the description ‘an animalcapable of receiving knowledge’ is trueof every man, and true of him qua man,it would be a property of man to be ‘ananimal capable of receiving knowledge’.commonplace rule means-for destructive

purposes, see if the description failsto be true of that of which the name istrue; and if the name fails to be trueof that of which the description istrue: for constructive purposes, on theother hand, see if the description too

is predicated of that of which the nameis predicated, and if the name too is

predicated of that of which thedescription is predicated.]



Next, for destructive purposes, see ifthe description fails to apply to thatto which the name applies, and if thename fails to apply to that to whichthe description applies: for then whatis stated to be a property will not bea property. Thus (e.g.) inasmuch as thedescription ‘a living being that

partakes of knowledge’ is true of God,while ‘man’ is not predicated of God,to be a living being that partakes of

knowledge’ could not be a property of man. For constructive purposes, on the

other hand, see if the name as well be predicated of that of which the

description is predicated, and if thedescription as well be predicated ofthat of which the name is predicated.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 asoul’ is true, and ‘having a soul’ istrue of that of which the predicate‘living creature’ is true; and so‘having a soul would be a property of

‘living creature’.

Next, for destructive purposes, see ifhe has rendered a subject as a propertyof that which is described as ‘in the



subject’: for then what has been statedto be a property will not be a

property. Thus (e.g.) inasmuch as hewho has rendered ‘fire’ as the propertyof ‘the body with the most rarefied

particles’, has rendered the subject asthe property of its predicate, ‘fire’could not be a property of ‘the bodywith the most rarefied particles’. Thereason why the subject will not be a

property of that which is found in the

subject is this, that then the samething will be the property of a numberof things that are specificallydifferent. For the same thing has quitea number of specifically different

predicates that belong to it alone, andthe subject will be a property of allof these, if any one states the

property in this way. For constructive purposes, on the other hand, see if he

has rendered what is found in thesubject as a property of the subject:for then what has been stated not to bea property will be a property, if it be

predicated only of the things of which

it has been stated to be the property.Thus (e.g.) he who has said that it isa 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 inthe manner in which a property is

predicated, and so the property ofearth would have been rightly stated.

Next, for destructive purposes, see ifhe has rendered the property as

partaken of: for then what is stated to be a property will not be a property.

For an attribute of which the subject

partakes is a constituent part of itsessence: and an attribute of that kindwould be a differentia applying to someone species. E.g. inasmuch as he whohas said that ‘walking on two feet’ is

property of man has rendered the property as partaken of, ‘walking on

two feet’ could not be a property of‘man’. For constructive purposes, onthe other hand, see if he has avoidedrendering the property as partaken of,or as showing the essence, though thesubject 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’ has rendered the propertyneither as partaken of nor as showingthe essence, though the subject is



predicated convertibly with it; and soto be ‘naturally sentient’ would be a

property of ‘animal’.

Next, for destructive purposes, see ifthe property cannot possibly belongsimultaneously, but must belong eitheras posterior or as prior to theattribute described in the name: forthen what is stated to be a propertywill not be a property either never, or

not always. Thus (e.g.) inasmuch as itis possible for the attribute ‘walkingthrough the market-place’ to belong toan object as prior and as posterior tothe attribute ‘man’, ‘walking throughthe market-place’ could not be a

property of ‘man’ either never, or notalways. For constructive purposes, onthe other hand, see if it always and ofnecessity belongs simultaneously,without being either a definition or adifferentia: for then what is statednot to be a property will be a

property. Thus (e.g.) the attribute ‘ananimal capable of receiving knowledge’

always and of necessity belongssimultaneously with the attribute‘man’, and is neither differentia nordefinition of its subject, and so ‘an



animal capable of receiving knowledge’would be a property of ‘man’.

Next, for destructive purposes, see ifthe same thing fails to be a propertyof things that are the same as thesubject, so far as they are the same:for then what 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 to certain persons’, it could not be a property of

the ‘desirable’ either to ‘appear goodto certain persons’: for ‘proper objectof pursuit’ and ‘desirable’ mean thesame. For constructive purposes, on theother hand, see if the same thing be a

property of something that is the sameas the subject, in so far as it is thesame. 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, ‘to have a tripartite soul’, it

would also be a property of a mortal,

in so far as he is a mortal, to have atripartite soul. This commonplace ruleis useful also in dealing with

Accident: for the same attributes oughteither to belong or not belong to the



same things, in so far as they are thesame.

Next, for destructive purposes, see ifthe property of things that are thesame in kind as the subject fails to bealways the same in kind as the alleged

property: for then neither will what isstated to be the property of thesubject in 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, it could not be a propertyof a man to move by his own initiative;for to stand and to move by his owninitiative are the same in kind,

because they belong to each of them inso far as each is an ‘animal’. Forconstructive purposes, on the otherhand, see if of things that are thesame in kind as the subject the

property that is the same as thealleged property is always true: forthen what is stated not to be a

property will be a property. Thus

(e.g.) since it is a property of man to be a ‘walking biped,’ it would also be

a property of a bird to be a ‘flying biped’: for each of these is the same

in kind, in so far as the one pair have



the sameness of species that fall underthe same genus, being under the genus‘animal’, while the other pair havethat of differentiae of the genus, viz.of ‘animal’. This commonplace rule isdeceptive whenever one of the

properties mentioned belongs to someone species only while the other

belongs to many, as does ‘walkingquadruped’.

Inasmuch as ‘same’ and ‘different’ areterms used in several senses, it is ajob to render to a sophisticalquestioner a property that belongs toone thing and that only. For anattribute that belongs to somethingqualified by an accident will also

belong to the accident taken along withthe subject which it qualifies; e.g. anattribute that belongs to ‘man’ will

belong also to ‘white man’, if there bea white man, and one that belongs to‘white man’ will belong also to ‘man’.One might, then, bring captiouscriticism against the majority of

properties, by representing the subjectas being one thing in itself, andanother thing when combined with itsaccident, saying, for example, that‘man’ is one thing, and white man’



another, and moreover by representingas different a certain state and whatis called after that state. For anattribute that belongs to the statewill belong also to what is calledafter that state, and one that belongsto what is called after a state will

belong also to the state: e.g. inasmuchas the condition of the scientist iscalled after his science, it could not

be a property of ‘science’ that it is

‘incontrovertible by argument’; forthen the scientist also will beincontrovertible by argument. Forconstructive purposes, however, youshould say that the subject of anaccident is not absolutely differentfrom 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 thesame thing for a man to be a man andfor a white man to be a white man.

Moreover, you should take a look alongat the inflections, and say that thedescription of the man of science is

wrong: one should say not ‘it’ but ‘heis incontrovertible by argument’; whilethe description of Science is wrongtoo: one should say not ‘it’ but ‘sheis incontrovertible by argument’. For



against an objector who sticks atnothing the defence should stick atnothing.

5

Next, for destructive purposes, see if,while intending to render an attributethat naturally belongs, he states it inhis language in such a way as toindicate one that invariably belongs:

for then it would be generally agreedthat what has been stated to be a

property is upset. Thus (e.g.) the manwho has said that ‘biped’ is a propertyof man intends to render the attributethat naturally belongs, but hisexpression actually indicates one thatinvariably belongs: accordingly,‘biped’ could not be a property of man:for not every man is possessed of twofeet. For constructive purposes, on theother hand, see if he intends to renderthe property that naturally belongs,and indicates it in that way in hislanguage: for then the property will

not be upset in this respect. Thus(e.g.) he who renders as a property of‘man’ the phrase ‘an animal capable ofreceiving knowledge’ both intends, and

by his language indicates, the property



that belongs by nature, and so ‘ananimal capable of receiving knowledge’would not be upset or shown in thatrespect not to be a property of man.

Moreover, as regards all the thingsthat are called as they are primarilyafter something else, or primarily inthemselves, it is a job to render the

property of such things. For if yourender a property as belonging to the

subject that is so called aftersomething else, then it will be true ofits primary subject as well; whereas ifyou state it of its primary subject,then it will be predicated also of thething that is so called after thisother. Thus (e.g.) if any one renders ,coloured’ as the property of ‘surface’,‘coloured’ will be true of body aswell; whereas if he render it of‘body’, it will be predicated also of‘surface’. Hence the name as well willnot be true of that of which thedescription is true.

In the case of some properties it mostly happens that some error is

incurred because of a failure to definehow as well as to what things the

property is stated to belong. For every



one tries to render as the property ofa thing something that belongs to iteither naturally, as ‘biped’ belongs to‘man’, or actually, as ‘having fourfingers’ belongs to a particular man,or specifically, as ‘consisting of mostrarefied particles’ belongs to ‘fire’,or absolutely, as ‘life’ to ‘living

being’, or one that belongs to a thingonly as called after something else, as‘wisdom’ to the ‘soul’, or on the other

hand primarily, as ‘wisdom’ to the‘rational faculty’, or because thething is in a certain state, as‘incontrovertible by argument’ belongsto a ‘scientist’ (for simply and solely

by reason of his being in a certainstate will he be ‘incontrovertible byargument’), or because it is the state

possessed by something, as‘incontrovertible by argument’ belongsto ‘science’, or because it is partakenof, as ‘sensation’ belongs to ‘animal’(for other things as well havesensation, e.g. man, but they have it

because they already partake of

‘animal’), or because it partakes ofsomething else, as ‘life’ belongs to a

particular kind of ‘living being’. Accordingly he makes a mistake if he

has failed to add the word ‘naturally’,





‘science’ or of the ‘scientist’. So heerrs if he has not indicated beforehandthat the property belongs because thething partakes of, or is partaken of

by, something; because then the property will belong to certain other

things as well. For if he renders it because its subject is partaken of, it

will belong to the things which partakeof it; whereas if he renders it becauseits subject partakes of something else,

it will belong to the things partakenof, as (e.g.) if he were to state‘life’ to be a property of a‘particular kind of living being’, orjust of ‘living being. So he errs if hehas not expressly distinguished the

property that belongs specifically, because then it will belong only to one

of the things that fall under the termof which he states the property: forthe superlative belongs only to one ofthem, e.g. ‘lightest’ as applied to‘fire’. Sometimes, too, a man may evenadd the word ‘specifically’, and still

make a mistake. For the things in

question should all be of one species,whenever the word ‘specifically’ isadded: and in some cases this does notoccur, as it does not, in fact, in thecase of fire. For fire is not all of



one species; for live coals and flameand light are each of them ‘fire’, butare of different species. The reasonwhy, whenever ‘specifically’ is added,there should not be any species otherthan the one mentioned, is this, thatif there be, then the property inquestion will belong to some of them ina greater and to others in a lessdegree, as happens with ‘consisting of

most rarefied particles’ in the case of

fire: for ‘light’ consists of morerarefied particles than live coals andflame. And this should not happenunless the name too be predicated in agreater degree of that of which thedescription is truer; otherwise therule that where the description istruer the name too should be truer isnot fulfilled. Moreover, in addition tothis, the same attribute will be the

property both of the term which has itabsolutely and of that element thereinwhich has it in the highest degree, asis the condition of the property‘consisting of most rarefied particles’

in the case of ‘fire’: for this sameattribute will be the property of‘light’ as well: for it is ‘light’ that‘consists of the most rarefied

particles’. If, then, any one else



renders a property in this way oneshould attack it; for oneself, oneshould not give occasion for thisobjection, but should define in what

manner one states the property at theactual time of making the statement.

Next, for destructive purposes, see ifhe has stated a thing as a property ofitself: for then what has been statedto be a property will not be a

property. For a thing itself alwaysshows its own essence, and what showsthe essence is not a property but adefinition. Thus (e.g.) he who has saidthat ‘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 a property of‘beautiful’. For constructive purposes,on the other hand, see if he hasavoided rendering a thing as a propertyof itself, but has yet stated aconvertible predicate: for then what isstated not to be a property will be a

property. Thus he who has stated‘animate substance’ as a property of‘living-creature’ has not stated‘living-creature’ as a property ofitself, but has rendered a convertible



predicate, so that ‘animate substance’would be a property of ‘living-creature’.

Next, in the case of things consistingof like parts, you should look and see,for destructive purposes, if the

property of the whole be not true ofthe part, 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 sometimesin rendering a property in the case ofthings that consist of like parts a man

may have his eye on the whole, whilesometimes he may address himself towhat is predicated of the part: andthen in neither case will it have beenrightly rendered. Take an instancereferring to the whole: the man who hassaid that it is a property of the ‘sea’to be ‘the largest volume of saltwater’, has stated the property ofsomething that consists of like parts,

but has rendered an attribute of such a

kind as is not true of the part (for a particular sea is not ‘the largest

volume of salt water’); and so thelargest volume of salt water’ could not

be a property of the ‘sea’. Now take



one referring to the part: the man whohas stated that it is a property of‘air’ to be ‘breathable’ has stated the

property of something that consists oflike parts, but he has stated anattribute such as, though true of someair, is still not predicable of thewhole (for the whole of the air is not

breathable); and so ‘breathable’ couldnot 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: forthen what has been stated not to be a

property will be a property. Thus(e.g.) while it is true of eartheverywhere that it naturally fallsdownwards, it is a property of thevarious particular pieces of earthtaken as ‘the Earth’, so that it would

be a property of ‘earth’ ‘naturally tofall downwards’.

6

Next, look from the point of view ofthe respective opposites, and first (a)from that of the contraries, and see,for destructive purposes, if the



contrary of the term rendered fails to be a property of the contrary subject.

For then neither will the contrary ofthe first be a property of the contraryof the second. Thus (e.g.) inasmuch asinjustice is contrary to justice, andthe lowest evil 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 ‘injustice’. For

constructive purposes, on the otherhand, see if the contrary is the

property of the contrary: for then alsothe contrary of the first will be the

property of the contrary of the second.Thus (e.g.) inasmuch as evil iscontrary to good, and objectionable todesirable, and ‘desirable’ is a

property of ‘good’, ‘objectionable’would be a property of ‘evil’.

Secondly (h) look from the point ofview of relative opposites and see, fordestructive purposes, if thecorrelative of the term rendered fails

to be a property of the correlative ofthe subject: for then neither will thecorrelative of the first be a propertyof the correlative of the second. Thus(e.g.) inasmuch as ‘double’ is relative



to ‘half’, and ‘in excess’ to‘exceeded’, while ‘in excess’ is not a

property of ‘double’, exceeded’ couldnot be a property of ‘half’. Forconstructive purposes, on the otherhand, see if the correlative of thealleged property is a property of thesubject’s correlative: for then alsothe correlative of the first will be a

property of the correlative of thesecond: e.g. inasmuch as ‘double’ is

relative to ‘half’, and the proportion1:2 is relative to the proportion 2:1,while it is a property of ‘double’ to

be ‘in the proportion of 2 to 1’, itwould be a property of ‘half’ to be ‘inthe proportion of 1 to 2’.

Thirdly (c) for destructive purposes,see if an attribute described in termsof a state (X) fails to be a propertyof the given state (Y): for thenneither will the attribute described interms of the privation (of X) be a

property of the privation (of Y). Alsoif, on the other hand, an attribute

described in terms of the privation (ofX) be not a property of the given

privation (of Y), neither will theattribute described in terms of thestate (X) be a property of the state



(Y). Thus, for example, inasmuch as itis not predicated as a property of‘deafness’ to be a ‘lack of sensation’,neither could it be a property of‘hearing’ to be a ‘sensation’. Forconstructive purposes, on the otherhand, see if an attribute described interms of a state (X) is a property ofthe given state (Y): for then also theattribute that is described in terms ofthe privation (of X) will be a property

of the privation (of Y). Also, if anattribute described in terms of a

privation (of X) be a property of the privation (of Y), then also the

attribute that is described in terms ofthe state (X) will be a property of thestate (Y). Thus (e.g.) inasmuch as ‘tosee’ is a property of ‘sight’, inasmuchas we have sight, ‘failure to see’would be a property of ‘blindness’,inasmuch as we have not got the sightwe should naturally have.

Next, look from the point of view of positive and negative terms; and first

(a) from the point of view of the predicates taken by themselves. This

common-place rule is useful only for adestructive purpose. Thus (e.g.) see ifthe positive term or the attribute



described in terms of it is a propertyof the subject: for then the negativeterm or the attribute described interms of it will not be a property ofthe subject. Also if, on the otherhand, the negative term or theattribute described in terms of it is a

property of the subject, then the positive term or the attribute

described in terms of it will not be a property of the subject: e.g. inasmuch

as ‘animate’ is a property of ‘livingcreature’, ‘inanimate’ could not be a

property of ‘living creature’.

Secondly (b) look from the point ofview of the predicates, positive ornegative, and their respectivesubjects; and see, for destructive

purposes, if the positive term falls to be a property of the positive subject:

for then neither will the negative term be a property of the negative subject. Also, if the negative term fails to be

a property of the negative subject,neither will the positive 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 property of ‘not-man’.

Also if ‘not-animal’ seems not to be a



property of ‘not-man’, neither will‘animal’ be a property of ‘man’. Forconstructive purposes, on the otherhand, see if the positive term is a

property of the positive subject: forthen the negative term will be a

property of the negative subject aswell. Also if the negative term be a

property of the negative subject, the positive will be a property of the positive as well. Thus (e.g.) inasmuch

as it is a property of ‘not-living being’ ‘not to live’, it would be a property of ‘living being’ ‘to live’:

also if it seems to be a property of‘living being’ ‘to live’, it will alsoseem to be a property of ‘not-living

being’ ‘not to live’.

Thirdly (c) look from the point of viewof the subjects taken by themselves,and see, for destructive purposes, ifthe property rendered is a property ofthe positive subject: for then the sameterm will not be a property of thenegative 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.)inasmuch as ‘animate’ is a property of‘living creature’, ‘animate’ could not



be a property of ‘not-living creature’.For constructive purposes, on the otherhand, if the term rendered fails to bea property of the affirmative subjectit would 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 doesnot belong at all to a negative, whilea negative term, though it belongs to a

positive, does not belong as a property.

Next, look from the point of view ofthe coordinate members of a division,and see, for destructive purposes, ifnone of the co-ordinate members(parallel with the property rendered)

be a property of any of the remainingset of co-ordinate members (parallelwith the subject): for then neitherwill the term stated be a property ofthat of which it is stated to be a

property. Thus (e.g.) inasmuch as‘sensible living being’ is not a

property of any of the other living beings, ‘intelligible living being’

could not be a property of God. Forconstructive purposes, on the otherhand, see if some one or other of the



remaining co-ordinate members (parallelwith the property rendered) be a

property of each of these co-ordinate members (parallel with the subject):

for then the remaining one too will bea property of that of which it has beenstated not to be a property. Thus(e.g.) inasmuch as it is a property of‘wisdom’ to be essentially ‘the naturalvirtue of the rational faculty’, then,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 thefaculty of desire’.

Next, look from the point of view ofthe inflexions, and see, fordestructive purposes, if the inflexionof the property rendered fails to be a

property of the inflexion of thesubject: for then neither will theother inflexion be a property of theother inflexion. Thus (e.g.) inasmuchas ‘beautifully’ is not a property of‘justly’, neither could ‘beautiful’ be

a property of ‘just’. For constructive purposes, on the other hand, see if the

inflexion of the property rendered is a property of the inflexion of the

subject: for then also the other



inflexion will be a property of theother inflexion. Thus (e.g.) inasmuchas ‘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 caseof the actual term mentioned should onelook at the inflexions, but also in thecase of its opposites, just as has beenlaid down in the case of the formercommonplace rules as well.’ Thus, for

destructive purposes, see if theinflexion of the opposite of the

property rendered fails to be the property of the inflexion of the

opposite of the subject: for thenneither will the inflexion of the otheropposite be a property of the inflexionof the other opposite. Thus (e.g.)inasmuch as ‘well’ is not a property of‘justly’, neither could ‘badly’ be a

property of ‘unjustly’. Forconstructive purposes, on the otherhand, see if the inflexion of theopposite of the property originallysuggested is a property of the

inflexion of the opposite of theoriginal subject: for then also theinflexion of the other opposite will bea property of the inflexion of theother opposite. Thus (e.g.) inasmuch as



‘best’ is a property of ‘the good’,‘worst’ also will be a property of ‘theevil’.

7

Next, look from the point of view ofthings that are in a like relation, andsee, for destructive purposes, if whatis in a relation like that of the

property rendered fails to be a

property of what is in a relation likethat of the subject: for then neitherwill what is in a relation like that ofthe first be a property of what is in arelation like that of the second. Thus(e.g.) inasmuch as the relation of the

builder towards the production of ahouse is like that of the doctortowards the production of health, andit is not a property of a doctor to

produce health, it could not be a property of a builder to produce a

house. For constructive purposes, onthe other hand, see if what is in arelation like that of the property

rendered is a property of what is in arelation like that of the subject: forthen also what is in a relation likethat of the first will be a property ofwhat is in a relation like that of the



second. Thus (e.g.) inasmuch as therelation of a doctor towards the

possession of ability to produce healthis like that of a trainer towards the

possession of ability to producevigour, and it is a property of atrainer to possess the ability to

produce vigour, it would be a propertyof a doctor to possess the ability to

produce health.

Next look from the point of view ofthings that are identically related,and see, for destructive purposes, ifthe predicate that is identicallyrelated towards two subjects fails to

be a property of the subject which isidentically related to it as thesubject in question; for then neitherwill the predicate that is identicallyrelated to both subjects be a propertyof the subject which is identicallyrelated to it as the first. If, on theother hand, the predicate which isidentically related to two subjects isthe property of the subject which is

identically related to it as thesubject in question, then it will not

be a property of that of which it has been stated to be a property. (e.g.)

inasmuch as prudence is identically



related to both the noble and the base,since it is knowledge of each of them,and it is not a property of prudence to

be knowledge of the noble, it could not be a property of prudence to be

knowledge of the base. If, on the otherhand, it is a property of prudence to

be the knowledge of the noble, it couldnot be a property of it to be theknowledge of the base.] For it isimpossible for the same thing to be a

property of more than one subject. Forconstructive purposes, on the otherhand, this commonplace rule is of nouse: for what is ‘identically related’is a single predicate in process ofcomparison with more than one subject.

Next, for destructive purposes, see ifthe predicate qualified by the verb ‘to

be’ fails to be a property of thesubject qualified by the verb ‘to be’:for then neither will the destructionof the one be a property of the otherqualified by the verb ‘to bedestroyed’, nor will the ‘becoming’the

one be a property of the otherqualified by the verb ‘to become’. Thus(e.g.) inasmuch as it is not a propertyof ‘man’ to be an animal, neither couldit be a property of becoming a man to



become an animal; nor could thedestruction of an animal be a propertyof the destruction of a man. In thesame way one should derive argumentsalso from ‘becoming’ to ‘being’ and‘being destroyed’, and from ‘beingdestroyed’ to ‘being’ and to ‘becoming’exactly as they have just been givenfrom ‘being’ to ‘becoming’ and ‘beingdestroyed’. For constructive purposes,on the other hand, see if the subject

set down as qualified by the verb ‘to be’ has the predicate set down as so

qualified, as its property: for thenalso the subject qualified by the very‘to become’ will have the predicatequalified by ‘to become’ as its

property, and the subject qualified bythe verb to be destroyed’ will have asits property the predicate renderedwith this qualification. Thus, forexample, inasmuch as it is a propertyof man to be 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 a man. In the same way one shouldderive arguments also from ‘becoming’and ‘being destroyed’ both to ‘being’and to the conclusions that follow from



them, exactly as was directed also forthe purpose of destruction.

Next take a look at the ‘idea’ of thesubject stated, and see, fordestructive purposes, if the suggested

property fails to belong to the ‘idea’in question, or fails to belong to itin virtue of that character whichcauses it to bear the description ofwhich the property was rendered: for

then what has been stated to be a property will not be a property. Thus

(e.g.) inasmuch as ‘being motionless’does not belong to ‘man-himself’ qua‘man’, but qua ‘idea’, it could not bea property of ‘man’ to be motionless.For constructive purposes, on the otherhand, see if the property in question

belongs to the idea, and belongs to itin that respect in virtue of whichthere is predicated of it thatcharacter of which the predicate inquestion has been stated not to be a

property: for then what has been statednot to be a property will be a

property. Thus (e.g.) inasmuch as it belongs to ‘living-creature-itself’ to be 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.

8

Next look from the point of view ofgreater and less degrees, and first (a)for destructive purposes, see if whatis more-P fails to be a property ofwhat is more-S: for then neither willwhat is less-P be a property of what is

less-S, nor least-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 a body, neither could being less highly coloured be a property of what is less a body, nor being coloured be a property of body at

all. For constructive purposes, on theother hand, see if what is more-P is a

property of what is more-S: for thenalso what is less-P will be a propertyof what is less S, and least-P ofleast-S, and most-P of most-S, and Psimply of S simply. Thus (e.g.)

inasmuch as a higher degree ofsensation is a property of a higherdegree of life, a lower degree ofsensation also would be a property of alower degree of life, and the highest



of the highest and the lowest of thelowest degree, and sensation simply oflife simply.

Also you should look at the argumentfrom a simple predication to the samequalified types of predication, andsee, for destructive purposes, if Psimply fails to be a property of Ssimply; for then neither will more-P bea property of more-S, nor less-P of

less-S, nor most-P of most-S, norleast-P of least-S. Thus (e.g.)inasmuch as ‘virtuous’ is not a

property of ‘man’, neither could ‘morevirtuous’ be a property of what is‘more human’. For constructive

purposes, on the other hand, see if Psimply is a property of S simply: forthen more P also will be a property of

more-S, and less-P of less-S, andleast-P of least-S, and most-P of most-S. Thus (e.g.) a tendency to moveupwards by nature is a property offire, and so also a greater tendency to

move upwards by nature would be a

property of what is more fiery. In thesame way too one should look at allthese matters from the point of view ofthe others as well.



Secondly (b) for destructive purposes,see if the more likely property failsto be a property of the more likelysubject: for then neither will the lesslikely property be a property of theless likely subject. Thus (e.g.)inasmuch as ‘perceiving’ is more likelyto be a property of ‘animal’ than‘knowing’ of ‘man’, and ‘perceiving’ isnot a property of ‘animal’, ‘knowing’could not be a property of ‘man’. For

constructive purposes, on the otherhand, see if the less likely propertyis a property of the less likelysubject; for then too the more likely

property will be a property of the morelikely subject. Thus (e.g.) inasmuch as‘to be naturally civilized’ is lesslikely to be a property of man than ‘tolive’ of an animal, and it is a

property of man to be naturallycivilized, it would be a property ofanimal to live.

Thirdly (c) for destructive purposes,see if the predicate fails to be a

property of that of which it is morelikely to be a property: for thenneither will it be a property of thatof which it is less likely to be a

property: while if it is a property of



the former, it will not be a propertyof 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 asurface, ‘to be coloured’ could not bea property of ‘body’; while if it is a

property of a ‘surface’, it could not be a property of a ‘body’. For

constructive purposes, on the otherhand, this commonplace rule is not of

any use: for it is impossible for thesame thing to be a property of morethan one thing.

Fourthly (d) for destructive purposes,see if what is more likely to be a

property of a given subject fails to beits property: for then neither willwhat is less likely to be a property ofit be its property. Thus (e.g.)inasmuch as ‘sensible’ is more likelythan ‘divisible’ to be a property of‘animal’, and ‘sensible’ is not a

property of animal, ‘divisible’ couldnot be a property of animal. For

constructive purposes, on the otherhand, see if what is less likely to bea property of it is a property; forthen what is more likely to be a

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 ofthe attributes that belong in a like

manner, and first (a) for destructive purposes, see if what is as much a property fails to be a property of that

of which it is as much a property: forthen neither will that which is as mucha property as it be a property of thatof which it is as much a property. Thus(e.g.) inasmuch as ‘desiring’ is as

much a property of the faculty ofdesire as reasoning’ is a property ofthe faculty of reason, and desiring isnot a property of the faculty ofdesire, reasoning could not be a

property of the faculty of reason. Forconstructive purposes, on the otherhand, see if what is as much a propertyis a property of that of which it is as

much a property: for then also what is

as much a property as it will be a property of that of which it is as much

a property. Thus (e.g.) inasmuch as itis as much a property of ‘the facultyof reason’ to be ‘the primary seat of



wisdom’ as it is of ‘the faculty ofdesire’ to be ‘the primary seat oftemperance’, and it is a property ofthe faculty of reason to be the primaryseat of wisdom, it would be a propertyof the faculty of desire to be the

primary seat of temperance.

Secondly (b) for destructive purposes,see if what is as much a property ofanything fails to be a property of it:

for then neither will what is as much a property be a property of it. Thus

(e.g.) inasmuch as ‘seeing’ is as mucha property of man as ‘hearing’, and‘seeing’ is not a property of man,‘hearing’ could not be a property of

man. For constructive purposes, on theother hand, see if what is as much a

property of it is its property: forthen what is as much a property of itas the former will be its property aswell. Thus (e.g.) it is as much a

property of the soul to be the primary possessor of a part that desires as of

a part that reasons, and it is a

property of the soul to be the primary possessor of a part that desires, and

so it be a property of the soul to bethe primary possessor of a part thatreasons.



Thirdly (c) for destructive purposes,see if it fails to be a property ofthat of which it is as much a property:for then neither will it be a propertyof that of which it is as much a

property as of the former, while if it be a property of the former, it will

not be a property of the other. Thus(e.g.) inasmuch as ‘to burn’ is as mucha property of ‘flame’ as of ‘live

coals’, and ‘to burn’ is not a propertyof 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. Forconstructive purposes, on the otherhand, this commonplace rule is of nouse.

The rule based on things that are in alike relation’ differs from the rule

based on attributes that belong in alike manner,’ because the former pointis secured by analogy, not fromreflection on the belonging of any

attribute, while the latter is judged by a comparison based on the fact that

an attribute belongs.



Next, for destructive purposes, see ifin rendering the property potentially,he has also through that potentialityrendered the property relatively tosomething that does not exist, when the

potentiality in question cannot belongto what does not exist: for then whatis stated to be a property will not bea property. Thus (e.g.) he who has saidthat ‘breathable’ is a property of‘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 relativelyto what does not exist:-for while air

may exist, even though there exist noanimal so constituted as to breathe theair, it is not possible to breathe itif no animal exist: so that it willnot, either, be a property of air to besuch as can be breathed at a time whenthere exists no animal such as to

breathe it and so it follows that‘breathable’ could not be a property ofair.

For constructive purposes, see if inrendering the property potentially herenders the property either relativelyto something that exists, or to



something that does not exist, when the potentiality in question can belong to

what does not exist: for then what has been stated not to be a property will be 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 potentially, has rendered the property

relatively to something that exists:for when ‘being’ exists, it will also

be capable of being acted upon or ofacting in a certain way: so that to be‘capable of being acted upon or ofacting’ would be a property of ‘being’.

Next, for destructive purposes, see ifhe has stated the property in thesuperlative: for then what has beenstated to be a property will not be a

property. For people who render the property in that way find that of the

object of which the description istrue, the name is not true as well: forthough the object perish thedescription will continue in being none

the less; for it belongs most nearly tosomething that is in being. An examplewould be supposing any one were torender ‘the lightest body’ as a

property of ‘fire’: for, though fire



perish, there eh re will still be someform of body that is the lightest, sothat ‘the lightest body’ could not be a

property of fire. For constructive purposes, on the other hand, see if he

has avoided rendering the property inthe superlative: for then the propertywill in this respect have been propertyof man has not rendered the propertycorrectly stated. Thus (e.g.) inasmuchas he in the superlative, the property

would in who states ‘a naturallycivilized animal’ as a this respecthave been correctly stated.

Book VI

1

THE discussion of Definitions fallsinto five parts. For you have to showeither (1) that it is not true at allto apply the expression as well to thatto which the term is applied (for thedefinition of Man ought to be true ofevery man); or (2) that though the

object has a genus, he has failed to put the object defined into the genus,

or to put it into the appropriate genus(for the framer of a definition shouldfirst place the object in its genus,



and then append its differences: for ofall the elements of the definition thegenus is usually supposed to be the

principal mark of the essence of whatis defined): or (3) that the expressionis not peculiar to the object (for, aswe said above as well, a definitionought to be peculiar): or else (4) seeif, though he has observed all theaforesaid cautions, he has yet failedto define the object, that is, to

express its essence. (5) It remains,apart from the foregoing, to see if hehas defined it, but defined itincorrectly.

Whether, then, the expression be notalso true of that of which the term istrue you should proceed to examineaccording to the commonplace rules thatrelate to Accident. For there too thequestion is always ‘Is so and so trueor untrue?’: for whenever we argue thatan accident belongs, we declare it to

be true, while whenever we argue thatit does not belong, we declare it to be

untrue. If, again, he has failed to place the object in the appropriate

genus, or if the expression be not peculiar to the object, we must go on

to examine the case according to the



commonplace rules that relate to genusand property.

It remains, then, to prescribe how toinvestigate whether the object has beeneither not defined at all, or elsedefined incorrectly. First, then, we

must proceed to examine if it has beendefined incorrectly: for with anythingit is easier to do it than to do itcorrectly. Clearly, then, more mistakes

are made in the latter task on accountof its greater difficulty. Accordinglythe attack becomes easier in the lattercase than in the former.

Incorrectness falls into two branches:(1) first, the use of obscure language(for the language of a definition oughtto be the very clearest possible,seeing that the whole purpose ofrendering it is to make somethingknown); (secondly, if the expressionused be longer than is necessary: forall additional matter in a definitionis superfluous. Again, each of the

aforesaid branches is divided into anumber of others.

2



One commonplace rule, then, in regardto obscurity is, See if the meaningintended by the definition involves anambiguity with any other, e.g.‘Becoming is a passage into being’, or‘Health is the balance of hot and coldelements’. Here ‘passage’ and ‘balance’are ambiguous terms: it is accordinglynot clear which of the several possiblesenses of the term he intends toconvey. Likewise also, if the term

defined be used in different senses andhe has spoken without distinguishing

between them: for then it is not clearto which of them the definitionrendered applies, and one can then

bring a captious objection on theground that the definition does notapply to all the things whosedefinition he has rendered: and thiskind of thing is particularly easy inthe case where the definer does not seethe ambiguity of his terms. Or, again,the questioner may himself distinguishthe various senses of the term renderedin the definition, and then institute

his argument against each: for if theexpression used be not adequate to thesubject in any of its senses, it isclear that he cannot have defined it inany sense aright.



Another rule is, See if he has used a metaphorical expression, as, for

instance, if he has defined knowledgeas ‘unsupplantable’, or the earth as a‘nurse’, or temperance as a ‘harmony’.For a metaphorical expression is alwaysobscure. It is possible, also, to arguesophistically against the user of a

metaphorical expression as though hehad used it in its literal sense: for

the definition stated will not apply tothe term defined, e.g. in the case oftemperance: for harmony is always found

between notes. Moreover, if harmony bethe genus of temperance, then the sameobject will occur in two genera ofwhich neither contains the other: forharmony does not contain virtue, norvirtue harmony. Again, see if he usesterms that are unfamiliar, as whenPlato describes the eye as ‘brow-shaded’, or a certain spider as poison-fanged’, or the marrow as ‘boneformed’.For an unusual phrase is alwaysobscure.

Sometimes a phrase is used neitherambiguously, nor yet metaphorically,nor yet literally, as when the law issaid to be the ‘measure’ or ‘image’ of



the things that are by nature just.Such phrases are worse than metaphor;for the latter does make its meaning tosome extent clear because of thelikeness involved; for those who use

metaphors do so always in view of somelikeness: whereas this kind of phrase

makes nothing clear; for there is nolikeness to justify the description‘measure’ or ‘image’, as applied to thelaw, nor is the law ordinarily so

called in a literal sense. So then, ifa man says that the law is literally a‘measure’ or an ‘image’, he speaksfalsely: for an image is something

produced by imitation, and this is notfound in the case of the law. If, onthe other hand, he does not mean theterm literally, it is clear that he hasused an unclear expression, and onethat is worse than any sort of

metaphorical expression.

Moreover, see if from the expressionused the definition of the contrary benot clear; for definitions that have

been correctly rendered also indicatetheir contraries as well. Or, again,see if, when it is merely stated byitself, it is not evident what itdefines: just as in the works of the



old painters, unless there were aninscription, the figures used to beunrecognizable.

3

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 definitionredundantly, first of all look and see

whether he has used any attribute that belongs universally, either to real

objects in general, or to all that fallunder the same genus as the objectdefined: for the mention of this issure to be redundant. For the genusought to divide the object from thingsin general, and the differentia fromany of the things contained in the samegenus. Now any term that belongs toeverything separates off the givenobject from absolutely nothing, whileany that belongs to all the things thatfall under the same genus does notseparate it off from the things

contained in the same genus. Anyaddition, 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 ofthe expression too is peculiar and

makes clear the essence of the term.Thus, in the definition of man, theaddition ‘capable of receivingknowledge’ is superfluous; for strikeit out, and still the expression is

peculiar and makes clear his essence.Speaking generally, everything is

superfluous upon whose removal theremainder still makes the term that is

being defined clear. Such, forinstance, would also be the definitionof the soul, assuming it to be statedas a ‘self-moving number’; for the soulis just ‘the self-moving’, as Platodefined it. Or perhaps the expressionused, though appropriate, yet does notdeclare the essence, if the word‘number’ be eliminated. Which of thetwo is the real state of the case it isdifficult to determine clearly: theright way to treat the matter in allcases is to be guided by convenience.

Thus (e.g.) it is said that thedefinition of phlegm is the ‘undigested

moisture that comes first off food’.Here the addition of the word‘undigested’ is superfluous, seeing



that ‘the first’ is one and not many,so that even when undigested’ is leftout the definition will still be

peculiar to the subject: for it isimpossible that both phlegm and alsosomething else should both be the firstto arise from the food. Or perhaps the

phlegm is not absolutely the firstthing to come off the food, but onlythe first of the undigested matters, sothat the addition ‘undigested’ is

required; for stated the other way thedefinition would not be true unless the

phlegm comes first of all.

Moreover, see if anything contained inthe definition fails to apply toeverything that falls under the samespecies: for this sort of definition isworse than those which include anattribute belonging to all thingsuniversally. For in that case, if theremainder of the expression be

peculiar, the whole too will be peculiar: for absolutely always, if to

something peculiar anything whatever

that is true be added, the whole too becomes peculiar. Whereas if any part

of the expression do not apply toeverything that falls under the samespecies, it is impossible that the



expression as a whole should be peculiar: for it will not be predicated

convertibly with the object; e.g. ‘awalking biped animal six feet high’:for an expression of that kind is not

predicated convertibly with the term, because the attribute ‘six feet high’

does not belong to everything thatfalls under the same species.

Again, see if he has said the same

thing more than once, saying (e.g.)‘desire’ is a ‘conation for the

pleasant’. For ‘desire’ is always ‘forthe pleasant’, so that what is the sameas desire will also be ‘for the

pleasant’. Accordingly our definitionof desire becomes ‘conation-for-the-

pleasant’: for the word ‘desire’ is theexact equivalent of the words ‘conationfor-the-pleasant’, so that both alikewill be ‘for the pleasant’. Or perhapsthere is no absurdity in this; forconsider this instance:-Man is a

biped’: therefore, what is the same as man is a biped: but ‘a walking biped

animal’ is the same as man, andtherefore walking biped animal is a

biped’. But this involves no realabsurdity. For ‘biped’ is not a

predicate of ‘walking animal’: if it



were, then we should certainly have‘biped’ predicated twice of the samething; but as a matter of fact thesubject said to be a biped is’a walking

biped animal’, so that the word ‘biped’is only used as a predicate once.Likewise also in the case of ‘desire’as well: for it is not ‘conation’ thatis said to be ‘for the pleasant’, butrather the whole idea, so that theretoo the predication is only made once.

Absurdity results, not when the sameword is uttered twice, but when thesame thing is more than once predicatedof a subject; e.g. if he says, likeXenocrates, that wisdom defines andcontemplates reality:’ for definitionis a certain type of contemplation, sothat by adding the words ‘andcontemplates’ over again he says thesame thing twice over. Likewise, too,those fail who say that ‘cooling’ is‘the privation of natural heat’. Forall privation is a privation of somenatural attribute, so that the additionof the word ‘natural’ is superfluous:

it would have been enough to say‘privation of heat’, for the word‘privation’ shows of itself that theheat meant is natural heat.



Again, see if a universal have been mentioned and then a particular case of

it be added as well, e.g. ‘Equity is aremission of what is expedient andjust’; for what is just is a branch ofwhat is expedient and is thereforeincluded in the latter term: its

mention is therefore redundant, anaddition of the particular after theuniversal has been already stated. Soalso, if he defines ‘medicine’ as

‘knowledge of what makes for health inanimals and men’, or ‘the law’ as ‘theimage of what is by nature noble andjust’; for what is just is a branch ofwhat is noble, so that he says the samething more than once.

4

Whether, then, a man defines a thingcorrectly or incorrectly you should

proceed to examine on these and similarlines. But whether he has mentioned anddefined its essence or no, should beexamined as follows: First of all, see

if he has failed to make the definitionthrough terms that are prior and moreintelligible. For the reason why thedefinition is rendered is to make knownthe term stated, and we make things



known by taking not any random terms, but such as are prior and more

intelligible, as is done indemonstrations (for so it is with allteaching and learning); accordingly, itis clear that a man who does not definethrough terms of this kind has notdefined at all. Otherwise, there will

be more than one definition of the samething: for clearly he who definesthrough terms that are prior and more

intelligible has also framed adefinition, and a better one, so that

both would then be definitions of thesame object. This sort of view,however, does not generally findacceptance: for of each real object theessence is single: if, then, there areto be a number of definitions of thesame thing, the essence of the objectwill be the same as it is representedto be in each of the definitions, andthese representations are not the same,inasmuch as the definitions aredifferent. Clearly, then, any one whohas not defined a thing through terms

that are prior and more intelligiblehas not defined it at all.

The statement that a definition has not been made through more intelligible



terms may be understood in two senses,either supposing that its terms areabsolutely less intelligible, orsupposing that they are lessintelligible to us: for either sense is

possible. Thus absolutely the prior is more intelligible than the posterior, a point, for instance, than a line, a

line than a plane, and a plane than asolid; just as also a unit is moreintelligible than a number; for it is

the prius and starting-point of allnumber. Likewise, also, a letter is

more intelligible than a syllable. Whereas to us it sometimes happens that

the converse is the case: for the solidfalls under perception most of all-morethan a plane-and a plane more than aline, and a line more than a point; for

most people learn things like theformer earlier than the latter; for anyordinary intelligence can grasp them,whereas the others require an exact andexceptional understanding.

Absolutely, then, it is better to try

to make what is posterior known throughwhat is prior, inasmuch as such a wayof procedure is more scientific. Ofcourse, in dealing with persons whocannot recognize things through terms



of that kind, it may perhaps benecessary to frame the expressionthrough terms that are intelligible tothem. Among definitions of this kindare those of a point, a line, and a

plane, all of which explain the prior by the posterior; for they say that a point is the limit of a line, a line of

a 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 thesame thing is more intelligible both tous and also absolutely, since a correctdefinition must define a thing throughits genus and its differentiae, andthese belong to the order of thingswhich are absolutely more intelligiblethan, and prior to, the species. Forannul the genus and differentia, andthe species too is annulled, so thatthese are prior to the species. Theyare also more intelligible; for if thespecies be known, the genus anddifferentia must of necessity be known

as well (for any one who knows what a man is knows also what ‘animal’ and

‘walking’ are), whereas if the genus orthe differentia be known it does notfollow of necessity that the species is



known as well: thus the species is lessintelligible. Moreover, those who saythat such definitions, viz. those which

proceed from what is intelligible tothis, that, or the other man, arereally and truly definitions, will haveto say that there are severaldefinitions of one and the same thing.For, as it happens, different thingsare more intelligible to different

people, not the same things to all; and

so a different definition would have to be rendered to each several person, if

the definition is to be constructedfrom what is more intelligible to

particular individuals. Moreover, tothe same people different things are

more intelligible at different times;first of all the objects of sense;then, as they become more sharpwitted,the converse; so that those who holdthat a definition ought to be renderedthrough what is more intelligible to

particular individuals would not haveto render the same definition at alltimes even to the same person. It is

clear, then, that the right way todefine is not through terms of thatkind, but through what is absolutely

more intelligible: for only in this waycould the definition come always to be



one and the same. Perhaps, also, whatis absolutely intelligible is what isintelligible, not to all, but to thosewho are in a sound state ofunderstanding, just as what isabsolutely healthy is what is healthyto those in a sound state of body. Allsuch points as this ought to be madevery precise, and made use of in thecourse of discussion as occasionrequires. The demolition of a

definition will most surely win ageneral approval if the definer happensto have framed his expression neitherfrom what is absolutely moreintelligible nor yet from what is so tous.

One form, then, of the failure to workthrough more intelligible terms is theexhibition of the prior through the

posterior, as we remarked before.’ Another form occurs if we find that the

definition has been rendered of what isat rest and definite through what isindefinite and in motion: for what is

still and definite is prior to what isindefinite 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 oppositesare always simultaneous by nature. Some

people think, also, that both areobjects of the same science, so thatthe one is not even more intelligiblethan the other. One must, however,observe that it is perhaps not possibleto define some things in any other way,

e.g. the double without the half, andall the terms that are essentiallyrelative: for in all such cases theessential being is the same as acertain relation to something, so thatit is impossible to understand the oneterm without the other, and accordinglyin the definition of the one the othertoo must be embraced. One ought tolearn up all such points as these, anduse them as occasion may seem torequire.

(2) Another is-if he has used the termdefined itself. This passes unobserved

when the actual name of the object isnot used, e.g. supposing any one haddefined 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 word for itsdefinition, 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 bringingin the ‘day’ he has brought in the sun.

(3) Again, see if he has defined onecoordinate 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 ofa division that are derived from thesame genus are simultaneous by natureand ‘odd’ and ‘even’ are such terms:for both are differentiae of number.

Likewise also, see if he has defined asuperior through a subordinate term,e.g. ‘An “even number” is “a numberdivisible into halves”’, or ‘”the good”is a “state of virtue” ‘. For ‘half’ isderived from ‘two’, and ‘two’ is aneven number: virtue also is a kind ofgood, so that the latter terms are

subordinate to the former. Moreover, inusing the subordinate term one is boundto use the other as well: for whoeveremploys the term ‘virtue’ employs theterm ‘good’, seeing that virtue is a



certain kind of good: likewise, also,whoever employs the term ‘half’ employsthe term ‘even’, for to be ‘divided inhalf’ means to be divided into two, andtwo is even.

5

Generally speaking, then, onecommonplace rule relates to the failureto frame the expression by means of

terms that are prior and moreintelligible: and of this thesubdivisions are those specified above.

A second is, see whether, though theobject is in a genus, it has not been

placed in a genus. This sort of erroris always found where the essence ofthe object does not stand first in theexpression, e.g. the definition of‘body’ as ‘that which has threedimensions’, or the definition of‘man’, supposing any one to give it, as‘that which knows how to count’: for itis not stated what it is that has threedimensions, or what it is that knows

how to count: whereas the genus is meant to indicate just this, and is

submitted first of the terms in thedefinition.



Moreover, see if, while the term to bedefined is used in relation to manythings, he has failed to render it inrelation to all of them; as (e.g.) ifhe define ‘grammar’ as the ‘knowledgehow to write from dictation’: for heought also to say that it is aknowledge how to read as well. For inrendering it as ‘knowledge of writing’has no more defined it than byrendering it as ‘knowledge of reading’:

neither in fact has succeeded, but onlyhe who mentions both these things,since it is impossible that thereshould be more than one definition ofthe same thing. It is only, however, insome cases that what has been saidcorresponds to the actual state ofthings: in some it does not, e.g. allthose terms which are not usedessentially in relation to both things:as medicine is said to deal with the

production of disease and health; forit is said essentially to do thelatter, but the former only byaccident: for it is absolutely alien to

medicine to produce disease. Here,then, the man who renders medicine asrelative to both of these things hasnot defined it any better than he who

mentions the one only. In fact he has



done it perhaps worse, 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 to

several things, see if he has renderedit as relative to the worse rather thanto the better; for every form ofknowledge and potentiality is generallythought to be relative to the best.

Again, if the thing in question be not placed in its own proper genus, one must examine it according to the

elementary rules in regard to genera,as has been said before.’

Moreover, see if he uses language whichtransgresses the genera of the thingshe defines, defining, e.g. justice as a‘state that produces equality’ or‘distributes what is equal’: for bydefining it so he passes outside thesphere of virtue, and so by leaving outthe genus of justice he fails to

express its essence: for the essence ofa thing must in each case bring in itsgenus. It is the same thing if theobject be not put into its nearestgenus; for the man who puts it into the



nearest one has stated all the highergenera, seeing that all the highergenera are predicated of the lower.Either, then, it ought to be put intoits nearest genus, or else to thehigher genus all the differentiae oughtto be appended whereby the nearestgenus is defined. For then he would nothave left out anything: but would

merely have mentioned the subordinategenus by an expression instead of by

name. On the other hand, he who mentions merely the higher genus by

itself, does not state the subordinategenus as well: in saying ‘plant’ a mandoes not specify ‘a tree’.

6

Again, in regard to the differentiae,we must examine in like manner whetherthe differentiae, too, that he hasstated be those of the genus. For if a

man has not defined the object by thedifferentiae peculiar to it, or has

mentioned something such as is utterly

incapable of being a differentia ofanything, e.g. ‘animal’ or ‘substance’,clearly he has not defined it at all:for the aforesaid terms do notdifferentiate anything at all. Further,



we must see whether the differentiastated possesses anything that is co-ordinate with it in a division; for, ifnot, clearly the one stated could not

be a differentia of the genus. For agenus is always divided by differentiaethat are co-ordinate members of adivision, as, for instance, by theterms ‘walking’, ‘flying’, ‘aquatic’,and ‘biped’. Or see if, though thecontrasted differentia exists, it yet

is not true of the genus, for then,clearly, neither of them could be adifferentia of the genus; fordifferentiae that are co-ordinates in adivision with the differentia of athing are all true of the genus towhich the thing belongs. Likewise,also, see if, though it be true, yetthe addition of it to the genus failsto make a species. For then, clearly,this could not be a specificdifferentia of the genus: for aspecific differentia, if added to thegenus, always makes a species. If,however, this be no true differentia,

no more is the one adduced, seeing thatit is a co-ordinate member of adivision with this.



Moreover, see if he divides the genus by a negation, as those do who define

line as ‘length without breadth’: forthis means simply that it has not any

breadth. The genus will then be foundto partake of its own species: for,since of everything either anaffirmation or its negation is true,length must always either lack breadthor possess it, so that ‘length’ aswell, i.e. the genus of ‘line’, will be

either with or without breadth. But‘length without breadth’ is thedefinition of a species, as also is‘length with breadth’: for ‘without

breadth’ and ‘with breadth’ aredifferentiae, and the genus anddifferentia constitute the definitionof the species. Hence the genus wouldadmit of the definition of its species.Likewise, also, it will admit of thedefinition of the differentia, seeingthat one or the other of the aforesaiddifferentiae is of necessity predicatedof the genus. The usefulness of this

principle is found in meeting those who

assert the existence of ‘Ideas’: for ifabsolute length exist, how will it be

predicable of the genus that it has breadth or that it lacks it? For one

assertion or the other will have to be



true of ‘length’ universally, if it isto be true of the genus at all: andthis is contrary to the fact: for thereexist both lengths which have, andlengths which have not, breadth. Hencethe only people against whom the rulecan be employed are those who assertthat a genus is always numerically one;and this is what is done by those whoassert the real existence of the‘Ideas’; for they allege that absolute

length and absolute animal are thegenus.

It may be that in some cases thedefiner is obliged to employ a negationas well, e.g. in defining privations.For ‘blind’ means a thing which cannotsee when its nature is to see. There isno difference between dividing thegenus by a negation, and dividing it bysuch an affirmation as is bound to havea negation as its co-ordinate in adivision, e.g. supposing he had definedsomething as ‘length possessed of

breadth’; for co-ordinate in the

division with that which is possessedof breadth is that which possesses no

breadth and that only, so that againthe genus is divided by a negation.



Again, see if he rendered the speciesas a differentia, as do those whodefine ‘contumely’ as ‘insolenceaccompanied by jeering’; for jeering isa kind of insolence, i.e. it is aspecies and not a differentia.

Moreover, see if he has stated thegenus as the differentia, e.g. ‘Virtueis a good or noble state: for ‘good’ isthe genus of ‘virtue’. Or possibly

‘good’ here is not the genus but thedifferentia, on the principle that thesame thing cannot be in two genera ofwhich neither contains the other: for‘good’ does not include ‘state’, norvice versa: for not every state is goodnor every good a ‘state’. Both, then,could not be genera, and consequently,if ‘state’ is the genus of virtue,clearly ‘good’ cannot be its genus: it

must rather be the differentia’. Moreover, ‘a state’ indicates the

essence of virtue, whereas ‘good’indicates not the essence but aquality: and to indicate a quality is

generally held to be the function ofthe differentia. See, further, whetherthe differentia rendered indicates anindividual rather than a quality: for



the general view is that thedifferentia always expresses a quality.

Look and see, further, whether thedifferentia belongs only by accident tothe object defined. For the differentiais never an accidental attribute, any

more than the genus is: for thedifferentia of a thing cannot both

belong and not belong to it.

Moreover, if either the differentia orthe species, or any of the things whichare under the species, is predicable ofthe genus, then he could not havedefined the term. For none of theaforesaid can possibly be predicated ofthe genus, seeing that the genus is theterm with the widest range of all.

Again, see if the genus be predicatedof the differentia; for the generalview is that the genus is predicated,not of the differentia, but of theobjects of which the differentia is

predicated. Animal (e.g.) is predicatedof ‘man’ or ‘ox’ or other walking

animals, not of the actual differentiaitself which we predicate of thespecies. 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 thespecies. Moreover, the differentiaewill be all either species orindividuals, if they are animals; forevery animal is either a species or anindividual.

Likewise you must inquire also if thespecies or any of the objects that comeunder it is predicated of the

differentia: for this is impossible,seeing that the differentia is a termwith a wider range than the variousspecies. Moreover, if any of thespecies be predicated of it, the resultwill be that the differentia is aspecies: if, for instance, ‘man’ be

predicated, the differentia is clearlythe human race. Again, see if thedifferentia fails to be prior to thespecies: for the differentia ought to

be posterior to the genus, but prior tothe species.

Look and see also if the differentia

mentioned belongs to a different genus,neither contained in nor containing thegenus in question. For the general viewis that the same differentia cannot beused of two non-subaltern genera. Else



the result will be that the samespecies as well will be in two non-subaltern genera: for each of thedifferentiae imports its own genus,e.g. ‘walking’ and ‘biped’ import withthem the genus ‘animal’. If, then, eachof the genera as well is true of thatof which the differentia is true, itclearly follows that the species must

be in two non-subaltern genera. Or perhaps it is not impossible for the

same differentia to be used of two non-subaltern genera, and we ought to addthe words ‘except they both besubordinate members of the same genus’.Thus ‘walking animal’ and ‘flyinganimal’ are non-subaltern genera, and‘biped’ is the differentia of both. Thewords ‘except they both be subordinate

members of the same genus’ oughttherefore to be added; for both theseare subordinate to ‘animal’. From this

possibility, that the same differentia may be used of two non-subaltern

genera, it is clear also that there isno necessity for the differentia to

carry with it the whole of the genus towhich it belongs, but only the one orthe other of its limbs together withthe genera that are higher than this,



as ‘biped’ carries with it either‘flying’ or ‘walking animal’.

See, too, if he has rendered ‘existencein’ something as the differentia of athing’s essence: for the general viewis that locality cannot differentiate

between one essence and another. Hence,too, people condemn those who divideanimals by means of the terms ‘walking’and ‘aquatic’, on the ground that

‘walking’ and ‘aquatic’ indicate merelocality. Or possibly in this case thecensure is undeserved; for ‘aquatic’does not mean ‘in’ anything; nor doesit denote a locality, but a certainquality: for even if the thing be onthe dry land, still it is aquatic: andlikewise a land-animal, even though it

be in the water, will still be a andnot an aquatic-animal. But all thesame, if ever the differentia doesdenote existence in something, clearlyhe will have made a bad mistake.

Again, see if he has rendered an

affection as the differentia: for everyaffection, if intensified, subverts theessence of the thing, while thedifferentia is not of that kind: forthe differentia is generally considered



rather to preserve that which itdifferentiates; and it is absolutelyimpossible for a thing to exist withoutits own special differentia: for ifthere be no ‘walking’, there will be no‘man’. In fact, we may lay downabsolutely that a thing cannot have asits differentia anything in respect ofwhich it is subject to alteration: forall things of that kind, ifintensified, destroy its essence. If,

then, a man has rendered anydifferentia of this kind, he has made a

mistake: for we undergo absolutely noalteration in respect of ourdifferentiae.

Again, see if he has failed to renderthe differentia of a relative termrelatively to something else; for thedifferentiae of relative terms arethemselves relative, as in the casealso of knowledge. This is classed asspeculative, practical and productive;and each of these denotes a relation:for it speculates upon something, and

produces something and does something.

Look and see also if the definerrenders each relative term relativelyto its natural purpose: for while in



some cases the particular relative termcan be used in relation to its natural

purpose only and to nothing else, somecan be used in relation to somethingelse as well. Thus sight can only beused for seeing, but a strigil can also

be used to dip up water. Still, if anyone were to define a strigil as aninstrument for dipping water, he has

made a mistake: for that is not itsnatural function. The definition of a

thing’s natural function is ‘that forwhich it would be used by the prudent

man, acting as such, and by the sciencethat 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 ofthe ‘soul,’ rather than of the‘reasoning faculty’: for ‘wisdom’ isthe virtue primarily of the reasoningfaculty: for it is in virtue of thisthat both the man and his soul are said

to be wise.

Moreover, if the thing of which theterm defined has been stated to be anaffection or disposition, or whatever



it may be, be unable to admit it, thedefiner has made a mistake. For everydisposition and every affection isformed naturally in that of which it isan affection or disposition, asknowledge, 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 ofsensation’, or that ‘perplexity’ is a

state of ‘equality between contraryreasonings’, or that ‘pain’ is a‘violent disruption of parts that arenaturally conjoined’. For sleep is notan attribute of sensation, whereas itought to be, if it is a failure ofsensation. Likewise, perplexity is notan attribute of opposite reasonings,nor pain of parts naturally conjoined:for then inanimate things will be in

pain, since pain will be present inthem. Similar in character, too, is thedefinition of ‘health’, say, as a‘balance of hot and cold elements’: forthen health will be necessarily

exhibited by the hot and cold elements:for balance of anything is an attributeinherent in those things of which it isthe balance, so that health would be anattribute of them. Moreover, people who



define in this way put effect forcause, or cause for effect. For thedisruption of parts naturally conjoinedis not pain, but only a cause of pain:nor again is a failure of sensationsleep, but the one is the cause of theother: for either we go to sleep

because sensation fails, or sensationfails because we go to sleep. Likewisealso an equality between contraryreasonings would be generally

considered to be a cause of perplexity:for it is when we reflect on both sidesof a question and find everything aliketo be in keeping with either coursethat we are perplexed which of the twowe are to do.

Moreover, with regard to all periods oftime look and see whether there be anydiscrepancy between the differentia andthe thing defined: e.g. supposing the‘immortal’ to be defined as a ‘livingthing immune at present fromdestruction’. For a living thing thatis immune ‘at present’ from destruction

will be immortal ‘at present’.Possibly, indeed, in this case thisresult does not follow, owing to theambiguity of the words ‘immune at

present from destruction’: for it may



mean either that the thing has not beendestroyed at present, or that it cannot

be destroyed at present, or that at present it is such that it never can be

destroyed. Whenever, then, we say thata living thing is at present immunefrom destruction, we mean that it is at

present a living thing of such a kindas never to be destroyed: and this isequivalent to saying that it isimmortal, so that it is not meant that

it is immortal only at present. Still,if ever it does happen that what has

been rendered according to thedefinition belongs in the present onlyor past, whereas what is meant by theword does not so belong, then the twocould not be the same. So, then, thiscommonplace rule ought to be followed,as we have said.

7

You should look and see also whetherthe term being defined is applied inconsideration of something other than

the definition rendered. Suppose (e.g.)a definition of ‘justice’ as the‘ability to distribute what is equal’.This would not be right, for ‘just’describes rather the man who chooses,



than the man who is able to distributewhat is equal: so that justice couldnot be an ability to distribute what isequal: for then also the most just manwould be the man with the most abilityto distribute what is equal.

Moreover, see if the thing admits ofdegrees, whereas what is renderedaccording to the definition does not,or, vice versa, what is rendered

according to the definition admits ofdegrees while the thing does not. Foreither both must admit them or elseneither, if indeed what is renderedaccording to the definition is the sameas the thing. Moreover, see if, while

both of them admit of degrees, they yetdo not both become greater together:e.g. suppose sexual love to be thedesire for intercourse: for he who is

more intensely in love has not a moreintense desire for intercourse, so that

both do not become intensified at once:they certainly should, however, hadthey been the same thing.

Moreover, suppose two things to be before you, see if the term to be

defined applies more particularly tothe one to which the content of the



definition is less applicable. Take,for instance, the definition of ‘fire’as the ‘body that consists of the mostrarefied particles’. For ‘fire’ denotesflame rather than light, but flame isless the body that consists of the mostrarefied particles than is light:whereas both ought to be moreapplicable to the same thing, if theyhad been the same. Again, see if theone expression applies alike to both

the objects before you, while the otherdoes not apply to both alike, but more

particularly to one of them.

Moreover, see if he renders thedefinition relative to two things takenseparately: thus, the beautiful’ is‘what is pleasant to the eyes or to theears”: or ‘the real’ is ‘what iscapable of being acted upon or ofacting’. For then the same thing will

be both beautiful and not beautiful,and likewise will be both real and notreal. For ‘pleasant to the ears’ will

be the same as ‘beautiful’, so that

‘not pleasant to the ears’ will be thesame as ‘not beautiful’: for ofidentical things the opposites, too,are identical, and the opposite of‘beautiful’ is ‘not beautiful’, while



of ‘pleasant to the ears’ the oppositeis not pleasant to the cars’: clearly,then, ‘not pleasant to the ears’ is thesame thing as ‘not beautiful’. If,therefore, something be pleasant to theeyes but not to the ears, it will be

both beautiful and not beautiful. Inlike manner we shall show also that thesame thing is both real and unreal.

Moreover, of both genera and

differentiae and all the other termsrendered in definitions you shouldframe definitions in lieu of the terms,and then see if there be anydiscrepancy between them.

8

If the term defined be relative, eitherin itself or in respect of its genus,see whether the definition fails to

mention that to which the term, eitherin itself or in respect of its genus,is relative, e.g. if he has defined‘knowledge’ as an ‘incontrovertible

conception’ or ‘wishing’ as ‘painlessconation’. For of everything relativethe essence is relative to somethingelse, seeing that the being of everyrelative term is identical with being



in a certain relation to something. Heought, therefore, to have said thatknowledge is ‘conception of a knowable’and that wishing is ‘conation for agood’. Likewise, also, if he hasdefined ‘grammar’ as ‘knowledge ofletters’: whereas in the definitionthere ought to be rendered either thething to which the term itself isrelative, or that, whatever it is, towhich its genus is relative. Or see if

a relative term has been described notin relation to its end, the end inanything being whatever is best in itor gives its purpose to the rest.Certainly it is what is best or finalthat should be stated, e.g. that desireis not for the pleasant but for

pleasure: for this is our purpose inchoosing what is pleasant as well.

Look and see also if that in relationto which he has rendered the term be a

process or an activity: for nothing ofthat kind is an end, for the completionof the activity or process is the end

rather than the process or activityitself. Or perhaps this rule is nottrue in all cases, for almost everybody

prefers the present experience of pleasure to its cessation, so that they



would count the activity as the endrather than its completion.

Again see in some cases if he hasfailed to distinguish the quantity orquality or place or other differentiaeof an object; e.g. the quality andquantity of the honour the striving forwhich makes a man ambitious: for all

men strive for honour, so that it isnot enough to define the ambitious man

as him who strives for honour, but theaforesaid differentiae must be added.Likewise, also, in defining thecovetous man the quantity of money heaims at, or in the case of theincontinent man the quality of the

pleasures, should be stated. For it isnot the man who gives way to any sortof pleasure whatever who is calledincontinent, but only he who gives wayto a certain kind of pleasure. Oragain, people sometimes define night asa ‘shadow on the earth’, or anearthquake as a movement of the earth’,or a cloud as ‘condensation of the

air’, or a wind as a ‘movement of theair’; whereas they ought to specify aswell quantity, quality, place, andcause. Likewise, also, in other casesof the kind: for by omitting any



differentiae whatever he fails to statethe essence of the term. One shouldalways attack deficiency. For a

movement of the earth does notconstitute an earthquake, nor a

movement of the air a wind,irrespective of its manner and theamount involved.

Moreover, in the case of conations, andin any other cases where it applies,

see if the word ‘apparent’ is left out,e.g. ‘wishing is a conation after thegood’, or ‘desire is a conation afterthe pleasant’-instead of saying ‘theapparently good’, or ‘pleasant’. Foroften those who exhibit the conation donot perceive what is good or pleasant,so that their aim need not be reallygood or pleasant, but only apparentlyso. They ought, therefore, to haverendered the definition alsoaccordingly. On the other hand, any onewho maintains the existence of Ideasought to be brought face to face withhis Ideas, even though he does render

the word in question: for there can beno Idea of anything merely apparent:the general view is that an Idea isalways spoken of in relation to anIdea: thus absolute desire is for the



absolutely pleasant, and absolutewishing is for the absolutely good;they therefore cannot be for anapparent good or an apparently

pleasant: for the existence of anabsolutely-apparently-good or pleasantwould be an absurdity.

9

Moreover, if the definition be of the

state of anything, look at what is inthe state, while if it be of what is inthe state, look at the state: andlikewise also in other cases of thekind. Thus if the pleasant be identicalwith the beneficial, then, too, the manwho is pleased is benefited. Speakinggenerally, in definitions of this sortit happens that what the definerdefines is in a sense more than onething: for in defining knowledge, a manin a sense defines ignorance as well,and likewise also what has knowledgeand what lacks it, and what it is toknow and to be ignorant. For if the

first be made clear, the others becomein a certain sense clear as well. Wehave, then, to be on our guard in allsuch cases against discrepancy, usingthe elementary principles drawn from



consideration of contraries and ofcoordinates.

Moreover, in the case of relativeterms, see if the species is renderedas relative to a species of that towhich the genus is rendered asrelative, e.g. supposing belief to berelative to some object of belief, seewhether a particular belief is maderelative to some particular object of

belief: and, if a multiple be relativeto a fraction, see whether a particular

multiple be made relative to a particular fraction. For if it be not

so rendered, clearly a mistake has been made.

See, also, if the opposite of the termhas the opposite definition, whether(e.g.) the definition of ‘half’ is theopposite of that of ‘double’: for if‘double’ is ‘that which exceeds another

by an equal amount to that other’,‘half’ is ‘that which is exceeded by anamount equal to itself’. In the same

way, too, with contraries. For to thecontrary term will apply the definitionthat is contrary in some one of theways in which contraries are conjoined.Thus (e.g.) if ‘useful’=’productive of



good’, ‘injurious’=productive of evil’or ‘destructive of good’, for one orthe other of thee is bound to becontrary to the term originally used.Suppose, then, neither of these thingsto be the contrary of the termoriginally used, then clearly neitherof the definitions rendered later could

be the definition of the contrary ofthe term originally defined: andtherefore the definition originally

rendered of the original term has not been rightly rendered either. Seeing, moreover, that of contraries, the one

is sometimes a word forced to denotethe privation of the other, as (e.g.)inequality is generally held to be the

privation of equality (for ‘unequal’ 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 othercannot then be defined through the onewhose form denotes the privation; forelse we should find that each is being

interpreted by the other. We must inthe case of contrary terms keep an eyeon this mistake, e.g. supposing any onewere to define equality as the contraryof inequality: for then he is defining



it through the term which denotes privation of it. Moreover, a man who so

defines is bound to use in hisdefinition the very term he isdefining; and this becomes clear, iffor the word we substitute itsdefinition. For to say ‘inequality’ isthe same as to say ‘privation ofequality’. Therefore equality sodefined will be ‘the contrary of the

privation of equality’, so that he

would have used the very word to bedefined. Suppose, however, that neitherof the contraries be so formed as todenote privation, but yet thedefinition of it be rendered in a

manner like the above, e.g. suppose‘good’ to be defined as ‘the contraryof evil’, then, since it is clear that‘evil’ too will be ‘the contrary ofgood’ (for the definition of thingsthat are contrary in this must berendered in a like manner), the resultagain is that he uses the very term

being defined: for ‘good’ is inherentin the definition of ‘evil’. If, then,

‘good’ be the contrary of evil, andevil be nothing other than the‘contrary of good’, then ‘good’ will bethe ‘contrary of the contrary of good’.



Clearly, then, he has used the veryword to be defined.

Moreover, see if in rendering a termformed to denote privation, he hasfailed to render the term of which itis the privation, e.g. the state, orcontrary, or whatever it may be whose

privation it is: also if he has omittedto add either any term at all in whichthe privation is naturally formed, or

else that in which it is naturallyformed primarily, e.g. whether indefining ‘ignorance’ a privation he hasfailed to say that it is the privationof ‘knowledge’; or has failed to add inwhat it is naturally formed, or, thoughhe has added this, has failed to renderthe thing in which it is primarilyformed, placing it (e.g.) in ‘man’ orin ‘the soul’, and not in the‘reasoning faculty’: for if in any ofthese 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

proper rendering of its essence muststate both of what it is the privationand what it 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 also would

be generally thought to be incurred inthe case of ‘error’ by any one who isnot using it as a merely negative term.For what is generally thought to be inerror is not that which has noknowledge, but rather that which has

been deceived, and for this reason we

do not talk of inanimate things or ofchildren as ‘erring’. ‘Error’, then, isnot used to denote a mere privation ofknowledge.

10

Moreover, see whether the likeinflexions in the definition apply tothe like inflexions of the term; e.g.if ‘beneficial’ means ‘productive ofhealth’, does ‘beneficially’ mean

productively of health’ and a‘benefactor’ a ‘producer of health’?

Look too and see whether the definitiongiven will apply to the Idea as well.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: forthe Idea (e.g. the absolute Man) is not

mortal, so that the definition will notfit the Idea. So always wherever thewords ‘capable of acting on’ or‘capable of being acted upon’ areadded, the definition and the Idea areabsolutely bound to be discrepant: forthose who assert the existence of Ideashold that they are incapable of beingacted upon, or of motion. In dealing

with these people even arguments ofthis kind are useful.

Further, see if he has rendered asingle common definition of terms thatare used ambiguously. For terms whosedefinition corresponding their commonname is one and the same, aresynonymous; if, then, the definitionapplies in a like manner to the wholerange of the ambiguous term, it is nottrue of any one of the objectsdescribed by the term. This is,

moreover, what happens to Dionysius’definition of ‘life’ when stated as ‘a

movement of a creature sustained bynutriment, congenitally present withit’: for this is found in plants as

much as in animals, whereas ‘life’ isgenerally understood to mean not one



kind of thing only, but to be one thingin animals and another in plants. It is

possible to hold the view that life isa synonymous term and is always used todescribe one thing only, and thereforeto render the definition in this way on

purpose: or it may quite well happenthat a man may see the ambiguouscharacter of the word, and wish torender the definition of the one senseonly, and yet fail to see that he has

rendered a definition common to bothsenses instead of one peculiar to thesense he intends. In either case,whichever course he pursues, he isequally at fault. Since ambiguous termssometimes pass unobserved, it is bestin questioning to treat such terms asthough they were synonymous (for thedefinition of the one sense will notapply to the other, so that theanswerer will be generally thought notto have defined it correctly, for to asynonymous term the definition shouldapply in its full range), whereas inanswering you should yourself

distinguish between the senses.Further, as some answerers call‘ambiguous’ what is really synonymous,whenever the definition rendered failsto apply universally, and, vice versa,



call synonymous what is reallyambiguous supposing their definitionapplies to both senses of the term, oneshould secure a preliminary admissionon such points, or else prove

beforehand that so-and-so is ambiguousor synonymous, as the case may be: for

people are more ready to agree whenthey do not foresee what theconsequence will be. If, however, noadmission has been made, and the man

asserts that what is really synonymousis ambiguous because the definition hehas rendered will not apply to thesecond sense as well, see if thedefinition of this second meaningapplies also to the other meanings: forif so, this meaning must clearly besynonymous with those others.Otherwise, there will be more than onedefinition of those other meanings, forthere are applicable to them twodistinct definitions in explanation ofthe term, viz. the one previouslyrendered and also the later one. Again,if any one were to define a term used

in several senses, and, finding thathis definition does not apply to themall, were to contend not that the termis ambiguous, but that even the termdoes not properly apply to all those



senses, just because his definitionwill not do so either, then one mayretort to such a man that though insome things one must not use thelanguage of the people, yet in aquestion of terminology one is bound toemploy the received and traditionalusage and not to upset matters of thatsort.

11

Suppose now that a definition has beenrendered of some complex term, takeaway the definition of one of theelements in the complex, and see ifalso the rest of the definition definesthe rest of it: if not, it is clearthat neither does the whole definitiondefine the whole complex. Suppose, e.g.that some one has defined a ‘finitestraight line’ as ‘the limit of afinite plane, such that its centre isin a line with its extremes’; if nowthe definition of a finite line’ be the‘limit of a finite plane’, the rest

(viz. ‘such that its centre is in aline with its extremes’) ought to be adefinition of straight’. But aninfinite straight line has neithercentre nor extremes and yet is straight



so that this remainder does not definethe remainder of the term.

Moreover, if the term defined be acompound notion, see if the definitionrendered be equimembral with the termdefined. A definition is said to beequimembral with the term defined whenthe number of the elements compoundedin the latter is the same as the numberof nouns and verbs in the definition.

For the exchange in such cases is boundto be merely one of term for term, inthe case of some if not of all, seeingthat there are no more terms used nowthan formerly; whereas in a definitionterms ought to be rendered by phrases,if possible in every case, or if not,in the majority. For at that rate,simple objects too could be defined by

merely calling them by a differentname, e.g. ‘cloak’ instead of‘doublet’.

The mistake is even worse, if actuallya less well known term be substituted,

e.g. ‘pellucid mortal’ for ‘white man’:for it is no definition, and moreoveris less intelligible when put in thatform.



Look and see also whether, in theexchange of words, the sense failsstill to be the same. Take, forinstance, the explanation of‘speculative knowledge’ as ‘speculativeconception’: for conception is not thesame as knowledge-as it certainly oughtto be if the whole is to be the sametoo: for though the word ‘speculative’is common to both expressions, yet theremainder is different.

Moreover, see if in replacing one ofthe terms by something else he hasexchanged the genus and not thedifferentia, as in the example justgiven: for ‘speculative’ is a lessfamiliar term than knowledge; for theone is the genus and the other thedifferentia, and the genus is alwaysthe most familiar term of all; so thatit is not this, but the differentia,that ought to have been changed, seeingthat it is the less familiar. It might

be held that this criticism isridiculous: because there is no reason

why the most familiar term should notdescribe the differentia, and not thegenus; in which case, clearly, the termto be altered would also be thatdenoting the genus and not the



differentia. If, however, a man issubstituting for a term not merelyanother term but a phrase, clearly itis of the differentia rather than ofthe genus that a definition should berendered, seeing that the object ofrendering the definition is to make thesubject familiar; for the differentiais less familiar than the genus.

If he has rendered the definition of

the differentia, see whether thedefinition rendered is common to it andsomething else as well: e.g. wheneverhe says that an odd number is a ‘numberwith a middle’, further definition isrequired of how it has a middle: forthe word ‘number’ is common to bothexpressions, and it is the word ‘odd’for which the phrase has beensubstituted. Now both a line and a bodyhave a middle, yet they are not ‘odd’;so that this could not be a definitionof ‘odd’. If, on the other hand, the

phrase ‘with a middle’ be used inseveral senses, the sense here intended

requires to be defined. So that thiswill either discredit the definition or

prove that it is no definition at all.

12



Again, see if the term of which he

renders the definition is a reality,whereas what is contained in thedefinition is not, e.g. Suppose ‘white’to be defined as ‘colour mingled withfire’: for what is bodiless cannot be

mingled with body, so that ‘colour’‘mingled with fire’ could not exist,whereas ‘white’ does exist.

Moreover, those who in the case ofrelative terms do not distinguish towhat the object is related, but havedescribed it only so as to include itamong too large a number of things, arewrong either wholly or in part; e.g.suppose some one to have defined‘medicine’ as a science of Reality’.For if medicine be not a science ofanything that is real, the definitionis clearly altogether false; while ifit be a science of some real thing, butnot of another, it is partly false; forit ought to hold of all reality, if itis said to be of Reality essentially

and not accidentally: as is the casewith other relative terms: for everyobject of knowledge is a term relativeto knowledge: likewise, also, withother relative terms, inasmuch as all



such are convertible. Moreover, if theright way to render account of a thing

be to render it as it is not in itself but accidentally, then each and every

relative term would be used in relationnot to one thing but to a number ofthings. For there is no reason why thesame thing should not be both real andwhite and good, so that it would be acorrect rendering to render the objectin relation to any one whatsoever of

these, if to render what it isaccidentally be a correct way to renderit. It is, moreover, impossible that adefinition of this sort should be

peculiar to the term rendered: for notonly but the majority of the othersciences too, have for their objectsome real thing, so that each will be ascience of reality. Clearly, then, sucha definition does not define anyscience at all; for a definition oughtto be peculiar to its own term, notgeneral.

Sometimes, again, people define not the

thing but only the thing in a good or perfect condition. Such is the

definition of a rhetorician as ‘one whocan always see what will persuade inthe given circumstances, and omit



nothing’; or of a thief, as ‘one who pilfers in secret’: for clearly, if

they each do this, then the one will bea good rhetorician, and the other agood thief: whereas it is not theactual pilfering in secret, but thewish to do it, that constitutes thethief.

Again, see if he has rendered what isdesirable for its own sake as desirable

for what it produces or does, or as inany way desirable because of somethingelse, e.g. by saying that justice is‘what preserves the laws’ or thatwisdom is ‘what produces happiness’;for what produces or preservessomething else is one of the thingsdesirable for something else. It might

be said that it is possible for what isdesirable in itself to be desirable forsomething else as well: but still todefine what is desirable in itself insuch a way is none the less wrong: forthe essence contains par excellencewhat is best in anything, and it is

better for a thing to be desirable initself than to be desirable forsomething else, so that this is ratherwhat the definition too ought to haveindicated.



13

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 and B’, thedefinition will be true of both and yetof neither of them; suppose, e.g.justice to be defined as ‘temperanceand courage.’ For if of two persons

each has one of the two only, both andyet neither will be just: for bothtogether have justice, and yet eachsingly fails to have it. Even if thesituation here described does not sofar appear very absurd because of theoccurrence of this kind of thing inother cases also (for it is quite

possible for two men to have a mina between them, though neither of them

has it by himself), yet least that theyshould have contrary attributes surelyseems quite absurd; and yet this willfollow if the one be temperate and yeta coward, and the other, though brave,

be a profligate; for then both willexhibit both justice and injustice: forif justice be temperance and bravery,then injustice will be cowardice and

profligacy. In general, too, all the



ways of showing that the whole is notthe same as the sum of its parts areuseful in meeting the type justdescribed; for a man who defines inthis way seems to assert that the partsare the same as the whole. Thearguments are particularly appropriatein cases where the process of puttingthe parts together is obvious, as in ahouse and other things of that sort:for there, clearly, you may have the

parts and yet not have the whole, sothat parts and whole cannot be thesame.

If, however, he has said that the term being defined is not ‘A and B’ but the

‘product of A and B’, look and see inthe first place if A and B cannot inthe nature of things have a single

product: for some things are so relatedto one another that nothing can come ofthem, e.g. a line and a number.

Moreover, see if the term that has beendefined is in the nature of thingsfound primarily in some single subject,

whereas the things which he has said produce it are not found primarily in

any single subject, but each in aseparate one. If so, clearly that termcould not be the product of these



things: for the whole is bound to be inthe 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 otherhand, both parts and whole are found

primarily in some single subject, seeif that medium is not the same, but onething in the case of the whole andanother in that of the parts. Again,see whether the parts perish together

with the whole: for it ought to happen,vice versa, that the whole perisheswhen the parts perish; when the whole

perishes, there is no necessity thatthe parts should perish too. Or again,see if the whole be good or evil, andthe parts neither, or, vice versa, ifthe parts be good or evil and the wholeneither. For it is impossible eitherfor a neutral thing to producesomething good or bad, or for thingsgood or bad to produce a neutral thing.Or again, see if the one thing is moredistinctly good 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 false opinion’: here the goodnessof courage exceeds the evil of falseopinion; accordingly the product of



these ought to have corresponded tothis excess, and to be either goodwithout qualification, or at least moregood than evil. Or it may be that thisdoes not necessarily follow, unlesseach be in itself good or bad; for manythings that are productive are not goodin themselves, but only in combination;or, per contra, they are good takensingly, and bad or neutral incombination. What has just been said is

most clearly illustrated in the case ofthings that make for health orsickness; for some drugs are such thateach taken alone is good, but if theyare both administered in a mixture,

bad.

Again, see whether the whole, as produced from a better and worse, fails

to be worse than the better and betterthan the worse element. This again,however, need not necessarily be thecase, unless the elements compounded bein 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 besynonymous with one of the elements:for it ought not to be, any more than



in the case of syllables: for thesyllable is not synonymous with any ofthe letters of which it is made up.

Moreover, see if he has failed to statethe manner of their composition: forthe mere mention of its elements is notenough to make the thing intelligible.For the essence of any compound thingis not merely that it is a product ofso-and-so, but that it is a product of

them compounded in such and such a way,just as in the case of a house: forhere the materials do not make a houseirrespective of the way they are puttogether.

If a man has defined an object as‘A+B’, the first thing to be said isthat ‘A+B’ means the same either as ‘Aand B’, or as the ‘product of A and B.’for ‘honey+water’ means either thehoney and the water, or the ‘drink madeof honey and water’. If, then, headmits that ‘A+B’ is + B’ is the sameas either of these two things, the same

criticisms will apply as have already been given for meeting each of them. Moreover, distinguish between the

different senses in which one thing may be said to be ‘+’ another, and see if



there is none of them in which A could be said to exist ‘+ B.’ Thus e.g.

supposing the expression to mean thatthey exist either in some identicalthing capable of containing them (ase.g. justice and courage are found inthe soul), or else in the same place orin the same time, and if this be in noway true of the A and B in question,clearly the definition rendered couldnot hold of anything, as there is no

possible way in which A can exist B’.If, however, among the various sensesabove distinguished, it be true that Aand B are each found in the same timeas the other, look and see if possiblythe two are not used in the samerelation. Thus e.g. suppose courage tohave been defined as ‘daring with rightreasoning’: here it is possible thatthe person exhibits daring in robbery,and right reasoning in regard to the

means of health: but he may have ‘theformer quality+the latter’ at the sametime, and not as yet be courageous!

Moreover, even though both be used in

the same relation as well, e.g. inrelation to medical treatment (for a

man may exhibit both daring and rightreasoning in respect of medicaltreatment), still, none the less, not



even this combination of ‘the one+theother ‘makes him ‘courageous’. For thetwo must not relate to any casualobject that is the same, any more thaneach to a different object; rather,they must relate to the function ofcourage, e.g. meeting the perils ofwar, or whatever is more properlyspeaking its function than this.

Some definitions rendered in this form

fail to come under the aforesaiddivision at all, e.g. a definition ofanger as ‘pain with a consciousness of

being slighted’. For what this means tosay is that it is because of aconsciousness of this sort that the

pain occurs; but to occur ‘because of’a thing is not the same as to occur ‘+a thing’ in any of its aforesaidsenses.

14

Again, if he have described the wholecompounded as the ‘composition’ of

these things (e.g. ‘a living creature’as a ‘composition of soul and body’),first of all see whether he has omittedto 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 enoughto say it is a composition, but youshould also go on to define the kind ofcomposition: for these things do notform flesh irrespective of the mannerof their composition, but whencompounded in one way they form flesh,when in another, bone. It appears,

moreover, that neither of the aforesaidsubstances is the same as a

‘composition’ at all: for a compositionalways has a decomposition as itscontrary, whereas neither of theaforesaid has any contrary. Moreover,if it is equally probable that everycompound is a composition or else thatnone is, and every kind of livingcreature, though a compound, is never acomposition, then no other compoundcould be a composition either.

Again, if in the nature of a thing twocontraries are equally liable to occur,and the thing has been defined throughthe one, clearly it has not been

defined; else there will be more thanone definition of the same thing; forhow is it any more a definition todefine it through this one than throughthe other, seeing that both alike are



naturally liable to occur in it? Suchis the definition of the soul, ifdefined as a substance capable ofreceiving knowledge: for it has a likecapacity for receiving ignorance.

Also, even when one cannot attack thedefinition as a whole for lack ofacquaintance with the whole, one shouldattack some part of it, if one knowsthat part and sees it to be incorrectly

rendered: for if the part bedemolished, so too is the wholedefinition. Where, again, a definitionis obscure, one should first of allcorrect and reshape it in order to makesome part of it clear and get a handlefor attack, and then proceed to examineit. For the answerer is bound either toaccept the sense as taken by thequestioner, or else himself to explainclearly whatever it is that hisdefinition means. Moreover, just as inthe assemblies the ordinary practice isto move an emendation of the existinglaw and, if the emendation is better,

they repeal the existing law, so oneought to do in the case of definitionsas well: one ought oneself to propose asecond definition: for if it is seen to

be better, and more indicative of the



object defined, clearly the definitionalready laid down will have beendemolished, on the principle that therecannot be more than one definition ofthe same thing.

In combating definitions it is alwaysone of the chief elementary principlesto take by oneself a happy shot at adefinition of the object before one, orto adopt some correctly expressed

definition. For one is bound, with the model (as it were) before one’s eyes,

to discern both any shortcoming in anyfeatures that the definition ought tohave, and also any superfluousaddition, so that one is bettersupplied with lines of attack.

As to definitions, then, let so muchsuffice.

Book VII

1

WHETHER two things are ‘the same’ or‘different’, in the most literal of the

meanings ascribed to ‘sameness’ (and wesaid’ that ‘the same’ applies in the

most literal sense to what is



numerically one), may be examined inthe light of their inflexions andcoordinates and opposites. For ifjustice be the same as courage, thentoo the just man is the same as the

brave man, and ‘justly’ is the same as‘bravely’. Likewise, too, in the caseof their opposites: for if two things

be the same, their opposites also will be the same, in any of the recognized

forms of opposition. For it is the same

thing to take the opposite of the oneor that of the other, seeing that theyare the same. Again it may be examinedin the light of those things which tendto produce or to destroy the things inquestion of their formation anddestruction, and in general of anything that is related in like manner toeach. For where things are absolutelythe same, their formations anddestructions also are the same, and soare the things that tend to produce orto destroy them. Look and see also, ina case where one of two things is saidto be something or other in a

superlative degree, if the other ofthese alleged identical things can also

be described by a superlative in thesame respect. Thus Xenocrates arguesthat the happy life and the good life



are the same, seeing that of all formsof life the good life is the mostdesirable and so also is the happylife: for ‘the most desirable’ and thegreatest’ apply but to one thing.’Likewise also in other cases of thekind. Each, however, of the two thingstermed ‘greatest’ or most desirable’

must be numerically one: otherwise no proof will have been given that they

are the same; for it does not follow

because Peloponnesians and Spartans arethe bravest of the Greeks, thatPeloponnesians are the same asSpartans, seeing that ‘Peloponnesian’is not any one person nor yet‘Spartan’; it only follows that the one

must be included under the other as‘Spartans’ are under ‘Peloponnesians’:for otherwise, if the one class be notincluded under the other, each will be

better than the other. For then thePeloponnesians are bound to be betterthan the Spartans, seeing that the oneclass is not included under the other;for they are better than anybody else.

Likewise also the Spartans must perforce be better than the

Peloponnesians; for they too are betterthan anybody else; each then is betterthan the other! Clearly therefore what



is styled ‘best’ and ‘greatest’ must bea single thing, if it is to be provedto be ‘the same’ as another. This alsois why Xenocrates fails to prove hiscase: for the happy life is notnumerically single, nor yet the goodlife, so that it does not follow that,

because they are both the mostdesirable, they are therefore the same,

but only that the one falls under theother.

Again, look and see if, supposing theone to be the same as something, theother also is the same as it: for ifthey be not both the same as the samething, clearly neither are they thesame as one another.

Moreover, examine them in the light oftheir accidents or of the things ofwhich they are accidents: for anyaccident belonging to the one must

belong also to the other, and if theone belong to anything as an accident,so must the other also. If in any of

these respects there is a discrepancy,clearly they are not the same.

See further whether, instead of both being found in one class of predicates,



the one signifies a quality and theother a quantity or relation. Again,see if the genus of each be not thesame, the one being ‘good’ and theother evil’, or the one being ‘virtue’and the other ‘knowledge’: or see if,though the genus is the same, thedifferentiae predicted of either be notthe same, the one (e.g.) beingdistinguished 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 itis not the case that a man desiresintercourse more intensely, the moreintensely he is in love, so that loveand the desire for intercourse are notthe same.

Moreover, examine them by means of anaddition, and see whether the addition

of each to the same thing fails to makethe same whole; or if the subtractionof the same thing from each leaves adifferent remainder. Suppose (e.g.)that he has declared ‘double a half’ to



be the same as ‘a multiple of a half’:then, subtracting the words ‘a half’from each, the remainders ought to havesignified the same thing: but they donot; for ‘double’ and ‘a multiple of’do not signify the same thing.

Inquire also not only if someimpossible consequence results directlyfrom the statement made, that A and Bare the same, but also whether it is

possible for a supposition to bring itabout; as happens to those who assertthat ‘empty’ is the same as ‘full ofair’: for clearly if the air beexhausted, the vessel will not be less

but more empty, though it will nolonger be full of air. So that by asupposition, which may be true or may

be false (it makes no differencewhich), the one character is annulledand not the other, showing that theyare not the same.

Speaking generally, one ought to be onthe look-out for any discrepancy

anywhere in any sort of predicate ofeach term, and in the things of whichthey are predicated. For all that is

predicated of the one should be predicated also of the other, and of



whatever the one is a predicate, theother should be a predicate of it aswell.

Moreover, as ‘sameness’ is a term usedin many senses, see whether things thatare the same in one way are the samealso in a different way. For there iseither no necessity or even no

possibility that things that are thesame specifically or generically should

be numerically the same, and it is withthe question whether they are or arenot the same in that sense that we areconcerned.

Moreover, see whether the one can existwithout the other; for, if so, theycould not be the same.

2

Such is the number of the commonplacerules that relate to ‘sameness’. It isclear from what has been said that allthe destructive commonplaces relating

to sameness are useful also inquestions of definition, as was said

before:’ for if what is signified bythe term and by the expression be notthe same, clearly the expression



rendered could not be a definition. None of the constructive commonplaces,

on the other hand, helps in the matterof definition; for it is not enough toshow the sameness of content betweenthe expression and the term, in orderto establish that the former is adefinition, but a definition must havealso all the other characters alreadyannounced.

3

This then is the way, and these thearguments, whereby the attempt todemolish a definition should always be

made. If, on the other hand, we desireto establish one, the first thing toobserve is that few if any who engagein discussion arrive at a definition byreasoning: they always assume somethingof the kind as their starting points-

both in geometry and in arithmetic andthe other studies of that kind. In thesecond place, to say accurately what adefinition 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 to a



thing’s definition and essence is quite possible. For if a definition is an

expression signifying the essence ofthe thing and the predicates containedtherein ought also to be the only oneswhich are predicated of the thing inthe category of essence; and genera anddifferentiae are so predicated in thatcategory: it is obvious that if onewere to get an admission that so and soare the only attributes predicated in

that category, the expressioncontaining so and so would of necessity

be a definition; for it is impossiblethat anything else should be adefinition, seeing that there is notanything else predicated of the thingin the category of essence.

That a definition may thus be reached by a process of reasoning is obvious.

The means whereby it should beestablished have been more preciselydefined elsewhere, but for the purposesof the inquiry now before us the samecommonplace rules serve. For we have to

examine into the contraries and otheropposites of the thing, surveying theexpressions used both as wholes and indetail: for if the opposite definitiondefines that opposite term, the



definition given must of necessity bethat of the term before us. Seeing,however, that contraries may beconjoined in more than one way, we haveto select from those contraries the onewhose contrary definition seems mostobvious. The expressions, then, have to

be examined each as a whole in the waywe have said, and also in detail asfollows. First of all, see that thegenus rendered is correctly rendered;

for if the contrary thing be found inthe contrary genus to that stated inthe definition, and the thing beforeyou is not in that same genus, then itwould clearly be in the contrary genus:for contraries must of necessity beeither in the same genus or in contrarygenera. The differentiae, too, that are

predicated of contraries we expect to be contrary, e.g. those of white and black, for the one tends to pierce the

vision, while the other tends tocompress it. So that if contrarydifferentiae to those in the definitionare predicated of the contrary term,

then those rendered in the definitionwould be predicated of the term beforeus. Seeing, then, that both the genusand the differentiae have been rightlyrendered, clearly the expression given



must be the right definition. It might be replied that there is no necessity

why contrary differentiae should be predicated of contraries, unless the

contraries be found within the samegenus: of things whose genera arethemselves contraries it may very well

be that the same differentia is used of both, e.g. of justice and injustice;

for the one is a virtue and the other avice of the soul: ‘of the soul’,

therefore, is the differentia in bothcases, seeing that the body as well hasits virtue and vice. But this much atleast is true, that the differentiae ofcontraries are either contrary or elsethe same. If, then, the contrarydifferentia to that given be predicatedof the contrary term and not of the onein hand, clearly the differentia stated

must be predicated of the latter.Speaking generally, seeing that thedefinition consists of genus anddifferentiae, if the definition of thecontrary term be apparent, thedefinition of the term before you will

be apparent also: for since itscontrary is found either in the samegenus or in the contrary genus, andlikewise also the differentiae

predicated of opposites are either



contrary to, or the same as, eachother, clearly of the term before youthere will be predicated either thesame genus as of its contrary, while,of its differentiae, either all arecontrary to those of its contrary, orat least some of them are so while therest remain the same; or, vice versa,the differentiae will be the same andthe genera contrary; or both genera anddifferentiae will be contrary. And that

is all; for that both should be thesame is not possible; else contrarieswill have the same definition.

Moreover, look at it from the point ofview of its inflexions and coordinates.For genera and definitions are bound tocorrespond in either case. Thus ifforgetfulness be the loss of knowledge,to forget is to lose knowledge, and tohave forgotten is to have lostknowledge. If, then, any one whateverof these is agreed to, the others mustof necessity be agreed to as well.Likewise, also, if destruction is the

decomposition of the thing’s essence,then to be destroyed is to have itsessence decomposed, and ‘destructively’

means ‘in such a way as to decomposeits essence’; if again ‘destructive’



means ‘apt to decompose something’sessence’, then also ‘destruction’ means‘the decomposition of its essence’.Likewise also with the rest: anadmission of any one of them whatever,and all the rest are admitted too.

Moreover, look at it from the point ofview of things that stand in relationsthat are like each other. For if‘healthy’ means ‘productive of health’,

‘vigorous’ too will mean ‘productive ofvigour’, and ‘useful’ will mean‘productive of good.’ For each of thesethings is related in like manner to itsown peculiar end, so that if one ofthem is defined as ‘productive of’ thatend, this will also be the definitionof each of the rest as well.

Moreover, look at it from the point ofand like degrees, in all the ways inwhich it is possible to establish aresult by comparing two and twotogether. Thus if A defines a betterthan B defines and B is a definition of

so too is A of a. Further, if A’s claimto define a is like B’s to define B,and B defines B, then A too defines a.This examination from the point of viewof greater degrees is of no use when a



single definition is compared with twothings, or two definitions with onething; for there cannot possibly be onedefinition of two things or two of thesame thing.

4

The most handy of all the commonplacearguments are those just mentioned andthose from co-ordinates and inflexions,

and these therefore are those which itis most important to master and to haveready to hand: for they are the mostuseful on the greatest number ofoccasions. Of the rest, too, the mostimportant are those of most generalapplication: for these are the mosteffective, e.g. that you should examinethe individual cases, and then look tosee in the case of their variousspecies whether the definition applies.For the species is synonymous with itsindividuals. This sort of inquiry is ofservice against those who assume theexistence of Ideas, as has been said

before.’ Moreover see if a man has useda term metaphorically, or predicated itof itself as though it were somethingdifferent. So too if any other of thecommonplace rules is of general



application and effective, it should beemployed.

5

That it is more difficult to establishthan to overthrow a definition, isobvious from considerations presentlyto be urged. For to see for oneself,and to secure from those whom one isquestioning, an admission of premisses

of this sort is no simple matter, e.g.that of the elements of the definitionrendered the one is genus and the otherdifferentia, and that only the genusand differentiae are predicated in thecategory of essence. Yet without these

premisses it is impossible to reason toa definition; for if any other thingsas well are predicated of the thing inthe category of essence, there is notelling whether the formula stated orsome other one is its definition, for adefinition is an expression indicatingthe essence of a thing. The point isclear also from the following: It is

easier to draw one conclusion than many. Now in demolishing a definition

it is sufficient to argue against one point only (for if we have overthrown

any single point whatsoever, we shall



have demolished the definition);whereas in establishing a definition,one is bound to bring people to theview that everything contained in thedefinition is attributable. Moreover,in establishing a case, the reasoning

brought forward must be universal: forthe definition put forward must be

predicated of everything of which theterm is predicated, and must moreover

be convertible, if the definition

rendered is to be peculiar to thesubject. In overthrowing a view, on theother hand, there is no longer anynecessity to show one’s pointuniversally: for it is enough to showthat the formula is untrue of any oneof the things embraced under the term.

Further, even supposing it should benecessary to overthrow something by auniversal proposition, not even so isthere any need to prove the converse ofthe proposition in the process ofoverthrowing the definition. For merelyto show that the definition fails to be

predicated of every one of the thingsof which the term is predicated, isenough to overthrow it universally: andthere is no need to prove the converseof this in order to show that the term



is predicated of things of which theexpression is not predicated. Moreover,even if it applies to everythingembraced under the term, but not to italone, the definition is therebydemolished.

The case stands likewise in regard tothe property and genus of a term also.For in both cases it is easier tooverthrow than to establish. As regards

the property this is clear from whathas been said: for as a rule the

property is rendered in a complex phrase, so that to overthrow it, it is

only necessary to demolish one of theterms used, whereas to establish it isnecessary to reason to them all. Then,too, nearly all the other rules thatapply to the definition will apply alsoto the property of a thing. For inestablishing a property one has to showthat it is true of everything includedunder the term in question, whereas tooverthrow one it is enough to show in asingle case only that it fails to

belong: further, even if it belongs toeverything falling under the term, butnot to that only, it is overthrown inthis case as well, as was explained inthe case of the definition. In regard



to the genus, it is clear that you are bound to establish it in one way only,

viz. by showing that it belongs inevery case, while of overthrowing itthere are two ways: for if it has beenshown that it belongs either never ornot in a certain case, the originalstatement has been demolished.

Moreover, in establishing a genus it isnot enough to show that it belongs, butalso that it belongs as genus has to be

shown; whereas in overthrowing it, itis enough to show its failure to belongeither in some particular case or inevery case. It appears, in fact, asthough, just as in other things todestroy is easier than to create, so inthese matters too to overthrow iseasier than to establish.

In the case of an accidental attributethe universal proposition is easier tooverthrow than to establish; for toestablish it, one has to show that it

belongs in every case, whereas tooverthrow it, it is enough to show that

it does not belong in one single case.The particular proposition is, on thecontrary, easier to establish than tooverthrow: for to establish it, it isenough to show that it belongs in a



particular instance, whereas tooverthrow it, it has to be shown thatit never belongs at all.

It is clear also that the easiest thingof all is to overthrow a definition.For on account of the number ofstatements involved we are presented inthe definition with the greatest numberof points for attack, and the more

plentiful the material, the quicker an

argument comes: for there is morelikelihood of a mistake occurring in alarge than in a small number of things.

Moreover, the other rules too may beused as means for attacking adefinition: for if either the formula

be not peculiar, or the genus rendered be the wrong one, or something included

in the formula fail to belong, thedefinition is thereby demolished. Onthe other hand, against the others wecannot bring all of the arguments drawnfrom definitions, nor yet of the rest:for only those relating to accidentalattributes apply generally to all the

aforesaid kinds of attribute. For whileeach of the aforesaid kinds ofattribute must belong to the thing inquestion, yet the genus may very wellnot belong as a property without as yet



being thereby demolished. Likewise alsothe property need not belong as agenus, nor the accident as a genus or

property, so long as they do belong. Sothat it is impossible to use one set asa basis of attack upon the other exceptin the case of definition. Clearly,then, it is the easiest of all thingsto demolish a definition, while toestablish one is the hardest. For thereone both has to establish all those

other points by reasoning (i.e. thatthe attributes stated belong, and thatthe genus rendered is the true genus,and that the formula is peculiar to theterm), and moreover, besides this, thatthe formula indicates the essence ofthe thing; and this has to be donecorrectly.

Of the rest, the property is mostnearly of this kind: for it is easierto demolish, because as a rule itcontains several terms; while it is thehardest to establish, both because ofthe number of things that people must

be brought to accept, and, besidesthis, because it belongs to its subjectalone and is predicated convertiblywith its subject.



The easiest thing of all to establishis an accidental predicate: for inother cases one has to show not onlythat the predicate belongs, but alsothat it belongs in such and such a

particular way: whereas in the case ofthe accident it is enough to show

merely that it belongs. On the otherhand, an accidental predicate is thehardest thing to overthrow, because itaffords the least material: for in

stating accident a man does not add howthe predicate belongs; and accordingly,while in other cases it is possible todemolish what is said in two ways, byshowing either that the predicate doesnot belong, or that it does not belongin the particular way stated, in thecase of an accidental predicate theonly way to demolish it is to show thatit does not belong at all.

The commonplace arguments through whichwe shall be well supplied with lines ofargument with regard to our several

problems have now been enumerated at

about sufficient length.

Book VIII

1



NEXT there fall to be discussed the problems of arrangement and method in pitting 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 oneto himself; thirdly and lastly, he must

proceed actually to put them to theother party. Now so far as the

selection of his ground is concernedthe problem is one alike for the

philosopher and the dialectician; buthow to go on to arrange his points andframe his questions concerns thedialectician only: for in every problemof that kind a reference to another

party is involved. Not so with the philosopher, and the man who is

investigating by himself: the premissesof his reasoning, although true andfamiliar, may be refused by theanswerer because they lie too near theoriginal statement and so he foreseeswhat will follow if he grants them: but

for this the philosopher does not care. Nay, he may possibly be even anxious to

secure axioms as familiar and as nearto the question in hand as possible:



for these are the bases on whichscientific reasonings are built up.

The sources from which one’scommonplace arguments should be drawnhave already been described:’ we havenow to discuss the arrangement andformation of questions and first todistinguish the premisses, other thanthe necessary premisses, which have to

be adopted. By necessary premisses are

meant those through which the actualreasoning is constructed. Those whichare secured other than these are offour kinds; they serve eitherinductively to secure the universal

premiss being granted, or to lendweight to the argument, or to concealthe conclusion, or to render theargument more clear. Beside these thereis no other premiss which need besecured: these are the ones whereby youshould try to multiply and formulateyour questions. Those which are used toconceal the conclusion serve acontroversial purpose only; but

inasmuch as an undertaking of this sortis always conducted against another

person, we are obliged to employ themas well.



The necessary premisses through whichthe reasoning is effected, ought not to

be propounded directly in so manywords. Rather one should soar as faraloof from them as possible. Thus ifone desires to secure an admission thatthe knowledge of contraries is one, oneshould ask him to admit it not ofcontraries, but of opposites: for, ifhe grants this, one will then arguethat the knowledge of contraries is

also the same, seeing that contrariesare opposites; if he does not, oneshould secure the admission byinduction, by formulating a propositionto that effect in the case of some

particular pair of contraries. For one must secure the necessary premisses

either by reasoning or by induction, orelse partly by one and partly by theother, although any propositions whichare too obvious to be denied may beformulated in so many words. This is

because the coming conclusion is lesseasily discerned at the greaterdistance and in the process of

induction, while at the same time, evenif one cannot reach the required

premisses in this way, it is still opento one to formulate them in so manywords. The premisses, other than these,





states only the final conclusion, it isunclear how it comes about; for theanswerer does not foresee on whatgrounds it is based, because the

previous syllogisms have not been madearticulate to him: while the finalsyllogism, showing the conclusion, islikely to be kept least articulate ifwe lay down not the secured

propositions on which it is based, butonly the grounds on which we reason to

them.

It is a useful rule, too, not to securethe admissions claimed as the bases ofthe syllogisms in their proper order,

but alternately those that conduce toone conclusion and those that conduceto another; for, if those which gotogether are set side by side, theconclusion that will result from themis more obvious in advance.

One should also, wherever possible,secure the universal premiss by adefinition relating not to the precise

terms themselves but to their co-ordinates; for people deceivethemselves, whenever the definition istaken in regard to a co-ordinate, intothinking that they are not making the



admission universally. An instancewould be, supposing one had to securethe admission that the angry mandesires vengeance on account of anapparent slight, and were to securethis, that ‘anger’ is a desire forvengeance on account of an apparentslight: for, clearly, if this weresecured, we should have universallywhat we intend. If, on the other hand,

people formulate propositions relating

to the actual terms themselves, theyoften find that the answerer refuses togrant them because on the actual termitself he is readier with hisobjection, e.g. that the ‘angry man’does not desire vengeance, because we

become angry with our parents, but wedo not desire vengeance on them. Verylikely the objection is not valid; forupon some people it is vengeance enoughto cause them pain and make them sorry;

but still it gives a certain plausibility and air of reasonableness

to the denial of the proposition. Inthe case, however, of the definition of

‘anger’ it is not so easy to find anobjection.

Moreover, formulate your proposition asthough you did so not for its own sake,



but in order to get at something else:for people are shy of granting what anopponent’s case really requires.Speaking generally, a questioner shouldleave it as far as possible doubtfulwhether he wishes to secure anadmission of his proposition or of itsopposite: 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 admissions

are plausible, and the universalinvolved is less patent; e.g. make theother person admit that as knowledgeand ignorance of contraries is thesame, so too perception of contrariesis the same; or vice versa, that sincethe perception is the same, so is theknowledge also. This argument resemblesinduction, but is not the same thing;for in induction it is the universalwhose admission is secured from the

particulars, whereas in arguments from

likeness, what is secured is not theuniversal under which all the likecases fall.



It is a good rule also, occasionally to bring an objection against oneself: for

answerers are put off their guardagainst those who appear to be arguingimpartially. It is useful too, to addthat ‘So and so is generally held orcommonly said’; for people are shy ofupsetting the received opinion unlessthey have some positive objection tourge: and at the same time they arecautious about upsetting such things

because they themselves too find themuseful. Moreover, do not be insistent,even though you really require the

point: for insistence always arousesthe more opposition. Further, formulateyour premiss as though it were a mereillustration: for people admit the morereadily a proposition made to servesome other purpose, and not required onits own account. Moreover, do notformulate the very proposition you needto secure, but rather something fromwhich that necessarily follows: for

people are more willing to admit thelatter, because it is not so clear from

this what the result will be, and ifthe one has been secured, the other has

been secured also. Again, one should put last the point which one most

wishes to have conceded; for people are



specially inclined to deny the firstquestions put to them, because most

people in asking questions put firstthe points which they are most eager tosecure. On the other hand, in dealingwith some people propositions of thissort should be put forward first: forill-tempered men admit most readilywhat comes first, unless the conclusionthat will result actually stares themin the face, while at the close of an

argument they show their ill-temper.Likewise also with those who considerthemselves smart at answering: for whenthey have admitted most of what youwant they finally talk clap-trap to theeffect that the conclusion does notfollow from their admissions: yet theysay ‘Yes’ readily, confident in theirown character, and imagining that theycannot suffer any reverse. Moreover, itis well to expand the argument andinsert things that it does not requireat all, as do those who draw falsegeometrical figures: for in the

multitude of details the whereabouts of

the fallacy is obscured. For thisreason also a questioner sometimesevades observation as he adds in acorner what, if he formulated it byitself, would not be granted.



For concealment, then, the rules whichshould be followed are the above.Ornament is attained by induction anddistinction of things closely akin.

What sort of process induction isobvious: as for distinction, aninstance of the kind of thing meant isthe distinction of one form ofknowledge as better than another by

being either more accurate, or

concerned with better objects; or thedistinction of sciences intospeculative, practical, and productive.For everything of this kind lendsadditional ornament to the argument,though there is no necessity to saythem, so far as the conclusion goes.

For clearness, examples and comparisonsshould be adduced, and let theillustrations be relevant and drawnfrom things that we know, as in Homerand not as in Choerilus; for then the

proposition is likely to becomeclearer.

2

In dialectics, syllogism should beemployed in reasoning against



dialecticians rather than against thecrowd: induction, on the other hand, is

most useful against the crowd. This point has been treated previously as

well.’ In induction, it is possible insome cases to ask the question in itsuniversal form, but in others this isnot easy, because there is noestablished general term that coversall the resemblances: in this case,when people need to secure the

universal, they use the phrase ‘in allcases of this sort’. But it is one ofthe very hardest things to distinguishwhich of the things adduced are ‘ofthis sort’, and which are not: and inthis connexion people often throw dustin each others’ eyes in theirdiscussion, the one party asserting thelikeness of things that are not alike,and the other disputing the likeness ofthings that are. One ought, therefore,to try oneself to coin a word to coverall things of the given sort, so as toleave no opportunity either to theanswerer to dispute, and say that the

thing advanced does not answer to alike description, or to the questionerto suggest falsely that it does answerto a like description, for many things



appear to answer to like descriptionsthat do not really do so.

If one has made an induction on thestrength of several cases and yet theanswerer refuses to grant the universal

proposition, then it is fair to demandhis objection. But until one hasoneself stated in what cases it is so,it is not fair to demand that he shallsay in what cases it is not so: for one

should make the induction first, andthen demand the objection. One ought,

moreover, to claim that the objectionsshould 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 forinstance two is the one prime numberamong the even numbers: for, unless hecan say that this subject is unique ofits kind, the objector ought to makehis 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 wellhave a colour or a foot or a hand otherthan his own, for a painter may have acolour that is not his own, and a cook



may have a foot that is not his own. To meet them, therefore, you should draw

the distinction before putting yourquestion in such cases: for so long asthe ambiguity remains undetected, solong will the objection to the

proposition be deemed valid. If,however, he checks the series ofquestions by an objection in regard notto some homonym, but to the actualthing asserted, the questioner should

withdraw the point objected to, andform the remainder into a universal

proposition, until he secures what herequires; e.g. in the case offorgetfulness and having forgotten: for

people refuse to admit that the man whohas lost his knowledge of a thing hasforgotten it, because if the thingalters, he has lost knowledge of it,

but he has not forgotten it. Accordingly the thing to do is to

withdraw the part objected to, andassert the remainder, e.g. that if a

person have lost knowledge of a thingwhile it still remains, he then has

forgotten it. One should similarlytreat those who object to the statementthat ‘the greater the good, the greaterthe evil that is its opposite’: forthey allege that health, which is a



less good thing than vigour, has agreater evil as its opposite: fordisease is a greater evil thandebility. In this case too, therefore,we have to withdraw the point objectedto; for when it has been withdrawn, the

man is more likely to admit the proposition, e.g. that ‘the greater

good has the greater evil as itsopposite, unless the one good involvesthe other as well’, as vigour involves

health. This should be done not onlywhen he formulates an objection, butalso if, without so doing, he refusesto admit the point because he foreseessomething of the kind: for if the pointobjected to be withdrawn, he will beforced to admit the proposition becausehe cannot foresee in the rest of it anycase where it does not hold true: if herefuse to admit it, then when asked foran objection he certainly will beunable to render one. Propositions thatare partly false and partly true are ofthis type: for in the case of these itis possible by withdrawing a part to

leave the rest true. If, however, youformulate the proposition on thestrength of many cases and he has noobjection to bring, you may claim thathe shall admit it: for a premiss is



valid in dialectics which thus holds inseveral instances and to which noobjection is forthcoming.

Whenever it is possible to reason tothe same conclusion either through orwithout a reduction per impossibile, ifone is demonstrating and not arguingdialectically it makes no differencewhich method of reasoning be adopted,

but in argument with another reasoning

per impossibile should be avoided. Forwhere one has reasoned without thereduction per impossibile, no disputecan arise; if, on the other hand, onedoes reason to an impossibleconclusion, unless its falsehood is too

plainly manifest, people deny that itis impossible, so that the questionersdo not get what they want.

One should put forward all propositionsthat hold true of several cases, and towhich either no objection whateverappears 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 theform of a question; if it be, and the



man shakes his head, it looks as if thereasoning had failed. For often, evenif it be not put as a question butadvanced as a consequence, people denyit, and then those who do not see thatit follows upon the previous admissionsdo not realize that those who deny ithave been refuted: when, then, the one

man merely asks it as a questionwithout even saying that it so follows,and the other denies it, it looks

altogether as if the reasoning hadfailed.

Not every universal question can form adialectical proposition as ordinarilyunderstood, e.g. ‘What is man?’ or ‘How

many meanings has “the good”?’ For adialectical premiss must be of a formto which it is possible to reply ‘Yes’or ‘No’, whereas to the aforesaid it isnot possible. For this reason questionsof this kind are not dialectical unlessthe questioner himself drawsdistinctions or divisions beforeexpressing them, e.g. ‘Good means this,

or this, does it not?’ For questions ofthis sort are easily answered by a Yesor a No. Hence one should endeavour toformulate propositions of this kind inthis form. It is at the same time also



perhaps fair to ask the other man how many meanings of ‘the good’ there are,

whenever you have yourselfdistinguished and formulated them, andhe will not admit them at all.

Any one who keeps on asking one thingfor a long time is a bad inquirer. Forif he does so though the personquestioned keeps on answering thequestions, clearly he asks a large

number of questions, or else asks thesame question a large number of times:in the one case he merely babbles, inthe other he fails to reason: forreasoning always consists of a smallnumber of premisses. If, on the otherhand, he does it because the personquestioned does not answer thequestions, he is at fault in not takinghim to task or breaking off thediscussion.

3

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 theorder of nature. For the former require



definition, while the latter have to bearrived at through many steps if onewishes to secure a continuous prooffrom first principles, or else alldiscussion about them wears the air of

mere sophistry: for to prove anythingis impossible unless one begins withthe appropriate principles, andconnects inference with inference tillthe last are reached. Now to definefirst principles is just what answerers

do not care to do, nor do they pay anyattention if the questioner makes adefinition: and yet until it is clearwhat it is that is proposed, it is noteasy to discuss it. This sort of thinghappens particularly in the case of thefirst principles: for while the other

propositions are shown through these,these cannot be shown through anythingelse: we are obliged to understandevery item of that sort by adefinition. The inferences, too, thatlie too close to the first principleare hard to treat in argument: for itis not possible to bring many arguments

in regard to them, because of the smallnumber of those steps, between theconclusion and the principle, wherebythe succeeding propositions have to beshown. The hardest, however, of all



definitions to treat in argument arethose that employ terms about which, inthe first place, it is uncertainwhether they are used in one sense orseveral, and, further, whether they areused literally or metaphorically by thedefiner. For because of theirobscurity, it is impossible to argueupon such terms; and because of theimpossibility of saying whether thisobscurity is due to their being used

metaphorically, it is impossible torefute them.

In general, it is safe to suppose that,whenever any problem provesintractable, it either needs definitionor else bears either several senses, ora metaphorical sense, or it is not farremoved from the first principles; orelse the reason is that we have yet todiscover in the first place just this-in which of the aforesaid directionsthe source of our difficulty lies: whenwe have made this clear, then obviouslyour business must be either to define

or to distinguish, or to supply theintermediate premisses: for it isthrough these that the finalconclusions are shown.



It often happens that a difficulty isfound in discussing or arguing a given

position because the definition has not been correctly rendered: e.g. ‘Has one

thing one contrary or many?’: here whenthe term ‘contraries’ has been properlydefined, it is easy to bring people tosee whether it is possible for the samething to have several contraries ornot: in the same way also with otherterms requiring definition. It appears

also in mathematics that the difficultyin using a figure is sometimes due to adefect in definition; e.g. in provingthat the line which cuts the plane

parallel to one side divides similarly both the line which it cuts and the

area; whereas if the definition begiven, the fact asserted becomesimmediately clear: for the areas havethe same fraction subtracted from themas have the sides: and this is thedefinition of ‘the same ratio’. The

most primary of the elementary principles are without exception very

easy to show, if the definitions

involved, e.g. the nature of a line orof a circle, be laid down; only thearguments that can be brought in regardto each of them are not many, becausethere are not many intermediate steps.



If, on the other hand, the definitionof the starting-points be not laiddown, to show them is difficult and mayeven prove quite impossible. The caseof the significance of verbalexpressions is like that of these

mathematical conceptions.

One may be sure then, whenever a position is hard to discuss, that one

or other of the aforesaid things has

happened to it. Whenever, on the otherhand, it is a harder task to argue tothe point claimed, i.e. the premiss,than to the resulting position, a doubt

may arise whether such claims should beadmitted or not: for if a man is goingto refuse to admit it and claim thatyou shall argue to it as well, he will

be giving the signal for a harderundertaking than was originally

proposed: if, on the other hand, hegrants it, he will be giving theoriginal thesis credence on thestrength of what is less credible thanitself. 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 toreason through premisses that are

better assured, he had better refuse.



In other words, in serious inquiry heought not to grant it, unless he be

more sure about it than about theconclusion; whereas in a dialecticalexercise he may do so if he is merelysatisfied of its truth. Clearly, then,the circumstances under which suchadmissions should be claimed aredifferent for a mere questioner and fora serious teacher.

4

As to the formulation, then, andarrangement of one’s questions, aboutenough has been said.

With regard to the giving of answers,we must first define what is the

business of a good answerer, as of agood questioner. The business of thequestioner is so to develop theargument as to make the answerer utterthe most extrvagant paradoxes thatnecessarily follow because of his

position: while that of the answerer is

to make it appear that it is not he whois responsible for the absurdity or

paradox, but only his position: for one may, perhaps, distinguish between the mistake of taking up a wrong position



to start with, and that of not maintaining it properly, when once

taken up.

5

Inasmuch as no rules are laid down forthose who argue for the sake oftraining and of examination:-and theaim of those engaged in teaching orlearning is quite different from that

of those engaged in a competition; asis the latter from that of those whodiscuss things together in the spiritof inquiry: for a learner should alwaysstate what he thinks: for no one iseven trying to teach him what is false;whereas in a competition the businessof the questioner is to appear by all

means to produce an effect upon theother, while that of the answerer is toappear unaffected by him; on the otherhand, in an assembly of disputantsdiscussing in the spirit not of acompetition but of an examination andinquiry, there are as yet no articulate

rules about what the answerer shouldaim at, and what kind of things heshould and should not grant for thecorrect or incorrect defence of his

position:-inasmuch, then, as we have no



tradition bequeathed to us by others,let us try to say something upon the

matter for ourselves.

The thesis laid down by the answerer before facing the questioner’s argument

is bound of necessity to be one that iseither generally accepted or generallyrejected or else is neither: and

moreover is so accepted or rejectedeither absolutely or else with a

restriction, e.g. by some given person, by the speaker or by some one else. The manner, however, of its acceptance or

rejection, whatever it be, makes nodifference: for the right way toanswer, i.e. to admit or to refuse toadmit what has been asked, will be thesame in either case. If, then, thestatement laid down by the answerer begenerally rejected, the conclusionaimed at by the questioner is bound to

be one generally accepted, whereas ifthe former be generally accepted, thelatter is generally rejected: for theconclusion which the questioner tries

to draw is always the opposite of thestatement laid down. If, on the otherhand, what is laid down is generallyneither rejected nor accepted, theconclusion will be of the same type as



well. Now since a man who reasonscorrectly demonstrates his proposedconclusion from premisses that are moregenerally accepted, and more familiar,it is clear that (1) where the viewlaid down by him is one that generallyis absolutely rejected, the answererought not to grant either what is thusabsolutely not accepted at all, or whatis accepted indeed, but accepted lessgenerally than the questioner’s

conclusion. For if the statement laiddown by the answerer be generallyrejected, the conclusion aimed at bythe questioner will be one that isgenerally accepted, so that the

premisses secured by the questionershould all be views generally accepted,and more generally accepted than his

proposed conclusion, if the lessfamiliar is to be inferred through the

more familiar. Consequently, if any ofthe questions put to him be not of thischaracter, the answerer should notgrant them. (2) If, on the other hand,the statement laid down by the answerer

be generally accepted withoutqualification, clearly the conclusionsought by the questioner will be onegenerally rejected withoutqualification. Accordingly, the



answerer should admit all views thatare generally accepted and, of thosethat are not generally accepted, allthat are less generally rejected thanthe conclusion sought by thequestioner. For then he will probably

be thought to have argued sufficientlywell. (3) Likewise, too, if thestatement laid down by the answerer beneither rejected generally norgenerally accepted; for then, too,

anything that appears to be true should be granted, and, of the views not

generally accepted, any that are moregenerally accepted than thequestioner’s conclusion; for in thatcase the result will be that thearguments will be more generallyaccepted. If, then, the view laid down

by the answerer be one that isgenerally accepted or rejected withoutqualification, then the views that areaccepted absolutely must be taken asthe standard of comparison: whereas ifthe view laid down be one that is notgenerally accepted or rejected, but

only by the answerer, then the standardwhereby the latter must judge what isgenerally accepted or not, and mustgrant or refuse to grant the pointasked, is himself. If, again, the



answerer be defending some one else’sopinion, then clearly it will be thelatter’s judgement to which he musthave regard in granting or denying thevarious points. This is why those, too,who introduce other’s opinions, e.g.that ‘good and evil are the same thing,as Heraclitus says,’ refuse to admitthe impossibility of contraries

belonging at the same time to the samething; not because they do not

themselves believe this, but because onHeraclitus’ principles one has to sayso. The same thing is done also bythose who take on the defence of oneanother’s positions; their aim being tospeak as would the man who stated the

position.

6

It is clear, then, what the aims of theanswerer should be, whether the

position he lays down be a viewgenerally accepted withoutqualification or accepted by some

definite person. Now every questionasked is bound to involve some viewthat is either generally held orgenerally rejected or neither, and isalso bound to be either relevant to the



argument or irrelevant: if then it be aview generally accepted and irrelevant,the answerer should grant it and remarkthat it is the accepted view: if it bea view not generally accepted andirrelevant, he should grant it but adda comment that it is not generallyaccepted, in order to avoid theappearance of being a simpleton. If it

be relevant and also be generallyaccepted, he should admit that it is

the view generally accepted but saythat it lies too close to the original

proposition, and that if it be grantedthe problem proposed collapses. If whatis claimed by the questioner berelevant but too generally rejected,the answerer, while admitting that ifit be granted the conclusion soughtfollows, should yet protest that the

proposition is too absurd to beadmitted. Suppose, again, it be a viewthat is neither rejected generally norgenerally accepted, then, if it beirrelevant to the argument, it may begranted without restriction; if,

however, it be relevant, the answerershould add the comment that, if it begranted, the original problemcollapses. For then the answerer willnot be held to be personally



accountable for what happens to him, ifhe grants the several points with hiseyes open, and also the questioner will

be able to draw his inference, seeingthat all the premisses that are moregenerally accepted than the conclusionare granted him. Those who try to drawan inference from premisses moregenerally rejected than the conclusionclearly do not reason correctly: hence,when men ask these things, they ought

not to be granted.

7

The questioner should be met in a like manner also in the case of terms used

obscurely, i.e. in several senses. Forthe answerer, if he does notunderstand, is always permitted to say‘I do not understand’: he is notcompelled to reply ‘Yes’ or ‘No’ to aquestion which may mean differentthings. Clearly, then, in the first

place, if what is said be not clear, heought not to hesitate to say that he

does not understand it; for often people encounter some difficulty from

assenting to questions that are notclearly put. If he understands thequestion and yet it covers many senses,



then supposing what it says to beuniversally true or false, he shouldgive it an unqualified assent ordenial: if, on the other hand, it be

partly true and partly false, he shouldadd a comment that it bears differentsenses, and also that in one it istrue, in the other false: for if heleave 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 othersense, he should say, ‘That was notwhat I had in view when I admitted it;I meant the other sense’: for if a termor expression covers more than onething, it is easy to disagree. If,however, the question is both clear andsimple, he should answer either ‘Yes’or ‘No’.

8

A premiss in reasoning always either isone of the constituent elements in thereasoning, or else goes to establishone of these: (and you can always tellwhen it is secured in order to



establish something else by the fact ofa number of similar questions being

put: for as a rule people secure theiruniversal by means either of inductionor of likeness):-accordingly the

particular propositions should all beadmitted, if they are true andgenerally held. On the other hand,against the universal one should try to

bring some negative instance; for to bring the argument to a standstill

without a negative instance, eitherreal or apparent, shows ill-temper. If,then, a man refuses to grant theuniversal when supported by manyinstances, although he has no negativeinstance to show, he obviously showsill-temper. If, moreover, he cannoteven attempt a counter-proof that it isnot true, far more likely is he to bethought ill-tempered-although evencounter-proof is not enough: for weoften hear arguments that are contraryto common opinions, whose solution isyet difficult, e.g. the argument ofZeno that it is impossible to move or

to traverse the stadium;-but still,this is no reason for omitting toassert the opposites of these views.If, then, a man refuses to admit the

proposition without having either a



negative instance or some counter-argument to bring against it, clearlyhe is ill-tempered: for ill-temper inargument consists in answering in waysother than the above, so as to wreckthe reasoning.

9

Before maintaining either a thesis or adefinition the answerer should try his

hand at attacking it by himself; forclearly his business is to oppose those

positions from which questionersdemolish what he has laid down.

He should beware of maintaining ahypothesis 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 wereto say that everything is in motion orthat nothing is; and also there are allthose which only a bad character wouldchoose, and which are implicitlyopposed to men’s wishes, e.g. that

pleasure is the good, and that to doinjustice is better than to suffer it.For people then hate him, supposing himto maintain them not for the sake of



argument but because he really thinksthem.

10

Of all arguments that reason to a falseconclusion the right solution is todemolish the point on which the fallacythat occurs depends: for the demolitionof any random point is no solution,even though the point demolished be

false. For the argument may contain many falsehoods, e.g. suppose some one

to secure the premisses, ‘He who sits,writes’ and ‘Socrates is sitting’: forfrom these it follows that ‘Socrates iswriting’. Now we may demolish the

proposition ‘Socrates is sitting’, andstill be no nearer a solution of theargument; it may be true that the pointclaimed is false; but it is not on thatthat fallacy of the argument depends:for supposing that any one shouldhappen to be sitting and not writing,it would be impossible in such a caseto apply the same solution.

Accordingly, it is not this that needsto be demolished, but rather that ‘Hewho sits, writes’: for he who sits doesnot always write. He, then, who hasdemolished the point on which the



fallacy depends, has given the solutionof the argument completely. Any one whoknows that it is on such and such a

point that the argument depends, knowsthe solution of it, just as in the caseof a figure falsely drawn. For it isnot enough to object, even if the pointdemolished be a falsehood, but thereason of the fallacy should also be

proved: for then it would be clearwhether the man makes his objection

with his eyes open or not.

There are four possible ways of preventing a man from working his

argument to a conclusion. It can bedone either by demolishing the point onwhich the falsehood that comes aboutdepends, or by stating an objectiondirected against the questioner: foroften when a solution has not as a

matter of fact been brought, yet thequestioner is rendered thereby unableto pursue the argument any farther.Thirdly, one may object to thequestions asked: for it may happen that

what the questioner wants does notfollow from the questions he has asked

because he has asked them badly,whereas if something additional begranted the conclusion comes about. If,



then, the questioner be unable to pursue his argument farther, the

objection would properly be directedagainst the questioner; if he can doso, then it would be against hisquestions. The fourth and worst kind ofobjection is that which is directed tothe time allowed for discussion: forsome people bring objections of a kindwhich would take longer to answer thanthe length of the discussion in hand.

There are then, as we said, four waysof making objections: but of them thefirst alone is a solution: the othersare just hindrances and stumbling-

blocks to prevent the conclusions.

11

Adverse criticism of an argument on itsown merits, and of it when presented inthe form of questions, are twodifferent things. For often the failureto carry through the argument correctlyin discussion is due to the person

questioned, because he will not grantthe steps of which a correct argument

might have been made against his position: for it is not in the power of

the one side only to effect properly a



result that depends on both alike. Accordingly it sometimes becomes

necessary to attack the speaker and nothis position, when the answerer lies inwait for the points that are contraryto the questioner and becomes abusiveas well: when people lose their tempersin this way, their argument becomes acontest, not a discussion. Moreover,since arguments of this kind are heldnot for the sake of instruction but for

purposes of practice and examination,clearly one has to reason not only totrue conclusions, but also to falseones, and not always through true

premisses, but sometimes through falseas well. For often, when a true

proposition is put forward, thedialectician is compelled to demolishit: and then false propositions have to

be formulated. Sometimes also when afalse proposition is put forward, ithas to be demolished by means of false

propositions: for it is possible for agiven man to believe what is not thefact more firmly than the truth.

Accordingly, if the argument be made todepend on something that he holds, itwill be easier to persuade or help him.He, however, who would rightly convertany one to a different opinion should



do so in a dialectical and not in acontentious manner, just as ageometrician should reasongeometrically, whether his conclusion

be false or true: what kind ofsyllogisms are dialectical has already

been said. The principle that a man whohinders the common business is a bad

partner, clearly applies to an argumentas well; for in arguments as well thereis a common aim in view, except with

mere contestants, for these cannot bothreach the same goal; for more than onecannot possibly win. It makes nodifference whether he effects this asanswerer or as questioner: for both hewho asks contentious questions is a baddialectician, and also he who inanswering fails to grant the obviousanswer or to understand the point ofthe questioner’s inquiry. What has beensaid, then, makes it clear that adversecriticism is not to be passed in a likestrain upon the argument on its own

merits, and upon the questioner: for it may very well be that the argument is

bad, but that the questioner has arguedwith the answerer in the best possibleway: for when men lose their tempers,it may perhaps be impossible to makeone’s inferences straight-forwardly as



one would wish: we have to do as wecan.

Inasmuch as it is indeterminate when people are claiming the admission of

contrary things, and when they areclaiming what originally they set outto prove-for often when they aretalking by themselves they say contrarythings, and admit afterwards what theyhave previously denied; for which

reason they often assent, whenquestioned, to contrary things and towhat originally had to be proved-theargument is sure to become vitiated.The responsibility, however, for thisrests with the answerer, because whilerefusing to grant other points, he doesgrant points of that kind. It is, then,clear that adverse criticism is not to

be passed in a like manner uponquestioners and upon their arguments.

In itself an argument is liable to fivekinds of adverse criticism:

(1) The first is when neither the proposed conclusion nor indeed any

conclusion at all is drawn from thequestions asked, and when most, if notall, of the premisses on which the



conclusion rests are false or generallyrejected, when, moreover, neither anywithdrawals nor additions nor bothtogether can bring the conclusionsabout.

(2) The second is, supposing thereasoning, though constructed from the

premisses, and in the manner, describedabove, were to be irrelevant to theoriginal position.

(3) The third is, supposing certainadditions would bring an inferenceabout but yet these additions were to

be weaker than those that were put asquestions and less generally held thanthe conclusion.

(4) Again, supposing certainwithdrawals could effect the same: forsometimes people secure more premissesthan are necessary, so that it is notthrough them that the inference comesabout.

(5) Moreover, suppose the premisses beless generally held and less crediblethan the conclusion, or if, thoughtrue, they require more trouble to

prove than the proposed view.



One must not claim that the reasoningto a proposed view shall in every caseequally be a view generally acceptedand convincing: for it is a directresult of the nature of things thatsome subjects of inquiry shall beeasier and some harder, so that if a

man brings people to accept his pointfrom opinions that are as generallyreceived as the case admits, he has

argued his case correctly. Clearly,then, not even the argument itself isopen to the same adverse criticism whentaken in relation to the proposedconclusion and when taken by itself.For there is nothing to prevent theargument being open to reproach initself, and yet commendable in relationto the proposed conclusion, or again,vice versa, being commendable initself, and yet open to reproach inrelation to the proposed conclusion,whenever there are many propositions

both generally held and also truewhereby it could easily be proved. It

is possible also that an argument, eventhough brought to a conclusion, maysometimes be worse than one which isnot so concluded, whenever the

premisses of the former are silly,



while its conclusion is not so; whereasthe latter, though requiring certainadditions, requires only such as aregenerally held and true, and moreoverdoes not rest as an argument on theseadditions. With those which bring abouta true conclusion by means of false

premisses, it is not fair to findfault: for a false conclusion must ofnecessity always be reached from afalse premiss, but a true conclusion

may sometimes be drawn even from false premisses; as is clear from the Analytics.

Whenever by the argument statedsomething is demonstrated, but thatsomething is other than what is wantedand has no bearing whatever on theconclusion, then no inference as to thelatter can be drawn from it: and ifthere appears to be, it will be asophism, not a proof. A philosopheme isa demonstrative inference: anepichireme is a dialectical inference:a sophism is a contentious inference:

an aporeme is an inference that reasonsdialectically to a contradiction.

If something were to be shown from premisses, both of which are views



generally accepted, but not acceptedwith like conviction, it may very well

be that the conclusion shown issomething held more strongly thaneither. If, on the other hand, generalopinion be for the one and neither fornor against the other, or if it be forthe one and against the other, then, ifthe pro and con be alike in the case ofthe premisses, they will be alike forthe conclusion also: if, on the other

hand, the one preponderates, theconclusion too will follow suit.

It is also a fault in reasoning when a man shows something through a long

chain of steps, when he might employfewer steps and those already includedin his argument: suppose him to beshowing (e.g.) that one opinion is more

properly so called than another, andsuppose him to make his postulates asfollows: ‘x-in-itself is more fully xthan anything else’: ‘there genuinelyexists an object of opinion in itself’:therefore ‘the object-of-opinion-in-

itself is more fully an object ofopinion than the particular objects ofopinion’. Now ‘a relative term is morefully itself when its correlate is morefully itself’: and ‘there exists a



genuine opinion-in-itself, which will be “opinion” in a more accurate sense

than the particular opinions’: and ithas been postulated both that ‘agenuine opinion-in-itself exists’, andthat ‘x-in-itself is more fully x thananything else’: therefore ‘this will beopinion in a more accurate sense’.

Wherein lies the viciousness of thereasoning? Simply in that it concealsthe ground on which the argument

depends.

12

An argument is clear in one, and thatthe most ordinary, sense, if it be so

brought to a conclusion as to make nofurther questions necessary: in anothersense, and this is the type mostusually advanced, when the propositionssecured are such as compel theconclusion, and the argument isconcluded through premisses that arethemselves conclusions: moreover, it isso also if some step is omitted that

generally is firmly accepted.

An argument is called fallacious infour 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 aconclusion but not to the conclusion

proposed-which happens principally inthe case of reductiones ad impossibile:(3) when it comes to the proposedconclusion but not according to the

mode of inquiry appropriate to thecase, as happens when a non-medicalargument is taken to be a medical one,or one which is not geometrical for a

geometrical argument, or one which isnot dialectical for dialectical,whether the result reached be true orfalse: (4) if the conclusion be reachedthrough false premisses: of this typethe conclusion is sometimes false,sometimes true: for while a falseconclusion is always the result offalse premisses, a true conclusion may

be drawn even from premisses that arenot true, as was said above as well.

Fallacy in argument is due to a mistakeof the arguer rather than of theargument: yet it is not always the

fault of the arguer either, but onlywhen he is not aware of it: for weoften accept on its merits in

preference to many true ones anargument which demolishes some true



proposition if it does so from premisses as far as possible generally

accepted. For an argument of that kinddoes demonstrate other things that aretrue: for one of the premisses laiddown ought never to be there at all,and this will then be demonstrated. If,however, a true conclusion were to bereached through premisses that arefalse and utterly childish, theargument is worse than many arguments

that lead to a false conclusion, thoughan 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?’; thethird, ‘Of what kind of premisses doesit consist?’: for if the latter, thoughfalse, be generally accepted, theargument is dialectical, whereas if,though true, they be generallyrejected, it is bad: if they be bothfalse and also entirely contrary togeneral opinion, clearly it is bad,

either altogether or else in relationto the particular matter in hand.

13



Of the ways in which a questioner may beg the original question and also beg

contraries the true account has beengiven in the Analytics:’ but an accounton the level of general opinion must begiven now.

People appear to beg their originalquestion in five ways: the first and

most obvious being if any one begs theactual point requiring to be shown:

this is easily detected when put in so many words; but it is more apt to

escape detection in the case ofdifferent terms, or a term and anexpression, that mean the same thing. Asecond way occurs whenever any one begsuniversally something which he has todemonstrate in a particular case:suppose (e.g.) he were trying to provethat the knowledge of contraries is oneand were to claim that the knowledge ofopposites 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 heundertakes to show universally: e.g. ifhe undertook to show that the knowledgeof contraries is always one, and begged



it of certain pairs of contraries: forhe also is generally considered to be

begging independently and by itselfwhat, together with a number of otherthings, he ought to have shown. Again,a man begs the question if he begs hisconclusion piecemeal: supposing e.g.that he had to show that medicine is ascience of what leads to health and todisease, and were to claim first theone, then the other; or, fifthly, if he

were to beg the one or the other of a pair of statements that necessarily

involve one other; e.g. if he had toshow that the diagonal isincommensurable with the side, and wereto beg that the side is incommensurablewith the diagonal.

The ways in which people assumecontraries are equal in number to thosein which they beg their originalquestion. For it would happen, firstly,if any one were to beg an oppositeaffirmation and negation; secondly, ifhe were to beg the contrary terms of an

antithesis, e.g. that the same thing isgood and evil; thirdly, suppose any onewere to claim something universally andthen proceed to beg its contradictoryin some particular case, e.g. if having



secured that the knowledge ofcontraries is one, he were to claimthat the knowledge of what makes forhealth or for disease is different; or,fourthly, suppose him, after

postulating the latter view, to try tosecure universally the contradictorystatement. Again, fifthly, suppose a

man begs the contrary of the conclusionwhich necessarily comes about throughthe premisses laid down; and this would

happen suppose, even without beggingthe opposites in so many words, he wereto beg two premisses such that thiscontradictory statement that isopposite to the first conclusion willfollow from them. The securing ofcontraries differs from begging theoriginal question in this way: in thelatter case the mistake lies in regardto the conclusion; for it is by aglance at the conclusion that we tellthat the original question has been

begged: whereas contrary views lie inthe premisses, viz. in a certainrelation which they bear to one

another.

14



The best way to secure training and practice in arguments of this kind is

in the first place to get into thehabit of converting the arguments. Forin this way we shall be better equippedfor dealing with the propositionstated, and after a few attempts weshall know several arguments by heart.For by ‘conversion’ of an argument is

meant the taking the reverse of theconclusion together with the remaining

propositions asked and so demolishingone of those that were conceded: for itfollows necessarily that if theconclusion be untrue, some one of the

premisses is demolished, seeing that,given all the premisses, the conclusionwas bound to follow. Always, in dealingwith any proposition, be on the look-out for a line of argument both pro andcon: and on discovering it at once setabout looking for the solution of it:for in this way you will soon find thatyou have trained yourself at the sametime in both asking questions andanswering them. If we cannot find any

one else to argue with, we should arguewith ourselves. Select, moreover,arguments relating to the same thesisand range them side by side: for this

produces a plentiful supply of



arguments for carrying a point by sheerforce, and in refutation also it is ofgreat service, whenever one is wellstocked with arguments pro and con: forthen you find yourself on your guardagainst contrary statements to the oneyou wish to secure. Moreover, ascontributing to knowledge and to

philosophic wisdom the power ofdiscerning and holding in one view theresults of either of two hypotheses is

no mean instrument; for it then onlyremains to make a right choice of oneof them. For a task of this kind acertain natural ability is required: infact real natural ability just is the

power right to choose the true and shunthe false. Men of natural ability cando this; for by a right liking ordisliking for whatever is proposed tothem they rightly select what is best.

It is best to know by heart argumentsupon those questions which are of mostfrequent occurrence, and particularlyin regard to those propositions which

are ultimate: for in discussing theseanswerers frequently give up indespair. Moreover, get a good stock ofdefinitions: and have those of familiarand primary ideas at your fingers’



ends: for it is through these thatreasonings are effected. You shouldtry, moreover, to master the headsunder which other arguments mostly tendto fall. For just as in geometry it isuseful to be practised in the elements,and in arithmetic to have the

multiplication table up to ten at one’sfingers’ ends-and indeed it makes agreat difference in one’s knowledge ofthe multiples of other numbers too-

likewise also in arguments it is agreat advantage to be well up in regardto first principles, and to have athorough knowledge of premisses at thetip of one’s tongue. For just as in a

person with a trained memory, a memoryof things themselves is immediatelycaused by the mere mention of theirloci, so these habits too will make a

man readier in reasoning, because hehas his premisses classified before his

mind’s eye, each under its number. Itis better to commit to memory a premissof general application than anargument: for it is difficult to be

even moderately ready with a first principle, or hypothesis.

Moreover, you should get into the habitof turning one argument into several,



and conceal your procedure as darkly asyou can: this kind of effect is best

produced by keeping as far as possibleaway from topics akin to the subject ofthe argument. This can be done witharguments that are entirely universal,e.g. the statement that ‘there cannot

be one knowledge of more than onething’: for that is the case with bothrelative terms and contraries and co-ordinates.

Records of discussions should be madein a universal form, even though onehas argued only some particular case:for this will enable one to turn asingle rule into several. A like ruleapplies in Rhetoric as well toenthymemes. For yourself, however, youshould as far as possible avoiduniversalizing your reasonings. Youshould, moreover, always examinearguments to see whether they rest on

principles of general application: forall particular arguments really reasonuniversally, as well, i.e. a particular

demonstration always contains auniversal demonstration, because it isimpossible to reason at all withoutusing universals.



You should display your training ininductive reasoning against a young

man, 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 thething in which they are respectivelytrained. In general, too, from yourexercises in argumentation you shouldtry to carry away either a syllogism on

some subject or a refutation or a proposition or an objection, or whether

some one put his question properly orimproperly (whether it was yourself orsome one else) and the point which madeit the one or the other. For this iswhat gives one ability, and the wholeobject of training is to acquireability, especially in regard to

propositions and objections. For it isthe skilled propounder and objector whois, speaking generally, a dialectician.To formulate a proposition is to form anumber of things into one-for theconclusion to which the argument leads

must be taken generally, as a singlething-whereas to formulate an objectionis to make one thing into many; for theobjector either distinguishes or



demolishes, partly granting, partlydenying the statements proposed.

Do not argue with every one, nor practise upon the man in the street:

for there are some people with whom anyargument is bound to degenerate. Foragainst any one who is ready to try all

means in order to seem not to be beaten, 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 with casual acquaintances, or bad argument is sure to result. For you

see how in practising together peoplecannot refrain from contentiousargument.

It is best also to have ready-madearguments relating to those questionsin which a very small stock willfurnish us with arguments serviceableon a very large number of occasions.These are those that are universal, andthose in regard to which it is rather

difficult to produce points forourselves from matters of everydayexperience.



On Sophistical Refutations

1

Let us now discuss sophisticrefutations, i.e. what appear to berefutations but are really fallaciesinstead. We will begin in the naturalorder with the first.

That some reasonings are genuine, while

others seem to be so but are not, isevident. This happens with arguments,as also elsewhere, through a certainlikeness between the genuine and thesham. For physically some people are ina vigorous condition, while others

merely seem to be so by blowing andrigging themselves out as the tribesmendo their victims for sacrifice; andsome people are beautiful thanks totheir beauty, while others seem to beso, by dint of embellishing themselves.So it is, too, with inanimate things;for of these, too, some are reallysilver and others gold, while others

are not and merely seem to be such toour sense; e.g. things made of lithargeand tin seem to be of silver, whilethose made of yellow metal look golden.In the same way both reasoning and



refutation are sometimes genuine,sometimes not, though inexperience may

make them appear so: for inexperienced people obtain only, as it were, a

distant view of these things. Forreasoning rests on certain statementssuch that they involve necessarily theassertion of something other than whathas been stated, through what has beenstated: refutation is reasoninginvolving the contradictory of the

given conclusion. Now some of them donot really achieve this, though theyseem to do so for a number of reasons;and of these the most prolific andusual domain is the argument that turnsupon names only. It is impossible in adiscussion to bring in the actualthings discussed: we use their names assymbols instead of them; and thereforewe suppose that what follows in thenames, follows in the things as well,just as people who calculate suppose inregard to their counters. But the twocases (names and things) are not alike.For names are finite and so is the sum-

total of formulae, while things areinfinite in number. Inevitably, then,the same formulae, and a single name,have a number of meanings. Accordinglyjust as, in counting, those who are not



clever in manipulating their countersare taken in by the experts, in thesame way in arguments too those who arenot well acquainted with the force ofnames misreason both in their owndiscussions and when they listen toothers. For this reason, then, and forothers to be mentioned later, thereexists both reasoning and refutationthat is apparent but not real. Now forsome people it is better worth while to

seem to be wise, than to be wisewithout seeming to be (for the art ofthe sophist is the semblance of wisdomwithout the reality, and the sophist isone who makes money from an apparent

but unreal wisdom); for them, then, itis clearly essential also to seem toaccomplish the task of a wise manrather than to accomplish it withoutseeming to do so. To reduce it to asingle point of contrast it is the

business of one who knows a thing,himself to avoid fallacies in thesubjects which he knows and to be ableto show up the man who makes them; and

of these accomplishments the onedepends on the faculty to render ananswer, and the other upon the securingof one. Those, then, who would besophists are bound to study the class



of arguments aforesaid: for it is worththeir while: for a faculty of this kindwill make a man seem to be wise, andthis is the purpose they happen to havein view.

Clearly, then, there exists a class ofarguments of this kind, and it is atthis kind of ability that those aimwhom we call sophists. Let us now go onto discuss how many kinds there are of

sophistical arguments, and how many innumber are the elements of which thisfaculty is composed, and how many

branches there happen to be of thisinquiry, and the other factors thatcontribute to this art.

2

Of arguments in dialogue form there arefour classes:

Didactic, Dialectical, Examination-arguments, and Contentious arguments.Didactic arguments are those that

reason from the principles appropriateto each subject and not from theopinions held by the answerer (for thelearner should take things on trust):dialectical arguments are those that



reason from premisses generallyaccepted, to the contradictory of agiven thesis: examination-arguments arethose that reason from premisses whichare accepted by the answerer and whichany one who pretends to possessknowledge of the subject is bound toknow-in what manner, has been definedin another treatise: contentiousarguments are those that reason orappear to reason to a conclusion from

premisses that appear to be generallyaccepted but are not so. The subject,then, of demonstrative arguments has

been discussed in the Analytics, whilethat of dialectic arguments andexamination-arguments has beendiscussed elsewhere: let us now proceedto speak of the arguments used incompetitions and contests.

3

First we must grasp the number of aimsentertained by those who argue ascompetitors and rivals to the death.

These are five in number, refutation,fallacy, paradox, solecism, and fifthlyto reduce the opponent in thediscussion to babbling-i.e. toconstrain him to repeat himself a



number of times: or it is to producethe appearance of each of these thingswithout the reality. For they choose if

possible plainly to refute the other party, or as the second best to show

that he is committing some fallacy, oras a third best to lead him into

paradox, or fourthly to reduce him tosolecism, i.e. to make the answerer, inconsequence of the argument, to use anungrammatical expression; or, as a last

resort, to make him repeat himself.

4

There are two styles of refutation: forsome depend on the language used, whilesome are independent of language. Thoseways of producing the false appearanceof an argument which depend on languageare six in number: they are ambiguity,amphiboly, combination, division ofwords, accent, form of expression. Ofthis we may assure ourselves both byinduction, and by syllogistic proof

based on this-and it may be on other

assumptions as well-that this is thenumber of ways in which we might fallto mean the same thing by the samenames or expressions. Arguments such asthe following depend upon ambiguity.



‘Those learn who know: for it is thosewho know their letters who learn theletters dictated to them’. For to‘learn’ is ambiguous; it signifies both‘to understand’ by the use ofknowledge, and also ‘to acquireknowledge’. Again, ‘Evils are good: forwhat needs to be is good, and evils

must needs be’. For ‘what needs to be’has a double meaning: it means what isinevitable, as often is the case with

evils, too (for evil of some kind isinevitable), while on the other hand wesay of good things as well that they‘need to be’. Moreover, ‘The same manis both seated and standing and he is

both sick and in health: for it is hewho stood up who is standing, and hewho is recovering who is in health: butit is the seated man who stood up, andthe sick man who was recovering’. For‘The sick man does so and so’, or ‘hasso and so done to him’ is not single in

meaning: sometimes it means ‘the manwho is sick or is seated now’,sometimes ‘the man who was sick

formerly’. Of course, the man who wasrecovering was the sick man, who reallywas sick at the time: but the man whois in health is not sick at the sametime: he is ‘the sick man’ in the sense



not that he is sick now, but that hewas sick formerly. Examples such as thefollowing depend upon amphiboly: ‘Iwish that you the enemy may capture’.

Also the thesis, ‘There must beknowledge of what one knows’: for it is

possible by this phrase to mean thatknowledge belongs to both the knowerand the known. Also, ‘There must besight of what one sees: one sees the

pillar: ergo the pillar has sight’.

Also, ‘What you profess to-be, that you profess to-be: you profess a stone to- be: ergo you profess-to-be a stone’. Also, ‘Speaking of the silent is possible’: for ‘speaking of the silent’

also has a double meaning: it may meanthat the speaker is silent or that thethings of which he speaks are so. Thereare three varieties of theseambiguities and amphibolies: (1) Wheneither the expression or the name hasstrictly more than one meaning, e.g.aetos and the ‘dog’; (2) when by customwe use them so; (3) when words thathave a simple sense taken alone have

more than one meaning in combination;e.g. ‘knowing letters’. For each word,

both ‘knowing’ and ‘letters’, possiblyhas a single meaning: but both togetherhave more than one-either that the



letters themselves have knowledge orthat someone else has it of them.

Amphiboly and ambiguity, then, dependon these modes of speech. Upon thecombination of words there dependinstances such as the following: ‘A mancan walk while sitting, and can writewhile not writing’. For the meaning isnot the same if one divides the wordsand if one combines them in saying that

‘it is possible to walk-while-sitting’and write while not writing]. The sameapplies to the latter phrase, too, ifone combines the words ‘to write-while-not-writing’: for then it means that hehas the power to write and not to writeat once; whereas if one does notcombine them, it means that when he isnot writing he has the power to write.

Also, ‘He now if he has learnt hisletters’. Moreover, there is the sayingthat ‘One single thing if you can carrya crowd you can carry too’.

Upon division depend the propositions

that 5 is 2 and 3, and odd, and thatthe greater is equal: for it is thatamount and more besides. For the same

phrase would not be thought always tohave the same meaning when divided and



when combined, e.g. ‘I made thee aslave once a free man’, and ‘God-like

Achilles left fifty a hundred men’.

An argument depending upon accent it isnot easy to construct in unwrittendiscussion; in written discussions andin poetry it is easier. Thus (e.g.)some people emend Homer against thosewho criticize as unnatural hisexpression to men ou kataputhetai

ombro. For they solve the difficulty bya change of accent, pronouncing the ouwith an acuter accent. Also, in the

passage about Agamemnon’s dream, theysay that Zeus did not himself say ‘Wegrant him the fulfilment of his

prayer’, but that he bade the dreamgrant it. Instances such as these,then, turn upon the accentuation.

Others come about owing to the form ofexpression used, when what is reallydifferent is expressed in the sameform, e.g. a masculine thing by afeminine termination, or a feminine

thing by a masculine, or a neuter byeither a masculine or a feminine; or,again, when a quality is expressed by atermination proper to quantity or viceversa, or what is active by a passive



word, or a state by an active word, andso forth with the other divisions

previously’ laid down. For it is possible to use an expression to denote

what does not belong to the class ofactions at all as though it did so

belong. Thus (e.g.) ‘flourishing’ is aword which in the form of itsexpression is like ‘cutting’ or‘building’: yet the one denotes acertain quality-i.e. a certain

condition-while the other denotes acertain action. In the same manner alsoin the other instances.

Refutations, then, that depend uponlanguage are drawn from these common-

place rules. Of fallacies, on the otherhand, that are independent of languagethere are seven kinds:

that which depends upon Accident:

the use of an expression absolutely ornot absolutely but with somequalification of respect or place, or

time, or relation:

that which depends upon ignorance ofwhat ‘refutation’ is:



that which depends upon the consequent:

that which depends upon assuming theoriginal conclusion:

stating as cause what is not the cause:

the making of more than one questioninto one.

5

Fallacies, then, that depend on Accident occur whenever any attribute

is claimed to belong in like manner toa thing and to its accident. For sincethe same thing has many accidents thereis no necessity that all the sameattributes should belong to all of athing’s predicates and to their subjectas well. Thus (e.g.), ‘If Coriscus bedifferent from “man”, he is differentfrom himself: for he is a man’: or ‘Ifhe be different from Socrates, andSocrates be a man, then’, they say, ‘hehas admitted that Coriscus is different

from a man, because it so happens(accidit) that the person from whom hesaid that he (Coriscus) is different isa man’.



Those that depend on whether anexpression is used absolutely or in acertain respect and not strictly, occurwhenever an expression used in a

particular sense is taken as though itwere used absolutely, e.g. in theargument ‘If what is not is the objectof an opinion, then what is not is’:for it is not the same thing ‘to be x’and ‘to be’ absolutely. Or again, ‘Whatis, is not, if it is not a particular

kind of being, e.g. if it is not a man.’ For it is not the same thing ‘not

to be x’ and ‘not to be’ at all: itlooks as if it were, because of thecloseness of the expression, i.e.

because ‘to be x’ is but littledifferent from ‘to be’, and ‘not to bex’ from ‘not to be’. Likewise also withany argument that turns upon the pointwhether an expression is used in acertain respect or used absolutely.Thus e.g. ‘Suppose an Indian to be

black all over, but white in respect ofhis teeth; then he is both white andnot white.’ Or if both characters

belong in a particular respect, then,they say, ‘contrary attributes belongat the same time’. This kind of thingis in some cases easily seen by anyone, e.g. suppose a man were to secure



the statement that the Ethiopian is 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 ofhis questions that therefore he had

proved dialectically that he was bothwhite and not white. But in some casesit often passes undetected, viz. in allcases where, whenever a statement is

made of something in a certain respect,

it would be generally thought that theabsolute statement follows as well; andalso in all cases where it is not easyto see which of the attributes ought to

be rendered strictly. A situation ofthis kind arises, where both theopposite attributes belong alike: forthen there is general support for theview that one must agree absolutely tothe assertion of both, or of neither:e.g. if a thing is half white and half

black, is it white or black?

Other fallacies occur because the terms‘proof’ or ‘refutation’ have not been

defined, and because something is leftout in their definition. For to refuteis to contradict one and the sameattribute-not merely the name, but thereality-and a name that is not merely



synonymous but the same name-and toconfute it from the propositionsgranted, necessarily, without includingin the reckoning the original point to

be proved, in the same respect andrelation and manner and time in whichit was asserted. A ‘false assertion’about anything has to be defined in thesame way. Some people, however, omitsome one of the said conditions andgive a merely apparent refutation,

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 show that it is

both double and not double of the samething, but not that it is so in thesame respect: for it is double inlength but not double in breadth. Or,it may be, they show it to be bothdouble and not double of the same thingand in the same respect and manner, butnot that it is so at the same time: andtherefore their refutation is merelyapparent. One might, with someviolence, bring this fallacy into the

group of fallacies dependent onlanguage as well.

Those that depend on the assumption ofthe original point to be proved, occur



in the same way, and in as many ways,as it is possible to beg the original

point; they appear to refute because men lack the power to keep their eyes

at once upon what is the same and whatis different.

The refutation which depends upon theconsequent arises because peoplesuppose that the relation ofconsequence is convertible. For

whenever, suppose A is, B necessarilyis, they then suppose also that if Bis, A necessarily is. This is also thesource of the deceptions that attendopinions based on sense-perception. For

people often suppose bile to be honey because honey is attended by a yellow

colour: also, since after rain theground is wet in consequence, wesuppose that if the ground is wet, ithas been raining; whereas that does notnecessarily follow. In rhetoric proofsfrom signs are based on consequences.For when rhetoricians wish to show thata man is an adulterer, they take hold

of some consequence of an adulterouslife, viz. that the man is smartlydressed, or that he is observed towander about at night. There are,however, many people of whom these



things are true, while the charge inquestion is untrue. It happens likethis also in real reasoning; e.g.

Melissus’ argument, that the universeis eternal, assumes that the universehas not come to be (for from what isnot nothing could possibly come to be)and that what has come to be has doneso from a first beginning. If,therefore, the universe has not come to

be, it has no first beginning, and is

therefore eternal. But this does notnecessarily follow: for even if whathas come to be always has a first

beginning, it does not also follow thatwhat has a first beginning has come to

be; any more than it follows that if a man in a fever be hot, a man who is hot must be in a fever.

The refutation which depends upontreating as cause what is not a cause,occurs whenever what is not a cause isinserted in the argument, as though therefutation depended upon it. This kindof thing happens in arguments that

reason ad impossible: for in these weare bound to demolish one of the

premisses. If, then, the false cause bereckoned in among the questions thatare necessary to establish the



resulting impossibility, it will often be thought that the refutation depends

upon it, e.g. in the proof that the‘soul’ and ‘life’ are not the same: forif coming-to-be be contrary to

perishing, then a particular form of perishing will have a particular form

of coming-to-be as its contrary: nowdeath is a particular form of perishingand 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 impossibilityresults all the same, even if one doesnot say that life is the same as thesoul, but merely says that life iscontrary to death, which is a form of

perishing, and that perishing has‘coming-to-be’ as its contrary.

Arguments of that kind, then, thoughnot inconclusive absolutely, areinconclusive 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 thatdepend upon the consequent and uponfalse cause. Those that depend upon the



making of two questions into one occurwhenever the plurality is undetectedand a single answer is returned as ifto a single question. Now, in somecases, it is easy to see that there is

more than one, and that an answer isnot to be given, e.g. ‘Does the earthconsist of sea, or the sky?’ But insome cases it is less easy, and then

people treat the question as one, andeither confess their defeat by failing

to answer the question, or are exposedto an apparent refutation. Thus ‘Is Aand is B a man?’ ‘Yes.’ ‘Then if anyone hits A and B, he will strike a man’(singular),’not men’ (plural). Oragain, where part is good and part bad,‘is the whole good or bad?’ Forwhichever he says, it is possible thathe might be thought to expose himselfto an apparent refutation or to make anapparently false statement: for to saythat something is good which is notgood, or not good which is good, is to

make a false statement. Sometimes,however, additional premisses may

actually give rise to a genuinerefutation; e.g. suppose a man were togrant that the descriptions ‘white’ and‘naked’ and ‘blind’ apply to one thingand to a number of things in a like



sense. For if ‘blind’ describes a thingthat cannot see though nature designedit to see, it will also describe thingsthat cannot see though nature designedthem to do so. Whenever, then, onething can see while another cannot,they will either both be able to see orelse both be blind; which isimpossible.

6

The right way, then, is either todivide apparent proofs and refutationsas above, or else to refer them all toignorance of what ‘refutation’ is, and

make that our starting-point: for it is possible to analyse all the aforesaid modes of fallacy into breaches of the

definition of a refutation. In thefirst place, we may see if they areinconclusive: for the conclusion oughtto result from the premisses laid down,so as to compel us necessarily to stateit and not merely to seem to compel us.

Next we should also take the definition

bit by bit, and try the fallacythereby. For of the fallacies thatconsist in language, some depend upon adouble meaning, e.g. ambiguity of wordsand of phrases, and the fallacy of like



verbal forms (for we habitually speakof everything as though it were a

particular substance)-while fallaciesof combination and division and accentarise because the phrase in question orthe term as altered is not the same aswas intended. Even this, however,should be the same, just as the thingsignified should be as well, if arefutation or proof is to be effected;e.g. if the point concerns a doublet,

then you should draw the conclusion ofa ‘doublet’, not of a ‘cloak’. For theformer conclusion also would be true,

but it has not been proved; we need afurther question to show that ‘doublet’

means the same thing, in order tosatisfy any one who asks why you thinkyour point proved.

Fallacies that depend on Accident areclear cases of ignoratio elenchi whenonce ‘proof’ has been defined. For thesame definition ought to hold good of‘refutation’ too, except that a mentionof ‘the contradictory’ is here added:

for a refutation is a proof of thecontradictory. If, then, there is no

proof as regards an accident ofanything, there is no refutation. Forsupposing, when A and B are, C must



necessarily be, and C is white, thereis no necessity for it to be white onaccount of the syllogism. So, if thetriangle has its angles equal to tworight-angles, and it happens to be afigure, or the simplest element orstarting point, it is not because it isa figure or a starting point orsimplest element that it has thischaracter. For the demonstration provesthe point about it not qua figure or

qua simplest element, but qua triangle.Likewise also in other cases. If, then,refutation is a proof, an argumentwhich argued per accidens could not bea refutation. It is, however, just inthis that the experts and men ofscience generally suffer refutation atthe hand of the unscientific: for thelatter meet the scientists withreasonings constituted per accidens;and the scientists for lack of the

power to draw distinctions either say‘Yes’ to their questions, or else

people suppose them to have said ‘Yes’,although they have not.

Those that depend upon whethersomething is said in a certain respectonly or said absolutely, are clearcases of ignoratio elenchi because the



affirmation and the denial are notconcerned with the same point. For of‘white in a certain respect’ thenegation is ‘not white in a certainrespect’, while of ‘white absolutely’it is ‘not white, absolutely’. If,then, a man treats the admission that athing is ‘white in a certain respect’as though it were said to be whiteabsolutely, he does not effect arefutation, but merely appears to do so

owing to ignorance of what refutationis.

The clearest cases of all, however, arethose that were previously described’as depending upon the definition of a‘refutation’: and this is also why theywere called by that name. For theappearance of a refutation is produced

because of the omission in thedefinition, and if we divide fallaciesin the above manner, we ought to set‘Defective definition’ as a common markupon them all.

Those that depend upon the assumptionof the original point and upon statingas the cause what is not the cause, areclearly shown to be cases of ignoratioelenchi through the definition thereof.



For the conclusion ought to come about‘because these things are so’, and thisdoes not happen where the premisses arenot causes of it: and again it shouldcome about without taking into accountthe original point, and this is not thecase with those arguments which dependupon begging the original point.

Those that depend upon the assumptionof the original point and upon stating

as the cause what is not the cause, areclearly shown to be cases of ignoratioelenchi through the definition thereof.For the conclusion ought to come about‘because these things are so’, and thisdoes not happen where the premisses arenot causes of it: and again it shouldcome about without taking into accountthe original point, and this is not thecase with those arguments which dependupon begging the original point.

Those that depend upon the consequentare a branch of Accident: for theconsequent is an accident, only it

differs from the accident in this, thatyou may secure an admission of theaccident in the case of one thing only(e.g. the identity of a yellow thingand honey and of a white thing and



swan), whereas the consequent alwaysinvolves more than one thing: for weclaim that things that are the same asone and the same thing are also thesame as one another, and this is theground of a refutation dependent on theconsequent. It is, however, not alwaystrue, e.g. suppose that and B are thesame as C per accidens; for both ‘snow’and the ‘swan’ are the same assomething white’. Or again, as in

Melissus’ argument, a man assumes thatto ‘have been generated’ and to ‘have a

beginning’ are the same thing, or to‘become equal’ and to ‘assume the same

magnitude’. For because what has beengenerated has a beginning, he claimsalso that what has a beginning has beengenerated, and argues as though bothwhat has been generated and what isfinite were the same because each has a

beginning. Likewise also in the case ofthings that are made equal he assumesthat if things that assume one and thesame magnitude become equal, then alsothings that become equal assume one

magnitude: i.e. he assumes theconsequent. Inasmuch, then, as arefutation depending on accidentconsists 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 into one

consist in our failure to dissect thedefinition of ‘proposition’. For a

proposition is a single statement abouta single thing. For the same definitionapplies to ‘one single thing only’ and

to the ‘thing’, simply, e.g. to ‘man’and to ‘one single man only’ andlikewise also in other cases. If, then,a ‘single proposition’ be one whichclaims a single thing of a singlething, a ‘proposition’, simply, willalso be the putting of a question ofthat kind. Now since a proof startsfrom propositions and refutation is a

proof, refutation, too, will start from propositions. If, then, a proposition

is a single statement about a singlething, it is obvious that this fallacytoo consists in ignorance of what arefutation is: for in it what is not a

proposition appears to be one. If,then, the answerer has returned ananswer as though to a single question,there will be a refutation; while if hehas returned one not really but





to distinguish what kind of things aresignified by the same and what bydifferent kinds of expression: for a

man who can do this is practically nextdoor to the understanding of the truth.

A special reason why a man is liable to be hurried into assent to the fallacy

is that we suppose every predicate ofeverything to be an individual thing,and we understand it as being one withthe thing: and we therefore treat it as

a substance: for it is to that which isone with a thing or substance, as alsoto substance itself, that‘individually’ and ‘being’ are deemedto belong in the fullest sense. Forthis reason, too, this type of fallacyis to be ranked among those that dependon language; in the first place,

because the deception is effected the more readily when we are inquiring into

a problem in company with others thanwhen we do so by ourselves (for aninquiry with another person is carriedon by means of speech, whereas aninquiry by oneself is carried on quite

as much by means of the object itself);secondly a man is liable to bedeceived, even when inquiring byhimself, when he takes speech as the

basis of his inquiry: moreover the



deception arises out of the likeness(of two different things), and thelikeness arises out of the language.

With those fallacies that depend upon Accident, deception comes about because

we cannot distinguish the sameness andotherness of terms, i.e. their unityand multiplicity, or what kinds of

predicate have all the same accidentsas their subject. Likewise also withthose that depend on the Consequent:

for the consequent is a branch of Accident. Moreover, in many cases

appearances point to this-and the claimis made that if is inseparable from B,so also is B from With those thatdepend upon an imperfection in thedefinition of a refutation, and withthose that depend upon the difference

between a qualified and an absolutestatement, the deception consists inthe smallness of the differenceinvolved; for we treat the limitationto the particular thing or respect or

manner or time as adding nothing to the meaning, and so grant the statement

universally. Likewise also in the caseof those that assume the original

point, and those of false cause, andall that treat a number of questions asone: for in all of them the deception



lies in the smallness of thedifference: for our failure to be quiteexact in our definition of ‘premiss’and of ‘proof’ is due to the aforesaidreason.

8

Since we know on how many pointsapparent 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 thething in question. These are thosewhich fail to refute and prove peopleto be ignorant according to the natureof the thing in question, which was thefunction of the art of examination. Nowthe art of examining is a branch ofdialectic: and this may prove a falseconclusion because of the ignorance ofthe answerer. Sophistic refutations on

the other hand, even though they provethe contradictory of his thesis, do not

make clear whether he is ignorant: forsophists entangle the scientist as wellwith these arguments.



That we know them by the same line ofinquiry is clear: for the sameconsiderations which make it appear toan audience that the points requiredfor the proof were asked in thequestions and that the conclusion was

proved, would make the answerer thinkso as well, so that false proof willoccur through all or some of these

means: for what a man has not been

asked but thinks he has granted, hewould also grant if he were asked. Ofcourse, in some cases the moment we addthe missing question, we also show upits falsity, e.g. in fallacies thatdepend on language and on solecism. Ifthen, fallacious proofs of thecontradictory of a thesis depend ontheir appearing to refute, it is clearthat the considerations on which both

proofs of false conclusions and anapparent refutation depend must be thesame in number. Now an apparentrefutation depends upon the elementsinvolved in a genuine one: for the

failure of one or other of these must make the refutation merely apparent,

e.g. that which depends on the failureof the conclusion to follow from theargument (the argument ad impossible)



and that which treats two questions asone and so depends upon a flaw in the

premiss, and that which depends on thesubstitution of an accident for anessential attribute, and-a branch ofthe last-that which depends upon theconsequent: more over, the conclusion

may follow not in fact but onlyverbally: then, instead of proving thecontradictory universally and in thesame respect and relation and manner,

the fallacy may be dependent on somelimit of extent or on one or other ofthese qualifications: moreover, thereis the assumption of the original pointto be proved, in violation of theclause ‘without reckoning in theoriginal point’. Thus we should havethe number of considerations on whichthe fallacious proofs depend: for theycould not depend on more, but all willdepend on the points aforesaid.

A sophistical refutation is arefutation not absolutely butrelatively to some one: and so is a

proof, in the same way. For unless thatwhich depends upon ambiguity assumesthat the ambiguous term has a single

meaning, and that which depends on likeverbal forms assumes that substance is



the only category, and the rest in thesame way, there will be neitherrefutations nor proofs, eitherabsolutely or relatively to theanswerer: whereas if they do assumethese things, they will stand,relatively to the answerer; butabsolutely they will not stand: forthey have not secured a statement thatdoes have a single meaning, but onlyone that appears to have, and that only

from this particular man.

9

The number of considerations on whichdepend the refutations of those who arerefuted, we ought not to try to graspwithout a knowledge of everything thatis. This, however, is not the provinceof any special study: for possibly thesciences are infinite in number, sothat obviously demonstrations may beinfinite too. Now refutations may betrue as well as false: for whenever itis possible to demonstrate something,

it is also possible to refute the manwho maintains the contradictory of thetruth; e.g. if a man has stated thatthe diagonal is commensurate with theside of the square, one might refute



him by demonstrating that it isincommensurate. Accordingly, to exhaustall possible refutations we shall haveto have scientific knowledge ofeverything: for some refutations dependupon the principles that rule ingeometry and the conclusions thatfollow from these, others upon thosethat rule in medicine, and others uponthose of the other sciences. For the

matter of that, the false refutations

likewise belong to the number of theinfinite: for according to every artthere is false proof, e.g. according togeometry there is false geometrical

proof, and according to medicine thereis false medical proof. By ‘accordingto the art’, I mean ‘according to the

principles of it’. Clearly, then, it isnot of all refutations, but only ofthose that depend upon dialectic thatwe need to grasp the common-placerules: for these stand in a commonrelation to every art and faculty. Andas regards the refutation that isaccording to one or other of the

particular sciences it is the task ofthat particular scientist to examinewhether it is merely apparent without

being real, and, if it be real, what isthe reason for it: whereas it is the



business of dialecticians so to examinethe refutation that proceeds from thecommon first principles that fall underno particular special study. For if wegrasp the startingpoints of theaccepted proofs on any subject whateverwe grasp those of the refutationscurrent on that subject. For arefutation is the proof of thecontradictory of a given thesis, sothat either one or two proofs of the

contradictory constitute a refutation. We grasp, then, the number of

considerations on which all suchdepend: if, however, we grasp this, wealso grasp their solutions as well; forthe objections to these are thesolutions of them. We also grasp thenumber of considerations on which thoserefutations depend, that are merelyapparent-apparent, I mean, not toeverybody, but to people of a certainstamp; for it is an indefinite task ifone is to inquire how many are theconsiderations that make them apparentto the man in the street. Accordingly

it is clear that the dialectician’s business is to be able to grasp on how many considerations depends the

formation, through the common first principles, of a refutation that is



either real or apparent, i.e. eitherdialectical or apparently dialectical,or suitable for an examination.

10

It is no true distinction betweenarguments which some people draw whenthey say that some arguments aredirected against the expression, andothers against the thought expressed:

for it is absurd to suppose that somearguments are directed against theexpression and others against thethought, and that they are not thesame. For what is failure to direct anargument against the thought exceptwhat occurs whenever a man does not inusing the expression think it to beused in his question in the same sensein which the person questioned grantedit? And this is the same thing as todirect the argument against theexpression. On the other hand, it isdirected against the thought whenever a

man uses the expression in the same

sense which the answerer had in mindwhen he granted it. If now any (i.e.

both the questioner and the personquestioned), in dealing with anexpression with more than one meaning,



were to suppose it to have one meaning-as e.g. it may be that ‘Being’ and‘One’ have many meanings, and yet boththe answerer answers and the questioner

puts his question supposing it to beone, and the argument is to the effectthat ‘All things are one’-will thisdiscussion be directed any more againstthe expression than against the thoughtof the person questioned? If, on theother hand, one of them supposes the

expression to have many meanings, it isclear that such a discussion will not

be directed against the thought. Such being the meanings of the phrases in

question, they clearly cannot describetwo separate classes of argument. For,in the first place, it is possible forany such argument as bears more thanone meaning to be directed against theexpression and against the thought, andnext it is possible for any argumentwhatsoever; for the fact of beingdirected against the thought consistsnot in the nature of the argument, butin the special attitude of the answerer

towards the points he concedes. Next,all of them may be directed to theexpression. For ‘to be directed againstthe expression’ means in this doctrine‘not to be directed against the





contradictory of a thesis. Accordingly,the reason of the falsity will beeither in the proof or in thecontradiction (for mention of the‘contradiction’ must be added), whilesometimes it is in both, if therefutation be merely apparent. In theargument that speaking of the silent is

possible it lies in the contradiction,not in the proof; in the argument thatone can give what one does not possess,

it lies in both; in the proof thatHomer’s poem is a figure through its

being a cycle it lies in the proof. Anargument that does not fail in eitherrespect is a true proof.

But, to return to the point whence ourargument digressed, are mathematicalreasonings directed against thethought, or not? And if any one thinks‘triangle’ to be a word with many

meanings, and granted it in somedifferent sense from the figure whichwas proved to contain two right angles,has the questioner here directed his

argument against the thought of theformer or not?

Moreover, if the expression bears manysenses, while the answerer does not



understand or suppose it to have them,surely the questioner here has directedhis argument against his thought! Orhow else ought he to put his questionexcept by suggesting a distinction-suppose one’s question to be speakingof the silent possible or not?’-asfollows, ‘Is the answer “No” in onesense, but “Yes” in another?’ If, then,any one were to answer that it was not

possible in any sense and the other

were to argue that it was, has not hisargument been directed against thethought of the answerer? Yet hisargument is supposed to be one of thosethat depend on the expression. There isnot, then, any definite kind ofarguments that is directed against thethought. Some arguments are, indeed,directed against the expression: butthese are not all even apparentrefutations, let alone all refutations.For there are also apparent refutationswhich do not depend upon language, e.g.those that depend upon accident, andothers.

If, however, any one claims that oneshould actually draw the distinction,and say, ‘By “speaking of the silent” I

mean, in one sense this and in the



other sense that’, surely to claim thisis in the first place absurd (forsometimes the questioner does not seethe ambiguity of his question, and hecannot possibly draw a distinctionwhich he does not think to be there):in the second place, what else but thiswill didactic argument be? For it will

make manifest the state of the case toone who has never considered, and doesnot know or suppose that there is any

other meaning but one. For what isthere to prevent the same thing alsohappening to us in cases where there isno double meaning? ‘Are the units infour equal to the twos? Observe thatthe twos are contained in four in onesense in this way, in another sense inthat’. Also, ‘Is the knowledge ofcontraries one or not? Observe thatsome contraries are known, while othersare unknown’. Thus the man who makesthis claim seems to be unaware of thedifference between didactic anddialectical argument, and of the factthat while he who argues didactically

should not ask questions but makethings clear himself, the other should

merely ask questions.



11

Moreover, to claim a ‘Yes’ or ‘No’answer is the business not of a man whois showing something, but of one who isholding an examination. For the art ofexamining is a branch of dialectic andhas in view not the man who hasknowledge, but the ignorant pretender.He, then, is a dialectician who regardsthe common principles with their

application to the particular matter inhand, while he who only appears to dothis is a sophist. Now for contentiousand sophistical reasoning: (1) one suchis a merely apparent reasoning, onsubjects on which dialectical reasoningis the proper method of examination,even though its conclusion be true: forit misleads us in regard to the cause:also (2) there are those misreasoningswhich do not conform to the line ofinquiry proper to the particularsubject, but are generally thought toconform to the art in question. Forfalse diagrams of geometrical figures

are not contentious (for the resultingfallacies conform to the subject of theart)-any more than is any false diagramthat may be offered in proof of atruth-e.g. Hippocrates’ figure or the



squaring of the circle by means of thelunules. But Bryson’s method ofsquaring the circle, even if the circleis thereby squared, is stillsophistical because it does not conformto the subject in hand. So, then, any

merely apparent reasoning about thesethings is a contentious argument, andany reasoning that merely appears toconform to the subject in hand, eventhough it be genuine reasoning, is a

contentious argument: for it is merelyapparent in its conformity to thesubject-matter, so that it is deceptiveand plays foul. For just as a foul in arace is a definite type of fault, andis a kind of foul fighting, so the artof contentious reasoning is foulfighting in disputation: for in theformer case those who are resolved towin at all costs snatch at everything,and so in the latter case docontentious reasoners. Those, then, whodo this in order to win the merevictory are generally considered to becontentious and quarrelsome persons,

while those who do it to win areputation with a view to making moneyare sophistical. For the art ofsophistry is, as we said,’ a kind ofart of money-making from a merely



apparent wisdom, and this is why theyaim at a merely apparent demonstration:and quarrelsome persons and sophists

both employ the same arguments, but notwith the same motives: and the sameargument will be sophistical andcontentious, but not in the samerespect; rather, it will be contentiousin so far as its aim is an apparentvictory, while in so far as its aim isan apparent wisdom, it will be

sophistical: for the art of sophistryis a certain appearance of wisdomwithout the reality. The contentiousargument stands in somewhat the samerelation to the dialectical as thedrawer of false diagrams to thegeometrician; for it beguiles by

misreasoning from the same principlesas dialectic uses, just as the drawerof a false diagram beguiles thegeometrician. But whereas the latter isnot a contentious reasoner, because he

bases his false diagram on the principles and conclusions that fall

under the art of geometry, the argument

which is subordinate to the principlesof dialectic will yet clearly becontentious as regards other subjects.Thus, e.g. though the squaring of thecircle by means of the lunules is not



contentious, Bryson’s solution iscontentious: and the former argumentcannot be adapted to any subject exceptgeometry, because it proceeds from

principles that are peculiar togeometry, whereas the latter can beadapted as an argument against all thenumber of people who do not know whatis or is not possible in each

particular context: for it will applyto them all. Or there is the method

whereby Antiphon squared the circle. Oragain, an argument which denied that itwas better to take a walk after dinner,

because of Zeno’s argument, would not be a proper argument for a doctor, because Zeno’s argument is of general

application. If, then, the relation ofthe contentious argument to thedialectical were exactly like that ofthe drawer of false diagrams to thegeometrician, a contentious argumentupon the aforesaid subjects could nothave existed. But, as it is, thedialectical argument is not concernedwith any definite kind of being, nor

does it show anything, nor is it evenan argument such as we find in thegeneral philosophy of being. For all

beings are not contained in any onekind, nor, if they were, could they



possibly fall under the same principles. Accordingly, no art that is

a method of showing the nature ofanything proceeds by asking questions:for it does not permit a man to grantwhichever he likes of the twoalternatives in the question: for theywill not both of them yield a proof.Dialectic, on the other hand, does

proceed by questioning, whereas if itwere concerned to show things, it would

have refrained from putting questions,even if not about everything, at leastabout the first principles and thespecial principles that apply to the

particular subject in hand. For supposethe answerer not to grant these, itwould then no longer have had anygrounds from which to argue any longeragainst the objection. Dialectic is atthe same time a mode of examination aswell. For neither is the art ofexamination an accomplishment of thesame kind as geometry, but one which a

man may possess, even though he has notknowledge. For it is possible even for

one without knowledge to hold anexamination of one who is withoutknowledge, if also the latter grantshim points taken not from thing that heknows or from the special principles of





such as to constitute a particularnature, i.e. a particular kind of

being, but are like negative terms,while other principles are not of thiskind but are special to particularsubjects; accordingly it is possiblefrom these general principles to holdan examination on everything, and thatthere should be a definite art of sodoing, and, moreover, an art which isnot of the same kind as those which

demonstrate. This is why thecontentious reasoner does not stand inthe same condition in all respects asthe drawer of a false diagram: for thecontentious reasoner will not be givento misreasoning from any definite classof principles, but will deal with everyclass.

These, then, are the types ofsophistical refutations: and that it

belongs to the dialectician to studythese, and to be able to effect them,is not difficult to see: for theinvestigation of premisses comprises

the whole of this study.

12



So much, then, for apparentrefutations. As for showing that theanswerer is committing some fallacy,and drawing his argument into paradox-for this was the second item of thesophist’s programme-in the first place,then, this is best brought about by acertain manner of questioning andthrough the question. For to put thequestion without framing it withreference to any definite subject is a

good bait for these purposes: for people are more inclined to make mistakes when they talk at large, and

they talk at large when they have nodefinite subject before them. Also the

putting of several questions, eventhough the position against which oneis arguing be quite definite, and theclaim that he shall say only what hethinks, create abundant opportunity fordrawing him into paradox or fallacy,and also, whether to any of thesequestions he replies ‘Yes’ or replies‘No’, of leading him on to statementsagainst which one is well off for a

line of attack. Nowadays, however, menare less able to play foul by these

means than they were formerly: for people rejoin with the question, ‘What

has that to do with the original



subject?’ It is, too, an elementaryrule for eliciting some fallacy or

paradox that one should never put acontroversial question straight away,

but say that one puts it from the wishfor information: for the process ofinquiry thus invited gives room for anattack.

A rule specially appropriate forshowing up a fallacy is the sophistic

rule, that one should draw the answereron to the kind of statements againstwhich one is well supplied witharguments: this can be done both

properly and improperly, as was said before.’ Again, to draw a paradoxical

statement, look and see to what schoolof philosophers the person arguing withyou belongs, and then question him asto some point wherein their doctrine is

paradoxical to most people: for withevery school there is some point ofthat kind. It is an elementary rule inthese matters to have a collection ofthe special ‘theses’ of the various

schools among your propositions. Thesolution recommended as appropriatehere, too, is to point out that the

paradox does not come about because of



the argument: whereas this is what hisopponent always really wants.

Moreover, argue from men’s wishes andtheir professed opinions. For people donot wish the same things as they saythey wish: they say what will look

best, whereas they wish what appears to be to their interest: e.g. they say

that a man ought to die nobly ratherthan to live in pleasure, and to live

in honest poverty rather than indishonourable riches; but they wish theopposite. Accordingly, a man who speaksaccording to his wishes must be ledinto stating the professed opinions of

people, while he who speaks accordingto these must be led into admittingthose that people keep hidden away: forin either case they are bound tointroduce a paradox; for they willspeak contrary either to men’s

professed or to their hidden opinions.

The widest range of common-placeargument for leading men into

paradoxical statement is that whichdepends on the standards of Nature andof the Law: it is so that bothCallicles is drawn as arguing in theGorgias, and that all the men of old



supposed the result to come about: fornature (they said) and law areopposites, and justice is a fine thing

by a legal standard, but not by that ofnature. Accordingly, they said, the manwhose statement agrees with thestandard of nature you should meet bythe standard of the law, but the manwho agrees with the law by leading himto the facts of nature: for in bothways paradoxical statements may be

committed. In their view the standardof nature was the truth, while that ofthe law was the opinion held by the

majority. So that it is clear thatthey, too, used to try either to refutethe answerer or to make him make

paradoxical statements, just as the menof to-day do as well.

Some questions are such that in bothforms the answer is paradoxical; e.g.‘Ought one to obey the wise or one’sfather?’ and ‘Ought one to do what isexpedient or what is just?’ and ‘Is it

preferable to suffer injustice or to do

an injury?’ You should lead people,then, into views opposite to the

majority and to the philosophers; ifany one speaks as do the expertreasoners, lead him into opposition to



the majority, while if he speaks as dothe majority, then into opposition tothe reasoners. For some say that ofnecessity the happy man is just,whereas it is paradoxical to the manythat a king should be happy. To lead a

man into paradoxes of this sort is thesame as to lead him into the oppositionof the standards of nature and law: forthe law represents the opinion of the

majority, whereas philosophers speak

according to the standard of nature andthe truth.

13

Paradoxes, then, you should seek toelicit by means of these common-placerules. Now as for making any one

babble, we have already said what we mean by ‘to babble’. This is the object

in view in all arguments of thefollowing kind: If it is all the sameto state a term and to state itsdefinition, the ‘double’ and ‘double ofhalf’ are the same: if then ‘double’ be

the ‘double of half’, it will be the‘double of half of half’. And if,instead of ‘double’, ‘double of half’

be again put, then the same expressionwill be repeated three times, ‘double



of half of half of half’. Also ‘desireis of the pleasant, isn’t it?’ desireis conation for the pleasant:accordingly, ‘desire’ is ‘conation forthe pleasant for the pleasant’.

All arguments of this kind occur indealing (1) with any relative termswhich not only have relative genera,

but are also themselves relative, andare rendered in relation to one and the

same thing, as e.g. conation isconation for something, and desire isdesire of something, and double isdouble of something, i.e. double ofhalf: also in dealing (2) with anyterms which, though they be notrelative terms at all, yet have theirsubstance, viz. the things of whichthey are the states or affections orwhat not, indicated as well in theirdefinition, they being predicated ofthese things. Thus e.g. ‘odd’ is a‘number containing a middle’: but thereis an ‘odd number’: therefore there isa ‘number-containing-a-middle number’.

Also, if snubness be a concavity of thenose, and there be a snub nose, thereis therefore a ‘concave-nose nose’.



People sometimes appear to produce thisresult, without really producing it,

because they do not add the questionwhether the expression ‘double’, just

by itself, has any meaning or no, andif so, whether it has the same meaning,or a different one; but they draw theirconclusion straight away. Still itseems, inasmuch as the word is thesame, to have the same meaning as well.

14

We have said before what kind of thing‘solecism’ is.’ It is possible both tocommit it, and to seem to do so withoutdoing so, and to do so without seemingto do so. Suppose, as Protagoras usedto say that menis (’wrath’) and pelex(’helmet’) are masculine: according tohim a man who calls wrath a‘destructress’ (oulomenen) commits asolecism, though he does not seem to doso to other people, where he who callsit a ‘destructor’ (oulomenon) commitsno solecism though he seems to do so.

It is clear, then, that any one could produce this effect by art as well: and

for this reason many arguments seem tolead to solecism which do not really do



so, as happens in the case ofrefutations.

Almost all apparent solecisms dependupon the word ‘this’ (tode), and uponoccasions when the inflection denotesneither a masculine nor a feminineobject but a neuter. For ‘he’ (outos)signifies a masculine, and ‘she’ (aute)feminine; but ‘this’ (touto), though

meant to signify a neuter, often also

signifies one or other of the former:e.g. ‘What is this?’ ‘It is Calliope’;‘it is a log’; ‘it is Coriscus’. Now inthe masculine and feminine theinflections are all different, whereasin the neuter some are and some arenot. Often, then, when ‘this’ (touto)has been granted, people reason as if‘him’ (touton) had been said: andlikewise also they substitute oneinflection for another. The fallacycomes about because ‘this’ (touto) is acommon form of several inflections: for‘this’ signifies sometimes ‘he’ (outos)and sometimes ‘him’ (touton). It should

signify them alternately; when combinedwith ‘is’ (esti) it should be ‘he’,while with ‘being’ it should be ‘him’:e.g. ‘Coriscus (Kopiskos) is’, but‘being Coriscus’ (Kopiskon). It happens



in the same way in the case of femininenouns as well, and in the case of theso-called ‘chattels’ that have feminineor masculine designations. For onlythose names which end in o and n, havethe designation proper to a chattel,e.g. xulon (’log’), schoinion (’rope’);those which do not end so have that ofa masculine or feminine object, thoughsome of them we apply to chattels: e.g.askos (’wineskin’) is a masculine noun,

and kline (’bed’) a feminine. For thisreason in cases of this kind as wellthere will be a difference of the samesort between a construction with ‘is’(esti) or with ‘being’ (to einai).

Also, Solecism resembles in a certainway those refutations which are said todepend on the like expression of unlikethings. For, just as there we come upona material solecism, so here we comeupon 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 ofcontentious arguments, and the



subdivisions of those types, and the methods for conducting them aforesaid.

But it makes no little difference ifthe materials for putting the question

be arranged in a certain manner with aview to concealment, as in the case ofdialectics. Following then upon what wehave said, this must be discussedfirst.

15

With a view then to refutation, oneresource is length-for it is difficultto keep several things in view at once;and to secure length the elementaryrules that have been stated before’should be employed. One resource, onthe other hand, is speed; for when

people are left behind they look aheadless. Moreover, there is anger andcontentiousness, for when agitatedeverybody is less able to take care ofhimself. Elementary rules for producinganger are 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 one has more than one argumentleading to the same conclusion, orwhether one has arguments to show both



that something is so, and that it isnot so: for the result is that he hasto be on his guard at the same timeeither against more than one line, oragainst contrary lines, of argument. Ingeneral, all the methods described

before of producing concealment areuseful also for purposes of contentiousargument: for the object of concealmentis to avoid detection, and the objectof this is to deceive.

To counter those who refuse to grantwhatever they suppose to help one’sargument, one should put the questionnegatively, as though desirous of theopposite answer, or at any rate asthough one put the question without

prejudice; for when it is obscure whatanswer one wants to secure, people areless refractory. Also when, in dealingwith particulars, a man grants theindividual case, when the induction isdone you should often not put theuniversal as a question, but take itfor granted and use it: for sometimes

people themselves suppose that theyhave granted it, and also appear to theaudience to have done so, for theyremember the induction and assume thatthe questions could not have been put



for nothing. In cases where there is noterm to indicate the universal, stillyou should avail yourself of theresemblance of the particulars to suityour purpose; for resemblance oftenescapes detection. Also, with a view toobtaining your premiss, you ought to

put it in your question side by sidewith its contrary. E.g. if it werenecessary to 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 everything?’; and to secure that ‘Anumber multiplied by a large number isa large number’, ask ‘Should one agreethat it is a large number or a smallone?’ For then, if compelled to choose,one will be more inclined to think it alarge one: for the placing of theircontraries close beside them makesthings look big to men, both relativelyand absolutely, and worse and better.

A strong appearance of having beenrefuted is often produced by the most

highly sophistical of all the unfairtricks of questioners, when without

proving anything, instead of puttingtheir final proposition as a question,they state it as a conclusion, as



though they had proved that ‘Thereforeso-and-so is not true’

It is also a sophistical trick, when a paradox has been laid down, first to propose at the start some view that is

generally accepted, and then claim thatthe answerer shall answer what hethinks about it, and to put one’squestion on matters of that kind in theform ‘Do you think that...?’ For then,

if the question be taken as one of the premisses of one’s argument, either a

refutation or a paradox is bound toresult; if he grants the view, arefutation; if he refuses to grant itor even to admit it as the receivedopinion, a paradox; if he refuses togrant it, but admits that it is thereceived opinion, something very like arefutation, results.

Moreover, just as in rhetoricaldiscourses, so also in those aimed atrefutation, you should examine thediscrepancies of the answerer’s

position either with his ownstatements, or with those of personswhom he admits to say and do aright,

moreover with those of people who aregenerally supposed to bear that kind of



character, or who are like them, orwith those of the majority or of all

men. Also just as answerers, too,often, when they are in process of

being confuted, draw a distinction, iftheir confutation is just about to take

place, so questioners also shouldresort to this from time to time tocounter objectors, pointing out,supposing that against one sense of thewords the objection holds, but not

against the other, that they have takenit in the latter sense, as e.g.Cleophon does in the Mandrobulus. Theyshould also break off their argumentand cut down their other lines ofattack, while in answering, if a man

perceives this being done beforehand,he should put in his objection and havehis say first. One should also leadattacks sometimes against positionsother than the one stated, on theunderstood condition that one cannotfind lines of attack against the viewlaid down, as Lycophron did whenordered to deliver a eulogy upon the

lyre. To counter those who demand‘Against what are you directing youreffort?’, since one is generallythought bound to state the charge made,while, on the other hand, some ways of



stating it make the defence too easy,you should state as your aim only thegeneral result that always happens inrefutations, namely the contradictionof his thesis —viz. that your effort isto deny what he has affirmed, or toaffirm what he denied: don’t say thatyou are trying to show that theknowledge of contraries is, or is not,the same. One must not ask one’sconclusion in the form of a premiss,

while some conclusions should not even be put as questions at all; one should

take and use it as granted.

16

We have now therefore dealt with thesources of questions, and the methodsof questioning in contentiousdisputations: next we have to speak ofanswering, and of how solutions should

be made, and of what requires them, andof what use is served by arguments ofthis 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 usin a better condition for seeing in how



many senses any term is used, and whatkind of resemblances and what kind ofdifferences occur between things and

between their names. In the second place they are useful for one’s own personal researches; for the man who is

easily committed to a fallacy by someone else, and does not perceive it, islikely to incur this fate of himselfalso on many occasions. Thirdly andlastly, they further contribute to

one’s reputation, viz. the reputationof being well trained in everything,and not inexperienced in anything: forthat a party to arguments should findfault with them, if he cannotdefinitely point out their weakness,creates a suspicion, making it seem asthough it were not the truth of the

matter but merely inexperience that puthim out of temper.

Answerers may clearly see how to meetarguments of this kind, if our previousaccount was right of the sources whencefallacies came, and also our

distinctions adequate of the forms ofdishonesty in putting questions. But itis not the same thing take an argumentin one’s hand and then to see and solveits faults, as it is to be able to meet



it quickly while being subjected toquestions: for what we know, we oftendo not know in a different context.

Moreover, just as in other things speedis enhanced by training, so it is witharguments too, so that supposing we areunpractised, even though a point beclear to us, we are often too late forthe right moment. Sometimes too ithappens as with diagrams; for there wecan sometimes analyse the figure, but

not construct it again: so too inrefutations, though we know the thingon which the connexion of the argumentdepends, we still are at a loss tosplit the argument apart.

17

First then, just as we say that weought sometimes to choose to provesomething in the general estimationrather than in truth, so also we havesometimes to solve arguments rather inthe general estimation than accordingto the truth. For it is a general rule

in fighting contentious persons, totreat them not as refuting, but as

merely appearing to refute: for we saythat they don’t really prove theircase, so that our object in correcting



them must be to dispel the appearanceof it. For if refutation be anunambiguous contradiction arrived atfrom certain views, there could be noneed to draw distinctions againstamphiboly and ambiguity: they do noteffect a proof. The only motive fordrawing further distinctions is thatthe conclusion reached looks like arefutation. What, then, we have to

beware of, is not being refuted, but

seeming to be, because of course theasking of amphibolies and of questionsthat turn upon ambiguity, and all theother tricks of that kind, conceal evena genuine refutation, and make ituncertain who is refuted and who isnot. For since one has the right at theend, when the conclusion is drawn, tosay that the only denial made of One’sstatement is ambiguous, no matter how

precisely he may have addressed hisargument to the very same point asoneself, it is not clear whether onehas been refuted: for it is not clearwhether at the moment one is speaking

the truth. If, on the other hand, onehad drawn a distinction, and questionedhim on the ambiguous term or theamphiboly, the refutation would nothave been a matter of uncertainty. Also



what is incidentally the object ofcontentious arguers, though less sonowadays than formerly, would have beenfulfilled, namely that the personquestioned should answer either ‘Yes’or ‘No’: whereas nowadays the improperforms in which questioners put theirquestions compel the party questionedto add something to his answer incorrection of the faultiness of the

proposition as put: for certainly, if

the questioner distinguishes his meaning adequately, the answerer is bound to reply either ‘Yes’ or ‘No’.

If any one is going to suppose that anargument which turns upon ambiguity isa refutation, it will be impossible foran answerer to escape being refuted ina sense: for in the case of visibleobjects one is bound of necessity todeny the term one has asserted, and toassert what one has denied. For theremedy which some people have for thisis quite unavailing. They say, not thatCoriscus is both musical and unmusical,

but that this Coriscus is musical andthis Coriscus unmusical. But this willnot do, for to say ‘this Coriscus isunmusical’, or ‘musical’, and to say‘this Coriscus’ is so, is to use the



same expression: and this he is bothaffirming and denying at once. ‘But

perhaps they do not mean the same.’ Well, nor did the simple name in the

former case: so where is thedifference? If, however, he is toascribe to the one person the simpletitle ‘Coriscus’, while to the other heis to add the prefix ‘one’ or ‘this’,he commits an absurdity: for the latteris no more applicable to the one than

to the other: for to whichever he addsit, it makes no difference.

All the same, since if a man does notdistinguish the senses of an amphiboly,it is not clear whether he has beenconfuted or has not been confuted, andsince in arguments the right todistinguish them is granted, it isevident that to grant the questionsimply without drawing any distinctionis a mistake, so that, even if not the

man himself, at any rate his argumentlooks as though it had been refuted. Itoften happens, however, that, though

they see the amphiboly, people hesitateto draw such distinctions, because ofthe dense crowd of persons who proposequestions of the kind, in order thatthey may not be thought to be



obstructionists at every turn: then,though they would never have supposedthat that was the point on which theargument turned, they often findthemselves faced by a paradox.

Accordingly, since the right of drawingthe distinction is granted, one shouldnot hesitate, as has been said before.

If people never made two questions intoone question, the fallacy that turns

upon ambiguity and amphiboly would nothave existed either, but either genuinerefutation or none. For what is thedifference between asking ‘Are Calliasand Themistocles musical?’ and what one

might have asked if they, beingdifferent, had had one name? For if theterm applied means more than one thing,he has asked more than one question. Ifthen it be not right to demand simplyto be given a single answer to twoquestions, it is evident that it is not

proper to give a simple answer to anyambiguous question, not even if the

predicate be true of all the subjects,

as some claim that one should. For thisis exactly as though he had asked ‘AreCoriscus and Callias at home or not athome?’, supposing them to be both in or

both out: for in both cases there is a



number of propositions: for though thesimple answer be true, that does not

make the question one. For it is possible for it to be true to answer

even countless different questions when put to one, all together with either a

‘Yes’ or a ‘No’: but still one shouldnot answer them with a single answer:for that is the death of discussion.Rather, the case is like as thoughdifferent things has actually had the

same name applied to them. If then, oneshould not give a single answer to twoquestions, it is evident that we shouldnot say simply ‘Yes’ or ‘No’ in thecase of ambiguous terms either: for theremark is simply a remark, not ananswer at all, although amongdisputants such remarks are looselydeemed to be answers, because they donot see what the consequence is.

As we said, then, inasmuch as certainrefutations are generally taken forsuch, though not such really, in thesame way also certain solutions will be

generally taken for solutions, thoughnot really such. Now these, we say,

must sometimes be advanced rather thanthe true solutions in contentiousreasonings and in the encounter with



ambiguity. The proper answer in sayingwhat 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, oneshould then be most careful to add that‘it seems’ so: for in that way oneavoids the impression of being eitherrefuted or paradoxical. Since it isclear what is meant by ‘begging the

original question’, and people thinkthat they must at all costs overthrowthe premisses that lie near theconclusion, and plead in excuse forrefusing to grant him some of them thathe is begging the original question, sowhenever any one claims from us a pointsuch as is bound to follow as aconsequence from our thesis, but isfalse or paradoxical, we must plead thesame: for the necessary consequencesare generally held to be a part of thethesis itself. Moreover, whenever theuniversal has been secured not under adefinite name, but by a comparison of

instances, one should say that thequestioner assumes it not in the sensein which it was granted nor in which he

proposed it in the premiss: for this



too is a point upon which a refutationoften depends.

If one is debarred from these defencesone must pass to the argument that theconclusion has not been properly shown,approaching it in the light of theaforesaid distinction between thedifferent kinds of fallacy.

In the case, then, of names that are

used literally one is bound to answereither simply or by drawing adistinction: the tacit understandingsimplied in our statements, e.g. inanswer to questions that are not putclearly but elliptically-it is uponthis that the consequent refutationdepends. For example, ‘Is what belongsto Athenians the property of

Athenians?’ Yes. ‘And so it is likewisein other cases. But observe; man

belongs to the animal kingdom, doesn’the?’ Yes. ‘Then man is the property ofthe animal kingdom.’ But this is afallacy: for we say that man ‘belongs

to’ the animal kingdom because he is ananimal, just as we say that Lysander‘belongs to’ the Spartans, because heis a Spartan. It is evident, then, that



where the premiss put forward is notclear, one must not grant it simply.

Whenever of two things it is generallythought that if the one is true theother is true of necessity, whereas, ifthe other is true, the first is nottrue of necessity, one should, if askedwhich of them is true, grant thesmaller one: for the larger the numberof premisses, the harder it is to draw

a conclusion from them. If, again, thesophist tries to secure that has acontrary while B has not, suppose whathe says is true, you should say thateach has a contrary, only for the onethere is no established name.

Since, again, in regard to some of theviews they express, most people wouldsay that any one who did not admit themwas telling a falsehood, while theywould not say this in regard to some,e.g. to any matters whereon opinion isdivided (for most people have nodistinct view whether the soul of

animals is destructible or immortal),accordingly (1) it is uncertain inwhich of two senses the premiss

proposed is usually meant-whether as maxims are (for people call by the name



of ‘maxims’ both true opinions andgeneral assertions) or like thedoctrine ‘the diagonal of a square isincommensurate with its side’: and

moreover (2) whenever opinions aredivided as to the truth, we then havesubjects of which it is very easy tochange the terminology undetected. For

because of the uncertainty in which ofthe two senses the premiss contains thetruth, one will not be thought to be

playing any trick, while because of thedivision of opinion, one will not bethought to be telling a falsehood.Change the terminology therefore, forthe change will make the positionirrefutable.

Moreover, whenever one foresees anyquestion coming, one should put inone’s objection and have one’s say

beforehand: for by doing so one islikely to embarrass the questioner mosteffectually.

18

Inasmuch as a proper solution is anexposure of false reasoning, showing onwhat kind of question the falsitydepends, and whereas ‘false reasoning’



has a double meaning-for it is usedeither if a false conclusion has been

proved, or if there is only an apparent proof and no real one-there must be both the kind of solution just

described,’ and also the correction ofa merely apparent proof, so as to showupon which of the questions theappearance depends. Thus it comes aboutthat one solves arguments that are

properly reasoned by demolishing them,

whereas one solves merely apparentarguments by drawing distinctions.

Again, inasmuch as of arguments thatare properly reasoned some have a trueand others a false conclusion, thosethat are false in respect of theirconclusion it is possible to solve intwo ways; for it is possible both bydemolishing one of the premisses asked,and by showing that the conclusion isnot the real state of the case: those,on the other hand, that are false inrespect of the premisses can be solvedonly by a demolition of one of them;for the conclusion is true. So that

those who wish to solve an argumentshould in the first place look and seeif it is properly reasoned, or isunreasoned; and next, whether theconclusion be true or false, in order



that we may effect the solution either by drawing some distinction or by

demolishing something, and demolishingit either in this way or in that, aswas laid down before. There is a verygreat deal of difference betweensolving an argument when beingsubjected to questions and when not:for to foresee traps is difficult,whereas to see them at one’s leisure iseasier.

19

Of the refutations, then, that dependupon ambiguity and amphiboly somecontain some question with more thanone meaning, while others contain aconclusion bearing a number of senses:e.g. in the proof that ‘speaking of thesilent’ is possible, the conclusion hasa double meaning, while in the proofthat ‘he who knows does not understandwhat he knows’ one of the questionscontains an amphiboly. Also the double-edged saying is true in one context but

not in another: it means something thatis and something that is not.

Whenever, then, the many senses lie inthe conclusion no refutation takes



place unless the sophist secures aswell the contradiction of theconclusion he means to prove; e.g. inthe proof that ‘seeing of the blind’ is

possible: for without the contradictionthere was no refutation. Whenever, onthe other hand, the many senses lie inthe questions, there is no necessity to

begin by denying the double-edged premiss: for this was not the goal of

the argument but only its support. At

the start, then, one should reply withregard to an ambiguity, whether of aterm or of a phrase, in this manner,that ‘in one sense it is so, and inanother not so’, as e.g. that ‘speakingof the silent’ is in one sense possible

but in another not possible: also thatin one sense ‘one should do what mustneeds be done’, but not in another: for‘what must needs be’ bears a number ofsenses. If, however, the ambiguityescapes one, one should correct it atthe end by making an addition to thequestion: ‘Is speaking of the silent

possible?’ ‘No, but to speak of while

he is silent is possible.’ Also, incases which contain the ambiguity intheir premisses, one should reply inlike manner: ‘Do people-then notunderstand what they know? “Yes, but



not those who know it in the mannerdescribed’: for it is not the samething to say that ‘those who knowcannot understand what they know’, andto say that ‘those who know somethingin this particular manner cannot doso’. In general, too, even though hedraws his conclusion in a quiteunambiguous manner, one should contendthat what he has negated is not thefact which one has asserted but only

its name; and that therefore there isno refutation.

20

It is evident also how one should solvethose refutations that depend upon thedivision and combination of words: forif the expression means somethingdifferent when divided and whencombined, as soon as one’s opponentdraws his conclusion one should takethe expression in the contrary way. Allsuch expressions as the followingdepend upon the combination or division

of the words: ‘Was X being beaten withthat with which you saw him being

beaten?’ and ‘Did you see him being beaten with that with which he was being beaten?’ This fallacy has also in



it an element of amphiboly in thequestions, but it really depends uponcombination. For the meaning thatdepends upon the division of the wordsis not really a double meaning (for theexpression when divided is not thesame), unless also the word that is

pronounced, according to its breathing,as eros and eros is a case of double

meaning. (In writing, indeed, a word isthe same whenever it is written of the

same letters and in the same manner—andeven there people nowadays put marks atthe side to show the pronunciation—butthe spoken words are not the same.)

Accordingly an expression that dependsupon division is not an ambiguous one.It is evident also that not allrefutations depend upon ambiguity assome people say they do.

The answerer, then, must divide theexpression: for ‘I-saw-a-man-being-

beaten with my eyes’ is not the same asto say ‘I saw a man being-beaten-with-

my-eyes’. Also there is the argument of

Euthydemus proving ‘Then you know nowin Sicily that there are triremes inPiraeus’: and again, ‘Can a good manwho is a cobbler be bad?’ ‘No.’ ‘But agood man may be a bad cobbler:



therefore a good cobbler will be bad.’ Again, ‘Things the knowledge of which

is good, are good things to learn,aren’t they?’ ‘Yes.’ ‘The knowledge,however, of evil is good: thereforeevil is a good thing to know.’ ‘Yes.But, you see, evil is both evil and athing-to-learn, so that evil is anevil-thing-to-learn, although theknowledge of evils is good.’ Again, ‘Isit true to say in the present moment

that you are born?’ ‘Yes.’ ‘Then youare born in the present moment.’ ‘No;the expression as divided has adifferent meaning: for it is true tosay-in-the-present-moment that “you are

born”, but not “You are born-in-the- present-moment”.’ Again, ‘Could you do

what you can, and as you can?’ ‘Yes.’‘But when not harping, you have the

power to harp: and therefore you couldharp when not harping.’ ‘No: he has notthe power to harp-while-not-harping;

merely, when he is not doing it, he hasthe power to do it.’ Some people solvethis last refutation in another way as

well. For, they say, if he has grantedthat he can do anything in the way hecan, still it does not follow that hecan harp when not harping: for it hasnot been granted that he will do



anything in every way in which he can;and it is not the same thing’ to do athing in the way he can’ and ‘to do itin every way in which he can’. Butevidently they do not solve it

properly: for of arguments that dependupon the same point the solution is thesame, whereas this will not fit allcases of the kind nor yet all ways of

putting the questions: it is validagainst the questioner, but not against

his argument.

21

Accentuation gives rise to nofallacious arguments, either as writtenor as spoken, except perhaps some fewthat might be made up; e.g. thefollowing argument. ‘Is ou katalueis ahouse?’ ‘Yes.’ ‘Is then ou katalueisthe negation of katalueis?’ ‘Yes.’ ‘Butyou said that ou katalueis is a house:therefore the house is a negation.’ Howone should solve this, is clear: forthe word does not mean the same when

spoken with an acuter and when spokenwith a graver accent.

22



It is clear also how one must meetthose fallacies that depend on theidentical expressions of things thatare not identical, seeing that we arein possession of the kinds of

predications. For the one man, say, hasgranted, when asked, that a termdenoting a substance does not belong asan attribute, while the other has shownthat some attribute belongs which is inthe Category of Relation or of

Quantity, but is usually thought todenote a substance because of itsexpression; e.g. in the followingargument: ‘Is it possible to be doingand to have done the same thing at thesame time?’ ‘No.’ ‘But, you see, it issurely possible to be seeing and tohave seen the same thing at the sametime, and in the same aspect.’ Again,‘Is any mode of passivity a mode ofactivity?’ ‘No.’ ‘Then “he is cut”, “heis burnt”, “he is struck by somesensible object” are alike inexpression and all denote some form of

passivity, while again “to say”, “to

run”, “to see” are like one like oneanother in expression: but, you see,“to see” is surely a form of beingstruck 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 possibleto do and to have done the same thingin the same time, were to say that itis possible to see and to have seen it,still he has not yet been refuted,suppose him to say that ‘to see’ is nota form of ‘doing’ (activity) but of‘passivity’: for this question isrequired as well, though he is supposed

by the listener to have already grantedit, when he granted that ‘to cut’ is aform of present, and ‘to have cut’ aform of past, activity, and so on withthe other things that have a likeexpression. For the listener adds therest by himself, thinking the meaningto be alike: whereas really the meaningis not alike, though it appears to beso because of the expression. The samething happens here as happens in casesof ambiguity: for in dealing withambiguous expressions the tyro inargument supposes the sophist to havenegated the fact which he (the tyro)

affirmed, and not merely the name:whereas there still wants the questionwhether in using the ambiguous term hehad a single meaning in view: for if he



grants that that was so, the refutationwill be effected.

Like the above are also the followingarguments. It is asked if a man haslost what he once had and afterwardshas not: for a man will no longer haveten dice even though he has only lostone die. No: rather it is that he haslost what he had before and has notnow; but there is no necessity for him

to have lost as much or as many thingsas he has not now. So then, he asks thequestions as to what he has, and drawsthe conclusion as to the whole numberthat he has: for ten is a number. Ifthen he had asked to begin with,whether a man no longer having thenumber of things he once had has lostthe whole number, no one would havegranted it, but would have said ‘Eitherthe whole number or one of them’. Alsothere is the argument that ‘a man maygive what he has not got’: for he hasnot got only one die. No: rather it isthat he has given not what he had not

got, but in a manner in which he hadnot got it, viz. just the one. For theword ‘only’ does not signify a

particular substance or quality ornumber, but a manner relation, e.g.



that it is not coupled with any other.It is therefore just as if he had asked‘Could a man give what he has not got?’and, on being given the answer ‘No’,were to ask if a man could give a thingquickly when he had not got it quickly,and, on this being granted, were toconclude that ‘a man could give what hehad not got’. It is quite evident thathe has not proved his point: for to‘give quickly’ is not to give a thing,

but to give in a certain manner; and a man could certainly give a thing in a manner in which he has not got it, e.g.

he might have got it with pleasure andgive it with pain.

Like these are also all arguments ofthe following kind: ‘Could a man strikea blow with a hand which he has notgot, or see with an eye which he hasnot got?’ For he has not got only oneeye. Some people solve this case, wherea man has more than one eye, or morethan one of anything else, by sayingalso that he has only one. Others also

solve it as they solve the refutationof the view that ‘what a man has, hehas received’: for A gave only onevote; and certainly B, they say, hasonly one vote from A. Others, again,



proceed by demolishing straight awaythe proposition asked, and admittingthat it is quite possible to have whatone has not received; e.g. to havereceived sweet wine, but then, owing toits going bad in the course of receipt,to have it sour. But, as was said alsoabove,’ all these persons direct theirsolutions against the man, not againsthis argument. For if this were agenuine solution, then, suppose any one

to grant the opposite, he could find nosolution, just as happens in othercases; e.g. suppose the true solutionto be ‘So-and-so is partly true and

partly not’, then, if the answerergrants the expression without anyqualification, the sophist’s conclusionfollows. If, on the other hand, theconclusion does not follow, then thatcould not be the true solution: andwhat we say in regard to the foregoingexamples is that, even if all thesophist’s premisses be granted, stillno proof is effected.

Moreover, the following too belong tothis group of arguments. ‘If something

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 itwas written: therefore the statementthat was written is at the same timefalse and true.’ But this isfallacious, for the falsity or truth ofa statement or opinion indicates not asubstance but a quality: for the sameaccount applies to the case of anopinion as well. Again, ‘Is what alearner learns what he learns?’ ‘Yes.’‘But suppose some one learns “slow”

quick’. Then his (the sophist’s) wordsdenote not what the learner learns buthow he learns it. Also, ‘Does a mantread upon what he walks through?‘Yes.’ ‘But X walks through a wholeday.’ No, rather the words denote notwhat he walks through, but when hewalks; just as when any one uses thewords ‘to drink the cup’ he denotes notwhat he drinks, but the vessel out ofwhich he drinks. Also, ‘Is it either bylearning or by discovery that a manknows what he knows?’ ‘Yes.’ ‘Butsuppose that of a pair of things he hasdiscovered one and learned the other,

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 proofthat there is a ‘third man’ distinctfrom Man and from individual men. Butthat is a fallacy, for ‘Man’, andindeed every general predicate, denotesnot an individual substance, but a

particular quality, or the beingrelated to something in a particular

manner, or something of that sort.Likewise also in the case of ‘Coriscus’and ‘Coriscus the musician’ there is

the problem, Are they the same ordifferent?’ For the one denotes anindividual substance and the other aquality, so that it cannot be isolated;though it is not the isolation whichcreates the ‘third man’, but theadmission that it is an individualsubstance. For ‘Man’ cannot be anindividual substance, as Callias is.

Nor is the case improved one whit evenif one were to call the clement he hasisolated not an individual substance

but a quality: for there will still bethe one beside the many, just as ‘Man’was. It is evident then that one must

not grant that what is a common predicate applying to a class

universally is an individual substance, but must say that denotes either a



quality, or a relation, or a quantity,or something of that kind.

23

It is a general rule in dealing witharguments that depend on language thatthe solution always follows theopposite of the point on which theargument turns: e.g. if the argumentdepends upon combination, then the

solution consists in division; if upondivision, then in combination. Again,if it depends on an acute accent, thesolution is a grave accent; if on agrave accent, it is an acute. If itdepends on ambiguity, one can solve it

by using the opposite term; e.g. if youfind yourself calling somethinginanimate, despite your previous denialthat it was so, show in what sense itis alive: if, on the other hand, onehas declared it to be inanimate and thesophist has proved it to be animate,say how it is inanimate. Likewise alsoin a case of amphiboly. If the argument

depends on likeness of expression, theopposite will be the solution. ‘Could a

man give what he has not got? ‘No, notwhat he has not got; but he could giveit in a way in which he has not got it,



e.g. one die by itself.’ Does a manknow either by learning or by discoveryeach thing that he knows, singly? butnot the things that he knows,collectively.’ Also a man treads,

perhaps, on any thing he walks through, but not on the time he walks through.

Likewise also in the case of the otherexamples.

24

In dealing with arguments that dependon Accident, one and the same solution

meets all cases. For since it isindeterminate when an attribute should

be ascribed to a thing, in cases whereit belongs to the accident of thething, and since in some cases it isgenerally agreed and people admit thatit belongs, while in others they denythat it need belong, we shouldtherefore, as soon as the conclusionhas been drawn, say in answer to themall alike, that there is no need forsuch an attribute to belong. One must,

however, be prepared to adduce anexample of the kind of attribute meant.

All arguments such as the followingdepend upon Accident. ‘Do you know whatI am going to ask 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?’ ‘Isthe product of a small number with asmall number a small number?’ For it isevident in all these cases that thereis no necessity for the attribute whichis true of the thing’s accident to betrue of the thing as well. For only tothings that are indistinguishable andone in essence is it generally agreed

that all the same attributes belong;whereas in the case of a good thing, to

be good is not the same as to be goingto be the subject of a question; nor inthe case of a man approaching, orwearing a mask, is ‘to be approaching’the same thing as ‘to be Coriscus’, sothat suppose I know Coriscus, but donot know the man who is approaching, itstill isn’t the case that I both knowand do not know the same man; nor,again, if this is mine and is also awork of art, is it therefore my work ofart, but my property or thing orsomething else. (The solution is after

the same manner in the other cases aswell.)

Some solve these refutations bydemolishing the original proposition



asked: for they say that it is possibleto know and not to know the same thing,only not in the same respect:accordingly, when they don’t know the

man who is coming towards them, but doknow Corsicus, they assert that they doknow and don’t know the same object,

but not in the same respect. Yet, as wehave already remarked, the correctionof arguments that depend upon the same

point ought to be the same, whereas

this one will not stand if one adoptsthe same principle in regard not toknowing something, but to being, or to

being is a in a certain state, e.g.suppose that X is father, and is alsoyours: for if in some cases this istrue and it is possible to know and notto know the same thing, yet with thatcase the solution stated has nothing todo. Certainly there is nothing to

prevent the same argument from having anumber of flaws; but it is not theexposition of any and every fault thatconstitutes a solution: for it is

possible for a man to show that a false

conclusion has been proved, but not toshow on what it depends, e.g. in thecase of Zeno’s argument to prove that

motion is impossible. So that even ifany one were to try to establish that



this doctrine is an impossible one, hestill is mistaken, and even if he

proved his case ten thousand timesover, still this is no solution ofZeno’s argument: for the solution wasall along an exposition of falsereasoning, showing on what its falsitydepends. If then he has not proved hiscase, or is trying to establish even atrue proposition, or a false one, in afalse manner, to point this out is a

true solution. Possibly, indeed, the present suggestion may very well apply

in some cases: but in these cases, atany rate, not even this would begenerally agreed: for he knows boththat Coriscus is Coriscus and that theapproaching figure is approaching. Toknow and not to know the same thing isgenerally thought to be possible, whene.g. one knows that X is white, butdoes not realize that he is musical:for in that way he does know and notknow the same thing, though not in thesame respect. But as to the approachingfigure and Coriscus he knows both that

it is approaching and that he isCoriscus.

A like mistake to that of those whom wehave mentioned is that of those who



solve the proof that every number is asmall number: for if, when theconclusion is not proved, they passthis over and say that a conclusion has

been proved and is true, on the groundthat every number is both great andsmall, they make a mistake.

Some people also use the principle ofambiguity to solve the aforesaidreasonings, e.g. the proof that ‘X is

your father’, or ‘son’, or ‘slave’. Yetit is evident that if the appearance a

proof depends upon a plurality of meanings, the term, or the expression

in question, ought to bear a number ofliteral senses, whereas no one speaksof A as being ‘B’s child’ in theliteral sense, if B is the child’s

master, but the combination dependsupon Accident. ‘Is A yours?’ ‘Yes.’‘And is A a child?’ ‘Yes.’ ‘Then thechild A is yours,’ because he happensto be both yours and a child; but he isnot ‘your child’.

There is also the proof that ‘something“of evils” is good’; for wisdom is a‘knowledge “of evils”’. But theexpression 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 ofcourse, on the other hand, that it hasa number of meanings-for we also saythat man is ‘of the animals’, thoughnot their property; and also that anyterm related to ‘evils’ in a wayexpressed by a genitive case is on thataccount a so-and-so ‘of evils’, thoughit is not one of the evils-but in thatcase the apparently different meanings

seem to depend on whether the term isused relatively or absolutely. ‘Yet itis conceivably possible to find a realambiguity in the phrase “Something ofevils is good”.’ Perhaps, but not withregard to the phrase in question. Itwould occur more nearly, suppose that‘A servant is good of the wicked’;though perhaps it is not quite foundeven there: for a thing may be ‘good’and be ‘X’s’ without being at the sametime ‘X’s good’. Nor is the saying that‘Man is of the animals’ a phrase with anumber of meanings: for a phrase doesnot become possessed of a number of

meanings merely suppose we express itelliptically: for we express ‘Give methe Iliad’ by quoting half a line ofit, e.g. ‘Give me “Sing, goddess, ofthe wrath...”’



25

Those arguments which depend upon anexpression that is valid of a

particular thing, or in a particularrespect, or place, or manner, orrelation, and not valid absolutely,should be solved by considering theconclusion in relation to itscontradictory, to see if any of these

things can possibly have happened toit. For it is impossible for contrariesand opposites and an affirmative and anegative to belong to the same thingabsolutely; there is, however, nothingto prevent each from belonging in a

particular respect or relation or manner, or to prevent one of them from belonging in a particular respect and

the other absolutely. So that if thisone belongs absolutely and that one ina particular respect, there is as yetno refutation. This is a feature onehas to find in the conclusion byexamining it in comparison with its

contradictory.

All arguments of the following kindhave 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 of being. Is it possible for thesame man at the same time to be akeeper and a breaker of his oath?’ ‘Canthe same man at the same time both obeyand disobey the same man?’ Or isn’t itthe case that being something in

particular and Being are not the same?On the other hand, Not-being, even if

it be something, need not also haveabsolute ‘being’ as well. Nor if a mankeeps his oath in this particularinstance or in this particular respect,is he bound also to be a keeper ofoaths absolutely, but he who swearsthat he will break his oath, and then

breaks it, keeps this particular oathonly; he is not a keeper of his oath:nor is the disobedient man ‘obedient’,though he obeys one particular command.The argument is similar, also, asregards the problem whether the same

man can at the same time say what is both false and true: but it appears to

be a troublesome question because it isnot easy to see in which of the twoconnexions the word ‘absolutely’ is to

be rendered-with ‘true’ or with‘false’. There is, however, nothing to



prevent it from being false absolutely,though true in some particular respector relation, i.e. being true in somethings, though not ‘true’ absolutely.Likewise also in cases of some

particular relation and place and time.For all arguments of the following kinddepend upon this.’ Is health, orwealth, a good thing?’ ‘Yes.’ ‘But tothe fool who does not use it aright itis not a good thing: therefore it is

both good and not good.’ ‘Is health, or political power, a good thing?’ ‘Yes.

“But sometimes it is not particularlygood: therefore the same thing is bothgood and not good to the same man.’ Orrather there is nothing to prevent athing, though good absolutely, beingnot good to a particular man, or beinggood to a particular man, and yet notgood or here. ‘Is that which the

prudent man would not wish, an evil?’‘Yes.’ ‘But to get rid of, he would notwish the good: therefore the good is anevil.’ But that is a mistake; for it isnot the same thing to say ‘The good is

an evil’ and ‘to get rid of the good isan evil’. Likewise also the argument ofthe thief is mistaken. For it is notthe case that if the thief is an evilthing, acquiring things is also evil:



what he wishes, therefore, is not whatis evil but what is good; for toacquire something good is good. Also,disease is an evil thing, but not toget rid of disease. ‘Is the just

preferable to the unjust, and whattakes place justly to what takes placeunjustly? ‘Yes.’ ‘But to to be put todeath unjustly is preferable.’ ‘Is itjust that each should have his own?’‘Yes.’ ‘But whatever decisions a man

comes to on the strength of his personal opinion, even if it be a false

opinion, are valid in law: thereforethe same result is both just andunjust.’ Also, should one decide infavour of him who says what is unjust?’‘The former.’ ‘But you see, it is justfor the injured party to say fully thethings he has suffered; and these arefallacies. For because to suffer athing unjustly is preferable, unjustways are not therefore preferable,though in this particular case theunjust may very well be better than thejust. Also, to have one’s own is just,

while to have what is another’s is notjust: all the same, the decision inquestion may very well be a justdecision, whatever it be that theopinion of the man who gave the



decision supports: for because it isjust in this particular case or in this

particular manner, it is not also justabsolutely. Likewise also, thoughthings are unjust, there is nothing to

prevent the speaking of them beingjust: for because to speak of things isjust, there is no necessity that thethings should be just, any more than

because to speak of things be of use,the things need be of use. Likewise

also in the case of what is just. Sothat it is not the case that becausethe things spoken of are unjust, thevictory goes to him who speaks unjustthings: for he speaks of things thatare just to speak of, thoughabsolutely, i.e. to suffer, they areunjust.

26

Refutations that depend on thedefinition of a refutation must,according to the plan sketched above,

be met by comparing together the

conclusion with its contradictory, andseeing that it shall involve the sameattribute in the same respect andrelation and manner and time. If thisadditional question be put at the



start, you should not admit that it isimpossible for the same thing to be

both double and not double, but grantthat it is possible, only not in such away as was agreed to constitute arefutation of your case. All thefollowing arguments depend upon a pointof that kind. ‘Does a man who knows Ato be A, know the thing called A?’ andin the same way, ‘is one who isignorant that A is A ignorant of the

thing called A?’ ‘Yes.’ ‘But one whoknows that Coriscus is Coriscus might

be ignorant of the fact that he is musical, so that he both knows and is

ignorant of the same thing.’ Is a thingfour cubits long greater than a thingthree cubits long?’ ‘Yes.’ ‘But a thing

might grow from three to four cubits inlength; ‘now what is ‘greater’ isgreater than a ‘less’: accordingly thething in question will be both greaterand less than itself in the samerespect.

27

As to refutations that depend on begging and assuming the original point

to be proved, suppose the nature of thequestion to be obvious, one should not



grant it, even though it be a viewgenerally held, but should tell him thetruth. Suppose, however, that itescapes one, then, thanks to the

badness of arguments of that kind, oneshould make one’s error recoil upon thequestioner, and say that he has broughtno argument: for a refutation must be

proved independently of the original point. Secondly, one should say that

the point was granted under the

impression that he intended not to useit as a premiss, but to reason againstit, in the opposite way from thatadopted in refutations on side issues.

28

Also, those refutations that bring oneto their conclusion through theconsequent you should show up in thecourse of the argument itself. The modein which consequences follow istwofold. For the argument either isthat as the universal follows on its

particular-as (e.g.) ‘animal’ follows

from ‘man’-so does the particular onits universal: for the claim is madethat if A is always found with B, thenB also is always found with A. Or elseit proceeds by way of the opposites of



the terms involved: for if A follows B,it is claimed that A’s opposite willfollow B’s opposite. On this latterclaim the argument of Melissus alsodepends: for he claims that becausethat which has come to be has a

beginning, that which has not come to be has none, so that if the heaven has

not come to be, it is also eternal. Butthat is not so; for the sequence isvice versa.

29

In the case of any refutations whosereasoning depends on some addition,look and see if upon its subtractionthe absurdity follows none the less:and then if so, the answerer should

point this out, and say that he grantedthe addition not because he reallythought it, but for the sake of theargument, whereas the questioner hasnot used it for the purpose of hisargument at all.

30

To meet those refutations which makeseveral questions into one, one shoulddraw a distinction between them



straight away at the start. For aquestion must be single to which thereis a single answer, so that one mustnot affirm or deny several things ofone thing, nor one thing of many, butone of one. But just as in the case ofambiguous terms, an attribute belongsto a term sometimes in both its senses,and sometimes in neither, so that asimple answer does one, as it happens,no harm despite the fact that the

question is not simple, so it is inthese cases of double questions too.

Whenever, then, the several attributes belong to the one subject, or the one

to the many, the man who gives a simpleanswer encounters no obstacle eventhough he has committed this mistake:

but whenever an attribute belongs toone subject but not to the other, orthere is a question of a number ofattributes belonging to a number ofsubjects and in one sense both belongto both, while in another sense, again,they do not, then there is trouble, sothat one must beware of this. Thus

(e.g.) in the following arguments:Supposing to be good and B evil, youwill, if you give a single answer about

both, be compelled to say that it istrue to call these good, and that it is



true to call them evil and likewise tocall them neither good nor evil (foreach of them has not each character),so that the same thing will be bothgood and evil and neither good norevil. Also, since everything is thesame as itself and different fromanything else, inasmuch as the man whoanswers double questions simply can be

made to say that several things are‘the same’ not as other things but ‘as

themselves’, and also that they aredifferent from themselves, it followsthat the same things must be both thesame as and different from themselves.

Moreover, if what is good becomes evilwhile what is evil is good, then they

must both become two. So of two unequalthings each being equal to itself, itwill follow that they are both equaland 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

affirmation and denial of the samething does not occur, except verbally:and this is not what we meant by arefutation. But it is clear that ifthere be not put a single question on a



number of points, but the answerer hasaffirmed or denied one attribute onlyof one subject only, the absurdity willnot come to pass.

31

With regard to those who draw one into

repeating the same thing a number oftimes, it is clear that one must notgrant that predications of relativeterms have any meaning in abstraction

by themselves, e.g. that ‘double’ is asignificant term apart from the whole

phrase ‘double of half’ merely on theground that it figures in it. For tenfigures in ‘ten minus one’ and in ‘notdo’, and generally the affirmation inthe negation; but for all that, supposeany one were to say, ‘This is notwhite’, he does not say that it iswhite. The bare word ‘double’, one may

perhaps say, has not even any meaning

at all, any more than has ‘the’ in ‘thehalf’: and even if it has a meaning,yet it has not the same meaning as inthe combination. Nor is ‘knowledge’ thesame thing in a specific branch of it



(suppose it, e.g. to be ‘medicalknowledge’) as it is in general: for ingeneral it was the ‘knowledge of theknowable’. In the case of terms thatare predicated of the terms throughwhich they are defined, you should saythe same thing, that the term definedis not the same in abstraction as it isin the whole phrase. For ‘concave’ hasa general meaning which is the same inthe case of a snub nose, and of a bandy

leg, but when added to eithersubstantive nothing prevents it fromdifferentiating its meaning; in fact it

bears one sense as applied to the nose,and another as applied to the leg: forin the former connexion it means ‘snub’and in the latter ‘bandyshaped’; i.e.it makes no difference whether you say‘a snub nose’ or ‘a concave nose’.

Moreover, the expression must not begranted in the nominative case: for itis a falsehood. For snubness is not aconcave nose but something (e.g. anaffection) belonging to a nose: hence,there is no absurdity in supposing that

the snub nose is a nose possessing theconcavity that belongs to a nose.

32



With regard to solecisms, we have previously said what it is that appears

to bring them about; the method oftheir solution will be clear in thecourse of the arguments themselves.Solecism is the result aimed at in allarguments of the following kind: ‘Is athing truly that which you truly callit?’ ‘Yes’. ‘But, speaking of a stone,you call him real: therefore of a stoneit follows that “him is real”.’ No:

rather, talking of a stone means notsaying which’ but ‘whom’, and not‘that’ but ‘him’. If, then, any onewere to ask, ‘Is a stone him whom youtruly call him?’ he would be generallythought not to be speaking good Greek,any more than if he were to ask, ‘Is hewhat you call her?’ Speak in this wayof a ‘stick’ or any neuter word, andthe difference does not break out. Forthis reason, also, no solecism isincurred, suppose any one asks, ‘Is athing what you say it to be?’ ‘Yes’.‘But, speaking of a stick, you call itreal: therefore, of a stick it follows

that it is real.’ ‘Stone’, however, and‘he’ have masculine designations. Nowsuppose some one were to ask, ‘Can “he”

be a she” (a female)?’, and then again,‘Well, but is not he Coriscus?’ and



then were to say, ‘Then he is a “she”,’he has not proved the solecism, even ifthe name ‘Coriscus’ does signify a‘she’, if, on the other hand, theanswerer does not grant this: this

point must be put as an additionalquestion: while if neither is it thefact nor does he grant it, then thesophist has not proved his case eitherin fact or as against the person he has

been questioning. In like manner, then,

in the above instance as well it must be definitely put that ‘he’ means the

stone. If, however, this neither is sonor is granted, the conclusion must not

be stated: though it followsapparently, because the case (theaccusative), that is really unlike,appears to be like the nominative. ‘Isit true to say that this object is whatyou call it by name?’ ‘Yes’. ‘But youcall it by the name of a shield: thisobject therefore is “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 ‘this object’s’. Nor againif ‘He is what you call him by name’,while ‘the name you call him by isCleon’s’, is he therefore ‘Cleon’s’:for he is not ‘Cleon’s’, for what was



said was that ‘He, not his, is what Icall him by name’. For the question, if

put in the latter way, would not even be Greek. ‘Do you know this?’ ‘Yes.’

‘But this is he: therefore you knowhe’. No: rather ‘this’ has not the same

meaning in ‘Do you know this?’ as in‘This is a stone’; in the first itstands for an accusative, in the secondfor a nominative case. ‘When you haveunderstanding of anything, do you

understand it?’ ‘Yes.’ ‘But you haveunderstanding of a stone: therefore youunderstand of a stone.’ No: the one

phrase is in the genitive, ‘of astone’, while the other is in theaccusative, ‘a stone’: and what wasgranted was that ‘you understand that,not of that, of which you haveunderstanding’, so that you understandnot ‘of a stone’, but ‘the stone’.

Thus that arguments of this kind do not prove solecism but merely appear to do

so, and both why they so appear and howyou should meet them, is clear from

what has been said.

33





symptom of this that they often fightabout their terms, e.g. whether the

meaning of ‘Being’ and ‘One’ is thesame in all their applications ordifferent; for some think that ‘Being’and ‘One’ mean the same; while otherssolve the argument of Zeno andParmenides by asserting that ‘One’ and‘Being’ are used in a number ofsenses), likewise also as regardsfallacies of Accident and each of the

other types, some of the arguments will be easier to see while others are more

difficult; also to grasp to which classa fallacy belongs, and whether it is arefutation or not a refutation, is notequally easy in all cases.

An incisive argument is one which produces the greatest perplexity: for

this is the one with the sharpest fang. Now perplexity is twofold, one which

occurs in reasoned arguments,respecting which of the propositionsasked one is to demolish, and the otherin contentious arguments, respecting

the manner in which one is to assent towhat is propounded. Therefore it is insyllogistic arguments that the moreincisive ones produce the keenestheart-searching. Now a syllogistic



argument is most incisive if from premisses that are as generally

accepted as possible it demolishes aconclusion that is accepted asgenerally as possible. For the oneargument, if the contradictory ischanged about, makes all the resultingsyllogisms alike in character: foralways from premisses that aregenerally accepted it will prove aconclusion, negative or positive as the

case may be, that is just as generallyaccepted; and therefore one is bound tofeel perplexed. An argument, then, ofthis kind is the most incisive, viz.the one that puts its conclusion on allfours with the propositions asked; andsecond comes the one that argues from

premisses, all of which are equallyconvincing: for this will produce anequal perplexity as to what kind of

premiss, of those asked, one shoulddemolish. Herein is a difficulty: forone must demolish something, but whatone must demolish is uncertain. Ofcontentious arguments, on the other

hand, the most incisive is the onewhich, in the first place, ischaracterized by an initial uncertaintywhether it has been properly reasonedor not; and also whether the solution



depends on a false premiss or on thedrawing of a distinction; while, of therest, the second place is held by thatwhose solution clearly depends upon adistinction or a demolition, and yet itdoes not reveal clearly which it is ofthe premisses asked, whose demolition,or the drawing of a distinction withinit, will bring the solution about, buteven leaves it vague whether it is onthe conclusion or on one of the

premisses that the deception depends.

Now sometimes an argument which has not been properly reasoned is silly,

supposing the assumptions required to be extremely contrary to the general

view or false; but sometimes it oughtnot to be held in contempt. Forwhenever some question is left out, ofthe kind that concerns both the subjectand the nerve of the argument, thereasoning that has both failed tosecure this as well, and also failed toreason properly, is silly; but whenwhat is omitted is some extraneous

question, then it is by no means to belightly despised, but the argument isquite respectable, though thequestioner has not put his questionswell.



Just as it is possible to bring asolution sometimes against theargument, at others against thequestioner and his mode of questioning,and at others against neither of these,likewise also it is possible to marshalone’s questions and reasoning bothagainst the thesis, and against theanswerer and against the time, wheneverthe solution requires a longer time to

examine than the period available.

34

As to the number, then, and kind ofsources whence fallacies arise indiscussion, and how we are to show thatour opponent is committing a fallacyand make him utter paradoxes; moreover,

by the use of what materials solescismis brought about, and how to questionand what is the way to arrange thequestions; moreover, as to the questionwhat use is served by all arguments ofthis kind, and concerning the

answerer’s part, both as a whole ingeneral, and in particular how to solvearguments and solecisms-on all thesethings let the foregoing discussionsuffice. It remains to recall our



original proposal and to bring ourdiscussion to a close with a few wordsupon it.

Our programme was, then, to discoversome faculty of reasoning about anytheme put before us from the mostgenerally accepted premisses that thereare. For that is the essential task ofthe art of discussion (dialectic) andof examination (peirastic). Inasmuch,

however, as it is annexed to it, onaccount of the near presence of the artof sophistry (sophistic), not only to

be able to conduct an examinationdialectically but also with a show ofknowledge, we therefore proposed forour treatise not only the aforesaid aimof being able to exact an account ofany view, but also the aim of ensuringthat in standing up to an argument weshall defend our thesis in the same

manner by means of views as generallyheld as possible. The reason of this wehave explained; for this, too, was whySocrates used to ask questions and not

to answer them; for he used to confessthat he did not know. We have madeclear, in the course of what precedes,the number both of the points withreference to which, and of the



materials from which, this will beaccomplished, and also from whatsources we can become well suppliedwith these: we have shown, moreover,how to question or arrange thequestioning as a whole, and the

problems concerning the answers andsolutions to be used against thereasonings of the questioner. We havealso cleared up the problems concerningall other matters that belong to the

same inquiry into arguments. Inaddition to this we have been throughthe subject of Fallacies, as we havealready stated above.

That our programme, then, has beenadequately completed is clear. But we

must not omit to notice what hashappened in regard to this inquiry. Forin the case of all discoveries theresults of previous labours that have

been handed down from others have beenadvanced bit by bit by those who havetaken them on, whereas the original

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