Lesson 9Propositions.We have seen that the first step of Deductive Reasoningis that which we call Concepts. The second step isthat which we call Propositions.In Logic, a Proposition is: A sentence, or part of a sentence,affirming or denying a connection between the terms; limitedto express assertions rather than extended to questions andcommands. Hyslop defines a Proposition as: any affirmationor denial of an agreement between two conceptions.Examples of Propositions are found in the following sentences:The rose is a flower; a horse is an animal; Chicago is a city; allof which are affirmations of agreement between the two termsinvolved; also in: A horse is not a zebra; pinks are not roses;the whale is not a fish; etc., which are denials of agreementbetween the terms.The Parts of a Proposition are: (1) the Subject, or that ofwhich something is affirmed or denied; (2) the Predicate, or thesomething which is affirmed or denied regarding the Subject;and (3) the Copula, or the verb serving as a link between theSubject and the Predicate.In the Proposition: Man is an animal, the term man is theSubject; the term an animal is the Predicate; and the word is, isThe Art of Logical Thinking58the Copula. The Copula is always some form of the verb to be,in the present tense indicative, in an affirmative Proposition;and the same with the negative particle affixed, in a negativeProposition. The Copula is not always directly expressed by theword is or is not, etc., but is instead expressed in some phrasewhich implies them. For instance, we say he runs, whichimplies he is running. In the same way, it may appear at timesas if the Predicate was missing, as in: God is, by which is meantGod is existing. In some cases, the Proposition is inverted, thePredicate appearing first in order, and the Subject last, as in:Blessed are the peacemakers; or Strong is Truth. In such casesjudgment must be used in determining the matter,in accordance with the character and meaning of the terms.An Affirmative Proposition is one in which the Predicate isaffirmed to agree with the Subject. A Negative Proposition isone in which the agreement of the Predicate and Subject isdenied. Examples of both of these classes have been given inthis Lesson.Another classification of Propositions divides them inthree classes, as follows (1) Categorical; (2) Hypothetical; (3)Disjunctive.A Categorical Proposition is one in which the affirmationor denial is made without reservation or qualification, as forinstance: Man is an animal; the rose is a flower, etc. The factasserted may not be true, but the statement is made positivelyas a statement of reality.A Hypothetical Proposition is one in which the affirmationor denial is made to depend upon certain conditions,circumstances or suppositions, as for instance: If the wateris boiling-hot, it will scald; or if the powder be damp, it willnot explode, etc. Jevons says: Hypothetical Propositions maygenerally be recognized by containing the little word if; but itis doubtful whether they really differ much from the ordinarypropositions. We may easily say that boiling water will scald,Propositions59and damp gunpowder will not explode, thus avoiding the useof the word if.A Disjunctive Proposition is one implying or assertingan alternative, and usually containing the conjunction or,sometimes together with either, as for instance: Lightning issheet or forked; Arches are either round or pointed; Anglesare either obtuse, right angled or acute.Another classification of Propositions divides them in twoclasses as follows: (1) Universal; (2) Particular.A Universal Proposition is one in which the whole quantityof the Subject is involved in the assertion or denial of thePredicate. For instance: All men are liars, by which is affirmedthat all of the entire race of men are in the category of liars, notsome men but all the men that are in existence. In the same waythe Proposition: No men are immortal is Universal, for it is auniversal denial.A Particular Proposition is one in which the affirmation ordenial of the Predicate involves only a part or portion of thewhole of the Subject, as for instance: Some men are atheists,or Some women are not vain, in which cases the affirmationor denial does not involve all or the whole of the Subject. Otherexamples are: A few men, etc.; many people, etc.; certainbooks, etc.; most people, etc.Hyslop says: The signs of the Universal Proposition, whenformally expressed, are all, every, each, any, and whole or wordswith equivalent import. The signs of Particular Propositions arealso certain adjectives of quantity, such as some, certain, a few,many, most or such others as denote at least a part of a class.The subject of the Distribution of Terms in Propositions isconsidered very important by Logicians, and as Hyslop says:has much importance in determining the legitimacy, or at leastthe intelligibility, of our reasoning and the assurance that itwill be accepted by others. Some authorities favor the term,Qualification of the Terms of Propositions, but the establishedusage favors the term Distribution.The Art of Logical Thinking60The definition of the Logical term, Distribution, is: Thedistinguishing of a universal whole into its several kinds of species;the employment of a term to its fullest extent; the applicationof a term to its fullest extent, so as to include all significationsor applications. A Term of a Proposition is distributed when itis employed in its fullest sense; that is to say, when it is employedso as to apply to each and every object, person or thing includedunder it. Thus in the proposition, All horses are animals, theterm horses is distributed; and in the proposition, Some horsesare thoroughbreds, the term horses is not distributed. Both ofthese examples relate to the distribution of the subject of theproposition. But the predicate of a proposition also may or maynot be distributed. For instance, in the proposition, All horsesare animals, the predicate, animals, is not distributed, thatis, not used in its fullest sense, for all animals are not horsesthere are some animals which are not horses and, therefore, thepredicate, animals, not being used in its fullest sense is said tobe not distributed. The proposition really means: All horsesare some animals.There is however another point to be remembered in theconsideration of Distribution of Terms of Propositions, whichBrooks expresses as follows: Distribution generally showsitself in the form of the expression, but sometimes it may bedetermined by the thought. Thus if we say, Men are mortal,we mean all men, and the term men is distributed. But if we sayBooks are necessary to a library, we mean, not all books butsome books. The test of distribution is whether the term appliesto each and every. Thus when we say men are mortal, it is trueof each and every man that he is mortal.The Rules of Distribution of the Terms of Proposition are asfollows:1. All universals distribute the subject.2. All particulars do not distribute the subject.3. All negatives distribute the predicate.4. All affirmatives do not distribute the predicate.Propositions61The above rules are based upon logical reasoning. The reasonfor the first two rules is quite obvious, for when the subject isuniversal, it follows that the whole subject is involved; when thesubject is particular it follows that only a part of the subjectis involved. In the case of the third rule, it will be seen that inevery negative proposition the whole of the predicate must bedenied the subject, as for instance, when we say: Some animalsare not horses, the whole class of horses is cut off from thesubject, and is thus distributed. In the case of the fourth rule, wemay readily see that in the affirmative proposition the wholeof the predicate is not denied the subject, as for instance, whenwe say that: Horses are animals, we do not mean that horsesare all the animals, but that they are merely a part or portionof the class animaltherefore, the predicate; animals, is notdistributed.In addition to the forms of Propositions given there isanother class of Propositions known as Definitive or SubstitutivePropositions, in which the Subject and the Predicate are exactlyalike in extent and rank. For instance, in the proposition,A triangle is a polygon of three sides the two terms areinterchangeable; that is, may be substituted for each other.Hence the term substitutive. The term definitive arises fromthe fact that the respective terms of this kind of a propositionnecessarily define each other. All logical definitions are expressedin this last mentioned form of proposition, for in such cases thesubject and the predicate are precisely equal to each other.The Art of Logical Thinking6263