Page images


quality at once common and peculiar to the individuals denoted by a term is called a property of the class denoted; a quality common to the class, but not peculiar to it, is called an accident.' The definition of a term is made up by selecting from the accidents of the term one to serve as a mark for the purpose of deterinining the genus, and from the properties one to serve as specific difference. These together constitute the essence of the term; which will therefore vary with the definition, and be determined by it. Thus, e. g., if we define man as a rational animal,"animal" will be the genus; tional" the specific difference; talking," laughing," "cooking,etc., properties; mortal," "carnivorous," " mainmal,etc., acci. dents. But we may, if we choose, define him variously as a talking, laughing, or cooking, mortal, carnivore, or mammal. The essence of

, a term therefore but another name for the meaning of the term. Properties not used for specific difference, and accidents not used for genus, do not enter into the essence of the term.

There is much confusion among logicians in the use of the term accident. The definition in the text is that of the best authorities, including Aristotle ; and the term should be consistently thus used,





$ 50. PROPOSITION DEFINED.-A proposition may be defined as the expression of a rela. tion of signification between two terms; which, of course, implies the expression of the corresponding relation between the notions ex. pressed in the terms.

§ 51. THE GRAMMATICAL PROPOSITION.— But here there is a difference between Logic and Grammar, or, we may say, between the logical and the grammatical proposition. In the latter, any of the innumerable relations existing between terms, or, what is the same thing, between the things denoted by them, whether past, present, or future, may be expressed as existing between the terms; and the relation may be expressed by any copula or connecting word, or the same word may be used to express both copula and predicate, as, 1.g., John struck William ”; “ The sun will rise at six o'clock to-morrow”; It rains”; The Carthaginians did not conquer Rome,” etc. But in Logic the only copula used is the present tense of the verb “ to be," with or without the negative particle; and the only interterminal relation considered is that of species and genus; which may be either affirmed or denied.

$ 52. THE LOGICAL PROPOSITION.- Accordingly the logical proposition is of two forms, the affirmative and the negative. In the former the relation of species and genus between the terms is affirmed,-as, l.g., “ Man is mortal," "Y is X,” etc.; in the latter it is denied,-as, e. g., Man is not perfect," “Y is not X,” etc. The affirmative proposition may be read, either, “ Y is X,” or Every Y is X,” or “ All Y's are X's”; or, to take the concrete example, "Man is mortal,” or

" Every man is mortal,” or “ All men are mortal,”—these expressions being all equivalent, and signifying equally that the subject class - or class denoted by the subject — is a species of the predicate class. The negative proposition may be read either as above or as follows: “No man is perfect,” “No Y is X,” etc. It is a cardinal postulate in Logic that all propositions may, and indeed — for purposes of logical analysis — must be converted into

logical form; as, e. g., the above examples into the following : “ John is the man who struck William "; Six o'clock is the hour at which the sun will rise to-morrow”; “ Rain is falling”; “ The Carthaginians are not [or, grammatically, we should say, were not ''] the conquerors of Rome." ;

$ 53. INTERPRETATION OF THE LOGICAL PROPOSITION.-In all logical propositions the copula is to be interpreted as meaning “ is contained in "or" is a species of," or the contrary, as the case may be. Hence in Logic the only

1 There are commonly recognized by logicians four forms of the proposition, designated respectively by the letters, A, E, I, and O, and called the “Universal Affirmative,” the Universal Negative,” the Particular Affirmative,” and the Particular Negative" (see infra, $ 88). But if in I and o we regard the expression some Y” – instead of “Y"- -as the subject of the proposition, these forms will become the same as A and E. Hence, propositions may, as in the text, be regarded as of two kinds only, namely, affirmative and negative ; the former affirming that the subject is included in the predicate class ; the latter denying that it is so included. This distinction agrees precisely with our definition, and will be sufficient for our present purposes, and, indeed, for all practical purposes.

? The affirmative proposition “ Y is X” is to be construed as asserting that the class Y is wholly included in the class X; the negative, “Y is not X,” that it is wholly excluded. But the class Y may denote a part of a class, as, e.g., “Some A”; in which case the proposition “Y is X,” or “Y is not X,” would be equivalent to the ordinary forms, “Some A is X."

“Some A is not X."


significative relation recognized is the relation of the inclusion or exclusion of the subject class in or from the predicate: and accordingly this may be called appropriately the logical relation. Yet the logical proposition is not less capacious of expression than the grammatical; for, as the latter may always be converted into the former, it follows that all relations may be expressed in the one as in the other. The only difference is that in the grammatical proposition the relations between the notions involved may be expressed either in the copula, or in the terms themselves; while in the logical proposition the only interterminal relation expressed (i. e., affirmed or denied) by the copula is that of species and genus, and all other relations between notions are expressed in the terms,- i. e., in complex terms.'

$ 54. THE CONVERSION OF PROPOSITIONS. -By conversion is meant the transposition of subject and predicatemi. e., making the predicate the subject, and the subject, predicate. But, such conversion, to be legitimate, must be illative, i.e., the force or conclusiveness of the proposition must not be affected. Thus the proposition, “Y is not X" (since the subject and predicate classes are mutually exclusive), may be converted into the proposition, “ X is not

1 This is admirably illustrated by Mr. Boole's system of signs, of which I append an epitome. See Appendix L.

« PreviousContinue »