« PreviousContinue »
$ 60. COLLECTIVE AND DISTRIBUTIVE INTERPRETATION.—There is, however, another difference of interpretation it is important to consider; and especially with reference to mathematical reasoning, which is to be considered presently. Common terms, or terms denoting classes of more than one, may be used either collectively or distributively,- i. e., the class denoted by the term may be regarded either as a whole made up of individuals,' or as a number of individuals constituting a class, or signified by the name. Thus, e. g., the term
man may be used to denote either the class
man,” as when we say, “ Man is mortal”; or the individuals composing the class, as when we say, “ A man is a mortal,” or “ Men are mortals.”
Whether a term is used collectively or distributively may be indicated, as in the above examples, by the expression, or may be simply understood; or the expression may be such as not to indicate either expressly or implicitly whether the term is used in the one way or the other. With regard to the subject of the proposition it is logically immaterial in which way the term is used. Thus, in the proposi. tion, “Y is X,” the subject is used collectively; and in the proposition, “ All Y's are X's,” or
When a concrete term is construed collectively, it becomes abstract, and is to be regarded as denoting, not a number of real individuals, but one quasi individual only.
“Every Y is an X,” or “A Y is an X," distri. butively; but the forms are logically equivalent.
So with regard to the predicate, where the terms are of equal extension, it is immaterial whether it be construed collectively or distributively, provided, if the predicate be construed collectively, that the subject also be thus construed. For to construe a term collectively is to regard the class denoted by it as an individual, and a term thus construed is therefore to be regarded as a singular term. But a singular term cannot be predicated of any but a singular term, with which it must exactly conform in signification; or, in other words, a singular term can be predicated of another singular term only in the equational proposition. Thus, 1.g., in the proposition, “ Y is X," it is immaterial whether we regard Y as denoting the class Y, or as signifying the significates composing the class. But the class X cannot be construed collectively unless we also construe the class Y in the same way, and unless also the two classes are co-extensive, or, in other words, unless the proposition can be put in the form, Y = X.
OF THE PREDICABLES
$ 61. DEFINITION AND DIVISION OF THE PREDICABLES. -A predicable may be defined as a term that may be made the predicate of an affirmative proposition. As explained above, such propositions may be either equational or non-equational. In the former case the predi. cate is of the same extension as the subject; in the latter, of greater extension. All predi. cables, therefore, may be divided into two classes,-namely, those that are equivalent to the subject, and those that are not equivalent. An equivalent predicable may be either definition or property; for each of these is precisely co-extensive with the subject ($ 49). Non. equivalent predicables must be either genera or accidents; either of which may always be predicated of the subject (16.). This is the division of predicables used by Aristotle.
862. TWOFOLD DIVISION OF PREDICABLES. -But the distinction between “ definition" and
property" seems, with relation to the subject of predicables, to be unimportant; for “ property" differs from “ de finition” only in the use made of the former (16.). And so with reference to the distinction between genus and accident (Ib.).
Hence it has been proposed " to abandon, as at least unnecessary for logical purposes" (or rather, we should say, for purposes of predication), “the distinctions between property and definition, genus and accident, and to form, as Aristotle has also done, two classes of predicables; one of predicables taken distributively and capable of becoming subjects in their respective judgments without limitation; the other of such as have a different extension. In the former the predicable has the same objects [i. e., significates] as the subjects, but different marks, or a different way of representing the marks. In the latter there is a difference, both in the marks and the objects (Thompson's Laws of Thought, $ 69.)'
$ 63. ONE KIND OF PREDICABLES ONLY.But even the twofold division of predicables, into equivalent and non-equivalent, is, from the traditional standpoint, of minor importance; for, as we have seen, the old Logic ordinarily takes no account of equational propositions, but these, like others, are regarded as importing simply the inclusion of the subject in the predicate; and in this mode of interpreting the proposition, we have, in effect, a complete doctrine of the predicables.
"The division of predicables most commonly used is that of Porphyry (Aristotle's Logical Treatises, Bohn's edition, Introduction of Porphyry; also Jevons's Lessons in Logic, p. 98). According to this division, “Specific Difference” is substituted for the" Definition" of Aristotle's division, and there is added as a fifth predicable, “ Species," as being predicable of individuals. But, as observed by Mansel (Aldrich's Logic, Preface), “whether this classification is an improvement, or is consist. ent with the Aristotelian doctrine, admits of considerable question." The view taken in the text is in every respect preferable (Thompson's Laws of Thought, pp. 136 et seq.).
OF THE RELATIONS BETWEEN TERMS
$ 64. OF THE RELATIONS OF TERMS GENERALLY.—The end of Logic is to determine the relations, and, as involved in this, the definitions, of terms, or (what is the same thing), of the notions expressed in terms (8 16). Of these notions, the most conspicuous are those existing between what are called relative words -as, e. g., father and son, wife and husband, higher and lower, etc., and also the active and passive forms of the verb, and all inflections of verb or noun, or, in a word, all paronyms, etc. But the term, relative, though applicable, is not peculiar to this class of words, and is, therefore, not altogether appropriate. Relations, more or less apparent, exist between all terms, and in the development of these consists the raison d'étre of Logic. Hence, properly speaking, no term can be said to be absolute, as opposed to relative. Forto consider only one of the most general of relations — any thing, or class of things (real or fictitious), must always be assignable to one of two classes, namely the class denoted by a given term, or to the class denoted by its negative'; and, in addition to this universal
'' This, of course, is true only on the assumption that we reject Particular Propositions, as proposed (8 52, note).