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Quantification of the Predi Cate

predicate, proposition and logic

QUANTIFICATION OF THE PREDI CATE, supplying to the predicate in a logical proposition a word, as or tall, * or proposition etc., to indicate whether the whole of it or only a part agrees with or differs- from the subject. In the proposition tall metals are elements' the subject is quantified by the use of 'all"; but the predicate is not quantified, and in form the proposition does not distinctly assert whether metals constitute the whole list of elements or not But by in serting *some before the predicate, gelements* is quantified — 'all metals are some elements." It was assumed by Aristotle and was maintained by all logicians after him till Ploucquet and Lambert in the 18th century and Sir William Hamilton in the 19th, that the predicate of all affirmative propositions is °undistributed" (not taken in its universal comprehension), while the predicate of a negative proposition is al ways distributed. But after Sir William Hamilton had given notoriety to the doctrine of quantification, this was seen to be an error, through which an infinite number of affirmative propositions which are universal in both terms are excluded from the system of formal logtc.

Among the numerous changes in the theory of formal logic which follows from the adoption of the quantified predicate the most important are the reduction of the conversion of proposi tions from three species to one, reduction of all the general laws of eategoriatl syllogisms to a single canon, and the abrogation of all the special laws of syllogism. Btit the doctrine of the quantification of the predicate has never been generally 'adopted in the exposition of formal logic, on the -ground that there is no proposition that cannot. be dealt with under the Aristotelian forms, 'and that quantification does not really simplify the 'theory. of logic. At present both the old Aristotelian-formed logic and ,the logic of qtantification have been sup planted by the symbolic logic. See Loom, Svaimuc.