Quantification of the Predicate, a phrase belonging to Logic, and introduced by Sir W. Hamilton. According to the Aristotelian Logic, propositions are divided, according to their quality, into affirmative and negative, and, according to their Quantity, into universal and particular ('All men are mortal,' 'Some men live eighty years'). If we combine the two divisions we obtain four kinds of propositions. Sir W. Hamilton affirmed that the statement of the Quantity of these various propositions is left incomplete; only the subject of each has its quantity expressed (all men, some men, no men); while there is implied or understood in every case a certain quantity of the predicate. Thus, 'All men are mortal,' is not fully stated; the meaning is, that all men are a part of mortal things, there being (possibly and probably) other mortal things besides men. Let this meaning be expressed, and we have a complete proposition to this effect: 'All men are some (or part of) mortals,' where quantity is assigned, not only to the subject, but also to the predicate. The first result of stating the quantity of the predicate is to give eight kinds of propositions instead of four; the next result is to modify the process called the Conversion of Propositions. Limitation (All A is B, some B is A) is resolved into simple conversion, or mere transposition of premises without further change. 'All A is some B;' 'Some B is all A.'
The multiplication of varieties of propositions is attended with the further consequence of greatly increasing the number of syllogisms, or forms of deductive reasoning (see SYLLOGISM). In the scholastic logic, as usually expounded, there are nineteen such forms, distributed under four figures (four in the first, four in the second, six in the third, five in the fourth). By ringing the changes on eight sorts of propositions, instead of the old number, four, thirty-six valid syllogisms can be formed in the first figure. Whether the increase serves any practical object is another question. Sir W. Hamilton also considered that the new system led to a simplification of the fundamental laws of the syllogism.
Professor De Morgan also invented and carried out into great detail a plan of expressing the quantity of the predicate. It should be noted that in the Contemporary Review of 1873 Professor Jevons, following Mr Herbert Spencer, recognised the fact that the discovery of the quantification of the predicate, regarded by him as the most fruitful discovery in abstract logical science since the time of Aristotle, was fully contained in George Bentham's Outlines of a New System of Logic. This work was published in 1827, and reviewed by Sir W. Hamilton in the Edinburgh Review, long ere he himself published anything on the doctrine of quantification. Boole's system of logic was based on his doctrine of quantification of the predicate. See Jevons's Logic; Bowen's Treatise on Logic (Cambridge, U.S., 1866).