Mental Philosophy: Including the Intellect, Sensibilities, and Will

by Joseph Haven

Assigns Induction its true Place.—Hamilton is the first, so far as I know, to elevate to its true place the inductive method of reasoning, making it coördinate with the deductive, and assigning its true character and value as a form of syllogism.

Recognizes the analytic Syllogism.—He is the first to bring to notice the claims of the analytic syllogism to a distinctive place and recognition in logic; a form of reasoning, which, however natural and necessary, and in use almost universal, had been strangely overlooked by logicians from Aristotle down.

Rejects Modality.—He strenuously and consistently rejects the modality of the proposition and the syllogism, on the ground that logic is not concerned with the character of the matter, whether it be true or false, necessary or contingent, but only with the form of statement, and consequently, all distinctions founded on the truth or falsity, the necessity or contingence of the matter, are utterly irrelevant to the science—a principle admitted by others, but not previously carried out to its true results.

Doctrine of Figure.—He shows that the figure of the syllogism is a matter accidental, rather than essential, that it may be even entirely unfigured; abolishes the fourth figure as superfluous; and sets aside, as quite useless and unnecessary, the old laborious processes of reducing and connecting the several figures to the first.

Rejects hypothetical Syllogism.—He throws out of the syllogism entirely, the so-called hypothetical forms, both conjunctive and disjunctive, as reducible to immediate inference, and not, therefore, to be included under syllogistic reasoning, which is always mediate.

The single Canon.—He reduces the several laws and canons of the figured syllogism to a single comprehensive canon.

Quantification of the Predicate.—But the most important discovery made by Hamilton in this science, is the quantification of the predicate. The predicate is always a given quantity in relation to the subject, and that quantity should be stated. This, logicians have always overlooked, quantifying only the subject, as, All men, Some men, etc., but never the predicate. Fully quantified, the proposition reads, All man is some animal, no animal, etc., i. e., some sort or species of animal. This doubles the number of possible propositions, giving eight in place of four, and gives a corresponding increase in the number of words. These eight propositions are shown to be, not only possible, but admissible and valid. They are thus enumerated and named:

		AFFIRMATIVE.	NEGATIVE.
I.	Toto-total;	All A is all B.	Any A is not any B.
II.	Toto-partial:	All A is some B.	Any A is not some B.
III.	Parti-total:	Some A is some B.	Some A is not some B.
IV.	Parti-partial:	Some A is some B.	Some A is not some B.

Reference.—For a more full and exact account of Hamilton's system, the reader is referred to the article on logic in the volume of Discussions on Philosophy and Literature, by Sir W. Hamilton; also, to "An Essay on the New Analytic of Logical Forms," by Thomas Spencer Baynes, L. L. B. On the history of logic in general, see Dictionnaire des Sciences Philosophiques—Article Logique, by Barthèleme St. Hilaire, Professor of Philosophy to the College of France, member of the Institute, etc., etc.; also, Blakey's History of Logic. The Memoir of St. Hilaire, on the logic of Aristotle, is one of the best works of modern times on the subject of which it treats.