The two Modes compared.—The precise relation of the two modes will best appear by the comparison of the following syllogisms. The inductive syllogism runs thus: x, y, z, are A; x, y, z, constitute B; therefore, B is A.
The deductive runs thus: B is A; x, y, z, constitute B; therefore, x, y, z, are A.
The latter, it will be seen at a glance, is the precise counterpart of the other, beginning where the former ends, and exactly reversing the several steps in their order.
The Law of each.—The general law or rule which governs the former, is, What belongs (or does not belong) to all the constituent parts, belongs (or does not belong) to the constituted whole. The law of the latter is, What belongs (or not) to the containing whole, belongs (or not) to all the contained parts.
Application of the inductive Method.—Applying the inductive method to a particular case, we reason thus: Magnets x, y, z, etc., including so many as I have observed, attract iron. But it is fair to presume that what I have observed as true of x, y, z, is equally true of e, f, g, and all other magnets; in other words, x, y, z, do represent, and may fairly be taken as constituting the whole class of magnets; consequently, I conclude that all magnets attract iron. Thus stated, the truth which was at first observed and affirmed only of particular instances, becomes a general proposition, and may, in turn, become the premiss of a process of deduction. Thus, from the general proposition, obtained as now explained by the inductive mode, that all horned animals ruminate, I may proceed, by the deductive mode, to infer that this is true of deer or goats, or any particular species or individual whose habits I have not as yet observed.
V. Different Forms of Syllogism.
The Form of Statement not invariable.—As there are different kinds of syllogism, so also there are different forms in which any kind of syllogism may be stated. These forms are not essential, pertaining to the nature of the syllogism itself, but accidental, pertaining merely to the order of announcing the several propositions. It has already been remarked, in speaking of the general structure of the syllogism, that the order of propositions is not essential. Either premiss may precede, either follow. Nay, we may state first the conclusion, and then the reasons, or grounds. This latter method, as Hamilton has shown in his New Analytic of Logical forms, is perfectly valid, though usually neglected by writers on logic. It is not only valid, but the more natural of the two methods. When asked if Socrates is mortal, it is more natural to say, He is mortal, for he is a man, and all men are mortal, than to say, All men are mortal, he is a man, and therefore, he is mortal. In fact, most of our reasoning takes the first of these forms. The two are designated by Hamilton, respectively, as the analytic and synthetic syllogism.
Order of Premises may vary.—As to the order of the premises, which shall precede the other, this, too, is quite unessential and accidental. The earlier method, practised by Greek, Arabian, Jewish and Latin schools, was to state first the minor premiss, precisely the reverse of our modern custom.
Order of Terms not essential.—The order of the terms, in the several propositions, is also accidental rather than essential. There are several possible and allowable arrangements of these terms with reference to the order of precedence and succession, giving rise to what are called figures of the syllogism. These arrangements and figures have usually been reckoned as four; three only are admitted by Hamilton, the fourth being abolished. The first figure occurs when the middle term is the subject of one premiss and the predicate of the other. The second figure gives the middle term the place of predicate in both premises. The third makes it the subject of both.