_Two Modes of procedure._--There are manifestly two entirely distinct modes of procedure in reasoning. We may infer from the whole to the parts, or from the parts to the whole. The former is called deductive, the latter inductive reasoning. The one is precisely the reverse of the other in method of procedure. Each is a perfectly valid method of reasoning, and each is, in itself, a distinct and valid kind of syllogism. Each requires the other. The deductive is wholly dependent on the inductive for its major premiss, which is only the conclusion of a previous induction, while, on the other hand, the induction is valuable chiefly as preparing the way for subsequent deduction. Each has equal claims with the other to be regarded as a distinct and independent form of syllogism. They have not, however, been so treated by logicians, but, on the contrary, the inductive method has been regarded, almost universally, as a mere appendage of the deductive, an imperfect form of one or another of the several figures of the syllogism deductive. Of this we shall have occasion to speak more fully in the historical sketch. _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.