analytical deduction of the second kind in the form, S-P, M-S, :. M-P; because, though both end in a universal conclusion, the limits of experience prevent induction from such inference as:-- Every experienced magnet attracts iron. Every magnet whatever is every experienced magnet. :. Every magnet whatever attracts iron. Still less can induction be reduced to analytical deduction of the first kind in the form--P-M, S-P, :. S-M, of which Newton has left so conspicuous an example in his _Principia_. As the example shows, that analytic process starts from the scientific knowledge of a universal and convertible law (every M is P, and every P is M), e.g. a mechanical law of all centripetal force, and ends in a particular application, e.g. this centripetal force of planets to the sun. But induction cannot start from a known law. Hence it is that Jevons, followed by Sigwart and Wundt, reduces it to deduction from a hypothesis in the form "Let every M be P, S is M, :. S is P." There is a superficial resemblance between induction and this hypothetical deduction. Both in a way use given particulars as evidence. But in induction the given particulars are the evidence by which we discover the universal, e.g. particular magnets attracting iron are the origin of an inference that all do; in hypothetical deduction, the universal is the evidence by which we explain the given particulars, as when we suppose undulating aether to explain the facts of heat and light. In the former process, the given particulars are the data from which we infer the universal; in the latter, they are only the consequent facts by which we verify it. Or rather, there are two uses of induction: inductive discovery before deduction, and inductive verification after deduction. But neither use of induction is the same as the deduction itself: the former precedes, the latter follows it. Lastly, the theory of Mill, though frequently adopted, e.g. by B. Erdmann, need not detain us long. Most inductions are made without any assumption of the uniformity of nature; for, whether it is itself induced, or a priori or postulated, this like every assumption is a judgment, and most men are incapable of judgment on so universal a scale, when they are quite capable of induction. The fact is that the uniformity of nature stands to induction as the axioms of syllogism do to syllogism; they are not premises, but conditions of inference, which ordinary men use spontaneously, as was pointed out in _Physical Realism_, and afterwards in Venn's _Empirical Logic_. The axiom of contradiction is not a major premise of a judgment: the _dictum de omni et nullo_ is not a major premise of a syllogism: the principle of uniformity is not a major premise of an induction. Induction, in fact, is no species of deduction; they are opposite processes, as Aristotle regarded them except in the one passage where he was reducing the former to the latter, and as Bacon always regarded them. But it is