Note 74 — Chapter VI · ANALYTICA PRIORA II.

Mr. John Stuart Mill says (Bk. II. ch. i. sect. 3): “Induction is inferring a proposition from premisses less general than itself, and Ratiocination is inferring a proposition from premisses equally or more general.” Again in another passage: “We have found that all Inference, consequently all Proof, and all discovery of truths not self-evident, consists of inductions, and the interpretation of inductions; that all our knowledge, not intuitive, comes to us exclusively from that source. What Induction is, therefore, and what conditions render it legitimate, cannot but be deemed the main question of logic — the question which includes all others. It is however one which professed writers on logic have almost entirely passed over. The generalities of the subject, indeed, have not been altogether neglected by metaphysicians; but, for want of sufficient acquaintance with the processes by which science has actually succeeded in establishing general truths, their analysis of the inductive operation, even when unexceptionable as to correctness, has not been specific enough to be made the foundation of practical rules, which might be for Induction itself what the rules of the Syllogism are for interpretation of Induction” (Bk. III. ch. i. s. 1. p. 313.) — “The business of Inductive Logic is to provide rules and models (such as the Syllogism and its rules are for ratiocination) to which if inductive arguments conform, those arguments are conclusive, and not otherwise. This is what the Four Methods profess to be, and what I believe they are universally considered to be by experimental philosophers, who had practised all of them long before any one sought to reduce the practice to theory” (Bk. III. ch. ix. s. 5, p. 471, 5th ed.) — See also the same point of view more copiously set forth, in Mr. Mill’s later work, ‘Examination of Sir W. Hamilton’s Philosophy’ (ch. xx. pp. 454-462, 3rd ed.): “It is only as a means to material truth that the formal (or to speak more clearly, the conditional) validity of an operation of thought is of any value; and even that value is only negative: we have not made the smallest positive advance towards right thinking, by merely keeping ourselves consistent in what is perhaps systematic error. This by no means implies that Formal Logic, even in its narrowest sense, is not of very great, though purely negative value.” — “Not only however is it indispensable that the larger Logic, which embraces all the general conditions of the ascertainment of truth, should be studied in addition to the smaller Logic, which only concerns itself with the conditions of consistency; but the smaller Logic ought to be (at least, finally) studied as part of the greater — as a portion of the means to the same end; and its relation to the other parts — to the other means — should be distinctly displayed.”