[62] Analyt. Prior. II. xxiii. p. 68, b. 27: δεῖ δὲ νοεῖν τὸ Γ τὸ ἐξ ἁπάντων τῶν καθ’ ἕκαστον συγκείμενον· ἡ γὰρ ἐπαγωγὴ διὰ πάντων. See Professor Bain’s ‘Inductive Logic,’ chap. i. s. 2, where this process is properly criticised.
Aristotle states very clearly:— “We believe everything either through Syllogism, or from Induction.�[63] Here, as well as in several other passages, he notes the two processes as essentially distinct. The Syllogism requires in its premisses at least one general proposition; nor does Aristotle conceive the “generalities as the original data:�[64] he derives them from antecedent Induction. The two processes are (as he says) opposite in a certain way; that is, they are complementary halves of the same whole; Induction being the establishment of those universals which are essential for the deductive march of the Syllogism; while the two together make up the entire process of scientific reasoning. But he forgets or relinquishes this antithesis, when he presents to us the Inductive process as a given variety of Syllogism. And the objection to such a doctrine becomes the more manifest, since in constructing his Inductive Syllogism, he is compelled to admit either that there is no middle term, or that the middle term is subject of the conclusion, in violation of the syllogistic canons.[65]
[63] Ibid. II. xxiii. p. 68, b. 13: ἅπαντα γὰρ πιστεύομεν ἢ διὰ συλλογισμοῦ ἢ ἐξ ἐπαγωγῆς. Here Induction includes Example, though in the next stage he puts the two apart. Compare Anal. Poster. I. i. p. 71, a. 9.
[64] See Mr. John Stuart Mill’s System of Logic, Bk. II. ch. iii. a. 4, p. 219, 5th ed.
[65] Aldrich (Artis Log. Rudim. ch. iii. 9, 2, p. 175) and Archbishop Whately (Elem. of Logic, ch. i. p. 209) agree in treating the argument of Induction as a defective or informal Syllogism: see also to the same purpose Sir W. Hamilton, Lectures on Logic, vol. i. p. 322. Aldrich treats it as a Syllogism in Barbara, with the minor suppressed; but Whately rejects this, because the minor necessary to be supplied is false. He maintains that the premiss suppressed is the major, not the minor. I dissent from both. It appears to me that the opinion which Whately pronounces to be a fallacy is the real truth: “Induction is a distinct kind of argument from the Syllogism� (p. 208). It is the essential property of the Syllogism, as defined by Aristotle and by every one after him, that the truth of the conclusion follows necessarily from the truth of its premisses: that you cannot admit the premisses and reject the conclusion without contradicting yourself. Now this is what the best Induction never attains; and I contend that the presence or absence of this important characteristic is quite enough to constitute “two distinct kinds of argument.� Whately objects to Aldrich (whom Hamilton defends) for supplying a suppressed minor, because it is “manifestly false� (p. 209). I object to Whately’s supplied major, because it is uncertified, and therefore cannot be used to prove any conclusion. By clothing arguments from Induction in syllogistic form, we invest them with a character of necessity which does not really belong to them. The establishment of general propositions, and the interpretation of them when established (to use the phraseology of Mr. Mill), must always be distinct mental processes; and the forms appropriate to the latter, involving necessary sequence, ought not to be employed to disguise the want of necessity — the varying and graduated probability, inherent in the former. Mr. Mill says (Syst. Log. Bk. III. ch. iii. s. 1, p. 343, 5th ed.:) — “As Whately remarks, every induction is a syllogism with the major premiss suppressed; or (as I prefer expressing it) every induction may be thrown into the form of a syllogism, by supplying a major premiss.� Even in this modified phraseology, I cannot admit the propriety of throwing Induction into syllogistic forms of argument. By doing this we efface the special character of Induction, as the jump from particular cases, more or fewer, to an universal proposition comprising them and an indefinite number of others besides. To state this in forms which imply that it is a necessary step, involving nothing more than the interpretation of a higher universal proposition, appears to me unphilosophical. Mr. Mill says with truth (in his admirable chapter explaining the real function of the major premiss in a Syllogism, p. 211), that the individual cases are all the evidence which we possess; the step from them to universal propositions ought not to be expressed in forms which suppose universal propositions to be already attained.
I will here add that, though Aldrich himself (as I stated at the beginning of this note) treats the argument from Induction as a defective or informal Syllogism, his anonymous Oxonian editor and commentator takes a sounder view. He says (pp. 176, 177, 184, ed. 1823. Oxon.):—
“The principles acquired by human powers may be considered as twofold. Some are intuitive, and are commonly called Axioms; the other class of general principles are those acquired by Induction. But it may be doubted whether this distinction is correct. It is highly probable, if not certain, that those primary Axioms generally esteemed intuitive, are in fact acquired by an inductive process; although that process is less discernible, because it takes place long before we think of tracing the actings of our own minds. It is often found necessary to facilitate the understanding of those Axioms, when they are first proposed to the judgment, by illustrations drawn from individual cases. But whether it is, as is generally supposed, the mere enunciation of the principle, or the principle itself, which requires the illustration, may admit of a doubt. It seems probable, however that, such illustrations are nothing more than a recurrence to the original method by which the knowledge of those principles was acquired. Thus, the repeated trial or observation of the necessary connection between mathematical coincidence and equality, first authorizes the general position or Axiom relative to that subject. If this conjecture is founded in fact, it follows that both primary and ultimate principles have the same nature and are alike acquired by the exercise of the inductive faculty.� “Those who acquiesce in the preceding observations will feel a regret to find Induction classed among defective or informal Syllogisms. It is in fact prior in its order to Syllogism; nor can syllogistic reasoning he carried on to any extent without previous Induction� (p. 184).
We must presume Syllogisms without a middle term, when we read:— “The Syllogism through a middle term is by nature prior, and of greater cognitive efficacy; but to us the Syllogism through Induction is plainer and clearer.�[66] Nor, indeed, is the saying, when literally taken, at all well-founded; for the pretended Syllogisms from Induction and Example, far from being clear and plain, are more involved and difficult to follow than Barbara and Celarent. Yet the substance of Aristotle’s thought is true and important, when considered as declaring the antithesis (not between varieties of Syllogisms, but) between Induction and Example on the one part, and Syllogism (Deduction) on the other. It is thus that he sets out the same antithesis elsewhere, both in the Analytica Posteriora and the Topica.[67] Prior and more cognizable by nature or absolutely, prior and more cognizable to us or in relation to us — these two are not merely distinct, but the one is the correlate and antithesis of the other.
[66] Analyt. Prior. II. xxiii. p. 68, b. 35: φύσει μὲν οὖν πρότερος καὶ γνωριμώτερος ὁ διὰ τοῦ μέσου συλλογισμός, ἡμῖν δ’ ἐναργέστερος ὁ διὰ τῆς ἐπαγωγῆς.
[67] Analyt. Post. I. ii. p. 72, a. 2, b. 29; Ethic. Nik. VI. iii. p. 1139, b. 28: ἡ μὲν δὴ ἐπαγωγὴ ἀρχή ἐστι καὶ τοῦ καθόλοῦ, ὁ δὲ συλλογισμὸς ἐκ τῶν καθόλου. εἰσὶν ἄρα ἀρχαὶ ἐξ ὧν ὁ συλλογισμός, ὧν οὐκ ἔστι συλλογισμός· ἐπαγωγὴ ἄρα. Compare Topica, I. xii. p. 105, a. 11; VI. iv. pp. 141, 142; Physica, I. i. p. 184, a. 16; Metaphysic. E. iv. p. 1029, b. 4-12. Compare also Trendelenburg’s explanation of this doctrine, Erläuterungen zu den Elementen der Aristotelischen Logik, sects. 18, 19, 20, p. 33, seq.