[58] Analyt. Prior. II. xxiv. p. 69, a. 1-19. Julius Pacius (p. 400) notes the unauthorized character of this so-called Paradeigmatic Syllogism, contradicting the rules of the figures laid down by Aristotle, and also the confused manner in which the scope of it is described: first, to infer from a single example to the universal; next, to infer from a single example through the universal to another parallel case. To which we may add the confused description in p. 69, a. 17, 18, where τὸ ἄκρον in the first of the two lines signifies the major extreme — in the second of the two the minor extreme. See Waitz’s note, p. 533.
If we turn to ch. xxvii. p. 70, a. 30-34, we shall find Aristotle on a different occasion disallowing altogether this so-called Syllogism from Example.
These chapters respecting Induction and Example are among the most obscure and perplexing in the Aristotelian Analytica. The attempt to throw both Induction and Example into the syllogistic form is alike complicated and unfortunate; moreover, the unsatisfactory reading and diversities in the text, among commentators and translators, show that the reasoning of Aristotle has hitherto been imperfectly apprehended.[59] From some of his phrases, we see that he was aware of the essential antithesis between Induction and Syllogism; yet the syllogistic forms appear to have exercised such fascination over his mind, that he could not be satisfied without trying to find some abnormal form of Syllogism to represent and give validity to Induction. In explaining generally what the Syllogism is, and what Induction is, he informs us that the Syllogism presupposes and rests upon the process of Induction as its postulate. For there can be no valid Syllogism without an universal proposition in one (at least) of the premisses; and he declares, unequivocally, that universal propositions are obtained only through Induction. How Induction operates through the particular facts of sense, remembered, compared, and coalescing into clusters held together by associating similarity, he has also told us; it is thus that Experience, with its universal notions and conjunctions, is obtained. But this important process is radically distinct from that of syllogizing, though it furnishes the basis upon which all syllogizing is built.
[59] Sir W. Hamilton (Lectures on Logic, vol. i. p. 319) says justly, that Aristotle has been very brief and unexplicit in his treatment of Induction. Yet the objections that Hamilton makes to Aristotle are very different from those which I should make. In the learned and valuable Appendix to his Lectures (vol. iv. pp. 358-369), he collects various interesting criticisms of logicians respecting Induction as handled by Aristotle. Ramus (in his Scholæ Dialecticæ, VIII. xi.) says very truly:— “Quid vero sit Inductio, perobscure ab Aristotele declaratur; nec ab interpretibus intelligitur, quo modo syllogismus per medium concludat majus extremum de minore; inductio, majus de medio per minus.�
The Inductive Syllogism, as constructed by Aristotle, requires a reciprocating minor premiss. It may, indeed, be cited (as I have already remarked) in support of Hamilton’s favourite precept of quantifying the predicate. The predicate of this minor must be assumed as quantified in thought, the subject being taken as co-extensive therewith. Therefore Hamilton’s demand that it shall be quantified in speech has really in this case that foundation which he erroneously claims for it in all cases. He complains that Lambert and some other logicians dispense with the necessity of quantifying the predicate of the minor by making it disjunctive; and adds the remarkable statement that “the recent German logicians, Herbart, Twesten, Drobisch, &c., following Lambert, make the Inductive Syllogism a byeword� (p. 366). I agree with them in thinking the attempted transformation of Induction into Syllogism very unfortunate, though my reasons are probably not the same as theirs.
Trendelenburg agrees with those who said that Aristotle’s doctrine about the Inductive Syllogism required that the minor should be disjunctively enunciated (Logische Untersuchungen, xiv. p. 175, xvi. pp. 262, 263; also Erläuterungen zu den Elementen der Aristotelischen Logik, ss. 34-36, p. 71). Ueberweg takes a similar view (System der Logik, sect. 128, p. 367, 3rd ed.). If the Inductive Inference is to be twisted into Syllogism, it seems more naturally to fall into an hypothetical syllogism, e. g.:—
If this, that, and the other magnet attract iron, all magnets attract iron;
But this, that, and the other magnet do attract iron: Ergo, &c.
The central idea of the Syllogism, as defined by Aristotle, is that of a conclusion following from given premisses by necessary sequence;[60] meaning by the term necessary thus much and no more — that you cannot grant the premisses, and deny the conclusion, without being inconsistent with yourself, or falling into contradiction. In all the various combinations of propositions, set forth by Aristotle as the different figures and modes of Syllogism, this property of necessary sequence is found. But it is a property which no Induction can ever possess.[61] When Aristotle professes to point out a particular mode of Syllogism to which Induction conforms, he can only do so by falsifying the process of Induction, and by not accurately distinguishing between what is observed and what is inferred. In the case which he takes to illustrate the Inductive Syllogism — the inference from all particular bile-less animals to the whole class bile-less — he assumes that we have ascertained the attribute to belong to all the particulars, and that the inductive inference consists in passing from all of them to the class-term; the passage from premisses to conclusion being here necessary, and thus falling under the definition of Syllogism; since, to grant the premisses, and yet to deny the conclusion, involves a contradiction. But this doctrine misconceives what the inductive inference really is. We never can observe all the particulars of a class, which is indefinite as to number of particulars, and definite only in respect of the attributes connoted by the class-term. We can only observe some of the particulars, a greater or smaller proportion. Now it is in the transition from these to the totality of particulars, that the real inductive inference consists; not in the transition from the totality to the class-term which denotes that totality and connotes its determining common attribute. In fact, the distinction between the totality of particulars and the meaning of the class-term, is one not commonly attended to; though it is worthy of note in an analysis of the intellectual process, and is therefore brought to view by Aristotle. But he employs it incorrectly as an intermediate step to slur over the radical distinction between Induction and Syllogism. He subjoins:[62]— “You must conceive the minor term C (in the Inductive Syllogism) as composed of all the particulars; for Induction is through all of them.â€� You may say that Induction is through all the particulars, if you distinguish this totality from the class-term, and if you treat the class-term as the ultimate terminus ad quem. But the Induction must first travel to all the particulars; being forced to take start from a part only, and then to jump onward far enough to cover the indefinite unobserved remainder. This jump is the real Induction; and this can never be brought under the definition of Syllogism; for in the best and most certain Induction the sequence is never a necessary one: you may grant the premisses and deny the conclusion without contradicting yourself.
[60] Alexander intimates that Aristotle enunciated “necessary sequenceâ€� as a part of his definition of Syllogism, for the express purpose of distinguishing it from Induction, which is a sequence not necessary (Schol. ad Top. p. 253, a. 19, Br.): τὸ δ’ ἐξ ἀνάγκης προσκείμενον ἐν τῷ ὅρῳ, τῆς ἐπαγωγῆς χωρίζει τὸν συλλογισμόν· ἔστι μὲν γὰρ καὶ ἐπαγωγὴ λόγος ἐν ᾧ τεθέντων τινῶν ἕτερόν τι τῶν κειμένων συμβαίνει, ἀλλ’ οὐκ ἐξ ἀνάγκης.
[61] Alexander (in his Scholia on the Metaphysica, E. i. p. 406, ed. Bonitz) observes truly: ἀλλ’ εἰ ἐκ τῆς αἰσθήσεως καὶ τῆς ἐπαγωγῆς πίστις, οὐκ ἔστιν ἀπόδειξις, πρὸς πᾶσαν γὰρ ἐπαγωγὴν δύναταί τις ἐνίστασθαι καὶ μὴ ἐᾷν τὸ καθόλου συμπεραίνειν.