[73] See the remarkable paragraph at the close of the Sophistici Elenchi, already quoted (supra, [p. 140, note]).
[74] 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.�
After adverting to another variety of ratiocinative procedure, which he calls Apagoge or Abduction (where the minor is hardly more evident than the conclusion, and might sometimes conveniently become a conclusion first to be proved),[75] Aristotle goes on to treat of Objection generally — the function of the dialectical respondent. The Enstasis or Objection is a proposition opposed not to a conclusion, but to the proposition set up by the defendant. When the proposition set up by him is universal, as it must be if he seeks to establish an universal conclusion, your objection may be either universal or particular: you may deny either the whole of his proposition, or only one portion of the particulars contained under it; the denial of one single particular, when substantiated, being enough to overthrow his universal. Accordingly, your objection, being thus variously opposed to the proposition, will lie in the syllogistic figures which admit opposite conclusions; that is, either in the First or Third; for the Second figure admits only negative conclusions not opposed to each other. If the defendant has set up an Universal Affirmative, you may deny the whole and establish a contrary negative, in the First figure; or you may deny a part only, and establish a contradictory negative, in the Third figure. The like, if he has set up an Universal Negative: you may impugn it either by an universal contrary affirmative, in the First figure; or by a particular contradictory affirmative, in the Third figure.[76]
[75] Analyt. Prior. II. xxv. p. 69, a. 20-36.
[76] Ibid. II. xxvi. p. 69, a. 37-b. 37.
In objecting to A universally, you take a term comprehending the original subject; in objecting particularly, a term comprehended by it. Of the new term in each case you deny the original predicate, and have thus, as a major premiss, E. For a minor premiss, you affirm, in the first case, the new term as predicate of the original subject (less comprehensive); in the second case, the original subject (more comprehensive) as predicate of the new term. This gives you, in the first case, a conclusion in Celarent (Fig. I.), and, in the second, a conclusion in Felapton (Fig. III.); opposed, the one universally or contrarily, the other particularly or contradictorily, to the original proposition.
The Enthymeme is a syllogism from Probabilities or Signs;[77] the two being not exactly the same. Probabilities are propositions commonly accepted, and true in the greater number of cases; such as, Envious men hate those whom they envy, Persons who are beloved look with affection on those who love them. We call it a Sign, when one fact is the antecedent or consequent of another, and therefore serves as mark or evidence thereof. The conjunction may be either constant, or frequent, or merely occasional: if constant, we obtain for the major premiss of our syllogism a proposition approaching that which is universally or necessarily true; if not constant but only frequent or occasional, the major premiss of our syllogism will at best only be probable. The constant conjunction will furnish us with a Syllogism or Enthymeme in the First figure; the significant mark being here a genuine middle term — subject in the major premiss, and predicate in the minor. We can then get a conclusion both affirmative and universally true. In other cases, we cannot obtain premisses for a syllogism in the First figure, but only for a syllogism in the Second or Third. In the Third figure, since we get by right no universal conclusions at all, but only particular conclusions, the conclusion of the Enthymeme, though it may happen to be true, is open to refutation. Where by the laws of Syllogism no affirmative conclusion whatever is possible, as in the Second figure, the conclusion obtained by Enthymeme is altogether suspicious. In contrast with the Sign in these figures, that which enters as an effective middle term into the First figure, should be distinguished under the name of Proof (τεκμήριον.)[78]
[77] Ibid. II. xxvii. p. 70, a. 10: ἐνθύμημα μὲν οὖν ἐστὶ συλλογισμὸς ἐξ εἰκότων ἢ σημείων· λαμβάνεται δὲ τὸ σημεῖον τριχῶς, ὁσαχῶς καὶ τὸ μέσον ἐν τοῖς σχήμασι.
[78] Analyt. Prior. II. xxvii. p. 70, a. 31-b. 6.
Aristotle throws in the remark (a. 24), that, when one premiss only of the Enthymeme is enunciated, it is a Sign; when the other is added, it becomes a Syllogism. In the examples given to illustrate the description of the Enthymeme, that which belongs to the First figure has its three terms and two propositions specified like a complete and regular Syllogism; but when we come to the Third and Second figures, Aristotle gives two alternate ways of stating each: one way in full, with both premisses enunciated, constituting a normal, though invalid, Syllogism; the other way, with only one of the premisses enunciated, the other being suppressed as well-known and familiar.