A similar doctrine is asserted, Analyt. Prior. I. xli. p. 49, b. 35, and still more clearly in De Memoria et Reminiscentia, p. 450, a. 2-12.
The process of Demonstration neither requires, nor countenances, the Platonic theory of Ideas — universal substances beyond and apart from particulars. But it does require that we should admit universal predications; that is, one and the same predicate truly applicable in the same sense to many different particulars. Unless this be so, there can be no universal major premiss, nor appropriate middle term, nor valid demonstrative syllogism.[33]
[33] Aristot. Analyt. Post. I. xi. p. 77, a. 5-9.
The Maxim or Axiom of Contradiction, in its most general enunciation, is never formally enunciated by any special science; but each of them assumes the Maxim so far as applicable to its own purpose, whenever the Reductio ad Absurdum is introduced.[34] It is in this and the other common principles or Axioms that all the sciences find their point of contact and communion; and that Dialectic also comes into communion with all of them, as also the science (First Philosophy) that scrutinizes the validity or demonstrability of the Axioms.[35] The dialectician is not confined to any one science, or to any definite subject-matter. His liberty of interrogation is unlimited; but his procedure is essentially interrogatory, and he is bound to accept the answer of the respondent — whatever it be, affirmative or negative — as premiss for any syllogism that he may construct. In this way he can never be sure of demonstrating any thing; for the affirmative and the negative will not be equally serviceable for that purpose. There is indeed also, in discussions on the separate sciences, a legitimate practice of scientific interrogation. Here the questions proper to be put are limited in number, and the answers proper to be made are determined beforehand by the truths of the science — say Geometry; still, an answer thus correctly made will serve to the interrogator as premiss for syllogistic demonstration.[36] The respondent must submit to have such answer tested by appeal to geometrical principia and to other geometrical propositions already proved as legitimate conclusions from the principia; if he finds himself involved in contradictions, he is confuted quâ geometer, and must correct or modify his answer. But he is not bound, quâ geometer, to undergo scrutiny as to the geometrical principia themselves; this would carry the dialogue out of the province of Geometry into that of First Philosophy and Dialectic. Care, indeed, must be taken to keep both questions and answers within the limits of the science. Now there can be no security for this restriction, except in the scientific competence of the auditors. Refrain, accordingly, from all geometrical discussions among men ignorant of geometry and confine yourself to geometrical auditors, who alone can distinguish what questions and answers are really appropriate. And what is here said about geometry, is equally true about the other special sciences.[37] Answers may be improper either as foreign to the science under debate, or as appertaining to the science, yet false as to the matter, or as equivocal in middle term; though this last is less likely to occur in Geometry, since the demonstrations are accompanied by diagrams, which help to render conspicuous any such ambiguity.[38] To an inductive proposition, bringing forward a single case as contributory to an ultimate generalization, no general objection should be offered; the objection should be reserved until the generalization itself is tendered.[39] Sometimes the mistake is made of drawing an affirmative conclusion from premisses in the Second figure; this is formally wrong, but the conclusion may in some cases be true, if the major premiss happens to be a reciprocating proposition, having its predicate co-extensive with its subject. This, however, cannot be presumed; nor can a conclusion be made to yield up its principles by necessary reciprocation; for we have already observed that, though the truth of the premisses certifies the truth of the conclusion, we cannot say vice versâ that the truth of the conclusion certifies the truth of the premisses. Yet propositions are more frequently found to reciprocate in scientific discussion than in Dialectic; because, in the former, we take no account of accidental properties, but only of definitions and what follows from them.[40]
[34] Ibid. a. 10, seq.
[35] Ibid. a. 26-30: καὶ εἴ τις καθόλου πειρῷτο δεικνύναι τὰ κοινά, οἷον ὅτι ἅπαν φάναι ἢ ἀποφάναι, ἢ ὅτι ἴσα ἀπὸ ἴσων, ἢ τῶν τοιούτων ἄττα. Compare Metaph. K. p. 1061, b. 18.
[36] Aristot. Analyt. Post. I. xii, p. 77, a. 36-40; Themistius, p. 40.
The text is here very obscure. He proceeds to distinguish Geometry especially (also other sciences, though less emphatically) from τὰ ἐν τοῖς διαλόγοις (I. xii. p. 78, a. 12).
Julius Pacius, ad Analyt. Post. I. viii. (he divides the chapters differently), p. 417, says:— “Differentia interrogationis dialecticæ et demonstrativæ hæc est. Dialecticus ita interrogat, ut optionem det adversario, utrum malit affirmare an negare. Demonstrator vero interrogat ut rem evidentiorem faciat; id est, ut doceat ex principiis auditori notis.�
[37] Ibid. I. xii. p. 77, b. 1-15; Themistius, p. 41: οὐ γὰρ ὥσπερ τῶν ἐνδόξων οἱ πολλοὶ κριταί, οὕτω καὶ τῶν κατ’ ἐπιστήμην οἱ ἀνεπιστήμονες.