[56] Analyt. Post. I. xix. p. 81, b. 10-17.
[57] Ibid. p. 81, b. 30-p. 82, a. 14.
[58] Ibid. p. 82, a. 15-20. M. Barthélemy St. Hilaire, p. 117:— “Ceci ne saurait s’appliquer aux termes réciproques, parce que dans les termes qui peuvent être attribués réciproquement l’un à l’autre, on ne peut pas dire qu’il y ait ni premier ni dernier rélativement à l’attribution.�
[59] Analyt. Post. I. xx., xxi. p. 82, a. 21-b. 36.
In Dialectical Syllogism it is enough if the premisses be admitted or reputed as propositions immediately true, whether they are so in reality or not; but in Scientific or Demonstrative Syllogism they must be so in reality: the demonstration is not complete unless it can be traced up to premisses that are thus immediately or directly true (without any intervening middle term).[60] That there are and must be such primary or immediate premisses, Aristotle now undertakes to prove, by some dialectical reasons, and other analytical or scientific reasons.[61] He himself thus distinguishes them; but the distinction is faintly marked, and amounts, at most, to this, that the analytical reasons advert only to essential predication, and to the conditions of scientific demonstration, while the dialectical reasons dwell upon these, but include something else besides, viz., accidental predication. The proof consists mainly in the declaration that, unless we assume some propositions to be true immediately, indivisibly, undemonstrably, — Definition, Demonstration, and Science would be alike impossible. If the ascending series of predicates is endless, so that we never arrive at a highest generic predicate; if the descending series of subjects is endless, so that we never reach a lowest subject, — no definition can ever be attained. The essential properties included in the definition, must be finite in number; and the accidental predicates must also be finite in number, since they have no existence except as attached to some essential subject, and since they must come under one or other of the nine later Categories.[62] If, then, the two extremes are thus fixed and finite — the highest predicate and the lowest subject — it is impossible that there can be an infinite series of terms between the two. The intervening terms must be finite in number. The Aristotelian theory therefore is, that there are certain propositions directly and immediately true, and others derived from them by demonstration through middle terms.[63] It is alike an error to assert that every thing can be demonstrated, and that nothing can be demonstrated.
[60] Ibid. xix. p. 81, b. 18-29.
[61] Ibid. xxi. p. 82, b. 35; xxii. p. 84, a. 7: λογικῶς μὲν οὖν ἐκ τούτων ἄν τις πιστεύσειε περὶ τοῦ λεχθέντος, ἀναλυτικῶς δὲ διὰ τῶνδε φανερὸν συντομώτερον. In Scholia, p. 227, a. 42, the same distinction is expressed by Philoponus in the terms λογικώτερα and πραγματωδέστερα. Compare Biese, Die Philosophie des Aristoteles, pp. 134, 261; Bassow, De Notionis Definitione, pp. 19, 20; Heyder, Aristot. u. Hegel. Dialektik, pp. 316, 317.
Aristotle, however, does not always adhere closely to the distinction. Thus, if we compare the logical or dialectical reasons given, p. 82, b. 37, seq., with the analytical, announced as beginning p. 84, a. 8, seq., we find the same main topic dwelt upon in both, namely, that to admit an infinite series excludes the possibility of Definition. Both Alexander and Ammonius agree in announcing this as the capital topic on which the proof turned; but Alexander inferred from hence that the argument was purely dialectical (λογικὸν ἐπιχείρημα), while Ammonius regarded it as a reason thoroughly convincing and evident: ὁ μέντοι φιλόσοφος (Ammonius) ἔλεγε μὴ διὰ τοῦτο λέγειν λογικὰ τὰ ἐπιχειρήματα· ἐναργὲς γὰρ ὅτι εἰσὶν ὁρισμοί, εἰ μὴ ἀκαταληψίαν εἰσαγάγωμεν (Schol. p. 227, a. 40, seq., Brand.).
[62] Analyt. Post. I. xxii. p. 83, a. 20, b. 14. Only eight of the ten Categories are here enumerated.
[63] Ibid. I. xxii. p. 84, a. 30-35. The paraphrase of Themistius (pp. 55-58, Spengel) states the Aristotelian reasoning in clearer language than Aristotle himself. Zabarella (Comm. in Analyt. Post. I. xviii.; context. 148, 150, 154) repeats that Aristotle’s proof is founded upon the undeniable fact that there are definitions, and that without them there could be no demonstration and no science. This excludes the supposition of an infinite series of predicates and of middle terms:— “Sumit rationem à definitione; si in predicatis in quid procederetur ad infinitum, sequeretur auferri definitionem et omnino essentiæ cognitionem; sed hoc dicendum non est, quum omnium consensioni adversetur� (p. 466, Ven. 1617).