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. [Footnote 60: Ibid. xix. p. 81, b. 18-29.] [Footnote 61: Ibid. xxi. p. 82, b. 35; xxii. p. 84, a. 7: [Greek: _logikô=s_ me\n ou)=n e)k tou/tôn a)/n tis pisteu/seie peri\ tou= lechthe/ntos, _a)nalutikô=s_ de\ dia\ tô=nde phanero\n suntomô/teron.] In Scholia, p. 227, a. 42, the same distinction is expressed by Philoponus in the terms [Greek: logikô/tera] and [Greek: pragmatôde/stera]. Compare Biese, Die Philosophie des Aristoteles, pp. 134, 261; Bassow, De Notionis Definitione, pp. 19, 20; Heyder, Aristot. u. Hegel. Dialektik, pp. 316, 317.