[Footnote 31: Ibid. p. 76, b. 36: [Greek: tou=to d' ou)ch u(po/thesis, ei) mê\ kai\ _to\ a)kou/ein_ u(po/thesi/n tis ei)=nai phê/sei]. For the meaning of [Greek: _to\ a)kou/ein_], compare [Greek: o( a)kou/ôn], infra, Analyt. Post. I. xxiv. p. 85, b. 22.] [Footnote 32: Ibid. p. 77, a. 1: [Greek: o( de\ geôme/três ou)de\n sumperai/netai tô=| tê/nde ei)=nai tê\n grammê\n ê(\n au)to\s e)/phthegktai, a)lla\ ta\ dia\ tou/tôn dêlou/mena.] Themistius, Paraphr. p. 37: [Greek: ô(/sper ou)d' oi( geôme/trai ke/chrêntai tai=s grammai=s u(pe\r ô(=n diale/gontai kai\ deiknu/ousin, a)ll' a(\s e)/chousin e)n tê=| psuchê=|, ô(=n ei)si\ su/mbola ai( grapho/menai.] 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] [Footnote 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