certain Induction the sequence is never a necessary one: you may grant the premisses and deny the conclusion without contradicting yourself. [Footnote 60: Alexander intimates that Aristotle enunciated "necessary sequence" as a part of his definition of Syllogism, for the express purpose of distinguishing it from Induction, which is a sequence _not necessary_ (Schol. ad Top. p. 253, a. 19, Br.): [Greek: to\ d' _e)x a)na/gkês_ proskei/menon e)n tô=| o(/rô|, tê=s **e)pagôgê=s chôri/zei to\n sullogismo/n; **e)/sti me\n ga\r kai\ e)pagôgê\ lo/gos e)n ô(=| tethe/ntôn tinô=n e(/tero/n ti tô=n keime/nôn sumbai/nei, a)ll' _ou)k_ e)x a)na/gkês.]] [Footnote 61: Alexander (in his Scholia on the Metaphysica, E. i. p. 406**, ed. Bonitz) observes truly: [Greek: a)ll' ei) e)k tê=s ai)sthê/seôs kai\ tê=s e)pagôgê=s pi/stis, ou)k e)/stin a)po/deixis, pro\s pa=san ga\r e)pagôgê\n du/natai/ tis e)ni/stasthai kai\ mê\ e)a=|n to\ katho/lou sumperai/nein.]] [Footnote 62: Analyt. Prior. II. xxiii. p. 68, b. 27: [Greek: dei= de\ noei=n to\ G to\ e)x a(pa/ntôn tô=n kath' e(/kaston sugkei/menon; ê( ga\r e)pagôgê\ dia\ pa/ntôn.] See Professor Bain's 'Inductive Logic,' chap. i. s. 2, where this process is properly criticised.] Aristotle states very clearly:--"We believe everything either through Syllogism, or from Induction."[63] Here, as well as in several other passages, he notes the two processes as essentially distinct. The Syllogism requires in its premisses at least one general proposition; nor does Aristotle conceive the "generalities as the original data:"[64] he derives them from antecedent Induction. The two processes are (as he says) opposite in a certain way; that is, they are complementary halves of the same whole; Induction being the establishment of those universals which are essential for the deductive march of the Syllogism; while the two together make up the entire process of scientific reasoning. But he forgets or relinquishes this antithesis, when he presents to us the Inductive process as a given variety of Syllogism. And the objection to such a doctrine becomes the more manifest, since in constructing his Inductive Syllogism, he is compelled to admit either that there is no middle term, or that the middle term is subject of the conclusion, in violation of the syllogistic canons.[65] [Footnote 63: Ibid. II. xxiii. p. 68, b. 13: [Greek: a(/panta ga\r pisteu/omen ê)\ dia\ sullogismou= ê)\ e)x e)pagôgê=s]. Here Induction includes Example, though in the next stage he puts the two apart. Compare Anal. Poster. I. i. p. 71, a. 9.] [Footnote 64: See Mr. John Stuart Mill's System of Logic, Bk. II. ch. iii. a. 4, p. 219, 5th ed.]