[Footnote 84: Analyt. Prior. II. xxvii. p. 70, a. 2-38. Compare what is said here about [Greek: ei)ko/s, sêmei=on, tekmê/rion], with the first chapter of the Topica, and the dialectic syllogism as there described: [Greek: o( e)x e)ndo/xôn sullogizo/menos].] [Footnote 85: Ibid. I. viii.-xxii. p. 29, b. 29-p. 40, b. 16.] What he calls the Necessary might indeed, from the point of view now reached, cease to be recognized as a separate mode at all. The Certain and the Problematical are real modes of the Proposition; objective correlates to the subjective phases called Belief and Doubt. But no proposition can be more than certain: the word _necessary_, in strictness, implies only a peculiarity of the evidence on which our belief is grounded. Granting certain given premisses to be true, a given conclusion must be true also, if we would avoid inconsistency and contradiction. CHAPTER VII. ANALYTICA POSTERIORA I. In the two books of Analytica Priora, Aristotle has carried us through the full doctrine of the functions and varieties of the Syllogism; with an intimation that it might be applied to two purposes--Demonstration and Dialectic. We are now introduced to these two distinct applications of the Syllogism: first, in the Analytica Posteriora, to Demonstration; next, in the Topica, to Dialectic. We are indeed distinctly told that, as far as the forms and rules of Syllogism go, these are alike applicable to both;[1] but the difference of matter and purpose in the two cases is so considerable as to require a distinct theory and precepts for the one and for the other. [Footnote 1: Analyt. Prior. I. xxx. p. 46, a. 4-10; Analyt. Post. I. ii. p. 71, a. 23.] The contrast between Dialectic (along with Rhetoric) on the one hand and Science on the other is one deeply present to the mind of Aristotle. He seems to have proceeded upon the same fundamental antithesis as that which appears in the Platonic dialogues; but to have modified it both in meaning and in terminology, dismissing at the same time various hypotheses with which Plato had connected it. The antithesis that both thinkers have in view is Opinion or Common Sense _versus_ Science or Special Teaching and Learning; those aptitudes, acquirements, sentiments, antipathies, &c., which a man imbibes and appropriates insensibly, partly by his own doing and suffering, partly by living amidst the drill and example of a given society--as distinguished from those accomplishments which he derives from a teacher already known to possess them, and in which both the time of his apprenticeship and the steps of his progress are alike assignable.