Thus, they take the subject man, and propose to prove that man is mortal. They begin by laying down that man is an animal, and that every animal is either mortal or immortal. Here, the most universal term, animal, is selected as middle or as medium of proof; while after all, the conclusion demonstrated is, not that man is mortal, but that man is either mortal or immortal. The position that man is mortal, is assumed but not proved.[69] Moreover, by this method of logical division, all the steps are affirmative and none negative; there cannot be any refutation of error. Nor can any proof be given thus respecting _genus_, or _proprium_, or _accidens_; the _genus_ is assumed, and the method proceeds from thence to _species_ and _differentia_. No doubtful matter can be settled, and no unknown point elucidated by this method; nothing can be done except to arrange in a certain order what is already ascertained and unquestionable. To many investigations, accordingly, the method is altogether inapplicable; while even where it is applicable, it leads to no useful conclusion.[70] [Footnote 69: Ibid. p. 46, b. 1-12.] [Footnote 70: Ibid. b. 26-37. Alexander in Schol. p. 180, b. 1.] We now come to that which Aristotle indicates as the third section of this First Book of the Analytica Priora. In the first section he explained the construction and constituents of Syllogism, the varieties of figure and mode, and the conditions indispensable to a valid conclusion. In the second section he tells us where we are to look for the premisses of syllogisms, and how we may obtain a stock of materials, apt and ready for use when required. There remains one more task to complete his plan--that he should teach the manner of reducing argumentation as it actually occurs (often invalid, and even when valid, often elliptical and disorderly), to the figures of syllogism as above set forth, for the purpose of testing its validity.[71] In performing this third part (Aristotle says) we shall at the same time confirm and illustrate the two preceding parts; for truth ought in every way to be consistent with itself.[72] [Footnote 71: Analyt. Prior. I. xxxii. p. 47, a. 2: [Greek: loipo\n ga\r e)/ti tou=to tê=s ske/pseôs; ei) ga\r tê/n te ge/nesin tô=n sullogismô=n theôroi=men kai\ tou= eu(ri/skein e)/choimen du/namin, e)/ti de\ tou\s gegenême/nous a)nalu/oimen ei)s ta\ proeirême/na schê/mata, te/los a)\n e)/choi ê( e)x a)rchê=s pro/thesis.]] [Footnote 72: Ibid. a. 8.]