Aristotle has hitherto regarded the Syllogism with a view to its _formal_ characteristics: he now makes an important observation which bears upon its _matter_. Formally speaking, **the two premisses are always assumed to be true; but in any real case of syllogism (form and matter combined) it is possible that either one or both may be false. Now, Aristotle remarks that if both the premisses are true (the syllogism being correct in form), the conclusion must of necessity be true; but that if either or both the premisses are false, the conclusion need not necessarily be false likewise. The premisses being false, the conclusion may nevertheless be true; but it will not be true because of or by reason of the premisses.[4] [Footnote 4: Analyt. Prior. II. ii. p. 53, b. 5-10: [Greek: e)x a)lêthô=n me\n ou)=n ou)k e)/sti pseu=dos sullogi/sasthai, e)k pseudô=n d' e)/stin a)lêthe/s, plê\n ou) dio/ti a)ll' o(/ti; tou= ga\r dio/ti ou)k e)/stin e)k pseudô=n sullogismo/s; di' ê(\n d' ai)ti/an, e)n toi=s e(pome/nois lechthê/setai.] The true conclusion is not true by reason of these false premisses, but by reason of certain other premisses which are true, and which may be produced to demonstrate it. Compare Analyt. Poster. I. ii. p. 71, b. 19.] First, he would prove that if the premisses be true, the conclusion must be true also; but the proof that he gives does not seem more evident than the _probandum_ itself. Assume that if A exists, B must exist also: it follows from hence (he argues) that if B does not exist, neither can A exist; which he announces as a _reductio ad absurdum_, seeing that it contradicts the fundamental supposition of the existence of A.[5] Here the _probans_ is indeed equally evident with the _probandum_, but not at all more evident; one who disputes the latter, will dispute the former also. Nothing is gained in the way of proof by making either of them dependent on the other. Both of them are alike self-evident; that is, if a man hesitates to admit either of them, you have no means of removing his scruples except by inviting him to try the general maxim upon as many particular cases as he chooses, and to see whether it does not hold good without a single exception. [Footnote 5: Ibid. II. ii. p. 53, b. 11-16.]