Of this reversing process, one variety is what is called the _Reductio ad Absurdum_; in which the conclusion is reversed by taking its contradictory (never its contrary), and then joining this last with one of the premisses, in order to prove the contradictory or contrary of the other premiss.[13] The _Reductio ad Absurdum_ is distinguished from the other modes of reversal by these characteristics: (1) That it takes the contradictory, and not the contrary, of the conclusion; (2) That it is destined to meet the case where an opponent declines to admit the conclusion; whereas the other cases of reversion are only intended as confirmatory evidence towards a person who already admits the conclusion; (3) That it does not appeal to or require any concession on the part of the opponent; for if he declines to admit the conclusion, you presume, as a matter of course, that he must adhere to the contradictory of the conclusion; and you therefore take this contradictory for granted (without asking his concurrence) as one of the bases of a new syllogism; (4) That it presumes as follows:--When, by the contradictory of the conclusion joined with one of the premisses, you have demonstrated the opposite of the other premiss, the original conclusion itself is shown to be beyond all impeachment on the score of form, _i.e._ beyond impeachment by any one who admits the premisses. You assume to be true, for the occasion, the very proposition which you mean finally to prove false; your purpose in the new syllogism is, not to demonstrate the original conclusion, but to prove it to be true by demonstrating its contradictory to be false.[14]** [Footnote 13: Analyt. Prior. II. xi. p. 61, a. 18, seq.] [Footnote 14: Ibid. p. 62, a. 11: [Greek: phanero\n ou)=n o(/ti ou) to\ e)nanti/on, a)lla\ to\ a)ntikei/menon, u(pothete/on e)n a(/pasi toi=s sullogismoi=s. ou(/tô ga\r to\ a)nagkai=on e)/stai kai\ to\ a)xi/ôma e)/ndoxon. ei) ga\r kata\ panto\s ê)\ kata/phasis ê)\ a)po/phasis, deichthe/ntos o(/ti ou)ch ê( a)po/phasis, a)na/gkê tê\n kata/phasin a)lêtheu/esthai.] See Scholia, p. 190, b. 40, seq., Brand.] By the _Reductio ad Absurdum_ you can in all the three figures demonstrate all the four varieties of conclusion, universal and particular, affirmative and negative; with the single exception, that you cannot by this method demonstrate in the First figure the Universal Affirmative.[15] With this exception, every true conclusion admits of being demonstrated by either of the two ways, either directly and ostensively, or by reduction to the impossible.[16] [Footnote 15: Ibid. p. 61, a. 35-p. 62, b. 10; xii. p. 62, a. 21. Alexander, ap. Schol. p. 191, a. 17-36, Brand.] [Footnote 16: Ibid. xiv. p. 63, b. 12-21.]