After this very subtle and obscure distinction between propositions _secundi adjacentis_, and those _tertii adjacentis_, in respect to the application of the negative, Aristotle touches on the relation of _contrariety_ between propositions. The universal affirmation _Omne est animal justum_ has for its contrary _Nullum est animal justum_. It is plain that both these propositions will never be true at once. But the negatives or contradictories of both may well be true at once: thus, _Non omne animal est justum_ (the contradictory of the first) and _Est aliquid animal justum_ (the contradictory of the second) may be and are both alike true. If the affirmative proposition _Omnis homo est non justus_ be true, the negative _Nullus est homo justus_ must also be true; if the affirmative _Est aliquis homo justus_ be true, the negative _Non omnis homo est non justus_ must also be true. In singular propositions, wherever the negative or denial is true, the indefinite affirmative ([Greek: e)k metathe/seôs], in the language of Theophrastus) corresponding to it will also be true; in universal propositions, the same will not always hold. Thus, if you ask, Is Sokrates wise? and receive for answer No, you are warranted in affirming, Sokrates is not wise (the indefinite affirmation). But if you ask, Are all men wise? and the answer is No, you are not warranted in affirming, All men are not wise. This last is the contrary of the proposition, All men are wise; and two contraries may both be false. You are warranted in declaring only the contradictory negative, Not all men are wise.[29] [Footnote 29: Aristot. De Interpret. p. 20, a. 16-30.] Neither the indefinite noun ([Greek: ou)k a)/nthrôpos]) nor the indefinite verb ([Greek: ou) tre/chei--ou) di/kaios]) is a real and true negation, though it appears to be such. For every negation ought to be either true or false; but _non homo_, if nothing be appended to it, is not more true or false (indeed less so) than _homo_.[30] [Footnote 30: Ibid. a. 31, seq.] The transposition of substantive and adjective makes no difference in the meaning of the phrase; _Est albus homo_ is equivalent to _Est homo albus_. If it were not equivalent, there would be two negations corresponding to the same affirmation; but we have shown that there can be only one negation corresponding to one affirmation, so as to make up an _Antiphasis_.[31] [Footnote 31: Ibid. b. 1-12. That [Greek: e)sti\ leuko\s a)/nthrôpos], and [Greek: e)sti\n a)/nthrôpos leuko/s], mean exactly the same, neither more nor less--we might have supposed that Aristotle would have asserted without any proof; that he would have been content [Greek: a)po\ tô=n pragma/tôn pistou=sthai] (to use the phrase of Ammonius in a portion of the Scholia, p. 121, a. 27). But he prefers to deduce it as a corollary from a general doctrine much less evident than the statement itself; and after all, his deduction is not conclusive, as Waitz has already remarked (ad Organ. I. p. 351).]