AEISTOTLE 0* THE LAW OF CONTRADICTION. 219 Animal, and not not-An mal, it will be true that Callias is animal, and not not-animal ; even though not-Callias be also Man, and not- man be also Animal. For the conclusion is not impaired though the Major be incommensurate to the Middle, and the Middle in- commensurate to the Minor. The principle that one or the other of two contradictories must be true, is assumed in indirect proof ; . . ." I confess I fail to see, either in Waitz or in Poste, any connex- ion between the first sentence and the rest of the passage. Surely Aristotle does not come to tell us at this late date, after having treated of the syllogism with the minutest detail in the Prior Analytics, that in the first mode of the first figure the middle term need not be co-extensive with the major, nor the minor with the middle. And assuming that he does tell us this very thing, what has that to do with the principle of contradiction ? Besides, what is the import of the first sentence ? According to Waitz, it means apparently that the law of contradiction is not explicitly stated as a premiss unless it is to appear explicitly also in the conclusion. One fails to see the significance of the statement. If all Aristotle means to say is that, owing to the universal certainty of this law, it need never be expressed in the premisses, being always implied, why should its explicit appear- ance in the conclusion make any difference ? In addition to these more general considerations it will appear, on an examination of the text, that the words will not bear the meaning Waitz puts upon them. More especially the words TO Se fjt.t.rrov ov&ev Sia^t'pei eivcu KCU p.rj etvcu AaySeiv ti KCU /AT) a.v6pu>irov arj@(<; war' o8' ei TO //.cVov KCU avro eo-rt /ecu /*T) avro cannot be interpreted as Waitz interprets them in the italicised lines above. Poste entitles his translation of this section, " Syllogism depends on the Axiom of Contradiction," and in an appendix (p. 135) at- tempts to show by a reference to the syllogism that the axiom of contradiction and the Dictum de omni et nullo are the same ; both of which views are, as it seems to me, the exact opposite of what Aristotle intends here, as I shall proceed to show. In the first sentence Aristotle makes the significant statement that the syllogism as such is independent of the principle of con- tradiction ; that therefore the conclusion does not exclude its opposite unless the major premiss does so. He then proceeds to show this in the syllogism : All Men are Animals Callias is a Man . . Callias is an Animal, in which the exclusion of not-animal in the major premiss is responsible for its exclusion in the conclusion, even if the principle of contradiction should not hold in the minor premiss, and in the minor term ; i.e., even if it were true that Callias is man and not- man (ti KOL /AT) avdpanroi' dXr/^e'?), and that he is Callias and not-
