Page:Mind (New Series) Volume 15.djvu/232

 218 ISAAC HUSIK : The passage in question occurs Posterior Analytics, L, 11, p. 77a, 10-22, and reads as follows: TO 8c /AT) v8eto'0ai d/Aa dvat Kai dirodvai 8' OVK aXr]6ts. TO oe /AeVov ouSev 8iaep eivai Kai /AT) civcu XaySeiv, w? 8' auTWS Kai TO TOLTOV. el yap fooOr), Kaff ov dvOpwTrov dXvj^es CITTCIV, ei Kai /AT) dv0pu)7roi' dA^es, dXA.' i fwvov avOpunrov ^<3ov eivou, p.T] ^wov 8e /AT; TTCK. yap dA^^es etTrerv KaAAtav, ei *cai /AT) KaAAtav, o/wos < {' ov /*^ 4 < J* OV S' ou. amov 8' OTI TO TrpwTOv ou fJuovov KO.TO. TOV tico~ov XcycTat dAXa xai KaT aAAou Sia TO eTvai CTTI TrXctovwv, WOT' ou8' ei TO /xe'o-ov KII auro eo-Ti KUI /AT) auro, Trpos TO o~u/A7Tpao*/Aa ovSev 8ia$epei. TO 8' a7raf dva.t T} a7ro<^avat 17 et? TO Waitz' commentary on the passage reads as follows (the italics are mine) : " Principium contradictionis quod dicitur in ipsam demonstra- tionem non assumitur, nisi etiam in conclusione expressum esse debeat : si A de omni B praedicari verum, non praedicari non verum sit, B vero de omni C praedicetur, A de omni C praedicari verum, non praedicari non verum est : in quo quidem syllogismo nihil interest (vs. 14), num A pradicetur et de B et de Non-B, B autem et de C et de Non-C. Nam si datum est animal praedicari de omni homine (ei yap eooOrj ^wov ivat TOVTO Ka.6' ov avOpwirov aXrfO^ eo-Ttv eiTreiv, vs. 15), etiam si verum sit animal pradicari etiam de Non-homine, dummodo homo sit animal, non-animal vero non praedicetur de homine, eadem utique proveniet conclusio, hanc dico, hominem quendam e.g. Calliam esse animal. (Per- spicuitatis causa hie adiecimus apodosin, qualis esse debebat, quam Aristoteles et cogitandi et scribendi alacritate abreptus non omisit quidem, sed turbavit.) Item enim, etiam si Non-Callias homo sit, de Callia homo praedicabitur, non-homo vero non praedicabitur. Quare etiam si A et de B praedicatur et de Non-B (tl TO irptaTov ov p.6vov KO.TO. TOV /AccTov XeycTtti dAXa Kai KO.T aAAov, VS. 19), B autem et de C et de Non-C (ei TO /ACO-OV Kai auro CO-TI Kai /AT) auro, VS. 20), dum- modo Non-A neque de B praedicetur neque de C, tamen conclusio eadem utique erit ' A praedicari de C '. Verum principio contra- dictionis (vs. 22) non uti solemus in demon strati one recta, sed in deductione ad absurdum quae dicitur. . . ." Edward Poste, 1 no doubt following Waitz, translates the passage as follows (italics mine) : " That of two contradictory predicates one must be false, is never expressed in demonstration, but implied in all direct proof. When we syllogise, we assume that the Major is truly affirmed of the Middle, and not truly denied, withmit caring whether the Middle can be truly denied of the Major. And so with respect to the Middle and Minor. For if we assume that All Man is 1 The Logic of Science, a Translation of the Posterior Analytics of Aris- totle, with notes and an introduction by Edward Poste, 1LA., Oxford, 1850.