Page:Mind (New Series) Volume 9.djvu/545

 JOHN BURNET, The Ethics of Aristotle. .VU necessarily analytic in method : that is, it starts from its Aprf or (in the order of yeVctrit ) WA.OS, and has to determine by analysis the steps or means necessary towards the realisation of its end. A difficulty in Mr. Burnet's account of the matter presents itself at the very outset. We are told ( 22) that the ip^ of Ethics (or Politics) " will not resemble the definitions from which deductive geometry starts, but rather the enunciation of a problem in geo- metrical construction, what in the older Greek geometry was culled a iiro0e<m ". In a note (p. xxxvi.) the following explanation of the use of the word inro<?co- is given. " The precise signification of V7ro#e<ns is o iiroTiOerai rts, that which one sets before oneself as a thing to be done or proved ; for the meaning of fanm'&pat is not very different from that of Trportde/uu. The vrrotfeww is properly the Q. E. D. or the Q. E. F. of a geometrical problem. It is a con- clusion assumed for purpose of analysis to be true, or an end assumed for purposes of deliberation to be realised. The method and terminology are alike Platonic, though in the Sixth Book of the Republic Plato insists that knowledge in the highest sense cannot be of this character, but must deduce everything from the Form of the Good. The analytic method proceeds i( wrotfe'o-eow- OUK r* APX>IV uAA* eirl Tf(vrrjv (510 b) ; the true method would not regard these V7ro0e<rs as <tpx<u. It is evidence of the Academic origin of the theory that we have in [Plato] Def.. 415 b, fantfco-tc &pi) AvairoBtiKTos." Now it is difficult to see how v7ro0c(T can be completely identified with the Q. E. D. (or Q. E. F.) of a geomet- rical proof. The same proposition (SP) can be regarded in three different ways : (1) as a irpo/3A.7;/xa put forward for proof, (2) as the assumption of a hypothetical reasoning, (3) as a tnuur^pw/M. It appears in the second aspect when the method of discovering the proof of SP is analytic. SP is assumed hypothetically, MP de- duced. If, then, (a) SP can be in turn deduced from MP, (b) Ml' is known to be true, the proof of SP has been effected. It is then in this aspect alone that SP can be described as o tmrfflm/ T. As a 7rpd/3Ai//ua put forward for proof it can be called o wpor&mt T. Mr. Burnet gives no authority for his view except Plato and the passage quoted from the Republic seems to prove the opposite. Plato distinguishes two movements of thought which correspond to geometrical synthesis and geometrical analysis. It is the former that is described in the words quoted by Mr. Burnet. Both pro- ceed from V7ro0'o-s or assumptions. But the synthetic move- ment is downwards towards a reXtvn;, while the analytic is upwards towards an apxy. The latter returns to its viro0r (and proves it), the former does not. As for the definition vwoBri<; aprf) AFoirdSfurros, it may indeed be evidence of " the Academic origin of the theory," but it is difficult to see how Mr. Burnet's view can be maintained in opposition to it. How could SP, which is hypothetically as- sumed in geometrical analysis, be described as Avam&dKTos, when the object of the analysis is to demonstrate it? When we turn to the passage (1151 a, 15) in book vu. where