THE PROBLEM OF INFINITY 169 



aimed at the Pythagoreans, 1 while others have held that 

 they were intended to refute the atomists. 2 M. Evellin, 

 on the contrary, holds that they constitute a refutation of 

 infinite divisibility, 3 while M. G. Noel, in the interests of 

 Hegel, maintains that the first two arguments refute 

 infinite divisibility, while the next two refute indivisibles. 4 

 Amid such a bewildering variety of interpretations, we 

 can at least not complain of any restrictions on our 

 liberty of choice. 



The historical questions raised by the above-mentioned 

 discussions are no doubt largely insoluble, owing to the 

 very scanty material from which our evidence is derived. 

 The points which seem fairly clear are the following : 

 (1) That, in spite of MM. Milhaud and Paul Tannery, 

 Zeno is anxious to prove that motion is really impossible, 

 and that he desires to prove this because he follows 

 Parmenides in denying plurality ; 5 (2) that the third and 

 fourth arguments proceed on the hypothesis of indi- 

 visibles, a hypothesis which, whether adopted by the 

 Pythagoreans or not, was certainly much advocated, as 

 may be seen from the treatise On Indivisible Lines attri- 

 buted to Aristotle. As regards the first two arguments, 

 they would seem to be valid on the hypothesis of indi- 

 visibles, and also, without this hypothesis, to be such as 



1 Cf. Gaston Milhaud, Les philosophes-ge'ometres de la Grece, p. 140 n. ; 

 Paul Tannery, Pour Phistoire de la science helle~ne, p. 249 ; Burnet, 

 op. cit., p. 362. 



2 Cf. R. K. Gaye, " On Aristotle, Physics, Z ix." Journal of Philology, 

 vol. xxxi., esp. p. in. Also Moritz Cantor, Vorlesungen iiber Geschichte 

 der Mathematik, 1st eel., vol. i., 1880, p. 168, who, however, subsequently 

 adopted Paul Tannery's opinion, Vorlesiwgen, 3rd ed. (vol. i. p. 200). 



3 " Le mouvement et les partisans des indivisibles," Revue de Me"ta- 

 physique et de Morale, vol. i. pp. 382-395. 



4 " Le mouvement et les arguments de Zenon d'lee," Revue de Mdta- 

 physique et de Morale, vol. i. pp. 107-125. 



6 Cf. M. Brochard, " Les pretendus sophismes de Zdnon d'Elee," Revue 

 de Metaphysique et de Morale, vol. i. pp. 209-215. 



