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. Noël, 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 indivisibles, a hypothesis which, whether adopted by the Pythagoreans or not, was certainly much advocated, as may be seen from the treatise On Indivisible Lines attributed to Aristotle. As regards the first two arguments, they would seem to be valid on the hypothesis of indivisibles, and also, without this hypothesis, to be such as
- ↑ Cf. Gaston Milhaud, Les philosophes-géomètres de la Grèce, p. 140 n.; Paul Tannery, Pour l’histoire de la science hellène, p. 249; Burnet, op. cit., p. 362.
- ↑ Cf. R. K. Gaye, “On Aristotle, Physics, Z ix.” Journal of Philology, vol. xxxi., esp. p. 111. Also Moritz Cantor, Vorlesungen über Geschichte der Mathematik, 1st ed., vol. i., 1880, p. 168, who, however, subsequently adopted Paul Tannery’s opinion, Vorlesungen, 3rd ed. (vol. i. p. 200).
- ↑ “Le mouvement et les partisans des indivisibles,” Revue de Métaphysique et de Morale, vol. i. pp. 382-395.
- ↑ “Le mouvement et les arguments de Zénon d’Élée,” Revue de Métaphysique et de Morale, vol. i. pp. 107-125.
- ↑ Cf. M. Brochard, “Les prétendus sophismes de Zénon d’Élée,” Revue de Métaphysique et de Morale, vol. i. pp. 209-215.
