Early Greek Philosophy by John Burnet, with Burnet's notes
158. Zeno and Pythagoreanism 160. The Fragments

From Chapter VIII., The Younger Eleatics

159. What Is the Unit?
The polemic of Zeno is clearly directed in the first instance against a certain view of the unit. Eudemos, in his Physics,26 quoted from him the saying that "if any one could tell him what the unit was, he would be able to say what things are." The commentary of Alexander on this, preserved by Simplicius, is quite satisfactory. "As Eudemos relates," he says, "Zeno the disciple of Parmenides tried to show that it was impossible that things could be a many, seeing that there was no unit in things, whereas 'many' means a number of units."27 Here we have a clear reference to the Pythagorean view that everything may be reduced to a sum of units, which is what Zeno denied.

Burnet's Notes


26. Simpl. Phys. p. 138, 32 (R. P. 134 a).

27. Simpl. Phys. p. 99, 13, ὡς γὰρ ἱστορεῖ, φησίν (Ἀλέξανδρος), Εὔδημος, Ζήνων ὁ Παρμενίδου γνώριμος ἐπειρᾶτο δεικνύναι ὅτι μὴ οἷόν τε τὰ ὄντα πολλὰ εἶναι τῷ μηδὲν εἶναι ἐν τοῖς οὖσιν ἕν, τὰ δὲ πολλὰ πλῆθος εἶναι ἑνάδων. This is the meaning of the statement that Zeno ἀνῄρει τὸ ἕν which is not Alexander's (as implied in R. P. 134 a), but goes back to no less an authority than Eudemos. It must be read in connexion with the words τὴν γὰρ στιγμὴν ὡς τὸ ἓν λέγει (Simpl. Phys. p. 99. 11).

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