pluralists, and then the criticism of Zeno. This, at any rate, seems to have been the view Aristotle took of the historical development.[1]
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,[2] 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."[3] 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.
160.The Fragments The fragments of Zeno himself also show that this was his line of argument. I give them according to the arrangement of Diels.
(1)
If what is had no magnitude, it would not even be. . . . But, if it is, each one must have a certain magnitude and a certain thickness, and must be at a certain distance from another, and the same may be said of what is in front of it; for it, too, will have magnitude, and something will be in front of it.[4] It is all the same to say this once and to say it always; for no such part of it
- ↑ Arist. Phys. A, 3. 187 a 1 (R. P: 134 b). See below, § 173.
- ↑ Simpl. Phys. p. 138, 32 (R. P. 134 a).
- ↑ 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).
- ↑ I formerly rendered "the same may be said of what surpasses it in smallness; for it too will have magnitude, and something will surpass it in smallness." This is Tannery's rendering, but I now agree with Diels in thinking that ἀπέχειν refers to μέγεθος and προέχειν to πάχος. Zeno is showing that the Pythagorean point must have three dimensions.
