Note 16 — Chapter II · GENERAL REMARKS ON THE EARLIER PHILOSOPHERS — GROWTH OF DIALECTIC — ZENO AND GORGIAS.

Aristotel. Metaphys. B. 4, p. 1001, b. 7. ἔτι εἰ ἀδιαίρετον αὐτὸ τὸ ἕν, κατὰ μὲν τὸ Ζήνωνος ἀξίωμα, οὐθὲν ἂν εἴη.

ὃ γὰρ μήτε προστιθέμενον μητὲ ἀφαιρούμενον ποιεῖ τι μεῖζον μηδὲ ἕλαττον, οὔ φησιν εἶναι τοῦτο τῶν ὄντων, ὡς δῆλον ὅτι ὄντος μεγέθους τοῦ ὄντος.

Seneca (Epistol. 88) and Alexander of Aphrodisias (see the passages of Themistius and Simplikius cited by Brandis, Handbuch Philos. i. p. 412-416) conceive Zeno as having dissented from Parmenides, and as having denied the existence, not only of τὰ πολλὰ, but also of τὸ ἕν. But Zeno seems to have adhered to Parmenides; and to have denied the existence of τὸ ἕν, only upon the hypothesis opposed to Parmenides — namely, that τὰ πολλὰ existed. Zeno argued thus:—Assuming that the Real or Absolute is essentially divisible and discontinuous, divisibility must be pushed to infinity, so that you never arrive at any ultimatum, or any real unit (ἀκριβῶς ἕν). If you admit τὰ πολλὰ, you renounce τὸ ἕν. The reasoning of Zeno, as far as we know it, is nearly all directed against the hypothesis of Entia plura discontinua. Tennemann (Gesch. Philos. i. 4, p. 205) thinks that the reasoning of Zeno is directed against the world of sense: in which I cannot agree with him.