Note 26 — Chapter II · GENERAL REMARKS ON THE EARLIER PHILOSOPHERS — GROWTH OF DIALECTIC — ZENO AND GORGIAS.

The scope of the Zenonian dialectic, as I have here described it, is set forth clearly by Plato, in his Parmenides, c. 3-6, p. 127, 128. Πῶς ὦ Ζήνων, τοῦτο λέγεις; εἰ πολλά ἐστι τὰ ὄντα, ὡς ἄρα δεῖ αὐτὰ ὅμοιά τε εἶναι καὶ ἀνόμοια, τοῦτο δὲ δὴ ἀδύνατον. — Οὐκοῦν εἰ ἀδύνατον τά τε ἀνόμοια ὅμοια εἶναι καὶ τὰ ὅμοια ἀνόμοια, ἀδύνατον δὴ καὶ πολλὰ εἶναι; εἰ γὰρ πολλὰ εἴη, πάσχοι ἂν τὰ ἀδύνατα. Ἆρα τοῦτό ἐστιν ὃ βούλονταί σου οἱ λόγοι; οὐκ ἀλλο τι ἢ διαμάχεσθαι παρὰ πάντα τὰ λεγόμενα, ὡς οὐ πολλά ἐστιν; Again, p. 128 D. Ἀντιλέγει οὖν τοῦτο τὸ γράμμα πρὸς τοὺς τα πολλὰ λέγοντας, καὶ ἀνταποδίδωσι ταῦτα καὶ πλείω, τοῦτο βουλόμενον δηλοῦν, ὡς ἔτι γελοιότερα πάσχοι ἂν αὐτῶν ἡ ὑπόθεσις, ἡ εἰ πολλά ἐστιν — ἢ ἡ τοῦ ἓν εἶναι — εἴ τις ἱκανῶς ἐπεξίοι.

Here Plato evidently represents Zeno as merely proving that contradictory conclusions followed, if you assumed a given hypothesis; which hypothesis was thereby shown to be inadmissible. But Plato alludes to Zeno in another place (Phædrus, c. 97, p. 261) under the name of the Eleatic Palamedes, as “showing his art in speaking, by making the same things appear to the hearers like and unlike, one and many, at rest and in motion”. In this last passage, the impression produced by Zeno’s argumentation is brought to view, apart from the scope and purpose with which he employed it: which scope and purpose are indicated in the passage above cited from the Parmenides.

So also Isokrates (Encom. Helen. init.) Ζήνωνα, τὸν ταὐτὰ δυνατὰ καὶ πάλιν ἀδύνατα πειρώμενον ἀποφαίνειν.