[24] Aristotel. Physic. vi. 9, p. 239, b. 30. τρίτος ὁ νῦν ῥηθείς, ὅτι ἡ ὀϊστὸς φερομένη ἕστηκεν.
A fourth argument[25] was derived from the case of two equal bodies moved with equal velocity in opposite directions, and passing each other. If the body A B were at rest, the other body C D would move along the whole length of C D in two minutes. But if C D be itself moving with equal velocity in the opposite direction, A B will pass along the whole length of C D in half that time, or one minute. Hence Zeno infers that the motion of A B is nothing absolute, or belonging to the thing in itself — for if that were so, it would not be varied according to the movement of C D. It is no more than a phenomenal fact, relative to us and our comparison.
[25] See the illustration of this argument at some length by Simplikius, especially the citation from Eudêmus at the close of it — ap. Scholia ad Aristotel. p. 414, ed. Brandis.
This argument, so far as I can understand its bearing, is not deduced (as those preceding are) from the premisses of opponents: but rests upon premisses of its own, and is intended to prove that motion is only relative.
General result and purpose of the Zenonian Dialectic. Nothing is knowable except the relative.
These Zenonian reasonings are memorable as the earliest known manifestations of Grecian dialectic, and are probably equal in acuteness and ingenuity to anything which it ever produced. Their bearing is not always accurately conceived. Most of them are argumenta ad hominem: consequences contradictory and inadmissible, but shown to follow legitimately from a given hypothesis, and therefore serving to disprove the hypothesis itself.[26] The hypothesis was one relating to the real, absolute, or ultra-phenomenal, which Parmenides maintained to be Ens Unum Continuum, while his opponents affirmed it to be essentially multiple and discontinuous. Upon the hypothesis of Parmenides, the Real and Absolute, being a continuous One, was obviously inconsistent with the movement and variety of the phenomenal world: Parmenides himself recognised the contradiction of the two, and his opponents made it a ground for deriding his doctrine.[27] The counter-hypothesis, of the discontinuous many, appeared at first sight not to be open to the same objection: it seemed to be more in harmony with the facts of the phenomenal and relative world, and to afford an absolute basis for them to rest upon. Against this delusive appearance the dialectic of Zeno was directed. He retorted upon the opponents, and showed that if the hypothesis of the Unum Continuum led to absurd consequences, that of the discontinuous many was pregnant with deductions yet more absurd and contradictory. He exhibits in detail several of these contradictory deductions, with a view to refute the hypothesis from whence they flow; and to prove that, far from performing what it promises, it is worse than useless, as entangling us in contradictory conclusions. The result of his reasoning, implied rather than announced, is — That neither of the two hypotheses are of any avail to supply a real and absolute basis for the phenomenal and relative world: That the latter must rest upon its own evidence, and must be interpreted, in so far as it can be interpreted at all, by its own analogies.
[26] 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.
[27] Plato, Parmenides, p. 128 D.