From Chapter VIII., The Younger Eleatics
In reality, this writing is a sort of reinforcement for the argument of Parmenides against those who try to turn it into ridicule on the ground that, if reality is one, the argument becomes involved in many absurdities and contradictions. This writing argues against those who uphold a Many, and gives them back as good and better than they gave; its aim is to show that their assumption of multiplicity will be involved in still more absurdities than the assumption of unity, if it is sufficiently worked out.
The method of Zeno was, in fact, to take one of his adversaries' fundamental postulates and deduce from it two contradictory conclusions.20 This is what Aristotle meant by calling him the inventor of dialectic, which is just the art of arguing, not from true premisses, but from premisses admitted by the other side. The theory of Parmenides had led to conclusions which contradicted the evidence of the senses, and Zeno's object was not to bring fresh proofs of the theory itself, but simply to show that his opponents' view led to contradictions of a precisely similar nature.
18. Cf. Diog. ix. 25 (R. P. 130).
19. Plato, Parm. 128 c (R. P. 130 d). If historians of philosophy had started from this careful statement of Plato's, instead of from Aristotle's loose references, they would not have failed to understand his arguments, as they all did before Tannery.
20. The technical terms used in Plato's Parmenides seem to be as old as Zeno himself. The ὑπόθεσις is the provisional assumption of the truth of a certain statement, and takes the form εἰ πολλά ἐστι or the like. The word does not mean the assumption of something as a foundation, but the setting before one's self of a statement as a problem to be solved (Ionic ὑποθέσθαι, Attic προθέσθαι). If the conclusions (τά συμβαίνοντα) which necessarily follow from the ὑπόθεσις are impossible, the ὑπόθεσις is "destroyed" (cf. Plato, Rep. 533 c 8, τὰς ὑποθέσεις ἀναιροῦσα). The author of the Περὶ ἀρχαίης ἰατρικῆς knows the word ὑπόθεσις in a similar sense.
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