these discourses were subdivided into sections, each dealing with some one presupposition of his adversaries.[1] We owe the preservation of Zeno's arguments on the one and many to Simplicius.[2] Those relating to motion have been preserved by Aristotle;[3] but he has restated them in his own language.
157.Dialectic. Aristotle in his Sophist[4] called Zeno the inventor of dialectic, and that, no doubt, is substantially true, though the beginnings at least of this method of arguing were contemporary with the foundation of the Eleatic school. Plato[5] gives us a spirited account of the style and purpose of Zeno's book, which he puts into his own mouth:
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.[6] This is what Aristotle meant
- ↑ Plato, Parm. 127 d. Plato speaks of the first ὑπόθεσις of the first λόγος, which shows that the book was really divided into separate sections. Proclus (in loc.) says there were forty of these λόγοι altogether.
- ↑ Simplicius expressly says in one place (p. 140, 30; R. P. 133) that he is quoting κατὰ λέξιν. I see no reason to doubt this, as the Academy would certainly have a copy of the work. In that case, the use of the Attic dialect by Zeno is significant.
- ↑ Arist. Phys. Z, 9. 239 b 9 sqq.
- ↑ Cf. Diog. ix. 25 (R. P. 130).
- ↑ 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.
- ↑ 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
