Eleatic Metaphysics in Plato's Parmenides: Zeno's Puzzle of Plurality

If you were to assert that there are many beings in the world—many houses, trees, people, objects, and so on—there is an obvious sense in which this would be true. What is harder to see, however, is the sense in which this is false. The discrete intelligibility and integrity of individual things obscure the deeper sense in which being and intelligibility are prior to individuals, which is a basic insight motivating Socrates' so-called theory of forms. In this article I argue that Zeno's puzzle of plurality in the Parmenides is a device for turning attention away from individual beings toward their being and intelligibility and that this metaphysical turn of Zeno's radicalizes a Socratic insight into the "mixing" of particulars. The first section of this article shows that the historical Zeno was involved in a project of critiquing the incoherent but unavoidable ways we have of describing our world. It is important to see this project of Zeno's as profoundly Eleatic in character and consistent with the "study of the one" outlined by Socrates in book 7 of the Republic. In the second part of the article this parallel between Zeno's and Socrates' "study of the one" is used to interpret the implications of Zeno's puzzle of plurality in the Parmenides. I conclude by proposing a metaphysics significantly different from the one normally attributed to Plato.

Zeno's Puzzles

I

The main conversation of the Parmenides begins just after Zeno has finished reading aloud from a treatise he wrote long ago in his youth. Socrates opens by asking for a clarification of Zeno's puzzle of plurality:¹ "If beings [τὰ ὄντα] are many [πολλά], it is necessary that they be both 'likes' [ὅμοια] and 'unlikes' [ἀνόμοια], but that this is impossible because 'likes' [ὅμοια] are not able to be unlikes [ἀνόμοια], and conversely 'unlikes' are not able to be likes?" (Parmenides, 127e1–3, my translation).² Zeno accepts this characterization of his treatise. Socrates concludes that Zeno is saying that there are not "many" or that there is no "plurality" (οὐ πολλά ἐστι [Parmenides, 127e10]). Many interpreters follow Socrates and take the hypothesis as a straightforward reductio ad absurdum. If beings are many, all particulars are both like and unlike.³ This implication is absurd, for like cannot be unlike. If "like" is even a little bit intelligible, it must at least be not unlike. If the very thing toward which we point to manifest likeness turns out to manifest unlikeness, then we make nonsense of the world. Black is no more black than it is white. Socrates attributes to Zeno the conclusion that the thesis "there are many beings" is absurd.

Interpreters generally accuse Zeno of either sophistry or incompetence in his attempt to defend the Parmenidean thesis "all is one." Some say Zeno mistakes relational predicates for essential characters, and they point out that what something is in relation to something else is contextually dependent and therefore not essential to the thing, as it seems Zeno must have intended.⁴ In Francis Cornford's (1939, 67) view, Plato considered Zeno a mere sophist who did not take his own arguments seriously. Similarly, Jonathan Barnes takes Zeno to have no serious metaphysical purpose; in Barnes's (1982, 186) view, Zeno is a clever, but not profound, thinker just as likely to produce trifling fallacies as he was to produce meaningful insight. In other cases where Zeno is not dismissed, he is tolerated as someone who wishes to inherit the mantle of Eleatic philosophy but falls short.⁵

Zeno's puzzles have a double meaning, one fitting the standard interpretation of Zeno as the young defender of the Parmenidean thesis and another fitting the more subtle and mature Zeno whom we see in the Parmenides. Zeno was once the young word-warrior who took offense at those whom in his view slighted Parmenides, but the Zeno who appears in the Parmenides is a serious person who has traveled to Athens to meet in private with other talented philosophers. This more mature Zeno is not interested in making or defending a position...