Several New Notions Introduced and Exploited, but not Made Explicit, by Zeno (of Elea)

Resumen

That Zeno availed himself of a number of previously unfamiliar (and often unknown) and very sophisticated notions, such as that of relative speed, a ten thousandth, infinite division and so on—almost a dozen mostly innovative notions—is a point one simply cannot deny. Yet, so far as I know, this feature of Zeno’s remains has never been highlighted and studied as they probably deserve with only one notable exception: a seminal paper by Cherubin-Mannucci 2011.

Let me state first some facts. That the paradox of the Millet Seed exploits the notion of to murioston (“the/a ten thousandth”) is clearly assumed by our main source (Simplicius), an adjective noun that, while murios as a notion is already at use in the Homeric poems, is totally unattested before; it is therefore unlikely that it had some circulation before Zeno. Moreover, this notion plays a key role; in fact, this paradox, left without to murioston, would simply collapse. But consider the Dichtomy (‘division in two parts’) paradox: what would remain, were the notion of infinite division not clearly at work, thus not yet clearly available to Zeno? Or the Stadium: what would remain, were the notions of relative motion and that of onkoi (‘masses’) not yet clearly available at least to him? To devise a Stadium without being able to rely upon them would have been extremely difficult!

This is the starting point of the paper, which is meant to account as clearly as I can for so fantastic a repository of totally unknown notions. It follows than, in my opinion, no professional account of Zeno’s paradoxes is conceivable without focusing one’s attention upon what ostensibly was a total novelty, and a new beginning.

A notable feature of these pages is the attention paid to what Gorgias and Plato knew about the Space paradox (sources usually excluded from the main collections).