Zeno's boêtheia tôi logôi : Thought problems about problems for thought

This essay addresses two central issues that continue to trouble interpretation of Zeno's paradoxes: 1) their solution, and 2) their place in the history of philosophy. I offer an account of Zeno's work as pointing to an inevitable paradox generated by our ways of thinking and speaking about things, especially about things as existing in the continua of space and time. In so doing, I connect Zeno's arguments to Parmenides' critique of "naming" in Fragment 8, an approach that I believe adds considerably to our understanding of both Zeno's puzzles and this enigmatic aspect of Parmenides' thought. The chief objection against all abstract reasonings is derived from the ideas of space and time; ideas, which, in common life and to a care- less view, are very clear and intelligible, but when they pass through the scrutiny of the profound sciences (and they are the chief object of these sciences) afford principles, which seem full of absurdity and contradiction. No priestly dogmas, invented on purpose to tame and subdue the rebellious reason of mankind, ever shocked common sense more than the doctrine of the infi nite divisibility of extension, with its consequences; as they are pompously displayed by all geome- tricians and metaphysicians, with a kind of triumph and exultation. A real quantity, infi nitely less than any fi nite quantity, containing quantities infi nitely less than itself, and so on in infi nitum; this is an edifi ce so bold and prodigious, that it is too weighty for any pretended demonstration to support, because it shocks the clearest and most natural principles of human reason.