Abstract
In a recent interesting discussion of Zeno's paradox of the arrow,l Jonathan Lear produces a reconstruction of the paradox which, he argues, the differential 'calculus is impotent to solve.'2 In opposition to the received wisdom (and a good deal of contemporary analysis), Lear maintains that Aristotle's response to the paradox is to the point. I find Lear's arguments for both theses compelling, given the assumptions he makes concerning what the 'modern concepts of the calculus' are. However, in the present paper I suggest that the 'conceptual equipment' supplied by a recent grounding of the differential and integral calculi in non-standard analysis is relevant to resolving the paradox as formulated by Lear. My second thesis is really more a 'tentative suggestion': perhaps some of the conceptual equipment of the nonstandard foundation of calculus, in particular, the concept of 'nontrivial divisible infinitesimals,' can be extracted from several difficult and much controverted passages pertaining to Chrysippean (or 'Stoic') doctrines of time, space, and motion.
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