A discrete solution for the paradox of Achilles an

Authors: Vincent Ardourel

Publish Date: 2015/02/24

Volume: 192, Issue: 9, Pages: 2843-2861

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Abstract

In this paper I present a discrete solution for the paradox of Achilles and the tortoise I argue that Achilles overtakes the tortoise after a finite number of steps of Zeno’s argument if time is represented as discrete I then answer two objections that could be made against this solution First I argue that the discrete solution is not an ad hoc solution It is embedded in a discrete formulation of classical mechanics Second I show that the discrete solution cannot be falsified experimentallyI thank the anonymous reviewers for their helpful comments and their contribution to enhancing the quality of this paper This work is a part of my PhD dissertation It has been written while at the IHPST UMR 8590 CNRS Université Paris 1 PanthéonSorbonne ENS and at SND FRE 3593 CNRS Université ParisSorbonne I would like to thank my supervisors Anouk Barberousse and Jacques Dubucs for their encouragements and their insightful comments Thanks also to people of the IHPST for their remarks which helped improve this paper Finally I am particularly grateful to my friend Clément Ruef for our discussions on the paper

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