History of Philosophy Quarterly 25 (3):187 - 201 (2008)

Jeanne Peijnenburg
University of Groningen
It is widely held that the paradox of Achilles and the Tortoise, introduced by Zeno of Elea around 460 B.C., was solved by mathematical advances in the nineteenth century. The techniques of Weierstrass, Dedekind and Cantor made it clear, according to this view, that Achilles’ difficulty in traversing an infinite number of intervals while trying to catch up with the tortoise does not involve a contradiction, let alone a logical absurdity. Yet ever since the nineteenth century there have been dissidents claiming that the apparatus of Weierstrass et al. has not resolved the paradox, and that serious problems remain. It seems that these claims have received unexpected support from recent developments in mathematical physics. This support has however remained largely unnoticed by historians of philosophy, presumably because the relevant debates are cast in mathematical-technical terms that are only accessible to people with the relevant training. That is unfortunate, since the debates in question might well profit from input by philosophers in general and historians of philosophy in particular. Below we will first recall the Achilles paradox, and describe the way in which nineteenth century mathematics supposedly solved it. Then we discuss recent work that contests this solution, reiterating the dissident dogma that no mathematical approach whatsoever can even come close to solving the original Achilles. We shall argue that this dissatisfaction with a mathematical solution is inadequate as it stands, but that it can perhaps be reformulated in the light of new developments in mathematical physics.
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References found in this work BETA

A Beautiful Supertask.Jon Perez Laraudogoitia - 1996 - Mind 105 (417):81-83.
Losing Energy in Classical, Relativistic and Quantum Mechanics.David Atkinson - 2006 - Studies in History and Philosophy of Modern Physics 38 (1):170-180.
Classical Particle Dynamics, Indeterminism and a Supertask.Jon Pérez Laraudogoitia - 1997 - British Journal for the Philosophy of Science 48 (1):49-54.
Losing Energy in Classical, Relativistic and Quantum Mechanics.David Atkinson - 2007 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 38 (1):170-180.

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Supertasks.Jon Pérez Laraudogoitia - 2008 - Stanford Encyclopedia of Philosophy.

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