Chapter

Aristotle, Zeno, and the Potential Infinite

David Bostock

in Space, Time, Matter, and Form

Published in print February 2006 | ISBN: 9780199286867
Published online May 2006 | e-ISBN: 9780191603532 | DOI: http://dx.doi.org/10.1093/0199286868.003.0007

Series: Oxford Aristotle Studies Series

 Aristotle, Zeno, and the Potential Infinite

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This essay argues that Aristotle misdescribes his own position when he sums it up as the claim that infinity can only be potential and never actual. He readily accepts that there are processes which are actually infinite, that is, never-ending. But he denies that there can ever be a time when an infinite process has been completed. This means that he has to find some fault with Zeno’s well-known argument of Achilles and the tortoise, which he does by introducing the idea that points do not exist until they are ‘actualized’. It is argued that this idea, though ingenious and certainly appropriate to the problem, does not work out in the end.

Keywords: Aristotle; Physics; infinity; Zeno; infinite processes

Chapter.  6470 words.  Illustrated.

Subjects: Ancient Philosophy

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