Article

Aristotle on the Infinite

Ursula Coope

in The Oxford Handbook of Aristotle

Published in print August 2012 | ISBN: 9780195187489
Published online November 2012 | | DOI: http://dx.doi.org/10.1093/oxfordhb/9780195187489.013.0011

Series: Oxford Handbooks in Philosophy

 Aristotle on the Infinite

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In Physics, Aristotle starts his positive account of the infinite by raising a problem: “[I]f one supposes it not to exist, many impossible things result, and equally if one supposes it to exist.” His views on time, extended magnitudes, and number imply that there must be some sense in which the infinite exists, for he holds that time has no beginning or end, magnitudes are infinitely divisible, and there is no highest number. In Aristotle's view, a plurality cannot escape having bounds if all of its members exist at once. Two interesting, and contrasting, interpretations of Aristotle's account can be found in the work of Jaako Hintikka and of Jonathan Lear. Hintikka tries to explain the sense in which the infinite is actually, and the sense in which its being is like the being of a day or a contest. Lear focuses on the sense in which the infinite is only potential, and emphasizes that an infinite, unlike a day or a contest, is always incomplete.

Keywords: Aristotle; infinite; Physics; time; magnitudes; plurality; Jaako Hintikka; Jonathan Lear; potential; day

Article.  10944 words. 

Subjects: Philosophy ; Classical Philosophy ; Metaphysics ; Philosophy of Mathematics and Logic

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