Aristotelian finitism

Synthese 192 (8):2345-2360 (2015)

Abstract
It is widely known that Aristotle rules out the existence of actual infinities but allows for potential infinities. However, precisely why Aristotle should deny the existence of actual infinities remains somewhat obscure and has received relatively little attention in the secondary literature. In this paper I investigate the motivations of Aristotle’s finitism and offer a careful examination of some of the arguments considered by Aristotle both in favour of and against the existence of actual infinities. I argue that Aristotle has good reason to resist the traditional arguments offered in favour of the existence of the infinite and that, while there is a lacuna in his own ‘logical’ arguments against actual infinities, his arguments against the existence of infinite magnitude and number are valid and more well grounded than commonly supposed.
Keywords Aristotle  Aristotelian commentators  Infinity  Mathematics  Metaphysics  Actual Infinity  Potential Infinity  Infinite Regress
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Reprint years 2015
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DOI 10.1007/s11229-015-0827-9
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References found in this work BETA

The Complete Works of Aristotle. The Revised Oxford Translation.Jonathan Barnes - 1986 - Revue Philosophique de la France Et de l'Etranger 176 (4):493-494.
The Foundations of Mathematics in the Theory of Sets.J. P. Mayberry - 2002 - Bulletin of Symbolic Logic 8 (3):424-426.

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