Aristotle's Philosophy of Mathematics

David Bostock

in The Oxford Handbook of Aristotle

Published in print August 2012 | ISBN: 9780195187489
Published online November 2012 | | DOI:

Series: Oxford Handbooks in Philosophy

Aristotle's Philosophy of Mathematics

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  • Classical Philosophy
  • Philosophy of Mathematics and Logic



Much of Aristotle's thought developed in reaction to Plato's views, and this is certainly true of his philosophy of mathematics. To judge from his dialogue, the Meno, the first thing that struck Plato as an interesting and important feature of mathematics was its epistemology: in this subject we can apparently just “draw knowledge out of ourselves.” Aristotle certainly thinks that Plato was wrong to “separate” the objects of mathematics from the familiar objects that we experience in this world. His main arguments on this point are in Chapter 2 of Book XIII of the Metaphysics. There are three distinct lines of argument: The first concerns the objects of geometry (that is, points, lines, planes, and solids); the second deals with the Platonist principles which are applied to arithmetic and geometry; the third is about substance as living things, especially animals, and perhaps man in particular. In addition to the above, this article also examines Aristotle's treatment of infinity.

Keywords: Aristotle; mathematics; Plato; philosophy; geometry; Metaphysics; arithmetic; substance; infinity; epistemology

Article.  14868 words. 

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

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