Aristotle on the Subject Matter of Geometry

Author: Pettigrew, Richard¹

Source: Phronesis: A Journal for Ancient Philosophy, Volume 54, Number 3, 2009 , pp. 239-260(22)

Publisher: BRILL

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Abstract:

I offer a new interpretation of Aristotle's philosophy of geometry, which he presents in greatest detail in Metaphysics M 3. On my interpretation, Aristotle holds that the points, lines, planes, and solids of geometry belong to the sensible realm, but not in a straightforward way. Rather, by considering Aristotle's second attempt to solve Zeno's Runner Paradox in Book VIII of the Physics, I explain how such objects exist in the sensibles in a special way. I conclude by considering the passages that lead Jonathan Lear to his fictionalist reading of Met. M3,1 and I argue that Aristotle is here describing useful heuristics for the teaching of geometry; he is not pronouncing on the meaning of mathematical talk.

Keywords: ARISTOTLE; GEOMETRY; POTENTIALITY; METAPHYSICS; INTERMEDIATES

Document Type: Research article

DOI: 10.1163/156852809X441340

Affiliations: 1: Department of Philosophy, University of Bristol, 9 Woodland Road, Bristol BS8 1TB, UK;, Email: Richard.Pettigrew@bristol.ac.uk

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