Aristotle on the subject matter of geometry

Phronesis 54 (3):239-260 (2009)
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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.

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Richard Pettigrew
University of Bristol

References found in this work

Aristotle’s Metaphysics: Books M and N.Julia Annas - 1976 - Philosophical Review 87 (3):479-485.
Aristotle on Geometrical Objects.Ian Mueller - 1970 - Archiv für Geschichte der Philosophie 52 (2):156-171.
XII*—Aristotelian Infinity.Jonathan Lear - 1980 - Proceedings of the Aristotelian Society 80 (1):187-210.
Aristotle on Mathematical Objects.Edward Hussey - 1991 - Apeiron 24 (4):105 - 133.

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