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
Bristol University

Citations of this work

New powers for Dispositionalism.Giacomo Giannini - 2022 - Synthese 200 (384):1-30.
Plato's Problem: An Introduction to Mathematical Platonism.Marco Panza & Andrea Sereni - 2013 - London and Basingstoke: Palgrave-Macmillan. Edited by Andrea Sereni & Marco Panza.
Aristotle's Theory of Abstraction.Allan Bäck - 2014 - Cham, Switzerland: Springer.

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