Aristotle on the subject matter of geometry

Phronesis 54 (3):239-260 (2009)
  Copy   BIBTEX

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.

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 93,098

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Similar books and articles

Analytics

Added to PP
2009-06-27

Downloads
177 (#114,381)

6 months
28 (#112,168)

Historical graph of downloads
How can I increase my downloads?

Author's Profile

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.

View all 8 references / Add more references