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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Keywords | POTENTIALITY METAPHYSICS INTERMEDIATES ARISTOTLE GEOMETRY |
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DOI | 10.1163/156852809x441340 |
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References found in this work BETA
The Foundations of Mathematics in the Theory of Sets.John P. Mayberry - 2000 - Cambridge University Press.
Aristotle on Geometrical Objects.Ian Mueller - 1970 - Archiv für Geschichte der Philosophie 52 (2):156-171.
J.P. Mayberry: The Foundations of Mathematics in the Theory of Sets. [REVIEW]W. W. Tait - 2002 - Bulletin of Symbolic Logic 8 (3):424-426.
XII—Aristotelian Infinity.Jonathan Lear - 1980 - Proceedings of the Aristotelian Society 80 (1):187-210.
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Citations of this work BETA
Plato's Problem: An Introduction to Mathematical Platonism.Marco Panza & Andrea Sereni - 2013 - London and Basingstoke: Palgrave-Macmillan.
New Powers for Dispositionalism.Giacomo Giannini - 2020 - Synthese (ST: New Foundations for Disposit):1-30.
Geometrical Objects as Properties of Sensibles: Aristotle’s Philosophy of Geometry.Emily Katz - 2019 - Phronesis 64 (4):465-513.
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