The Role of Symmetry in Mathematics

Foundations of Science 22 (3):495-515 (2017)
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Abstract

Over the past few decades the notion of symmetry has played a major role in physics and in the philosophy of physics. Philosophers have used symmetry to discuss the ontology and seeming objectivity of the laws of physics. We introduce several notions of symmetry in mathematics and explain how they can also be used in resolving different problems in the philosophy of mathematics. We use symmetry to discuss the objectivity of mathematics, the role of mathematical objects, the unreasonable effectiveness of mathematics and the relationship of mathematics to physics.

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Mark Zelcer
Queensborough Community College (CUNY)

References found in this work

Mathematical truth.Paul Benacerraf - 1973 - Journal of Philosophy 70 (19):661-679.
What numbers could not be.Paul Benacerraf - 1965 - Philosophical Review 74 (1):47-73.
Laws and Symmetry.Bas C. Van Fraassen - 1989 - Revue Philosophique de la France Et de l'Etranger 182 (3):327-329.
The unreasonable effectiveness of mathematics in the natural sciences.Eugene Wigner - 1960 - Communications in Pure and Applied Mathematics 13:1-14.

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