Authors
Mark Zelcer
Queensborough Community College (CUNY)
Abstract
We state the defining characteristic of mathematics as a type of symmetry where one can change the connotation of a mathematical statement in a certain way when the statement's truth value remains the same. This view of mathematics as satisfying such symmetry places mathematics as comparable with modern views of physics and science where, over the past century, symmetry also plays a defining role. We explore the very nature of mathematics and its relationship with natural science from this perspective. This point of view helps clarify some standard problems in the philosophy of mathematics.
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References found in this work BETA

What Numbers Could Not Be.Paul Benacerraf - 1965 - Philosophical Review 74 (1):47-73.
The Unreasonable Effectiveness of Mathematics in the Natural Sciences.Eugene Wigner - 1960 - Communications in Pure and Applied Mathematics 13:1-14.
Reifying Mathematics? Prediction and Symmetry Classification.Sorin Bangu - 2008 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 39 (2):239-258.
The Partial Unification of Domains, Hybrids, and the Growth of Mathematical Knowledge.Emily R. Grosholz - 2000 - In Emily Grosholz & Herbert Breger (eds.), The Growth of Mathematical Knowledge. Kluwer Academic Publishers. pp. 81--91.
A Cause for Concern: Standard Abstracta and Causation.Jody Azzouni - 2008 - Philosophia Mathematica 16 (3):397-401.

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Citations of this work BETA

The Role of Symmetry in Mathematics.Noson S. Yanofsky & Mark Zelcer - 2017 - Foundations of Science 22 (3):495-515.

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