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Mathematics and Reality

Published online by Cambridge University Press:  01 April 2022

Stewart Shapiro
Stewart Shapiro*
Affiliation:
Department of Philosophy, Ohio State University of Newark
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Abstract

The subject of this paper is the philosophical problem of accounting for the relationship between mathematics and non-mathematical reality. The first section, devoted to the importance of the problem, suggests that many of the reasons for engaging in philosophy at all make an account of the relationship between mathematics and reality a priority, not only in philosophy of mathematics and philosophy of science, but also in general epistemology/metaphysics. This is followed by a (rather brief) survey of the major, traditional philosophies of mathematics indicating how each is prepared to deal with the present problem. It is shown that (the standard formulations of) some views seem to deny outright that there is a relationship between mathematics and any non-mathematical reality; such philosophies are clearly unacceptable. Other views leave the relationship rather mysterious and, thus, are incomplete at best. The final, more speculative section provides the direction of a positive account. A structuralist philosophy of mathematics is outlined and it is proposed that mathematics applies to reality though the discovery of mathematical structures underlying the non-mathematical universe.

Type
Research Article
Information
Philosophy of Science , Volume 50 , Issue 4 , December 1983 , pp. 523 - 548
Copyright
Copyright © Philosophy of Science Association 1983

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Footnotes

†

I would like to thank Mike Resnik, John Corcoran, Robert Kraut, Mark Steiner, and Bill Lycan for many useful comments on previous versions of this paper and for encouragement to continue the project. I would also like to thank, as groups, the members of the Kenyon Symposium, the Ohio State University Philosophy Colloquium, the Buffalo Logic Colloquium, and the Hebrew University Philosophy Colloquium for devoting a session to this project and for providing many thoughtful and useful comments.

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