Mathematics and reality

Philosophy of Science 50 (4):523-548 (1983)
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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.

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Stewart Shapiro
Ohio State University

Citations of this work

Models and fiction.Roman Frigg - 2010 - Synthese 172 (2):251-268.
Models and fictions in science.Peter Godfrey-Smith - 2009 - Philosophical Studies 143 (1):101 - 116.

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References found in this work

What numbers could not be.Paul Benacerraf - 1965 - Philosophical Review 74 (1):47-73.
Language, Truth, and Logic.A. J. Ayer - 1936 - Philosophy 23 (85):173-176.
Truth and Other Enigmas.Michael Dummett - 1980 - Revue Philosophique de la France Et de l'Etranger 170 (1):62-65.

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