Mathematics and Reality
Stewart Shapiro
Philosophy of Science
Vol. 50, No. 4 (Dec., 1983), pp. 523548
Published by: University of Chicago Press on behalf of the Philosophy of Science Association
Stable URL: http://www.jstor.org/stable/187555
Page Count: 26
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Abstract
The subject of this paper is the philosophical problem of accounting for the relationship between mathematics and nonmathematical 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 nonmathematical 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 nonmathematical universe.
Notes and References
This item contains 56 references.
[Footnotes]

2This reference contains 4 citations:
 Cohen (1971)
 Curry (1958)
 Robinson (1965).
 Resnik (1980, Chapter 2)

3Resnik (1980, pp. 6263)

4This reference contains 2 citations:
 Harman (1975)
 Dummett (1973).

5This reference contains 2 citations:
 Ayer (1946)
 Hempel (1945)

6Glymour (1980)

7This reference contains 4 citations:
 Gödel (1964)
 Gödel (1964)
 "the 'given' underlying mathematics is closely related to the abstract ele ments contained in our empirical ideas" (p. 272).
 Maddy (1980).

9Barbut 1970

10This reference contains 2 citations:
 Resnik (1981)
 (1982)

13Resnik (1980, Chapter 5)

14Resnik (1981).

15Kraut (1980)

16This reference contains 2 citations:
 Resnik (1982)
 note 7 above

17This reference contains 3 citations:
 Hartry Field (1980, pp. 3133)
 M. Resnik in Nous
 D. Malament in the Journal of Philosophy.

21Turnbull (1978)

22This reference contains 2 citations:
 Polya (1954)
 (1977)

24Nelson Goodman (1972)

25note 17 above

27Shapiro (1983)
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