Chapter

Mathematics and Its Philosophy

Stewart Shapiro

in Philosophy of Mathematics

Published in print October 2000 | ISBN: 9780195139303
Published online November 2003 | e-ISBN: 9780199833658 | DOI: http://dx.doi.org/10.1093/0195139305.003.0002
 Mathematics and Its Philosophy

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This chapter deals with the relationship between the practice of mathematics and the philosophy of mathematics. The philosopher of mathematics is, or should be, concerned with mathematics as it is practiced, and so I demur from “philosophy first”, the view that philosophical considerations should set the stage for and determine the proper practice of mathematics. The rejected orientation is sometimes called “first philosophy”. The other extreme, “philosophy last if at all”, is also unhealthy. Mathematics and its philosophy are autonomous disciplines, each with its own questions and problems, and neither dominating the other. Ideally, there should be fruitful interactions between them. The perspective is compared and contrasted with Quine's and Maddy's naturalism.

Keywords: Maddy; mathematics; naturalism; philosophy; philosophy of mathematics; Quine

Chapter.  8059 words. 

Subjects: Philosophy of Mathematics and Logic

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