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Philosophy of MathematicsStructure and Ontology$
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Stewart Shapiro

Print publication date: 2000

Print ISBN-13: 9780195139303

Published to Oxford Scholarship Online: November 2003

DOI: 10.1093/0195139305.001.0001

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Mathematics and Its Philosophy

Mathematics and Its Philosophy

(p.21) 1 Mathematics and Its Philosophy
Philosophy of Mathematics

Stewart Shapiro (Contributor Webpage)

Oxford University Press

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

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