Journal Article

On the Explanatory Role of Mathematics in Empirical Science

Robert W. Batterman

in The British Journal for the Philosophy of Science

Published on behalf of British Society for the Philosophy of Science

Volume 61, issue 1, pages 1-25
Published in print March 2010 | ISSN: 0007-0882
Published online June 2009 | e-ISSN: 1464-3537 | DOI: http://dx.doi.org/10.1093/bjps/axp018
On the Explanatory Role of Mathematics in Empirical Science

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This paper examines contemporary attempts to explicate the explanatory role of mathematics in the physical sciences. Most such approaches involve developing so-called mapping accounts of the relationships between the physical world and mathematical structures. The paper argues that the use of idealizations in physical theorizing poses serious difficulties for such mapping accounts. A new approach to the applicability of mathematics is proposed.

Introduction

Mathematical Explanations I: Entities

Mathematical Explanations II: Operations

Mapping Accounts: Strengths

Mapping Accounts: Idealizations 5.1

Pincock and matching models

5.2

Bueno, Colyvan, and the inferential conception

Mapping Accounts: Limitations

Suggestions for a New Approach

Conclusion

Journal Article.  10040 words.  Illustrated.

Subjects: Philosophy of Science ; Science and Mathematics

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