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The British Journal for the Philosophy of Science Advance Access published online on June 17, 2009
The British Journal for the Philosophy of Science, doi:10.1093/bjps/axp018
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© The Author (2009). Published by Oxford University Press. For Permissions, please email: journals.permissions@oxfordjournals.org

On the Explanatory Role of Mathematics in Empirical Science

Robert W. Batterman

University of Western Ontario, Department of Philosophy, Talbot College, London, Ontario N6A 3K7, Canada rbatterm{at}uwo.ca


  Abstract

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.

  1. Introduction
  2. Mathematical Explanations I: Entities
  3. Mathematical Explanations II: Operations
  4. Mapping Accounts: Strengths
  5. Mapping Accounts: Idealizations
    5.1 Pincock and matching models
    5.2 Bueno, Colyvan, and the inferential conception

  6. Mapping Accounts: Limitations
  7. Suggestions for a New Approach
  8. Conclusion


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