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The British Journal for the Philosophy of Science Advance Access published online on June 30, 2009
The British Journal for the Philosophy of Science, doi:10.1093/bjps/axp025
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© The Author (2009). Published by Oxford University Press. For Permissions, please email: journals.permissions@oxfordjournals.org

Mathematical Explanation in Science

Alan Baker

Department of Philosophy, Swarthmore College, Swarthmore, PA 19081, USA abaker1{at}swarthmore.edu


  Abstract

Does mathematics ever play an explanatory role in science? If so then this opens the way for scientific realists to argue for the existence of mathematical entities using inference to the best explanation. Elsewhere I have argued, using a case study involving the prime-numbered life cycles of periodical cicadas, that there are examples of indispensable mathematical explanations of purely physical phenomena. In this paper I respond to objections to this claim that have been made by various philosophers, and I discuss potential future directions of research for each side in the debate over the existence of abstract mathematical objects.

  1. Introduction: Mathematical Explanation
  2. Indispensability and Explanation
  3. Is the Mathematics Indispensable to the Explanation?
    3.1 Object-level arbitrariness
    3.2 Concept-level arbitrariness
    3.3 Theory-level arbitrariness

  4. Is the Explanandum ‘Purely Physical’?
  5. Is the Mathematics Explanatory in Its Own Right?
  6. Does Inference to the Best Explanation Apply to Mathematics?
    6.1 Leng's first argument
    6.2 Leng's second argument
    6.3 Leng's third argument

  7. Conclusions


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