Journal Article

Mathematical Explanation in Science

Alan Baker

in The British Journal for the Philosophy of Science

Published on behalf of British Society for the Philosophy of Science

Volume 60, issue 3, pages 611-633
Published in print September 2009 | ISSN: 0007-0882
Published online June 2009 | e-ISSN: 1464-3537 | DOI:
Mathematical Explanation in Science

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  • Philosophy of Science
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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.

Introduction: Mathematical Explanation

Indispensability and Explanation

Is the Mathematics Indispensable to the Explanation? 3.1

Object-level arbitrariness


Concept-level arbitrariness


Theory-level arbitrariness

Is the Explanandum ‘Purely Physical’?

Is the Mathematics Explanatory in Its Own Right?

Does Inference to the Best Explanation Apply to Mathematics? 6.1

Leng's first argument


Leng's second argument


Leng's third argument


Journal Article.  9186 words. 

Subjects: Philosophy of Science ; Science and Mathematics

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