Mathematical Explanation in Science

British Journal for the Philosophy of Science 60 (3):611-633 (2009)
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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.

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Alan Baker
Swarthmore College

Citations of this work

What is the Benacerraf Problem?Justin Clarke-Doane - 2017 - In Fabrice Pataut Jody Azzouni, Paul Benacerraf Justin Clarke-Doane, Jacques Dubucs S├ębastien Gandon, Brice Halimi Jon Perez Laraudogoitia, Mary Leng Ana Leon-Mejia, Antonio Leon-Sanchez Marco Panza, Fabrice Pataut Philippe de Rouilhan & Andrea Sereni Stuart Shapiro (eds.), New Perspectives on the Philosophy of Paul Benacerraf: Truth, Objects, Infinity (Fabrice Pataut, Editor). Springer.
What Makes a Scientific Explanation Distinctively Mathematical?Marc Lange - 2013 - British Journal for the Philosophy of Science 64 (3):485-511.
The Narrow Ontic Counterfactual Account of Distinctively Mathematical Explanation.Mark Povich - 2021 - British Journal for the Philosophy of Science 72 (2):511-543.

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References found in this work

There are no abstract objects.Cian Dorr - 2008 - In Theodore Sider, John Hawthorne & Dean W. Zimmerman (eds.), Contemporary Debates in Metaphysics. Blackwell.
The explanatory power of phase spaces.Aidan Lyon & Mark Colyvan - 2008 - Philosophia Mathematica 16 (2):227-243.

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