Mathematical Explanation: A Pythagorean Proposal

British Journal for the Philosophy of Science (forthcoming)
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Mathematics appears to play an explanatory role in science. This, in turn, is thought to pave a way toward mathematical Platonism. A central challenge for mathematical Platonists, however, is to provide an account of how mathematical explanations work. I propose a property-based account: physical systems possess mathematical properties, which either guarantee the presence of other mathematical properties and, by extension, the physical states that possess them; or rule out other mathematical properties, and their associated physical states. I explain why Platonists should accept that physical systems have mathematical properties, and why a property based account is better than existing accounts of mathematical explanation. I close by considering whether nominalists can accept the view I propose here. I argue that they cannot.

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Sam Baron
Australian Catholic University

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References found in this work

On what grounds what.Jonathan Schaffer - 2009 - In David Manley, David J. Chalmers & Ryan Wasserman (eds.), Metametaphysics: New Essays on the Foundations of Ontology. Oxford University Press. pp. 347-383.
The Indispensability of Mathematics.Mark Colyvan - 2001 - Oxford, England: Oxford University Press.
Mathematics and Scientific Representation.Christopher Pincock - 2012 - Oxford and New York: Oxford University Press USA.
What Makes a Scientific Explanation Distinctively Mathematical?Marc Lange - 2013 - British Journal for the Philosophy of Science 64 (3):485-511.

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