Platonic Relations and Mathematical Explanations

Philosophical Quarterly 71 (3):623-644 (2021)
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Abstract

Some scientific explanations appear to turn on pure mathematical claims. The enhanced indispensability argument appeals to these ‘mathematical explanations’ in support of mathematical platonism. I argue that the success of this argument rests on the claim that mathematical explanations locate pure mathematical facts on which their physical explananda depend, and that any account of mathematical explanation that supports this claim fails to provide an adequate understanding of mathematical explanation.

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Robert Knowles
Swansea University

Citations of this work

Grounding Functionalism and Explanatory Unificationism.Alexios Stamatiadis-bréhier - 2023 - Journal of the American Philosophical Association 9 (4):799-819.
Platonism and Intra-mathematical Explanation.Sam Baron - forthcoming - Philosophical Quarterly.

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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.
No Work for a Theory of Grounding.Jessica M. Wilson - 2014 - Inquiry: An Interdisciplinary Journal of Philosophy 57 (5-6):535-579.
Metaphysical Dependence: Grounding and Reduction.Gideon Rosen - 2010 - In Bob Hale & Aviv Hoffmann (eds.), Modality: Metaphysics, Logic, and Epistemology. Oxford University Press. pp. 109-135.
Realism, Mathematics & Modality.Hartry H. Field - 1989 - New York, NY, USA: Blackwell.

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