The Metaphysics of Mathematical Explanation in Science: Platonist and Nominalist Problems and Aristotelian Solutions

Fisher, Patrick

doi:10.5840/acpaproc20231027152

Proceedings of the American Catholic Philosophical Association

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published on October 30, 2023

Patrick Fisher

https://doi.org/10.5840/acpaproc20231027152

The Metaphysics of Mathematical Explanation in Science
Platonist and Nominalist Problems and Aristotelian Solutions

Debates between contemporary platonist and nominalist conceptions of the metaphysical status of mathematical objects have recently included discussions of explanations of physical phenomena in which mathematics plays an indispensable role, termed mathematical explanations in science (MES). I will argue that MES requires an ontology that can (1) ground claims about mathematical necessity as distinct from physical necessity and (2) explain how that mathematical necessity applies to the physical world. I contend that nominalism fails to meet the first criterion and platonism the second. I then articulate an alternative, Aristotelian approach to mathematical objects and defend such a view as meeting both criteria.

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