Fraser, Robert (2026) The Problem of Extra-Mathematical Explanation. [Preprint]
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The Problem of Extra-Mathematical Explanation Final.pdf Download (266kB) |
Abstract
We sometimes appeal to pure mathematical facts to explain physical phenomena. But it is unclear how a pure mathematical fact could possibly explain something physical. I develop a concrete formulation of this problem informed by the view that explanations of physical phenomena are backed by relations of dependence. I show that prominent analyses of mathematical explanations of physical phenomena fail to provide satisfying solutions to the problem, and I develop a novel analysis that succeeds in their place. I claim that a mathematical explanation of a physical phenomenon works by establishing that its target shares dependencies with a fact that is independently-understood. My analysis dissolves the problem and enjoys many other benefits besides.
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| Item Type: | Preprint | ||||||
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| Keywords: | Scientific Explanation; Mathematical Explanation; Indispensability Argument; Dependence | ||||||
| Subjects: | Specific Sciences > Mathematics > Applicability Specific Sciences > Mathematics > Epistemology Specific Sciences > Mathematics > Explanation Specific Sciences > Mathematics > Ontology Specific Sciences > Mathematics |
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| Depositing User: | Dr. Robert Fraser | ||||||
| Date Deposited: | 02 Apr 2026 12:33 | ||||||
| Last Modified: | 02 Apr 2026 12:33 | ||||||
| Item ID: | 28856 | ||||||
| Subjects: | Specific Sciences > Mathematics > Applicability Specific Sciences > Mathematics > Epistemology Specific Sciences > Mathematics > Explanation Specific Sciences > Mathematics > Ontology Specific Sciences > Mathematics |
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| Date: | 1 April 2026 | ||||||
| URI: | https://philsci-archive.pitt.edu/id/eprint/28856 |
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