Mathematical Explanation by Law

Abstract

Call an explanation in which a non-mathematical fact is explained—in part or in whole—by mathematical facts: an extra-mathematical explanation. Such explanations have attracted a great deal of interest recently in arguments over mathematical realism. In this article, a theory of extra-mathematical explanation is developed. The theory is modelled on a deductive-nomological theory of scientific explanation. A basic DN account of extra-mathematical explanation is proposed and then redeveloped in the light of two difficulties that the basic theory faces. The final view appeals to relevance logic and uses resources in information theory to understand the explanatory relationship between mathematical and physical facts. 1Introduction2Anchoring3The Basic Deductive-Mathematical Account4The Genuineness Problem5Irrelevance6Relevance and Information7Objections and Replies 7.1Against relevance logic7.2Too epistemic7.3Informational containment8Conclusion

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References found in this work

How the Laws of Physics Lie.Nancy Cartwright - 1983 - Oxford, England: Oxford University Press.
Modal Logic as Metaphysics.Timothy Williamson - 2013 - Oxford, England: Oxford University Press.

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Citations of this work

The Narrow Ontic Counterfactual Account of Distinctively Mathematical Explanation.Mark Povich - 2019 - British Journal for the Philosophy of Science 72 (2):511-543.
There Are No Mathematical Explanations.Jaakko Kuorikoski - 2021 - Philosophy of Science 88 (2):189-212.
A Deductive-Nomological Model for Mathematical Scientific Explanation.Eduardo Castro - 2020 - Principia: An International Journal of Epistemology 24 (1):1-27.

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