Mathematical Explanation by Law

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The British Journal for the Philosophy of Science

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Sam, Baron
Oxford University Press
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article description
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 paper, a theory of extra-mathematical explanation is developed. The theory is modeled 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.