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 (DN) 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. 1. Introduction2. Anchoring3. The Basic Deductive-Mathematical Account4. The Genuineness Problem5. Irrelevance6. Relevance and Information7. Objections and Replies 7.1. Against relevance logic7.2. Too epistemic7.3. Informational containment8. Conclusion

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