Mathematical Explanation by Law

Sam Baron

Research output: Contribution to journalArticle


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.

Original languageEnglish
Pages (from-to)683-717
Number of pages35
JournalThe British Journal for the Philosophy of Science
Issue number3
Publication statusPublished - Sep 2019

Cite this