The ins and outs of mathematical explanation
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Proofs of mathematical theorems tell us that the theorem is true, but some proofs go further and tell us why the theorem is true. That is, some, but not all, proofs are explanatory. Call this intramathematical explanation. It has been argued that whenever there are physical applications of the
theorems in question, we also have mathematical explanations of physical phenomena. Call this extramathematical explanation. In this paper I will
consider both intra and extramathematical explanations and discuss why they are of philosophical interest. I will also make some speculative remarks about two promising accounts for a theory of mathematical explanation.
This talk is part of the HPS Philosophy Workshop series.
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