Aspects of Mathematical Explanation

03/13/2013 - 4:15pm
03/13/2013 - 5:15pm
Marc Lange, University of North Carolina at Chapel Hill

Unlike explanation in science, explanation in mathematics has received relatively scant attention from philosophers. Whereas there are canonical examples of scientific explanations (as well as canonical examples of failed attempts at scientific explanation), few (if any) examples have become widely accepted as exhibiting the distinction between proofs that explain why some mathematical theorem holds and proofs that merely prove that the theorem holds. In this talk, I will propose some very simple examples (drawn from several branches of mathematics) and argue that they suggest a particular account of explanation in mathematics (at least, of those explanations consisting of proofs). I will compare this account of explanation in mathematics to others that have been offered. Among the aspects of mathematical explanation that I will touch upon are symmetry, unification, mathematical coincidence, and natural mathematical properties.

Freeburg Forum, Kravis LC62, Claremont McKenna College
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