Friday, March 15, 2013
William Bennett Munro Memorial Seminar
Aspects of Mathematical Explanation
Marc Lange, Professor of Philosophy, University of North Carolina at Chapel Hill
Compared to scientific explanation, with which philosophy of science has been seriously engaged for at least six decades, explanation in mathematics has been little explored by philosophers. Its relative neglect is remarkable and unfortunate. Mathematical proofs that explain why some theorem holds have often been distinguished by mathematicians from proofs that merely establish that some theorem holds. By means of several suggestive examples, I will argue that two mathematical proofs may prove the same theorem from the same axioms, though only one of these proofs is explanatory. My goal in this paper will be to identify the ground of this distinction -- at least in an important range of cases.