Aspects of Mathematical Explanation: Symmetry, Unity, and Salience

Philosophical Review 123 (4):485-531 (2014)
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Abstract

Unlike explanation in science, explanation in mathematics has received relatively scant attention from philosophers. Whereas there are canonical examples of scientific explanations, there are few examples that have become widely accepted as exhibiting the distinction between mathematical proofs that explain why some mathematical theorem holds and proofs that merely prove that the theorem holds without revealing the reason why it holds. This essay offers some examples of proofs that mathematicians have considered explanatory, and it argues that these examples suggest a particular account of explanation in mathematics. The essay compares its account to Steiner's and Kitcher's. Among the topics that arise are proofs that exploit symmetries, mathematical coincidences, brute-force proofs, simplicity in mathematics, merely clever proofs, and proofs that unify what other proofs treat as separate cases

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Marc Lange
University of North Carolina, Chapel Hill

Citations of this work

Metaphysically explanatory unification.David Mark Kovacs - 2020 - Philosophical Studies 177 (6):1659-1683.
Grounding and the Argument From Explanatoriness.David Mark Kovacs - 2017 - Philosophical Studies 174 (12):2927-2952.
Mathematical Explanation by Law.Sam Baron - 2019 - British Journal for the Philosophy of Science 70 (3):683-717.

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References found in this work

The Scientific Image.William Demopoulos & Bas C. van Fraassen - 1982 - Philosophical Review 91 (4):603.
The Structure of Science.Ernest Nagel - 1961 - Les Etudes Philosophiques 17 (2):275-275.
The Scientific Image.Michael Friedman - 1982 - Journal of Philosophy 79 (5):274-283.

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