Explanation in mathematics: Proofs and practice

Philosophy Compass 14 (11):e12629 (2019)
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Abstract

Mathematicians distinguish between proofs that explain their results and those that merely prove. This paper explores the nature of explanatory proofs, their role in mathematical practice, and some of the reasons why philosophers should care about them. Among the questions addressed are the following: what kinds of proofs are generally explanatory (or not)? What makes a proof explanatory? Do all mathematical explanations involve proof in an essential way? Are there really such things as explanatory proofs, and if so, how do they relate to the sorts of explanation encountered in philosophy of science and metaphysics?

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William D'Alessandro
University of Oxford

References found in this work

Thinking about mechanisms.Peter Machamer, Lindley Darden & Carl F. Craver - 2000 - Philosophy of Science 67 (1):1-25.
Essence and modality.Kit Fine - 1994 - Philosophical Perspectives 8 (Logic and Language):1-16.
Studies in the logic of explanation.Carl Gustav Hempel & Paul Oppenheim - 1948 - Philosophy of Science 15 (2):135-175.
Explanation: a mechanist alternative.William Bechtel & Adele Abrahamsen - 2005 - Studies in History and Philosophy of Biological and Biomedical Sciences 36 (2):421-441.
No understanding without explanation.Michael Strevens - 2013 - Studies in History and Philosophy of Science Part A 44 (3):510-515.

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