Philosophy Compass 14 (11) (2019)

William D'Alessandro
Ludwig Maximilians Universität, München
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?
Keywords mathematical explanation  explanatory proof  proof  philosophy of mathematics  explanation  mathematical practice  mathematical proof  grounding  understanding  explanation and understanding
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DOI 10.1111/phc3.12629
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