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Explanation Beyond CausationPhilosophical Perspectives on Non-Causal Explanations$
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Alexander Reutlinger and Juha Saatsi

Print publication date: 2018

Print ISBN-13: 9780198777946

Published to Oxford Scholarship Online: June 2018

DOI: 10.1093/oso/9780198777946.001.0001

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PRINTED FROM OXFORD SCHOLARSHIP ONLINE (oxford.universitypressscholarship.com). (c) Copyright Oxford University Press, 2021. All Rights Reserved. An individual user may print out a PDF of a single chapter of a monograph in OSO for personal use. date: 23 September 2021

Two Flavours of Mathematical Explanation

Two Flavours of Mathematical Explanation

(p.231) 11 Two Flavours of Mathematical Explanation
Explanation Beyond Causation

Mark Colyvan

John Cusbert

Kelvin McQueen

Oxford University Press

A proof of a mathematical theorem tells us that the theorem is true (or should be accepted), but some proofs go further and tell us why the theorem is true (or should be accepted). That is, some, but not all, proofs are explanatory. Call this intra-mathematical explanation and it is to be contrasted with extra-mathematical explanation, where mathematics explains things external to mathematics. This chapter focuses on the intra-mathematical case. The authors consider a couple of examples of explanatory proofs from contemporary mathematics. They determine whether these proofs share some common feature that may account for their explanatoriness. The authors conclude with two plausible, but competing, accounts of mathematical explanation and suggest that there might be more than one kind of explanation at work in mathematics.

Keywords:   free group theorem, group theory, mathematical explanation, intra-mathematical explanation, mathematical proofs, philosophy of mathematics, reduction, unification

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