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The Philosophy of Mathematical Practice$
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Paolo Mancosu

Print publication date: 2008

Print ISBN-13: 9780199296453

Published to Oxford Scholarship Online: February 2010

DOI: 10.1093/acprof:oso/9780199296453.001.0001

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Purity as an Ideal of Proof

Purity as an Ideal of Proof

(p.179) 7 Purity as an Ideal of Proof
The Philosophy of Mathematical Practice

Michael Detlefsen (Contributor Webpage)

Oxford University Press

This chapter sketches the development of purity as an ideal of mathematical proof from antiquity through the 20th century. The basic thought behind this ideal is that a proof of a proposition ought not to have to appeal to notions other than those contained in the proposition in order to justify it. A proof that does appeal to such extraneous notions thus strays at points from its proper topic and is not in all its parts relevant. Attention is also given to the common idea that the discipline of seeking purity in proofs has intervenient benefits for those who practice it.

Keywords:   purity, topical purity, prime number theorem, intermediate value theorem

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