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INFORMAL PROOF, FORMAL PROOF, FORMALISM

Published online by Cambridge University Press:  07 August 2015

ALAN WEIR
ALAN WEIR*
Affiliation:
Philosophy, University of Glasgow
*
*PHILOSOPHY, SGOIL NAN DAONNACHDAN OILTHIGH GHLASCHU\UNIVERSITY OF GLASGOW GLASGOW, G12 8QQ, SCOTLAND E-mail: [email protected]
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Abstract

Increases in the use of automated theorem-provers have renewed focus on the relationship between the informal proofs normally found in mathematical research and fully formalised derivations. Whereas some claim that any correct proof will be underwritten by a fully formal proof, sceptics demur. In this paper I look at the relevance of these issues for formalism, construed as an anti-platonistic metaphysical doctrine. I argue that there are strong reasons to doubt that all proofs are fully formalisable, if formal proofs are required to be finitary, but that, on a proper view of the way in which formal proofs idealise actual practice, this restriction is unjustified and formalism is not threatened.

Type
Research Article
Information
The Review of Symbolic Logic , Volume 9 , Issue 1 , March 2016 , pp. 23 - 43
Copyright
Copyright © Association for Symbolic Logic 2015 

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