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Philosophia Mathematica Advance Access published online on June 2, 2008
Philosophia Mathematica, doi:10.1093/philmat/nkn015
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© The Author [2008]. Published by Oxford University Press. All rights reserved. For permissions, please email: journals.permissions@oxfordjournals.org

On Formally Measuring and Eliminating Extraneous Notions in Proofs{dagger}

Andrew Arana*

* Department of Philosophy, 201 Dickens Hall, Kansas State University, Manhattan, Kansas 66506–0803 U.S.A. aarana{at}ksu.edu

Many mathematicians and philosophers of mathematics believe some proofs contain elements extraneous to what is being proved. In this paper I discuss extraneousness generally, and then consider a specific proposal for measuring extraneousness syntactically. This specific proposal uses Gentzen's cut-elimination theorem. I argue that the proposal fails, and that we should be skeptical about the usefulness of syntactic extraneousness measures.

{dagger} Thanks to Jeremy Avigad, David Corfield, Bruce Glymour, Marco Panza, Doug Patterson, and Neil Tennant for helpful comments on earlier versions of this paper.


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