On formally measuring and eliminating extraneous notions in proofs

Philosophia Mathematica 17 (2):208–219 (2009)
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.
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DOI 10.1093/philmat/nkn015
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