A Problem with the Dependence of Informal Proofs on Formal Proofs

Philosophia Mathematica 23 (3):295-310 (2015)
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Abstract

Derivationists, those wishing to explain the correctness and rigour of informal proofs in terms of associated formal proofs, are generally held to be supported by the success of the project of translating informal proofs into computer-checkable formal counterparts. I argue, however, that this project is a false friend for the derivationists because there are too many different associated formal proofs for each informal proof, leading to a serious worry of overgeneration. I press this worry primarily against Azzouni's derivation-indicator account, but conclude that overgeneration is a major obstacle to a successful account of informal proofs in this direction

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References found in this work

Proofs and refutations: the logic of mathematical discovery.Imre Lakatos (ed.) - 1976 - New York: Cambridge University Press.
The Philosophy of Mathematical Practice.Paolo Mancosu (ed.) - 2008 - Oxford, England: Oxford University Press.
Proofs and refutations (IV).I. Lakatos - 1963 - British Journal for the Philosophy of Science 14 (56):296-342.
What Does It Mean to Say That Logic is Formal?John MacFarlane - 2000 - Dissertation, University of Pittsburgh
Proofs and Refutations.Imre Lakatos - 1980 - Noûs 14 (3):474-478.

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