INFORMAL PROOF, FORMAL PROOF, FORMALISM

ALAN WEIR
2015 The Review of Symbolic Logic  
AbstractIncreases 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
more » ... 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.
doi:10.1017/s1755020315000234 fatcat:aw2kgf7yifdc7kxgffbcmjqudy