Transferable and Fixable Proofs

Abstract

A proof ${\cal P}$ of a theorem T is transferable when it's possible for a typical expert to become convinced of T solely on the basis of their prior knowledge and the information contained in ${\cal P}$ . Easwaran has argued that transferability is a constraint on acceptable proof. Meanwhile, a proof ${\cal P}$ is fixable when it's possible for other experts to correct any mistakes ${\cal P}$ contains without having to develop significant new mathematics. Habgood-Coote and Tanswell have observed that some acceptable proofs are both fixable and in need of fixing, in the sense that they contain non-trivial mistakes. The claim that acceptable proofs must be transferable seems quite plausible. The claim that some acceptable proofs need fixing seems plausible too. Unfortunately, these attractive suggestions stand in tension with one another. I argue that the transferability requirement is the problem. Acceptable proofs need to only satisfy a weaker requirement I call “corrigibility.” I explain why, despite appearances, the corrigibility standard is preferable to stricter alternatives.