Plausibility and probability in deductive reasoning

We consider the problem of rational uncertainty about unproven mathematical statements, which Gödel and others have remarked on. Using Bayesian-inspired arguments we build a normative model of fair bets under deductive uncertainty which draws from both probability and the theory of algorithms. We comment on connections to Zeilberger’s notion of “semi-rigorous proofs”, particularly that inherent subjectivity is an obstacle.