Plausibility and probability in deductive reasoning

08/29/2017

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by   Andrew MacFie, et al.

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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.