Plausibility and probability in deductive reasoning
This work addresses foundational issues in mathematical reasoning and decision theory, with potential implications for fields like logic and finance, though it appears incremental in building on existing ideas from Gödel and Zeilberger.
The paper tackles the problem of rational uncertainty about unproven mathematical statements by developing a normative model of fair bets under deductive uncertainty, using Bayesian-inspired arguments that integrate probability and algorithmic theory.
We consider the problem of rational uncertainty about unproven mathematical statements, remarked on by Gödel and others. 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 would be present. We also discuss a financial view with models of arbitrage where traders have limited computational resources.