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arXiv · 1708.09032

Plausibility and probability in deductive reasoning

Andrew MacFie
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Abstract

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.

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Andrew MacFie. 2019-12-16. Plausibility and probability in deductive reasoning. https://arxiv.org/abs/1708.09032

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