Plausibility and probability in deductive reasoning
Artificial Intelligence
2019-12-17 v6
Abstract
We consider the problem of rational uncertainty about unproven mathematical statements, remarked on by G\"odel 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.
Cite
@article{arxiv.1708.09032,
title = {Plausibility and probability in deductive reasoning},
author = {Andrew MacFie},
journal= {arXiv preprint arXiv:1708.09032},
year = {2019}
}