Huttegger, Simon and Walsh, Sean and Zaffora Blando, Francesca (2025) Bayesian Convergence for Computably Bounded Agents. [Preprint]

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Abstract

In this article, we pursue two goals. Firstly, we argue that computable probability theory offers a fitting framework for modeling the credences of computably bounded--and, thus, more realistic--Bayesian reasoners. Secondly, we develop a Bayesian perspective on algorithmic randomness: a branch of computability theory that provides a formal account of what it takes for a sequence of observations (a data stream) to be probabilistically typical in an algorithmically specifiable way. In particular, we argue that adopting such a perspective leads to novel insights for one of the pillars of Bayesian epistemology: Bayesian convergence to the truth. In (Huttegger et al., 2024), we showed that, for Bayesian agents whose credences are given by computable probability measures, the data streams that guarantee convergence to the truth coincide with the algorithmically random ones. Here we put these results to use to counter various skeptical arguments which target the philosophical significance of Bayesian convergence-to-the-truth theorems.

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Item Type:	Preprint
Creators:	Creators Email ORCID Huttegger, Simon shuttegg@uci.edu 0000-0003-2374-3889 Walsh, Sean walsh@ucla.edu 0009-0007-5460-778X Zaffora Blando, Francesca fzaffora@andrew.cmu.edu 0009-0004-9065-9198
Keywords:	Bayesian Epistemology; Bayesian Convergence to the Truth; Computably Bounded Agents; Computable Probability Theory; Algorithmic Randomness
Subjects:	Specific Sciences > Mathematics > Logic Specific Sciences > Computation/Information General Issues > Confirmation/Induction Specific Sciences > Probability/Statistics
Depositing User:	Dr. Francesca Zaffora Blando
Date Deposited:	29 Oct 2025 12:29
Last Modified:	29 Oct 2025 12:29
Item ID:	27049
Subjects:	Specific Sciences > Mathematics > Logic Specific Sciences > Computation/Information General Issues > Confirmation/Induction Specific Sciences > Probability/Statistics
Date:	2025
URI:	https://philsci-archive.pitt.edu/id/eprint/27049

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