Lopez-Wild, Josiah (2024) Computable Bayesian Epistemology. [Preprint]

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	Text Computable_Bayesian_Epistemology (2).pdf Download (407kB)

Abstract

Bayesian epistemology is broadly concerned with providing norms for rational belief and learning using the mathematics of probability theory. But many authors have worried that the theory is too idealized to accurately describe real agents. In this paper I argue that Bayesian epistemology can describe more realistic agents while retaining sufficient generality by introducing ideas from a branch of mathematics called computable analysis. I call this program computable Bayesian epistemology. I situate this program by contrasting it with an ongoing debate about ideal versus bounded rationality. I then present foundational ideas from computable analysis and demonstrate their usefulness by proving the main result: on countably generated spaces there are no computable, finitely additive probability measures. On this basis I argue that bounded agents cannot have finitely additive credences, and so countable additivity is the appropriate norm of rationality. I conclude by discussing prospects for this research program.

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Item Type:	Preprint
Creators:	Creators Email ORCID Lopez-Wild, Josiah josiah.lopezwild@gmail.com 0009-0000-4847-4481
Keywords:	Bayesian epistemology, computability, computable analysis, probability theory, finite additivity
Subjects:	Specific Sciences > Computation/Information General Issues > Decision Theory Specific Sciences > Probability/Statistics
Depositing User:	Mr. Josiah Lopez-Wild
Date Deposited:	02 Sep 2024 12:27
Last Modified:	02 Sep 2024 12:27
Item ID:	23862
Subjects:	Specific Sciences > Computation/Information General Issues > Decision Theory Specific Sciences > Probability/Statistics
Date:	2024
URI:	https://philsci-archive.pitt.edu/id/eprint/23862

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