Non-measurability, imprecise credences, and imprecise chances

Journal article


Isaacs, Yoaav, Hájek, Alan and Hawthorne, John. (2022). Non-measurability, imprecise credences, and imprecise chances. Mind. 131(523), pp. 894-918. https://doi.org/10.1093/mind/fzab031
AuthorsIsaacs, Yoaav, Hájek, Alan and Hawthorne, John
Abstract

We offer a new motivation for imprecise probabilities. We argue that there are propositions to which precise probability cannot be assigned, but to which imprecise probability can be assigned. In such cases the alternative to imprecise probability is not precise probability, but no probability at all. And an imprecise probability is substantially better than no probability at all. Our argument is based on the mathematical phenomenon of non-measurable sets. Non-measurable propositions cannot receive precise probabilities, but there is a natural way for them to receive imprecise probabilities. The mathematics of non-measurable sets is arcane, but its epistemological import is far-reaching; even apparently mundane propositions are liable to be affected by non-measurability. The phenomenon of non-measurability dramatically reshapes the dialectic between critics and proponents of imprecise credence. Non-measurability offers natural rejoinders to prominent critics of imprecise credence. Non-measurability even reverses some of the critics’ arguments—by the very lights that have been used to argue against imprecise credences, imprecise credences are better than precise credences.

Year2022
JournalMind
Journal citation131 (523), pp. 894-918
PublisherOxford University Press
ISSN0026-4423
Digital Object Identifier (DOI)https://doi.org/10.1093/mind/fzab031
Scopus EID2-s2.0-85144808155
Page range894-918
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All rights reserved
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Controlled
Output statusPublished
Publication dates
Online08 Nov 2021
Publication process dates
Deposited17 May 2023
Place of publicationUnited Kingdom
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