Non-Measurability, Imprecise Credences, and Imprecise Chances

Mind 131 (523):892-916 (2021)
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– 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.



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Author Profiles

Yoaav Isaacs
Baylor University
Alan Hajek
Australian National University
John Hawthorne
Australian Catholic University

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Knowledge and its Limits.Timothy Williamson - 2000 - Oxford, GB: Oxford University Press.
Fact, Fiction, and Forecast.Nelson Goodman - 1955 - Harvard University Press.
Studies in the Way of Words.Herbert Paul Grice - 1989 - Cambridge: Harvard University Press.
Convention: A Philosophical Study.David Kellogg Lewis - 1969 - Cambridge, MA, USA: Wiley-Blackwell.
Logical Foundations of Probability.Rudolf Carnap - 1950 - Chicago, IL, USA: Chicago University of Chicago Press.

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