Rigged lotteries: a diachronic problem for reducing belief to credence

Synthese 195 (3):1355-1373 (2018)
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Abstract

Lin and Kelly :957–981, 2012) and Leitgeb :1338–1389, 2013, Philos Rev 123:131–171, 2014), offer similar solutions to the Lottery Paradox, defining acceptance rules which determine a rational agent’s beliefs in terms of broader features of her credal state than just her isolated credences in individual propositions. I express each proposal as a method for obtaining an ordering over a partition from a credence function, and then a belief set from the ordering. Although these proposals avoid the original Lottery Paradox, I raise a diachronic case which illustrates that neither satisfies both Lin and Kelly’s constraint that the update on orderings track the update on credence functions, and the intuitive constraint that credence of at least 0.5 is necessary for rational belief. I conclude by suggesting that we reformulate these proposals in terms of orderings over entire algebras based on partitions rather than orderings just over the partitions themselves. Reformulating both rules in this way yields acceptance rules which avoid the Lottery Paradox while satisfying both the tracking and likeliness constraints.

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Jonathan Wright
University of Southern California

Citations of this work

Prefaces, Knowledge, and Questions.Frank Hong - 2023 - Ergo: An Open Access Journal of Philosophy 10.

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References found in this work

Belief, Credence, and Pragmatic Encroachment.Jacob Ross & Mark Schroeder - 2014 - Philosophy and Phenomenological Research 88 (2):259-288.
Probability and the logic of rational belief.Henry Ely Kyburg - 1961 - Middletown, Conn.,: Wesleyan University Press.
Gambling with truth.Isaac Levi - 1967 - Cambridge,: MIT Press.

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