Sleeping Beauty, Countable Additivity, and Rational Dilemmas

Philosophical Review 119 (4):411-447 (2010)
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Abstract

Currently, the most popular views about how to update de se or self-locating beliefs entail the one-third solution to the Sleeping Beauty problem.2 Another widely held view is that an agent‘s credences should be countably additive.3 In what follows, I will argue that there is a deep tension between these two positions. For the assumptions that underlie the one-third solution to the Sleeping Beauty problem entail a more general principle, which I call the Generalized Thirder Principle, and there are situations in which the latter principle and the principle of Countable Additivity cannot be jointly satisfied. The most plausible response to this tension, I argue, is to accept both of these principles, and to maintain that when an agent cannot satisfy them both, she is faced with a rational dilemma.

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Jake Ross
University of Southern California

Citations of this work

Epistemic Dilemmas: A Guide.Nick Hughes - forthcoming - In Essays on Epistemic Dilemmas. Oxford: Oxford University Press.
Dilemmic Epistemology.Nick Hughes - 2019 - Synthese 196 (10):4059-4090.
Conceptual limitations, puzzlement, and epistemic dilemmas.Deigan Michael - 2023 - Philosophical Studies 180 (9):2771-2796.
Time-Slice Rationality and Self-Locating Belief.David Builes - 2020 - Philosophical Studies 177 (10):3033-3049.

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