Three Puzzles about Lotteries

In Igor Douven (ed.), Lotteries, Knowledge, and Rational Belief. Cambridge University Press (forthcoming)

Julia Staffel
University of Colorado, Boulder
In this article, I discuss three distinct but related puzzles involving lotteries: Kyburg’s lottery paradox, the statistical evidence problem, and the Harman-Vogel paradox. Kyburg’s lottery paradox is the following well-known problem: if we identify rational outright belief with a rational credence above a threshold, we seem to be forced to admit either that one can have inconsistent rational beliefs, or that one cannot rationally believe anything one is not certain of. The statistical evidence problem arises from the observation that people seem to resist forming outright beliefs whenever the available evidence for the claim under consideration is purely statistical. We need explanations of whether it is in fact irrational to form such beliefs, and of whether a clear distinction can be drawn between statistical and non-statistical evidence. The Harman-Vogel paradox is usually presented as a paradox about knowledge: we tend to assume that we can know so-called ordinary propositions, such as the claim that I will be in Barcelona next spring. Yet, we hesitate to make knowledge claims regarding so-called lottery propositions, such as the claim that I won’t die in a car crash in the next few months, even if these lottery propositions are obviously entailed by the ordinary propositions we claim to know. Depending on one’s view about the relationship between rational belief and knowledge, the Harman-Vogel paradox has ramifications for a theory of rational outright belief. Formal theories of the relationship between rational credence and rational belief, such as Leitgeb’s stability theory, tend to focus mostly on handling Kyburg’s lottery paradox, but not the other two puzzles I mention. My aim in this article is to draw out relationships and differences between the puzzles, and to examine to what extent existing formal solutions to Kyburg’s lottery paradox help with answering the statistical evidence problem and the Harman-Vogel paradox.
Keywords Lottery  rational belief  credence  stability  belief
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References found in this work BETA

Knowledge and Lotteries.John Hawthorne - 2003 - Oxford University Press.
The Stability Theory of Belief.Hannes Leitgeb - 2014 - Philosophical Review 123 (2):131-171.
Accuracy, Coherence, and Evidence.Branden Fitelson & Kenny Easwaran - 2015 - Oxford Studies in Epistemology 5:61-96.
Beliefs, Degrees of Belief, and the Lockean Thesis.Richard Foley - 2009 - In Franz Huber & Christoph Schmidt-Petri (eds.), Degrees of Belief. Springer. pp. 37-47.

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