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Conditional Probabilities

In Richard Pettigrew & Jonathan Weisberg (eds.), The Open Handbook of Formal Epistemology. PhilPapers Foundation. pp. 131-198 (2019)

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  1. Non-Measurability, Imprecise Credences, and Imprecise Chances.Yoaav Isaacs, Alan Hájek & John Hawthorne - forthcoming - Mind:fzab031.
    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 (...)
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  • An Improved Dutch Book Theorem for Conditionalization.Michael Rescorla - forthcoming - Erkenntnis:1-29.
    Lewis proved a Dutch book theorem for Conditionalization. The theorem shows that an agent who follows any credal update rule other than Conditionalization is vulnerable to bets that inflict a sure loss. Lewis’s theorem is tailored to factive formulations of Conditionalization, i.e. formulations on which the conditioning proposition is true. Yet many scientific and philosophical applications of Bayesian decision theory require a non-factive formulation, i.e. a formulation on which the conditioning proposition may be false. I prove a Dutch book theorem (...)
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  • Chance Deference De Se.J. Dmitri Gallow - manuscript
    Principles of chance deference face two kinds of problems. In the first place, they face difficulties with a priori knowable contingencies. In the second place, they face difficulties in cases where you've lost track of the time. I provide a generalisation of these principles which handles these problem cases. The generalisation has surprising consequences for Adam Elga's Sleeping Beauty puzzle.
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  • Solving a Paradox of Evidential Equivalence.Cian Dorr, John Hawthorne & Yoaav Isaacs - 2021 - Mind 130 (520):1159–82.
    David Builes presents a paradox concerning how confident you should be that any given member of an infinite collection of fair coins landed heads, conditional on the information that they were all flipped and only finitely many of them landed heads. We argue that if you should have any conditional credence at all, it should be 1/2.
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  • Humeanisms: Metaphysical and Epistemological.Aaron Segal - 2020 - Synthese 199 (1-2):905-925.
    Classic inductive skepticism–the epistemological claim that we have no good reason to believe that the unobserved resembles the observed–is plausibly everyone’s lot, whether or not they embrace Hume’s metaphysical claim that distinct existents are “entirely loose and separate”. But contemporary advocates of a Humean metaphysic accept a metaphysical claim stronger than Hume’s own. I argue that their view plausibly gives rise to a radical inductive skepticism–according to which we are downright irrational in believing as we do about the unobserved–that we (...)
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  • Kolmogorov Conditionalizers Can Be Dutch Booked.Alexander Meehan & Snow Zhang - forthcoming - Review of Symbolic Logic:1-36.
    A vexing question in Bayesian epistemology is how an agent should update on evidence which she assigned zero prior credence. Some theorists have suggested that, in such cases, the agent should update by Kolmogorov conditionalization, a norm based on Kolmogorov’s theory of regular conditional distributions. However, it turns out that in some situations, a Kolmogorov conditionalizer will plan to always assign a posterior credence of zero to the evidence she learns. Intuitively, such a plan is irrational and easily Dutch bookable. (...)
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  • You Say You Want a Revolution: Two Notions of Probabilistic Independence.Alexander Meehan - 2021 - Philosophical Studies 178 (10):3319-3351.
    Branden Fitelson and Alan Hájek have suggested that it is finally time for a “revolution” in which we jettison Kolmogorov’s axiomatization of probability, and move to an alternative like Popper’s. According to these authors, not only did Kolmogorov fail to give an adequate analysis of conditional probability, he also failed to give an adequate account of another central notion in probability theory: probabilistic independence. This paper defends Kolmogorov, with a focus on this independence charge. I show that Kolmogorov’s sophisticated theory (...)
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  • Wishing, Decision Theory, and Two-Dimensional Content.Kyle H. Blumberg - forthcoming - Journal of Philosophy.
    This paper is about two requirements on wish reports whose interaction motivates a novel semantics for these ascriptions. The first requirement concerns the ambiguities that arise when determiner phrases, e.g. definite descriptions, interact with `wish'. More specifically, several theorists have recently argued that attitude ascriptions featuring counterfactual attitude verbs license interpretations on which the determiner phrase is interpreted relative to the subject's beliefs. The second requirement involves the fact that desire reports in general require decision-theoretic notions for their analysis. The (...)
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  • Ranking Theory.Franz Huber - 2019 - In Richard Pettigrew & Jonathan Weisberg (eds.), The Open Handbook of Formal Epistemology. PhilPapers Foundation. pp. 397-436.
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  • Full & Partial Belief.Konstantin Genin - 2019 - In Richard Pettigrew & Jonathan Weisberg (eds.), The Open Handbook of Formal Epistemology. PhilPapers Foundation. pp. 437-498.
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