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  1. Primitive conditional probabilities, subset relations and comparative regularity.Joshua Thong - 2023 - Analysis 84 (3):547–555.
    Rational agents seem more confident in any possible event than in an impossible event. But if rational credences are real-valued, then there are some possible events that are assigned 0 credence nonetheless. How do we differentiate these events from impossible events then when we order events? de Finetti (1975), Hájek (2012) and Easwaran (2014) suggest that when ordering events, conditional credences and subset relations are as relevant as unconditional credences. I present a counterexample to all their proposals in this paper. (...)
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  • Internality, transfer, and infinitesimal modeling of infinite processes†.Emanuele Bottazzi & Mikhail G. Katz - forthcoming - Philosophia Mathematica.
    ABSTRACTA probability model is underdetermined when there is no rational reason to assign a particular infinitesimal value as the probability of single events. Pruss claims that hyperreal probabilities are underdetermined. The claim is based upon external hyperreal-valued measures. We show that internal hyperfinite measures are not underdetermined. The importance of internality stems from the fact that Robinson’s transfer principle only applies to internal entities. We also evaluate the claim that transferless ordered fields may have advantages over hyperreals in probabilistic modeling. (...)
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  • Weintraub’s response to Williamson’s coin flip argument.Matthew W. Parker - 2021 - European Journal for Philosophy of Science 11 (3):1-21.
    A probability distribution is regular if it does not assign probability zero to any possible event. Williamson argued that we should not require probabilities to be regular, for if we do, certain “isomorphic” physical events must have different probabilities, which is implausible. His remarks suggest an assumption that chances are determined by intrinsic, qualitative circumstances. Weintraub responds that Williamson’s coin flip events differ in their inclusion relations to each other, or the inclusion relations between their times, and this can account (...)
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  • Infinite Lotteries, Spinners, Applicability of Hyperreals†.Emanuele Bottazzi & Mikhail G. Katz - 2021 - Philosophia Mathematica 29 (1):88-109.
    We analyze recent criticisms of the use of hyperreal probabilities as expressed by Pruss, Easwaran, Parker, and Williamson. We show that the alleged arbitrariness of hyperreal fields can be avoided by working in the Kanovei–Shelah model or in saturated models. We argue that some of the objections to hyperreal probabilities arise from hidden biases that favor Archimedean models. We discuss the advantage of the hyperreals over transferless fields with infinitesimals. In Paper II we analyze two underdetermination theorems by Pruss and (...)
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