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  1. 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 - forthcoming - Philosophia Mathematica.
    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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