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  1. Chance and the Continuum Hypothesis.Daniel Hoek - 2021 - Philosophy and Phenomenological Research 103 (3):639-60.
    This paper presents and defends an argument that the continuum hypothesis is false, based on considerations about objective chance and an old theorem due to Banach and Kuratowski. More specifically, I argue that the probabilistic inductive methods standardly used in science presuppose that every proposition about the outcome of a chancy process has a certain chance between 0 and 1. I also argue in favour of the standard view that chances are countably additive. Since it is possible to randomly pick (...)
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  • 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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  • Hyperintensionality and Normativity.Federico L. G. Faroldi - 2019 - Cham, Switzerland: Springer Verlag.
    Presenting the first comprehensive, in-depth study of hyperintensionality, this book equips readers with the basic tools needed to appreciate some of current and future debates in the philosophy of language, semantics, and metaphysics. After introducing and explaining the major approaches to hyperintensionality found in the literature, the book tackles its systematic connections to normativity and offers some contributions to the current debates. The book offers undergraduate and graduate students an essential introduction to the topic, while also helping professionals in related (...)
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  • Cardinality Arguments Against Regular Probability Measures.Thomas Hofweber - 2014 - Thought: A Journal of Philosophy 3 (2):166-175.
    Cardinality arguments against regular probability measures aim to show that no matter which ordered field ℍ we select as the measures for probability, we can find some event space F of sufficiently large cardinality such that there can be no regular probability measure from F into ℍ. In particular, taking ℍ to be hyperreal numbers won't help to guarantee that probability measures can always be regular. I argue that such cardinality arguments fail, since they rely on the wrong conception of (...)
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  • Infinitesimal Probabilities.Sylvia Wenmackers - 2016 - In Richard Pettigrew & Jonathan Weisberg (eds.), The Open Handbook of Formal Epistemology. PhilPapers Foundation. pp. 199-265.
    Non-Archimedean probability functions allow us to combine regularity with perfect additivity. We discuss the philosophical motivation for a particular choice of axioms for a non-Archimedean probability theory and answer some philosophical objections that have been raised against infinitesimal probabilities in general.
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