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584Cantor, Choice, and ParadoxThe Philosophical Review. forthcoming.I propose a revision of Cantor’s account of set size that understands comparisons of set size fundamentally in terms of surjections rather than injections. This revised account is equivalent to Cantor's account if the Axiom of Choice is true, but its consequences differ from those of Cantor’s if the Axiom of Choice is false. I argue that the revised account is an intuitive generalization of Cantor’s account, blocks paradoxes—most notably, that a set can be partitioned into a set that is bigger t…Read more
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84The qualitative paradox of non-conglomerabilitySynthese 195 (3): 1181-1210. 2018.A probability function is non-conglomerable just in case there is some proposition E and partition \ of the space of possible outcomes such that the probability of E conditional on any member of \ is bounded by two values yet the unconditional probability of E is not bounded by those values. The paradox of non-conglomerability is the counterintuitive—and controversial—claim that a rational agent’s subjective probability function can be non-conglomerable. In this paper, I present a qualitative an…Read more
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23Fair Infinite Lotteries, Qualitative Probability, and RegularityPhilosophy of Science 89 (4): 824-844. 2022.A number of philosophers have thought that fair lotteries over countably infinite sets of outcomes are conceptually incoherent by virtue of violating countable additivity. In this article, I show that a qualitative analogue of this argument generalizes to an argument against the conceptual coherence of a much wider class of fair infinite lotteries—including continuous uniform distributions. I argue that this result suggests that fair lotteries over countably infinite sets of outcomes are no more…Read more
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Carnegie Mellon UniversityPost-doctoral Fellow
Pittsburgh, Pennsylvania, United States of America
Areas of Specialization
Metaphysics and Epistemology |
Science, Logic, and Mathematics |
Philosophy of Probability |