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Arithmetic is NecessaryJournal of Philosophical Logic. forthcoming.(Goodsell, Journal of Philosophical Logic, 51(1), 127-150 2022) establishes the noncontingency of sentences of first-order arithmetic, in a plausible higher-order modal logic. Here, the same result is derived using significantly weaker assumptions. Most notably, the assumption of rigid comprehension—that every property is coextensive with a modally rigid one—is weakened to the assumption that the Boolean algebra of properties under necessitation is countably complete. The results are generalized…Read more
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This paper presents a new system of logic, LF, that is intended to be used as the foundation of the formalization of science. That is, deductive validity according to LF is to be used as the criterion for assessing what follows from the verdicts, hypotheses, or conjectures of any science. In work currently in progress, we argue for the unique suitability of LF for the formalization of logic, mathematics, syntax, and semantics. The present document specifies the language and rules of LF, lays out…Read more
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Decision Theory UnboundNoûs. forthcoming.
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Unbounded UtilityDissertation, University of Southern California. 2023.
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Tossing Morgenbesser’s CoinAnalysis 82 (2): 214-221. 2022.
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Arithmetic is DeterminateJournal of Philosophical Logic 51 (1): 127-150. 2021.Orthodoxy holds that there is a determinate fact of the matter about every arithmetical claim. Little argument has been supplied in favour of orthodoxy, and work of Field, Warren and Waxman, and others suggests that the presumption in its favour is unjustified. This paper supports orthodoxy by establishing the determinacy of arithmetic in a well-motivated modal plural logic. Recasting this result in higher-order logic reveals that even the nominalist who thinks that there are only finitely many …Read more
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A St Petersburg Paradox for risky welfare aggregationAnalysis 81 (3): 420-426. 2021.
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What is an Extended Simple Region?Philosophy and Phenomenological Research 101 (3): 649-659. 2019.The notion of an extended simple region (henceforth ESR) has recently been marshalled in the service of arguments for a variety of conclusions. Exactly how to understand the idea of extendedness as it applies to simple regions, however, has been largely ignored, or, perhaps better, assumed. In this paper we first (§1) outline what we take to be the standard way that philosophers are thinking about extendedness, namely as an intrinsic property of regions. We then introduce an alternative pictur…Read more
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