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109Elusive PropositionsJournal of Philosophical Logic 50 (4): 705-725. 2021.David Kaplan observed in Kaplan that the principle \\) cannot be verified at a world in a standard possible worlds model for a quantified bimodal propositional language. This raises a puzzle for certain interpretations of the operator Q: it seems that some proposition p is such that is not possible to query p, and p alone. On the other hand, Arthur Prior had observed in Prior that on pain of contradiction, ∀p is Q only if one true proposition is Q and one false proposition is Q. The two observat…Read more
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103Bad company generalizedSynthese 170 (3). 2009.The paper is concerned with the bad company problem as an instance of a more general difficulty in the philosophy of mathematics. The paper focuses on the prospects of stability as a necessary condition on acceptability. However, the conclusion of the paper is largely negative. As a solution to the bad company problem, stability would undermine the prospects of a neo-Fregean foundation for set theory, and, as a solution to the more general difficulty, it would impose an unreasonable constraint o…Read more
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101Ramified structurePhilosophical Studies 180 (5-6): 1651-1674. 2022.The Russell–Myhill theorem threatens a familiar structured conception of propositions according to which two sentences express the same proposition only if they share the same syntactic structure and their corresponding syntactic constituents share the same semantic value. Given the role of the principle of universal instantiation in the derivation of the theorem in simple type theory, one may hope to rehabilitate the core of the structured view of propositions in ramified type theory, where the…Read more
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100IntroductionIn Agustin Rayo & Gabriel Uzquiano (eds.), Absolute Generality, Oxford University Press. 2006.Whether or not we achieve absolute generality in philosophical inquiry, most philosophers would agree that ordinary inquiry is rarely, if ever, absolutely general. Even if the quantifiers involved in an ordinary assertion are not explicitly restricted, we generally take the assertion’s domain of discourse to be implicitly restricted by context.1 Suppose someone asserts (2) while waiting for a plane to take off.
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91Quantification, Inference, and OntologyAnalysis 78 (2): 303-315. 2018.Thomas Hofweber has written a very rich book. In line with the conviction that ontology should be informed by linguistic considerations, he develops a systematic approach to central ontological questions as they arise in different regions of discourse. More generally, the book seeks to cast light upon the nature of ontology and its proper place in enquiry. His preferred methodology is not without consequence: it promises, for example, to solve what otherwise look like intractable philosophical p…Read more
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75Atomism and CompositionThought: A Journal of Philosophy 6 (4): 232-240. 2017.Atomism is the thesis that every object is composed of atoms. This principle is generally regimented by means of an atomicity axiom according to which every object has atomic parts. But there appears to be a sense that something is amiss with atomistic mereology. We look at three concerns, which, while importantly different, involve infinite descending chains of proper parts and have led some to question standard formalizations of atomism and composition in mereology.
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66Review of Volker Halbach, Leon Horsten (eds), Principles of Truth (review)Notre Dame Philosophical Reviews 2003 (4). 2003.
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50Ineffability within the limits of abstraction aloneIn Philip A. Ebert & Marcus Rossberg (eds.), Abstractionism: Essays in Philosophy of Mathematics, Oxford University Press Uk. 2016.The purpose of this article is to assess the prospects for a Scottish neo-logicist foundation for a set theory. We show how to reformulate a key aspect of our set theory as a neo-logicist abstraction principle. That puts the enterprise on the neo-logicist map, and allows us to assess its prospects, both as a mathematical theory in its own right and in terms of the foundational role that has been advertised for set theory. On the positive side, we show that our abstraction based theory can be mod…Read more
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49Semantic nominalismDialectica 59 (2). 2005.The aim of the present paper is twofold. One task is to argue that our use of the numerical vocabulary in theory and applications determines the reference of the numerical terms more precisely than up to isomorphism. In particular our use of the numerical vocabulary in modal and counterfactual contexts of application excludes contingent existents as candidate referents for the numerical terms. The second task is to explore the impact of this conclusion on what I call semantic nominalism, which i…Read more
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36Hale Bob and Wright Crispin. The reason's proper study: Essays toward a neo-Fregean philosophy of mathematics. Oxford University Press, New York. 2001, 472 pp (review)Bulletin of Symbolic Logic 12 (2): 291-294. 2006.
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31Mereological Harmony 1Oxford Studies in Metaphysics 6. 2011.This chapter takes a close look at the thought that mereological relations on material objects mirror, and are mirrored by, parallel mereological relations on their exact locations. This hypothesis is made more precise by means of a battery of principles from which more substantive consequences are derived. Mereological harmony turns out to entail, for example, that atomistic space is an inhospitable environment for material gunk or that Whiteheadian space is not a hospitable environment for une…Read more
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13Semantic NominalismDialectica 59 (2): 265-282. 2005.The aim of the present paper is twofold. One task is to argue that our use of the numerical vocabulary in theory and applications determines the reference of the numerical terms more precisely than up to isomorphism. In particular our use of the numerical vocabulary in modal and counterfactual contexts of application excludes contingent existents as candidate referents for the numerical terms. The second task is to explore the impact of this conclusion on what I call semantic nominalism, which i…Read more
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2Unrestricted Unrestricted Quantification: the cardinal problem of absolute generalityIn Agustín Rayo & Gabriel Uzquiano (eds.), Absolute Generality, Oxford University Press. pp. 305--32. 2006.
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Ontology and the Foundations of MathematicsDissertation, Massachusetts Institute of Technology. 1999."Ontology and the Foundations of Mathematics" consists of three papers concerned with ontological issues in the foundations of mathematics. Chapter 1, "Numbers and Persons," confronts the problem of the inscrutability of numerical reference and argues that, even if inscrutable, the reference of the numerals, as we ordinarily use them, is determined much more precisely than up to isomorphism. We argue that the truth conditions of a variety of numerical modal and counterfactual sentences place ser…Read more
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Mereological HarmonyIn Karen Bennett & Dean W. Zimmerman (eds.), Oxford Studies in Metaphysics: Volume 6, Oxford University Press Uk. 2011.
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