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225Absolute generality (edited book)Oxford University Press. 2006.The problem of absolute generality has attracted much attention in recent philosophy. Agustin Rayo and Gabriel Uzquiano have assembled a distinguished team of contributors to write new essays on the topic. They investigate the question of whether it is possible to attain absolute generality in thought and language and the ramifications of this question in the philosophy of logic and mathematics.
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811Modality and ParadoxPhilosophy Compass 10 (4): 284-300. 2015.Philosophers often explain what could be the case in terms of what is, in fact, the case at one possible world or another. They may differ in what they take possible worlds to be or in their gloss of what is for something to be the case at a possible world. Still, they stand united by the threat of paradox. A family of paradoxes akin to the set-theoretic antinomies seem to allow one to derive a contradiction from apparently plausible principles. Some of them concern the interaction between propo…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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205Review of M. Potter, Set theory and its philosophy: A critical introduction (review)Philosophia Mathematica 13 (3): 308-346. 2005.
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104Bad 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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577How Many Angels Can Dance on the Point of a Needle? Transcendental Theology Meets Modal MetaphysicsMind 120 (477): 53-81. 2011.We argue that certain modal questions raise serious problems for a modal metaphysics on which we are permitted to quantify unrestrictedly over all possibilia. In particular, we argue that, on reasonable assumptions, both David Lewis's modal realism and Timothy Williamson's necessitism are saddled with the remarkable conclusion that there is some cardinal number of the form ℵα such that there could not be more than ℵα-many angels in existence. In the last section, we make use of similar ideas to …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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292Plural Quantification and ModalityProceedings of the Aristotelian Society 111 (2pt2): 219-250. 2011.Identity is a modally inflexible relation: two objects are necessarily identical or necessarily distinct. However, identity is not alone in this respect. We will look at the relation that one object bears to some objects if and only if it is one of them. In particular, we will consider the credentials of the thesis that no matter what some objects are, an object is necessarily one of them or necessarily not one of them
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37Hale 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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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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615Mereology and modalityIn Shieva Kleinschmidt (ed.), Mereology and Location, Oxford University Press. pp. 33-56. 2014.Do mereological fusions have their parts necessarily? None of the axioms of non-modal formulations of classical mereology appear to speak directly to this question. And yet a great many philosophers who take the part-whole relation to be governed by classical mereology seem to assume that they do. In addition to this, many philosophers who make allowance for the part-whole relation to obtain merely contingently between a part and a mereological fusion tend to depart from non-modal formulations o…Read more
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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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121Before Effect Without Zeno CausalityNoûs 46 (2): 259-264. 2012.We argue that not all cases of before-effect involve causation and ask how to demarcate cases of before-effect in which the events that follow exert causal influence over the before-effect from cases in which they do not
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162Well- and non-well-founded Fregean extensionsJournal of Philosophical Logic 33 (5): 437-465. 2004.George Boolos has described an interpretation of a fragment of ZFC in a consistent second-order theory whose only axiom is a modification of Frege's inconsistent Axiom V. We build on Boolos's interpretation and study the models of a variety of such theories obtained by amending Axiom V in the spirit of a limitation of size principle. After providing a complete structural description of all well-founded models, we turn to the non-well-founded ones. We show how to build models in which foundation …Read more
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1602Higher-order free logic and the Prior-Kaplan paradoxCanadian Journal of Philosophy 46 (4-5): 493-541. 2016.The principle of universal instantiation plays a pivotal role both in the derivation of intensional paradoxes such as Prior’s paradox and Kaplan’s paradox and the debate between necessitism and contingentism. We outline a distinctively free logical approach to the intensional paradoxes and note how the free logical outlook allows one to distinguish two different, though allied themes in higher-order necessitism. We examine the costs of this solution and compare it with the more familiar ramifica…Read more
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Metaphysics |
Logic and Philosophy of Logic |
Philosophy of Mathematics |