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Profile: Gabriel Uzquiano (University of Southern California)
  1. Gabriel Uzquiano (2015). Modality and Paradox. Philosophy Compass 10 (4):284-300.
    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. (...)
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  2.  78
    Andrew Bacon, John Hawthorne & Gabriel Uzquiano (2016). Higher-Order Free Logic and the Prior-Kaplan Paradox. Canadian Journal of Philosophy 46 (4-5):493-541.
    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 ramificationist approaches to higher-order logic. Our assessment (...)
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  3. Gabriel Uzquiano, Quantification and Quantifiers. Stanford Encyclopedia of Philosophy.
  4. Gabriel Uzquiano (2015). Varieties of Indefinite Extensibility. Notre Dame Journal of Formal Logic 56 (1):147-166.
    We look at recent accounts of the indefinite extensibility of the concept set and compare them with a certain linguistic model of indefinite extensibility. We suggest that the linguistic model has much to recommend over alternative accounts of indefinite extensibility, and we defend it against three prima facie objections.
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  5.  16
    Gabriel Uzquiano & Agustin Rayo (eds.) (2006). Absolute Generality. Oxford University Press.
    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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  6. Gabriel Uzquiano (2014). Mereology and Modality. In Shieva Kleinschmidt (ed.), Mereology and Location. Oxford University Press 33-56.
    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 of classical mereology at (...)
     
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  7.  66
    Agustín Rayo & Gabriel Uzquiano (eds.) (2006). Absolute Generality. Oxford University Press.
    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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  8. Gabriel Uzquiano (2015). Recombination and Paradox. Philosophers' Imprint 15 (19).
    The doctrine that whatever could exist does exist leads to a proliferation of possibly concrete objects given certain principles of recombination. If, for example, there could have been a large infinite number of concrete objects, then there is at least the same number of possibly concrete objects in existence. And further cardinality considerations point to a tension between the preceding doctrine and the Cantorian conception of the absolutely infinite. This paper develops a parallel problem for a variety of possible worlds (...)
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  9. Gabriel Uzquiano (2015). A Neglected Resolution of Russell’s Paradox of Propositions. Review of Symbolic Logic 8 (2):328-344.
    Bertrand Russell offered an influential paradox of propositions in Appendix B of The Principles of Mathematics, but there is little agreement as to what to conclude from it. We suggest that Russell's paradox is best regarded as a limitative result on propositional granularity. Some propositions are, on pain of contradiction, unable to discriminate between classes with different members: whatever they predicate of one, they predicate of the other. When accepted, this remarkable fact should cast some doubt upon some of the (...)
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  10.  88
    Gabriel Uzquiano (2004). Plurals and Simples. The Monist 87 (3):429-451.
  11. Gabriel Uzquiano (2011). Mereological Harmony. In Karen Bennett & Dean Zimmerman (eds.), Oxford Studies in Metaphysics. Oxford University Press
    This paper 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 unextended material atoms.
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  12. Gabriel Uzquiano (2010). How to Solve the Hardest Logic Puzzle Ever in Two Questions. Analysis 70 (1):39-44.
    Rabern and Rabern (2008) have noted the need to modify `the hardest logic puzzle ever’ as presented in Boolos 1996 in order to avoid trivialization. Their paper ends with a two-question solution to the original puzzle, which does not carry over to the amended puzzle. The purpose of this note is to offer a two-question solution to the latter puzzle, which is, after all, the one with a claim to being the hardest logic puzzle ever.
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  13. Gabriel Uzquiano (2011). Plural Quantification and Modality. Proceedings of the Aristotelian Society 111 (2pt2):219-250.
    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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  14. Gabriel Uzquiano (2004). The Supreme Court and the Supreme Court Justices: A Metaphysical Puzzle. Noûs 38 (1):135–153.
  15.  70
    Agustin Rayo & Gabriel Uzquiano (1999). Toward a Theory of Second-Order Consequence. Notre Dame Journal of Formal Logic 40 (3):315-325.
    There is little doubt that a second-order axiomatization of Zermelo-Fraenkel set theory plus the axiom of choice (ZFC) is desirable. One advantage of such an axiomatization is that it permits us to express the principles underlying the first-order schemata of separation and replacement. Another is its almost-categoricity: M is a model of second-order ZFC if and only if it is isomorphic to a model of the form Vκ, ∈ ∩ (Vκ × Vκ) , for κ a strongly inaccessible ordinal.
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  16. Gabriel Uzquiano (2006). The Price of Universality. Philosophical Studies 129 (1):137 - 169.
    I present a puzzle for absolutely unrestricted quantification. One important advantage of absolutely unrestricted quantification is that it allows us to entertain perfectly general theories. Whereas most of our theories restrict attention to one or another parcel of reality, other theories are genuinely comprehensive taking absolutely all objects into their domain. The puzzle arises when we notice that absolutely unrestricted theories sometimes impose incompatible constraints on the size of the universe.
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  17. Øystein Linnebo & Gabriel Uzquiano (2009). Which Abstraction Principles Are Acceptable? Some Limitative Results. British Journal for the Philosophy of Science 60 (2):239-252.
    Neo-Fregean logicism attempts to base mathematics on abstraction principles. Since not all abstraction principles are acceptable, the neo-Fregeans need an account of which ones are. One of the most promising accounts is in terms of the notion of stability; roughly, that an abstraction principle is acceptable just in case it is satisfiable in all domains of sufficiently large cardinality. We present two counterexamples to stability as a sufficient condition for acceptability and argue that these counterexamples can be avoided only by (...)
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  18. Gabriel Uzquiano (2003). Plural Quantification and Classes. Philosophia Mathematica 11 (1):67-81.
    When viewed as the most comprehensive theory of collections, set theory leaves no room for classes. But the vocabulary of classes, it is argued, provides us with compact and, sometimes, irreplaceable formulations of largecardinal hypotheses that are prominent in much very important and very interesting work in set theory. Fortunately, George Boolos has persuasively argued that plural quantification over the universe of all sets need not commit us to classes. This paper suggests that we retain the vocabulary of classes, but (...)
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  19.  94
    Gabriel Uzquiano (2004). An Infinitary Paradox of Denotation. Analysis 64 (2):128–131.
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  20.  62
    Gabriel Uzquiano (2006). Receptacles. Philosophical Perspectives 20 (1):427–451.
    This paper looks at the question of what regions of space are possibly exactly occupied by a material object.
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  21.  6
    Gabriel Uzquiano, Editor’s Introduction.
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  22.  38
    Gabriel Uzquiano (2009). Bad Company Generalized. Synthese 170 (3):331 - 347.
    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 on (...)
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  23.  11
    Gabriel Uzquiano (2015). Editor’s Introduction. Theoria: Revista de Teoría, Historia y Fundamentos de la Ciencia 30 (3):315-316.
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  24.  60
    Gabriel Uzquiano (2004). The Paradox of the Knower Without Epistemic Closure? Mind 113 (449):95-107.
  25.  14
    Gabriel Uzquiano (2015). Guest Editor’s Introduction. Theoria. An International Journal for Theory, History and Foundations of Science 30 (3):315-316.
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  26.  62
    Ignacio Jané & Gabriel Uzquiano (2004). Well- and Non-Well-Founded Fregean Extensions. Journal of Philosophical Logic 33 (5):437-465.
    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 (...)
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  27.  44
    Gabriel Uzquiano (1999). Models of Second-Order Zermelo Set Theory. Bulletin of Symbolic Logic 5 (3):289-302.
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  28.  68
    Agustin Rayo & Gabriel Uzquiano (2006). Introduction. In Agustin Rayo & Gabriel Uzquiano (eds.), Absolute Generality. Oxford University Press
    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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  29.  59
    Gabriel Uzquiano (2005). Review of M. Potter, Set Theory and its Philosophy: A Critical Introduction. [REVIEW] Philosophia Mathematica 13 (3):308-346.
  30. Gabriel Uzquiano (2006). Unrestricted Unrestricted Quantification: The Cardinal Problem of Absolute Generality. In Agustín Rayo & Gabriel Uzquiano (eds.), Absolute Generality. Oxford University Press 305--32.
     
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  31.  54
    Gabriel Uzquiano (2002). Categoricity Theorems and Conceptions of Set. Journal of Philosophical Logic 31 (2):181-196.
    Two models of second-order ZFC need not be isomorphic to each other, but at least one is isomorphic to an initial segment of the other. The situation is subtler for impure set theory, but Vann McGee has recently proved a categoricity result for second-order ZFCU plus the axiom that the urelements form a set. Two models of this theory with the same universe of discourse need not be isomorphic to each other, but the pure sets of one are isomorphic to (...)
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  32.  84
    Stewart Shapiro & Gabriel Uzquiano (2008). Frege Meets Zermelo: A Perspective on Ineffability and Reflection. Review of Symbolic Logic 1 (2):241-266.
    1. Philosophical background: iteration, ineffability, reflection. There are at least two heuristic motivations for the axioms of standard set theory, by which we mean, as usual, first-order Zermelo–Fraenkel set theory with the axiom of choice : the iterative conception and limitation of size . Each strand provides a rather hospitable environment for the hypothesis that the set-theoretic universe is ineffable, which is our target in this paper, although the motivation is different in each case.
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  33.  52
    Gabriel Uzquiano (2012). Before-Effect Without Zeno Causality. Noûs 46 (2):259-264.
    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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  34.  37
    Gabriel Uzquiano (2003). Review of Volker Halbach, Leon Horsten (Eds), Principles of Truth. [REVIEW] Notre Dame Philosophical Reviews 2003 (4).
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  35.  11
    Michael Detlefsen, Erich Reck, Colin McLarty, Rohit Parikh, Larry Moss, Scott Weinstein, Gabriel Uzquiano, Grigori Mints & Richard Zach (2001). The Minneapolis Hyatt Regency, Minneapolis, Minnesota May 3–4, 2001. Bulletin of Symbolic Logic 7 (3).
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  36.  7
    Gabriel Uzquiano (2006). Hale 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.
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  37.  34
    Gabriel Uzquiano (2005). Semantic Nominalism. Dialectica 59 (2):265–282.
    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 is (...)
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  38.  5
    Michael Detlefsen, Erich Reck, Colin McLarty, Rohit Parikh, Larry Moss, Scott Weinstein, Gabriel Uzquiano, Grigori Mints & Richard Zach (2001). 2000-2001 Spring Meeting of the Association for Symbolic Logic. Bulletin of Symbolic Logic 7 (3):413-419.
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  39.  2
    Gabriel Uzquiano (2006). The Price of Universality. Philosophical Studies 129 (1):137-169.
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  40.  17
    N. M. L. Nathan & Gabriel Uzquiano (2005). Metaphysics. Philosophical Books 46 (3):268-271.
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  41.  5
    Gabriel Uzquiano (2007). Erata: Receptacles. Noûs 41 (2):354 -.
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  42. Gabriel Uzquiano, An Infinitary Paradox of Denotation.
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  43. Gabriel Uzquiano (1999). Ontology and the Foundations of Mathematics. Dissertation, Massachusetts Institute of Technology
    "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 serious constraints on the sorts of items (...)
     
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  44. Gabriel Uzquiano (2006). Oxford University. Philosophical Perspectives 20:427.
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