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  1. Agustin Rayo, An Account of Possibility.
    I develop an account of the sorts of considerations that should go into determining where the limits of possibility lie. (This is part of a series of four closely related papers. The other three are ‘On Specifying Truth-Conditions’, ‘Ontological Commitment’ and ‘An Actualist’s Guide to Quantifying-In’.).
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  2. Agustin Rayo, Phil 285 - Special Topics: A Vagueness Primer.
    The seminar is intended as an introduction to vagueness. We'll survey some prominent accounts of vagueness, so that people get a sense of what `accounting for vagueness' is all about, and why it's hard.
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  3. Agustin Rayo, Phil 10: Introduction to Logic.
    Students in this class are expected to complete work on their own. Both problem sets and exams should consist entirely of the student's own work; they must not be copied from other students or any other source. Failure to comply constitutes plagiarism and is a serious violation of class and University policy. Cases of academic dishonesty will be pursued to the fullest extent possible.
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  4. Øystein Linnebo & Agustín Rayo (2014). Reply to Florio and Shapiro. Mind 123 (489):175-181.
    Florio and Shapiro take issue with an argument in ‘Hierarchies Ontological and Ideological’ for the conclusion that the set-theoretic hierarchy is open-ended. Here we clarify and reinforce the argument in light of their concerns.
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  5. Agustín Rayo (2014). Nominalism, Trivialism, Logicism. Philosophia Mathematica:nku013.
    This paper extracts some of the main theses in the philosophy of mathematics from my book, The Construction of Logical Space. I show that there are important limits to the availability of nominalistic paraphrase functions for mathematical languages, and suggest a way around the problem by developing a method for specifying nominalistic contents without corresponding nominalistic paraphrases. Although much of the material in this paper is drawn from the book — and from an earlier paper — I hope the present (...)
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  6. Agustín Rayo (2014). Reply to Critics. Inquiry 57 (4):498-534.
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  7. Agustín Rayo (2013). A Plea for Semantic Localism. Noûs 47 (4):647-679.
    The purpose of this paper is to defend a conception of language that does not rely on linguistic meanings, and use it to address the Sorites and Liar paradoxes.
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  8. Øystein Linnebo & Agustín Rayo (2012). Hierarchies Ontological and Ideological. Mind 121 (482):269 - 308.
    Gödel claimed that Zermelo-Fraenkel set theory is 'what becomes of the theory of types if certain superfluous restrictions are removed'. The aim of this paper is to develop a clearer understanding of Gödel's remark, and of the surrounding philosophical terrain. In connection with this, we discuss some technical issues concerning infinitary type theories and the programme of developing the semantics for higher-order languages in other higher-order languages.
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  9. Agustin Rayo (2012). An Actualist´s Guide to Quantifying In. Critica 44 (132):3-34.
    I develop a device for simulating quantification over merely possible objects from the perspective of a modal actualist ---someone who thinks that everything that exists actually exists.
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  10. Agustín Rayo (2012). 4. Absolute Generality Reconsidered. Oxford Studies in Metaphysics 7:93.
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  11. Agustín Rayo (2011). Completud. In. In Luis Vega and Paula Olmos (ed.), Compendio de Lógica, Argumentación y Retórica. Editorial Trotta. 100--102.
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  12. Agustín Rayo (2010). A Puzzle About Ineffable Propositions. Australasian Journal of Philosophy 89 (2):289 - 295.
    I will argue for localism about credal assignments: the view that credal assignments are well-defined only relative to suitably constrained sets of possibilities. I will motivate the position by suggesting that it is the best way of addressing a puzzle devised by Roger White.
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  13. Agustín Rayo (2008). Vague Representation. Mind 117 (466):329-373.
    The goal of this paper is to develop a theory of content for vague language. My proposal is based on the following three theses: (1) language-mastery is not rulebased— it involves a certain kind of decision-making; (2) a theory of content is to be thought of instrumentally—it is a tool for making sense of our linguistic practice; and (3) linguistic contents are only locally defined—they are only defined relative to suitably constrained sets of possibilities. CiteULike Connotea Del.icio.us What's this?
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  14. Agustin Rayo (2008). On Specifying Truth-Conditions. Philosophical Review 117 (3):385 - 443.
    This essay is a study of ontological commitment, focused on the special case of arithmetical discourse. It tries to get clear about what would be involved in a defense of the claim that arithmetical assertions are ontologically innocent and about why ontological innocence matters. The essay proceeds by questioning traditional assumptions about the connection between the objects that are used to specify the truth-conditions of a sentence, on the one hand, and the objects whose existence is required in order for (...)
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  15. Agustín Rayo (2007). Ontological Commitment. Philosophy Compass 2 (3):428–444.
    I propose a way of thinking aboout content, and a related way of thinking about ontological commitment. (This is part of a series of four closely related papers. The other three are ‘On Specifying Truth-Conditions’, ‘An Actualist’s Guide to Quantifying In’ and ‘An Account of Possibility’.).
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  16. Agustín Rayo (2007). Plurals. Philosophy Compass 2 (3):411–427.
    Forthcoming in Philosophical Compass. I explain why plural quantifiers and predicates have been thought to be philosophically significant.
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  17. Agustín Rayo & P. D. Welch (2007). Field on Revenge. In J. C. Beall (ed.), Revenge of the Liar: New Essays on the Paradox. Oxford University Press.
     
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  18. Agustin Rayo (2006). Beyond Plurals. In Agustín Rayo & Gabriel Uzquiano (eds.), Absolute Generality. Oxford University Press. 220--54.
    I have two main objectives. The first is to get a better understanding of what is at issue between friends and foes of higher-order quantification, and of what it would mean to extend a Boolos-style treatment of second-order quantification to third- and higherorder quantification. The second objective is to argue that in the presence of absolutely general quantification, proper semantic theorizing is essentially unstable: it is impossible to provide a suitably general semantics for a given language in a language of (...)
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  19. 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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  20. 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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  21. 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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  22. Agustin Rayo (2005). Nota Crítica Sobre La Paradoja de Orayen. [REVIEW] Critica 37 (109):99 - 115.
    La Paradoja de Orayen es dos cosas en una. Primeramente, es un homenaje al filósofo argentino Raúl Orayen (1942–2003). Pocos filósofos hispanoamericanos han gozado de la solidez intelectual y agudeza filosófica de Orayen, y pocos han sido tan queridos. Se trata, pues, de un homenaje bien merecido y que mucho agradecemos los que tuvimos la fortuna de interactuar con Raúl y aprender de él. En segundo lugar, el libro es una contribución a la filosofía hispanoamericana. Alberto Moretti y Guillermo Hurtado (...)
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  23. Agustín Rayo (2005). Review: Nota Crítica Sobre La Paradoja de Orayen. [REVIEW] Critica 37 (109):99 - 115.
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  24. Agustín Rayo (2004). Frege's Correlation. Analysis 64 (2):119–122.
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  25. Agustín Rayo (2003). When Does ‘Everything’ Mean Everything? Analysis 63 (278):100–106.
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  26. Agustín Rayo & Timothy Williamson (2003). A Completeness Theorem for Unrestricted First-Order Languages. In Jc Beall (ed.), Liars and Heaps. Oxford University Press.
    Here is an account of logical consequence inspired by Bolzano and Tarski. Logical validity is a property of arguments. An argument is a pair of a set of interpreted sentences (the premises) and an interpreted sentence (the conclusion). Whether an argument is logically valid depends only on its logical form. The logical form of an argument is fixed by the syntax of its constituent sentences, the meanings of their logical constituents and the syntactic differences between their non-logical constituents, treated as (...)
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  27. Agustín Rayo (2002). Frege's Unofficial Arithmetic. Journal of Symbolic Logic 67 (4):1623-1638.
    I show that any sentence of nth-order (pure or applied) arithmetic can be expressed with no loss of compositionality as a second-order sentence containing no arithmetical vocabulary, and use this result to prove a completeness theorem for applied arithmetic. More specifically, I set forth an enriched second-order language L, a sentence A of L (which is true on the intended interpretation of L), and a compositionally recursive transformation Tr defined on formulas of L, and show that they have the following (...)
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  28. Agustín Rayo (2002). Word and Objects. Noûs 36 (3):436–464.
    The aim of this essay is to show that the subject-matter of ontology is richer than one might have thought. Our route will be indirect. We will argue that there are circumstances under which standard first-order regimentation is unacceptable, and that more appropriate varieties of regimentation lead to unexpected kinds of ontological commitment.
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  29. Agustin Rayo & Stephen Yablo (2001). Nominalism Through de-Nominalization. Noûs 35 (1):74–92.
  30. Vann McGee & Agustín Rayo (2000). A Puzzle About de Rebus Beliefs. Analysis 60 (4):297–299.
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  31. Agustin Rayo (2000). A Puzzle About De Rebus Beliefs. Analysis 60 (4):297 - 299.
    George Boolos (1984, 1985) has extensively investigated plural quantifi- cation, as found in such locutions as the Geach-Kaplan sentence There are critics who admire only one another, and he found that their logic cannot be adequately formalized within the first-order predicate calculus. If we try to formalize the sentence by a paraphrase using individual variables that range over critics, or over sets or collections or fusions of critics, we misrepresent its logical structure. To represent plural quantification adequately requires the logical (...)
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  32. Agustin Rayo (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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