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121Vague representationMind 117 (466): 329-373. 2008.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 …Read more
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239This is a supplementary document to my "Why I am not an Absolutist (Or a First-Orderist)", which is forthcoming in a volume on higher-order logic edited by Peter Fritz and Nick Jones.
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37Erratum to: Beta-Conversion and the Being ConstraintAristotelian Society Supplementary Volume 95 (1): 1-1. 2021.
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100Beta-Conversion and the Being ConstraintAristotelian Society Supplementary Volume 95 (1): 253-286. 2021.Modal contingentists face a dilemma: there are two attractive principles of which they can only accept one. In this paper I show that the most natural way of resolving the dilemma leads to expressive limitations. I then develop an alternative resolution. In addition to overcoming the expressive limitations, the alternative picture allows for an attractive account of arithmetic and for a style of semantic theorizing that can be helpful to contingentists.
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36A completeness theorem for unrestricted first- order languagesIn J. C. Beall (ed.), Liars and Heaps: New Essays on Paradox, Oxford University Press Uk. pp. 331-356. 2003.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 constit…Read more
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1342Fragmentation and logical omniscienceNoûs 56 (3): 716-741. 2022.It would be good to have a Bayesian decision theory that assesses our decisions and thinking according to everyday standards of rationality — standards that do not require logical omniscience (Garber 1983, Hacking 1967). To that end we develop a “fragmented” decision theory in which a single state of mind is represented by a family of credence functions, each associated with a distinct choice condition (Lewis 1982, Stalnaker 1984). The theory imposes a local coherence assumption guaranteeing tha…Read more
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184On the Open-Endedness of Logical SpacePhilosophers' Imprint 20. 2020.Modal logicism is the view that a metaphysical possibility is just a non-absurd way for the world to be. I argue that modal logicists should see metaphysical possibility as "open ended'': any given possibilities can be used to characterize further possibilities. I then develop a formal framework for modal languages that is a good fit for the modal logicist and show that it delivers some attractive results.
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73The Construction of Logical SpaceOxford University Press. 2013.Our conception of logical space is the set of distinctions we use to navigate the world. Agustn Rayo argues that this is shaped by acceptance or rejection of 'just is'-statements: e.g. 'to be composed of water just is to be composed of H2O'. He offers a novel conception of metaphysical possibility, and a new trivialist philosophy of mathematics
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1. evidential symmetry let's say that propositions P and Q are evidentially symmetrical (I'll write this asp & q) for a subject if his evidence no more supports one than the other. I mean to understand evidence very broadly here to encompass whatever we haveIn Tamar Szabó Gendler & John Hawthorne (eds.), Oxford Studies in Epistemology, Oxford University Press. pp. 161. 2005.
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188Toward a Theory of Second-Order ConsequenceNotre Dame Journal of Formal Logic 40 (3): 315-325. 1999.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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47Hofweber's Philosophy of MathematicsPhilosophy and Phenomenological Research 94 (2): 474-480. 2017.
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Logicism ReconsideredIn Stewart Shapiro (ed.), Oxford Handbook of Philosophy of Mathematics and Logic, Oxford University Press. 2005.Roughly, logicism is the view that mathematics is logic. This chapter identifies several distinct logicist theses, and shows that their truth-values can be established on minimal assumptions. There is also a discussion of “Neo-Logicism.”
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100IntroductionIn Agustín 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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214Absolute 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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220PluralsPhilosophy Compass 2 (3). 2007.Forthcoming in Philosophical Compass. I explain why plural quantifiers and predicates have been thought to be philosophically significant.
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2Field on revengeIn J. C. Beall (ed.), Revenge of the liar: new essays on the paradox, Oxford University Press. 2007.
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1117Fragmentation and information accessIn Cristina Borgoni, Dirk Kindermann & Andrea Onofri (eds.), The Fragmented Mind, Oxford University Press. 2021.In order to predict and explain behavior, one cannot specify the mental state of an agent merely by saying what information she possesses. Instead one must specify what information is available to an agent relative to various purposes. Specifying mental states in this way allows us to accommodate cases of imperfect recall, cognitive accomplishments involved in logical deduction, the mental states of confused or fragmented subjects, and the difference between propositional knowledge and know-ho…Read more
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104Reply to CriticsInquiry: An Interdisciplinary Journal of Philosophy 57 (4): 498-534. 2014.Cameron, Eklund, Hofweber, Linnebo, Russell and Sider have written critical essays on my book, The Construction of Logical Space (Oxford: Oxford University Press, 2013). Here I offer some replies
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493Ontological commitmentPhilosophy Compass 2 (3). 2007.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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17CompletudIn Luis Vega and Paula Olmos (ed.), Compendio de Lógica, Argumentación y Retórica, Editorial Trotta. pp. 100--102. 2011.
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121An Actualist's Guide to Quantifying InCritica 44 (132): 3-34. 2012.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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145The 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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76Frege's unofficial arithmeticJournal of Symbolic Logic 67 (4): 1623-1638. 2002.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 th…Read more
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120A Puzzle About Ineffable PropositionsAustralasian Journal of Philosophy 89 (2). 2011.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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415Hierarchies Ontological and IdeologicalMind 121 (482). 2012.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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66Replies to Greco and TurnerPhilosophical Studies 172 (10): 2617-2620. 2015.Dan Greco and Jason Turner wrote two fantastic critiques of my book, The Construction of Logical Space. Greco’s critique suggests that the book can be given a Kuhnian interpretation, with a Carnapian twist. Here I embrace that interpretation. Turner criticizes one of the views I develop in the book. Here I identify an avenue of resistance
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32Ontological Commitment1Philosophy Compass 2 (3): 428-444. 2007.I propose a way of thinking about content, and a related way of thinking about ontological commitment.
Cambridge, Massachusetts, United States of America
Areas of Specialization
Metaphysics |
Logic and Philosophy of Logic |
Philosophy of Language |
Areas of Interest
Epistemology |