•  400
    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
  •  380
    Ontological commitment
    Philosophy 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’.).
  •  322
    A Plea for Semantic Localism
    Noûs 47 (4): 647-679. 2013.
    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
  •  279
    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
  •  171
    A puzzle about de rebus beliefs
    with Vann McGee
    Analysis 60 (4). 2000.
    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…Read more
  •  162
    Reply to Florio and Shapiro
    Mind 123 (489): 175-181. 2014.
    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.
  •  158
    Absolute 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.
  •  156
    4. Absolute Generality Reconsidered
    Oxford Studies in Metaphysics 7 93. 2012.
  •  153
    Plurals
    Philosophy Compass 2 (3). 2007.
    Forthcoming in Philosophical Compass. I explain why plural quantifiers and predicates have been thought to be philosophically significant.
  •  152
    Essence Without Fundamentality
    Theoria : An International Journal for Theory, History and Fundations of Science 30 (3): 349-363. 2015.
    I argue for a conception of essence that does not rely on distinctions of metaphysical fundamentality.
  •  146
    Nominalism, Trivialism, Logicism
    Philosophia Mathematica 23 (1). 2015.
    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 t…Read more
  •  142
    On Specifying Truth-Conditions
    Philosophical Review 117 (3): 385-443. 2008.
    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 requir…Read more
  •  136
    Word and objects
    Noûs 36 (3). 2002.
    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.
  •  123
    Toward a Theory of Second-Order Consequence
    with Augustín Rayo and Gabriel Uzquiano
    Notre 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.
  •  114
    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.
  •  104
  •  96
    An Actualist's Guide to Quantifying In
    Critica 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
  •  92
    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’.).
  •  83
    A Puzzle About Ineffable Propositions
    Australasian 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
  •  80
    A completeness theorem for unrestricted first- order languages
    with Timothy Williamson
    In Jc Beall (ed.), Liars and Heaps, Oxford University Press. 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
  •  80
    The World is the Totality of Facts, Not of Things
    Philosophical Issues 27 (1): 250-278. 2017.
  •  78
    Beyond Plurals
    In Agustín Rayo & Gabriel Uzquiano (eds.), Absolute Generality, Oxford University Press. pp. 220--54. 2006.
    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 langu…Read more
  •  78
    Introduction
    In 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.
  •  69
    Reply to Critics
    Inquiry: 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
  •  65
    Frege's unofficial arithmetic
    Journal 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
  •  62
    On the Open-Endedness of Logical Space
    Philosophers' 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.
  •  52
    The Construction of Logical Space
    Oxford 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
  •  50
    Replies to Greco and Turner
    Philosophical 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