•  107
    Vague representation
    Mind 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
  •  186
    This 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.
  •  31
    Erratum to: Beta-Conversion and the Being Constraint
    Aristotelian Society Supplementary Volume 95 (1): 1-1. 2021.
  •  78
    Beta-Conversion and the Being Constraint
    Aristotelian 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.
  •  119
    A completeness theorem for unrestricted first- order languages
    with Timothy Williamson
    In Jc Beall (ed.), Liars and Heaps: New Essays on Paradox, Clarendon Press. 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
  •  1154
    Fragmentation and logical omniscience
    with Adam Elga
    Noûs 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
  •  172
    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.
  •  102
    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
  •  169
    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.
  •  41
    Hofweber's Philosophy of Mathematics
    Philosophy and Phenomenological Research 94 (2): 474-480. 2017.
  •  91
    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.
  •  219
    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.
  •  138
    The World is the Totality of Facts, Not of Things
    Philosophical Issues 27 (1): 250-278. 2017.
  •  17
    Completud
    In Luis Vega and Paula Olmos (ed.), Compendio de Lógica, Argumentación y Retórica, Editorial Trotta. pp. 100--102. 2011.
  •  113
    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
  •  140
    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.
  •  73
    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
  •  102
    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
  •  413
    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
  •  60
    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
  •  25
    Ontological Commitment1
    Philosophy Compass 2 (3): 428-444. 2007.
    I propose a way of thinking about content, and a related way of thinking about ontological commitment.
  •  236
    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.
  •  130
    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’.).
  • Plural Predication
    Dissertation, Massachusetts Institute of Technology. 2000.
    My thesis consists of three self-contained but interconnected papers. In the first one, 'Word and Objects', I assume that it is possible to quantify over absolutely everything, and show that certain English sentences containing collective predicates resist paraphrase in first-order languages and even in first-order languages enriched with plural quantifiers. To capture such sentences I develop a language containing plural predicates . ;The introduction of plural predicates leads to an extension …Read more
  •  23
    Nota Crítica Sobre La Paradoja de Orayen (review)
    Critica 37 (109). 2005.
    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 Hurtad…Read more
  •  366
    A Plea for Semantic Localism
    Noûs 47 (4): 647-679. 2011.
    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
  •  178
    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.
  •  176
    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.
  •  207
    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