•  37
    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). On the resulting theory, rationality requires ordinary agents to …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
  •  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.
  •  78
    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.
  •  31
    Hofweber's Philosophy of Mathematics
    Philosophy and Phenomenological Research 94 (2): 474-480. 2017.
  •  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.
  •  80
    The World is the Totality of Facts, Not of Things
    Philosophical Issues 27 (1): 250-278. 2017.
  •  1
    Absolute Generality
    with Gabriel Uzquiano Cruz
    Critica 41 (121): 67-84. 2009.
  •  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
  • 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
  •  20
    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
  •  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
  •  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
  •  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.
  •  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
  •  104
  •  156
    4. Absolute Generality Reconsidered
    Oxford Studies in Metaphysics 7 93. 2012.
  •  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
  •  13
    Review: Nota Crítica Sobre La Paradoja de Orayen (review)
    Critica 37 (109). 2005.
  •  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
  •  17
    In Luis Vega and Paula Olmos (ed.), Compendio de Lógica, Argumentación y Retórica, Editorial Trotta. pp. 100--102. 2011.
  •  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’.).
  •  153
    Philosophy Compass 2 (3). 2007.
    Forthcoming in Philosophical Compass. I explain why plural quantifiers and predicates have been thought to be philosophically significant.
  •  1
    Field on revenge
    with Philip Welch
    In J. C. Beall (ed.), Revenge of the Liar: New Essays on the Paradox, Oxford University Press. 2007.
  •  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
  •  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.
  •  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