Agustin Rayo
My Philosophical Views
Fragmentation and logical omniscience
with Adam Elga
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
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 be logically competent and to engage in trains of thought that increase the unification of their states of mind. But rationality does not require ordinary agents to be logically omniscient.
Philosophy of Mind, MiscellaneousDecision Theory
On the Open-Endedness of Logical Space
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.
The Construction of Logical Space
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
ModalityAreas of Mathematics
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.
Unrestricted QuantificationLogical Consequence and EntailmentSecond-Order LogicModel Theory
with Gabriel Uzquiano
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.
Unrestricted Quantification
Nominalism through de-nominalization
with Stephen Yablo
Noûs 35 (1). 2001.
Second-Order LogicPredicate LogicPlural QuantificationMetaontologyAbstract Objects
Hofweber's Philosophy of Mathematics
Philosophy and Phenomenological Research 94 (2): 474-480. 2017.
Absolute Generality (edited book)
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.
Unrestricted QuantificationUniversalsLogical Semantics and Logical TruthHigher-Order Logic, MiscRuss…Read more
Unrestricted QuantificationUniversalsLogical Semantics and Logical TruthHigher-Order Logic, MiscRussell's Paradox
The World is the Totality of Facts, Not of Things
Philosophical Issues 27 (1): 250-278. 2017.
Absolute Generality
with Gabriel Uzquiano Cruz
Critica 41 (121): 67-84. 2009.
Fragmentation and information access
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
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-how
The Nature of ReasoningTacit and Dispositional Belief
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
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 of Quine's criterion of ontological commitment. I argue that theories containing plural predicates can have plural ontological commitments in addition to singular ones. In this sense, I argue that the subject-matter of ontology is richer than one might have thought. ;Plural predicates turn out to be tremendously fruitful. For example, they provide us with natural formalizations for English plural definite descriptions and generalized quantifiers. They also allow us to state important set theoretic propositions, and give a formal semantics for second-order languages. Such a formal semantics is developed in the second paper, 'Toward a Theory of Second-Order Consequence', which is a collaboration with Gabriel Uzquiano. ;In the third paper, 'Frege's Unofficial Arithmetic', I consider an application of plural predicates to the philosophy of mathematics. By developing a suggestion of the later Frege, I show that any arithmetical predicate can be transformed into a plural predicate in such a way that the arithmetical predicate is true of the number of the Fs just in case the plural predicate is true of the Fs themselves. ;The transformation is important both because it can be put to use by nominalists about arithmetic and neo-Fregeans, and because it provides the foundations for an account of applied arithmetic
Plural Quantification
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
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 tuvieron el acierto de reconocer el valor de un proyecto que la prematura muerte de Orayen dejó inconcluso, y apreciar su potencial para generar discusión filosófica de alto nivel. El resultado es un volumen que recompensará la atención de sus lectores, y dará al trabajo de Orayen justa prominencia en el mundo hispanoamericano
Latin American Philosophy of Science, Logic, and Mathematics
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
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 the same logical type. I claim that this leads to a trilemma: one must choose between giving up absolutely general quantification, settling for the view that adequate semantic theorizing about certain languages is essentially beyond our reach, and countenancing an open-ended hierarchy of languages of ever ascending logical type. I conclude by suggesting that the hierarchy may be the least unattractive of the options on the table.
Specific Expressions, MiscPlural QuantificationUnrestricted Quantification
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
NamesActualism and Possibilism
Word and objects
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.
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
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 the truth-conditions thereby specified to be satisfied, on the other. This allows one to set forth an assignment of truth-conditions to arithmetical sentences whereby nothing is required of the world in order for the truth-conditions of a truth of pure arithmetic to be satisfied. The essay then argues that such an assignment can be used to account for the a priori knowability of certain arithmetical truths
Truth-Conditional TheoriesOntological Commitment
Frege's correlation
Analysis 64 (2). 2004.
Frege: Abstraction Principles
4. Absolute Generality Reconsidered
Oxford Studies in Metaphysics 7 93. 2012.
Hierarchies Ontological and Ideological
with Øystein Linnebo
Mind 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
Unrestricted QuantificationHigher-Order Logic, MiscSet Theory as a Foundation, Misc
Review: Nota Crítica Sobre La Paradoja de Orayen (review)
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
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 discussion will earn its keep by motivating the ideas in a new way, and by suggesting further applications
Mathematical Nominalism
Completud
In Luis Vega and Paula Olmos (ed.), Compendio de Lógica, Argumentación y Retórica, Editorial Trotta. pp. 100--102. 2011.
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'.).
When does 'everything' mean everything?
Philosophy Compass 2 (3). 2007.
Forthcoming in Philosophical Compass. I explain why plural quantifiers and predicates have been thought to be philosophically significant.
Plural QuantificationPredicates
Field on revenge
with Philip Welch
In J. C. Beall (ed.), Revenge of the Liar: New Essays on the Paradox, Oxford University Press. 2007.
ParadoxesLiar Paradox
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
Epistemological States and PropertiesBeliefKripke's Puzzle About Belief
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.
Higher-Order Logic, MiscSet Theory as a Foundation, MiscLogical Semantics and Logical Truth
Reply to Critics
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