Agustín Rayo

I work in the intersection of philosophy of logic and philosophy of language. I am especially interested in connections between possibility and content, and in the phenomenon of vagueness, but I've also done work on higher-order resources, unrestricted quantification, truth and the philosophy of mathematics. I received my PhD from MIT in 2001.

Work in Progress

'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'.)


'An Actualist's Guide to Quantifying-In'
I offer solutions to a puzzle about intentional identity and a related puzzle about empty names. (This is part of a series of four closely related papers. The other three are 'On Specifying Truth-Conditions', 'Ontological Commitment' and 'An Account of Possibility'.)


'A Puzzle for Structuralism' (with Gabriel Uzquiano)
Structuralism comprises a family of views which are united by the thought that the subject-matter of a mathematical theory is a mathematical structure. Different structuralist views presuppose different accounts of what mathematical structures are. But most of them agree that mathematicians would be in a position to identify the relevant structure if they could supply an axiomatization of the relevant theory which is (i) satisfiable, (ii) recursive, and (iii) categorical. We observe that, under the assumption that a certain form of Reflection is true, no recursive and satisfiable second-order axiomatization of set theory is categorical. The aim of the paper is to assess the prospects of structuralism in light of this limitative result. We look, in particular, at the prospects of relaxing condition (iii) to allow for partial categoricity results that help identify the relevant structure on the assumption that attention is restricted to models in which the (first-order) domain is absolutely unrestricted. We end the paper with a dilemma for Structuralism.

Articles

'Towards a Trivialist Account of Mathematics'
To appear in Bueno and Linnebo (eds.), New Waves in Philosophy of Mathematics

I defend mathematical trivialism: the view that the truths of pure mathematics have trivial truth-conditions and the falsities of pure mathematics have trivial falsity-conditions.


'On Specifying Truth-Conditions'
The Philosophical Review (forthcoming)

I develop a technique for specifying truth-conditions. (This is part of a series of four closely related papers. The other three are 'An Account of Possibility', 'Ontological Commitment' and 'An Actualist's Guide to Quantifying-In'.)


'Vague Representation'
Mind vol. 117 pp. 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 rule-based -- 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.


'Ontological Commitment' [Penultimate Version]
Philosophical Compass vol. 2, 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'.)


'Field on Revenge' (with P.D. Welch)
In The Revenge of the Liar, ed. JC Beall, Oxford University Press, 2007.

In a series of recent papers, Hartry Field has proposed a novel class of solutions to the semantic paradoxes, and argued that the new solutions are 'revenge-immune'. He has argued, in particular, that by building on a sufficiently expressive language one can get a language which is able to express its own semantic theory, including its own truth predicates and any intelligible determinacy predicates. The purpose of this note is to argue that the plausibility of Field's revenge-immunity claim depends crucially on the status of higher-order languages. We show that by availing oneself of higher-order resources one can give an explicit characterization of the key semantic notion underlying Field's proposal, and note that inconsistency would ensue if the languages under discussion were expressive enough to capture this notion.


'Plurals' [Penultimate Version]
Philosophical Compass vol. 2, 2007

I explain why plural quantifiers and predicates have been thought to be philosophically significant.


'Beyond Plurals'
In Rayo and Uzquiano (eds.) Absolute Generality, OUP, 2006.

The paper has 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 higher-order 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.


'Logicism Reconsidered'
In Shapiro (ed.) The Oxford Handbook for Logic and the Philosophy of Mathematics, OUP, 2005.

I show that the truth-values of various logicist theses can be conclusively established on minimal assumptions. In addition, I develop a notion of 'content-recarving' as a constraint on logicism, and offer a critique of 'Neo-Logicism'.


'Frege's Correlation'
Analysis 64(2), April 2004.*

This is a philosophical companion to 'Frege's Unofficial Arithmetic'. I offer an explanation of why is it that mathematical knowledge can be relevant to knowledge about the natural world.


'A Completeness Theorem for Unrestricted First-Order Languages' (with Tim Williamson)
In JC Beall (ed.) Liars and Heaps, OUP, 2003.

We identify a sound and complete axiomatization for first-order languages containing logically unrestricted quantifiers, that is, quantifiers that range, as a matter of logic, over everything there is.


'Success by Default?'
Philosophia Mathematica 11(3), 2003, pp. 305-322.

I argue that Neo-Fregean accounts of arithmetical language and arithmetical knowledge tacitly rely on a thesis I call [Success by Default]--the thesis that, in the absence of reasons to the contrary, we are justified in thinking that certain stipulations are successful. Since Neo-Fregeans have yet to supply an adequate defense of [Success by Default], I conclude that there is an important gap in Neo-Fregean accounts of arithmetical language and knowledge. I end the paper by offering a naturalistic remedy.


'When does 'everything' mean everything?'    [Ingenta]
Analysis 63(2), April 2003.*

I offer an argument for the possibility of determinately quantifying over absolutely everything.


'Frege's Unofficial Arithmetic'
The Journal of Symbolic Logic 67(4), December 2002 pp. 1623-1638.

This is a technical companion of to 'Frege's Correlation'. I show that n th-order arithmetic can be expressed within second-order logic in a way which preserves compositionality.


'Word and Objects'    [Ingenta]
Noûs, 36(3), 2002, pp. 436-464.

I argue that, if we admit the possibility of quantifying over everything, languages of regimentation involving plural variables and predicates are better suited to meet our needs than their first-order counterparts.


'Nominalism Through De-Nominalization' (with Steve Yablo)    [Ingenta]
Noûs 35(1), 2001, pp. 74-92.

We offer a translation method from second-order logic into English which adequately deals with the predicative nature of second-order variables and with non-monadic higher-order quantification.


'A Puzzle about de rebus Belief' (with Vann McGee)    [Ingenta]
Analysis, 60(4), October 2000, pp. 297-299.*

We show that an account of de rebus belief that parallels the standard account of de re belief leads to contradiction.


'Toward a Theory of Second-Order Consequence' (with Gabriel Uzquiano)    [Project Euclid]
The Notre Dame Journal of Formal Logic, 40(3), 1999, pp. 315-325.

We offer a definition of truth in a model for second-order languages which is adequate when the objects in our domain of discourse are too many to form a set.

Edited Volume

Absolute Generality (with Gabriel Uzquiano) Oxford University Press, 2006.
(Here is the volume's Introduction.)

Work in Spanish

'Nota crítica sobre La Paradoja de Orayen '
Crítica: Revista Hispanoamericana de Filosofía, vol 63, 2003, pp. 99-115. Reprinted in García de la Sienra (ed.) Reflexiones sobre la paradoja de Orayen, IIF-UNAM, 2008.

I offer an account of Orayen's Paradox.

Teaching

Big Number Duel (IAP -a. Vol. 37, No. 109 (abril 2005): 992007, with Adam Elga)


24.118 - Paradox and Infinity (Fall 2006)


24.400 - Proseminar I (Spring 2006, with Rae Langton)


24.251 - Introduction to the Philosophy of Language (Spring 2006)


24.729 - Topics in Philosophy of Language - Vagueness (Fall 2005)


24.118 - Paradox & Infinity (Fall 2005)


PHIL 285 - Special Topics: A Vagueness Primer (Spring 2005)


PHIL 10 - Introduction to Logic (Spring 2005)


PHIL 134 - Philosophy of Language (Winter 2005)


PHIL 120 - Symbolic Logic I (Fall 2004)