Agustín Rayo

Our conception of logical space is the set of distinctions we use to navigate the world. In The Construction of Logical Space I defend the idea that one's conception of logical space is shaped by one's acceptance or rejection of 'just is'-statements: statements like 'to be composed of water just is to be composed of H2O', or 'for the number of the dinosaurs to be zero just is for there to be no dinosaurs'. The resulting picture is used to articulate a conception of metaphysical possibility that does not depend on a reduction of the modal to the non-modal, and to develop a trivialist philosophy of mathematics, according to which the truths of pure mathematics have trivial truth-conditions.

I defend a conception of language according to which sentences don't usually have stable meanings, and use it to address the Sorites and Liar paradoxes.

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.

I argue that the root of vagueness lies not in the type of semantic-value that is best associated with an expression, but in the type of linguistic practice that renders the expression meaningful. More specifically, I suggest that whereas conventions about how to use sentences involving only attributions of vague predicates to clear cases are often prevalent to a very high degree, conventions about how to use sentences involving attributions of vague predicates to borderline cases are prevalent, if at all, to lesser degrees. (I wrote this paper a long time ago, and have since have grown dissatisfied with its content. See footnote 1 of the paper for further explanation, and 'Vague Representation' for my current position of vagueness.)

I offer a response to the Unexplained Supervenience Objection: the complaint that postulating unexplained supervenience in accounting for the phenomenon of vagueness is methodologically perverse in the same general kind of way that setting forth a theory sufficiently lacking in simplicity is methodologically perverse.

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.

I characterize a variety of mathematical Platonism according to which, e.g. for the number of the planets to be eight just is for there to be eight planets, and argue that Neo-Fregeans should be seen as defending such a view.

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.

I develop a technique for specifying truth-conditions, and use it to address a puzzle in the philosophy of mathematics.

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'.

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.

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.

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.

Years ago, when I was young and reckless, I believed that there was such a thing as an all- inclusive domain. Now I have come to see the error of my ways.

I propose a way of thinking about content, and a related way of thinking about ontological commitment.

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.

We characterize the problem of absolute generality, and draw a map of the relevant philosophical terrain.

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

Frege famously set forth the claim that the concept horse is not a concept. I develop a view of concepts and objects whereby Frege's claim is essentially correct.

We assess the claim that there is no significant difference between the ontological hierarchy of sets and the ideological hierarchy of type theory, and discuss some technical issues concerning infinitary type theory.

We respond to Florio and Shapiro's "Set Theory, Type Theory, and Absolute Generality", which is a response to our "Hierarchies Ontological and Ideological".

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.

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

This is a critical review of Orayen's Paradox , a collection of essays devoted to the work of the late Argentine philosopher Raul Orayen.

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.

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.

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

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.

I develop a device for simulating quantification over merely possible objects from the perspective of a modal actualist.

I argue for localism about credal assignments: the view that credal assignments are only well-defined relative to suitably constrained sets of possibilities. The position is motivated by suggesting that it is the best way of addressing a puzzle devised by Roger White.