Professor Ray is Associate Professor of Philosophy. His main interests lie in philosophical logic—which is a quite loosely identified domain whose common thread is the application of formal methods to philosophical problems. Topics in this area range from philosophy of logic and philosophy of language to some problems of metaphysics, and includes the analysis of philosophical paradoxes and special topics such as the concept of truth.
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Representative Publications
"On the Matter of Essential Richness", Journal of Philosophical Logic 34 (2005): 433-457. Alfred Tarski (1944) wrote that "the condition of the 'essential richness' of the metalanguage proves to be, not only necessary, but also sufficient for the construction of a satisfactory definition of truth." But it has remained unclear what Tarski meant by an 'essentially richer' metalanguage. Moreover, DeVidi & Solomon (1999) have argued that there is nothing that Tarski could have meant by that phrase which would make his pronouncement true.
We develop an answer to the historical question of what Tarski meant by 'essentially richer' and pinpoint the general result that stands behind his essential richness claim. In defense of Tarski, we then show that each of the several arguments of DeVidi & Solomon are either moot or mistaken.
One of the fruits of our investigation is the reclamation of what Tarski took to be his central result on truth. This is a reclamation since: i) if one does not understand 'essential richness', one does not know what that result is, and ii) we must unearth a heretofore unrecognized change that occurs in Tarski's view—an alteration of his main thesis in light of a failing he discovered in it. [pdf file, requires password]
"Williamson's Master Argument on Vagueness", Synthese 138 (2004): 175-206. According to Timothy Williamson's epistemic view, vague predicates have precise extensions, we just don't know where their boundaries lie. It is a central challenge to his view to explain why we would be so ignorant, if precise borderlines were really there. He offers a novel argument to show that our insuperable ignorance "is just what independently justified epistemic principles would lead one to expect". This paper carefully formulates and critically examines Williamson's argument. It is shown that the argument does not explain our ignorance, and is not really apt for doing so. Williamson's unjustified commitment to a controversial and crucial assumption is noted. It is also argued in three different ways that his argument is, in any case, self-defeating - the same principles that drive the argument can be applied to undermine one of its premises. Along the way, Williamson's unstated commitment to a number of other controversial doctrines comes to light.
"Tarski, the Liar, and Truth Definitions", Blackwell Companion to Philosophical Logic, Ed. Dale Jacquette. Malden, MA: Blackwell, 2002. pp. 164-176. Alfred Tarski's work on truth has become a touchstone for a great deal of philosophical work on truth. A good grasp of it is critical for understanding the contemporary literature on truth and semantics. In this paper, I will present a fresh interpretation of Tarski's view, one which aims to draw it out more fully in areas of philosophical interest. This has required extrapolation (e.g., drawing explicit implications for concepts and properties) and reverse engineering (e.g., introducing the notion of full conceptual warrant) for which I will not offer textual justification here. My purpose is to introduce Tarski's central ideas briefly and in the most tenacious way I can. It is my hope that this brief study will prove useful as a basis for further investigation. [pdf file, requires password]
"Vagueness and the Sorites Paradox," with Kirk Ludwig, Language and Mind (Philosophical Perspectives 16). Ed. James Tomberlin. Atascadero, California: Ridgeview Press, 2002. pp. 419-461. A sorites argument is a symptom of the vagueness of the predicate with which it is constructed. A vague predicate admits of at least one dimension of variation (and typically more than one) in its intended range along which we are at a loss when to say the predicate ceases to apply, though we start out confident that it does. It is this feature of them that the sorites arguments exploit. Exactly how is part of the subject of this paper. The majority of philosophers writing on vagueness take it to be a kind of semantic phenomenon. If we are right, they are correct in this assumption, which is surely the default position, but they have not so far provided a satisfactory account of the implications of this or a satisfactory diagnosis of the sorites arguments. Other philosophers have urged more exotic responses, which range from the view that the fault lies not in our language, but in the world, which they propose to be populated with vague objects which our semantics precisely reflects, to the view that the world and language are both perfectly in order, but that the fault lies with our knowledge of the properties of the words we use (epistemicism). In contrast to the exotica to which some philosophers have found themselves driven in an attempt to respond to the sorites puzzles, we undertake a defense of the commonsense view that vague terms are semantically vague. Our strategy is to take fresh look at the phenomenon of vagueness. Rather than attempting to adjudicate between different extant theories, we begin with certain pre-theoretic intuitions about vague terms, and a default position on classical logic. The aim is to see whether (i) a natural story can be told which will explain the vagueness phenomenon and the puzzling nature of soritical arguments, and, in the course of this, to see whether (ii) there arises any compelling pressure to give up the natural stance. We conclude that there is a simple and natural story to be told, and we tell it, and that there is no good reason to abandon our intuitively compelling starting point. The importance of the strategy lies in its dialectical structure. Not all positions on vagueness are on a par. Some are so incredible that even their defenders think of them as positions of last resort, positions to which we must be driven by the power of philosophical argument. We aim to show that there is no pressure to adopt these incredible positions, obviating the need to respond to them directly. If we are right, semantic vagueness is neither surprising, nor threatening. It provides no reason to suppose that the logic of natural languages is not classical or to give up any independently plausible principle of bivalence. Properly understood, it provides us with a satisfying diagnosis of the sorites argumentation. It would be rash to claim to have any completely novel view about a topic so well worked as vagueness. But we believe that the subject, though ancient, still retains its power to inform and challenge us. In particular, we will argue that taking seriously the central phenomenon of predicate vagueness-the "boundarylessness" of vague predicates-on the commonsense assumption that vagueness is semantic, leads ineluctably to the view that no sentences containing vague expressions (henceforth 'vague sentences') are truth-evaluable. This runs counter to much of the literature on vagueness, which commonly assumes that, though some applications of vague predicates to objects fail to be truth-evaluable, in clear positive and negative cases vague sentences are unproblematically true or false. It is clarity on this, and related points, that removes the puzzles associated with vagueness, and helps us to a satisfying diagnosis of why the sorites arguments both seem compelling and yet so obviously a bit of trickery. We give a proof that semantically vague predicates neither apply nor fail-to-apply to anything, and that consequently it is a mistake to diagnose sorites arguments, as is commonly done, by attempting to locate in them a false premise. Sorites arguments are not sound, but not unsound either. We offer an explanation of their appeal, and defend our position against a variety of worries that might arise about it. The plan of the paper is as follows. We first introduce an important distinction in terms of which we characterize what has gone wrong with vague predicates. We characterize what we believe to be our natural starting point in thinking about the phenomenon of vagueness, from which only a powerful argument should move us, and then trace out the consequences of accepting this starting point. We consider the charge that among the consequences of semantic vagueness are that we must give up classical logic and the principle of bivalence, which has figured prominently in arguments for epistemicism. We argue there are no such consequences of our view: neither the view that the logic of natural languages is classical, nor any plausible principle of bivalence, need be given up. Next, we offer a diagnosis of what has gone wrong in sorites arguments on the basis of our account. We then present an argument to show that our account must be accepted on pain of embracing (in one way or another) the epistemic view of "vagueness", i.e., of denying that there are any semantically vague terms at all. Next, we discuss some worries that may arise about the intelligibility of our linguistic practices if our account is correct. We argue none of these worries should force us from our intuitive starting point. Finally, we cast a quick glance at other forms of semantic incompleteness.
"De Re Modality: Lessons from Quine", Knowledge, Language and Logic: Questions for Quine. Ed. Petr Kotatko and Alex Orenstein. Dordrecht: Kluwer, 2000. pp. 347-365. The aim of the paper is twofold: i) to give a logically explicit formulation of a slight generalization of Quine's master argument about de re modality - an argument which imposes important constraints on modal semantics, ii) to briefly present my favored account of modal locutions (especially locutions of the de re metaphysical flavor) and show how it successfully copes with Quine's argument. Though Quine made this argument so many years ago, it is still widely misunderstood, and so careful attention to detail seems warranted. From what I have seen, philosophers' attitudes towards Quine's master argument fall into two kinds: i) there are those that think that the argument has no force, because it is based on some mistake (usually, something about definite descriptions), and ii) there are those that think that the argument poses some insuperable barrier to any kind of de re modality. Neither of these attitudes is justified. So, I hope to make plain along the way that a) the original version of Quine's argument is sound, b) there is a version of this same basic argument which imposes very definite constraints on any proposed account of de re "metaphysical" modality in particular, and c) there is an account that satisfies these constraints. Part 1 of the paper is concerned with laying out and discussing three versions of Quine's argument, in the service of establishing points (a) and (b).
In Part 2 of the paper, I briefly sketch what I take to be a very promising, and also very Quinean account of de re modality -- one that respects the constraint on modal semantics that Quine's argument reveals and comports well with the few positive remarks Quine makes, for example, in Word and Object regarding our use of modal locutions. This will put us in a position to see that the proposed account does not fly in the face of Quine's master argument."Semantics for Opaque Contexts", with Kirk Ludwig, Philosophical Perspectives 12: Language, Mind, and Ontology. Ed. James Tomberlin. 1998, 141-166. In this paper, we outline an approach to giving extensional truth-theoretic semantics for what have traditionally been seen as opaque sentential contexts. We outline an approach to providing a compositional truth-theoretic semantics for opaque contexts which does not require quantifying over intensional entities of any kind, and meets standard objections to such accounts. The account we present aims to meet the following desiderata on a semantic theory T for opaque contexts: (D1) T can be formulated in a first-order extensional language; (D2) T does not require quantification over intensional entitiesi.e., meanings, propositions, properties, relations, or the likein its treatment of opaque contexts; (D3) T captures the entailment relations that hold in virtue of form between sentences in the language for which it is a theory; (D4) T has a finite number of axioms. If the approach outlined here is correct, it resolves a longstanding complex of problems in metaphysics, the philosophy of mind and the philosophy of language.[pdf file, requires password]
"Logical Consequence: A Defense of Tarski" Journal of Philosophical Logic 25 (1996): 617-677. In his classic 1936 essay "On the Concept of Logical Consequence", Alfred Tarski used the notion of satisfaction to give a semantic characterization of the logical properties. Tarski is generally credited with introducing the model-theoretic characterization of the logical properties familiar to us today. However, in his book, The Concept of Logical Consequence, Etchemendy argues that Tarski's account is inadequate for quite a number of reasons, and is actually incompatible with the standard model-theoretic account. Many of his criticisms are meant to apply to the model-theoretic account as well.
In this paper, I discuss the following four critical charges that Etchemendy makes against Tarski and his account of logical properties: 1) a) Tarski's account of logical consequence diverges from the standard model-theoretic account at points where the latter account gets it right. b) Tarski's account cannot be brought into line with the model-theoretic account, because the two are fundamentally incompatible. 2) There are simple counterexamples (enumerated by Etchemendy) which show that Tarski's account is wrong. 3) Tarski committed a modal fallacy when arguing that his account captures our pre-theoretic concept of logical consequence, and so obscured an essential weakness of the account. 4) Tarski's account depends on there being a distinction between the "logical terms" and the "non-logical terms" of a language, but (according to Etchemendy) there are very simple (even first-order) languages for which no such distinction can be made.
Etchemendy's critique raises historical and philosophical questions about important foundational work. However, Etchemendy is mistaken about each of these central criticisms. In the course of justifying that claim, I give a sustained explication and defense of Tarski's account. Moreover, since I will argue that Tarski's account and the model-theoretic account really do come to the same thing, my subsequent defense of Tarski's account against Etchemendy's other attacks doubles as a defense against criticisms that would apply equally to the familiar model-theoretic account of the logical properties."Ontology-Free Modal Semantics", Journal of Philosophical Logic 25 (1996): 333-361. The problem with model-theoretic modal semantics is that it provides only the formal beginnings of an account of the semantics of modal languages. In the case of non-modal language, we bridge the gap between semantics and mere model theory, by claiming that a sentence is true just in case it is true in an intended model. Truth in a model is given by the model theory, and an intended model is a model which has as domain the actual objects of discourse, and which relates these objects in an appropriate manner. However, the same strategy applied to the modal case seems to require an intended modal model whose domain includes mere possibilia.
Building on recent work by Christopher Menzel (Nous 1990), I give an account of model-theoretic semantics for modal languages which does not require mere possibilia or intensional entities of any kind. Menzel has offered a representational account of model-theoretic modal semantics that accords with actualist scruples, since it does not require possibilia. However, Menzel's view is in the company of other actualists who seek to eliminate possible worlds, but whose accounts tolerate other sorts of abstract, intensional entities, such as possible states of affairs. Menzel's account crucially depends on the existence of properties and relations in intension.
I offer a purely extensional, representational account and prove that it does all the work that Menzel's account does. The result of this endeavor is an account of model-theoretic semantics for modal languages requiring nothing but pure sets and the actual objects of discourse. Since model-theoretic semantics admits sets anyway, this account adds nothing ontologically beyond what is prima facie presupposed by the model theory itself. Thus, the result is truly an ontology-free model-theoretic semantics for modal languages. That is to say, getting genuine modal semantics out of the model theory is ontologically cost-free. Since my extensional account is demonstrably no less adequate, and yet is at the same time more ontologically frugal, it is certainly to be preferred."Thinking in L", Nous 29 (1995): 378-396. Stephen Schiffer has argued that natural languages do not have compositional semantics. But it has been widely held that compositional semantics is required in order to explain how it is possible that we have the linguistic capacities that we do. In particular, our use of natural languages is productive in the sense that there are indefinitely many sentences that we have never heard or considered before, but which we are nonetheless capable of understanding. How is this possible? Compositionality evidently supplies a clear answer to that question, because it guarantees that there is some way of determining the meaning of each sentence of the language from a fixed and finite base of semantic value assignments. This poses a serious challenge to Schiffer's negative thesis.
Schiffer proposes to answer this challenge in a way that will also provide a solution to the language-relation problem. This is the problem of specifying what relation must obtain between a population P and a language L in order for L to be a language of P. Schiffer's strategy is to reduce the problem for public languages to that of specifying the language-relation for languages of thought-specifying what it is to think in a language.
I will show in a precise way that Schiffer has neither met the productivity challenge nor solved the language-relation problem. Using Schiffer's characterization of what it is to think in a language, I show that if an agent thinks in some language L, then there is an infinity of languages that the agent also thinks in with the very same sentence tokens, but with arbitrarily different meanings. Thus, Schiffer has clearly not given a sufficient condition for an agent to think in a language, and Schiffer cannot do with less than a sufficient condition. Moreover, I will argue that Schiffer cannot avail himself of various attempts in the literature to address similar problems.
