Greg Ray

Logical consequence: A defense of Tarski

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 Tarskis 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 the logical properties:(1)(a)Tarskis account of logical consequence diverges from the standard model-theoretic account at points where the latter account gets it right.(b)Tarskis 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 Tarskis account is wrong.(3)Tarski committed a modal fallacy when arguing that his account captures our pre-theoretical concept of logical consequence, and so obscured an essential weakness of the account.(4)Tarskis 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. Etchemendys 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 Tarskis account. Moreover, since I will argue that Tarskis account and the model-theoretic account really do come to the same thing, my subsequent defense of Tarskis account against Etchemendys other attacks doubles as a defense against criticisms that would apply equally to the familiar model-theoretic account of the logical properties.

Unity in the Variety of Quotation

This chapter argues that while quotation marks are polysemous, the thread that runs through all uses of quotation marks that involve reference to expressions is pure quotation, in which an expression formed by enclosing another expression in quotation marks refers to that enclosed expression. We defend a version of the so-called disquotational theory of pure quotation and show how this device is used in direct discourse and attitude attributions, in exposition in scholarly contexts, and in so-called mixed quotation in indirect discourse and attitude attributions. We argue that uses of quotation marks that extend beyond pure quotation have two features in common. First, the expressions appearing in quotation marks are intended to be understood, and that they are intended to be understood is essential to the function that such quotations play in communication, though this does not always involve the expressions contributing their extensional properties to fixing truth conditions for the sentences in which they appear. Second, they appeal to a relation to the expression appearing in quotation marks that plays a role in determining the truth conditions of the sentences in which they appear.

ON THE MATTER OF ESSENTIAL RICHNESS

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 and Solomon (1999) have argued in this Journal 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 and 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 Tarskis view – an alteration of his main thesis in light of a failing he discovered in it.

TARSKI AND THE METALINGUISTIC LIAR

I offer an interpretation of a familiar, but poorly understood portion of Tarski’s work on truth – bringing to light a number of unnoticed aspects of Tarski’s work. A serious misreading of this part of Tarski to be found in Scott Soames’ Understanding Truth is treated in detail. Soames’reading vies with the textual evidence, and would make Tarski’s position inconsistent in an unsubtle way. I show that Soames does not finally have a coherent interpretation of Tarski. This is unfortunate, since Soames ultimately arrogates to himself a key position that he has denied to Tarski and which is rightfully Tarski’s own.

De Re Modality: Lessons From Quine

The aim of this 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. Let me apologize in advance for spending a good deal of time, as I do in this paper, making explicit an argument that Quine laid out so many years ago and that has been very often discussed and alluded to since. However, I have come to the conviction that this argument is still widely misunderstood, and so the careful attention to detail seems warranted. In espousing my favored view of modal locutions in various venues, a broad appeal to “Quinean considerations” has often been made by way articulating a worry for me. Sometimes the objection is simply: “But what about Quine’s argument?” Since I think of the view I am promoting as very nearly Quinean, this response has always puzzled me. 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 this paper will be concerned with laying out and discussing three versions of Quine’s argument, in the service of establishing points (a) and (b).

Ontology-free modal semantics

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, Menzels 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. Menzels 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 Menzels 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 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 adeguate, and yet is at the same time more ontologically frugal, it is certainly to be preferred.

Thinking in L

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 Schiffers 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. Schiffers 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 Schiffers 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.

The 37th annual meeting of the Society for Exact Philosophy

This special issue of Synthese is devoted to papers from the 37th annual meeting of the Society for Exact Philosophy (SEP). In 2009, thirty-nine years after its inaugural meeting held at McGill University in Montreal in 1970,1 the Society met in Edmonton, Alberta and showed its continued vigor with a most excellent conference organized by Bernard Linsky and F. Jeffrey Pelletier with the generous support of the University of Edmonton.