Bringing together powerful new tools from set theory and the philosophy of language, this book proposes a solution to one of the few unresolved paradoxes from antiquity, the Paradox of the Liar. Treating truth as a property of propositions, not sentences, the authors model two distinct conceptions of propositions: one based on the standard notion used by Bertrand Russell, among others, and the other based on J.L. Austin's work on truth. Comparing these two accounts, the authors show that while the (...) Russellian conception of the relation between sentences, propositions, and truth is crucially flawed in limiting cases, the Austinian perspective has fruitful applications to the analysis of semantic paradox. In the course of their study of a language admitting circular reference and containing its own truth predicate, Barwise and Etchemendy also develop a wide range of model-theoretic techniques--based on a new set-theoretic tool, Peter Aczel's theory of hypersets--that open up new avenues in logical and formal semantics. (shrink)

In this book, Scott Soames illuminates the notion of truth and the role it plays in our ordinary thought as well as in our logical, philosophical, and scientific theories. Soames aims to integrate and deepen the most significant insights on truth from a variety of sources. He powerfully brings together the best technical work and the most important philosophical reflection on truth and shows how each can illuminate the other. Investigating such questions as whether we need a truth predicate at (...) all, what theoretical tasks it allows us to accomplish, and how we are to understand the content of any predicate capable of accomplishing these tasks, Soames organizes his discussion into three parts. Part I addresses crucial foundational issues as it identifies the bearers of truth, provides a basis for distinguishing truth from other notions, and formulates positive responses to well-known forms of truth-skepticism. Part II explicates the formal theories of Alfred Tarski and Saul Kripke and evaluates the philosophical significance of their work. It discusses their treatments of the Liar paradox, the relationship between truth and proof, the notion of a partially defined predicate, the concepts of logical truth and logical consequence, and the connection between truth and meaning. Part III extends important lessons drawn from Tarski and Kripke into new domains: vague predicates, the Sorites paradox, and the development of a larger, deflationary perspective on truth. Throughout the book, Soames examines a wide range of deflationary theories of truth, and attempts to separate what is correct and worth preserving in them from what is not. In doing so, he seeks to clear up many of the most significant philosophical doubts about truth. Written for a general audience while offering engaging material to the specialist, this rich study will be profitably read by both. (shrink)

About twenty-five years ago, Charles Parsons published a paper that began by asking why we still discuss the Liar Paradox. Today, the question seems all the more apt. In the ensuing years we have seen not only Parsons’ work (1974), but seminal work of Saul Kripke (1975), and a huge number of other important papers. Too many to list. Surely, one of them must have solved it! In a way, most of them have. Most papers on the Liar Paradox offer (...) some explanation of the behavior of paradoxical sentences, and most also offer some extension for the predicate ‘true’ that they think is adequate, at least in some restricted setting. But if this is a solution, then the problem we face is far from a lack of solutions; rather, we have an overabundance of conflicting ones. Kripke’s work alone provides us with uncountably many different extensions for the truth predicate. Even if it so happens that one of these is a conclusive solution, we do not seem to know which one, or why. We should also ask, given that we are faced with many technically elegant but contradictory views, if they are really all addressing the same problem. What we lack is not solutions, but a way to compare and evaluate the many ones we have. (shrink)

A formal theory of truth, alternative to tarski's 'orthodox' theory, based on truth-value gaps, is presented. the theory is proposed as a fairly plausible model for natural language and as one which allows rigorous definitions to be given for various intuitive concepts, such as those of 'grounded' and 'paradoxical' sentences.

This paper presents an approach to truth and the Liar paradox which combines elements of context dependence and hierarchy. This approach is developed formally, using the techniques of model theory in admissible sets. Special attention is paid to showing how starting with some ideas about context drawn from linguistics and philosophy of language, we can see the Liar sentence to be context dependent. Once this context dependence is properly understood, it is argued, a hierarchical structure emerges which is neither ad (...) hoc nor unnatural. (shrink)

If we try to evaluate the sentence on line 1 we ¯nd ourselves going in an unending cycle. For this reason alone we may conclude that the sentence is not true. Moreover we are driven to this conclusion by an elementary argument: If the sentence is true then what it asserts is true, but what it asserts is that the sentence on line 1 is not true. Consequently the sentence on line 1 is not true. But when we write this (...) true conclusion on line 2 we ¯nd ourselves repeating the very same sentence. It seems that we are unable to deny the truth of the sentence on line 1 without asserting it at the same time. (shrink)

Of all the cases made against classical logic, Michael Dummett's is the most deeply considered. Issuing from a systematic and original conception of the discipline, it constitutes one of the most distinctive achievements of twentieth century British philosophy. Although Dummett builds on the work of Brouwer and Heyting, he provides the case against classical logic with a new, explicit and general foundation in the philosophy of language. Dummett's central arguments, widely celebrated if not widely endorsed, concern the implications of the (...) relation between meaning and use for both the inference rules that govern logical connectives and the relation between truth and its recognition. It is less often noted that Dummett has a further argument against classical logic, one based on the semantic and set-theoretic paradoxes. That is the topic of this paper. (shrink)

Dummett's account of the semantic paradoxes in terms of his theory of indefinitely extensible concepts is compared with Bürge's account in terms of indexicality. Dummett's appeal to intuitionistic logic does not block the paradoxes but Bürge's attempt to avoid the Strengthened Liar is unconvincing. It is argued that in order to avoid the Strengthened Liar and other semantic paradoxes involving nonindexical expressions (constants), one must postulate that when we reflect on the paradoxes there are slight shifts in the meaning (not (...) just reference) we ascribe to metalinguistic expressions (in particular 'say', and derivatively 'true' and 'false'). Consideration of metaphor and gradual linguistic change suggests that such semantic shifts are consistent with language-learning and communication. On this account there is no threat to classical logic, bivalence or the fundamental principles governing 'true' and 'false'. (shrink)

This book develops a framework for analysing strategic rationality, a notion central to contemporary game theory, which is the formal study of the interaction of rational agents and which has proved extremely fruitful in economics, political theory and business management. The author argues that a logical paradox lies at the root of a number of persistent puzzles in game theory, in particular those concerning rational agents who seek to establish some kind of reputation. Building on the work of Parsons, Burge, (...) Gaifman and Barwise and Etchemendy, Robert Koons constructs a context-sensitive solution to the whole family of liar-like paradoxes including, for the first time, a detailed account of how the interpretation of paradoxical statements is fixed by context. This analysis provides an understanding of how the rational agent model can account for the emergence of rules, practices and institutions. (shrink)