This book is about one of the most baffling of all paradoxes – the famous Liar paradox. Suppose we say: 'We are lying now'. Then if we are lying, we are telling the truth; and if we are telling the truth we are lying. This paradox is more than an intriguing puzzle, since it involves the concept of truth. Thus any coherent theory of truth must deal with the Liar. Keith Simmons discusses the solutions proposed by medieval philosophers and offers (...) his own solutions and in the process assesses other attempts to solve the paradox. Unlike such attempts, Simmons' 'singularity' solution does not abandon classical semantics and does not appeal to the kind of hierarchical view found in Barwise's and Etchemendy's The Liar. Moreover, Simmons' solution resolves the vexing problem of semantic universality – the problem of whether there are semantic concepts beyond the expressive reach of a natural language such as English. (shrink)

This volume is designed to set out some of the central issues in the theory of truth. It draws together, for the first time, the debates between philosophers who favor 'robust' or 'substantive' theories of truth, and those other, 'deflationist' or minimalists, who deny that such theories can be given. The editors provide a substantial introduction, in which they look at how the debates relate to further issues, such as the Liar paradox and formal truth theories.

This book aims to provide a solution to the semantic paradoxes. It argues for a unified solution to the paradoxes generated by our concepts of denotation, predicate extension, and truth. The solution makes two main claims. The first is that our semantic expressions 'denotes', 'extension' and 'true' are context-sensitive. The second, inspired by a brief, tantalizing remark of Godel's, is that these expressions are significant everywhere except for certain singularities, in analogy with division by zero. A formal theory of singularities (...) is presented and applied to a wide variety of versions of the definability paradoxes, Russell's paradox, and the Liar paradox. Keith Simmons argues that the singularity theory satisfies the following desiderata: it recognizes that the proper setting of the semantic paradoxes is natural language, not regimented formal languages; it minimizes any revision to our semantic concepts; it respects as far as possible Tarski's intuition that natural languages are universal; it responds adequately to the threat of revenge paradoxes; and it preserves classical logic and semantics. Simmons draws out the consequences of the singularity theory for deflationary views of our semantic concepts, and concludes that if we accept the singularity theory, we must reject deflationism. (shrink)

This dissertation is a critical examination of dialetheism, the view that there are true contradictions. Dialetheism's proponents argue that adopting the view will allow us to solve hitherto unsolved problems, including the well-known logical paradoxes. ;Dialetheism faces three kinds of challenge. Challenges of the first kind put in doubt the intrinsic coherence of dialetheism. It can be claimed, for example, that it is incoherent for a claim to be both true and false; that claims known to be false cannot be (...) accepted; that claims known to be false cannot be rationally accepted; and that dialetheism entails the falsity of some of its own theoretical claims. The second kind of challenge concerns the use of paraconsistent logics, which dialetheists must adopt on pain of accepting the truth of every proposition. I examine a number of paraconsistent logics, and conclude that either they come at an unacceptably high price or they do not support the dialetheist project. ;I devote most attention to the third kind of challenge, according to which dialetheism fails to provide the promised solutions to the paradoxes and other previously intractable problems, and so we lose the major motivation for the theory. Proponents claim that dialetheism allows for the solution of numerous problems, particularly in metaphysics, law, and logic. In the case of metaphysics, it is claimed that dialetheism allows us to deal with puzzles involving change, vagueness, and motion. However, I argue that the proposed solution does not eliminate the old metaphysical problems, and in fact gives rise to new ones. In the case of law, it is claimed that dialetheism can allow us to deal with legal contradiction. I argue there are more plausible means of solving such conflicts. The strongest case for dialetheism is that it allows us to solve logical and semantic paradoxes of self-reference, some of which have endured for well over two thousand years. I construct a paradox that the dialetheist cannot accommodate, and which shows that dialetheism never provided a solution to the paradoxes at all, even in their more familiar forms. (shrink)

I argue for an account of semantic paradox that requires minimal logical revision. I first consider a phenomenon that is common to the paradoxes of definability, Russell’s paradox and the Liar. The phenomenon—which I call Repetition—is this: given a paradoxical expression, we can go on to produce a semantically unproblematic expression composed of the very same words. I argue that Kripke’s and Field’s theories of truth make heavy weather of Repetition, and suggest a simpler contextual account. I go on to (...) outline a ‘singularity’ theory of semantical predicates in the spirit of remarks of Gödel. According to this theory, ‘denotes’, ‘extension’ and ‘true’ are context-sensitive expression that apply almost everywhere on a given occasion of use, except for certain singular points. I then turn to revenge paradoxes, and argue that even the dialetheist is subject to revenge. I then examine how the singularity theory responds to revenge. (shrink)

Consider the following argument written on the board in room 227: 1 = 1. So, the argument on the board in room 227 is not valid. This argument generates a paradox. The aim of this paper is to present a resolution of this paradox and related paradoxes of validity, including a version of the Curry paradox. The proposal stresses the close connections between these validity paradoxes and paradoxes of truth and paradoxes of denotation. So a more general aim is to (...) provide a unified response to semantic paradox. The positive proposal is in part inspired by a brief, tantalizing suggestion of Gödel’s, that the paradoxes might appear “as something analogous to dividing by zero”—so that the concept of validity, for example, is everywhere applicable except for certain singular points or singularities. A second central claim is that ‘valid’ is a context-sensitive predicate. The key notions of this contextual-singularity theory are presented and applied to a variety of cases. Any purported solution to paradox must deal with the phenomenon of revenge, and a response to revenge is outlined. The paper closes with remarks about the accommodation of Tarski’s claim that natural languages are universal. (shrink)

In this paper, I examine a solution to the Liar paradox found in the work of Ockham, Burley, and Pseudo-Sherwood. I reject the accounts of this solution offered by modern commentators. I argue that this medieval line suggests a non-hierarchical solution to the Liar, according to which ?true? is analysed as an indexical term, and paradox is avoided by minimal restrictions on tokens of ?true?. In certain respects, this solution resembles the recent approaches of Charles Parsons and Tyler Burge; in (...) other respects, it is related to a suggestion of Gödel. But, as a whole, it suggests an original solution to the Liar paradox, quite unlike any current proposals. (shrink)

In 1905, Richard discovered his paradox of definability, and in a letter written that year he presented both the paradox and a solution to it.Soon afterwards, Poincaré endorsed a variant of Richard?s solution.In this paper, I critically examine Richard?s and Poincaré?s ways out.I draw on an objection of Peano?s, and argue that their stated solutions do not work.But I also claim that their writings suggest another way out, different from their stated solutions, and different from the orthodox Tarskian approach.I argue (...) that this second solution does not prevent the return of the paradox. (shrink)

University of North Carolina at Chapel Hill.

In this paper, I raise some interconnected concerns for Paul Horwich’s minimal theory of truth, framed by these three questions: How should the minimal theory be formulated? How does the minimal theory address the liar paradox? What is the explanatory role of the concept of truth? I conclude that we cannot be linguistic or conceptual deflationists about truth.

A Curry paradox about truth is generated by the following sentence, written on the board in room 101:If the sentence on the board in room 101 is true then 1 ≠ 1.A Curry paradox about validity is generated by the following argument, written on the board in room 102:The argument on the board in room 102 is valid. Therefore, 1 ≠ 1.Though the sentence and the argument generate Curry paradoxes, they also generate more basic paradoxes, in a sense to be (...) made clear. I argue that if we solve these more basic paradoxes, we have solutions to both kinds of Curry paradox. The positive proposal is in part inspired by a brief remark of Gödel’s, that the paradoxes might appear “as something analogous to dividing by zero”—so that the concepts of truth and validity, for example, are everywhere applicable except for certain singular points or singularities. A second central claim is that 'true' and 'valid' are context-sensitive predicates. This contextual-singularity approach to the Curry paradoxes applies also to other paradoxes of truth, validity, denotation, and predicate-extension. So a more general aim of the paper is to provide a unified response to semantic paradox. (shrink)

There is a core metaphysical claim shared by all deflationists: truth is not a genuine, substantive property. But anyone who denies that truth is a genuine property must still make sense of our pervasive truth talk. In addressing questions about the meaning and function of ‘true’, deflationists engage in a linguistic or semantic project, a project that typically goes hand-in-hand with a deflationary account of the concept of truth. A thoroughgoing deflationary account of truth will go beyond the negative metaphysical (...) claim about truth and the positive linguistic account of the word ‘true’: it will also maintain that the concept of truth is a ‘thin’ concept that bears no substantive conceptual connections to other concepts to which it is traditionally tied. (shrink)

In this paper I present two new paradoxes, a definability paradox (related to the paradoxes of Berry, Richard and König), and a paradox about extensions (related to Russell’s paradox). However, unlike the familiar definability paradoxes and Russell’s paradox, these new paradoxes involve no self-reference or circularity.

This chapter contains sections titled: Introduction Semantic Paradoxes: Some Proposals Sets and Extensions Three Paradoxes A Contextual Approach A Singularity Proposal Universality.

University of North Carolina at Chapel Hill.