Keith Simmons

DEFLATIONARY TRUTH AND THE LIAR

The topic of this paper lies at the intersection of two contemporary debates about truth. One debate is concerned with the nature of truth, and its protagonists are the correspondence theorist and the deflationist. The focus of the other debate is the Liar, where the challenge is to provide a theory of truth that adequately addresses semantical paradox. There has been surprinsigly little contact between this two debates, despite their common interest in the concept of truth. Yet I think that they do bear on one another, and that is what I shall be arguing here. I shall argue that the deflationary conception of truth is severely compromised by the Liar in ways that the correspondence conception is not

The diagonal argument and the Liar

There are arguments found in various areas of mathematical logic that are taken to form a family: the family of diagonal arguments. Much of recursion theory may be described as a theory of diagonalization; diagonal arguments establish basic results of set theory; and they play a central role in the proofs of the limitative theorems of Godel and Tarski. Diagonal arguments also give rise to set-theoretical and semantical paradoxes. What do these arguments have in common what makes an argument a diagonal argument? And why do some diagonal arguments lead to theorems, while others lead to paradox? In this paper, I attempt to answer these questions. Cantors first uses of the diagonal argument are presented in Section II. In Section III, I answer the first question by providing a general analysis of the diagonal argument. This analysis is then brought to bear on the second question. In Section IV, I give an account of the difference between good diagonal arguments (those leading to theorems) and bad diagonal arguments (those leading to paradox). The main philosophical interest of the diagonal argument, I believe, lies in its relation to the Liar paradox. The familiar Liar is generated by our ordinary semantical concepts of truth and falsity. Its proper setting is natural language, in which our ordinary semantic terms appear. As Tarski has made clear, this means that the Liar is inextricably linked with another vexed semantical problem, that of universality. Perhaps the central question here is this: Are natural languages universal? Roughly speaking, a language is universal in Tarskis sense if it can say everything there is to be said. If natural languages are universal in this sense, then they can say everying there is to be said about their own semantics. But then it would seem that natural languages fall foul of the Liar.

A paradox of definability: Richard’S and poincaré’S ways out

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, Poincare endorsed a variant of Richard’s solution.In this paper, I critically examine Richard’s and Poincare’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

On a medieval solution to the liar paradox

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 Godel. But, as a whole, it suggests an original solution to the Liar paradox, quite unlike any current proposals.