Universality and the Liar

Abstract

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.

A Contextual-Hierarchical Approach to Truth and the Liar Paradox

“…This is clear for the classical objections of Kripke [32], as I have build into the hierarchy as much self-application of the truth relation as Kripke himself provides. I also believe it holds for some more recent criticisms, such as those of Simmons [48,49], though a more thorough discussion of this will have to wait for another occasion. 24 The theme of reflection appears in a number of works, including the classic papers of Kripke [32] and Parsons [43].…”

“…With Parsons [43], I shall ultimately propose that there is a quantifier domain restriction phenomenon at work, though an extraordinary one. A more common idea [3,30,48,49] is to suppose that the truth predicate itself contains a hidden indexical component. 3 Let me briefly note that I do not think this is a promising option.…”

“…Two useful starting places are Stanley and Szabó [55] and von Fintel [62]. 3 Koons [30] and Simmons [48,49] build upon the work of Burge [3], but make some significant departures. How far their commitments to an index on the truth predicate go is not entirely easy to judge.…”

“…How far their commitments to an index on the truth predicate go is not entirely easy to judge. For instance, the object language in some of the formal discussion of Simmons [48] does not contain an indexed truth predicate, though indexed sentences are evaluated and indexed truth predicates are introduced. In later work [49], Simmons does appear to more thoroughly rely upon an indexed truth predicate.…”

“…22 22 Most context-based approaches to the paradox, including those of Barwise and Etchemendy [2], Burge [3], Gaifman [10,11], Koons [30], and Parsons [43], wind up with some aspects of hierarchy, though these authors differ on the nature of the hierarchy and the amount of emphasis they place upon it. A more difficult case to classify is Simmons [48,49]. He comes to some conclusions that seem to me to be hierarchical, but explicitly…”