Universality and the Liar: An Essay on Truth and the Diagonal Argument

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.

Preface; 1. The Liar paradox; 2. The diagonal argument; 3. The diagonal argument and the Liar, I; 4. The diagonal argument and the Liar, II; 5. A medieval solution to the Liar; 6. A singularity solution to the Liar; 7. A formal account of singularities; 8. Applications and further singularities; 9. Semantic universality; Notes; Bibliography; Index.