Abstract

Chapter 1 presents the aim of the book: to provide a solution to the semantic paradoxes. 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 Gödel’s, is that these expressions are significant everywhere except for certain _singularities_, in analogy with division by zero. The chapter lays out two related desiderata for a solution. A solution should recognize that the proper setting of the semantic paradoxes is natural language, not regimented formal languages. And the solution should respect Tarski’s intuition that natural languages are universal, in the sense that they have the potential to say anything that can be said in any language.