Revenge, II

Abstract

Chapter 9 begins by examining the impact of revenge paradoxes on contextual theories of truth, including those of Parsons, Burge, Barwise and Etchemendy, and Glanzberg. These theories are hierarchical, and so are subject to revenge paradoxes that, roughly speaking, quantify over all levels. But the singularity theory is not hierarchical, and so is not subject to this kind of revenge. This chapter argues that a use of ‘true’ (or ‘denotes’ or ‘extension’) in a given context applies everywhere except to its singularities, and what escapes its reach is captured by other uses of ‘true’ in other contexts. Moreover, any use of ‘true’ applies even to the truths of the singularity theory, since these theoretical truths are not identified as singularities. The chapter concludes that the singularity theory is not compromised by revenge paradoxes, and respects Tarski’s intuition that natural languages are universal, while preserving classical logic and semantics.