Truth, revenge, and the limits of semantic closure

Abstract

This thesis examines the prospects for a sufficiently expressive language to contain a fully general, self-applicable truth predicate without incurring semantic incompleteness. It does so through a comparative analysis of Tarski’s truth hierarchy, Kripke’s fixed-point theory, Gupta and Belnap’s revision theory, and Field’s paracomplete approach, focusing on how each responds to the Liar paradox and the problem of revenge. Field’s claim of revenge immunity is then reassessed in the light of Welch’s boundedness result, leading to a broader discussion of whether semantic closure is a suitable standard of success for theories of truth and suggesting that revenge immunity may be better understood comparatively.