Abstract

This dissertation is a critical examination of three truth-gap theories as resolutions to the semantical paradoxes and a comparison of these theories with Tarski's classical resolution. Chapter I sets forth the semantical paradoxes and represents them in a simple and elegant language in which self-reference is possible. Several obvious solutions to the paradoxes are then discussed and dismissed in order to develop criteria for a good resolution of the semantical paradoxes. We then critically examine Tarski's philosophical solution to the semantical paradoxes and model his formal solution to the antinomy of the liar in our self-referential language. Chapter II presents Robert L. Martin's "Category Solution" to the paradox of the liar. The language developed in Chapter I is modified to model Martin and Woodruff's result that a formal language L can contain its own truth predicate 'true-in-L'. We then critically evaluate the "Category Solution". Chapter III presents Bas van Fraassen's "Presupposition Solution" to the paradox of the liar. Again, the language developed in Chapter I is modified to model van Fraassen's solution, and then we critically evaluate van Fraassen's solution to the liar. Chapter IV is a critical exposition and evaluation of Saul Kripke's theory of truth based on the concept of "semantic grounding". As in the previous chapters, the language of Chapter I is modified to model Kripke's truth-gap theory and Kripke's application of fixed-point theorems to semantics. Both Kripke's resolution of the antinomy of the liar within his formal language and Kripke's theory of truth are critically evaluated. Chapter V presents a synopsis of our argument against the truth-gap theories as resolutions to the semantical paradoxes and provides a diagnosis why the truth-gap solutions fail. We reaffirm a Tarskian approach to the semantical paradoxes