Abstract

In the first chapter, I do two things. I discuss general philosophical motivations for studying languages which contain their own truth predicates: I discuss the history of the subject to some extent, starting with Tarski and examining briefly the work of Gupta, Herzberger, and Kripke. I also give an overview of the system itself, that is, I describe the language, the model theory and its axioms, and discuss some of the motivations, philosophical and technical for its properties. ;The second chapter gives the model theory. I also give several "existence" theorems, that is, I show that certain kinds of desirable models exist so that the system is not any more restrictive than, say, standard model theory. ;The third chapter gives the axiomatization for the model theory. Intuitively, it might come as somewhat of a surprise that languages with truth and falsity predicates are axiomatizable, but it does not follow, in the broad way this is understood, that languages with their own truth and falsity predicates are languages rich enough to do their own truth theory or syntax. Such special languages within the broader structure I have defined may be singled out model-theoretically or axiomatically and studied further. ;I also give completeness and consistency proofs for the axioms in terms of the model theory of the second chapter. The completeness proof is an unusual variant of standard Henkin completeness proofs. ;The last chapter describes a way of marking out the problematic sentences which have given rise to the literature on the paradoxes and languages with their own truth and falsity predicates in the first place. Such sentences are usually presented informally, but there is no way of recognizing them in a significant intertheoretic way. Since such sentences are problematical from a classical point of view I attempt to recognize them in a classical setting. The tools used here more closely resemble recent other work in the literature than anything earlier in the dissertation