A Theory of Truth for Propositions

This is joint work with Philip Welch.

The paper will deal with the following question: Is it possible to formulate a theory of truth which solves or avoids semantic paradoxes in the same way as modern set theory solves or avoids the set-theoretic paradoxes? In order to answer this question, we first axiomatize a theory of propositions and propositional functions that form a cumulative hierarchy very much like the cumulative hierarchy of sets, and we then formulate an axiomatic theory of truth and satisfaction for such propositions and propositional functions that is very much like Tarski's theory of truth. Finally, we argue for the resulting package along the lines of standard arguments for modern set theory.