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.