Abstract

This chapter is a technical digression with two aims: The first is to make explicit the proof theory and model theory for the first-order modal logic that has been proposed as a framework for regimented languages. The model theory is a version of possible-worlds semantics that allows the domains of individuals to vary from world to world. The second task is to make explicit a representation of the formal theory of propositions proposed in Chapter 2 in this modal framework. The first task includes giving a completeness theorem for the modal logic. The second task includes an argument that there is no paradox in a theory of propositions with a truth predicate that applies to the propositions expressed in the language of that theory.