Revisiting and Type-freeing Church’s Approach to Semantic Paradoxes

T. We simplify and slightly modify the theory of types that Church provided with semantic primitive predicates. Two goals are pursued. The first goal is to present a simple application of Church’s approach to paradoxes and to point out some aspects of this ap- proach. The second, perhaps more interesting, goal is to show that when type distinctions are removed some basic Churchian principles need to be restricted and different restrictions correspond to Tarski’s and Kripke’s different approaches to truth. Finally, we briefly hint at how to move in the direction of Field’s recent approach to truth by giving up some specific essential points of the Churchian frame- work.