The construction of propositional functions begins with possible worlds and the assumption that there are sets. Let us call the set of possible worlds W. A proposition is a set of possible worlds. The proposition that Zermela barks, for example, is all the sets of worlds in which Zermela barks. We also need to assume that there is a set I of possible individuals (i.e., the individuals that exist in at least one possible world). We now have all the materials to construct a simple type-theoretic hierarchy of functions. 