Unification of universes in set theory

that must continue to name what it seems to name is 'ART'. Our ontology must therefore resemble in one respect that of New foundations, rather than those of the various theories of classes considered earlier in this paper: it must number among its classes the wholly exhaustive class. What, finally, of y'x where y is an individual? This question is analogous to the earlier question of 'x e y' where y is an individual; and that question seemed best settled by identifying individuals with their unit classes. Now the way of settling the present question which promises parallel benefits is this: identify each individual y with its constant function ALy the function whose value is y for every argument. The sort of logical function theory to which these reflecions and analogies point is one, then, with the following traits. Functional abstraction, predication, and equality are the primitive ideas. The variables are general and the grammar simple, but some of the abstracts are irregularly construed. Non-functions, or what would otherwise be non-functions, are identified with their own constant functions. There is, finally, a class of everything. How elegant a theory might be framed within these conditions is an open question.