ABSTRACT
It would be one thing for a species of AR to be ontologically problematic in any, or even all, of the ways discussed in Chapter 14, but it would be quite another matter for its ontological claims to be inconsistent. Yet commitment to various claims about sets threatens to show that such inconsistency is afoot in some, or perhaps even all, species of AR. The PW-paradoxes are a family of arguments to this effect. The PW-paradoxes depend on Cantor’s theorem which will be stated here as follows:
(CT) For any set S, every subset of S is smaller than P(S).1
