Perhaps the best way to state the suggested solution [of the   Russell-Zermelo contradiction] is to say that, if a collection of   terms can only be defined by a variable propositional function,   then, though a class as many may be admitted, a class as one must be   denied. We took it as axiomatic that the class as one is to be found   wherever there is a class as many; but this axiom need not be   universally admitted, and appears to have been the source of the   contradiction. By denying it, therefore, the whole difficulty will   be overcome.