...words the second necessary part of the paradox is fallacious. A like confusion is responsible for the paradox of the class of classes that are not members of themselves. This Russell has stated so: (x < w) < (x < x)' which leads to the result (w < w) < (w < w)' on substitution...

...this assumption which was "the source of the contradiction" (ibid.). In particular, in regard to his paradox of the class of classes that are not members of themselves, Russell found that he could only conclude that "the classes which as ones are not members of themselves...

...importance to logic. He contrasted them with the logical and mathematical paradoxes, such as Russell's famous paradox of the class of classes that are not members of themselves, which can be avoided by means of a simple, nonramified theory of types. But Goldfarb argues that the...