The Man from the Future
Appearance
1. Made in Budapest
2. To Infinity and Beyond
- Von Neumann rigorously defines a class as a collection of sets that share a property. In his theory it is no longer possible to speak meaningfully of either a "set of all sets" or a "class of all classes"; only a "class of all sets". His formulation elegantly avoids the contradictions of Russell's paradox without all the restrictions of type theory. There is no "set of all sets that are not members of themselves" but there is a "class of all sets that are not members of themselves." Crucially, this class is not a member of itself because it is not a set (it's a class!).