Isn’t that exactly what happened? The phrase “set of all sets that do not contain themselves” isn’t really expressible in Zermelo-Fraenkel set theory, since that has a more limited selection of ways to construct new sets and “the set of everything that satisfies property X” is not one of them.
Isn’t that exactly what happened? The phrase “set of all sets that do not contain themselves” isn’t really expressible in Zermelo-Fraenkel set theory, since that has a more limited selection of ways to construct new sets and “the set of everything that satisfies property X” is not one of them.