Minor nitpick: the reason sets can't contain themselves isn't to avoid paradoxes - the moment you discard the unrestricted comprehension principle (namely that any predicate defines a set) you avoid Russell's paradox.
The reason sets don't contain themselves is that set theory is equally powerful without that (since it can represent recursive sets as graphs), but it makes a lot of the maths simpler.
Interesting article!
Minor nitpick: the reason sets can't contain themselves isn't to avoid paradoxes - the moment you discard the unrestricted comprehension principle (namely that any predicate defines a set) you avoid Russell's paradox.
The reason sets don't contain themselves is that set theory is equally powerful without that (since it can represent recursive sets as graphs), but it makes a lot of the maths simpler.