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Wouldn’t the set without nothing be more fundamental?

Brilliant. Go to the top of the class, er, set. Oops, forgot, sets have no order. List, then.

Ordered list, I mean.

Does the set of sets that exclude themselves exclude itself?

No, because it isn't a set, but rather a class.

A concept created at least partially to resolve this paradox.

That's a well-known old paradox, or close. Good on you, cobber. (AU slang :)

See Russells's paradox: