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The question is, does the set of all sets that do not contain sets which contain sets that don't cause logical paradoxes contain a set which doesn't not cause a paradox or not?
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1/ Your phrasing is sloppy. Sets don't "cause" anything. The classic way to parse this is in terms of Frege's Axiom V, the so called Axiom of Abstraction.
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2/ Put in set theoretical terms a statement which asserts a property of a set if and only if the set does not have that property is self-contradictory. Russell's version is self containing iff not self containing.
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If this was meant to be a metaparadox, I'm not sure that it was formulated correctly. If it was just meant to be confusing, then good joke.
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Can have both, as both the ones that cause a paradox and the ones that do not, can lack sets which contain sets that don't cause logical paradoxes.
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