Resolution of The Paradox
Modern axiomatic set theory such as ZF and ZFC circumvents this antinomy by simply not allowing construction of sets with unrestricted comprehension terms like "all sets with the property ", as it was for example possible in Gottlob Frege's axiom system. New Foundations uses a different solution.
Read more about this topic: Burali-Forti Paradox
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“When a paradox is widely believed, it is no longer recognized as a paradox.”
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