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
Famous quotes containing the words resolution and/or paradox:
“The changes in our life must come from the impossibility to live otherwise than according to the demands of our conscience ... not from our mental resolution to try a new form of life.”
—Leo Tolstoy (1828–1910)
“The conclusion suggested by these arguments might be called the paradox of theorizing. It asserts that if the terms and the general principles of a scientific theory serve their purpose, i. e., if they establish the definite connections among observable phenomena, then they can be dispensed with since any chain of laws and interpretive statements establishing such a connection should then be replaceable by a law which directly links observational antecedents to observational consequents.”
—C.G. (Carl Gustav)