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I'd consider the Russel Paradox to be a poor specification. If you have a database of the city's residents and selected the people who shaved themselves, and again to select the people shaved by the barber, he would appear in both lists. Implicit in the statement is that all men are shaved, and that the barber is male.
It is a matter of identifying your categories correctly. So, the barber shaves his customers, who don't shave themselves. Everybody else shaves himself. The barber isn't his own customer, so we have no problem.
As for the chicken and egg, the egg always comes first. Darwinian evolution explains the origin of eggs, They are an economical means for multicellular creatures to reproduce. Each egg is created for this purpose. It would have been a puzzle for Socrates who knew nothing about the origin of species.
You can always find contradictions in logical systems. E. W. Dijkstra disliked set theory. He showed that Russel's statement expressed in predicate form simply evaluated to FALSE. From a programming point of view these are specification errors.
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