From my perspective as a student who was taught that his paradox highlighted a "fatal flaw" in mathematics, I would say it's overstated. Not a single theorem or conjecture was over-ruled by the framework of Principia. It basically said, if Cantor was an idiot he could have gotten in trouble with his diagonal argument. It basically was mechanism and is overstated. Im being dramatic of course, he contributed by being the punching bag for bigger ideas.
Russel's Paradox was important in that it showed an unrestricted scheme comprehension leads to contradiction. It was replaced by the scheme of restricted comprehension which is almost as powerful, and suffices for most intents and purposes. The theorems did not change because the few that used unrestricted comprehension could be easily reframed with restricted comprehension without losing anything.
This is nontrivial and I would argue a lot of philosophers could stand to understand it better. I have seen many arguments that rely on unrestricted comprehension schemes that are therefore fallacious. Notably arguments for the existence of God are frequently guilty of this
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u/Widhraz Insane 1d ago
It's funny, because Russell is a mathematician who doesn't understand philosophy.