[ProfHewitt]

[Gödel 1931] tried to formally prove the proposition that there are true but unprovable propositions, which had been previously intuited by others.

Unfortunately, the [Gödel 1931] proof fails for the claimed Russell's system for the foundations of mathematics.

The following has an explanation of what went wrong in this and many other cases in foundations of mathematics for computer science:

    Vanquishing ‘Monsters’ in Foundations of Computer Science: Euclid, Dedekind, Russell, Gödel, Wittgenstein, Church, and Turing didn't get them all ...

https://papers.ssrn.com/abstract=3603021