Actually, [Gödel 1931] claimed that the incompleteness result was for Russell's Principia Mathematica, which is much stronger than a first-order theory of the

Actually, [Gödel 1931] claimed that the incompleteness result was for Russell's Principia Mathematica, which is much stronger than a first-order theory of the natural numbers. Also, Gödel's incompleteness result was not for the liar paradox. Instead, it was for the proposition I'mUnprovable, which [Gödel 1931] claimed to have constructed. However, [Wittgenstein 1937-1944] showed that I'mUnprovable leads to inconsistency in the foundations of mathematics. Fortunately, I'mUnprovable cannot be constructed in foundations because the attempted construction violates order on propositions. Furthermore, Gödel did not have a proof of the second incompleteness result at the time he wrote to von Neumann [von Plato 2018]. von Neumann never realized the deception by Gödel because it was discovered after both had died.