They already knew that. You’re treading an old worn out logical positivist path, that was inspired by Wittgenstein who worked closely with Russell (both mathematicians and philosophers) and he later saw his error, rejected his positivist followers and explained how truth is not a correspondence to facts, rather meaning is derived from use in language. This applies to all languages, formal and informal, including math and logic.
And we determined that the resulting incompleteness proofs are valid mathematical proofs whose logical correctness has been verified by computer. https://formalizedformallogic.github.io/Catalogue/Arithmetic/G___del___s-First-Incompleteness-Theorem/#goedel-1
They already knew that. You’re treading an old worn out logical positivist path, that was inspired by Wittgenstein who worked closely with Russell (both mathematicians and philosophers) and he later saw his error, rejected his positivist followers and explained how truth is not a correspondence to facts, rather meaning is derived from use in language. This applies to all languages, formal and informal, including math and logic.