@user170039 From Gödel's perspective, and I should have added "PM program in its original form". On conventional reading, Wittgenstein of the "notorious paragraph" (and possibly Russell) took Gödel to make a formal argument against PM, deriving a contradiction in it. If that were the case Wittgenstein was right to argue that Gödel's "contradiction" comes from illicitly detaching true from provable

But that was not Gödel's argument, although he made a remark in the preface to his paper that is bound to mislead in this direction. If we take his paper as an argument against PM it was informal: he instead presented a sentence G that was intuitively true but not derivable in PM. He showed further that adding more axioms to PM would not fix it. So PM could not fulfill its all-encompassing ambition of equating true to provable and deriving all truths of arithmetic.

I do not think taking G as "nonsense", as Chen does, and hence not a sentence of PM is very plausible, it seemed meaningful enough to Wittgenstein and others. True = provable was adopted by intuitionists, but for them G was not a problem, better yet Gödel handed them an argument for their claim that "intuition" behind truth/provability can not be captured by any formal system. "Open systems" seems like a step in a similar direction.