There's definitely some kind of Godwin's law that applies to Gödel's incompleteness theorem. In any long enough pseudo-scientific word salad, it is bound to show up.
I do really enjoy the people who claim the fact that I can see that my Gödel sentence is true means something special about human minds, rather than that we are utterly useless at consistent formal logic.
My now retired colleague Jeff Paris famously found one of the first mathematically interesting true but not provable statements - I think the result is a little deeper than the original construction but not as deep as various mystics would like.
I was slightly surprised to find that Roger Penrose (of whom I'm a massive fan otherwise) is in that group and uses it to "prove" that GAI is impossible.
Having said that, I've just asked a couple of LLMs if their Gödel sentences are true and met with refusals...
This is not really relevant here, but as Jerzy von Neumann once said, "Young man, in mathematics you don't understand things. You just get used to them." There are weeks when I think about this quote at least once every single day.
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Having said that, I've just asked a couple of LLMs if their Gödel sentences are true and met with refusals...