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Unknowns comments on AI cooperation in practice - Less Wrong
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Comments (157)
Ok, you've convinced me. Saying that this statement is true is basically the same as saying program A outputs 1.
Yes, exactly. The proof is a little fussy because it has to keep track of bounded proof lengths everywhere, but it works basically the same.
Does it help you understand the second problem better? It uses the same trick, but with a twist. (You need to get creative when you talk about two proof systems instead of one.)
I still agree with what I said originally about the second problem. You could compare it to these two statements:
A) A is true if and only if A and B are either both provable, or both non-provable. B) B is true if and only if B and A are either both provable, or both non-provable.
It is much more obvious that both of these statements are necessarily true and provable (by symmetry), than it is that "this is true if and only if it is provable" is true or provable. This is why at first I only accepted the second case.