# GDC3 comments on Decision Theories: A Semi-Formal Analysis, Part III - Less Wrong

22 14 April 2012 07:34PM

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Comment author: 15 April 2012 09:31:29PM 2 points [-]

There's a gap in the proof that X and Y cooperate. You may know how to close it, but if it's possible it's not obvious enough so the extra steps should be added to the article. More importantly, if it can't be closed the theorem might not be true.

The gap: We hypothesize that statement S is provable in (system of X). Therefore X will Cooperate. This guarantees that T is true, by definition, but not that Y will prove that T is true. Presumable Y can recreate the proof of S being true, but it cannot conclude that X will cooperate unless it also can prove that X will prove it.

I cannot see how to resolve this without stepping out of a specific formal system, which would make Lob's Theorem unusable.

Am I missing something?

Comment author: 15 April 2012 10:52:56PM 2 points [-]

It does work out, but you're right to raise that question; Vladimir Nesov's footnote unpacks those issues.