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Vladimir_Nesov comments on What a reduction of "could" could look like - Less Wrong
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Note that by proving "agent()==1 implies world()==1000000", and then performing action 1, you essentially conclude that "world()==1000000" was valid in the first place. "You had the mojo all along", as Aaronson said (on Löb's theorem). Decision making is all about lack of logical transparency, inability to see the whole theory from its axioms.
Woah, I just noticed the weird alternative proof of Löb's theorem contained in that PDF. Can't even tell if it's correct. Thanks!