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cousin_it comments on Decision Theories, Part 3.5: Halt, Melt and Catch Fire - Less Wrong
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If program A which uses a specific proof ordering can find a proof of some theorem about program A, and program B which uses a different proof ordering can find a proof of the opposite theorem about program B, that doesn't imply inconsistency.
Hence he's assuming that A = B, if I understand correctly.
He's saying that program A can find a proof that it cooperates with program A, but if we slightly change the proof ordering in program A and obtain program B, then program B can find a proof that it defects against program B. I still don't see the inconsistency.
Yes, this is what I meant. Thanks!
Ok, so the proof ordering is considered part of the program, I assumed it was an external input to be universally quantified. Thanks for the clarification.