Eliezer_Yudkowsky comments on Timeless Decision Theory: Problems I Can't Solve
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TDT allows you to use whatever you can prove mathematically. If you can prove that two computations have the same output because their global structures are isomorphic, it doesn't matter if the internal structure is twisty or involves regresses you haven't yet resolved. However, you need a license to use that sort of mathematical reasoning in the first place, which is provided by TDT but not CDT.