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Unknowns comments on A problem with Timeless Decision Theory (TDT) - Less Wrong
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By "unsolvable" I mean that you're screwed over in final outcomes, not that TDT fails to have an output.
The interesting part of the problem is that, whatever you decide, you deduce facts about the background such that you know that what you are doing is the wrong thing. However, if you do anything differently, you would have to make a different deduction about the background facts, and again know that what you were doing was the wrong thing. Since we don't believe that our decision is capable of affecting the background facts, the background facts ought to be a fixed constant, and we should be able to alter our decision without affecting the background facts... however, as soon as we do so, our inference about the unalterable background facts changes. It's not 100% clear how to square this with TDT.
This is like trying to decide whether this statement is true:
"You will decide that this statement is false."
There is nothing paradoxical about this statement. It is either true or false. The only problem is that you can't get it right.