I totally agree we can be coherently uncertain about logical facts, like whether P=NP. FDT has bigger problems then that.
When writing this I tried actually doing the thing where you predict a distribution, and only 21% of LessWrong users were persuaded they might be imaginary and being imagined by me, which is pretty low accuracy considering they were in fact imaginary and being imagined by me. Insisting that the experience of qualia can’t be doubted did come up a few times, but not as aggressively as you’re pushing it here. I tried to cover it in the “highly detailed internal subjective experience” counterargument, and in my introduction, but I could have been stronger on that.
I agree that the same argument on philosophers or average people would be much less successful even then that, but that’s a fact about them, not about the theory.
https://www.lesswrong.com/tag/functional-decision-theory argues for choosing as if you’re choosing the policy you’d follow in some situation before you learnt any of the relevant infortmation. In many games, having a policy of making certain choicese (that others could perhaps predict, and adjust their own choices accordingly) gets you better outcomes then just always doing what seems like a good idea ta the time. For example if someone credibly threatens you might be better off paying them to go away, but before you got the threat you would’ve prefered to commit yourself to never pay up so that people don’t threaten you in the first place.
A problem with arguments of the form “I expect that predictably not paying up will cause them not to threaten me” is that at the time you recieve the threat, you now know that argument to be wrong. They’ve proven to be somebody who still threatens you even though you do FDT, at which point you can simultaneously prove that refusing the threat doesn’t work and so you should pay up (because you’ve already seen the threat) and that you shouldn’t pay up for whatever FDT logic you were using before. Behaviour of agents who can prove a contradiction that is directly relevant to their decision function seems undefined. There needs to be some logical structure that lets you pick which information causes your choice, despite having enough in total to derive contradictions.
My alternative solution is that you aren’t convinced by the information you see, that they’ve actually already threatened you. It’s also possible you’re still inside their imagination as they decide whether to issue the threat. Whenever something is conditional on your actions in an epistemic state without being conditional on that epistemic state actually being valid (such as if someone predicts how you’d respond to a hypothetical threat before they issue it, knowing you’ll know it’s too late to stop when you get it) then there’s a ghost being lied to and you should think maybe you’re that ghost to justify ignoring the threat, rather than try to make decisions during a logically impossible situation.