And it would probably take more bits of information than the human mind can handle to actually be in the situation where you can be justified in believing Omega's claim about the possibility of dust specking 3^^^3 people
(Omega resets both copies & repeats this process a gajillion times until they find the combination of words which creates in you the correct state of belief)
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What does that get you? Yes, we can hypothesize all sort of you-like things which come to believe arbitrary things. But you aren't them; you don't know what it is like to be them.
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Yes, you can't access that epistemic state and nearly everyone who thinks they can is confabulating (that goes for much more mundane thought experiments, too). But is it invalid to reflect on what you'd want that you to choose?
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Note that if Omega can run path-to-victory against you, he can force you to choose whatever outcome he wants. What you choose after you've been pathed to believe Omega can path is now dependent on Omega's own goal.
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We can assume omega does this to set the question and not to influence the result, otherwise why bother.
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