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Jack comments on Avoiding doomsday: a "proof" of the self-indication assumption - Less Wrong
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Then if you take the money Omega was just wrong. Full stop. And in this case if you take the dollar expected gain is a dollar.
Or else you need to clarify.
Assuming that you won't actually take the money, what would a plan to take the money mean? It's a kind of retroactive impossibility, where among two options one is impossible not because you can't push that button, but because you won't be there to push it. Usual impossibility is just additional info for the could-should picture of the game, to be updated on, so that you exclude the option from consideration. This kind of impossibility is conceptually trickier.
I don't see how my non-existence gets implied. Why isn't a plan to take the money either a plan that will fail to work (you're arm won't respond to your brain's commands, you'll die, you'll tunnel to the Moon etc.) or a plan that would imply Omega was wrong and shouldn't have made the offer?
My existence is already posited one you've said that Omega has offered me this deal. What happens after that bears on whether or not Omega is correct and what properties I have (i.e. what I am).
There exists (x) &e there exists (y) such that Ox & Iy & ($xy <--> N$yx)
Where O= is Omega, I= is me, $= offer one dollar to, N$= won't take dollar from. I don't see how one can take that, add new information, and conclude ~ there exists (y).