1) OK taking a limit is an idea I hadn’t thought of. It might even defeat my argument that your answer depends on how Omega achieves this. On the other hand:
a) I am not sure what the rest of my beliefs would look like anymore if I saw enough evidence to convince me that Omega was right all the time with probability 1-1/3^^^3 .
b) I doubt that the above is even possible, since given my argument you shouldn’t be able to convince me that the probability is less than say 10^-10 that I am a simulation talking to something that is not actually Omega.
3) I am not sure why you think that the simulation is not causally a copy of you. Either that or I am not sure what your distinction between statistical and causal is.
3+4) I agree that one of the weaknesses of this theory is that it depends heavily, among other things, on a somewhat controversial theory of identity/ what it means to win. Though I don’t see why the amount that you identify with an imperfect copy of yourself should be arbitrary, or at very least if that’s the case why its a problem for the dependence of your actions on Omega’s degree of perfection to be arbitrary, but not a problem for your identification with imperfect copies of yourself to be.
1) OK taking a limit is an idea I hadn’t thought of. It might even defeat my argument that your answer depends on how Omega achieves this. On the other hand:
a) I am not sure what the rest of my beliefs would look like anymore if I saw enough evidence to convince me that Omega was right all the time with probability 1-1/3^^^3 .
b) I doubt that the above is even possible, since given my argument you shouldn’t be able to convince me that the probability is less than say 10^-10 that I am a simulation talking to something that is not actually Omega.
3) I am not sure why you think that the simulation is not causally a copy of you. Either that or I am not sure what your distinction between statistical and causal is.
3+4) I agree that one of the weaknesses of this theory is that it depends heavily, among other things, on a somewhat controversial theory of identity/ what it means to win. Though I don’t see why the amount that you identify with an imperfect copy of yourself should be arbitrary, or at very least if that’s the case why its a problem for the dependence of your actions on Omega’s degree of perfection to be arbitrary, but not a problem for your identification with imperfect copies of yourself to be.