You seem to be saying that your choice is already made up from your prior mind-state
If your choice is not made up from your prior mind state, then Omega would not be able to predict your actions from it. However, it is a premise of the scenario that he can. Therefore your choice is made up from your prior mind state.
If your choice is not made up from your prior mind state, then Omega would not be able to predict your actions from it.
Not necessarily. We don’t know how Omega makes his predictions.
But regardless, I think my fundamental point still stands: the debate is over physics/reality, not decision theory. If the question specified how physics/reality works, the decision theory part would be easy.
Indeed- to make it more clear, consider a prior mind state that says “when presented with this, I’ll flip a coin to decide (or look at some other random variable).” In this situation, Omega can, at best, predict your choice with 50⁄50 odds. Whether Omega is even a coherent idea depends a great deal on your model of choices.
If given prior mind-state S1 and a blue room I choose A, and given S1 and a pink room I choose B, S1 does not determine whether I choose A or B, but Omega (knowing S1 and the color of the room in which I’ll be offered the choice) can predict whether I choose A or B.
If your choice is not made up from your prior mind state, then Omega would not be able to predict your actions from it. However, it is a premise of the scenario that he can. Therefore your choice is made up from your prior mind state.
Not necessarily. We don’t know how Omega makes his predictions.
But regardless, I think my fundamental point still stands: the debate is over physics/reality, not decision theory. If the question specified how physics/reality works, the decision theory part would be easy.
Indeed- to make it more clear, consider a prior mind state that says “when presented with this, I’ll flip a coin to decide (or look at some other random variable).” In this situation, Omega can, at best, predict your choice with 50⁄50 odds. Whether Omega is even a coherent idea depends a great deal on your model of choices.
If given prior mind-state S1 and a blue room I choose A, and given S1 and a pink room I choose B, S1 does not determine whether I choose A or B, but Omega (knowing S1 and the color of the room in which I’ll be offered the choice) can predict whether I choose A or B.