This time, Omega asks you to consider the counterfactual world in which the device still shows “Working” after 5 minutes. Should counter-factual Omega still write “Even” on the test?
It should write whatever you would write if you observed no answer, in this case we have indifference between the answers (betting with confidence 50%).
In a different Omega-suggested counterfactual world, a black swan flies in the window after 4 1⁄2 minutes and the display shows “Disproven”. You know that this means that either a). Arithmetic is inconsistent. b). The theorem prover device is unreliable. or c). Omega is messing with you.
If device is unreliable, it’s unreliable in your own event in the same sense, so your answer could be wrong (as improbably), so the original solution stands (i.e. you write “odd” in the counterfactual). Even if Omega proves to you that arithmetic is inconsistent, this won’t cause you to abandon morality, just to change the way you use arithmetic. Omega is not lying by problem statement.
And subjective probabilities cannot flow backward in time (surviving the erasure of the evidence that produced those subjective probabilities). Even Omega cannot mediate this kind of paradoxical information flow.
We discussed in the other thread how your description of this idea doesn’t make sense to me. I have no idea what your statement means, so can’t rule whether I disagree with it, but certainly I can’t agree with what I don’t understand.
Ok, so we seem to be in agreement regarding everything except my attempt to capture the rules with the (admittedly meaningless if taken literally) slogan “subjective probabilities cannot flow backward in time”.
It is interesting that neither of us sees any practical difference between necessary facts (the true value of Q) and contingent facts (whether the calculator made a mistake) in this exercise. The reason apparently being that we can only construct counterfactuals on contingent facts (for example, observations). We can’t directly go counterfactual on necessary facts—only on observations that provide evidence regarding necessary facts. But it is impossible for observations to provide so much evidence regarding a necessary fact that we are justified in telling Omega that his counterfactual is impossible.
But that apparently means that dragging Omega into this problem didn’t change anything—his presence just confused people. (I notice that Shokwave—the one person who you claimed had understood the problem—is now saying that the value of Q is different in the counterfactual worlds). I am becoming ever more convinced that allowing Omega into a decision-theory example is as harmful as allowing a GoTo statement into a computer program. But then, as my analogy reveals, I am from a completely different generation.
We can’t directly go counterfactual on necessary facts—only on observations that provide evidence regarding necessary facts.
Yes we can. Omega could offer you to control worlds where Q is actually odd.
I notice that Shokwave—the one person who you claimed had understood the problem—is now saying that the value of Q is different in the counterfactual worlds
Link? The value of Q is uncertain, and this holds in considering either possible observation.
We can’t directly go counterfactual on necessary facts—only on observations that provide evidence regarding necessary facts.
Yes we can. Omega could offer you to control worlds where Q is actually odd.
I want to answer “No he can’t. Not if I am in a world in which Q is actually even. Not if we are talking about the same arithmetic formula Q in each case.” But I’m coming to realize that we may not even be talking the same language. For example, I don’t really understand what is meant by “Omega could offer you to control worlds where ___”. Are you suggesting that Omega could make the offer, though he might not have to deliver anything should such worlds not exist?
I notice that Shokwave … is now saying that the value of Q is different in the counterfactual worlds
Link? The value of Q is uncertain, and this holds in considering either possible observation.
Are you suggesting that Omega could make the offer, though he might not have to deliver anything should such worlds not exist?
Yes. The offer would be, to enact a given property in all possible worlds of specified event. If there are no possible worlds in that event, this requirement is met by doing nothing.
I notice that Shokwave—the one person who you claimed had understood the problem—is now saying that the value of Q is different in the counterfactual worlds
I wish. If I understood the problem, I would be solving it. As far as I’ve noticed, he claimed I had the updateless analysis mostly right.
It should write whatever you would write if you observed no answer, in this case we have indifference between the answers (betting with confidence 50%).
If device is unreliable, it’s unreliable in your own event in the same sense, so your answer could be wrong (as improbably), so the original solution stands (i.e. you write “odd” in the counterfactual). Even if Omega proves to you that arithmetic is inconsistent, this won’t cause you to abandon morality, just to change the way you use arithmetic. Omega is not lying by problem statement.
We discussed in the other thread how your description of this idea doesn’t make sense to me. I have no idea what your statement means, so can’t rule whether I disagree with it, but certainly I can’t agree with what I don’t understand.
Ok, so we seem to be in agreement regarding everything except my attempt to capture the rules with the (admittedly meaningless if taken literally) slogan “subjective probabilities cannot flow backward in time”.
It is interesting that neither of us sees any practical difference between necessary facts (the true value of Q) and contingent facts (whether the calculator made a mistake) in this exercise. The reason apparently being that we can only construct counterfactuals on contingent facts (for example, observations). We can’t directly go counterfactual on necessary facts—only on observations that provide evidence regarding necessary facts. But it is impossible for observations to provide so much evidence regarding a necessary fact that we are justified in telling Omega that his counterfactual is impossible.
But that apparently means that dragging Omega into this problem didn’t change anything—his presence just confused people. (I notice that Shokwave—the one person who you claimed had understood the problem—is now saying that the value of Q is different in the counterfactual worlds). I am becoming ever more convinced that allowing Omega into a decision-theory example is as harmful as allowing a GoTo statement into a computer program. But then, as my analogy reveals, I am from a completely different generation.
Yes we can. Omega could offer you to control worlds where Q is actually odd.
Link? The value of Q is uncertain, and this holds in considering either possible observation.
I want to answer “No he can’t. Not if I am in a world in which Q is actually even. Not if we are talking about the same arithmetic formula Q in each case.” But I’m coming to realize that we may not even be talking the same language. For example, I don’t really understand what is meant by “Omega could offer you to control worlds where ___”. Are you suggesting that Omega could make the offer, though he might not have to deliver anything should such worlds not exist?
I was referring to this
Yes. The offer would be, to enact a given property in all possible worlds of specified event. If there are no possible worlds in that event, this requirement is met by doing nothing.
I wish. If I understood the problem, I would be solving it. As far as I’ve noticed, he claimed I had the updateless analysis mostly right.