“You’re failing to distinguish between though experiments that are only mildly-fantastic, like ones assuming perfectly fair coins, when real ones have (say) a 50.01% chance of landing heads, versus highly-fantastic thought experiments, such as ones assuming that on Sunday you know exactly, in complete detail, what all your experiences will be on Monday.”
I’m not failing to distinguish anything. I’m intentionally not bothering to distinguish what the problem statement says we should treat as indistinguishable. “While awake she obtains no information that would help her infer the day of the week.” Whether or not you think it is more realistic, the problem you are solving is not the Sleeping Beauty Problem.
And I’m not saying that Beauty’s experiences are the same. I’m just following the instructions in the problems statement, that says any information contained in the experiences of one day cannot be used to infer anything about the other.
And this is exactly what makes thought experiments interesting. Isolating one factor, and determining what its effect is when treated alone.
“Your Argument 1 doesn’t seem persuasive to me, because I don’t see how Beauty can be said to have prior beliefs when she is unconscious.”And she similarly can have different beliefs, then she can project during the experiment, than she had on Sunday. If she can project back a state in the past, why does it matter if she was awake. (If you want a comparison, you seem to be saying that the Sailor’s Child can’t hold a belief about the coin that was flipped before he was born.)
If you want real experiences in Argument #2, go back and read the Tim and Tom version. I just get tired of people saying “you changed the problem” when all I did was introduce an element that instantiates the day with out proving information, which is valid an necessary.
In #3, I have no problem with experiences that an external observers sees as differentiating the day, as long as Beauty can’t. The differences can exist, but provide Beauty with no information that identifies the day to her.
I think there’s no point in continuing this discussion. As far as I can tell, you are willing to admit that Beauty will have a variety of experiences on Monday, which will very probably be different from those she will have on Tuesday (if awake), although (by the conditons of the problem) she doesn’t know ahead of time how the two days will differ. But you are saying that she is NOT ALLOWED to use the fact that she has such experiences when reasoning about whether the coin landed heads. Debates in which one party to the discussion just says by fiat that the other party isn’t allowed to use certain forms of reasoning are pointless.
She is allowed any reasoning she wants to use. The condition explicitly stated in the thought problem (see https://en.wikipedia.org/wiki/Thought_experiment, for why we shouldn’t care about realism) is that experiences during the day will not help her to deduce what day it is, not that she can’t use it to determine her initial belief about the day or the coin.
What this means, is that if Xi represents her ordered experiences, with X0 representing only the experience of waking up as defined by the experiment, that Pr(Today=Monday|Xi+1) = Pr(Today=Monday|Xi) for all i>=0. Not that she can’t define Pr(Today=Monday|X0).
But you are right, there is no point in continuing if you insist on violating the problem statement.
As you’re defined it, the thought experiment is simply impossible to run in principle, since if you apply standard principles of probability, Pr(Today=Monday|Xi+1) is NOT equal to Pr(Today=Monday|Xi). It’s like saying that as a condition of your thought experiment, arguments about the solution must assume that pi is exactly equal to three.
And the purpose of a thought experiment, is to define how ideal concepts work when you can’t run them in principle. And strawman arguments do not change that.
“You’re failing to distinguish between though experiments that are only mildly-fantastic, like ones assuming perfectly fair coins, when real ones have (say) a 50.01% chance of landing heads, versus highly-fantastic thought experiments, such as ones assuming that on Sunday you know exactly, in complete detail, what all your experiences will be on Monday.”
I’m not failing to distinguish anything. I’m intentionally not bothering to distinguish what the problem statement says we should treat as indistinguishable. “While awake she obtains no information that would help her infer the day of the week.” Whether or not you think it is more realistic, the problem you are solving is not the Sleeping Beauty Problem.
And I’m not saying that Beauty’s experiences are the same. I’m just following the instructions in the problems statement, that says any information contained in the experiences of one day cannot be used to infer anything about the other.
And this is exactly what makes thought experiments interesting. Isolating one factor, and determining what its effect is when treated alone.
“Your Argument 1 doesn’t seem persuasive to me, because I don’t see how Beauty can be said to have prior beliefs when she is unconscious.” And she similarly can have different beliefs, then she can project during the experiment, than she had on Sunday. If she can project back a state in the past, why does it matter if she was awake. (If you want a comparison, you seem to be saying that the Sailor’s Child can’t hold a belief about the coin that was flipped before he was born.)
If you want real experiences in Argument #2, go back and read the Tim and Tom version. I just get tired of people saying “you changed the problem” when all I did was introduce an element that instantiates the day with out proving information, which is valid an necessary.
In #3, I have no problem with experiences that an external observers sees as differentiating the day, as long as Beauty can’t. The differences can exist, but provide Beauty with no information that identifies the day to her.
I think there’s no point in continuing this discussion. As far as I can tell, you are willing to admit that Beauty will have a variety of experiences on Monday, which will very probably be different from those she will have on Tuesday (if awake), although (by the conditons of the problem) she doesn’t know ahead of time how the two days will differ. But you are saying that she is NOT ALLOWED to use the fact that she has such experiences when reasoning about whether the coin landed heads. Debates in which one party to the discussion just says by fiat that the other party isn’t allowed to use certain forms of reasoning are pointless.
She is allowed any reasoning she wants to use. The condition explicitly stated in the thought problem (see https://en.wikipedia.org/wiki/Thought_experiment, for why we shouldn’t care about realism) is that experiences during the day will not help her to deduce what day it is, not that she can’t use it to determine her initial belief about the day or the coin.
What this means, is that if Xi represents her ordered experiences, with X0 representing only the experience of waking up as defined by the experiment, that Pr(Today=Monday|Xi+1) = Pr(Today=Monday|Xi) for all i>=0. Not that she can’t define Pr(Today=Monday|X0).
But you are right, there is no point in continuing if you insist on violating the problem statement.
As you’re defined it, the thought experiment is simply impossible to run in principle, since if you apply standard principles of probability, Pr(Today=Monday|Xi+1) is NOT equal to Pr(Today=Monday|Xi). It’s like saying that as a condition of your thought experiment, arguments about the solution must assume that pi is exactly equal to three.
And the purpose of a thought experiment, is to define how ideal concepts work when you can’t run them in principle. And strawman arguments do not change that.