My point is that SB must have reason to think that she exists in the “Monday or Tuesday” waking schedule, for her to assign a credence to Heads based on that schedule. If she is awake, but has any reason to think she is not in that situation, her credence must take that into account.
You told her that she would be asked for her credence on Monday and maybe on Tuesday. “What’s Beauty credence for Heads when she wakes on Wednesday and doesn’t remember any of her awakenings on Monday/Tuesday?” is irrelevant because you are allowing for the case where that is not true yet you want her to believe it is. That is lying to her, in the context of the information you want her to use.
But she can from an opinion. “My credence should be halfer/thirder answer if Wednesday has not yet dawned, or 1⁄2 if it has. Since the cue I was told would happen—being asked for my credence—has not yet occurred, I am uncertain which and so can’t give a more definitive answer.” And if you give that cue on Wednesday, you are lying even if you promised you wouldn’t.
And yes, my mathematical model corresponds to SB’s reality when she is asked for her credence. That is the entire point. If you think otherwise, I’d love to hear an explanation instead of a dissertation that does not apply.
You told her that she would be asked for her credence on Monday and maybe on Tuesday. “What’s Beauty credence for Heads when she wakes on Wednesday and doesn’t remember any of her awakenings on Monday/Tuesday?” is irrelevant because you are allowing for the case where that is not true yet you want her to believe it is. That is lying to her, in the context of the information you want her to use.
No lies are necessary. I didn’t have to tell her beforehand that she will be asked any questions at all. Or I could have told her that she will be asked on Monday and Tuesday (if she is awake) without knowing which day it is and then she will be asked on Wednesday, knowing that it is indeed Wednesday. None of it changes the experiment. And even if I didn’t ask her about her credence that the coin is Heads on Wednesday, she still has to have some probability estimate doesn’t she?
The point of the Wednesday question is to highlight, that, what you mean by “credence”, isn’t actually a probability estimate that the coin is Heads. What you are talking about, is the probability that the coin is Heads, weighted by the number of times this question is asked. Which is a meaningful category. But confusing it with the probability that the coin is Heads can be extremely misleading
AINC: “What’s Beauty credence for Heads when she wakes on Wednesday and doesn’t remember any of her awakenings on Monday/Tuesday?”
If she has no reason to think this is not one of her awakenings on Monday/Tuesday, then her credence is the same as it would have been then: 1⁄2 if she is a halfer, and 1⁄3 if she is a thirder.
AINC: “If it’s 1⁄2 what is the reason for the change from 1/3?”
The only way it could change from 1⁄3 to 1⁄2, is if she is a thirder and you tell her that it is Wednesday. And the reason it changes is that you changes the state of her information, not because anything about the coin itself has changed.
But if you think her credence should be based on the actual day, even when you didn’t tell her that is was Wednesday, then you have told an implicit lie. You are asking her to formulate a credence based on Monday/Tuesday, but expecting her answer to be consistent with Wednesday.
AINC: The point of the Wednesday question is to highlight, that, what you mean by “credence”, isn’t actually a probability estimate that the coin is Heads.
And the point of my answer, is that it is actually a conditional probability based on an unusual state of information.
My point is that SB must have reason to think that she exists in the “Monday or Tuesday” waking schedule, for her to assign a credence to Heads based on that schedule. If she is awake, but has any reason to think she is not in that situation, her credence must take that into account.
You told her that she would be asked for her credence on Monday and maybe on Tuesday. “What’s Beauty credence for Heads when she wakes on Wednesday and doesn’t remember any of her awakenings on Monday/Tuesday?” is irrelevant because you are allowing for the case where that is not true yet you want her to believe it is. That is lying to her, in the context of the information you want her to use.
But she can from an opinion. “My credence should be halfer/thirder answer if Wednesday has not yet dawned, or 1⁄2 if it has. Since the cue I was told would happen—being asked for my credence—has not yet occurred, I am uncertain which and so can’t give a more definitive answer.” And if you give that cue on Wednesday, you are lying even if you promised you wouldn’t.
And yes, my mathematical model corresponds to SB’s reality when she is asked for her credence. That is the entire point. If you think otherwise, I’d love to hear an explanation instead of a dissertation that does not apply.
No lies are necessary. I didn’t have to tell her beforehand that she will be asked any questions at all. Or I could have told her that she will be asked on Monday and Tuesday (if she is awake) without knowing which day it is and then she will be asked on Wednesday, knowing that it is indeed Wednesday. None of it changes the experiment. And even if I didn’t ask her about her credence that the coin is Heads on Wednesday, she still has to have some probability estimate doesn’t she?
The point of the Wednesday question is to highlight, that, what you mean by “credence”, isn’t actually a probability estimate that the coin is Heads. What you are talking about, is the probability that the coin is Heads, weighted by the number of times this question is asked. Which is a meaningful category. But confusing it with the probability that the coin is Heads can be extremely misleading
AINC: “What’s Beauty credence for Heads when she wakes on Wednesday and doesn’t remember any of her awakenings on Monday/Tuesday?”
If she has no reason to think this is not one of her awakenings on Monday/Tuesday, then her credence is the same as it would have been then: 1⁄2 if she is a halfer, and 1⁄3 if she is a thirder.
AINC: “If it’s 1⁄2 what is the reason for the change from 1/3?”
The only way it could change from 1⁄3 to 1⁄2, is if she is a thirder and you tell her that it is Wednesday. And the reason it changes is that you changes the state of her information, not because anything about the coin itself has changed.
But if you think her credence should be based on the actual day, even when you didn’t tell her that is was Wednesday, then you have told an implicit lie. You are asking her to formulate a credence based on Monday/Tuesday, but expecting her answer to be consistent with Wednesday.
AINC: The point of the Wednesday question is to highlight, that, what you mean by “credence”, isn’t actually a probability estimate that the coin is Heads.
And the point of my answer, is that it is actually a conditional probability based on an unusual state of information.