Please specify this “now” thingy you are talking about, using formal logic. If this is a meaningful event for the setting, surely there wouldn’t be any problems.
Are you talking about Monday xor Tuesday? Monday or Tuesday? Monday and Tuesday? Something else?
Well, idk. My opinion here is that you bite some weird bullet, which I’m very ambivalent to. I think “now” question makes total sense and you factor it out into some separate parts from your model.
Like, can you add to the sleeping beauty some additional decision problems including the calendar? Will it work seamlessly?
Well, idk. My opinion here is that you bite some weird bullet, which I’m very ambivalent too. I think “now” question makes total sense and you factor it out into some separate parts from your model.
The counter-intuitiveness comes from us not being accustomed to reasoning under amnesia and repetition of the same experience. It’s understandable that initially we would think that question about “now”/”today” makes sense as we are used to situation where it indeed does. But then we can clearly see that in such situations there is no problem with formally defining what event we mean by it. Contrary to SB, where such event is ill-defined.
Like, can you add to the sleeping beauty some additional decision problems including the calendar? Will it work seamlessly?
Oh absolutely.
Suppose that on every awakening the Beauty is proposed to bet that “Today is Monday” What odds is she supposed to take?
“Today is Monday” is ill-defined, but she can construct a corresponding betting scheme using events “Monday awakening happens” and “Tuesday awakening happens” like this:
So, she shakes the box contemplatively. There is mechanical calendar. She knows the betting odds of it displaying “Monday” but not the credence. She thinks it’s really really weird
What state the calendar is when?
On Monday it’s Monday. On Tuesday it’s Tuesday. And “Today” is ill-defined, there is no coherent state for it.
Well, now! She looks at the box and thinks there is definitely a calendar in some state. What state? What would happen if i open it?
Please specify this “now” thingy you are talking about, using formal logic. If this is a meaningful event for the setting, surely there wouldn’t be any problems.
Are you talking about Monday xor Tuesday? Monday or Tuesday? Monday and Tuesday? Something else?
Well, idk. My opinion here is that you bite some weird bullet, which I’m very ambivalent to. I think “now” question makes total sense and you factor it out into some separate parts from your model.
Like, can you add to the sleeping beauty some additional decision problems including the calendar? Will it work seamlessly?
The counter-intuitiveness comes from us not being accustomed to reasoning under amnesia and repetition of the same experience. It’s understandable that initially we would think that question about “now”/”today” makes sense as we are used to situation where it indeed does. But then we can clearly see that in such situations there is no problem with formally defining what event we mean by it. Contrary to SB, where such event is ill-defined.
Oh absolutely.
Suppose that on every awakening the Beauty is proposed to bet that “Today is Monday” What odds is she supposed to take?
“Today is Monday” is ill-defined, but she can construct a corresponding betting scheme using events “Monday awakening happens” and “Tuesday awakening happens” like this:
E(Monday) = P(Monday)U(Monday) - P(Tuesday)U(Tuesday)
P(Monday) = 1; P(Tuesday) = 1⁄2, therefore
E(Monday) = U(Monday) − 1/2U(Tuesday)
solving E(Monday)=0 for U(Monday):
U(Monday) = 1/2U(Tuesday)
Which means 2:1 betting odds
As you see everything is quite seamless.
So, she shakes the box contemplatively. There is mechanical calendar. She knows the betting odds of it displaying “Monday” but not the credence. She thinks it’s really really weird