The question “What is the probability of Heads?” is about the coin, not about your location in time or possible worlds.
This is, I think, the key thing that those smart people disagree with you about.
Suppose Alice and Bob are sitting in different rooms. Alice flips a coin and looks at it—it’s Heads. What is the probability that the coin is Tails? Obviously, it’s 0% right? That’s just a fact about the coin. So I go to Bob in the other room and and ask Bob what’s the probability the coin is Tails, and Bob tells me it’s 50%, and I say “Wrong, you’ve failed to know a basic fact about the coin. Since it was already flipped the probability was already either 0% or 100%, and maybe if you didn’t know which it was you should just say you can’t assign a probability or something.”
Now, suppose there are two universes that differ only by the polarization of a photon coming from a distant star, due to hit Earth in a few hours. And I go into the universe where that polarization is left-handed (rather than right-handed), and in that universe the probability that the photon is right-handed is 0% - it’s just a fact about the photon. So I go to the copy of Carol that lives in this universe and ask Carol what’s the probability the photon has right-handed polarization, and Carol tells me it’s 50%, and I say “Wrong, you’ve failed to know a basic fact about the photon. Since it’s already on its way the probability was already either 0% or 100%, and maybe if you don’t know which it was you should just say you can’t assign a probability or something.”
Now, suppose there are two universes that differ outside of the room that Dave is currently in, but are the same within Dave’s room. Say, in one universe all the stuff outside the room is arranged is it is today in our universe, while in the other universe all the stuff outside the room is arranged as it was ten years ago. And I go into the universe where all the stuff outside the room is arranged as it was ten years ago, which I will shorthand as it being 2014 (just a fact about calendars, memories, the positions of galaxies, etc.), and ask Dave what’s the probability that the year outside is 2024, and Dave tells me it’s 50%...
Yes, Bob is right. Because the probability is not a property of the coin. It’s ‘about’ the coin in a sense, but it also depends on Bob’s knowledge, including knowledge about location in time (Dave) or possible worlds (Carol).
This is, I think, the key thing that those smart people disagree with you about.
Suppose Alice and Bob are sitting in different rooms. Alice flips a coin and looks at it—it’s Heads. What is the probability that the coin is Tails? Obviously, it’s 0% right? That’s just a fact about the coin. So I go to Bob in the other room and and ask Bob what’s the probability the coin is Tails, and Bob tells me it’s 50%, and I say “Wrong, you’ve failed to know a basic fact about the coin. Since it was already flipped the probability was already either 0% or 100%, and maybe if you didn’t know which it was you should just say you can’t assign a probability or something.”
Now, suppose there are two universes that differ only by the polarization of a photon coming from a distant star, due to hit Earth in a few hours. And I go into the universe where that polarization is left-handed (rather than right-handed), and in that universe the probability that the photon is right-handed is 0% - it’s just a fact about the photon. So I go to the copy of Carol that lives in this universe and ask Carol what’s the probability the photon has right-handed polarization, and Carol tells me it’s 50%, and I say “Wrong, you’ve failed to know a basic fact about the photon. Since it’s already on its way the probability was already either 0% or 100%, and maybe if you don’t know which it was you should just say you can’t assign a probability or something.”
Now, suppose there are two universes that differ outside of the room that Dave is currently in, but are the same within Dave’s room. Say, in one universe all the stuff outside the room is arranged is it is today in our universe, while in the other universe all the stuff outside the room is arranged as it was ten years ago. And I go into the universe where all the stuff outside the room is arranged as it was ten years ago, which I will shorthand as it being 2014 (just a fact about calendars, memories, the positions of galaxies, etc.), and ask Dave what’s the probability that the year outside is 2024, and Dave tells me it’s 50%...
I mean I am not convinced by the claim that Bob is wrong.
Bob’s prior probability is 50%. Bob sees no new evidence to update this prior so the probability remains at 50%.
I don’t favour an objective notion of probabilities. From my OP:
So I am unconvinced by your thought experiments? Observing nothing new I think the observers priors should remain unchanged.
I feel like I’m not getting the distinction you’re trying to draw out with your analogy.
Yes, Bob is right. Because the probability is not a property of the coin. It’s ‘about’ the coin in a sense, but it also depends on Bob’s knowledge, including knowledge about location in time (Dave) or possible worlds (Carol).