But the development of probability theory and the way that it is applied in practice were guided by implicit assumptions about observers.
I don’t think that’s true, but even if it is an accurate description of the history, that’s irrelevant—we have justifications for probability theory that make no assumptions whatsoever about observers.
You seemed to argue in your first post that selection effects were not routinely handled within standard probability theory.
No, I argued that this isn’t a case of selection effects.
Certainly agreed as to logic (which does not include probability theory).
Why are you ignoring what I wrote about proofs that probability theory is either a or the uniquely determined extension of classical propositional logic to handle degrees of certainty? That places probability theory squarely in the logical camp. It is a logic.
in which we made certain implicit assumptions about observers
No, we made no such implicit assumptions. There are no assumptions, implicit or otherwise, about observers at all. If you think otherwise, show me where they occur in Cox’s Theorem or in my theorem.
I’m going to wait to address that until you clarify what you mean by applying standard probability theory, since you offered a fairly narrow view of what this means in your original post, and seemed to contradict it in your point 3 in the comment.
I have no idea what you’re talking about here.
My position is that “the information available” should not be interpreted as simply the existence of at least one agent making the same observations you are, while declining to make any inferences at all about the number of such agents (beyond that it is at least 1).
Um, there’s only one agent here, but if by “agent” you mean the pair (person, day), then the above is just wrong—it’s very clearly part of the model that if the coin comes up Heads, there is exactly one day on which the remembered observations could be made, and if the coin comes up Tails, there are exactly two days on which the remembered observations could be made. I even worked out the probabilities that the observations occurred on just Monday, just Tuesday, or both Monday and Tuesday.
Listen, if you want to argue against my analysis, you need to
1. Propose a different model of what Beauty knows on Sunday, and/or
2. Propose a different proposition that expresses the additional information Beauty has on Monday/Tuesday and that accounts for her altered probabilities. This proposition should be possible to sensibly state and talk about on Sunday, Monday, Tuesday, or Wednesday, by either Beauty or one of the experimenters, and mean the same thing in all these cases.
I don’t think that’s true, but even if it is an accurate description of the history, that’s irrelevant—we have justifications for probability theory that make no assumptions whatsoever about observers.
No, I argued that this isn’t a case of selection effects.
Why are you ignoring what I wrote about proofs that probability theory is either a or the uniquely determined extension of classical propositional logic to handle degrees of certainty? That places probability theory squarely in the logical camp. It is a logic.
No, we made no such implicit assumptions. There are no assumptions, implicit or otherwise, about observers at all. If you think otherwise, show me where they occur in Cox’s Theorem or in my theorem.
I have no idea what you’re talking about here.
Um, there’s only one agent here, but if by “agent” you mean the pair (person, day), then the above is just wrong—it’s very clearly part of the model that if the coin comes up Heads, there is exactly one day on which the remembered observations could be made, and if the coin comes up Tails, there are exactly two days on which the remembered observations could be made. I even worked out the probabilities that the observations occurred on just Monday, just Tuesday, or both Monday and Tuesday.
Listen, if you want to argue against my analysis, you need to
1. Propose a different model of what Beauty knows on Sunday, and/or
2. Propose a different proposition that expresses the additional information Beauty has on Monday/Tuesday and that accounts for her altered probabilities. This proposition should be possible to sensibly state and talk about on Sunday, Monday, Tuesday, or Wednesday, by either Beauty or one of the experimenters, and mean the same thing in all these cases.