I understand that you do not assume Beauty’s experiences are identical on Monday and Tuesday. Rather, my understanding is that you assume that “the set of things it is possible for Beauty to experience on Monday” is identical to “the set of things it is possible for Beauty to experience on Tuesday”. Is my understanding incorrect?
Ah! I see I misread what you wrote. As you point out, it is implausible in real life that the set of possible experiences on Monday is exactly the same as the set of possible experiences on Tuesday, or at least it’s implausible that the probability distributions over possible experiences on Monday and on Tuesday are exactly the same. I think it would be fine to assume for a thought experiment that they are the same, however. The reason it would be fine is that you could also not assume they are the same, but just that they are very similar, which is indeed plausible, and the result would be that at most Beauty will obtain some small amount of information about whether it is Monday or Tuesday from what her experiences are, which will change her probability of the coin having landed Heads by only a small amount. Similarly, we don’t have to assume PERFECT memory erasure. And we don’t have to assume (as we usually do) that Beauty has exactly ZERO probability of dying after Monday and before she might have been woken on Tuesday. Etc, etc.
I understand that you do not assume Beauty’s experiences are identical on Monday and Tuesday. Rather, my understanding is that you assume that “the set of things it is possible for Beauty to experience on Monday” is identical to “the set of things it is possible for Beauty to experience on Tuesday”. Is my understanding incorrect?
Ah! I see I misread what you wrote. As you point out, it is implausible in real life that the set of possible experiences on Monday is exactly the same as the set of possible experiences on Tuesday, or at least it’s implausible that the probability distributions over possible experiences on Monday and on Tuesday are exactly the same. I think it would be fine to assume for a thought experiment that they are the same, however. The reason it would be fine is that you could also not assume they are the same, but just that they are very similar, which is indeed plausible, and the result would be that at most Beauty will obtain some small amount of information about whether it is Monday or Tuesday from what her experiences are, which will change her probability of the coin having landed Heads by only a small amount. Similarly, we don’t have to assume PERFECT memory erasure. And we don’t have to assume (as we usually do) that Beauty has exactly ZERO probability of dying after Monday and before she might have been woken on Tuesday. Etc, etc.