Right. I see no need to extend standard probability, because the mildly fantastic aspect of Sleeping Beauty does not take it outside the realm of standard probability theory and its applications.
Note that all actual applications of probability and decision theory involve “indexicals”, since whenever I make a decision (often based on probabilities) I am concerned with the effect this decision will have on me, or on things I value. Note all the uses of “I” and “me”. They occur in every application of probability and decision theory that I actually care about. If the occurrence of such indexicals was generally problematic, probability theory would be of no use to me (or anyone).
“If the occurrence of such indexicals was generally problematic, probability theory would be of no use to me (or anyone)”—Except that de-indexicalising is often trivial—“If I eat ice-cream, what is the chance that I will enjoy it” → “If Chris Leong eats ice-cream, what is the probability that Chris Leong will enjoy it”.
Anyway, to the extent that this approach works, it works just as well for Beauty. Beauty has unique experiences all the time. You (or more importantly, Beauty herself) can identify Beauty-at-any-moment by what her recent thoughts and experiences have been, which are of course different on Monday and Tuesday (if she is awake then). There is no difficulty in applying standard probability and decision theory.
At least there’s no problem if you are solving the usual Sleeping Beauty problem. I suspect that you are simply refusing to solve this problem, and instead are insisting on solving only a different problem. You’re not saying exactly what that problem is, but it seems to involve something like Beauty having exactly the same experiences on Monday as on Tuesday, which is of course impossible for any real human.
Right. I see no need to extend standard probability, because the mildly fantastic aspect of Sleeping Beauty does not take it outside the realm of standard probability theory and its applications.
Note that all actual applications of probability and decision theory involve “indexicals”, since whenever I make a decision (often based on probabilities) I am concerned with the effect this decision will have on me, or on things I value. Note all the uses of “I” and “me”. They occur in every application of probability and decision theory that I actually care about. If the occurrence of such indexicals was generally problematic, probability theory would be of no use to me (or anyone).
“If the occurrence of such indexicals was generally problematic, probability theory would be of no use to me (or anyone)”—Except that de-indexicalising is often trivial—“If I eat ice-cream, what is the chance that I will enjoy it” → “If Chris Leong eats ice-cream, what is the probability that Chris Leong will enjoy it”.
What makes you think that you are “Chris Leong”?
Anyway, to the extent that this approach works, it works just as well for Beauty. Beauty has unique experiences all the time. You (or more importantly, Beauty herself) can identify Beauty-at-any-moment by what her recent thoughts and experiences have been, which are of course different on Monday and Tuesday (if she is awake then). There is no difficulty in applying standard probability and decision theory.
At least there’s no problem if you are solving the usual Sleeping Beauty problem. I suspect that you are simply refusing to solve this problem, and instead are insisting on solving only a different problem. You’re not saying exactly what that problem is, but it seems to involve something like Beauty having exactly the same experiences on Monday as on Tuesday, which is of course impossible for any real human.