Like a number of people (including Elga), you’re converting an almost-doable thought experiment into one that may be impossible in principle. If the experiment is done with some not-yet-invented but plausible memory-erasing drug, but is otherwise realistic, Beauty will not have the same experiences when woken Monday and when woken Tuesday. Various aspects of her sensed environment, as well as internal thoughts, will be different for the two awakenings. We just assume that none of these differences allow her to infer the day of the week.
Second, if she should wager as if the probability of Heads is 1⁄3, in what sense is the probability of Heads not actually 1/3? The only point of probabilities is to influence actions. (Also, it is not just “some” situations where she should wager on the basis that the probability of Heads is 1⁄3. That’s always what she should do.)
Two points…
Like a number of people (including Elga), you’re converting an almost-doable thought experiment into one that may be impossible in principle. If the experiment is done with some not-yet-invented but plausible memory-erasing drug, but is otherwise realistic, Beauty will not have the same experiences when woken Monday and when woken Tuesday. Various aspects of her sensed environment, as well as internal thoughts, will be different for the two awakenings. We just assume that none of these differences allow her to infer the day of the week.
Second, if she should wager as if the probability of Heads is 1⁄3, in what sense is the probability of Heads not actually 1/3? The only point of probabilities is to influence actions. (Also, it is not just “some” situations where she should wager on the basis that the probability of Heads is 1⁄3. That’s always what she should do.)