Sleeping Beauty: reply to Elga

1. The problem Researchers at the Experimental Philosophy Laboratory have decided to carry out the following experiment. First they will tell Sleeping Beauty all that I am about to tell you in this paragraph, and they will see to it that she fully believes all she is told. Then on Sunday evening they will put her to sleep. On Monday they will awaken her briefly. At first they will not tell her what day it is, but later they will tell her that it is Monday. Then they will subject her to memory erasure. Perhaps they will again awaken her briefly on Tuesday. Whether they do will depend on the toss of a fair coin: if heads they will awaken her only on Monday, if tails they will awaken her on Tuesday as well. On Wednesday the experiment will be over and she will be allowed to wake up. The three possible brief awakenings during the experiment will be indistinguishable: she will have the same total evidence at her Monday awakening whatever the result of the coin toss may be, and if she is awakened on Tuesday the memory erasure on Monday will make sure that her total evidence at the Tuesday awakening is exactly the same as at the Monday awakening. However, she will be able, and she will be taught how, to distinguish her brief awakenings during the experiment from her Wednesday awakening after the experiment is over, and indeed from all other actual awakenings there have ever been, or ever will be. Let’s assume that Beauty is a paragon of probabilistic rationality, and always assigns the credences (subjective probabilities) she ought to. We shall need to consider her credence functions at three different times. Let P be her credence function just after she is awakened on Monday. Let P+ be her credence function just after she’s told that it’s Monday. Let P- be her credence function just before she’s put to sleep on Sunday, but after she’s been told how the experiment is to work. At the beginning of her Monday awakening, what credence does Beauty assign to the hypothesis HEADS that the result of the coin toss is heads? What credence does she assign to the hypothesis TAILS that it’s tails? Adam Elga (2000) argues that P(HEADS) = 1/3, P(TAILS) = 2/3. I disagree, and argue that P(HEADS) = P(TAILS) = 1/2.