# ANA61 3

## Transcript

1 ANALYSIS 61.3 JULY 2001 Sleeping Beauty: reply to Elga David Lewis 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 be her credence function just after she is awakened on Monday. Let P + be her her credence function just after she’s told that it’s Monday. Let P - 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 1/3, P(TAILS) = 2/3. I disagree, and Elga (2000) argues that P(HEADS) = P(TAILS) = 1/2. = argue that P(HEADS) A nalysis 61.3, July 2001, pp. 171–76. © David Lewis

2 172 david lewis I haven’t said yet whether the coin was to be tossed before or after the Monday awakening. Elga’s argument applies in the first instance to the case that it is tossed after; but he thinks, and I agree, that the answer to our ques- tion should be the same in both cases. My argument will apply equally to both cases. 2. Common ground What gives our disagreement much of its interest is that we agree on so much else (including much that not everyone would agree with). Let me begin by running through the undisputed common ground. We agree that there are two kinds of possibilities to which credences may be given. There are possibilities about what sort of possible world is actual; and there are possibilities about who one is and when one is and what sort of world one lives in. Following Quine (1969), we shall represent the latter : possible worlds with designated possibilities as classes of centred worlds centred individuals-at-times within them. Call the classes of centred worlds possibilities . (We could represent the former possibilities, the uncentred possibilities un centred possible worlds; but we needn’t bother, , as classes of since we can subsume the uncentred possibilities under the centred ones.) It may happen that two centred worlds are situated within the same uncen- tred possible world: only their designated individuals-at-times differ. If so, collocated . I call them When Beauty awakens during the experiment, three centred epistemic possibilities are compatible with her total evidence: : HEADS and it’s Monday, H 1 T : TAILS and it’s Monday, 1 T : TAILS and it’s Tuesday. 2 Elga writes, ‘Since being in T , and is subjectively just like being in T 2 1 , since exactly the same propositions are true whether you are in T or T 1 2 even a highly restricted principle of indifference yields that you ought then to have equal credence in each’ (144). By ‘proposition’ he means an uncen- tred possibility. The reason the same propositions are true whether Beauty or T is in T are collo- is that the centred worlds that are members of T 1 2 1 cated with the corresponding members of T . 2 1 So we have a I accept Elga’s ‘highly restricted principle of indifference’. further point of agreement: 1 By ignoring the collocation of corresponding members of the two epistemic possibil- ities, we would get a less restricted principle of indifference, which would tell us that ). That would afford a swift shortcut to Elga’s conclusion – much P(T ) = P(T = ) P(H 1 1 2 too swift, and Elga is wise to have nothing to do with it. It has bizarre consequences: ) and P(T ) if, for instance, that it makes exactly no difference to the equality of P(H 1 1