Sleeping Beauty meets Monday

Abstract

The Sleeping Beauty problem-first presented by A. Elga in a philosophical context-has captured much attention. The problem, we contend, is more aptly regarded as a paradox: apparently, there are cases where one ought to change one's credence in an event's taking place even though one gains no new information or evidence, or alternatively, one ought to have a credence other than 1/2 in the outcome of a future coin toss even though one knows that the coin is fair. In this paper we argue for two claims. First, that Sleeping Beauty does gain potentially new relevant information upon waking up on Monday. Second, his credence shift is warranted provided it accords with a calculation that is a result of conditionalization on the relevant information: "this day is an experiment waking day" (a day within the experiment on which one is woken up). Since Sleeping Beauty knows what days d could refer to, he can calculate the probability that the referred to waking day is a Monday or a Tuesday providing an adequate resolution of the paradox.

Demystifying the Mystery Room

“…Let us compare this analysis to that of the Sleeping Beauty problem. Karlander and Spectre (2010) agree with Weintraub (2004) that Sleeping Beauty learns something by awakening. In addition, they observe that during the first awakening, one can demonstratively refer to the awakening as 'this awakening': "It is customary to take this name as rigidly designating [an awakening], in this case [the first one], even if one does not know [which awakening] it is.…”

Inertia, Optimism and Beauty

“…But that does not mean that she needs to use the information that she has been awakened (or that she is awake) to eliminate H TUE . 19 She may need to be awake in order to fix the reference of an indexical like "today" in "Today is Tuesday and the coin lands heads", but that does not mean that she needs to use the information that she is awake in order to fix the reference of "today" or to eliminate H TUE . 20 The two options do not exclude each other; the thirder might claim that Beauty both gains and loses relevant evidence.…”

The Epistemology and Auto-Epistemology of Temporal Self-Location and Forgetfulness

“…Why accept it? as far as I know, Karlander and Spectre (2010) were the first to explicitly introduce this assumption. In fact, though, they don't have much of an argument.…”

“…this is the denominator of the formula (2) given by Karlander and Spectre (2010). Here, we have used P -(A now | now = Mo) = 1 and P -(A now | now = Tu) = 1/2, which are beyond doubt.…”

“…that's the path of Karlander and Spectre (2010). However, let me make a small detour via the calculation of P'(now = Mo), the value of which is interesting in itself:…”