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Synthese (2009) 168:295312
Knowledge, Rationality & Action 605622 DOI 10.1007/s11229-008-9443-2
Received: 3 June 2008 / Accepted: 13 November 2008 / Published online: 14 December 2008 Springer Science+Business Media B.V. 2008
Abstract In this paper, I argue for a view largely favorable to the Thirder view: when Sleeping Beauty wakes up on Monday, her credence in the coins landing heads is less than 1/2. Lets call this the Lesser view. For my argument, I (i) criticize Strict Conditionalization as the rule for changing de se credences; (ii) develop a new rule; and (iii) defend it by Gaifmans Expert Principle. Finally, I defend the Lesser view by making use of this new rule.
Keywords Sleeping Beauty De se belief Self-locating belief De se credence
Updating rule
1 Introduction
Suppose that Sleeping Beauty (hereafter: SB), a paragon of probabilistic rationality, knows the following facts on Sunday: A group of evil experimenters put her to sleep on that day. Next, they toss a fair coin. Case 1: (H) The coin lands heads. In this case, they wake up SB only on Monday. Case 2: (T ) The coin lands tails. In this case, they wake up SB for the rst time on Monday, inject a drug that erases her memory of Monday, and wake her up for the second time on Tuesday. In either case, the experiment is over on Wednesday.
For brevity, let s be the last moment on Sunday at which she is conscious and m be the moment of waking up on Monday. Accordingly, let Cm and Cs be her credence functions at m and s. Here is a question: What is SBs credence at m in H? There have been two dominant answers: According to the Thirder view, Cm(H) = 1/3
N. Kim (B)
University of Massachusetts, Amherst, MA, USA e-mail: newitx@gmail.com
Sleeping Beauty and shifted Jeffrey conditionalization
Namjoong Kim
123
296 Synthese (2009) 168:295312
(Elga 2000). According to the Halfer view, Cm(H) = 1/2 (Lewis 2001). Paradoxically, both views seem to have good arguments in their favor.
Halfers contend: Let W be that SB wakes up today with the memory of Sunday as the last memory. When SB was put to sleep on Sunday, she fully expected to receive W as her next...