When Sleeping Beauty First Awakes

David Atkinson, Jeanne Peijnenburg

Abstract


Ever since its introduction, the Sleeping Beauty Problem has been fought over by the halfers against the thirders. We distinguish three interpretations of the original problem as described in Adam Elga’s seminal paper on the subject. Elga’s intended interpretation leads to the position of the thirders; but the other readings result in that of the halfers. We show that all three of these results can be obtained by making use of objective probabilities in a four-dimensional rather than a three-dimensional space. Our reasoning avoids various problems, not only of Dutch Book and other subjectivist approaches, but also of earlier treatments in terms of objective probabilities.


References


Arntzenius, F. (2003). Some problems for conditionalization and reflection. Journal of Philosophy 100: 356–70.

Bovens, L. (2010). Judy Benjamin is a Sleeping Beauty. Analysis 70: 23–6.

Bovens, L. and Ferreira, J.L. (2010). Monty Hall drives a wedge between Judy Benjamin and the Sleeping Beauty. Analysis 70: 473–81.

Bradley, D. and Leitgeb, H. (2006). When betting odds and credences come apart: more worries for Dutch Book arguments. Analysis 66: 119– 26.

Bradley, D. (2003). A note on Dorr’s argument for 1 . Analysis 63: 266–68.

Bradley, D. (2011). Confirmation in a branching world: the Everett in- terpretation and Sleeping Beauty. British Journal for the Philosophy of Science 62: 323–43.

Cisewski, J., Kadane, J.B., Schervish, M.J., Seidenfeld, T. and Stern, R. (2016). Sleeping Beauty’s credences. Forthcoming in Philosophy of Science. http://www.journals.uchicago.edu/doi/abs/10.1086/685741

Cozic, M. (2011). Imaging and Sleeping Beauty: a case for double-halfers. International Journal of Approximate Reasoning 52: 137–43.

Dieks, D. (2007). Reasoning about the future: doom and Beauty. Synthese 156: 427–39.

Dorr, C. (2002). Sleeping Beauty: in defense of Elga. Analysis 62: 292– 96.

Draper, K. and Pust, J. (2008). Diachronic Dutch books and Sleeping Beauty. Synthese 164: 281–87.

Elga, A. (2000). Self-locating belief and the Sleeping Beauty problem. Analysis 60: 143–47.

Groisman, B. (2008). The end of Sleeping Beauty’s nightmare. British Journal for the Philosophy of Science: 409–16.

Groisman, B., Hallakoun, N. and Vaidman, L. (2013). The measure of existence of a quantum world and the Sleeping Beauty Problem. Analysis 73: 695–706.

Hawley, P. (2013). Inertia, optimism and Beauty. Noûs 47: 85–103.

Hitchcock, C. (2004). Beauty and the bets. Synthese 139: 405–20.

Horgan, T. (2004). Sleeping Beauty awakened: new odds at the dawn of the new day. Analysis 64: 10–21.

Horgan, T. (2007). Synchronic Bayesian updating and the generalized Sleeping Beauty problem. Analysis 67: 50–59.

Horgan, T. (2008). Synchronic Bayesian updating and the generalized Sleeping Beauty problem: reply to Pust. Synthese 160: 155–159.

Horgan, T. and Mahtani, A. (2013). Generalized conditionalization and the Sleeping Beauty problem. Erkenntnis 78: 333–351.

Kim, N. (2015). Titelbaum’s theory of de se updating and two versions of Sleeping Beauty. Erkenntnis 80: 1217–1236.

Lewis, D. (1980). A Subjectivist’s Guide to Objective Chance, in Richard C. Jeffrey (ed.), Studies in Inductive Logic and Probability, Volume II. Berkeley: University of California Press, 263–293.

Lewis, D. (2001). Sleeping Beauty: Reply to Elga. Analysis 61: 171–76.

Lewis, P. (2007). Quantum Sleeping Beauty. Analysis 67: 59–65.

Lewis, P. (2010). Credence and self-location. Synthese 175: 369–82.

Monton, B. (2002). Sleeping Beauty and the forgetful Bayesian. Analysis 62: 47–53.

OSCAR Seminar, The (2008). An objectivist argument for thirdism. Analysis 68: 149–55.

Pust, J. (2008). Horgan on Sleeping Beauty. Synthese. 160: 97–101.

Pust, J. (2011). Sleeping Beauty and direct inference. Analysis 71: 290– 293.

Pust, J. (2012). Conditionalization and essentially indexical credence. Analysis 109: 295–315.

Pust, J. (2014). Beauty and Generalized Conditionalization: Reply to Horgan and Mahtani. Erkenntnis 79: 687–700.

Ross, J. (2010). Sleeping Beauty, countable additivity, and rational dilemma. Philosophical Review 119: 411–47.

Titelbaum, M.G. (2015). Reply to Kim’s two versions of Sleeping Beauty. Erkenntnis 80:1237–1243.

White, R. (2006). The generalized Sleeping Beauty problem: a challenge for thirders. Analysis 2006: 114–19.

Wilson, A. (2013). Everettian confirmation and Sleeping Beauty. British Journal for the Philosophy of Science 64: 709–37.


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