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Sleeping beauty should be imprecise. (English) Zbl 1307.03006
Summary: The traditional solutions to the Sleeping Beauty problem say that Beauty should have either a sharp 1/3 or sharp 1/2 credence that the coin flip was heads when she wakes. But Beauty’s evidence is incomplete so that it doesn’t warrant a precise credence, I claim. Instead, Beauty ought to have a properly imprecise credence when she wakes. In particular, her representor ought to assign \(R(\mathrm{Heads})=[0,1/2]\). I show, perhaps surprisingly, that this solution can account for the many of the intuitions that motivate the traditional solutions. I also offer a new objection to A. Elga’s [“Self-locating belief and the Sleeping Beauty problem”, Anal. 60, No. 2, 143–147 (2000; doi:10.1093/analys/60.2.143)] restricted version of the principle of indifference, which an opponent may try to use to collapse the imprecision.

MSC:
03A05 Philosophical and critical aspects of logic and foundations
60A05 Axioms; other general questions in probability
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[1] Bovens, L, Judy Benjamin is a sleeping beauty, Analysis, 70, 23-26, (2010)
[2] Bovens, L; Ferreira, JL, Monty Hall drives a wedge between judy Benjamin and the sleeping beauty: A reply to bovens, Analysis, 70, 473-481, (2010)
[3] Easwaran, K. (2014). Regularity and hyperreal credences. Philosophical Review, 123(1), 1-41.
[4] Elga, A, Self-locating belief and the sleeping beauty problem, Analysis, 60, 143-147, (2000)
[5] Elga, A, Defeating Dr. evil with self-locating belief, Philosophy and Phenomenological Research, 69, 383-396, (2004)
[6] Hájek, A, What conditional probability could not be, Synthese, 137, 273-323, (2003) · Zbl 1047.03003
[7] Jeffrey, R. (1983). The logic of decision. Chicago: University of Chicago Press.
[8] Joyce, JM, How probabilities reflect evidence, Philosophical Perspectives, 19, 153-178, (2005)
[9] Joyce, JM, A defense of imprecise credences in inference and decision making, Philosophical Perspectives, 24, 281-323, (2010)
[10] Joyce, J. M. (2010b). Do imprecise credences make sense? Retrieved, from http://fitelson.org/joyce_hplms_2x2. Accessed 19 March 2014.
[11] Kaplan, M. (1996). Decision theory as philosophy. Cambridge: Cambridge University Press. · Zbl 0885.62004
[12] Levi, I. (1980). The enterprise of knowledge. Cambridge, MA: MIT Press.
[13] Lewis, D. (1980). A subjectivist’s guide to objective chance. In R. C. Jeffery (Ed.), Studies in inductive logic and probability (Vol. 2, pp. 83-132). Berkeley: University of California Press. (Reprinted in Philosophical Papers, Vol. II, pp. 83-113).
[14] Lewis, D, Sleeping beauty: reply to elga, Analysis, 61, 171-176, (2001)
[15] Monton, B, Sleeping beauty and the forgetful Bayesian, Analysis, 62, 47-8211, (2002)
[16] Pust, J. (2011).Sleeping beauty and direct inference. Analysis, 71(2), 290-293.
[17] Seminar, O, An objectivist argument for thirdism, Analysis, 68, 149-155, (2008) · Zbl 1143.03320
[18] Sturgeon, S, Reason and the grain of belief, Noûs, 42, 139-165, (2008)
[19] Titelbaum, MG, Ten reasons to care about the sleeping beauty problem, Philosophy Compass, 8, 1003-1017, (2013)
[20] Van Fraassen, B. C. (1989). Laws and symmetry. Oxford: Oxford University Press.
[21] Fraassen, BC; Dunn, J (ed.); Gupta, A (ed.), Figures in a probability landscape, 345-356, (1990), Dordrecht
[22] Fraassen, BC, Belief and the problem of ulysses and the sirens, Philosophical Studies, 77, 7-37, (1995)
[23] Fraassen, BC, Vague expectation value loss, Philosophical Studies, 127, 483-491, (2006)
[24] White, R. (2009). Evidential symmetry and mushy credence. In T. Szabo Gendler & J. Hawthorne (Eds.), Oxford studies in epistemology. Oxford: Oxford University Press.
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