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The British Journal for the Philosophy of Science Advance Access originally published online on July 21, 2008
The British Journal for the Philosophy of Science 2008 59(3):409-416; doi:10.1093/bjps/axn015
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© The Author (2008). Published by Oxford University Press on behalf of British Society for the Philosophy of Science. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

The End of Sleeping Beauty's Nightmare

Berry Groisman

Centre for Quantum Computation Department of Applied Mathematics and Theoretical Physics University of Cambridge, Cambridge CB3 0WA, UK

b.groisman{at}damtp.cam.ac.uk


  Abstract

The way a rational agent changes her belief in certain propositions/hypotheses in the light of new evidence lies at the heart of Bayesian inference. The basic natural assumption, as summarized in van Fraassen's Reflection Principle ([1984]), would be that in the absence of new evidence the belief should not change. Yet, there are examples that are claimed to violate this assumption. The apparent paradox presented by such examples, if not settled, would demonstrate the inconsistency and/or incompleteness of the Bayesian approach, and without eliminating this inconsistency, the approach cannot be regarded as scientific. The Sleeping Beauty Problem is just such an example. The existing attempts to solve the problem fall into three categories. The first two share the view that new evidence is absent, but differ about the conclusion of whether Sleeping Beauty should change her belief or not, and why. The third category is characterized by the view that, after all, new evidence (although hidden from the initial view) is involved. My solution is radically different and does not fall into either of these categories. I deflate the paradox by arguing that the two different degrees of belief presented in the Sleeping Beauty Problem are in fact beliefs in two different propositions, i.e., there is no need to explain the (un)change of belief.

  1. The Sleeping Beauty Problem
  2. The Problem Deflated
    2.1 From contradiction to consistency
    2.2 The inanimate version
    2.3 Back to SB

  3. Summary


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