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Symmetry 2011, 3(3), 636-652; URLﾘﾝｸ(doi.org)
Symmetry and the Brown-Freiling Refutation of the Continuum Hypothesis
Paul Bartha
Department of Philosophy, University of British Columbia, Vancouver, BC V6T 1Z1, Canada
Received: 25 July 2011 / Revised: 27 August 2011 / Accepted: 1 September 2011 / Published: 6 September 2011
(This article belongs to the Special Issue Symmetry in Probability and Inference)
Abstract
Freiling [1] and Brown [2] have put forward a probabilistic reductio argument intended to refute the Continuum Hypothesis.
The argument relies heavily upon intuitions about symmetry in a particular scenario.
This paper argues that the argument fails, but is still of interest for two reasons.
First, the failure is unusual in that the symmetry intuitions are demonstrably coherent, even though other constraints make it impossible to find a probability model for the scenario.
Second, the best probability models have properties analogous to non-conglomerability, motivating a proposed extension of that concept (and corresponding limits on Bayesian conditionalization).
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