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Symmetry and the Brown-Freiling Refutation of the Continuum Hypothesis

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Author(s): Paul Bartha

Journal: Symmetry
ISSN 2073-8994

Volume: 3;
Issue: 3;
Start page: 636;
Date: 2011;
Original page

Keywords: symmetry | probability | Continuum Hypothesis | conglomerability | finitely additive measures | paradoxical sets

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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