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Symmetry and the Brown-Freiling Refutation of the Continuum Hypothesis
Department of Philosophy, University of British Columbia, Vancouver, BC V6T 1Z1, Canada
Received: 25 July 2011; in revised form: 27 August 2011 / Accepted: 1 September 2011 / Published: 6 September 2011
Abstract: Freiling  and Brown  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).
Keywords: symmetry; probability; Continuum Hypothesis; conglomerability; finitely additive measures; paradoxical sets
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MDPI and ACS Style
Bartha, P. Symmetry and the Brown-Freiling Refutation of the Continuum Hypothesis. Symmetry 2011, 3, 636-652.
Bartha P. Symmetry and the Brown-Freiling Refutation of the Continuum Hypothesis. Symmetry. 2011; 3(3):636-652.
Bartha, Paul. 2011. "Symmetry and the Brown-Freiling Refutation of the Continuum Hypothesis." Symmetry 3, no. 3: 636-652.