Next Article in Journal
Next Article in Special Issue
Previous Article in Journal
Previous Article in Special Issue
Symmetry 2011, 3(3), 636-652; doi:10.3390/sym3030636
Article

Symmetry and the Brown-Freiling Refutation of the Continuum Hypothesis

Received: 25 July 2011; in revised form: 27 August 2011 / Accepted: 1 September 2011 / Published: 6 September 2011
(This article belongs to the Special Issue Symmetry in Probability and Inference)
Download PDF [278 KB, uploaded 6 September 2011]
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).
Keywords: symmetry; probability; Continuum Hypothesis; conglomerability; finitely additive measures; paradoxical sets symmetry; probability; Continuum Hypothesis; conglomerability; finitely additive measures; paradoxical sets
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Export to BibTeX |
EndNote


MDPI and ACS Style

Bartha, P. Symmetry and the Brown-Freiling Refutation of the Continuum Hypothesis. Symmetry 2011, 3, 636-652.

AMA Style

Bartha P. Symmetry and the Brown-Freiling Refutation of the Continuum Hypothesis. Symmetry. 2011; 3(3):636-652.

Chicago/Turabian Style

Bartha, Paul. 2011. "Symmetry and the Brown-Freiling Refutation of the Continuum Hypothesis." Symmetry 3, no. 3: 636-652.


Symmetry EISSN 2073-8994 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert