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Symmetry and the Brown-Freiling Refutation of the Continuum Hypothesis Bartha, Paul

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).

Item Metadata

Title
Symmetry and the Brown-Freiling Refutation of the Continuum Hypothesis
Creator
Bartha, Paul
Publisher
Multidisciplinary Digital Publishing Institute
Date Issued
2011-09-06
Description
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).
Subject
Symmetry; Probability; Continuum Hypothesis; Conglomerability; Finitely additive measures; Paradoxical sets
Genre
Article
Type
Text
Language
eng
Date Available
2019-04-04
Provider
Vancouver : University of British Columbia Library
Rights
CC BY 3.0
DOI
10.14288/1.0377812
URI
http://hdl.handle.net/2429/69458
Affiliation
Arts, Faculty of; Philosophy, Department of
Citation
Symmetry 3 (3): 636-652 (2011)
Publisher DOI
10.3390/sym3030636
Peer Review Status
Reviewed
Scholarly Level
Faculty
Rights URI
https://creativecommons.org/licenses/by-nc-sa/3.0/
Aggregated Source Repository
DSpace

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CC BY 3.0