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Probability and Symmetry

Published online by Cambridge University Press:  01 April 2022

Paul Bartha and
Richard Johns
Paul Bartha
Affiliation:
University of British Columbia
Richard Johns*
Affiliation:
University of British Columbia
*
†Send requests for reprints to Paul Bartha, Department of Philosophy, University of British Columbia, Vancouver, BC V6T1Z1 Canada; email: bartha@interchange.ubc.ca.
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Abstract

The Principle of Indifference, which dictates that we ought to assign two outcomes equal probability in the absence of known reasons to do otherwise, is vulnerable to well-known objections. Nevertheless, the appeal of the principle, and of symmetry-based assignments of equal probability, persists. We show that, relative to a given class of symmetries satisfying certain properties, we are justified in calling certain outcomes equally probable, and more generally, in defining what we call relative probabilities. Relative probabilities are useful in providing a generalized approach to conditionalization. The technique is illustrated by application to simple examples.

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