Hostname: page-component-8448b6f56d-xtgtn Total loading time: 0 Render date: 2024-04-19T00:37:02.439Z Has data issue: false hasContentIssue false
  • English
  • Français

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.
Get access Rights & Permissions [Opens in a new window]

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.

Type
Foundations of Probability
Information
Philosophy of Science , Volume 68 , Issue S3: No. 3 Supplement: Proceedings of the 2000 Biennial Meeting of the Philosophy of Science Association. Part I: Contributed Papers Sep., 2001 , 2001 , pp. S109 - S122
Copyright
Copyright © Philosophy of Science Association 2001

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Bartha, Paul and Hitchcock, Christopher (1999), “The Shooting-room Paradox and Conditionalizing on ‘Measurably Challenged’ Sets”, Synthese 118:403–437.CrossRefGoogle Scholar
Bertrand, Joseph (1889), Calcul des Probabilités. Paris: Gauthier-Villars.Google Scholar
de Finetti, Bruno (1975), Theory of Probability, Vols. 1 and 2. Translated by Machí, A. and Smith, A.. New York: Wiley.Google Scholar
Hacking, Ian (1975), The Emergence of Probability. Cambridge: Cambridge University Press.Google Scholar
Howson, Colin and Urbach, Peter (1993), Scientific Reasoning: The Bayesian Approach, 2nd ed. La Salle: Open Court Press.Google Scholar
Jeffrey, Richard (1983), The Logic of Decision, 2nd ed. Chicago: University of Chicago Press.Google Scholar
Laplace, Pierre Simon (1820), Oeuvres completes. Paris: M.V. Courcier.Google Scholar
McGee, Vann (1994), “Learning the Impossible”, in Eels, Ellery and Skyrms, Brian (eds.), Probability and Conditionals. Cambridge: Cambridge University Press, 179–199.Google Scholar
Ramsey, Frank (1931), “Truth and Probability”, in Braithwaite, Richard Bevan (ed.), The Foundations of Mathematics and other Logical Essays. London: Routledge and Kegan Paul, 156–198.Google Scholar
Rudin, Walter (1974), Real and Complex Analysis, 2nd ed. New York: McGraw-Hill.Google Scholar
Strevens, Michael (1998), “Inferring Probabilities from Symmetries”, Nous 32:231–246.CrossRefGoogle Scholar