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On the Formal Consistency of the Principal Principle

Published online by Cambridge University Press:  01 January 2022

Gergei Bana
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Abstract

Rédei and Gyenis suggest that Lewis’s Principal Principle is meaningful only if it satisfies certain consistency conditions: starting from any assignment of credences to some algebra of events, we must always be able to extend our algebra with events as “the value of the objective chance of event E is p” and assign credences to such events in a consistent manner. I show that this extension is possible. However, I also argue that this requirement is unnecessary: the Principal Principle concerns subjective beliefs about objective chance; hence, events concerning those probabilities are meant to be in the algebra initially.

Type
The Principal Principle
Information
Philosophy of Science , Volume 83 , Issue 5 , December 2016 , pp. 988 - 1001
Copyright
Copyright © The Philosophy of Science Association

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Footnotes

†

Special thanks are due to Miklós Rédei for introducing me to the issues surrounding the Principal Principle, for numerous discussions on the topic, and for inviting me to present this material at the Principal Principle Symposium of the 2014 PSA Biennial Meeting. I am indebted to Carl Hoefer as well for his valuable comments at the symposium. I would further like to express my gratitude for the discussions with Zalán Gyenis and with the Budapest-Krakow Research Group on Probability, Causality and Determinism.

References

Diaconis, P., and Zabell, S. L.. 1982. “Updating Subjective Probability.” Journal of the American Statistical Association 770 (380): 822–30.Google Scholar
Lewis, D. 1980. “A Subjectivist’s Guide to Objective Chance.” In Studies in Inductive Logic and Probability, Vol. 2, ed. R. C. Jeffrey, 263–93. Berkeley: University of California Press.CrossRefGoogle Scholar
Pettigrew, R. 2012. “Accuracy, Chance and the Principal Principle.” Philosophical Review 121:241–75.CrossRefGoogle Scholar
Rédei, Miklós, and Gyenis, Zalán. 2013. “Can Bayesian Agents Always Be Rational? A Principled Analysis of Consistency of an Abstract Principal Principle.” PhilSci Archive. http://philsci-archive.pitt.edu/10085/.Google Scholar