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Ignorance and Indifference*

Published online by Cambridge University Press:  01 January 2022

John D. Norton
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Abstract

The epistemic state of complete ignorance is not a probability distribution. In it, we assign the same, unique, ignorance degree of belief to any contingent outcome and each of its contingent, disjunctive parts. That this is the appropriate way to represent complete ignorance is established by two instruments, each individually strong enough to identify this state. They are the principle of indifference (PI) and the notion that ignorance is invariant under certain redescriptions of the outcome space, here developed into the ‘principle of invariance of ignorance’ (PII). Both instruments are so innocuous as almost to be platitudes. Yet the literature in probabilistic epistemology has misdiagnosed them as paradoxical or defective since they generate inconsistencies when conjoined with the assumption that an epistemic state must be a probability distribution. To underscore the need to drop this assumption, I express PII in its most defensible form as relating symmetric descriptions and show that paradoxes still arise if we assume the ignorance state to be a probability distribution.

Type
Research Article
Information
Philosophy of Science , Volume 75 , Issue 1 , January 2008 , pp. 45 - 68
Copyright
Copyright © The Philosophy of Science Association

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References

Bertrand, Joseph (1907), Calcul des probabilités. Paris: Gauthier-Villars.Google Scholar
Borel, Émile ([1950] 1965), Elements of the Theory of Probability. Translated by Freund, John E.. Originally published as Eléments de la théorie des probabilités (Paris: Albin Michel). Englewood Cliffs, NJ: Prentice-Hall.Google Scholar
Galavotti, Maria Carla (2005), Philosophical Introduction to Probability. Stanford, CA: CSLI.Google Scholar
Gillies, Donald (2000), Philosophical Theories of Probability. London: Routledge.Google Scholar
Howson, Colin, and Urbach, Peter (1996), Scientific Reasoning: The Bayesian Approach. LaSalle, IL: Open Court.Google Scholar
Jaynes, E. T. (1973), “The Well-Posed Problem”, The Well-Posed Problem 3:477–493.Google Scholar
Jaynes, E. T. (2003), Probability Theory: The Logic of Science. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Jeffreys, Harold (1961), Theory of Probability. Oxford: Oxford University Press.Google Scholar
Kass, Robert E., and Wasserman, Larry (1996), “The Selection of Prior Distributions by Formal Rules”, The Selection of Prior Distributions by Formal Rules 91:1343–1370.Google Scholar
Keynes, John Maynard ([1921] 1979), A Treatise of Probability. Reprint. (London: Macmillan). New York: AMS.Google Scholar
Laplace, Pierre-Simon ([1825] 1995), Philosophical Essay on Probabilities. Translated by Dale, Andrew I.. Originally published as Essai philosophique sur les probabilités (Paris: Bachelier). New York: Springer-Verlag.Google Scholar
Norton, John (2007a), “Disbelief as the Dual of Belief”, Disbelief as the Dual of Belief 21:231–252.Google Scholar
Norton, John (2007b), “Probability Disassembled”, Probability Disassembled 58:141–171.Google Scholar
Shafer, Glen (1976), A Mathematical Theory of Evidence. Princeton, NJ: Princeton University Press.CrossRefGoogle Scholar
van Fraassen, Bas (1989), Laws and Symmetries. Oxford: Clarendon.CrossRefGoogle Scholar
von Mises, Richard ([1951] 1981), Probability, Truth and Statistics. English edition prepared by Hilda Geiringer from the 3rd German edition (London: George Allen & Unwin). New York: Dover.Google Scholar