Ignorance and Indifference

Philosophy of Science 75 (1):45-68 (2008)
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. *Received February 2007; revised July 2007. †To contact the author, please write to: Department of History and Philosophy of Science, University of Pittsburgh, Pittsburgh, PA 15260; e-mail: jdnorton@pitt.edu.
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    References found in this work BETA
    Edwin T. Jaynes (1973). The Well-Posed Problem. Foundations of Physics 3 (4):477-493.
    John D. Norton (2007). Disbelief as the Dual of Belief. International Studies in the Philosophy of Science 21 (3):231 – 252.

    View all 7 references

    Citations of this work BETA
    Jill North (2010). An Empirical Approach to Symmetry and Probability. Studies in History and Philosophy of Science Part B 41 (1):27-40.
    Greg Novack (2010). A Defense of the Principle of Indifference. Journal of Philosophical Logic 39 (6):655-678.

    View all 8 citations

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