Accuracy, Chance, and the Principal Principle

Philosophical Review 121 (2):241-275 (2012)
In ‘A Non-Pragmatic Vindication of Probabilism’, Jim Joyce attempts to ‘depragmatize’ de Finetti’s prevision argument for the claim that our partial beliefs ought to satisfy the axioms of probability calculus. In this paper, I adapt Joyce’s argument to give a non-pragmatic vindication of various versions of David Lewis’ Principal Principle, such as the version based on Isaac Levi's account of admissibility, Michael Thau and Ned Hall's New Principle, and Jenann Ismael's Generalized Principal Principle. Joyce enumerates properties that must be had by any measure of the distance from a set of partial beliefs to the set of truth values; he shows that, on any such measure, and for any set of partial beliefs that violates the probability axioms, there is a set that satisfies those axioms that is closer to every possible set of truth values. I replace truth values by objective chances in his argument; I show that for any set of partial beliefs that violates the probability axioms or a version of the Principal Principle, there is a set that satisfies them that is closer to every possible set of objective chances.
Keywords Principal Principle  gradational accuracy  objective chance  scoring rules  partial beliefs  subjective probability  epistemic norms  probabilism
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DOI 10.1215/00318108-1539098
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How Valuable Are Chances?H. Orri Stefánsson & Richard Bradley - 2015 - Philosophy of Science 82 (4):602-625.
Immoderately Rational.Sophie Horowitz - 2014 - Philosophical Studies 167 (1):41-56.
Scoring Imprecise Credences: A Mildly Immodest Proposal.Conor Mayo‐Wilson & Gregory Wheeler - 2016 - Philosophy and Phenomenological Research 92 (1):55-78.
Gradational Accuracy and Nonclassical Semantics.J. R. G. Williams - 2012 - Review of Symbolic Logic 5 (4):513-537.

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