Arguments for–or against–Probabilism?

British Journal for the Philosophy of Science 59 (4):793-819 (2008)
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Abstract

Four important arguments for probabilism—the Dutch Book, representation theorem, calibration, and gradational accuracy arguments—have a strikingly similar structure. Each begins with a mathematical theorem, a conditional with an existentially quantified consequent, of the general form: if your credences are not probabilities, then there is a way in which your rationality is impugned.Each argument concludes that rationality requires your credences to be probabilities.I contend that each argument is invalid as formulated. In each case there is a mirror-image theorem and a corresponding argument of exactly equal strength that concludes that rationality requires your credences not to be probabilities. Some further consideration is needed to break this symmetry in favour of probabilism. I discuss the extent to which the original arguments can be buttressed.1. Introduction2. The Dutch Book Argument2.1. Saving the Dutch Book argument2.2. ‘The Dutch Book argument merely dramatizes an inconsistency in the attitudes of an agent whose credences violate probability theory’3. Representation Theorem-based Arguments4. The Calibration Argument5. The Gradational Accuracy Argument6. Conclusion.

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Alan Hajek
Australian National University

Citations of this work

The material theory of induction.John D. Norton - 2021 - Calgary, Alberta, Canada: University of Calgary Press.
Accuracy, Risk, and the Principle of Indifference.Richard Pettigrew - 2016 - Philosophy and Phenomenological Research 92 (1):35-59.
Regularity and Hyperreal Credences.Kenny Easwaran - 2014 - Philosophical Review 123 (1):1-41.

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References found in this work

A nonpragmatic vindication of probabilism.James M. Joyce - 1998 - Philosophy of Science 65 (4):575-603.
On indeterminate probabilities.Isaac Levi - 1974 - Journal of Philosophy 71 (13):391-418.
On Indeterminate Probabilities.Isaac Levi - 1978 - Journal of Philosophy 71 (13):233--261.
Coherence and the axioms of confirmation.Abner Shimony - 1955 - Journal of Symbolic Logic 20 (1):1-28.

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