Journal Article

Arguments for–or against–Probabilism?

Alan Hájek

in The British Journal for the Philosophy of Science

Published on behalf of British Society for the Philosophy of Science

Volume 59, issue 4, pages 793-819
Published in print December 2008 | ISSN: 0007-0882
Published online December 2008 | e-ISSN: 1464-3537 | DOI:
Arguments for–or against–Probabilism?

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  • Science and Mathematics


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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.


The Dutch Book Argument


Saving the Dutch Book argument


‘The Dutch Book argument merely dramatizes an inconsistency in the attitudes of an agent whose credences violate probability theory’

Representation Theorem-based Arguments

The Calibration Argument

The Gradational Accuracy Argument


Journal Article.  11067 words. 

Subjects: Philosophy of Science ; Science and Mathematics

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