Arguments for–or against–Probabilism?
Research School of Social Science, Australian National University, Canberra, ACT 0200, Australia
alanh{at}coombs.anu.edu.au
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Abstract |
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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.
- Introduction
- The Dutch Book Argument
- 2.1 Saving the Dutch Book argument
- 2.2 ‘The Dutch Book argument merely dramatizes an inconsistency in the attitudes of an agent whose credences violate probability theory’
- 2.2 ‘The Dutch Book argument merely dramatizes an inconsistency in the attitudes of an agent whose credences violate probability theory’
- 2.1 Saving the Dutch Book argument
- Representation Theorem-based Arguments
- The Calibration Argument
- The Gradational Accuracy Argument
- Conclusion