Arguments for–or against–Probabilism?: Articles

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’ Representation Theorem-based Arguments The Calibration Argument The Gradational Accuracy Argument Conclusion