## 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.

Original language | English |
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Pages (from-to) | 793-819 |

Number of pages | 27 |

Journal | British Journal for the Philosophy of Science |

Volume | 59 |

Issue number | 4 |

DOIs | |

Publication status | Published - Dec 2008 |