## Abstract

Some philosophers have claimed that it is meaningless or paradoxical to consider the probability of a probability. Others have however argued that second-order probabilities do not pose any particular problem. We side with the latter group. On condition that the relevant distinctions are taken into account, second-order probabilities can be shown to be perfectly consistent.

May the same be said of an infinite hierarchy of higher-order probabilities? Is it consistent to speak of a probability of a probability, and of a probability of a probability of a probability, and so on, ad infinitum? We argue that it is, for it can be shown that there exists an infinite system of probabilities that has a model. In particular, we define a regress of higher-order probabilities that leads to a convergent series which determines an infinite-order probability value. We demonstrate the consistency of the regress by constructing a model based on coin-making machines. (C) 2013 Elsevier Inc. All rights reserved.

Original language | English |
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Pages (from-to) | 1351-1360 |

Number of pages | 10 |

Journal | International Journal of Approximate Reasoning |

Volume | 54 |

Issue number | 9 |

DOIs | |

Publication status | Published - Nov-2013 |

## Keywords

- Model
- Higher-order probability
- Infinite regress