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• W1994667018 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. • We show that an infinite hierarchy of probabilities of probabilities is consistent. • The proof consists in a model involving coin-making machines. • Weak conditions are given for the convergence of the infinite system." @default.
• W1994667018 created "2016-06-24" @default.
• W1994667018 creator A5010404442 @default.
• W1994667018 creator A5027132789 @default.
• W1994667018 date "2013-11-01" @default.
• W1994667018 modified "2023-09-29" @default.
• W1994667018 title "A consistent set of infinite-order probabilities" @default.
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• W1994667018 doi "https://doi.org/10.1016/j.ijar.2013.04.015" @default.
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