# A Consistent Set of Infinite-Order Probabilities

Atkinson, David and Peijnenburg, Jeanne (2013) A Consistent Set of Infinite-Order Probabilities. [Preprint]

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## 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, {\em 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.

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Item Type: Preprint
Creators:
CreatorsEmailORCID
Atkinson, Davidd.atkinson@rug.nl
Peijnenburg, Jeanne
Keywords: model, higher-order probability, infinite regress
Subjects: General Issues > Models and Idealization
Specific Sciences > Probability/Statistics
Depositing User: David Atkinson
Date Deposited: 28 Apr 2013 22:20
Item ID: 9707
Subjects: General Issues > Models and Idealization
Specific Sciences > Probability/Statistics
Date: 2013
URI: http://philsci-archive.pitt.edu/id/eprint/9707