Atkinson, David and Peijnenburg, Jeanne (2013) A Consistent Set of InfiniteOrder 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 secondorder probabilities do not pose any particular problem. We side with the latter group. On condition that the relevant distinctions are taken into account, secondorder probabilities can be shown to be perfectly consistent.
May the same be said of an infinite hierarchy of higherorder 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 higherorder probabilities that leads to a convergent series which determines an infiniteorder probability value. We demonstrate the consistency of the regress by constructing a model based on coinmaking machines.
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Item Type:  Preprint  

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Keywords:  model, higherorder probability, infinite regress  
Subjects:  General Issues > Models and Idealization Specific Sciences > Probability/Statistics 

Depositing User:  David Atkinson  
Date Deposited:  28 Apr 2013 22:20  
Last Modified:  28 Apr 2013 22:20  
Item ID:  9707  
Subjects:  General Issues > Models and Idealization Specific Sciences > Probability/Statistics 

Date:  2013  
URI:  http://philsciarchive.pitt.edu/id/eprint/9707 
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