November, Dan D
(2019)
The Indifference Principle, its Paradoxes and Kolmogorov's Probability Space.
[Preprint]
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Abstract
In this paper I show that the validity of the Indifference Principle (IP), in light of its related paradoxes, is still an open question. I do so by offering an analysis of the Indifference Principle and its related paradoxes in the way they occur in Kolmogorov's probability theory. As such this analysis is relevant to all interpretations of his theory. I describe the conditions that any mathematical formalization of the Indifference Principle must satisfy. Consequently, I show that a mathematical formalization of the Indifference Principle has to be a set of constraints on probability spaces which mathematically describe the same events. I claim that the question whether IP-related paradoxes undermine the validity of the Indifference Principle depends on whether such a set of constraints exist. Since currently there is no mathematical proof of the existence of such a set of constraints, nor of the impossibility of there being one, the validity of the Indifference Principle remains undecided.
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