On Bertrand's paradox

Analysis 70 (1):30-35 (2010)
The Principle of Indifference is a central element of the ‘classical’ conception of probability, but, for all its strong intuitive appeal, it is widely believed that it faces a devastating objection: the so-called (by Poincare´) ‘Bertrand paradoxes’ (in essence, cases in which the same probability question receives different answers). The puzzle has fascinated many since its discovery, and a series of clever solutions (followed promptly by equally clever rebuttals) have been proposed. However, despite the long-standing interest in this problem, an important assumption, necessary for its generation, has been overlooked. My aim in this paper is to identify this assumption. Since what it claims turns out to be prima facie problematic, I will urge that the burden of proof now shifts to the objectors to PI; they have to provide reasons why this assumption holds.
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References found in this work BETA
Paul Bartha & Richard Johns (2001). Probability and Symmetry. Proceedings of the Philosophy of Science Association 2001 (3):S109-.
Paul Castell (1998). A Consistent Restriction of the Principle of Indifference. British Journal for the Philosophy of Science 49 (3):387-395.
Antony Eagle (2005). Randomness Is Unpredictability. British Journal for the Philosophy of Science 56 (4):749-790.
Edwin T. Jaynes (1973). The Well-Posed Problem. Foundations of Physics 3 (4):477-493.

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