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A Resolution of Bertrand's Paradox
Published online by Cambridge University Press: 01 April 2022
Abstract
Bertrand's random-chord paradox purports to illustrate the inconsistency of the principle of indifference when applied to problems in which the number of possible cases is infinite. This paper shows that Bertrand's original problem is vaguely posed, but demonstrates that clearly stated variations lead to different, but theoretically and empirically self-consistent solutions. The resolution of the paradox lies in appreciating how different geometric entities, represented by uniformly distributed random variables, give rise to respectively different nonuniform distributions of random chords, and hence to different probabilities. The principle of indifference appears consistently applicable to infinite sets provided that problems can be formulated unambiguously.
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- Copyright © 1994 by the Philosophy of Science Association
Footnotes
I would like to express my gratitude to Bill Boos, Roy Douglas, Dorothy Edgington, J. Howard Sobel, and the referee for Philosophy of Science for their insightful commentaries. This paper was originally read in March 1992, at a Colloquium in the Department of Philosophy, University of British Columbia.
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