Philosophy of Science 74 (2):150-175 (2007)

Authors
Nicholas Shackel
Cardiff University
Abstract
The principle of indifference is supposed to suffice for the rational assignation of probabilities to possibilities. Bertrand advances a probability problem, now known as his paradox, to which the principle is supposed to apply; yet, just because the problem is ill‐posed in a technical sense, applying it leads to a contradiction. Examining an ambiguity in the notion of an ill‐posed problem shows that there are precisely two strategies for resolving the paradox: the distinction strategy and the well‐posing strategy. The main contenders for resolving the paradox, Marinoff and Jaynes, offer solutions which exemplify these two strategies. I show that Marinoff’s attempt at the distinction strategy fails, and I offer a general refutation of this strategy. The situation for the well‐posing strategy is more complex. Careful formulation of the paradox within measure theory shows that one of Bertrand’s original three options can be ruled out but also shows that piecemeal attempts at the well‐posing strategy will not succeed. What is required is an appeal to general principle. I show that Jaynes’s use of such a principle, the symmetry requirement, fails to resolve the paradox; that a notion of metaindifference also fails; and that, while the well‐posing strategy may not be conclusively refutable, there is no reason to think that it can succeed. So the current situation is this. The failure of Marinoff’s and Jaynes’s solutions means that the paradox remains unresolved, and of the only two strategies for resolution, one is refuted and we have no reason to think the other will succeed. Consequently, Bertrand’s paradox continues to stand in refutation of the principle of indifference.
Keywords No keywords specified (fix it)
Categories (categorize this paper)
DOI 10.1086/519028
Options
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

References found in this work BETA

Laws and Symmetry.Bas C. van Fraassen - 1989 - Oxford University Press.
Paradoxes from A to Z.Michael Clark - 2004 - Revue Philosophique de la France Et de l'Etranger 194 (3):374-375.
Countable Additivity and Subjective Probability.J. Williamson - 1999 - British Journal for the Philosophy of Science 50 (3):401-416.
The Well-Posed Problem.Edwin T. Jaynes - 1973 - Foundations of Physics 3 (4):477-493.

View all 8 references / Add more references

Citations of this work BETA

Cluelessness.Hilary Greaves - 2016 - Proceedings of the Aristotelian Society 116 (3):311-339.
The Implementation, Interpretation, and Justification of Likelihoods in Cosmology.C. D. McCoy - 2018 - Studies in History and Philosophy of Modern Physics 62:19-35.
An Empirical Approach to Symmetry and Probability.Jill North - 2010 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 41 (1):27-40.
Refutation by Elimination.John Turri - 2010 - Analysis 70 (1):35-39.

View all 16 citations / Add more citations

Similar books and articles

Dissolving the Wine/Water Paradox.Jeffrey M. Mikkelson - 2004 - British Journal for the Philosophy of Science 55 (1):137-145.
The Fallacy of Intrinsic Distributions.Amos Nathan - 1984 - Philosophy of Science 51 (4):677-684.
Should We Respond to Evil with Indifference?Brian Weatherson - 2005 - Philosophy and Phenomenological Research 70 (3):613–635.
The Sequential Lottery Paradox.I. Douven - 2012 - Analysis 72 (1):55-57.
On Bertrand's Paradox.Sorin Bangu - 2010 - Analysis 70 (1):30-35.
A Resolution of Bertrand's Paradox.Louis Marinoff - 1994 - Philosophy of Science 61 (1):1-24.

Analytics

Added to PP index
2009-01-28

Total views
1,937 ( #1,245 of 2,342,397 )

Recent downloads (6 months)
19 ( #34,553 of 2,342,397 )

How can I increase my downloads?

Downloads

My notes