Abstract
Any adequate theory of chance must accommodate some version of David Lewis's ‘Principal Principle’, and Lewis has argued forcibly that believers in primitive propensities have a problem in explaining what makes the Principle true. But Lewis can only derive (a revised version of) the Principle from his own Humean theory by putting constraints on inductive rationality which cannot be given a Humean rationale.
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DOI 10.1093/bjps/49.3.371
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References found in this work BETA

New Work for a Theory of Universals.David Lewis - 1983 - Australasian Journal of Philosophy 61 (4):343-377.
Humean Supervenience Debugged.David K. Lewis - 1994 - Mind 103 (412):473--490.
On The Plurality of Worlds.Graeme Forbes - 1988 - Philosophical Quarterly 38 (151):222-240.
New Work For a Theory of Universals.David K. Lewis - 1983 - In D. H. Mellor & Alex Oliver (eds.), Properties. Oxford University Press.
A Subjectivist’s Guide to Objective Chance.David K. Lewis - 1980 - In Richard C. Jeffrey (ed.), Studies in Inductive Logic and Probability, Volume II. Berkeley: University of California Press. pp. 263-293.

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Citations of this work BETA

David Lewis’s Humean Theory of Objective Chance.Barry Loewer - 2004 - Philosophy of Science 71 (5):1115--25.
Two Mistakes About Credence and Chance.Ned Hall - 2004 - Australasian Journal of Philosophy 82 (1):93 – 111.
Who's Afraid of Undermining?Peter B. M. Vranas - 2002 - Erkenntnis 57 (2):151-174.
Chance Versus Randomness.Antony Eagle - 2010 - Stanford Encyclopedia of Philosophy.

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Two Mistakes About Credence and Chance.Ned Hall - 2004 - Australasian Journal of Philosophy 82 (1):93 – 111.
Principled Chances.Jonathan Schaffer - 2003 - British Journal for the Philosophy of Science 54 (1):27-41.

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