A Counterexample to the Principal Principle

25 01 2008

In his paper ‘A Subjectivist’s Guide to Objective Chance’, Lewis proposes an intimate connection between subjective probabilities and objective chances: the Principal Principle. In Lewis’s eyes, this principle captures almost all there is to know about our conception of objective chances.

In a forthcoming paper entitled ‘Knowledge and Objective Chance’, Hawthorne and Lasonen mention in passing a counterexample to the Principal Principle (a draft of which you can find here). Essentially, they think that instances of the contingent a priori provide a source of potential counterexamples. This idea stands in an interesting relation to a recent paper of Williamson (‘Indicative versus Subjunctive, Congruential versus Non-Hyperintensional Contexts’), in which the modal status of statements involving objective and subjective probabilities is discussed (a draft of which you can find there). It seems to me that Williamson’s considerations may provide a deeper reason to explain why we should not expect something like the Principal Principle to hold. In the following note, I will present a structurally similar counterexample by way of relating it to Williamson’s claims about the modal nature of the two kinds of probability.

Posted by Moritz.

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