The Principal Principle does not imply the Principle of Indifference

In a recent paper in the British Journal for the Philosophy of Science, James Hawthorne, Jürgen Landes, Christian Wallmann, and Jon Williamson (henceforth HLWW) argue that the Principal Principle entails the Principle of Indifference. In this paper, I argue that it does not. Lewis’ version of the Principal Principle notoriously depends on a notion of admissibility, which Lewis uses to restrict its application. HLWW do not give a precise account either, but they do appeal to two principles concerning admissibility, which they call Condition 1 and Condition 2. There are two ways of reading their argument, depending on how you understand the status of Conditions 1 and 2. Reading 1: The correct account of admissibility is determined independently of these two principles, and yet these two principles follow from that correct account. Reading 2: The correct account of admissibility is determined in part by these two principles, so that the principles follow from that account but only because the correct account is constrained so that it must satisfy them. HLWW then show that, given an account of admissibility on which Conditions 1 and 2 hold, the Principal Principle entails the Principle of Indifference. I will argue that, on either reading of the argument, it fails. I will argue that there is a plausible account of admissibility on which Conditions 1 and 2 are false. That defeats the first reading of the argument. I will then argue that the intuitions that lead us to assent to Condition 2 also lead us to assent to other very closely related principles that are inconsistent with Condition 2. This, I claim, casts doubt on the reliability of those intuitions, and thus removes our justification for Condition 2. This defeats the second reading of the HLWW argument. Thus, the argument fails.