The Principal Principle and subjective Bayesianism

Abstract

This paper poses a problem for Lewis' Principal Principle in a subjective Bayesian framework: we show that, where chances inform degrees of belief, subjective Bayesianism fails to validate normal informal standards of what is reasonable. This problem points to a tension between the Principal Principle and the claim that conditional degrees of belief are conditional probabilities. However, one version of objective Bayesianism has a straightforward resolution to this problem, because it avoids this latter claim. The problem, then, offers some support to this version of objective Bayesianism. Keywords Bayesianism • Principal principle • Subjective Bayesianism • Objective Bayesianism • Pooling We show in Section 1 that standard subjective Bayesianism has a problem in accommodating David Lewis' Principal Principle. In Section 2, we see that the problem does not beset a recent version of objective Bayesianism. In Section 3, we consider three possible ways in which a subjectivist might try to avoid the problem but we argue that none of these suggestions succeed. We conclude that the problem favours objective Bayesianism over subjective Bayesianism (Section 4). In Section 4 we also compare our results to some other lines of recent work.

Direct Inference and Probabilistic Accounts of Induction

“…The Principal Principle is immune to the problem for PNRC posed above, because reference classes have no bearing when the chances are single-case. However, the Principal Principle faces the following problem, due to Wallmann and Williamson ( 2020 ).…”

“…The problem is that assignments 6-8 are inconsistent (Wallmann and Williamson 2020 , §3.1). Arguably, then, neither the standard Bayesian framework nor that of logical probability can adequately accommodate the Principal Principle.…”

“… , where X says that the chance at t of A , conditional on E , is x . However, Wallmann and Williamson ( 2020 , §3.2) show that the Conditional Principal Principle does not avoid the problem for the Principal Principle outlined above. See Wallmann and Williamson ( 2020 ) for more detail and for responses to further suggestions for avoiding the above problem.…”

“… , where X says that the chance at t of A , conditional on E , is x . However, Wallmann and Williamson ( 2020 , §3.2) show that the Conditional Principal Principle does not avoid the problem for the Principal Principle outlined above.…”

The Principal Principle, admissibility, and normal informal standards of what is reasonable

“…There has been a lot of interesting work on the Principal Principle in recent years. Some researchers have identified problems with the principle: for example, it has been argued that the Principal Principle conflicts with the requirement to have accurate degrees of belief (Easwaran and Fitelson 2012) and that it creates tensions with the claim that conditional beliefs are conditional probabilities (Wallmann and Hawthorne 2018;Wallmann and Williamson 2020). Further topics of interest have included the notion of admissibility (Meacham 2010) and the relation between the Principal Principle and Humeanism (Black 1998).…”