? Calibration and convexity : response to Gregory Wheeler ?

In his ‘Objective Bayesian calibration and the problem of non-convex evidence’, Gregory Wheeler criticises the principle I invoke in Williamson (2010) for calibrating degrees of belief with chances. Bayesian epistemologists commonly appeal to some sort of Calibration norm that says that degrees of belief should be calibrated to known chances. Typically they invoke a principle variously known as the Straight Rule, Miller’s Principle or the Principal Principle, which says that if one’s evidence E contains the claim that the chance of proposition θ is x, then one should set one’s degree of belief in θ relative to that evidence, PE (θ), to x, as long as one doesn’t have further evidence that trumps or contradicts the chance statement.1 This type of principle calls for generalisation because often we don’t have precise chance values as evidence, but constraints on chances—e.g., the constraint that the chance of θ is at least .7. In Williamson (2010) I offer the following generalisation: