In “A Nonpragmatic Vindication of Probabilism,” James M. Joyce attempts to “depragmatize” de Finetti’s prevision argument for the claim that our credences ought to satisfy the axioms of the probability calculus. This article adapts Joyce’s argument to give nonpragmatic vindications of David Lewis’s original Principal Principle as well as recent reformulations due to Ned Hall and Jenann Ismael. Joyce enumerates properties that a function must have if it is to measure the distance from a set of credences to a set of truth values; he shows that, on any such measure, and for any set of credences that violates the probability axioms, there is a set that satisfies those axioms that is closer to every possible set of truth values. This article replaces truth values with objective chances in this argument; it shows that for any set of credences that violates the probability axioms or the Principal Principle, there is a set that satisfies both that is closer to every possible set of objective chances and similarly for Ned Hall’s New Principle and Jenann Ismael’s Generalized Principal Principle. Along the way, the article provides new arguments for some of Joyce’s central conditions on distance measures, and it answers two pressing objections to Joyce’s strategy.