Inductive Immodesty and Lawlikeness

Extract

David Lewis [2] suggests that an adequate inductive method should be immodest, i.e. recommend itself as at least as accurate as any of its rivals. On this basis he works out a solution to the intricate problem of choosing among Carnap's λ-methods. Lewis himself points out certain undesirable consequences of his solution. I will argue that the solution breaks down for a more general reason than that indicated by Lewis; like other procedures for estimating degrees of belief I am familiar with, it overlooks the component of lawlikeness of inductive situations. This is not to object to the requirement of immodesty; I only want to draw attention to certain assumptions which Lewis makes in deriving his equations and which seem to be unjustified.