In a recent paper [2] David Lewis offered an extremely interesting and, if correct, important solution to the main unsolved problem of Carnap's program for inductive logic—the choice of an appropriate C-function. The gist of Lewis' solution is to first obtain a pilot sample from the target population and then select, on the basis of this sample, from among the immodestλ-methods. An immodest inductive method is one which estimates that the mean squared error of its estimates of population relative frequencies (...) is less than or equal that of any other inductive method. By great ingenuity Lewis apparently shows that on any evidence e there is one and only one immodest λ-method. I will attempt to show that Lewis made a conceptual error in formulating the equations to be solved and that when it is corrected it can be easily demonstrated that all admissible λ-methods are immodest and hence that Lewis' criterion is of no value. (shrink)

Inductive methods can be used to estimate the accuracies of inductive methods. Call a method immodest if it estimates that it is at least as accurate as any of its rivals. It would be unreasonable to adopt any but an immodest method. Under certain assumptions, exactly one of Carnap's lambda-methods is immodest. This may seem to solve the problem of choosing among the lambda-methods; but sometimes the immodest lambda-method is λ =0, which it would not be reasonable to adopt. We (...) should therefore reconsider the assumptions that led to this conclusion: for instance, the measure of accuracy. (shrink)

In this influential study of central issues in the philosophy of science, Paul Horwich elaborates on an important conception of probability, diagnosing the failure of previous attempts to resolve these issues as stemming from a too-rigid conception of belief. Adopting a Bayesian strategy, he argues for a probabilistic approach, yielding a more complete understanding of the characteristics of scientific reasoning and methodology. Presented in a fresh twenty-first-century series livery, and including a specially commissioned preface written by Colin Howson, illuminating its (...) enduring importance and relevance to philosophical enquiry, this engaging work has been revived for a new generation of readers. (shrink)

Concepts and problems; The calculus of inductive probability; Alternative inductive logics and the justification of induction; Probability and action; The pragmatic theory of inductive probability; The logic of causal statements as a formal language; The logic of causal statements as a model of natural language; The dispositional theory of empirical probability; Cause and chance in space - time systems; The presupposition of theory induction; Chance, cause, and reason.