Lewis on Immodest Inductive Models

Extract

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 (=an inductive method). The gist of Lewis' solution is to first obtain a pilot sample from the target population (a time-honored procedure in statistical methodology) 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.