Abstract

This is the latest volume to appear in the distinguished series, Monographs in Modern Logic edited by Geoffrey Keene. Like its predecessors it is explicitly designed to introduce to a broad range of readers an important aspect of modern logic. This particular study is highly creditable; it is concerned with the general problem of ‘deciding what beliefs are reasonable when certain other beliefs are assumed to be true’. To this purpose the first few chapters are devoted to the discussion and use of nondeductive rules and inductive and predictive inferences, hypothesis and predictive inference, and probability and predictive inference Their topics are very competently discussed. The greater part of the exposition in these chapters and throughout the entire book is restricted to special cases of simple inductive problems and simple predictive problems. The chapter on hypothesis and predictive inference has an excellent introduction to the problem of entrenchment rules. In the chapter on probability and predictive inference Carnap’s solution of inductive and predictive problems is very ably analyzed. However, the analysis does presuppose some familiarity on the part of the reader with the nature of set theory. The problems of simple statistical inference are discussed in the chapter on statistical inference but too briefly to do full justice to the principal demands such a subject usually imposes. We thought the chapter on Bayesian statistical inference much more effective and comprehensive. Here the discussion centered on two types of theories which endeavor to apply probability measures to hypotheses, namely, those of Carnap and of the statistician Harold Jeffreys. These theories are examples of what the author describes as logical theories of probability measure in contrast to the subjective theory of probability. Briefly mentioned in connection with the latter are the philosopher F P Ramsey and the statistician L J Savage. A fairly recent book dealing with this entire problem, the Logic of Decision by R C Jeffrey might be added to the excellent bibliography provided by the author. The chapter on statistical decision and utility provides a simpler study of just what is involved in the making of logical decisions. Here the author comments on the set of acts, outcomes, and states which are involved in making formal decisions and the relation of these to a utility ordering or order of preferences. One issue of this analysis is the interesting construction of a utility scale representing a more sophisticated treatment of utility order by abstracting certain utility properties.