Isaac Levi

(1930 - 2018)

This comprehensive discussion of the problem of rational belief develops the subject on the pattern of Bayesian decision theory. The analogy with decision theory introduces philosophical issues not usually encountered in logical studies and suggests some promising new approaches to old problems."We owe Professor Levi a debt of gratitude for producing a book of such excellence. His own approach to inductive inference is not only original and profound, it also clarifies and transforms the work of his predecessors. In short, the book deserves to become a classic....There is a great deal of interest in the book besides these basic matters [forumlating rules of acceptance]. Some of the most interesting chapters are those that examine the implications of such rules. The discussions of probability, generalization, and various forms of inference are brilliant and enlightening. Indeed, the problems and methods elaborated by Professor Levi in his book serve as a new foundation for the study of inductive inference."--Keith Lehrer, Nous"Levi's book is an extremely interesting report on 'tentative and speculative first steps' toward a decision-theoretic approach to inductive inference....Professor Levi is to be congratulated on his ingenious development and application of this approach...."--Richard C. Jeffrey, The Journal of Philosophy

An argument is advanced to show why E-admissibility should be preferred over maximality as a principle of rational choice where rationality is understood as minimal rationality. Consideration is given to the distinction between second best and second worst options in three way choice that is ignored according to maximality. It is shown why the behavior exhibited in addressing the problems posed by Allais (Econometrica 21:503–546, 1952) and by Ellsberg (Q Econ 75:643–669, 1961) do not violate the independence postulate according to minimal rationality