E. T. Jaynes' resolution of Bertrand's paradox in terms of invariance principles is criticized. An experimental setup is considered which generates general solutions to Bertrand's problem by rotating a line around a point a distancer+d from a circle of radiusr. The general solution obtained is neither translationally nor scale invariant, but depends on the value ofr/d. Only in the limitr/d » 0, when the line is just translating across the circle, is the distribution translationally invariant and scale invariant. In this (...) limiting case the distribution found is just that obtained by Jaynes. (shrink)

On the three most widely discussed contemporary justifications of induction, the inductive justification, the pragmatic justification, and the analytic justification (or dissolution of the problem), none has received widespread acceptance. There are specific problems with each of these approaches and a general problem that affects all three. The purpose of this paper is to provide a fourth justification of induction which is less problematic than or at least problematic in different ways from-the three traditional justifications.

The book attempts to develop an account of simplicity in terms of testability, and to use this account to provide an adequate characterization of induction, one immune to the class of problems suggested by Nelson Goodman. It is then shown that the past success of induction, thus characterized, constitutes evidence for its future success. A qualitative measure of confirmation is developed, and this measure - along with the considerations of simplicity - is used to provide an account of the consilience (...) of inductions, and also an inductivist account of the structure and progress of scientific theory. An appendix extends the treatment of simplicity to statistical distributions and provides a reasonable interpretation of the maximum entropy principle. Thus, this book is an attempt to characterize induction in terms of a well-defined notion of simplicity and to use that characterization as a basis of an account of empirical, and in particular, scientific reasoning. (shrink)