Interpretations of Probability

Abstract

The interpretation of probability offered in the preceding chapters is unorthodox in a number of respects. It is a logical interpretation, but it does not satisfy the axioms of the conventional probability calculus (if only because that calculus deals with real numbers, rather than with intervals of them). It involves limiting frequencies, yet probability statements are taken to be logically true, and thus to be devoid of empirical content. Probability is taken to be legislative for rational belief, and thus as a guide in life, but the usual constraints embodied in the requirements of coherence are not satisfied. Since one can hardly claim that those who have spent all or a large part of their lives contemplating the complexities of the use and meaning of probability have been totally blind, it behooves anyone who wants to claim that they are all wrong to show either how they have been plausibly led astray, or how the interpretations they have offered may be construed as special cases of a more general and pervasive interpretation.