Abstract

This paper is a sequel to the joint publication of Scott and Krauss in which the first aspects of a mathematical theory are developed which might be called "First Order Probability Logic". No attempt will be made to present this additional material in a self-contained form. We will use the same notation and terminology as introduced and explained in Scott and Krauss, and we will frequently refer to the theorems stated and proved in the preceding paper. The main objective of this study is to show that the probability of symmetric probability systems may be represented as a "weighted average" of what might be called "product probabilities". We then discuss some applications of our results to Carnap's "Principle of instantial relevance", which plays an important role in his system of inductive logic.