The Principles of Probability: From Formal Logic to Measure Theory to the Principle of Indifference

This book presents a logical system that is able to capture all aspects of modern probability as it is practiced today. The system is then used to rigorously formulate the principle of indifference.

Using nine rules of inductive inference, a calculus of probability is developed that operates directly on sentences – without reference to outcomes or sample spaces. Its surprising strength is expressed by three embedding theorems, based on an underlying many-worlds semantics in which random vari...