1. In Part I we have been occupied with the epistemology of our subject, that is to say, with what we know about the characteristics and the justification of probable knowledge. In Part II I pass to its formal logic. I am not certain of how much positive value this Part will prove to the reader. My object in it is to show that, starting from the philosophical ideas of Part I, we can deduce by rigorous methods out of simple and precise definitions the usually accepted results, such as the theorems of the addition and multiplication of probabilities and of inverse probability. The reader will readily perceive that this Part would never have been written except under the influence of Mr Russell's Principia Mathematica. But I am sensible that it may suffer from the overelaboration and artificiality of this method without the justification which its grandeur of scale affords to that great work. In common, however, with other examples of formal method, this attempt has had the negative advantage of compelling the author to make his ideas precise and of discovering fallacies and mistakes. It is a part of the spade-work which a conscientious author has to undertake; though the process of doing it may be of greater value to him than the results can be to the reader, who is concerned to know, as a safeguard of the reliability of the rest of the construction, that the thing can be done, rather than to examine the architectural plans in detail.