Towards the Logic of Probability

Abstract

The theory of probability has a curious dual position: on the one hand, the validity of probability judgments forms a part of the subject matter of logic; on the other hand, its applications, for example, to games of chance, to mass phenomena and in particular in modern physics, often produce such complex combinations of the basic operations that a large part of the theory of probability consists in solutions to the resultant counting problems. The present introductory text cannot hope to deal with the mathematical techniques involved, techniques which in some cases yield merely approximate descriptions of the underlying conditions by means of an ‘escape into infinity’. We shall, on the contrary, restrict ourselves to problems concerning the modes of validity of propositions, although occasionally we shall refer to results by way of example but ithout giving demonstrations. For the requisite mathematics the reader is referred to Jeffreys [1].