ABSTRACT
There are two traditions in the philosophy of probability. We shall call them the scientific and the logical, using these words in a sense which will be defined more precisely later. Of the two the logical is the older. It was first adumbrated by Leibniz at a time when only the most rudimentary beginnings had been made with the mathematical theory. The scientific approach is of much more recent origin. It was first developed in the middle of the nineteenth century by the Cambridge school of Ellis and Venn and can be considered as a ‘British empiricist’ reaction against the ‘Continental rationalism’ of Laplace and his followers. It is not my purpose, however, to trace the early history of the subject in detail. I shall begin rather with the years 1919 and 1921 which saw the publication of an important work in each of the two traditions: in the scientific tradition von Mises’ Grundlagen der Wahrscheinlichkeitsrechnung (1919) and in the logical Keynes’ Treatise on Probability (1921). Needless to say, both these authors drew heavily on the work of their predecessors; but they both worked out their respective approaches in greater detail than had previously been attempted, and, in particular, both tried to develop the formal calculus of probabilities from their respective philosophical standpoints. I will begin by summarizing their ideas; a procedure which will throw into sharp relief the problems to be dealt with in what follows.
