ABSTRACT
In this Chapter I propose to treat the theory of probability as a branch of pure mathematics, in which we deduce the consequences of certain axioms without seeking to assign this or that interpretation 1 to them. It is to be observed that, while interpretation, in this field, is controversial, the mathematical calculus itself commands the same measure of agreement as any other branch of mathematics. This situation is in no way peculiar. The interpretation of the infinitesimal calculus was for nearly two hundred years a matter as to which mathematicians and philosophers debated; Leibniz held that it involved actual infinitesimals, and it was not till Weierstrass that this view was definitely disproved. To take an even more fundamental example: there has never been any dispute as to elementary arithmetic, and yet the definition of the natural numbers is still a matter of controversy. We need not be surprised, therefore, that there is doubt as to the definition of probability though there is none (or very little) as to the calculus of probability.
