The theory of statistics, like other scientific theories, can be divided into three fairly distinct sections; they are (1) the foundations of the theory, (2) the superstructure, and (3) the principles of application. It is, of course, possible to divide the subject in different ways; for example, the word ‘methodology’ is sometimes used to cover part of (2) and (3). But I find it helpful in thinking about the subject to make the division that I have indicated.It is my purpose to show that actuarial science is essentially a particular application of the theory of statistics, that there is nothing very special about its superstructure and that in its application to practical affairs the universal principles apply. But I first want to make it clear that while I include the combination of compound interest functions with other actuarial functions as part of actuarial science I do not regard finance and investment as part of actuarial science proper. While treating finance and investment as a part of economics I appreciate that they represent an essential ingredient in the equipment of the practising actuary.