ABSTRACT
My earlier description of von Mises’ theory of probability suggests that he would have adopted something like the following account of special sciences in general. Suppose we wish to set up an exact or mathematical science. Our first task must be to delimit the subject matter of the putative science. Thus in geometry we deal with the spatial relations of bodies, in mechanics with their motion and states of equilibrium, in probability theory with repeated ‘random’ events. Because we are empiricists the next step must be to discover certain laws which are obeyed by the events or bodies with which we are dealing. Thus, for example, having devised methods of measurement we might discover that the angles of a triangle are 180°, similarly we might obtain Galileo's law that freely falling bodies have constant acceleration, and finally for probability theory we have of course the Law of Stability of Statistical Frequencies. We now cast these laws into the form of a few simple mathematical propositions. Two important points must be noted here. First, the mathematical concepts used must be precisely defined in terms of observables (the definitional thesis). Unless we do this the mathematical calculus would be unconnected with the empirical world. The concepts we use may be called by the same names as certain pre-scientific concepts of ordinary language (square, force, probability). In the theory, however, they do not have their everyday sense but a precise sense given by the definition. A second point is that the mathematical propositions do not represent reality exactly but are an abstraction or simplification of it.
