IN this chapter I shall only deal with the probability of events and the problems it raises. They arise in connection with the theory of games of chance, and with the probabilistic laws of physics. I shall leave the problems of what may be called the probability of hypotheses--such questions as whether a frequently tested hypothesis is more probable than one which has been little tested--to be discussed in sections 79 to 85 under the title of "'Corroboration'".
Ideas involving the theory of probability play a decisive part in modern physics. Yet we still lack a satisfactory, consistent definition of probability; or, what amounts to much the same, we still lack a satisfactory axiomatic system for the calculus of probability. The relations between probability and experience are also still in need of clarification. In investigating this problem we shall discover what will at first seem an almost insuperable objection to my methodological views. For although probability statements play such a vitally important rôle in empirical science, they turn out to be in principle impervious to strict falsification. Yet this very stumbling block will become a touchstone upon which to test my theory, in order to find out what it is worth.
Thus we are confronted with two tasks. The first is to provide new foundations for the calculus of probability. This I shall try to do by developing the theory of probability as a frequency theory, along the lines followed by Richard von Mises, but without the use of what he calls the 'axiom of convergence' (or 'limit axiom'), and with a somewhat weakened 'axiom of randomness'. The second task is to elucidate the relations between probability and experience. This means solving what I call the problem of decidability of probability statements.
My hope is that these investigations will help to relieve the present