Among the manifold problems that are connected with the concept of probability, we have to differentiate between those that are within the individual sciences and those that are a part of epistemology in general. For example, the problem of contemporary physics "causal or statistical lawfulness of elementary processes' doubtless is very important and topical but the epistemologist, for the purpose of a deeper clarification, first has to examine what is really meant by the concept of the law of probability. To date, only a very few thinkers have noticed that there is a serious difficulty here at all (see P. Ehrenfest,Mathem. Enzykl. IV, §30; M. Schlick, Allgemeine Erkenntnislehre [1925], p. 359f; and H. Reichenbach in his recent lecture in Prague). As a clear solution for this problem has not yet been presented and as I am convinced on grounds of principle that logic cannot be replaced or supplemented by a logic of probability (and indeed there is no need for such), I take the liberty to discuss this problem in some more detail and to suggest a way to its solution which, to my mind, seems to be the only one feasible.