ABSTRACT
In deriving the empirical laws of probability from the axioms of the theory, we had to make use of what I called a ‘methodological rule for neglecting small probabilities under certain circumstances’. Apart from an analogy with Newtonian mechanics, I have so far offered no justification for such a rule, and it is time now to look intothe matter more closely. The problem is perhaps best approached by way of a difficulty in Popper's account of scientific method, which was clearly explained by Popper himself as follows (1934, p. 146):
The relations between probability and experience are also 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 role 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 try my theory, in order to find out what it is worth.
