Probability, statistics, and the theory of errors

Dr. Fisher and I seem to agree on the formal correctness of each other’s mathematical development, when once the initial assumptions are given. But in the data and in the interpretation of the conclusions I can find no basis of agreement to use as the starting-point in a reply to his criticisms. It seems to be necessary therefore for me to begin at an earlier stage and explain why a theory of probability is necessary, and what is the scope of such a theory. By “probability” I mean probability and not frequency, as Fisher seems to think, seeing that he introduces the latter word in restating my argument. If in the process I have to repeat a certain amount of matter previously published, but with which Fisher shows no acquaintance, I must ask the reader’s indulgence. It is a commonplace of logic that if two propositionsp andq are so related thatp impliesq , thenq does not necessarily implyp . Yet in scientific work, as in ordinary life, we habitually argue in a way that resembles in form the inference thatq does implyp . We state a theory and develop its consequences to the point where they yield deductions verifiable by observation. If these are found to be true, we say that the theory is “verified”; further, we proceed to draw other inferences from the theory and to expect them to be verified in the future. So far as scientific and philosophical writers have considered this dilemma, or so far as it is possible to infer their beliefs from their methods of presentation, there seem to be three main attitudes.