Probability and scientific method

I argued in my previous paper that the opinions (1) that all inference beyond the immediate data of experience is meaningless, and (2) that the whole of scientific knowledge can be established independently of experience, are both logically tenable, at a price, but that neither corresponds with ordinary scientific or common-sense belief. It was obvious that Fisher would be the first to agree with me in rejecting the second alternative; his attitude to the first was less clear. I also maintained that we need a theory of scientific inference that will agree with ordinary beliefs about its validity, and that any such theory would involve as ana priori element the notion of probability and some of the fundamental rules for its assessment. By their very nature these rules cannot be established by experience: they must be judged by their plausibility, the internal consistency of the theory based on them, and the agreement or otherwise of the results with general belief. Fisher objects to the introduction of ana priori element, and I should agree with him to the extent thata priori hypotheses should be reduced to a minimum, but that minimum must be sufficient to give a general theory. I was originally somewhat attracted by the wish to define probability in terms of frequency, but found that the existing theory of Venn failed in its objects. It avoided noa priori hypothesis, several having been used but not stated, and its results, when interpreted in terms of the definition, were not in a practically applicable form. As the arguments have already been published twice, I do not repeat them. Fisher departs from Venn by defining a probability as the ratio of two infinite numbers; but then no probability would have a definite value. Later in this paper, however, he obtains definite values for probabilities, and it is not clear how he gets them. (At this stage he generally uses the word “frequency” in place of “probability,” but I think he is treating them as synonymous.) There is a gap in his argument at this point; but the results, relating to the probability of a set of observations given the hypothesis, agree in all cases with those of thea priori theory, on the supposition, presumably valid, that the probability of any particular observation is determined by the constants of the assumed law of distribution alone, and is not disturbed by the previous observations.