Frequencies, Probabilities, and Positivism Gustav Bergmann Philosophy and Phenomenological Research, Vol. 6, No. 1. (Sep., 1945), pp. 26-44. Stable URL: http://links.jstor.org/sici?sici=0031-8205%28194509%296%3A1%3C26%3AFPAP%3E2.0.CO%3B2-2 Philosophy and Phenomenological Research is currently published by International Phenomenological Society.
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FREQUENCIES, PROBABILITIES, AND POSITIVISM
The area of agreement betrveen Professor Williams and myself is so limited that I do not quite know how to go about the task of discussing his essay. There seems to be little point in restating the well-known arguments in favor of the frequency theory, the less so since only a few years ago I presented these arguments and analyzed some of them, without any particular claim to originality, in a paper to ~vhichProfessor Williams refers. Yet I sympathize with his irritation a t some of the philosophical claimsin the narrower meaning of 'philosophical'in the form in which they are sometimes made by frequency theorists whose main competence lies in the field of mathematics and within the philosophy of science, that is, within an analysis of the concepts and methods of science, as used by science, from a basis of common-sense realism or, as some prefer to put it, in terms of a physicalistic thing language. This notion of the philosophy of science, if taken seriously, has two consequences. First, its analyses are epistemologically or, if you please, metaphysically quite unproblematic and noncontroversial. Conversely, they do not prejudge one's philosophical views. An illustration should show what I mean. Einstein's analysis of nonlocal simultaneity, which is one of the outstanding achievements of the philosophy of science, has not, as is sometimes claimed, "proved" any form of philosophical empiricism, subjectivism, or positivism; it has, in particular, not disproved ontological realism. I n order to square himself with Einstein's analysis a prerelativistic realist would merely have to say this: "hZy former belief that there is, in the external world, a two-term relation espressed by 'x is nonlocally simultaneous with y' is mistaken. I know now that there is, in the external world, a three-term relation expressed by 'x is nonlocally simultaneous with y in (system) Z.' " What light is thrown on the knowledge claims of our realist by so fundamental an error is a different matter-but again a matter to be decided inside the ring, to borrow an apt phrase from Titchener, by philosophical analysts, not by scientists or mathematicians. Second, a philosophical position that cannot or will not "square itself" with the results of the philosophy of science does not meet one of the requirements any philosophical position must meet if it is to deserve serious consideration. In terms of the illustration I have used before, some-let us hope, fictitious-realist might insist that there is, out there, a two-term-relation of nonlocal simultaneity with which Einstein was not even concerned, since his is merely a mathematical theory, introduced for the sake of mensurational convenience and calculational simplicity. Such n critic would not understand the theory of relativity nor would he, according to my bias, understand the nature and function of philosophical analysis.
Philosophy of science, then, is not the whole of philosophy. On this I would insist as emphatically as would, I believe, Professor Williams. It will, I hope, facilitate communication if I state at the outset this fundamental item of agreement. But then again, it may very well be that the analysis of some of our confused preanalytic notions presents, in fact, a problem in the philosophy of science. In such cases any attempt "to return the subject to the proper philosophical arena" (p. 449)' is doomed to failure, simply because it suffers from what I should like to call mixing of levels of analysis. Probability is, in my opinion, one of these cases. With respect to it the task of philosophy proper consists, therefore, mainly in certifying that and showing cause why this is so, or, as one could also put it, in squaring itself with the more specialized and less presuppositionless analysis in question. But at this point Professor Williams would disagree and, probably, insist that I am swayed by my positivistic bias. So let me stop to inquire about his philosophical presuppositions. Professor Williams is an ontological realist of the materialistic variety. Also, he advocates an epistemology which permits him to maintain that "philosophical theories" are something like scientific theories about "the universe as a whole" (p. 473). Any doubt the article under discussion may leave on this point is quickly eliminated by even a casual reading of another ~ it is fair to say, indeed Professor Williams recent essay of its a u t h ~ r . Now almost says so himself, that he attacks the frequency theory because he wishes to undermine the philosophical subjectivism, experientialism, operationism, positivism, or phenomenalism (take whichever expression you prefer!) which he believes to be the philosophical presupposition of the frequency theory. Here we are on the track of what is, to my mind, the basic fallacy of his approach to probability. Let me draw together the several threads and state my argument categorically. Whatever it may mean to speak of presuppositionless analysis-this is, indeed, a line of thought that is easily overworked and leads, if so overworked, to confusion -the philosophy of science is less presuppositionless than philosophy proper. Probability theory lies in the realm of the philosophy of science; the frequency theorist is, therefore, a philosopher of science, not an epistemologist or metaphysician. In particular, the philosophy of science starts from, or presupposes, common-sense realism, a t least with respect to such objects as stones, chairs, dice, and laboratory equipment. (The common-sense assumptions concerning the existence of other minds do not concern us in connection with the topic a t hand.) To the Page references are t o Professor Williams' article in this Journal, Vol. V (1945), pp. 449484. Detailed references to publications listed in Professor Williams' bibliography have been onlitted. Philosophical Review, Vol. LIII, (1944),pp. 417-443.
philosopher of science and, therefore, to the frequency theorist, stones, chairs, and dice "do exist and are knowable" (p. 481); to him "marbles nestling metaphysically in their bag" (p. 457) are just as admissible, accessible, or, if you please, just as real as observations, operations, or manipulations, past, present, or future. To believe, as Professor Williams does, that there is anything metaphysical about such nestling and that, therefore, the frequentist shuns certain "reference classes" as incompatible with his own nonrealistic metaphysics, all but hopelessly confuses the issue. And the confusion is of the kind that arises from what I have called mixing I shall not levels of analysis. Since this is not a paper on operationi~rn,~ say more about the antioperationist slant which pervades and, to my mind, unnecessarily con~plicatesProfessor Williams' whole argument. Also, I feel that it is fair to proceed in this manner since I shall presently examine some of his criticisms of the frequency theory within a realistic frame of reference. Having thus gravted for the task a t hand, though for reasons of my own, what he is so anxious to have us grant, namely, that there is a knowable world and that we do know, under appropriate circumstances, some characters of some parts of it, Ishall feel free to ask how we know some of the things about which tve all agree that we do know them. Or is it, within the philosophy or methodology of science, an irrelevant question to ask ho~vthe physcist knows, if he does know it, that there are mountains on the other side of the moon; how the historian has ascertained that Brutns murdered Caesar? If not, then it is not an irrelevant question either to ask how "the Laplacean can justly hope to derive from his probability," that is, if I understand correctly, from his knowledge that one quarter of the marbles in the bag are red, "the probability, relative to that evidence, that about 25 per cent of the drawings mill be red" (p. 474). But I see that this is already one of the questions I intend to examine in the next section. The critical remarks ~vhichI have assembled in the following sections (11-T') are not meant to be exhaustive, but they touch, in an order that naturally suggests itself, what I believe to be the main points of Professor Elsewhere I have attempted a conservative formulation of the operationist thesis t h a t squares itself with, but is not predicated upon, a positivistic metaphysics. See American Journal of Physics, 11, 1943,248-258,335-342; Psychological Review (jointly with I
