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Probability, Many-Valued Logics, and Physics

Published online by Cambridge University Press:  14 March 2022

Henry Margenau
Henry Margenau*
Affiliation:
Yale University, New Haven, Conn.
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Extract

The present paper is concerned chiefly with the problem of scientific prediction. It aims at a factual analysis of the processes leading to prediction, and ventures an appraisal, in the light of this analysis, of some modern and unconventional theories of probability and truth. But although prediction is here chosen as the central issue of discussion, I do not wish to imply that, in its usual sense, it is the only or even the dominant issue of scientific research.

Type
Research Article
Information
Philosophy of Science , Volume 6 , Issue 1 , January 1939 , pp. 65 - 87
Copyright
Copyright © The Philosophy of Science Association

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References

Notes

1 The reader is asked to pardon the vagueness of the terms. The matter is discussed more adequately and fully in my papers on Methodology, Phil, of Science, 2, 49; 2, 164, 1935.

2 I am fully aware that the distinction just made meets with widespread disapproval among logical positivists and physicists. To clarify my position I may perhaps be permitted to say that I admire the successes achieved by the syntactic analysis of the Vienna circle in clarifying the calculus of propositions. But I am forced to regard their fundamental proposals as an interesting “Philosophie des Als-Ob” which proceeds on the tentative rule that we ignore all “pseudo problems.” This very statement implies that there must be a deeper sense in which the problems, arbitrarily ignored, still persist. Positivistic ignoration is a useful artifice indeed for it promises to solve the remaining problems with greater ease. However, methodology of science, unlike some parts of science itself, automatically breaks across positivistic landmarks, as the present distinction shows. In deference to the merits of positivistic procedures I should like to call propositions whose meaning is not clear in the formal idiom (Cf. Carnap) forbidden propositions, distinguishing them from “meaningless” ones which may be defined in other ways.

3 C. H. Prescott, Jr. Phil, of Science, 5, 237, 1938.

4 Cf, for instance, R. v. Mises, Wahrscheinlichkeitsrechnung.

5 A. Kolmogeroff, Grundbegriffe der Wahrscheinlichkeitsrechnung.

H. Cramér, Random Variables and Probability Distributions.

6 C. E. Bures, Phil, of Science, 5, 1, 1938.

7 This and many similar examples may be found in C.V.L. Charlier, Vórlesungen über die Grundzüge der mathematischen Statistik.

8 This phrase is being used to avoid fixing the exact meaning of experimental error, which may be taken to be the mean deviation from the mean, the standard deviation for measurements under “identical” conditions, or any other index used by scientists for such purposes. The following relation is illuminating in this connection: If we define

then formula (i) may be seen to be identical with

9 H. Reichenbach, Leiden, 1935.

10 H. Reichenbach, Phil. of Science, 5, 21, 1938.

11 E. Nagel, Mind, 45, 501, 1936.

12 H. Reichenbach, Erkenntnis, 1935, p. 267.

13 E. Nagel, Mind 45, 501, 1936.

14 H. Margcnau, Phil, of Science, 1, 133, (1934); 4, 337, (1937).