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A Critical Survey of Recent Contributions
Published online by Cambridge University Press: 14 March 2022
It is the purpose of this paper to review the present status of discussion concerning the concept of probability. The exposition will consist of six sections: (1) A brief statement of the most important traditional views of the concept of probability: subjective and objective; (a) A brief criticism of two traditionally important conceptions: a priori probability and the Principle of Indifference; (3) A criticism of an outstanding example of the subjective theory of probability, the theory of F. P. Ramsey; (4) A criticism of the most widely known of the objective logical theories of probability, the theory of J. M. Keynes; (5) Some remarks concerning the results of the recent work of Reichenbach and von Mises with particular reference to clarification of the concept of probability; (6) A summary of the case for the frequency interpretation of probability, revealing its basic importance in the light of present evidence.
1 Carnap, R., “Testability and Meaning,” Philosophy of Science, October, 1936.
2 Page 159, Ramsey, Frank Plumpton, The Foundations of Mathematics and Other Logical Essays, New York, 1931.
3 Page 169, Ibid.
4 Page 171, Ibid., Italics in the original.
5 Page 177, Ibid.
6 Keynes, John Maynard, A Treatise on Probability, London, 1921.
7 Reichenbach, Hans, Wahrscheinlichkeilslehre, Leiden, 1935; Mises, Richard von, Wahrscheinlichkeit, Statistik und Wahrheit, Wien, 1928; Wahrscheinlichkeitsrechnung und ihre Anwendung in der Statistik und theoretischen Physik, Leipzig und Wien, 1931.
8 Cf. Nisbet, R. H., “The Foundations of Probability,” Mind, 1926.
9 This geometric interpretation is in terms of measure as found in mengenlehre. This definition has been developed by Waismann and Wittgenstein. Given a defined class A, the measure mA of this class is a surface segment. Given another class B, having at least one element in common with A, then the probability of the occurrence of an event of B is the ratio of the measure of the conjunction of A and B to the measure of A.
10 Mises, Richard von and Pollaczek-Geiringer, H., Encyclopaedia of the Social Sciences. New York, 1934, Vol. 12, “Probability.”
11 Page 206. op. cit.
12 Lindsay, R. B. and Margenau, Henry, The Foundations of Physics. New York, 1936. cf. also Nagel, Ernest, “A Frequency Theory of Probability,” Journal of Philosophy, 1933; “The Meaning of Probability,” Journal of the American Statistical Association, 1936.
13 Cf. Nagel, op. cit.; also Reichenbach, op. cit.
14 Peirce, Charles Sanders, Pragmatism and Pragmaticism. (Vol. 5 of “Collected Papers,” ed. by Hartshorne and Weiss), Cambridge, 1934.
15 Feigl, H., “The Logical Character of Induction,” Philosophy of Science, 1934.
16 Nisbet, op. cit.
17 Page 103, Keynes, op. cit.
