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Extensionality and Randomness in Probability Sequences

Published online by Cambridge University Press:  14 March 2022

S. Cannavo
S. Cannavo*
Affiliation:
Brooklyn College
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Abstract

The charge that the limit-frequency theory of probability is inconsistent due to incompatibility between the required features of randomness and limit convergence is inapplicable when probability sequences are taken to be empirically (i.e., extensionally) generated, as they must be on a strictly empirical conception of probability.

All past attempts to meet this charge by formulating constructive definitions of randomness that would still allow for a demonstrable limit-convergence have, in their exclusive concern with logically (i.e., intensionally) prescribed sequences, left the logic of extensional classes essentially untouched. In the light of a strict differentiation between intensional and extensional classes a generalized approach is possible under which several closely connected senses of randomness, i.e., the formal, material, restricted and unrestricted senses may be easily distinguished and related to the notion of relevance.

Type
Research Article
Information
Philosophy of Science , Volume 33 , Issue 2 , June 1966 , pp. 134 - 146
Copyright
Copyright © 1966 by The Philosophy of Science Association

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References

[1] Church, A., “An Unsolvable Problem of Elementary Number Theory,” American Journal of Mathematics LVIII, pp. 345-363. “On the Concept of a Random Sequence,” Bulletin of the American Mathematical Society XLVI, (1940), p. 130.Google Scholar
[2] Copeland, A. H., “Point-Set Theory Applied to the Random Selection of Digits of an Admissible Number,” American Journal of Mathematics LVI (1936), pp. 181–192.10.2307/2371066CrossRefGoogle Scholar
[3] Mises, R. von, Probability Statistics and Truth, trans. J. Neyman, D. Sholl, and E. Rabinowitch, London, 1939, p. 33.Google Scholar
[4] Langhop, E. E. and Mathews, J. C., “Invariance of Probabilities in Finite Sample Spaces Under Stochastic Operations,” The American Mathematical Monthly 71 (1964), pp. 841–849.10.1080/00029890.1964.11992341CrossRefGoogle Scholar
[5] Mises, R. von, Wahrscheinlichkeitsrechnung, Leipzig, 1931, p. 12.Google Scholar
[6] Reichenbach, H., The Theory of Probability, Berkeley, 1949.Google Scholar
[7] Russel, B., Human Knowledge, New York, 1948, p. 367.Google Scholar
[8] Wright, G. H. von, A Treatise on Induction and Probability, New York, 1951. “On Probability,” Mind XLIX (1940), pp. 265-283.Google Scholar