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An Orthodox Statistical Resolution of the Paradox of Confirmation

Published online by Cambridge University Press:  14 March 2022

Ronald N. Giere
Ronald N. Giere*
Affiliation:
Indiana University
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Abstract

Several authors, e.g. Patrick Suppes and I. J. Good, have recently argued that the paradox of confirmation can be resolved within the developing subjective Bayesian account of inductive reasoning. The aim of this paper is to show that the paradox can also be resolved by the rival orthodox account of hypothesis testing currently employed by most statisticians and scientists. The key to the orthodox statistical resolution is the rejection of a generalized version of Hempel's instantiation condition, namely, the condition that a PQ is inductively relevant to the hypothesis (x)(Px ⊃ Qx) even in the absence of all further information. Though their reasons differ, it turns out that Bayesian and orthodox statisticians agree that this condition lies at the heart of the paradox.

Type
Research Article
Information
Philosophy of Science , Volume 37 , Issue 3 , September 1970 , pp. 354 - 362
Copyright
Copyright © 1970 by The Philosophy of Science Association

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Footnotes

†

The author's work on the foundations of statistics has been supported in part by the National Science Foundation under grant GS 2525.

References

REFERENCES

[1] Black, Max., “Notes on the ‘Paradoxes of Confirmation’,” in Aspects of Inductive Logic (eds., J. Hintikka and P. Suppes), North Holland, Amsterdam, 1966.10.1016/S0049-237X(08)71669-0CrossRefGoogle Scholar
[2] Carnap, R., Logical Foundations of Probability, University of Chicago Press, Chicago, 1950; 2nd edit., 1962.Google Scholar
[3] Good, I. J., “The White Shoe is a Red Herring,” Brit. J. Phil. Sci., vol. 17, 1966-67, p. 322.10.1093/bjps/17.4.322CrossRefGoogle Scholar
[4] Goodman, N., Fact, Fiction and Forecast, Harvard Univ. Press, Cambridge, Mass., 1955.Google Scholar
[5] Hays, W. L., Statistics for Psychologists, Holt, Rinehart and Winston, New York, 1963.Google Scholar
[6] Hempel, C. G., “Le Problème de la Vérité,” Theoria (Goteborg), vol. 3, 1937.Google Scholar
[7] Hempel, C. G., “A Purely Syntactical Definition of Confirmation,” J. Syn. Log., vol. 8, 1943.Google Scholar
[8] Hempel, C. G., “Studies in the Logic of Confirmation,” Mind, vol. 54, 1945, pp. 1–26, 97-121.10.1093/mind/LIV.213.1CrossRefGoogle Scholar
[9] Hempel, C. G., Aspects of Scientific Explanation, Free Press, New York, 1965.Google Scholar
[10] Hempel, C. G., “The White Shoe: No Red Herring,” Brit. J. Phil. Sci., vol. 18, 1967-68, pp. 239–240.10.1093/bjps/18.3.239CrossRefGoogle Scholar
[11] Hodges, J. L. and Lehman, E. L., Basic Concepts of Probability and Statistics, Holden and Day, San Francisco, 1964.Google Scholar
[12] Jeffrey, R. C., The Logic of Decision, McGraw-Hill, New York, 1965.Google Scholar
[13] Kendall, M. G. and Stuart, A., The Advanced Theory of Statistics, vols. 1 and 2, Charles Griffin & Co., London, 1958, 1961.Google Scholar
[14] Keynes, John Maynard, A Treatise on Probability, London: Macmillan, 1921.Google Scholar
[15] Kyburg, H. E. Jr., “Recent Work in Inductive Logic,” Amer. Phil. Quart., 1 (1964), pp. 249–287.Google Scholar
[16] Kyburg, H. E. Jr. and Smokier, H. E. (eds.), Studies in Subjective Probability, Wiley, New York, 1964.Google Scholar
[17] Lehman, E. L., Testing Statistical Hypotheses, Wiley, New York, 1959.Google Scholar
[18] Morgenbesser, S., “Goodman on the Ravens,” J. Phil., vol. 59, 1962, pp. 493–495.10.2307/2023221CrossRefGoogle Scholar
[19] Neyman, J., A Selection of Early Statistical Papers of J. Neyman, Univ. of California Press, Berkeley, 1967.10.1525/9780520327016CrossRefGoogle Scholar
[20] Neyman, J. and Pearson, E. S., Joint Statistical Papers, Univ. of California Press, Berkeley, 1967.10.1525/9780520339897CrossRefGoogle Scholar
[21] Popper, K. R., The Logic of Scientific Discovery, Hutchinson, London, 1959.Google Scholar
[22] Scheffler, I., The Anatomy of Inquiry, Knopf, New York, 1963.Google Scholar
[23] Schlaifer, H., Introduction to Statistics for Business Decisions, McGraw-Hill, New York, 1961.Google Scholar
[24] Suppes, P., “A Bayesian Approach to the Paradoxes of Confirmation,” Aspects of Inductive Logic (eds. J. Hintikka and P. Suppes), North-Holland, Amsterdam, 1966.10.1016/S0049-237X(08)71670-7CrossRefGoogle Scholar
[25] Watkins, J., “Confirmation, the Paradoxes and Positivism,” The Critical Approach to Science and Philosophy (ed. Bunge, Mario), Free Press, New York, 1964.Google Scholar