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Mathematical Proof and Experimental Proof

Published online by Cambridge University Press:  14 March 2022

Arthur H. Copeland Sr.*
Affiliation:
The University of Michigan

Abstract

In studies of scientific methodology, surprisingly little attention has been given to tests of hypotheses. Such testing constitutes a methodology common to various scientific disciplines and is an essential factor in the development of science since it determines which theories are retained. The classical theory of tests is a major accomplishment but requires modification in order to produce a theory that accounts for the success of science. The revised theory is an analysis of the nondeductive aspect of scientific reasoning. It results in a new definition of probability and a nonclassical point of view with regard to the foundations of probability.

Type
Research Article
Copyright
Copyright © Philosophy of Science Association 1966

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References

[1] Bernoulli, Jacob, Ars Conjectandi Basileœ (1713).Google Scholar
[2] Braithwaite, R. B., Scientific Explanation, Cambridge (1955).Google Scholar
[3] Brunk, H. D., An Introduction to Mathematical Statistics, Boston (1960).CrossRefGoogle Scholar
[4] Burks, Arthur W., “A Pragmatic-Human Theory of Probability,” in The Philosophy of C. I. Lewis, edited by P. A. Schilpp (forthcoming).Google Scholar
[5] Carnap, Rudolf, Logical Foundations of Probability, Chicago (1950).Google Scholar
[6] Carnap, Rudolf, “The Two Concepts of Probability,” Readings in the Philosophy of Science, edited by H. Feigl and M. Brodbeck, New York (1953), 438455.Google Scholar
[7] Church, Alonzo, “On the Concept of Random Sequence,” Bulletin American Soc. Vol. 46, No. 2, 130135.CrossRefGoogle Scholar
[8] Copeland, A. H. Sr., “Statistical Induction and the Foundations of Probability I and II,” Theoria, Vol. XXVII (1962).Google Scholar
[9] Cramer, H., Elements of the Theory of Probability, New York, (1956).Google Scholar
[10] DeFinetti, Bruno, “Sul Significato Della Probibilita,” Fund. Math. Vol. 17, 299329.Google Scholar
[11] DeFinetti, Bruno, “La Logique de la Probabilité,” Actes Congress Inst. de Phil. Soc., Paris (1932, 1936).Google Scholar
[12] DeFinetti, Bruno, “La Prevision, ses Lois Logique, ses Sources Subjective,” Ann. Inst. H. Poincare (1936) 168.Google Scholar
[13] Frank, Philipp, Philosophy of Science, Englewood Cliffs, New Jersey (1957).Google Scholar
[14] Hume, David, An Inquiry Concerning Human Understanding, Chicago (1949). Originally published under the title Philosophical essays.Google Scholar
[15] Keynes, John Maynard, A Treatise on Probability, London, New York (1929).Google Scholar
[16] Kolmogoroff, A., “Grundbegriffe der Wahrscheinlichkeitsrechnung,” Erg. Math. 2, No. 3 (1933).CrossRefGoogle Scholar
[17] Nagel, Ernest, Principles of the Theory of Probability, International Encyclopedia of Unified Science, Vol. 1, part 2, 341422.Google Scholar
[18] Neyman, Jerzy and Pearson, E. S., “On the Problem of Most Efficient Tests of Statistical Hypotheses,” Phil. Trans. Royal Soc. Series A231 (1933) 289337.Google Scholar
[19] Popper, Karl R., The Logic of Scientific Discovery, New York (1959).CrossRefGoogle Scholar
[20] Popper, Karl R., “The Propensity Interpretation of Probability,” British Jour. of the Phil. of Sci. Vol. X, No. 37, 2542.Google Scholar
[21] Reichenbach, Hans, Wahrscheinlichkeitslehre, eine Untersuchung über die Logischen und Mathematischen Grundlagen der Wahrscheinlichkeitsrechnung, Leiden (1935).Google Scholar
[22] Reichenbach, Hans, “The Logical Foundations of the Concept of Probability,” Readings in the Philosophy of Science, edited by H. Feigl and M. Brodbeck, New York (1953).Google Scholar
[23] Savage, L. J., Foundations of Statistics, New York (1933).Google Scholar
[24] Venn, John, The Logic of Chance, London, New York (1866).Google Scholar
[25] Vietoris, L., “Häufigkeit und Wahrscheinlichkeit,” Studium Gen. 0, 8596.Google Scholar
[26] v. Mises, Richard, “Grundlagen der Wahrscheinlichkeitsrechnung,” Math. Zeitschr. Band 5, 5299.CrossRefGoogle Scholar
[27] v. Mises, Richard, Probability, Statistics and Truth, New York (1939).Google Scholar
[28] Wald, Abraham, Sequential Analysis, New York, London (1947).Google Scholar