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Confirming Power of Observations Metricized for Decisions among Hypotheses, Part II

Published online by Cambridge University Press:  14 March 2022

Henry A. Finch
Henry A. Finch*
Affiliation:
The Pennsylvania State University
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Extract

At this juncture, we must not minimize grave concerns which remain. As Jeffreys [28, 29] and Carnap [10] have candidly admitted, and as Fisher [20] has strenously insisted in his luminous assessment of the meaning and limitations of Bayes' theorem, there apparently must exist for the possibility of the successive application of Bayes' theorem to a hypothesis on the basis of a sequence of experimental observations, an initial evidence or judgment base, say e′, which is not itself compounded out of new observation and a prior evidence base. For e′, Pr(H) must be estimated for the first time, so to speak. Setting aside any investigation here as to whether an epistemology [52, 53, 54] which looks to Carneades as well as Plato-Aristotle, and to Hegel as well as Locke, must be bound eternally to the notion of unreconstructible “first” terms in the sequences of controlled inquiry, it must in any case be admitted that attainability of the initial estimate Pr(H/e′) is a task of enormous difficulty, as one may for example, notice in Peirce's [44] very bitter struggle with it. To assume that “initial” prior probabilities are impossible of achievement is an a priori dispair which is, as usual, no more warranted than a priori optimism. There do exist interesting proposals for making the required kind of “first” estimates in Carnap, Wald, and Jeffreys; in Jeffreys [28] the entire situation is vividly characterized and the ingenious suggestion offered that even for an infinite number of relevant hypotheses each of them may be assigned positive probabilities “even on no observational information at all” by ordering these positive probabilities in a converging series, whose sum is equal to 1, by judgments of comparative (mathematical) simplicity. Those like myself who have never encountered, even in Einstein [18], an independent or simple criterion of simplicity of laws will not, of course, consider Jeffreys' proposal to be even nearly definitive; yet it serves well to challenge the dogmatic despair concerning the usefulness and relevance of Bayes' theorem.

Type
Research Article
Information
Philosophy of Science , Volume 27 , Issue 4 , October 1960 , pp. 391 - 404
Copyright
Copyright © 1959 by Philosophy of Science Association

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Footnotes

*

Part I of this article appeared in Volume 27, No. 3 (July, 1960) of this journal.

References

Bayes, T., “An Essay towards solving a Problem in the Doctrine of Chances.” Phil. Trans. Royal Soc. LII, 1763.Google Scholar
Birge, R. T. in The Physical Review, 40, No. 1, 260.Google Scholar
Bohm, D. Causality and Chance in Modern Physics. Routledge and Kegan Paul, 1957, Chapter 5.Google Scholar
Boltzmann, L. Populare Schriften, Chapters 3 and 19, Barth, 1905.Google Scholar
Braithwaite, R. B., Scientific Explanation, Cambridge, 1955.Google Scholar
Broda, E., Ludwig Boltzmann. Mensch, Physiker, Philosoph. Deuticke, 1955.Google Scholar
Bronowski, J., concluding essay “Science as Foresight.” in What is Science, edited by J. R. Newman, Simon and Schuster, 1955.Google Scholar
Carnap, R. Logical Foundations of Probability. Chicago, 1950.Google Scholar
Carnap, R. “Remarks on Popper's note on Content and Degree of Confirmation,” British Journal for Philosophy of Science, 7, 27, 1956, p. 243.Google Scholar
Carnap, R. “The Two Concepts of Probability” reprinted in Readings in the Philosophy of Science, Ed. H. Feigl and M. Brodbeck, Appelton Century Crofts, 1953, p. 438 ff.Google Scholar
Churchman, C. W., “Notes on a Pragmatic Theory of Induction.” Scientific Monthly 79, 3, 1955, pp. 149–51.Google Scholar
Churchman, C. W. “Statistics, Pragmatics, and Induction,” Philosophy of Science, 15, 3, July, 1948.CrossRefGoogle Scholar
Churchman, C. W. “Science and Morality” in AAAS Symposium Vol., 1959, on Low-Level Radiation, 1959.Google Scholar
D'Alembert article “Experimentale” conveniently available in J. Lough's The Encyclopedie of Diderot and D'Alembert, Cambridge, 1954, pp. 68 ff.Google Scholar
Deming, W. E. “Facsimiles of Two Papers by Bayes,” U. S. Department of Agriculture, 1940.Google Scholar
Deming, W. E. Statistical Adjustment of Data, Wiley, 1943, especially Chap, 9.Google Scholar
Fragment 11 of Philolaus in Diels Fragmente der Vorsokratiker, Berlin, 1903.Google Scholar
Einstein, A., Zur Methodik der Theoretischen Physik in Mein Weltbild, Ullstein, 1955, pp. 166–7.Google Scholar
Finch, H. A., “An Explication of Counterfactuals by Probability Theory,” Philosophy and Phenomenological Research. 18, 3 March, 1958.CrossRefGoogle Scholar
Fisher, R. A., Statistical Methods and Scientific Inference, Oliver and Boyd, 1956.Google Scholar
Fisher, R. A., “The Logic of Inductive Inference” in Contributions to Mathematical Statistics, Wiley, N. Y., 1950.Google Scholar
Gnedenko, G. W. and Chintschin, A. J., Elementare Einführung in Wahrscheinlichkeitsrechnung, trans. from the Russian, Berlin, 1955, Chapter 4, section 12.Google Scholar
Good, I. J., “Mathematical Tools,” in Uncertainty and Business Decisions, Chapter 3, edited by C. F. Carter, G. P. Meredith and G. L. S. Shackle, Liverpool, 1957.Google Scholar
Goodman, N., Fact, Fiction and Forecast, Harvard, 1955, pp. 68–73.Google Scholar
Hempel, C. G., Fundamentals of Concept Formation in Empirical Science, Chicago, 1952, p. 18.Google Scholar
Herschel, J. W. F., Preliminary Discourse on the Study of Natural Philosophy, Longmans, 1851, p. 153.10.5962/bhl.title.19835CrossRefGoogle Scholar
Hertz, H., The Principles of Mechanics, trans. D. E. Jones and J. T. Walley, Macmillan 1899, pp. 1–41.Google Scholar
Jeffreys, H., “Probability Theory in Astronomy,” Monthly Notices of the Royal Astronomical Society 117, 3, 1957, especially pages 347-349.10.1093/mnras/117.3.347CrossRefGoogle Scholar
Jeffreys, H., Theory of Probability. Oxford, 1948, pp. 38–41.Google Scholar
Jevons, W. S., Studies in Deductive Logic, Macmillan, 1908, Chapter 24.Google Scholar
Kemeny, J. G. and Oppenheim, P., “Degree of Factual Support,” Philosophy of Science, 19, 4, October, 1952.10.1086/287214CrossRefGoogle Scholar
Keyser, C. J., Mathematics as a Culture Clue, Scripta Mathematica, 1947, pp. 24–28.Google Scholar
Kierkegaard, S., Edifying Discourses, vol. IV, first discourse, Minneapolis, 1946, p. 34.Google Scholar
Körner, S., Conceptual Thinking, Cambridge, 1955, Chapters XVII-XVIII.Google Scholar
Kolmogoroff, A., Grundbegriffe der Wahrscheinlichkeitsrechnung, Chelsea, 1946.Google Scholar
Laplace, P. S., Theorie Analytique des Probabilités, Gauthier-Villars, 1886, Livre II, 183-86.Google Scholar
Leblanc, H., “On Chances and Estimated Chances of Being True.” Revue Philosophique de Louvain, Tome 57, May, 1959.CrossRefGoogle Scholar
“Legendre on Least Squares,” in A Source Book in Mathematics, edited D. E. Smith, Dover, 1959, Vol. II, p. 576.Google Scholar
Luce, R. D. and Raiffa, H., Games and Decisions, N. Y., 1957, p. 310.Google Scholar
Munroe, M. E., Theory of Probability, McGraw Hill, 1951, p. 19, Theorem Id and pp. 42–44.Google Scholar
Nernst, O., Theoretische Chemie, Stuttgart, 1909, p. 3.Google Scholar
Newton, Isaac, Mathematical Principles of Natural Philosophy, ed. Cajori, F., University of California Press, 1934, Book II, pp. 398–400.Google Scholar
Neyman, J., First Course in Probability and Statistics, Holt, 1950, Chapter 5.Google Scholar
Noether, E. and editors, T. Cavailles, Briefwechsel Cantor-Dedekind, Hermann, 1937, p. 34.Google Scholar
Peirce, C. S., Values in a Universe of Chance, Selected Writings, edited by P. P. Wiener, Doubleday, 1958, p. 302, pp. 371–3.Google Scholar
Poincairé, H., La Valeur de la Science, Flammarion, 1929, pp. 69–70.Google Scholar
Popper, K., British Journal for Philosophy of Science, 5, 18, 1954 and 7, 28, 1957.Google Scholar
Popper, K., British Journal for Philosophy of Science, 7, 27, 1956, p. 244.Google Scholar
Ramsey, F. P., The Foundation of Mathematics, Kegan Paul, 1931, p. 181.Google Scholar
Rescher, N., “A Theory of Evidence,” Philosophy of Science, 25, 1, January, 1958, p. 87.CrossRefGoogle Scholar
Rosenbloom, P., The Elements of Mathematical Logic, Dover, 1950, p. 198.Google Scholar
Rothstein, J., “A Physicist's Thoughts on the Formal Structure and Psychological Motivation of Theory and Observation, Revue Internationale de Philosophie, 1957, 40.Google Scholar
Singer, E. A., Mind as Behavior, Adams, 1924, pp. 85, 183, 150-53.Google Scholar
Singer, E. A. Jr., Experience and Reflection, edited C. W. Churchman, Philadelphia, 1959.CrossRefGoogle Scholar
Singer, E. A., “Philosophy of Experiment,” Symposium 1, 2, April, 1930, p. 149 ff, pp. 157–8.Google Scholar
Shannon, C. and Weaver, W., The Mathematical Theory of Communication, University of Illinois, 1949, Section 6, Chapter 1.Google Scholar
Touloukian, Y. S., The Concept of Entropy in Communication, Living Organisms and Thermodynamics, Research Bulletin 130, Purdue Engineering Experiment Station, 1956.Google Scholar
Wright, G. H. von, The Logical Problem of Induction, Blackwell, 1957, p. 93.Google Scholar
Wright, G. H. von, Logical Studies, London, 1957.Google Scholar
Wald, A., Sequential Analysis, Wiley, 1947, Chapter 1.Google Scholar