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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.

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