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log[P(h/eb)/P(h/b)] Is the One True Measure of Confirmation

Published online by Cambridge University Press:  01 April 2022

Peter Milne
Peter Milne*
Affiliation:
Department of Philosophy University of Edinburgh
*
†Send reprint requests to the author, Department of Philosophy, University of Edinburgh, David Hume Tower, George Square, Edinburgh, EH8 9JX, Scotland, or email: [email protected].
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Extract

Plausibly, when we adopt a probabilistic standpoint any measure Cb(h, e) of the degree to which evidence e confirms (or is evidentially relevant to) hypothesis (or theory) h relative to background knowledge b should meet these five desiderata:

(1) Cb(h,e) > 0 when P(h/eb) > P(h/b; Cb(h,e) < 0 when P(h/eb) < P(h/b); Cb(h,e) = 0 when P(h/eb) = P(h/b).

(2) Cb(h,e) is some function of the values P(·/b) and P(·/·b) assume on the at most sixteen truth-functional combinations of e and h.

(3) If P(e/hb) < P(f/hb) and P(e/b) = P(f/b) then Cb(h,e) ≤ Cb(h,f); if P(e/hb) = P(f/hb) and P(e/b) < P(f/b) then Cb(h,e) ≥ Cb(h,f).

(4) Cb(h,ef) – Cb(h,eg) is fully determined by Cb(h,e) and Cbe(h,f) – Cbe(h,g); if Cb(h,ef) = 0 then Cb(h,e) + Cbe(h,f) = 0.

(5) If P(e/hb) = P(e/tb) then Cb(h,e) = Cb(t,e).

Type
Research Article
Information
Philosophy of Science , Volume 63 , Issue 1 , March 1996 , pp. 21 - 26
Copyright
Copyright © 1996 by the Philosophy of Science Association

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References

Aczél, J. (1966), Lectures on Functional Equations and their Applications. New York and London: Academic Press.Google Scholar
Brown, H. (1994), “Reason, Judgment and Bayes's Law”, Philosophy of Science 61: 351–369.CrossRefGoogle Scholar
Dennett, D. (ed.) (1987), The Philosophical Lexicon (eighth edition), New York: American Philosophical Association.Google Scholar
Edwards, A. W. F. (1972), Likelihood. Cambridge: Cambridge University Press.Google Scholar
Good, I. J. (1950), Probability and the Weighing of Evidence. London: Griffin.Google Scholar
Hacking, I. (1965), Logic of Statistical Inference. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Howson, C. and Urbach, P. (1993), Scientific Reasoning: The Bayesian Approach (second edition). La Salle: Open Court.Google Scholar
Milne, P. (1995), “A Bayesian Defence of Popperian Science?”, Analysis 55: 213–215.CrossRefGoogle Scholar
Salmon, W. (1975) “Confirmation and Relevance”, in Maxwell, G. and M. Anderson, R. Jr., (eds.), Minnesota Studies in the Philosophy of Science, Vol. VI, Induction, Probability, and Confirmation. Minneapolis: University of Minnesota Press, pp. 3–36.Google Scholar
Sober, E. (1993), “Epistemology for Empiricists”, in French, P. A., Uehling, T. E. Jr., and Wettstein, H. K. (eds.), Midwest Studies in Philosophy, Vol. XVIII, Philosophy of Science. Notre Dame: University of Notre Dame Press, pp. 34–61.Google Scholar