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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: Peter.Milne@ed.ac.uk.
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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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