popper-logic-scientific-discovery

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new appendices
A THIRD NOTE ON DEGREE OF
CORROBORATION OR CONFIRMATION
In this note I wish to make a number of comments on the problem of
the weight of evidence, and on statistical tests.
1. The theory of corroboration or ‘confirmation’ proposed in my
two previous notes on ‘Degree of Confirmation’ 1 is able to solve with
ease the so-called problem of the weight of evidence.
This problem was first raised by Peirce, and discussed in some detail
by Keynes who usually spoke of the ‘weight of an argument’ or of the
‘amount of evidence’. The term ‘the weight of evidence’ is taken from
J. M. Keynes and from I. J. Good. 2 Considerations of the ‘weight of
evidence’ lead, within the subjective theory of probability, to paradoxes
which, in my opinion, are insoluble within the framework of
this theory.
2. By the subjective theory of probability, or the subjective interpretation
of the calculus of probability, I mean a theory that interprets
probability as a measure of our ignorance, or of our partial knowledge,
or, say, of the degree of the rationality of our beliefs, in the light of the
evidence available to us.
(I may mention, in parentheses, that the more customary term,
‘degree of rational belief’, may be a symptom of a slight confusion,
since what is intended is ‘degree of rationality of a belief’. The confusion
arises as follows. Probability is first explained as a measure of the
strength or intensity of a belief or conviction—measurable, say, by our
readiness to accept odds in betting. Next it is realized that the intensity
of our belief often depends, in fact, upon our wishes or fears rather
1 This Journal, 1954, 5, 143, 324, and 359; and 1957, 7, 350. See also 1955, 6, and 1956,
7, 244, 249. To the first paragraph of my ‘Second Note’, a reference should be added to a
paper by R. Carnap and Y. Bar-Hillel, ‘Semantic Information’, this Journal, 1953, 4, 147 sqq.
Moreover, the first sentence of note 1 on p. 351 should read, ‘Op. cit., p. 83’, rather than as
at present, because the reference is to Dr. Hamblin’s thesis. *(This last correction has been
made in the version printed in this book).
2 Cf. C. S. Peirce, Collected Papers, 1932, Vol. 2, p. 421 (first published 1878); J. M. Keynes, A
Treatise on Probability, 1921, pp. 71 to 78 (see also 312 sq., ‘the amount of evidence’, and the
Index); I. J. Good, Probability and the Weight of Evidence, 1950, pp. 62f. See also C. I. Lewis, An
Analysis of Knowledge and Valuation, 1946, pp. 292 sq.; and R. Carnap, Logical Foundations of
Probability, 1950, pp. 554 sq.