popper-logic-scientific-discovery

not as much as can be formalized. But one cannot completely formalize
the idea of a sincere and ingenious attempt. 8
The particular way in which C(x, y) is here defined I consider
unimportant. What may be important are the desiderata, and the fact that
they can be satisfied together.
A SECOND NOTE ON DEGREE OF CONFIRMATION
1 The suggestion has been made by Professor J. G. Kemeny 1 (with a
reference to my definition of content), and independently by Dr. C. L.
Hamblin 2 that the content of x, denoted by ‘C(x)’, should be measured
by—log 2P(x) instead of 1—P(x), as I originally suggested. (I am
here using my own symbols.) If this suggestion is adopted, then my
desiderata 3 for degree of confirmation of x by y, denoted by C(x, y), have
8 There are many ways of getting nearer to this idea. For example, we may put a
premium on crucial experiments by defining
Ca, b(h) = (C(h, eb) � n
1/(n + 1)
C(h, ci, ea)) where c1, c2, . . . , is the sequence of experiments made between the moments of time, ta and tb. We have ta < t1 � ti � tn = tb. ea and eb are the total evidence (which may include
laws) accepted at ta and tb. We postulate P(ci, eb) = 1 and (to ensure that only new experiments
are counted) P(ci, ea) ≠ 1 and P(ci, Ucj) ≠ 1, whenever j < i. (‘Ucj’ is the spatio-temporal
universalization of cj.) * Today, I should be inclined to treat this question in a different way. We may, very
simply, distinguish between the formula ‘C(x, y)’ (or ‘C(x, y, z)’) and the applications of this
formula to what we mean, intuitively, by corroboration, or acceptability. Then it suffices
to say that C(x, y) must not be interpreted as degree of corroboration, and must not be
applied to problems of acceptability, unless y represents the (total) results of sincere
attempts to refute x. See also point *14 of my ‘Third Note’, below.
I have here put ‘total’ in brackets, because there is another possibility to be considered:
we may confine our tests to a certain field of application F (cf. the old appendix i, and
appendix *viii), we may thus relativize C, and write ‘CF (x, y)’. The total corroboration of
a theory may then be said, simply, to be the sum of its corroborations in its various
(independent) fields of application.
1 John G. Kemeny, Journal of Symbolic Logic, 1953, 18, p. 297. (Kemeny’s reference is to my
Logik der Forschung.)
2 C. L. Hamblin, ‘Language and the Theory of Information’, a thesis submitted to the
University of London in May 1955 (unpublished); see p. 62. Dr. Hamblin produced this
definition independently of Professor Kemeny’s paper (to which he refers in his thesis).
3 ‘Degree of Confirmation’, this Journal, 1954, 5, 143 sqq.; see also p. 334.
i=1
appendix *ix 419