popper-logic-scientific-discovery

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new appendices
them, there is a logical interpretation which takes probability as a generalization
of deducibility. But this probability logic has little to do with
our hypothetical estimates of chances or of odds; for the probability
statements in which we express these estimates are always hypothetical
appraisals of the objective possibilities inherent in the particular situation—
in the objective conditions of the situation, for example in the experimental
set-up. These hypothetical estimates (which are not derivable from
anything else, but freely conjectured, although they may be suggested
by symmetry considerations, or by statistical material) can in many
important cases be submitted to statistical tests. They are never estimates
of our own nescience: the opposite view, as Poincaré saw so
clearly, is the consequence of a (possibly unconscious) determinist
view of the world. 10
From this point of view, a ‘rational gambler’ always tries to estimate
the objective odds. The odds which he is ready to accept do not represent a
measure of his ‘degree of belief’ (as is usually assumed), but they are,
rather, the object of his belief. He believes that there are, objectively,
such odds: he believes in a probabilistic hypothesis h. If we wish to
measure, behaviouristically, the degree of his belief (in these odds or in
anything else) then we might have to find out, perhaps, what proportion
of his fortune he is ready to risk on a one-to-one bet that his
belief—his estimate of the odds—was correct, provided that this can
be ascertained.
As to degree of corroboration, it is nothing but a measure of the
degree to which a hypothesis h has been tested, and of the degree to
which it has stood up to tests. It must not be interpreted, therefore, as a
degree of the rationality of our belief in the truth of h; indeed, we know
that C(h, e) = 0 whenever h is logically true. Rather, it is a measure of
the rationality of accepting, tentatively, a problematic guess, knowing
that it is a guess—but one that has undergone searching examinations.
*13. The foregoing twelve points constitute the ‘Third Note’, as
published in the B.J.P.S. Two further remarks may be added, in order to
make more explicit some of the more formal considerations which are
implicit in this note.
10 Cf. H. Poincaré, Science and Method, 1914, IV, 1. (This chapter was first published in La
Revue du mois, 1907, 3, pp. 257–276, and in The Monist, 1912, 22, pp. 31–52.)