popper-logic-scientific-discovery

APPENDIX *vii
Zero Probability and the
Fine-Structure of Probability
and of Content
In the book, a sharp distinction is made between the idea of the probability
of a hypothesis, and its degree of corroboration. It is asserted that if we
say of a hypothesis that it is well corroborated, we do not say more than
that it has been severely tested (it must be thus a hypothesis with a high
degree of testability) and that it has stood up well to the severest tests
we were able to design so far. And it is further asserted that degree of
corroboration cannot be a probability, because it cannot satisfy the laws of the
probability calculus. For the laws of the probability calculus demand
that, of two hypotheses, the one that is logically stronger, or more
informative, or better testable, and thus the one which can be better
corroborated, is always less probable—on any given evidence—than the
other. (See especially sections 82 and 83.)
Thus a higher degree of corroboration will, in general, be combined
with a lower degree of probability; which shows not only that we must
distinguish sharply between probability (in the sense of the probability
calculus) and degree of corroboration or confirmation, but also that the
probabilistic theory of induction, or the idea of an inductive probability, is untenable.
The impossibility of an inductive probability is illustrated in the