popper-logic-scientific-discovery

corroboration, or how a theory stands up to tests 267
rules; for instance the rule that we shall not continue to accord a
positive degree of corroboration to a theory which has been falsified
by an inter-subjectively testable experiment based upon a falsifying
hypothesis (cf. sections 8 and 22). (We may, however, under certain
circumstances accord a positive degree of corroboration to another
theory, even though it follows a kindred line of thought. An example
is Einstein’s photon theory, with its kinship to Newton’s corpuscular
theory of light.) In general we regard an inter-subjectively testable
falsification as final (provided it is well tested): this is the way in
which the asymmetry between verification and falsification of theories
makes itself felt. Each of these methodological points contributes
in its own peculiar way to the historical development of science as a
process of step by step approximations. A corroborative appraisal
made at a later date—that is, an appraisal made after new basic statements
have been added to those already accepted—can replace a positive
degree of corroboration by a negative one, but not vice versa. And
although I believe that in the history of science it is always the theory
and not the experiment, always the idea and not the observation,
which opens up the way to new knowledge, I also believe that it is
always the experiment which saves us from following a track that
leads nowhere: which helps us out of the rut, and which challenges
us to find a new way.
Thus the degree of falsifiability or of simplicity of a theory enters
into the appraisal of its corroboration. And this appraisal may be
regarded as one of the logical relations between the theory and the
accepted basic statements: as an appraisal that takes into consideration
the severity of the tests to which the theory has been
subjected.
we can compare degrees of corroboration (for example, those of Newton’s and of Einstein’s
theory of gravity). Moreover, this definition makes it even possible to attribute
numerical degrees of corroboration to statistical hypotheses, and perhaps even to other
statements provided we can attribute degrees of (absolute and relative) logical probability
to them and to the evidence statements. See also appendix *ix.