popper-logic-scientific-discovery

ecome clear to us that a high degree of simplicity is nevertheless
linked with a high degree of corroboration. For a high degree of testability
or corroborability is the same as a high prior improbability or
simplicity.
The problem of corroboration will be discussed in the next
appendix.
Addendum, 1967
If we remember what has been said in the old appendix i (p. 283)
about the dimension of a theory, a, relative to a field F, that is, dF(a), and what has
been said in the present appendix about the ‘weakest falsifiers’ of a theory,
we can introduce a measure of the simplicity or the content of a relative to F,
CtF (a), as follows:
Ct F(a) = 1/(d F(a) + 1)
appendix *viii 401
This is a measure of the fine structure of the content of a theory (relative to
F); for it may be applicable where the probabilities become indistinguishable,
because p(a) = 0.
Incidentally, simplicity should always be regarded as relative to a given
problem of explanation. (See note 24 to chapter 10, p. 241, of my Conjectures
and Refutations, in the (revised) second edition, 1965 (and later).)
Addendum, 1972
We sometimes discover a new connection between scientific problems.
Thus if the simplicity of a theory is relative to the problems which the
theory tries to solve, then it is, to some degree, also relative to the
historical problem-situation. With this it becomes clear that the problems
of the content and simplicity of a theory may change in the
course of the historical development of a science.