popper-logic-scientific-discovery

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new appendices
thus becomes something like formal simplicity; but otherwise my
theory of simplicity agrees with that of Wrinch and Jeffreys in this
point.) They also saw clearly that simplicity is one of the things aimed
at by scientists—that these prefer a simpler theory to a more complicated
one, and that they therefore try the simplest theories first. On
all these points, Wrinch and Jeffreys were right. They were also right in
believing that there are comparatively few simple theories, and many
complex ones whose numbers increase with the number of their
parameters.
This last fact may have led them to believe that the complex theories
were the less probable ones (since the available probability was somehow
to be divided among the various theories). And since they also
assumed that a high degree of probability was indicative of a high
degree of knowledge and therefore was one of the scientist’s aims, they
may have thought that it was intuitively evident that the simpler (and
therefore more desirable) theory was to be identified with the more
probable (and therefore more desirable) theory; for otherwise the aims
of the scientist would become inconsistent. Thus the simplicity postulate
appeared to be necessary on intuitive grounds and therefore a
fortiori consistent.
But once we realize that the scientist does not and cannot aim at a
high degree of probability, and that the opposite impression is due to
mistaking the intuitive idea of probability for another intuitive idea
(here labelled ‘degree of corroboration’), 10 it will also become clear to
us that simplicity, or paucity of parameters, is linked with, and tends to
increase with, improbability rather than probability. And so it will also
10 It is shown in point 8 of my ‘Third Note’, reprinted in appendix *ix, that if h is a
statistical hypothesis asserting ‘p(a,b) = 1’, then after n severe tests passed by the hypothesis
h, its degree of corroboration will be n/(n + 2) = 1 − (2/(n + 2)). There is a striking
similarity between this formula and Laplace’s ‘rule of succession’ according to which the
probability that h will pass its next test is (n + 1)/(n + 2) = 1 − (1/(n + 2)). The numerical
similarity of these results, together with the failure to distinguish between probability
and corroboration, may explain why Laplace’s and similar results were intuitively
felt to be satisfactory. I believe Laplace’s result to be mistaken because I believe that his
assumptions (I have in mind what I call the ‘Laplacean distribution’) do not apply to the
cases he has in mind; but these assumptions apply to other cases; they allow us to
estimate the absolute probability of a report on a statistical sample. Cf. my ‘Third Note’
(appendix *ix).