popper-logic-scientific-discovery

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some structural components of a theory of experience
been deduced from a probability estimate in the manner indicated,
then we must assume that the probability estimate is falsified.
Such considerations may help us to understand pronouncements like
the following of Eddington’s in which he distinguishes two kinds of
physical laws: ‘Some things never happen in the physical world because
they are impossible; others because they are too improbable. The laws which
forbid the first are primary laws; the laws which forbid the second are
secondary laws.’ 2 Although this formulation is perhaps not beyond
criticism (I should prefer to abstain from non-testable assertions about
whether or not extremely improbable things occur), it agrees well with
the physicist’s application of probability theory.
Other cases to which probability theory may be applied, such as
statistical fluctuations, or the statistics of chance-like individual events,
are reducible to the case we have been discussing, that of the precisely
measurable macro effect. By statistical fluctuations I understand
phenomena such as the Brownian movement. Here the interval
of precision of measurement (± φ) is smaller than the interval ∆p
characteristic of the number n of micro events contributing to the
effect; hence measurable deviations from p are to be expected as highly
probable. The fact that such deviations occur will be testable, since the
fluctuation itself becomes a reproducible effect; and to this effect my
earlier arguments apply: fluctuations beyond a certain magnitude
(beyond some interval ∆p) must not be reproducible, according to my
methodological requirements, nor long sequences of fluctuations in
one and the same direction, etc. Corresponding arguments would hold
for the statistics of chance-like individual events.
I may now summarize my arguments regarding the problem of
decidability.
Our question was: How can probability hypotheses—which, we
have seen, are non-falsifiable—play the part of natural laws in empirical
science? Our answer is this: Probability statements, in so far as they are
not falsifiable, are metaphysical and without empirical significance;
and in so far as they are used as empirical statements they are used as
falsifiable statements.
2 Eddington, The Nature of the Physical World, 1928, p. 75.