popper-logic-scientific-discovery

probability 197
But this answer raises another question: How is it possible that probability
statements—which are not falsifiable—can be used as falsifiable
statements? (The fact that they can be so used is not in doubt: the
physicist knows well enough when to regard a probability assumption
as falsified.) This question, we find, has two aspects. On the one hand,
we must make the possibility of using probability statements understandable
in terms of their logical form. On the other hand, we must
analyse the rules governing their use as falsifiable statements.
According to section 66, accepted basic statements may agree more
or less well with some proposed probability estimate; they may represent
better, or less well, a typical segment of a probability sequence.
This provides the opportunity for the application of some kind of
methodological rule; a rule, for instance, which might demand that the
agreement between basic statements and the probability estimate
should conform to some minimum standard. Thus the rule might draw
some arbitrary line and decree that only reasonably representative segments
(or reasonably ‘fair samples’) are ‘permitted’, while atypical or
non-representative segments are ‘forbidden’.
A closer analysis of this suggestion showed us that the dividing line
between what is permitted and what is forbidden need not be drawn
quite as arbitrarily as might have been thought at first. And in particular,
that there is no need to draw it ‘tolerantly’. For it is possible to
frame the rule in such a way that the dividing line between what is
permitted and what is forbidden is determined, just as in the case of
other laws, by the attainable precision of our measurements.
Our methodological rule, proposed in accordance with the criterion
of demarcation, does not forbid the occurrence of atypical segments;
neither does it forbid the repeated occurrence of deviations (which, of
course, are typical for probability sequences). What this rule forbids is
the predictable and reproducible occurrence of systematic deviations;
such as deviations in a particular direction, or the occurrence of segments
which are atypical in a definite way. Thus it requires not a mere
rough agreement, but the best possible one for everything that is reproducible
and testable; in short, for all reproducible effects.