popper-logic-scientific-discovery

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some structural components of a theory of experience
contradict the estimate. In fact, we must expect it to occur: this is a
consequence of our estimate. The hope that the calculable rarity of any
such segment will be a means of falsifying the probability estimate
proves illusory, since even a frequent occurrence of a long and greatly
deviating segment may always be said to be nothing but one occurrence
of an even longer and more greatly deviating segment. Thus there
are no sequences of events, given to us extensionally, and therefore no
finite n-tuple of basic statements, which could falsify a probability
statement.
Only an infinite sequence of events—defined intensionally by a
rule—could contradict a probability estimate. But this means, in view
of the considerations set forth in section 38 (cf. section 43), that probability
hypotheses are unfalsifiable because their dimension is infinite.
We should therefore really describe them as empirically uninformative,
as void of empirical content. 1
Yet any such view is clearly unacceptable in face of the successes which
physics has achieved with predictions obtained from hypothetical
estimates of probabilities. (This is the same argument as has been used
here much earlier against the interpretation of probability statements as
tautologies by the subjective theory.) Many of these estimates are not
inferior in scientific significance to any other physical hypothesis (for
example, to one of a determinist character). And a physicist is usually
quite well able to decide whether he may for the time being accept
some particular probability hypothesis as ‘empirically confirmed’, or
whether he ought to reject it as ‘practically falsified’, i.e., as useless for
purposes of prediction. It is fairly clear that this ‘practical falsification’
can be obtained only through a methodological decision to regard
highly improbable events as ruled out—as prohibited. But with what
right can they be so regarded? Where are we to draw the line? Where
does this ‘high improbability’ begin?
Since there can be no doubt, from a purely logical point of view,
about the fact that probability statements cannot be falsified, the
equally indubitable fact that we use them empirically must appear
as a fatal blow to my basic ideas on method which depend crucially
1 But not as void of ‘logical content’ (cf. section 35); for clearly, not every frequency
hypothesis holds tautologically for every sequence.