popper-logic-scientific-discovery

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with the help of the concept of relative frequency (following von
Mises). 2 Reichenbach’s attempts to extend this concept so as to include
the so-called ‘inductive probability’ or the ‘probability of hypotheses’
are doomed to failure, in my opinion, although I have no objection
whatever against the idea of a ‘truth-frequency’ within a sequence of
statements 3 which he tries to invoke. For hypotheses cannot be satisfactorily
interpreted as sequences of statements; 4 and even if one
accepts this interpretation, nothing is gained: one is only led to various
utterly unsatisfactory definitions of the probability of a hypothesis. For
example, one is led to a definition which attributes the probability 1/2
—instead of 0—to a hypothesis which has been falsified a thousand
times; for this attribution would have to be made if the hypothesis is
falsified by every second result of its tests. One might perhaps consider
the possibility of interpreting the hypothesis not as a sequence of
statements but rather as an element of a sequence of hypotheses, 5 and of
attributing to it a certain probability value qua element of such a
sequence (though not on the basis of a ‘truth-frequency’, but rather on
the basis of a ‘falsity-frequency’ within that sequence). But this attempt
is also quite unsatisfactory. Simple considerations lead to the result that
it is impossible in this way to arrive at a probability concept which
would satisfy even the very modest demand that a falsifying observation
should produce a marked decrease in the probability of the
hypothesis.
I think that we shall have to get accustomed to the idea that we must
not look upon science as a ‘body of knowledge’, but rather as a system
of hypotheses; that is to say, as a system of guesses or anticipations
which in principle cannot be justified, but with which we work as long
as they stand up to tests, and of which we are never justified in saying
that we know that they are ‘true’ or ‘more or less certain’ or even
‘probable’.
2 Op. cit., pp. 94 ff. *(that is, sections 47 to 51).
3 This concept is due to Whitehead.
4 Reichenbach interprets ‘the assertions of the natural sciences’ as sequences of statements
in his Wahrscheinlichkeitslogik, p. 15. (Ber. d. Preuss. Akad., phys.-math. Klasse, 29, 1932,
p. 488.)
5 This would correspond to the view upheld by Grelling in our present discussion; cf.
Erkenntnis 5, pp. 168 f.