popper-logic-scientific-discovery

426
new appendices
(3)
P(a) = P(a, e).
But according to the subjective theory, (3) means that e is, on the whole,
(absolutely) irrelevant information with respect to a.
Now this is a little startling; for it means, more explicitly, that our
so-called ‘degree of rational belief’ in the hypothesis, a, ought to be completely
unaffected by the accumulated evidential knowledge, e; that the absence of any
statistical evidence concerning z justifies precisely the same ‘degree of
rational belief’ as the weighty evidence of millions of observations
which, prima facie, support or confirm or strengthen our belief.
4. I do not think that this paradox can be solved within the framework
of the subjective theory, for the following reason.
The fundamental postulate of the subjective theory is the postulate that degrees
of the rationality of beliefs in the light of evidence exhibit a linear order:
that they can be measured, like degrees of temperature, on a onedimensional
scale. But from Peirce to Good, all attempts to solve the
problem of the weight of evidence within the framework of the subjective
theory proceed by introducing, in addition to probability, another
measure of the rationality of belief in the light of evidence. Whether this new
measure is called ‘another dimension of probability’, or ‘degree of
reliability in the light of the evidence’, or ‘weight of evidence’ is quite
irrelevant. What is relevant is the (implicit) admission that it is not
possible to attribute linear order to degrees of the rationality of beliefs
in the light of the evidence: that there may be more than one way in which
evidence may affect the rationality of a belief. This admission is sufficient to
overthrow the fundamental postulate on which the subjective theory is
based.
Thus the naïve belief that there really are intrinsically different kinds
of entities, some to be called, perhaps, ‘degree of the rationality of
belief’ and others ‘degree of reliability’ or of ‘evidential support’, is no
more able to rescue the subjective theory than the equally naïve belief
that these various measures ‘explicate’ different ‘explicanda’; for the
claim that there exists an ‘explicandum’ here—such as ‘degree of rational
belief—capable of ‘explication’ in terms of probability stands or falls
with what I have called the ‘fundamental postulate’.
5. All these difficulties disappear as soon as we interpret our
probabilities objectively. (It does not matter, in the context of the