popper-logic-scientific-discovery

versa. The better testable statement, i.e. the one with the higher degree
of falsifiability, is the one which is logically less probable; and the
statement which is less well testable is the one which is logically more
probable.
As will be shown in section 72, numerical probability can be linked
with logical probability, and thus with degree of falsifiability. It is
possible to interpret numerical probability as applying to a subsequence
(picked out from the logical probability relation) for which a
system of measurement can be defined, on the basis of frequency estimates.
These observations on the comparison of degrees of falsifiability do
not hold only for universal statements, or for systems of theories; they
can be extended so as to apply to singular statements. Thus they hold,
for example, for theories in conjunction with initial conditions. In this
case the class of potential falsifiers must not be mistaken for a class of
events—for a class of homotypic basic statements—since it is a class
of occurrences. (This remark has some bearing on the connection
between logical and numerical probability which will be analysed in
section 72.)
35 EMPIRICAL CONTENT, ENTAILMENT, AND
DEGREES OF FALSIFIABILITY
It was said in section 31 that what I call the empirical content of a statement
increases with its degree of falsifiability: the more a statement
forbids, the more it says about the world of experience. (Cf. section 6.)
What I call ‘empirical content’ is closely related to, but not identical
with, the concept ‘content’ as defined, for instance, by Carnap. 1 For the
latter I will use the term ‘logical content’, to distinguish it from that of
empirical content.
I define the empirical content of a statement p as the class of its potential
falsifiers (cf. section 31). The logical content is defined, with the help of
the concept of derivability, as the class of all non-tautological statements
which are derivable from the statement in question. (It may be
called its ‘consequence class’.) So the logical content of p is at least equal
to (i.e. greater than or equal to) that of a statement q, if q is derivable
1 Carnap, Erkenntnis 2, 1932, p. 458.
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