popper-logic-scientific-discovery

of degrees of falsifiability to a large extent upon derivability relations.
Both relations show the form of lattices which are totally connected in
the self-contradiction and in the tautology (cf. section 34). This may be
expressed by saying that a self-contradiction entails every statement
and that a tautology is entailed by every statement. Moreover, empirical
statements, as we have seen, can be characterized as those whose
degree of falsifiability falls into the open interval which is bounded by
the degrees of falsifiability of self-contradictions on the one side, and
of tautologies on the other. Similarly, synthetic statements in general
(including those which are non-empirical) are placed, by the entailment
relation, in the open interval between self-contradiction and
tautology.
To the positivist thesis that all non-empirical (metaphysical)
statements are ‘meaningless’ there would thus correspond the thesis
that my distinction between empirical and synthetic statements, or
between empirical and logical content, is superfluous; for all synthetic
statements would have to be empirical—all that are genuine, that is,
and not mere pseudo-statements. But this way of using words,
though feasible, seems to me more likely to confuse the issue than
to clarify it.
Thus I regard the comparison of the empirical content of two statements
as equivalent to the comparison of their degrees of falsifiability.
This makes our methodological rule that those theories should be
given preference which can be most severely tested (cf. the anticonventionalist
rules in section 20) equivalent to a rule favouring
theories with the highest possible empirical content.
36 LEVELS OF UNIVERSALITY AND
DEGREES OF PRECISION
degrees of testability 105
There are other methodological demands which may be reduced to
the demand for the highest possible empirical content. Two of these
are outstanding: the demand for the highest attainable level (or
degree) of universality, and the demand for the highest attainable degree
of precision.
With this in mind we may examine the following conceivable
natural laws: