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some structural components of a theory of experience
falsifiability. We have Fsb(c) >Fsb(e) >0.* 2 If we arbitrarily put
Fsb(c) = 1, i.e. arbitrarily assign the number 1 to the degree of falsifiability
of a self-contradictory statement, then we may even define an
empirical statement e by the condition 1 > Fsb(e) > 0. In accordance
with this formula, Fsb(e) always falls within the interval between 0 and
1, excluding these limits, i.e. within the ‘open interval’ bounded by
these numbers. By excluding contradiction and tautology (as well as
metaphysical statements) the formula expresses at the same time both
the requirement of consistency and that of falsifiability.
34 THE STRUCTURE OF THE SUBCLASS
RELATION. LOGICAL PROBABILITY
We have defined the comparison of the degree of falsifiability of two
statements with the help of the subclass relation; it therefore shares all
the structural properties of the latter. The question of comparability can
be elucidated with the help of a diagram (fig. 1), in which certain
subclass relations are depicted on the left, and the corresponding
Figure 1
* 2 See however now appendix *vii.