I`d value the generous help here of the enlightened reader:
(Karl Popper) Logic of Scientific Discovery > 33 Degrees of Falsifiability compared by means of the subclass relation
Here we have the definition of subclass:
(1) A statement x is said to be ‘falsifiable in a higher degree’ or
better testable’ than a statement y, or in symbols: Fsb(x) > Fsb(y), if and
only if the class of potential falsifiers of x includes the class of the
potential falsifiers of y as a proper subclass.
Fsb(y)
is a subclass of Fsb(x)
.
The following text puzzles me:
If (1) applies, there will always be a non-empty complement class.
In the case of universal statements, this complement class must be
infinite. It is not possible, therefore, for the two (strictly universal)
theories to differ in that one of them forbids a finite number of single
occurrences permitted by the other.
The first senctece i understood (If (1) applies, there will always be a non-empty complement class.)
My question is:
Why must this complement class be infinite in the case of universal statements?
In the following picture you can see Fsb(x)
containing Fsb(y)
. The non-empty complement class ist limited by the borders of the rectangle Fsb(x)
.
The following sentence completely eludes my undertanding:
It is not possible, therefore, for the two (strictly universal)
theories to differ in that one of them forbids a finite number of single
occurrences permitted by the other.
Probably Fsb(y)
permits a finite number of single occurrences that would be permited by the other here Fsb(x)
.