If we overlook the fact that propositions have a
sense which
is independent of their truth or falsehood, it easily seems as if true
and false were two equally justified relations between the sign and what
is signified.
(We might then say e.g. that
“
q”
signifies in the true way what
“not-
q”
signifies in the false way).
But are not true and false in fact equally justified?
Could we not express ourselves by means of false propositions just
as well as hitherto with true ones, so long as we know that they are
meant falsely?
No!
For a proposition is then true when
3
it is as we assert in this proposition; and
accordingly if by “
q” we mean
“
not-q”, and it is as we
mean to assert, then in the new interpretation
“
q” is actually true and
not false.
But it is important that we
can mean the same by
“
q” as by
“not-q”, for it shows that
neither to the symbol “not” nor to the manner of its
combination with “
q” does a characteristic
of the denotation of “
q” correspond.
4