If we overlook the fact that propositions have a
sense which is
independent of their truth or falsehood, it easily seems as if true
& false were two equally justified relations between the sign
& 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 & 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?
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No!
For a proposition is then true when it is as we assert in this
proposition; & accordingly if by
“
q” we mean
“not-
q”, & it
is as we mean to assert, then in the new interpretation
“
q” is actually true
&
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.
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