5.42 It is self-evident that C, z, etc. are not relations in the sense in
which right and left etc. are relations. The interdefinability of Frege's
and Russell's 'primitive signs' of logic is enough to show that they are
not primitive signs, still less signs for relations. And it is obvious that
the 'z' defined by means of 'P' and 'C' is identical with the one that
figures with 'P' in the definition of 'C'; and that the second 'C' is
identical with the first one; and so on.
5.43 Even at first sight it seems scarcely credible that there should
follow from one fact p infinitely many others , namely PPp, PPPPp, etc. And
it is no less remarkable that the infinite number of propositions of logic
(mathematics) follow from half a dozen 'primitive propositions'. But in
fact all the propositions of logic say the same thing, to wit nothing.
5.44 Truth-functions are not material functions. For example, an
affirmation can be produced by double negation: in such a case does it
follow that in some sense negation is contained in affirmation? Does 'PPp'
negate Pp, or does it affirm p--or both? The proposition 'PPp' is not about
negation, as if negation were an object: on the other hand, the possibility
of negation is already written into affirmation. And if there were an
object called 'P', it would follow that 'PPp' said something different from
what 'p' said, just because the one proposition would then be about P and
the other would not.
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