ropositions.

5.32 All truth-functions are results of successive applications to
elementary propositions of a finite number of truth-operations.

5.4 At this point it becomes manifest that there are no 'logical
objects' or 'logical constants' (in Frege's and Russell's sense).

5.41 The reason is that the results of truth-operations on
truth-functions are always identical whenever they are one and the same
truth-function of elementary propositions.

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.

5.441 This vanishing of the apparent logical constants also occurs in
the case of 'P(dx). Pfx', which says the same as '(x). fx', and in the
case of '(dx). fx. x = a', which says the same as 'fa'.

5.442 If we are given a proposition, then with it we are also given the
results of all truth-operations that have it as their base.

5.45 If there are primitive logical signs, then any logic that fails
to show clearly how they are placed relatively to one another and to
justify their existence will be incorrect. The construction of lo