ields a different
sense, and so does its ending with a different stem.)

4.04 In a proposition there must be exactly as many distinguishable
parts as in the situation that it represents. The two must possess the
same logical (mathematical) multiplicity. (Compare Hertz's Mechanics on
dynamical models.)

4.041 This mathematical multiplicity, of course, cannot itself be the
subject of depiction. One cannot get away from it when depicting.

4.0411. If, for example, we wanted to express what we now write as '(x).
fx' by putting an affix in front of 'fx'--for instance by writing
'Gen. fx'--it would not be adequate: we should not know what was
being generalized. If we wanted to signalize it with an affix 'g'--for
instance by writing 'f(xg)'--that would not be adequate either: we
should not know the scope of the generality-sign. If we were to try to
do it by introducing a mark into the argument-places--for instance by
writing '(G,G). F(G,G)' --it would not be adequate: we should not be
able to establish the identity of the variables. And so on. All these
modes of signifying are inadequate because they lack the necessary
mathematical multiplicity.

4.0412 For the same reason the idealist's appeal to 'spatial spectacles'
is inadequate to explain the seeing of spatial relations, because it
cannot explain the multiplicity of these relations.

4.05 Reality is compared with propositions.

4.06 A proposition can be true or false only in virtue of being a
picture of reality.

4.061 It must not be overlooked that a proposition has a sense that is
independent of the facts: otherwise one can easily suppose that true and
false are relations of equal status between signs and what they signify.
In that case one could say, for example, that 'p' signified in the true
way what 'Pp' signified in the false way, etc.

4.062 Can we not make ourselves understood with false propositions just
as we have done up till now with true ones?--So long as it is known that
they are meant to be false.--No! For a proposition is true if we use it
to say that things stand in a certain way, and they do; and if by 'p' we
mean Pp and things stand as we mean that they do, then, construed in the
new way, 'p' is true and not false.

4.0621 But it is important that the signs 'p' and 'Pp' can say the same
thing. For it shows that nothing in reality corresponds to the sign
'P'. The occurrence of negation in a proposition is not enough to
charac