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.