TRACTATUS LOGICO-PHILOSOPHICUS

(Even the proposition “ambulo” is composite, for its stem gives a different sense with another termination, or its termination with another stem.)

4.04 In the proposition there must be exactly as many thing distinguishable as there are in the state of affairs, which it represents.

They must both possess the same logical (mathematical) multiplicity (cf. Hertz’s Mechanics, on Dynamic Models).

4.041 This mathematical multiplicity naturally cannot in its turn be represented. One cannot get outside it in the representation.

4.0411 If we tried, for example, to express what is expressed by “(*x*).*fx*” by putting an index before *fx*, like: “Gen.*fx*”, it would not do, we should not know what was generalized. If we tried to show it by an index *g*, like: “*f*(*x _{g}*)” it would not do—we should not know the scope of the generalization.

If we were to try it by introducing a mark in the argument places, like “(*G, G*).*F*(*G, G*)”, it would not do—we could not determine the identity of the variables, etc.

All these ways of symbolizing are inadequate because they have not the necessary mathematical multiplicity.

4.0412 For the same reason the idealist explanation of the seeing of spatial relations through “spatial spectacles” does not do, because it cannot explain the multiplicity of these relations.

4.05 Reality is compared with the proposition.

4.06 Propositions can be true or false only by being pictures of the reality.

4.061 If one does not observe that propositions have a sense independent of the facts, one can easily believe that true and false are two relations71