4.025 When translating one language into another, we do not proceed by translating each proposition of the one into a proposition of the other, but merely by translating the constituents of propositions. (And the dictionary translates not only substantives, but also verbs, adjectives, and conjunctions, etc.; and it treats them all in the same way.)

4.026 The meanings of simple signs (words) must be explained to us if we are to understand them.  With propositions, however, we make ourselves understood.

4.027 It belongs to the essence of a proposition that it should be able to communicate a new sense to us.

4.03 A proposition must use old expressions to communicate a new sense.  A proposition communicates a situation to us, and so it must be essentially connected with the situation.  And the connexion is precisely that it is its logical picture.  A proposition states something only in so far as it is a picture.

4.031 In a proposition a situation is, as it were, constructed by way of experiment.  Instead of, ’This proposition has such and such a sense, we can simply say, ‘This proposition represents such and such a situation’.

4.0311 One name stands for one thing, another for another thing, and they are combined with one another.  In this way the whole group—­like a tableau vivant—­presents a state of affairs.

4.0312 The possibility of propositions is based on the principle that objects have signs as their representatives.  My fundamental idea is that the ‘logical constants’ are not representatives; that there can be no representatives of the logic of facts.

4.032 It is only in so far as a proposition is logically articulated that it is a picture of a situation. (Even the proposition, ‘Ambulo’, is composite:  for its stem with a different ending yields 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.