Tractatus Logico-Philosophicus | Page 8

it is
true.) It is understood by anyone who understands its constituents.
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.
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
characterize its sense (PPp = p). The propositions 'p' and 'Pp' have
opposite sense, but there corresponds to them one and the same reality.
4.063 An analogy to illustrate the concept of truth: imagine a black spot
on white paper: you can describe the shape of the spot by saying, for
each point on the sheet, whether it is black or white. To the fact that a
point is black