Tractatus Logico-Philosophicus | Page 6

3.33 In logical syntax the meaning of a sign should never play a role. It
must be possible to establish logical syntax without mentioning the
meaning of a sign: only the description of expressions may be
presupposed.
3.331 From this observation we turn to Russell's 'theory of types'. It can
be seen that Russell must be wrong, because he had to mention the
meaning of signs when establishing the rules for them.
3.332 No proposition can make a statement about itself, because a
propositional sign cannot be contained in itself (that is the whole of the
'theory of types').
3.333 The reason why a function cannot be its own argument is that the
sign for a function already contains the prototype of its argument, and it
cannot contain itself. For let us suppose that the function F(fx) could be
its own argument: in that case there would be a proposition 'F(F(fx))',
in which the outer function F and the inner function F must have
different meanings, since the inner one has the form O(f(x)) and the
outer one has the form Y(O(fx)). Only the letter 'F' is common to the
two functions, but the letter by itself signifies nothing. This
immediately becomes clear if instead of 'F(Fu)' we write '(do) : F(Ou) .
Ou = Fu'. That disposes of Russell's paradox.
3.334 The rules of logical syntax must go without saying, once we
know how each individual sign signifies.
3.34 A proposition possesses essential and accidental features.
Accidental features are those that result from the particular way in
which the propositional sign is produced. Essential features are those
without which the proposition could not express its sense.
3.341 So what is essential in a proposition is what all propositions that
can express the same sense have in common. And similarly, in general,
what is essential in a symbol is what all symbols that can serve the

same purpose have in common.
3.3411 So one could say that the real name of an object was what all
symbols that signified it had in common. Thus, one by one, all kinds of
composition would prove to be unessential to a name.
3.342 Although there is something arbitrary in our notations, this much
is not arbitrary--that when we have determined one thing arbitrarily,
something else is necessarily the case. (This derives from the essence
of notation.)
3.3421 A particular mode of signifying may be unimportant but it is
always important that it is a possible mode of signifying. And that is
generally so in philosophy: again and again the individual case turns
out to be unimportant, but the possibility of each individual case
discloses something about the essence of the world.
3.343 Definitions are rules for translating from one language into
another. Any correct sign-language must be translatable into any other
in accordance with such rules: it is this that they all have in common.
3.344 What signifies in a symbol is what is common to all the symbols
that the rules of logical syntax allow us to substitute for it.
3.3441 For instance, we can express what is common to all notations
for truth-functions in the following way: they have in common that, for
example, the notation that uses 'Pp' ('not p') and 'p C g' ('p or g') can be
substituted for any of them. (This serves to characterize the way in
which something general can be disclosed by the possibility of a
specific notation.)
3.3442 Nor does analysis resolve the sign for a complex in an arbitrary
way, so that it would have a different resolution every time that it was
incorporated in a different proposition.
3.4 A proposition determines a place in logical space. The existence of
this logical place is guaranteed by the mere existence of the
constituents--by the existence of the proposition with a sense.

3.41 The propositional sign with logical coordinates--that is the logical
place.
3.411 In geometry and logic alike a place is a possibility: something
can exist in it.
3.42 A proposition can determine only one place in logical space:
nevertheless the whole of logical space must already be given by it.
(Otherwise negation, logical sum, logical product, etc., would introduce
more and more new elements in co-ordination.) (The logical
scaffolding surrounding a picture determines logical space. The force
of a proposition reaches through the whole of logical space.)
3.5 A propositional sign, applied and thought out, is a thought.
4. A thought is a proposition with a sense.
4.001 The totality of propositions is language.
4.022 Man possesses the ability to construct languages capable of
expressing every sense, without having any idea how each word has
meaning or what its meaning is--just as people speak without knowing
how the individual sounds are produced. Everyday language is a part of
the human organism and is no