easily produced
(the whole of philosophy is full of them).

3.325 In order to avoid such errors we must make use of a sign-language
that excludes them by not using the same sign for different symbols and
by not using in a superficially similar way signs that have different
modes of signification: that is to say, a sign-language that is governed
by logical grammar--by logical syntax. (The conceptual notation of Frege
and Russell is such a language, though, it is true, it fails to exclude
all mistakes.)

3.326 In order to recognize a symbol by its sign we must observe how it
is used with a sense.

3.327 A sign does not determine a logical form unless it is taken
together with its logico-syntactical employment.

3.328 If a sign is useless, it is meaningless. That is the point of
Occam's maxim. (If everything behaves as if a sign had meaning, then it
does have meaning.)

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