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