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.