Any valid symbolic language must be translatable.

A proposition possesses essential and accidental features. Accidental features are those that result from the particular way in which the propositional sign is created, while essential features enable it to make sense. So what is essential in a particular proposition is what all propositions that can express the same sense have in common. And in the same way, what is generally essential in a symbol is what all symbols that can serve the same purpose have in common.

So one could say: All symbols that signify an object have its actual name in common. Thus, it would follow that no particular composition is essential to a name.

There is indeed something arbitrary in the notations we use, but this is not arbitrary: That once we have fixed on one thing arbitrarily, then something else must necessarily be the case. (This lies in the nature of notation.) A particular notation may be unimportant but that it is possible is always important. 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 nature of the world.

Definitions are rules for translating from one language into another. Any valid symbolic language must be translatable into any other in accordance with such rules: This they all have in common. What denotes in a symbol is what is common to all the substitute symbols that the rules of logical syntax allow.

For instance, what all notations for the truth function have in common can be expressed in this way: They all have in common that the notation '~p' ('not p') and 'p ∨ g' ('p or g') can replace any of them. (This characterizes the way in which a specific notation can disclose something general.)

The sign of a complex is not resolved arbitrarily upon analysis; its resolution would not be different when it is incorporated in a different sentence structure.