3.342 In our notations there is indeed something arbitrary, but this is not arbitrary: if we have determined something arbitrarily then something else must be the case. (This stems from the essence of the notation.)
Or: This depends on the essence of notation. The best candidate for something arbitrary in a notation would seem to be the signs used, that “dog” (rather than “chien” or “Hund” say) means dog, and so on. But from this arbitrary designation, once the meaning has been defined or determined, any necessary truths about dogs (that they are animals, say) will then be necessarily true of “dogs.” It is the designation or determination or definition that produces the necessity. The essence of notation then seems to have something to do with definition, which sounds right and certainly fits the general Tractarian view of language as representing designated objects in states of affairs.