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Arbitrary/Arbitrariness/Convention: number systems are arbitrary. - Otherwise a different notation would correspond to different facts.
Of course you can give sense to new sentences and symbols. - That is why the conventions are called arbitrary.
Arbitrariness/Arbitrary/Law/Physics/Laws of Nature/Wittgenstein: E.g. perturbations: it is arbitrary whether we declare our laws to be right, and say we just do not see the planet, or whether we call the laws incorrect. - If we say that a planet must be nearby, we define a grammatical rule.
The laws of logic, such as those of the sentence of the excluded third are arbitrary! - In fact, we often use contradictions. - E.g. I like it and I do not like it.
Arbitrariness/Arbitrary/Grammar/Rules/Purpose/Wittgenstein/Schulte: E.g. the rules of cooking are not arbitrary, because they are defined by the purpose of cooking. - On the other hand: Grammar: is not defined by the purpose of language - only the grammatical rules constitute the meaning. - Therefore, they are not committed to any meaning. - ((s) Grammar/Wittgenstein: = logic).
Not Arbitrary/Tractatus: the sign of the complex does not dissolve arbitrarily. - E.g. aRb.
Vorlesungen 1930-35 Frankfurt 1989
Das Blaue Buch - Eine Philosophische Betrachtung Frankfurt 1984
Tractatus Logico Philosophicus Frankfurt/M 1960