The problem pursued in this presentation concerns the role of Arbitrariness in linguistic expressions. Saussurean Arbitrariness is due to the conventional sound-meaning-relation of linguistic expressions. It is systematically projected (but not reduced) from Lexical Items to linguistic expressions of unrestricted complexity by the operation of Merge. This raises the question, whether this arbitrariness is an incidental byproduct of the systems complexity, which could be avoided under conditions of optimal design. With this perspective, language is compared to mental systems of comparable complexity, but without arbitrariness. Obviously, neither the visual system nor the system of music (which consists like language in auditory signals with combinatorial structure) involves arbitrariness in any sense akin to language. The by no means trivial conclusion is, that due to the conventional nature of symbolic signs, linguistic expressions can correspond to structures of any possible domain, differing thereby especially from iconic signs. The upshot of this conclusion: arbitrariness provides the space, by means of which language allows to talk about anything that can be subject to mental awareness. Arbitrariness does not fall short of optimal design, but rather allows language to be the organ of thought and its expression, which it is.