The matter of arbitrariness in language is primarily associated with the work of the Swiss linguist, Ferdinand de Saussure (1857-1913), whose book of lectures, Cours de linguistique Générale, is widely recognized to have laid the foundations of European structural linguistics in the twentieth century. One of Saussure’s most quoted positions points out that the meaning of words is arbitrary, in that, for instance, the word arbre in French and its equivalent tree in English have nothing to do “naturally” with the object they signify. Any other sequence of sounds could in theory designate the same object. These are just the words French and English happen to have inherited from their history.
However, Saussure’s observations about sound and meaning, which lie at the heart of what he called semiology, i. e., the science of signs (often erroneously thought to be the equivalent of Peirce’s sem[e]iotic), are fundamentally flawed by stressing the arbitrariness of words/linguistic signs. What is arbitrary are the RULES of language structure, not the relationship between words and what they mean in different languages.
This was brought home to Y-H-B while I watched the women’s finals of the Miami Tennis Open on TV this weekend and listened to the commentators consistently mispronouncing the name of the Czech winner, Petra Kvitová, namely by inserting a schwa (/ə/) between the initial consonant cluster (kv-) of her surname. Since the commentators were both native speakers of English, they only did what the phonetic rules of English permitted: there are no English words with an initial cluster [kv-], hence the natural insertion of a schwa between the two consonants. Czech, on the other hand, routinely permits such clusters.
This is where the notion of arbitrariness comes in. English arbitrarily does not tolerate such clusters, whereas Czech does. Hence it is in the phonetic rules that the arbitrariness resides, not in what the words containing such sound sequences mean.