Arbitrariness
The basic principle of the arbitrariness of the sign (l'arbitraire du signe) in the extract is: there is no natural reason why a particular sign should be attached to a particular concept.
In Figure 2 above, the signified "tree" is impossible to represent because the signified is entirely conceptual. There is no definitive (ideal, archetypical) "tree". Even the picture of a tree Saussure used to represent the signified is itself just another signifier. This aside, it is Saussure's argument that it is only the consistency in the system of signs that allows communication of the concept each sign signifies.
The object itself – a real tree, in the real world – is the referent. For Saussure, the arbitrary involves not the link between the sign and its referent but that between the signifier and the signified in the interior of the sign.
In Jabberwocky, Lewis Carroll exploits the arbitrary nature of the sign in its use of nonsense words. The poem also demonstrates very clearly the concept of the sign as a two sided psychological entity, since it is impossible to read the nonsense words without assigning a possible meaning to them. We naturally assume that there is a signified to accompany the signifier.
The concepts of signifier and signified could be compared with the Freudian concepts of latent and manifest meaning. Freud was also inclined to make the assumption that signifiers and signifieds are inseparably bound. Humans tend to assume that all expressions of language mean something.
In further support of the arbitrary nature of the sign, Saussure goes on to argue that if words stood for pre-existing concepts they would have exact equivalents in meaning from one language to the next and this is not so. Different languages divide up the world differently. To explain this, Saussure uses the word bœuf as an example. He cites the fact that while, in English, we have different words for the animal and the meat product: Ox and beef, in French, bœuf is used to refer to both concepts. A perception of difference between the two concepts is absent from the French vocabulary. In Saussure's view, particular words are born out of a particular society's needs, rather than out of a need to label a pre-existing set of concepts.
But the picture is actually more complicated, through the integral notion of 'relative motivation'. Relative motivation refers to the compositionality of the linguistic system, along the lines of an immediate constituent analysis. This is to say that, at the level of langue, hierarchically nested signifiers have relatively determined signified. An obvious example is in the English number system: That is, though twenty and two might be arbitrary representations of a numerical concept, twenty-two, twenty-three etc. are constrained by those more arbitrary meanings. The tense of verbs provides another obvious example: The meaning of "kicked" is relatively motivated by the meanings of "kick-" and "-ed". But, most simply, this captures the insight that the value of a syntagm—a system-level sentence—is a function of the value of the signs occurring in it. It is for this reason that Leonard Bloomfield called the lexicon the set of fundamental irregularities of the language. (Note how much of the 'meaningfulness' of 'The Jabberwocky' is due to these sorts of compositional relationships!)
A further issue is onomatopoeia. Saussure recognised that his opponents could argue that with onomatopoeia there is a direct link between word and meaning, signifier and signified. However, Saussure argues that, on closer etymological investigation, onomatopoeic words can, in fact, be coincidental, evolving from non-onomatopoeic origins. The example he uses is the French and English onomatopoeic words for a dog's bark, that is Ouaf Ouaf and Bow Wow.
Finally, Saussure considers interjections and dismisses this obstacle with much the same argument i.e. the sign / signifier link is less natural than it initially appears. He invites readers to note the contrast in pain interjection in French (aie) and English (ouch).
Read more about this topic: Course In General Linguistics