The first well-known property (as emphasized by Saussure 1916) is that there is no motivated relationship between sounds and meanings. This is simply observed in the fact that the same meaning is usually expressed by a different sounding-word in a different language (think of house, maison, casa). For words such as hotdog, desk, dog, bike, hamburger, cranberry, sweetbread, their meanings have nothing to do with their shapes. For example, the word hotdog has no relationship with a dog which is or feels hot. There is just an arbitrary relationship between the word’s sound and its meaning: this relationship is decided by the convention of the community the speakers belong to.However, onomatopoeia shows there can be some link. And for sign language phonology, there is a very extensive link between the spatial and movement aspects of the gestures and the spatial and movement elements of the described situation. There is still a certain arbitrariness to the codified conventions of, let us say, vocabulary, but there is a significant relationship which plays a role in interpretation (and mnemonics).
They go on to discuss another principle:
The second important feature of language, and one more central to syntax, is that language makes infinite use of finite set of rules or principles, the observation of which led the development of generative linguistics in the 20th century (cf. Chomsky 1965). A language is a system for combining its parts in infinitely many ways. One piece of evidence of the system can be observed in word-order restrictions. If a sentence is an arrangement of words and we have 5 words such as man, ball, a, the, and kicked, how many possible combinations can we have from these five words? More importantly, are all of these combinations grammatical sentences? Mathematically, the number of possible combinations of 5 words is 5! (factorial), equalling 120 instances. But among these 120 possible combinations, only 6 form grammatical English sentences:Now at the general level, I think this claim is quite true of sign languages. However, there is a problem in generalizing the idea that rules are strictly combinatorial. This is an artifact of the serializing channel of phonemes, while sign languages have multiple concurrent channels of emic elements, that combine in space-dependent ways. So you can't take factorials to characterize sign language rules.
They cite Chomsky's notion of grammatical competence an internalized: "Competence refers to speakers’ internalized knowledge of their language." They side with Chomsky's Cartesian "meaning-in-the-head" position. But can't meaning be at least partly in the world? Taking a Gibsonian ecological psychology stance (or the position of Clark and Chalmers), can't we use the external perceived word as a major memory support structure? This might be a bit limited for sounds of speech, but there is more opportunities with the spaces of signs. Think of how pronouns in sign language are created in discourse. Signers establish a place in space, then refer back to it by pointing. Or they might count of a set of individuals on their fingers, then come back to each finger. So knowledge, including rules, may not be completely in the head. This reminds me of Barwise's realism about types and "constraints" (relations between two situation-types) in his relational theory of meaning. If situation-theoretic constraints are realities in the extramental world, then it seems meaning is in the world, and it is attunement to constraints that is (partly) in the head. I say partly, because attunement to language in practice cannot be a "private language," it involves a shared scheme of individuation of linguistic conventions. There may be some innate base for the conventions, the neural correlates of a the bare bones of a linguistic type system, but the cognitive structures get tuned to a speech communities linguistic constraints. Even a cat gets their binocular vision tuned to the regularities of the external world, a proven by monocular cats with no depth vision.
I am sure I will have more commentary to come.
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[1] English Syntax: An Introduction Jong-Bok Kim and Peter Sells
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