I've never been a big fan of importing concepts from one discipline into an otherwise unrelated discipline, as when linguists, trying to be as scientific as they could be, imported the notion from chemistry that complex entities (compounds) are composed of more basic building blocks (elements). Within linguistics the sound (phone) was said to be the most basic building block of a language; that these are combined to form morphemes, which are the smallest meaning bearing units; that words are composed of morphemes; that phrases are composed of words; and that sentences are composed of phrases. All of this gives a bottom up analysis of sentence structure. The appeal of such a view of linguistic structure is clear. It seems to fit.
According to this account, each sentence was independent of all the others. Noam Chomsky in his book Syntactic Structures blasted this way of conceiving of language apart, arguing that there exists a set of basic linguistic structures in any language, called "deep structures" and that there exists a set of transformations that map these deep structures into the more complex surface structures that underlie actual sentences. The deep structures were said to be semantically interpretable and consisted of a "tree like" top down structure not so different from the earlier model that terminated in morphemes. Surface structures were also tree like and transformations were therefore viewed as devices (mathematical operations) that map trees into trees.
This allowed linguists to account for the obvious linguistic similarities that exist between sentences like John will leave, Will John leave?, and I know that John will leave. This intuitively very satisfactory model of linguistic structure was taught to introductory students for some years after most linguists had abandoned it. Naturally, a variety of fields imported the "deep structure" - "surface structure" model into their very different disciplines. Check out this page from a search I made at Amazon.com, for instance.
Such importations of concepts from one discipline which seems to be successful into another less well-understood discipline may be a useful, possibly even necessary way of trying to gain a foothold in less well-understood disciplines even though the models imported are usually, probably always, abandoned by their creators. Chemists no longer look at compounds in the way they used to and linguists no longer employ Chomsky's distinction between deep structure and surface structure.
There is another kind of importation of concepts from one discipline into another that I have also never found particularly enlightening. This arises when people talk and write about such things as "the language of mathematics" or "the language of music" or "the language of art." Not surprisingly, one can also find "the mathematics of language," and "the music of language" I haven't found "the art of language" but "language arts" is a commonly found class-room topic.
Talk about the language of music or the language of art comes from those that are professional or amateur observers or teachers of the disciplines involved, perhaps to give it greater cachet . Of the three phrases mentioned earlier, the first, "The Language of Mathematics," fails to be interesting on the grounds that there are a lot of different sorts of mathematics and there would be no single "language" of them. A notion like "the language of algebra," on the other hand, makes perfectly good literal sense though, of course, one must jettison the phonetic and morphological sides of language to do so. Propositional logic, which is a species of algebra, has a syntax (rules for forming well-formed constructions), as well as a semantics in that the connectives (and, or, if...then, not) have fixed interpretations. Obviously the propositional variables ("P" and "Q" and the rest) do not have fixed interpretations. So propositions of the form "P and Q" are open sentences, so to speak.
The notion that there exists a language of music, where we are using the word "language" literally, can be made a little bit sensible in that one must follow certain rules to form "well-formed" music, for instance, rules to avoid the creation of atonal music or rules to ensure that music is harmonic. Singers who do Barbershop Harmony, which is so bad that it ought to be outlawed, are surely following very strict rules. In these cases, to make sense of "the language of music" one must strip most of what is interesting about language away to make the metaphor work. For instance, musical phrases and sentences (if there are such things) do not have literal meanings.
Which brings us to the concept "the language of art." There is simply no way to make literal sense out of the idea that there is such a thing as the language of art and if one cannot make literal sense out of the notion, why in the world would anyone find it useful. However, it is fun to talk about "the meaning of meaning in art," which I shall blog on shortly.
[I have revised this blog because it was a mess due to the fact that I was still in recovery from the holiday football games which kept me up way past my bedtime.]