The question raised is: Can a marking that conveys a general idea be called writing, or must all writing represent specific units of speech?
To this question, the great linguist Leonard Bloomfield apparently gives his answer when he states, "Writing is merely a device for recording speech."
Bloomfield was addressing several questions of his day. Before Bloomberg, linguistics was sort of like a slightly more holistic version of philology, which might be found as a subset of some philosophy or history department. Certainly that was the sort of linguistics I perceived the field to be before I got
Anyway, Bloomfield was probably commenting on the idea of an ideographic writing system, or even an ideographic language -- a communication system that doesn't ultimately have sound as its foundations. For those in the dark about the meaning of "ideographic" -- there's a popular conception of the Chinese writing system as an organised system of pictographs, with each character standing for an object or an idea, and the characters interacting with each other as though they were abstract symbols, functions and variables performing operations on each other. For example, when a Sinophone expresses "I love forest(s)" in Chinese writing, the ideographic viewpoint would analyse the writing as a graphically-symbolic representation of the ideas contained in such a statement, as though the written statement was an abstract depiction of the first person hugging several trees. (At least I think the character's origin is that of hugging, based on the old ancient seal script way of writing the character 爱 -- ai, or to love. I'm probably very wrong though.)
But of course, the ideographic viewpoint is all wrong. There's a fairly good essay on why exactly the ideographic viewpoint is wrong in an article called "The Ideographic Myth". Victor Mair -- a linguist, sinologist, a professor at the University of Pennsylvania -- has also blogged a few posts about it on Language Log. The basic summary of the arguments is that the Chinese writing system is not actually pictorial, in as much as we do not mean an ox's head every time we write the letter A, which has its origins in the Proto-Canaanite symbol Aleph. (I do not dispute however, that knowing such origins make characters more fun or easier to learn.) On top of that, only a minority of characters in the Chinese writing system have pictorial origins -- frequently, other characters, representing semantically-unrelated meanings, are borrowed and then combined with a few other radicals to form a new character to represent some word. Why? The character that was borrowed simply carried the same (or even just similar) sound. One complication that often makes this less obvious today is that the spoken language has changed since the Chinese writing system was first invented, on top of the fact that the characters themselves evolve, so words with initially the same pronunciation might diverge, not to mention the divergence of the characters themselves. This can often obscure the Chinese writing system's highly phonetic nature. Like English and French, the Chinese writing system doesn't do a good job of updating itself with the spoken language. In fact, it would be rather hard to do that today, because Old Chinese has since diverged into a plethora of mutually-unintelligible language families (colloquially known as "dialects"). Such divergence shows further evidence of the necessity of a phonetic basis in a writing system, because each Chinese language has a "colloquial writing system", with different character sets, different vocabulary frequencies, different idioms, different word orders for different constructions. However, because the Chinese writing system itself is fairly stable, you can occasionally say, write a Mandarin phrase using Chinese characters and have a Cantonese speaker be able to interpret it -- but the effect is rather like reading Latin. Sometimes, speakers of different Chinese languages cannot interpret each other's writing at all!
Bloomfield posed more general arguments. He was arguing that as far as communication goes, the foundation of it is based on spoken language. Sure we can perform all sorts of symbolic operations in our heads, but when we fluently communicate such operations, we must use a system based on spoken language.
The mechanisms of reading and writing are pretty wondrous biologically -- they take advantage of the fact that we're capable of repeating sounds in our heads. There are various theories of memory based on this, as well as various theories of reading and language processing, and some exploration of the different types of working memory that might be involved linguistically -- as well as long-term acquisition of grammar and vocabulary (at an L1/native level -- second language learning is a bit more complicated). Some concepts that might be interesting to people working in phonics include Baddeley's model of working memory, including concepts like a "phonological loop". Of course the theory is highly incomplete, but it's a good place to start, and there are many experimental precursors to the model that demonstrate the necessity for a phonetic basis to reading.
For a writing system to express precise and fluent thoughts, it must be dependent on sound -- because that is the basis of communication. Sure there's art and music ... but you can't really communicate fluent and precise ideas with them, only gists. Could you communicate something like Newton's laws of physics to someone who didn't know them based on a picture, or a series of pictures? Take for example, the former practice of some of the Plains Natives to draw symbols on teepees for communciation -- such systems were really imprecise, and used for communication purposes that didn't have too many symbolic operations -- like "need bow-wood, twine; offer leather" or "off to river 3 days" as well as various artful depictions. In contrast, look at the complexity of many Native American languages, such as Cherokee and Sioux. Known as polysynthetic languages, they have high levels of inflection and morphological agreement, with agreement between subject, verb, direct and indirect objects, clauses. Certainly quite complex enough to express instructions on the precise order of steps to take to cook a buffalo recipe, explain the finer principles of riflemanship to a young child, suggest how you should take this flank to corner Custer and cut him off from the other Union troops, or argue why we need to stop the practice of counting coups because the situation dictates that our survival is dependent on seizing every defensive advantage possible.
You can't do this with teepee writing. There's just not enough complexity, or even vocabulary. The Chinese writing system probably evolved from a pictorial convention not unlike teepee symbols -- representing things for sale, things for buying, common objects, weather, etc. But as you wanted to use the system for more and more things, you got bogged down with the picture aspect. Really, try a convenient arrangement of symbols to symbolically depict the idea that Charlie tried to intercept a letter sent from Alice to Bob, but that Alice and Bob already know of his intentions and have come up with a plan to trick Charlie. The eureka moment was when the system switched from depicting ideas to depicting sounds. Sure, you're still using a little drawing of the sun to represent the word for sun, but now you can also use it for words with unrelated meanings (an English equivalent would be using a symbol for "sun" for the word "asunder", or combining it with a radical element related to "math" to make the word "sum"). The system exploded with the sudden possibilities. The side effect is that since you were now representing sounds and not ideas, you could drastically simplify many of the characters. Characters with elaborate depictions of mountains, trees and fields were reduced to series of short quick strokes to the extent that often you can't figure out what the character originally depicted.
There are some who argue that language is essentially a learned social construct, and this argument was probably in vogue during Bloomberg's day (the era also spawned the Sapir-Whorf hypothesis). If you can make a language on a phonetic basis -- why not one on an ideographic basis, or one that exists only in writing? But scientific evidence shows a huge biologically-determined component to language. Granted there is a huge memetic (culturally-transmitted) aspect, which is what makes it so fascinating to study (especially from an evolutionary dynamics standpoint), but an interesting thing to note is that the children of all the world learn their native language at around the same timelines. Indeed, intralanguage variance (for the time it takes for a child to learn to speak fluently) generally exceeds interlanguage variance by far. It's strong evidence that many aspects of language are human universals and are biologically/genetically constrained.