Michael Johnson gives the following argument for compositionality in his article on the Internet Encyclopedia of Philosophy:
We are capable of understanding a very large number—perhaps an infinite number—of sentences that we have never heard before. …
If we understand the meaning of a new sentence whose meaning we haven’t been specifically taught before, it must be that we can work out its meaning from information available to us when we hear that sentence and other things that we have already learned.
Suppose for a moment that English is a compositional language, in the sense that the meaning of a sentence of English can be computed (worked out) from its syntactic structure and the meanings of its morphemes. This would explain how one could understand a novel utterance [shouldn’t this be “sentence”?] such as There is a cauliflower-shaped spacecraft from Saturn on television. English speakers who have never learned the meaning of this sentence specifically have nevertheless learned the meanings of each of the words in it: cauliflower, shape, the past tense morpheme -ed, spacecraft, and so forth. Furthermore, part of mastering a language involves acquiring the ability to parse sentences of that language, that is, to figure out their syntactic structure—for example, figuring out that cauliflower-shaped modifies spacecraft, but on television doesn’t modify Saturn. Thus if English is compositional, English speakers have all they need to understand novel English sentences they have never encountered before—provided those sentences don’t contain unfamiliar words. (Michael Johnson, “Compositionality” , Internet Encyclopedia of Philosophy¸ accessed 11 April, 2015)
This is one version of a familiar line of argument. However, it doesn’t seem clear to me what precisely it is supposed to prove. I had never heard the sentence, “There is a cauliflower-shaped spacecraft from Saturn on television” until I read this article. I immediately recognized it as an English sentence, and I suppose I can say I understood it: it didn’t bewilder me, I understood how it was meant to be taken. (This was partly due, no doubt, to the context in which I encountered the sentence, as an instance of “sentences-understood-though-never-before-heard”.)
I could, as it were, identify the place of the sentence in the language calculus. Or we might say, I can state its truth-conditions (“the sentence p is true if and only if p”). But considered as an achievement, it seems to me, this is tautologous. Mastery of the system gives me mastery of the system; the question, however, is what enables us to reach beyond the language cage. After all, compositionality I take it is supposed to explain how we are able to communicate by means of combinations of words we have never encountered before, and all its seems to explain is how we are able to recognize combinations of words as the combinations of words they are. Suggesting that understanding a sentence takes us beyond mere recognition because it enables us to tell what the truth-conditions of the sentence are is no help: for one thing, this is true only if truth-conditions are understood as tautologically conveyed by the sentence itself. (“’Snow is white’ is true if and only if snow is white.” ) Second, if I don’t understand what the speaker is up to I don’t know how he means for his words to be related to the question of truth: is he trying to tell me something, musing on a formulation, telling a joke, composing a line for a science fiction story, planning the interior design of a room (“On top of the television set there will be this funny-shaped spacecraft-looking thing.”)?
In fact, the condition that I must know the words in the sentence in order to understand it – in this sense – seems gratuitous, as long as I know what grammatical categories they belong to. Thus, to cite a famous example, while I have no idea what a runcible is, I have no difficulty understanding that the sentence “Smith kept a runcible at Abbotsford” is true if and only if Smith did indeed keep a runcible at Abbotsford. Why should my familiarity with the words have a bearing on my ability to extract the truth-conditions from the sentence?
The idea seems to be that compositionality can explain the mysterious leap from simply hearing a sequence of words to a state called “understanding the sentence …”, a state which, although it does not yet tell me what I am to do with the words spoken, yet puts me in a position to deal with them wherever I might encounter them. And I doubt whether any such state needs to be postulated.