The SCAT hypothesis of meaning holds that the components of meaning are Structure, Context, And Text, not necessarily in that order. I name this hypothesis and make it explicit because it is common to suppose, to the contrary, that meaning is determined only by text. This erroneous supposition I call the "textualist fallacy."
It is easy to show that meaning is more than the sum of the words in a text. The fact that "Oscar is taller than Nigel" does not mean the same thing as "Nigel is taller than Oscar," despite the fact that they contain exactly the same words, is proof enough. This, however, can be explained by invoking linearity rather than structure or context, so it does not prove that structure and context are components of meaning.
But there is abundant evidence that structure contributes to meaning. For example, the phrasal ambiguity as in "old men and women adore me" (the subject is either old men and all women, or old men and old women) is not explained by word order, but is explained by assuming an internal structure for the sentence. If "old" is grouped with "men" and the result grouped with "and women," then we get the first meaning. If, on the other hand, "men" is first grouped with "and women" and the result is grouped with "old," we get the second meaning. Since different structures give rise to different meanings, structure must play a role in determining the meaning.
There is also abundant evidence that context contributes to meaning. In "John's pen," for example, we don't know the nature of the relationship between John and the pen until we have some context. In a context-free environment like I just presented, it is natural to interpret the relation as ownership, such that John owns the pen. But put in other contexts, many other relations are possible. John could be the creator of the pen, the inventor of the kind of pen, the person who is currently holding the pen, or even just the person who pointed to the pen.
The examples of the contribution of structure and the contribution of context are single examples of phenomena that are pervasive. To see the pervasiveness of context, take the meaning of any extended text, comparing it to the meaning of each individual word, for example by looking it up in a dictionary. Many words will have multiple definitions (and even the best dictionaries significantly understate the number of senses of many words), but the extended text will permit far fewer meanings than the product of the definitions of the words. This is because context will eliminate many of the theoretically possible meanings.
To see the pervasiveness of structure, read an introduction to linguistic analysis, such as Steven Pinker's The Language Instinct.
The SCAT hypothesis represents the narrowest possible theory consistent with the basic realities of language. It may be that other factors, like linearity, will have to be added.
The textualist fallacy is not something I just invented for pedagogical reasons. People fall for it all the time. Even legal scholars fall for it. In separate posts I will show how a recent scholarly paper falls for the textualist fallacy, and I will suggest that even the Supreme Court fell for it in a landmark opinion.