In the world of structural linguistics, we tend to associate structural analysis with parsing and parsing with well-formedness. Thus, we have structural rules to tell us whether or not a string of words is legitimately a sentence. Unfortunately, as soon as we move from "standard expository prose" to the ways in which we actually use language (including speech acts), this concept of well-formedness loses much of its value. So then we fall back and say, "Well, we are just using the rules to describe the string of words (or utterances, or whatever)." However, that just begs the question. Why do we need such a description? Is it just a basis for representation in some database, even if we are not sure why we want that database in the first place?
I would argue that there is a bit more at stake; and that is because, as a rule, those descriptions tend to be hierarchical. That means that, between two elements, there tend to be (but not necessarily always) subordinate-superordinate relations. Put another we, there is information that is serving to elaborate; and it is associated with the information being elaborated. This allows us to prioritize the entire structure, sorting out those elements that matter most from those serving to elaborate.
The most important insight in Ray Monk's How to Read Wittgenstein has to do with the numbering system in the Tractatus. This numbering system is very strictly tree-structured; so, as Monk demonstrates, while the book is a depth-first traversal of the tree, the reader tends to get a better understanding by traversing the tree breadth-first. In other words get the important points under your belt first, even if you need to be convinced of some of them; you can get the convincing later when you descend into the elaborations. Not all texts are written this way, but this is the perfect example of how sorting things out is best served by structural analysis.
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