Saturday Morning Breakfast Cereal had comic a while back about political speech. The idea was that, if you replace everything except nouns with nonsensical words, people will still be able to follow the speech. They concluded that if you can get the point from the nouns, the rest is a waste of space. Of course, it was a joke. But it still shows us something about language.
However, this is not a feature of political speech, but language in general. It is often packed with information, and people are very good at deciphering meaning from fragments
That is because language is not an arbitrary collection of words parsed together by an arbitrary syntax. Instead, it reflects our knowledge about the world by being categorized into frames of knowledge. (This is known as frame semantics.)
In this case, it is the political frame that we can infer, not from the text itself, but from the context it is presented in (paratext, to use the fancy term). This provides us with important clues on how to approach the text and gives us a starting point from which to continue interpretation.
But of course, more is omitted in this situation than simply words. From the rest of the text we would infer things like connotations, attitudes and further elaborations on the frame of interpretation. And these matter, because otherwise we won’t recognize things like irony or sarcasm, or other very natural ways of using language.
To put it in differently: there is more to language than words.