Linguistics is great, but it can’t do everything. You can’t use linguistics to be a more successful salesman, or tell a funnier joke, or describe why a poem is beautiful. All of these things are intimately related to language, but fall outside the purview of its scientific study in the same way that being a great chef falls outside the purview of organic chemistry. What linguistics studies is the building blocks various languages make available to their speakers. The rest is up to them.
So we need a dividing line that tells us where the building blocks stop and the magic begins. Of course this is a contentious issue without a clear cut answer, but for the sake of adding some focus let me propose one: linguistics is the study of how compositional structures give rise to the literal meaning of natural language utterances. This is purposefully narrow–it may, for instance, leave Grice out in the cold–but I would claim is still a decent description of the bulk of the field as it is practiced. In particular, a focus on literal meaning is a means of shying away from all the things mentioned in the paragraph above that linguistics can’t do.
In addition to being a convincing account of how you can get seemingly boundless expressiveness out of a seemingly finite set of symbols, compositionality gives you real methodological traction. Conversations’ meaning is a function of their utterances. Utterances have meaning by virtue of the words they contain. Words’ meaning is a product of their morphemes and so on down to the famous “arbitrariness of the sign” proposed by Ferdinand de Saussure, the granddaddy of us all. This is all very tractable and PhD-able because it has an end point at the morpheme level. By definition, the bottoming out on arbitrariness cannot happen below there, though sometimes it can happen higher up. What I find striking is the relative skimpiness of the taxonomy of higher up cases. To my knowledge there are only really two commonly agreed upon types, and no universal jargon to describe them, but I think people would know what I mean if I call them idioms and metaphors.
Idioms are sequences of words whose meaning is not compositional. The classic example is “Sam kicked the bucket” meaning “Sam died”. Dying has nothing to do with kicking or buckets. If you were a non-native speaker of English, you wouldn’t be able to reason out what this means. Presumably there’s a historical connection between the concepts, but it may be completely opaque to present-day speakers, who just memorize “kicked the bucket” en bloc as another synonym for “died”.
The other kind of of non-literal meaning is basically “everything else”. I’m going to call this category “metaphorical”, and while I doubt most linguists would object, it’s telling that “metaphor” does not have a clear technical definition. Crucially, though, it is a case where the meaning of a phrase is non-literal, but nevertheless compositional. For example, I could say to you, “Sam is a cyclone in a sweater vest”, reasonably expecting you to interpret this to mean that Sam is a person whose dynamic personality is belied by an unremarkable exterior. This is non-literal–Sam is not actually a conical configuration of high speed winds–but it is also compositional. The metaphor turns on the interlocutor’s familiarity with the power of cyclones and the nebbishy connotations of sweater vests. The meaning of the whole is a function of the meaning of its parts. It’s just that the function is a highly complex, contingent, and culturally determined one. Characterizing these connections is a very difficult task, so a lot of times you say the hell with it and stick to clean room sentences.
Even if we want to draw a bright line at literal compositionality, I’m surprised that this taxonomy is not more filled out, if only for the sake of making the line brighter. The best attempt I know to delve into this area from the linguistics side is George Lakoff’s Metaphors We Live By. Are there others?