non-compositionality
A number of the problems of the first solution are avoided if each collocation as a whole is seen as the relevant definition-bearing unit. On this approach, the meaning of the collocation is not constructed composition ally; we learn one definition for the unit cut the grass, another for cut one’s foot, and a third for cut a CD. Thus, the fact that in cutting the grass, a mower or a scythe is the instrument of the action, and that in cutting a disc it is a CD-burner, is not part of the meaning of cut itself, but is a property of the collocation as a whole. This avoids several of the problems of the compositional solution:
• we do not have to advance a general definition of cut that will work in every context, as we do in the general-meaning version of the compositional solution
• we do not have the problem of word-sense disambiguation, since each collocation carries its own definition.
Here is another consideration in favour of non-compositionality. It is not just cut whose meaning is determined by its collocational environment: the collocation also determines what reading is operative for cut’s object. Thus, English speakers know that cutting the grass refers to the grown grass blades, whereas planting the grass refers to grass seeds or shoots, and smoking grass refers to the leaves of a completely different plant. They also know that it is the physical CD that is involved in cutting a disc, but the ‘acoustic’ object in listening to a disc. Because both verb and object have different meanings in different collocations, it seems reasonable to think that the basic meaning bearing unit is the collocation as a whole, not the individual words.
Unfortunately, this solution is just as problematic as the compositional one. It seems precisely to ignore our intuition of the compositionality of the meanings of the collocations: the reason that cut the grass has the interpretation it does is, surely, something about the combination of the meanings of cut and the meaning of grass. It is not an arbitrary fact that cut the grass means what it does: instead, the meaning of the phrase is dependent on the meaning of its components, and this is the reason that this meaning is not conveyed by some other sequence of different elements like plant the tree. And if one takes the analogy of the ‘mental lexicon’ seriously, this option also involves the threat of an explosion in the number of entries. Analysing each collocation involving cut as having a separately specified meaning would lead to an enormous amount of repetition and redundancy in the mental lexicon, and would fail to extract the generalization that the meaning of cut in each such collocation is significantly similar to its meaning in other collocations. We can summarize the choices here in Figure 2.1:

These arguments are obviously shaped by many assumptions about the nature and limits of linguistic competence. In the absence of a clear understanding of how the brain actually does process and store language, linguists have assumed that their description of assumed linguistic competence should reflect the same criteria of economy and non-redundancy that operate in real paper dictionaries. Thus, much linguistic research has assumed that the mental lexicon does not contain a huge number of independently listed entries, but that it extracts the maxi mum number of generalizations about the meaning of a verb like cut across all its collocational contexts, in order to present the most economical, least redundant entry. As a result, it has been the topmost solution in Figure 2.1 that has traditionally been considered preferable. We will see in later chapters how this assumption has been challenged in more recent theories of language. One of these, in particular, known as cognitive linguistics, specifically rejects the dichotomous reasoning we see embodied in the claim that either the separate listing or the compositional approach should be adopted to the question of the mental representation of the meaning of collocations like these. According to linguists in the line of Langacker (1987), this sort of thinking is an example of the exclusionary fallacy, the idea that ‘one analysis, motivation, categorization, cause, function or explanation for a linguistic phenomenon necessarily precludes another’ (Langacker 1987: 28). Langacker continues:
From a broad, pretheoretical perspective, this assumption is gratuitous and in fact rather dubious, in view of what we know about the multiplicity of interacting synchronic and diachronic factors that determine the shape and import of linguistic expressions. (ibid)
Thus, even though it might seem inelegant to list all the different collocations of cut separately in the lexicon, this option should obviously not be rejected if it somehow turns out (for example, through neuroscientific experimentation) that this is, in fact, what speakers (unconsciously) do. And this discovery would not of itself invalidate the idea that speakers also simultaneously represent cut as having an independent meaning or set of meanings which enter into composition each time the verb gains a new set of arguments.