Words as radial categories
In this section, we present Lakoff’s account of the semantics of over, which has been highly influential in the development of cognitive lexical semantics. Lakoff’s account was based on ideas proposed in a master’s thesis by Claudia Brugman, his former student. As we have already indicated, the idea underpinning Lakoff’s approach was that a lexical item like over constitutes a conceptual category of distinct but related (polysemous) senses. Furthermore, these senses, as part of single category, can be judged as more prototypical (central) or less prototypical (peripheral). This means that word senses exhibit typicality effects, like the cognitive categories that we saw in Chapter 8. For instance the ABOVE sense of over in example (1a) would be judged by most native speakers of English as a ‘better’ example of over than the CONTROL sense in example (2). While the prototypical ABOVE sense of over relates to a spatial configuration, the CONTROL sense does not. The intuition that the spatial meanings are somehow prototypical led Brugman and Lakoff (1988) and Lakoff (1987) to argue that the CONTROL sense of over is derived metaphorically from the more prototypical spatial meaning of over. However, this approach departs in important ways from the monosemy account that we sketched above, as we will see.
Lakoff (1987) proposed that words represent radial categories. As we saw in Chapter 8, a radial category is a conceptual category in which the range of concepts are organised relative to a central or prototypical concept. The radial category representing lexical concepts has the same structure, with the range of lexical concepts (or senses) organised with respect to a prototypical lexical concept or sense. This means that lexical conceptual categories have structure: more prototypical senses are ‘closer’ to the central prototype, while less proto typical senses are ‘further from’ the prototype (peripheral senses). In cognitive semantics, radial categories are modelled in terms of a radiating lattice configuration, as shown in Figure 10.1. In this diagram, each distinct sense is represented by a node (indicated by a black circle). While all senses are related by virtue of belonging to the same conceptual category, arrows between nodes indicate a close relationship between senses.
Central to this approach is the assumption that radial categories of senses are represented or instantiated in long-term semantic memory. (In cognitive semantics, the term ‘semantic memory’ is used interchangeably with the more traditional term ‘(mental) lexicon’.) According to this view, the reason we are able to use over with a CONTROL meaning is because this sense of over is instantiated in long-term memory. This means that the range of senses associated with over are conventionalised (Chapter 4). In other words, most native speakers of English simply ‘know’ the range of senses associated with over. From this perspective, a radial category is not a device for generating distinct meanings from the central or prototypical sense. Instead, it is a model of how distinct but related meanings are stored in semantic memory. In this important respect, the cognitive account of word meaning departs from the monosemy account, which holds that a single abstract sense is stored which is ‘filled in’ by context on each occasion of use.

An important concern for cognitive semanticists has been to explain how polysemy arises. Because cognitive semanticists assume that linguistic categories are no different, in principle, from other kinds of conceptual categories, it follows that linguistic categories are structured by the same general cognitive mechanisms that structure non-linguistic conceptual categories. According to this view, less prototypical senses are derived from more prototypical senses by cognitive mechanisms that facilitate meaning extension, including conceptual metaphor and image schema transformations (Chapter 6). These mechanisms result in the systematic extension of lexical categories resulting in meaning chains. This gives rise to polysemy: a semantic network for a single lexical item that consists of multiple related senses. It follows that the radial category in Figure 10.1 also represents a semantic network. A semantic network might consist of a number of distinct senses that are peripheral and hence not strictly predictable with respect to the prototype, but which are nevertheless motivated by the application of general cognitive mechanisms. In addition, this model predicts the emergence of senses that are intermediate with respect to the prototype and the peripheral senses. The process that connects these central and peripheral senses is called chaining. In the next section, we explore in more detail how this process works. Table 10.1 summarises the main assumptions that characterise the cognitive approach to lexical semantics.