it carries in the analysis of meaning. As stated by Wierzbicka (1985: 11), ‘‘It goes without saying that polysemy must never be postulated lightly, and that it has always to be justified on language-internal grounds; but to reject polysemy in a dogmatic and a priori fashion is just as foolish as to postulate it without justifi- cation.’’ In this respect, Cognitive Linguistics tries to do justice to earlier opinions like that of Stephen Ullmann (whose 1951 book is an excellent overview of the development of linguistic semantics from its nineteenth-century beginnings to the middle of the twentieth century), who stated that polysemy is ‘‘the pivot of se- mantic analysis’’ (1951: 117). The specific perspective taken by Cognitive Linguistics in the study of poly- semy is to analyze polysemy as a form of categorization. In the course of this chapter, I will present four features that are crucial for the cognitive linguistic approach and its relation to polysemy: the flexibility of meaning, the prototype- theoretical model of semantic structure, the radial set model, and the schematic network model. 2 I will conclude by presenting major open questions for Cognitive Linguistics as well as prospects and areas of possible future research on these matters. Given the wide range of the material to be considered, it would be impossible to exhaust the topic at hand (polysemy, radial sets, and schematic networks), but an attempt will be made to present some main features of cognitive linguistic theorizing with reference to these semantic issues. Cognitive Linguistics, in fact, has been prolific in studying semantic questions. Even though classical polysemy refers first of all to lexis, Cognitive linguistic tools make it possible to observe polysemic effects in phonology, morphology, and syntax (e.g., Taylor 1989). Poly- semic words abound in the language used in early childhood in language devel- opment (see Tomasello 1992) and in language games. 3 The phenomenon of po- lysemy also accounts for a great number of cases of historical change in language by explaining synchronic variation as resulting from diachronic change. Numerous scholars have employed the Cognitive Linguistics paradigm (and its approach to polysemy) to show the direction of lexical change in language (see, e.g., Sweetser 1990; Lewandowska-Tomaszczyk 1992; Cuyckens 1995, 1999; Geeraerts 1997; Blank and Koch 1999; Bybee 2000; Nerlich and Clarke 2003). 4 Newman (1996: 270), in his study of give verbs across languages, uses the examples of the semantics of give in English to postulate the existence of connections between, or interrelatedness of, the numerous polysemic chains evident in individual languages. Such studies en- compass both the diachronic and synchronic dimensions. Research on polysemy and prototypes in Cognitive Linguistics is extensive. 5 Cognitive Linguistics opens a whole new vista on these issues, whereby it is assumed that there exist no clear boundaries between linguistic and encyclopedic meanings and that boundaries between categories are blurred. How exactly, then, does Cognitive Linguistics proceed? 140 barbara lewandowska-tomaszczyk 2. Polysemy Tests and the Flexibility of Meaning The descriptive models of polysemy that Cognitive Linguistics focuses on (proto- typicality, radial sets, schematic networks) share a concern for the flexibility of meaning. As a first step, we may have a look at existing polysemy tests and the way they reveal the flexibility of meaning. A number of tests, thoroughly discussed in Geeraerts (1993), Tuggy (1993), and Dunbar (2001) and conveniently summa- rized in Ravin and Leacock (2000), have been proposed in the logical, philosoph- ical, and linguistic literature to distinguish polysemy from vagueness. An exami- nation of these tests shows that they do not necessarily detect the same meaning phenomena: what has to be considered a different meaning is not a self-evident matter. 2.1. The Logical Test The diagnostic polysemy test proposed by Quine (1960) states that a word is polysemic if an assertion involving that word can be both true and false of the same referent. Quine’s test shows that vague meanings (i.e., meanings that are unmarked for a certain category distinction) do not pass the logical test. If the word student were polysemic between a reading ‘male student’ and ‘female student’, then it would be possible, according to the test, to truthfully utter sentence (1); that is, for any given student, only one of the readings would be applicable. The awkwardness of (1) shows, however, that student is vague or unmarked rather than polysemic with regard to the distinction between ‘male student’ and ‘female student’. (1) I gave the book to a student but not to a student. Analyzing the status of the form port, on the other hand, Geeraerts ( 1993: 229) shows that it passes the test, so it is polysemic between the two readings ‘harbor’ and ‘certain type of fortified wine’: (2) Sandeman is a port (in a bottle) but not a port (with ships). As (2) shows, Quine’s test does not seem to discriminate between polysemy and homonymy, given that the two readings of port are homonymous. A similar example with the word light provided by Quine (1960: 129) also passes the poly- semy test: (3) The feather is light (not heavy) but not light (dark). Quine (1960: 129) concludes that ‘‘an ambiguous term such as light may be at once clearly true of various objects (such as dark feathers) and clearly false of them.’’ In this case, the ambiguity involves readings that are etymologically unrelated; the two readings are homonyms rather than polysemes. In fact, the distinction between polysemy, prototypes, and radial categories 141 polysemy and hom onymy is traditionally made by invoking historical criteria. Iden- tical forms with historically related meanings are polysemic items and are distin- guished from those words, usually referred to as homonyms, whose forms happen to be identical for historical reasons but whose meanings are etymologically unrelated. In some cases, originally homonymic forms may be reanalyzed as being con- ceptually related: a conceptual connection may be synchronically established be- tween word meanings that are not historically related. Langacker (1987: 387) gives the following example: Sometimes, as with the central senses of tree, the similarities are cognitively sa- lient and would likely be noticed even in the absence of common symbolization. In other instances the resemblance is quite tenuous. Many speakers treat the mean- ing of ear implied by ear of corn as an extension from the prototypical value of ear as a body-part term; it is doubtful that the concepts would ever be compared were it not for their identical symbolization. The cognitive distance and entrenchment of such categorizing relationships are obviously variable. Homonymy represents a limiting case, where the comparison of two identically symbolized concepts re- veals no similarity that is salient or plausible enough to establish a categorization achieving unit status. For a speaker who fails to notice any special resemblance among the meanings of bill (proper name; request for payment; protrusion on a bird, cap, or platypus), the semantic units do not unite to form a network and are connected only via their common symbolic correspondent. An analysis of the semantic reanalysis processes that take place in such cases may be found in Geeraerts (1997: 130–50). Taylor (1989) and Blank (2003) present examples of the converse case, when words that are historically related come to be perceived as unrelated by contemporary users of the language. Taylor (1989) mentions En- glish a pupil at school and the pupil of the eye; Blank (2003: 276) mentions French voler ‘to fly’ and voler ‘to steal’ and German Schloss ‘lock’ and ‘castle’. What can be observed here then is the diachronic flexibility of meaning, specifically regarding the borderline between polysemy and homonymy: meanings that are historically unrelated may come to be perceived as related, and, conversely, existing percep- tions of semantic relatedness may wither. 2.2. The Linguistic Ambiguity Test A second diagnostic test for polysemy was originally formulated by Zwicky and Sadock (1975) and later rephrased by Cruse (1986). This test is of a linguistic nature. One version of the test says that when polysemic words are used in one sentence, they result in a zeugmatic combination, as in the example of the word expire: (4) ?Arthur and his driving license expired last Thursday. Discussing the word dissertation, Cruse showed that the incompatibility of readings (which would establish polysemy) is heavily context-bound and is thus a question of degree rather than an all-or-nothing matter: 142 barbara lewandowska-tomaszczyk (5) ?Judy’s dissertation is thought provoking and yellowed with age. (6) Judy’s dissertation is still thought provoking although yellowed with age. According to (5), the material and the abstract reading of dissertation (referring either to a book as a concrete volume or to a body of knowledge as an intellectual achievement) appear to be polysemicly incompatible. The context presented in (6), however, suggests that the two interpretations do not constitute different senses. Another version of the linguistic test involves the use of the anaphoric so do construction as in: (7) I was busy dressing, and so were they. The use of a polysemic item in the two clauses (e.g., dressing in the sense of putting on a dress, etc., in the first clause, and dressing in the sense of, say, military troops coming to the proper alignment, in the so do part) renders a zeugmatic combi- nation. However, when the sense of dressing in both of the clauses is simply vague between putting on different kinds of clothes, the sentence is acceptable. 2.3. The Definitional Test Finally, there is the most classical, definitional test, whose origin can be traced back to Aristotle’s Metaphysics. A word is considered polysemic if more than a single definition is needed to account for its meaning. In semantic field theories and their extensions involving feature matrices (Katz and Fodor 1963), this principle was interpreted in terms of sets of necessary and sufficient conditions for category membership. In other words, if no single set of necessary and sufficient conditions suffices to account for the meaning of a word, the word is considered polysemic. Basic criticism, referred to as Plato’s Problem by Laurence and Margolis (1999: 14), which has been leveled against the Classical Theory of concepts, states that for most concepts definitions are difficult to give. We see, to conclude, that none of the three basic tests as such is without problems. On top of the problems that issue from the contextual flexibility of meaning, we may note that the three tests do not necessarily yield the same results. One of the examples mentioned by Geeraerts (1993) involves autohyponymous words. 6 In such words, a general sense includes a more specific one, such as egg ‘reproductive body from various animals’, ‘egg from a bird, with a yellow yolk, surrounded by a hard shell’, and so on (see Lehrer 2003: 229)ordog ‘member of the species Canis fa- miliaris’ (general reading) and ‘male member of the species Canis familiaris’ (re- stricted reading). The distinction between the two readings of dog can be estab- lished by means of the logical test, given that a sentence like Mirza is a dog but not a dog is fully acceptable when Mirza is female. The definitional test, however, cannot establish a distinction between both readings, because the more restricted reference polysemy, prototypes, and radial categories 143 is always included in the more encompassing definition. The fact that there is no complete correspondence between polysemy tests, then, suggests that meaning is a flexible phenomenon and that the boundaries between homonymy, polysemy, and vagueness are not rigid. 3. Prototype Theory The suggestion that categorial meaning is flexible receives an initial expression in prototype theory. (The term ‘‘initial expression’’ is used here because we will see later on that a further extension toward a schematic network model of semantic structure is necessary.) The starting point of the prototypical conception of cate- gorial structure is summarized in the following statement: When describing categories analytically, most traditions of thought have treated category membership as a digital, all-or-none phenomenon. That is, much work in philosophy, psychology, linguistics, and anthropology assumes that ca- tegories are logical bounded entities, membership in which is defined by an item’s possession of a simple set of criterial features, in which all instances possessing the criterial attributes have a full and equal degree of membership. In contrast, it has recently been argued that some natural categories are analog and must be represented logically in a manner which reflects their analog structure. (Rosch and Mervis 1975: 573–74) The traditional conception rejected in this statement is sometimes referred to as the Classical Theory of concepts, which has had a long history in philosophy dating back to antiquity (e.g., Aristotle 1984; Plato 1981; Locke [1697] 1960; Carnap 1978). Its main tenet is that concepts have definitional structure in the sense that they encode necessary and sufficient conditions for their application. 7 For exam- ple, the concept ‘bachelor’ can be interpreted in terms of the Classical Theory as a complex mental representation that is composed of a set of features (semantic markers) such as male, adult, and not married (see Katz and Fodor 1963). In this section, I will discuss the way in which Cognitive Linguistics developed a prototype- based conception of semantic structure that goes against the Classical Theory. Two basic steps need to be taken: the identification of various prototype effects and the development of a radial set model of semantic structure as a generic model un- derlying the prototype effects—and which at the same time applies to polysemic sets of meanings. The third part of this section presents a number of additional issues concerning prototypicality and radial sets. 144 barbara lewandowska-tomaszczyk 3.1. Prototype Effects In contrast with the so-called Classical Theory, features that are frequently men- tioned as typical of a prototype-theoretical conception include the following (first proposed by Geeraerts 1989): a. Prototypical categories exhibit degrees of typicality; not every member is equally representative for a category. b. Prototypical categories are blurred at the edges. c. Prototypical categories cannot be defined by means of a single set of cri- terial (necessary and sufficient) attributes. d. Prototypical categories exhibit a family resemblance structure, or more generally, their semantic structure takes the form of a radial set of clustered and overlapping readings. Let us have a closer look at these four characteristics. Feature (a) involves the recognition that category membership may be graded: some members of a category are better, more typical members of the category than others. One of the first contributions pointing to this was Berlin and Kay’s (1969) discovery of focal colors, that is, the best examples of basic colors, which showed that these categories are not uniform and contain central and peripheral members. Berlin and Kay’s studies were found to match Eleanor Rosch’s experiments (Heider 1971, 1972), where she showed that such central colors were psychologically real even for the speakers of the languages which do not name such colors at all. They function as special cognitive reference points and ‘‘best examples’’ or prototypes, more representative of the cat- egory than other members. These asymmetries between the prototypical and pe- ripheral category members were experimentally confirmed to be present in direct goodness-of-examples rating, true-false reaction times, production of examples, asymmetries in similarity ratings, and generalization. The discoveries concerning graded category membership were first modeled by Zadeh (1965) in a form of set theory known as fuzzy set theory, in which additional values between 0 and 1 are allowed to capture category membership gradation. When the attention is shifted from the center of a conceptual category to the periphery, it appears that membership gradience may involve two different situa- tions. Some categories like bird have rigid boundaries, in the sense that both sparrows and penguins are clearly within the category boundaries, even though the former are better exemplars of the category than the latter. Some other categories, on the other hand, such as colors or old person, do not have rigid boundaries and the graded category membership correlates with uncertainty concerning the bor- derline of the concept: where exactly does old age begin? This leads to characteristic (b): in some cases, the boundaries of a concept may be vague. Characteristics (a) and (b) both involve the members (exemplars or subclasses) of a concept: some members are more typical than others, and sometimes mem- bership status may be unclear. Characteristic (c) looks at the definitional structure of the category rather than the membership structure. It involves the absence of polysemy, prototypes, and radial categories 145 classical definitions for a category: if no definition in terms of necessary and suf- ficient attributes is available for a category, then that category is defined less rigidly than the classical model of definitions predicts. Instead of a single description con- sisting of individually necessary and jointly sufficient features, the definition takes the form of a cluster of partial descriptions. Suggestions in this direction were first formulated within philosophy by Wittgenstein (1953) and Quine (1953, 1960), then in psychology by Rosch (1973), and others. Wittgenstein showed that a concept such as ‘game’ could not be adequately defined according to the classical model. Instead, the members of such categories are related by what he called family resemblance. Family resemblance involves a polythetic,orsimilarity classification, where members of a class share some of the characteristics, none of which, however, is sufficient for class membership. Such cases contrast with what is called in science monothetic classes, characterized by sets of discrete, singly necessary and jointly sufficient cri- teria. Polythetic classification may be schematically represented as a pattern, where, for instance, three categories A, B, and C display different but overlapping sets of properties: A: p, q, r; B: r, s, t; C: t, u, v (see Needham 1972). Members of class A share one property with class B, which shares one property with class C, even though class A and C have no common characteristics. No common core can thus be identified for all category members (see, e.g., Fodor 1981 for the analysis of paint and Fillmore 1982 for the discussion of climb). Another line of criticism concerning the Classical Theory (after Laurence and Margolis 1999) is associated with the problem of an- alyticity and analytic inferences it was to account for. In his critique of analyticity in ‘‘Two Dogmas of Empiricism,’’ Quine (1953) successfully argued that there is no tenable analytic-synthetic distinction that would underlie the Classical Theory. It will be clear that characteristics (c) and (d) are mutually related: it is precisely the absence of a classical definition as signaled by (c) that leads to a definition in terms of family resemblances, as indicated by (d). If we cannot find a set of features shared by all birds that is sufficient to distinguish birds from non-birds, then our definition of ‘bird’ will have to take the form of a cluster of overlapping sets of features that each describe classes of birds. In contrast with the example just given, however, there might well be a set of common features (like the fact that all birds are born from eggs), but the set of common features is not sufficient to distinguish birds from other specifies (likereptiles,asfar as the reproductive system is involved). Such common features, even though they are jointly not distinctive enough for the category as a whole, will carry more structural weight in the definition of ‘bird’ than the features that are shared by only a subset of birds. And even among the features that are not common to all birds, some will be more frequent than others: not all birds have wings (think of the kiwi) and not all birds can fly (think of the ostrich and the chicken), but still, having wings or being able to fly are salient features of the category bird. We see, in other words, that the elements of a family resemblance definition need not carry equal weight: some features or clusters of features may be more important for the description of the category than others. 146 barbara lewandowska-tomaszczyk 3.2. Radial Sets and Polysemy: The Extended Version of Prototype Theory Characteristic (d) is applied even more broadly in the context of Cognitive Lin- guistics. Note, as argued in Geeraerts (1987), that the so-called absence of classical definitions as such does not suffice to establish the nonorthodox, prototype-based nature of lexical categories. Even in the classical model, the absence of a single definition in terms of necessary and sufficient attributes is a regular feature of lexical categories; in fact, in those cases where they are polysemic, if a polysemic category is conceived of as one that cannot be adequately described by means of a single definition, then it necessarily fits the description of (c) mentioned above. This means that characteristic (c) is only a nontraditional feature of lexical meaning when it applies to each of the polysemic readings of a lexical item. For the polysemic lexical item as a whole, characteristic (c) simply coincides with the definitional test of polysemy that was introduced earlier. But then what about characteristic (d) when we look at a polysemic lexical item as a whole, and not at each of the polysemic readings separately? One of the most fruitful insights of Cognitive Linguistics is the recognition that the definitional structure of a polysemic lexical item is similar to the definitional structure of a single meaning. When we look at the relationship between different meanings of a lexical item, we are likely to encounter the same phenomena that are typical of single meanings. For one thing, there may be demarcation problems: it may not be easy to draw a sharp line between one meaning and the other. (This is in line, of course, with what we said earlier about the relationship between the different polysemy tests.) For another, one meaning may carry more structural weight than others, in the sense that it directly or indirectly lies at the basis of other meanings. Observe, for instance, that bird might be used metaphorically to indicate an airplane (as in A gigantic silver bird approached from the west). That metaphorical extension from the ‘biological species’ reading would certainly be less salient than the latter as such. This is true from a logical point of view (to the extent that the metaphorical reading is a semantic extension of the former), from a psychological point of view (to the extent that the metaphorical reading is less likely to be permanently stored in the mental lexicon of the language user), and from a statistical point of view (to the extent that the metaphorical reading is less common than the literal one). The recognition that the same structural characteristics that apply to single meanings also apply to polysemic sets of meanings is the basis for the radial set model of conceptual structure. According to Kleiber (1990), the shift from single meanings to polysemic clusters of meanings introduces the second stage of the development of prototype theory. The first stage, dubbed the standard version of prototype theory by Kleiber, involves members of one category and thus represents an intracategorial perspective. The second stage (an extended version, in Kleiber’s parlance) represents cases of intercategorial polysemy and involves members of more than one category. polysemy, prototypes, and radial categories 147 Brugman and Lakoff (1988; see also Lakoff 1987) describe the radial set model in the following terms. Polysemic words consist of a number of radially related cate- gories even though each of the polysemic senses can itself display a complex pro- totype structure. The central radial category member provides a cognitive model that motivates the noncentral senses. The extended senses clustered around the central category are related by a variety of possible links such as image schema transformations, metaphor, metonymy, or by partial vis-a ` -vis holistic profiling of distinct segments of the whole sense. Some subtypes of, for instance, the category mother are (predictable) exten- sions of the central member of the category (e.g., biological mother or stepmother). Some others, however, develop when the central category does not productively generate a new subcategory, but rather when convention and culture condition the development of an unpredictable category. Such new submembers are considered members of radial models of categorization. Lakoff (1987: 83) gives an example of the Trobriands radial extension of the concept ‘mother’ to cover cases where a bio- logical mother gives her child to an older woman in the community to bring it up or, as in traditional Japanese culture, to the mother’s sister. What Lakoff proposes is that ‘‘the center, or prototype, of the category is predictable. And while the non- central members are not predictable from the central member, they are ‘motivated’ by it, in the sense that they bear family resemblances to it’’ (65). The main properties of radial structures have been characterized by Lakoff (1987: 379) as follows: a. A radially structured category possesses no single representation. Both central and noncentral subcategories have their own representations, and no properties of subcategories can be predicated from the central subcategory. The noncentral categories can be treated as variants of a pro- totypical (central) model with no one core in common. All subcatego- ries can be seen as bearing family resemblance to one another. b. The noncentral subcategories are motivated by the central member; they are neither predictable nor arbitrary. c. An experientialist theory of thought and reason employing all kinds of cognitive models (i.e., propositional, metaphorical, metonymic, and image-schematic) is needed to account for the types of links between the central and noncentral category members. The concept of radial categorization may have interesting theoretical implications for the relationship between language and culture. The Triobrands’ mother, ex- tended to include non-mothers in the European sense, can be considered a poly- semic extension from the perspective of European culture. However, in the Tro- briand culture, it could be treated as a full-fledged central category member. Radial structures, as observed by Lakoff (1987), provide one of the strongest arguments against the objectivist treatment of cognition and semantics. Radial categories do not objectively exist in the outside reality. Instead, together with the existence of polysemic chains, they provide evidence for a theory of cognitive models that are 148 barbara lewandowska-tomaszczyk shaped in accordance with the speakers’ perspective and their construal of the scene (see Langacker 1987, 1991). The cognitive models at work in radial categories, in other words, may be culturally specific; they do not so much reflect how reality is carved up objectively, but rather how the mind creates different realities. Such cases as the English adoptive mother and surrogate mother and the Japanese classifier hon constitute culture-bound category variants according to Lakoff. The variants, however, are not arbitrary even though they are not predictable. They are motivated and constrained by the central subcategory: a plausible explanation for the periph- eral extensions can be provided a posteriori. In addition to lexical concepts such as ‘anger’ (Lakoff and Kovecses 1987), ‘truth’, and ‘knowledge’, linguistic categories like ‘nouns’ and ‘verbs’ and linguistic constructions like there is have been shown to possess a polysemic radial structure. For instance, Janda (1990) discusses the radial structure of the category of gram- matical case in Czech and shows the dynamic nature of the category with the cat- egory members, which enter both stable and new dynamic alliances. In fact, as Lakoff (1987: 463) notes, in a cognitively based grammar, all grammar ‘‘will be a radial category of grammatical constructions, where each construction pairs a cog- nitive model (which characterizes meaning) with corresponding aspects of lin- guistic form.’’ He further proposes to account for the theory of grammatical con- structions in terms of a general theory of symbolic models, which are understood as ‘‘pairings of models of form with other cognitive models’’ (467). ‘‘Grammatical constructions,’’ in Lakoff’s wording, ‘‘are organized via prototype theory, using ra- dially structured constructional categories’’ (584). 3.3. Additional Features of Prototypicality There are three more things to mention regarding prototypicality: we have to look into the sources of prototypicality, we have to examine the relationship between the Geeraerts’s (1989) characteristics (a)–(d), and we have to say something about the application of prototype theory outside the lexical realm in which it was originally developed. To begin with, it is generally taken for granted that the different prototype effects enumerated in characteristics (a)–(d) may have different sources. Two major explanations stand out. First, prototype effects (and gradience in particular) may result from the fact that concepts function as mental reference points. When we come across new phenom- ena, we tend to interpret them in terms of existing categories (see Geeraerts 1997 for an extended discussion in terms of efficiency and cognitive economy). These cate- gories then function as Idealized Cognitive Models, as Lakoff (1987) calls them; they are, so to speak, the yardstick by which we measure new objects and events. In the case of gradience, then, different degrees of matching can be observed between an Idealized Cognitive Model referring to a given object or event and the particular object and polysemy, prototypes, and radial categories 149 . by partial vis-a ` -vis holistic profiling of distinct segments of the whole sense. Some subtypes of, for instance, the category mother are (predictable) exten- sions of the central member of the. separately? One of the most fruitful insights of Cognitive Linguistics is the recognition that the definitional structure of a polysemic lexical item is similar to the definitional structure of a single. to the middle of the twentieth century), who stated that polysemy is ‘ the pivot of se- mantic analysis’’ (1951: 117). The specific perspective taken by Cognitive Linguistics in the study of poly- semy