The Oxford Handbook of Cognitive Linguistics Part 19 pot

event. In the concept ‘bachelor’, discussed first by Katz and Fodor (1963)intermsof feature matrices, then by Fillmore (1982)andLakoff(1987) in the cognitive frame- work, a partial fit is observed between an Idealized Cognitive Model of ‘bachelor’ and the concept of ‘bachelor’ as applied, for instance, to the pope. Second, prototypicality may involve cognitive economy in yet another sense. Categories exist at different levels, and some of the levels were discovered to be more basic than others. Berlin, Breedlove, and Raven ( 1974) and Hunn (1977) showed, for instance, that the level of the biological genus in Tzeltal plant and animal taxonomies is psychologically basic—that is, more salient than other category levels, more readily acquired, recalled, etc. (see Rosch and Mervis 1975; Schmid, this volume, chapter 5). It is precisely at these basic levels that categories exhibit a maximization of perceived similarities among category members and a minimi- zation of perceived similarities among different categories. As such, the features of such basic-level categories have high cue validities: they are good predictors of whether something belongs to the category or not. More generally, the prototype categories may find their source in an overall attempt to maximize cue validity, in other words, to group things together in such a way that the members of a category are maximally similar within the category and maximally dissimilar with regard to other categories. Let us now turn toward a closer examination of the relationship between fea- tures (a)–(d). Following Geeraerts (1989), we may observe that the features (a)–(d) are not necessarily coextensive; they do not always co-occur. There is now a con- sensus in the linguistic literature on prototypicality that the characteristics enu- merated above are prototypicality effects that may be exhibited in various com- binations by individual lexical items and may have very different sources. Also, the four features are systematically related along two dimensions. On the one hand, characteristics (a) and (c) take into account the referential, extensional structure of a category. In particular, they have a look at the members of a category; they observe, respectively, that not all members of a category are equal in representa- tiveness for that category and that the referential boundaries of a category are not always determinate. On the other hand, these two aspects (nonequality and non- discreteness) recur on the intensional level, where the definitional rather than the referential structure of a category is envisaged. For one thing, nondiscreteness shows up in the fact that there is no single definition in terms of necessary and sufficient attributes for a prototypical concept. For another, the clustering of meanings that is typical of family resemblances and radial sets implies that not every reading is structurally equally important (and a similar observation can be made with regard to the components into which those meanings may be analyzed). If, for instance, one has a family resemblance relationship of the form AB, BC, CD, DE, then the cases BC and CD have greater structural weight than AB and DE. The concept of prototypicality, in short, is itself a prototypically clustered one in which the concepts of nondiscreteness and nonequality (either on the inten- sional or on the extensional level) play a major distinctive role. Nondiscreteness 150 barbara lewandowska-tomaszczyk involves the existence of demarcation problems and the flexible applicability of categories. Nonequality involves the fact that categories have internal structure: not all members or readings that fall within the boundaries of the category need have equal status, but some may be more central than others; categories often con- sist of a dominant core area surrounded by a less salient periphery. The distinction between nondiscreteness (the existence of demarcation prob- lems) and nonequality (the existence of an internal structure involving a categorial core versus a periphery) cross-classifies with the distinction between an intensional perspective (which looks at the senses of a lexical item and their definition) and an extensional perspective (which looks at the referential range of application of a lexical item or that of an individual sense of that item). The cross-classification between both relevant distinctions (the distinction between nondiscreteness and nonequality and the distinction between an intensional and an extensional per- spective) yields a two-dimensional conceptual map of prototypicality effects, in which the four characteristics mentioned before are charted in their mutual rela- tionships. Table 6.1 schematically represents these relationships. Characteristic (a) illustrates the extensional nonequality of semantic struc- tures: some members of a category are more typical or more salient representatives of the category than others. Characteristic (b) instantiates intensional nonequality: the readings of a lexical item may form a set with one or more core cases sur- rounded by peripheral readings emanating from the central, most salient readings. Characteristic (c) manifests the notion of extensional nondiscreteness: there may be fluctuations at the boundary of a category. And characteristic (d) represents intensional nondiscreteness: the definitional demarcation of lexical categories may be problematic when measured against the classical requirement that definitions take the form of a set of necessary attributes that are jointly sufficient to delimit the category in contrast with others. Table 6.1. The main prototype effects and their mutual relationships EXTENSIONALLY (on the referential level) INTENSIONALLY (on the level of senses) NON-EQUALITY (salient effects, internal structure with core and periphery) [a] differences of salience among members of a category [b] clustering of readings into family resemblances and radial sets NON-DISCRETENESS (demarcation problems, flexible applicability) [c] fluctuations at the edges of a category [d] absence of definitions in terms of necessary and sufficient attributes polysemy, prototypes, and radial categories 151 4. Schematic Networks Prototypicality and the radial set model do not exhaust the insights into the structure of polysemy developed within Cognitive Linguistics. A further step to be taken involves the notion of schematic networks (see also Tuggy, this volume, chapter 4). 4.1. Parsimony or Polysemy? To see how a prototype-theoretical, radial set model of semantic structure ties in with the notion of schematic network, we may start from the granularity question: Which level of detail is most appropriate for semantic description? The challenge of polysemy for language theorists is to find out whether it is possible to predict the polysemic chains a given word can build up, to identify the mechanisms that underlie such extensions, and to account for the motivation which makes it possible for a language user to interpret the meanings in context. But it also involves the question of the granularity of definition, of the level at which the relatedness of the senses can be best observed and captured. The question of the granularity of definition touches upon one of the most important properties of semantic analysis. It involves a discussion of whether it is the monosemy, the polysemy, or the homonymy approach which most adequately accounts for lexical meanings. The monosemy approach strives for more schema- ticity in semantic analysis and more parsimonious schematic definitions. The po- lysemy approach prefers fine-grained, maximally specific analyses, while the hom- onymy approach does not assume any relatedness of meanings between items having the same form. 8 One can detect a radical homonymy position in generative analyses of lexi- cal senses (Katz and Fodor 1963), where a practical disregard for the polysemy- homonymy distinction can be observed. Lexical meanings are represented there as sets of matrices of linguistic (semantic-syntactic) properties, strict subcategoriza- tion features (semantic markers), and their combinatorics (accounted for by se- lectional restriction rules). Cognitive linguists (e.g., Langacker 1991; Geeraerts 1993; Tuggy 1993; Sandra and Rice 1995) have put forward arguments in favor of basically the polysemy position in semantic analysis. The monosemy position is represented by work such as that by Ruhl (1989), who takes issue with Lakoff and Johnson (1980) about the polysemy stand. The monosemy position, as presented by Ruhl, argues in favor of the distinction between a lexical item’s semantic part—an ab- stract, minimum representation of its meaning—and an identifying part of the meaning that is contextual (i.e., pragmatic). This approach is grounded in the structuralist tradition (see Bierwisch 1983 for similar views) 9 and makes a clear di- vision between (abstract) semantics and (elaborated) pragmatics in the form of 152 barbara lewandowska-tomaszczyk contextual implication and world knowledge (see also Dunbar 2001: 9 and, more recently, Tyler and Evans 2003 for their concept of a protoscene). 10 There are several diachronic arguments against such a concept of monosemy. First of all, the diachronic study of the world’s languages rather unambiguously suggests that the direction of semantic development is from the concrete to the abstract (Traugott 1982; Sweetser 1990) and not vice versa. Secondly, polysemy usually develops from the more salient to the less salient sense. 11 In his seminal article, in which he takes issue with Sandra (1998) and to a certain extent with Croft (1998), Tuggy (1999) presents further evidence for polysemy and identifies what he calls ‘‘an open-minded preference or pre-expectation of polysemic analyses’’ over either monosemic or homonymic accounts (356–57). His justification involves three points, two of which are methodological. First, as Tuggy has it, it is harder to prove a negative (‘‘there is no mental connection between meanings’’) than a positive (‘‘there are some connections’’). Second, it is reasonable to assume that the majority of cases fall in the middle of a continuum (the continuum, that is, between absolute monosemy and radical homonymy) rather than at the extremes. And finally, lin- guistic evidence for polysemy is abundant. 12 This does not mean, however, that attempts to account for polysemy in terms of a single common structure are absent in the cognitive linguistic framework. Lakoff (1987), Brugman (1981), Brugman and Lakoff (1988), and, more recently, Janssen (2003) posit similar configurational image schemas to underlie the rela- tionships between polysemic senses (see Brugman 1990, Lakoff 1990, and Turner 1990 for the discussion of the Invariance Hypothesis). The schemas supposedly preserve their Gestalt configuration across diverse polysemic senses of the same lexical form. Underlying the meaning of such forms is a core set of image schemas, such as: container, source, goal, link, up, and down, and image schema transformations. Furthermore, Lakoff (1987: 440) proposes that there exist natural relationships among image schemas and that these motivate polysemy. Examples here include the schema transformations between multiple and mass schemas or the relationship between the image schemas path and end of path (see Bennett 1975, quoted in Lakoff 1987 ): (9) Sam walked over the hill. (path) (10) Sam lives over the hill. ( end of path) However, whereas the radical monosemy position defends an abstract, minimal semantic representation for a decontextualized general sense from which polysemic instances are derived by contextual (pragmatic) constraints, Cognitive Linguistics tends to defend the view that polysemic senses of one lexical item form interrelated sets. Whereas monosemy assumes a minimal, narrow semantic representation, Cog- nitive Linguistics tends to favor a rich form of representation in which each lexical meaning is an access point to a network of related categories. Radial sets constitute one type of network, but the schematic network model as developed by Langacker (1987) and presented in detail in Tuggy (this volume, chapter 4 ) goes one step polysemy, prototypes, and radial categories 153 further: it introduces different levels of abstraction into the model. Within a se- mantic network, readings that are separate at one level of granularity may be sub- sumed under an overarching reading at a less specific level. The discussion between a monosemy stand and a polysemy stand then receives an answer not in terms of an either-or opposition, but in terms of an and-and complementarity. If there is an abstract schema that overarches the more concrete readings, it may coexist with the latter at a different hierarchical level of the network. In such a framework, the definitional test of polysemy can be regarded as a search for a schema subsuming related senses (see Tuggy 1993). 13 It is not exactly clear, though, whether a more schematic reading need always consist of a definition in terms of necessary and sufficient conditions; in the actual practice of applying the schematic network model, this is certainly not always the case. Also, the knowledge base captured by the schematic network is dynamic, whereas a monosemy approach is static. Cases of reanalysis (e.g., light or ear) can naturally be accounted for in such an approach. In other words, the categorization underlying linguistic meanings, as any other kind of categorization, is not given once and for all; rather, the categorization process is a dynamic creative activity, both for an individual and for a linguistic. 14 Polysemy, as understood in cognitive terms, is an exponent of the absence of clear boundaries between semantics and pragmatics (as it is an exponent of the absence of clear boundaries between lexicon and syntax; see note 14). Indeed, the thesis of the encyclopedic nature of linguistic meaning and semantic description and, concomitantly, the rejection of a strict dichotomy between encyclopedic and linguistic meaning clearly lead to the rejection of a parsimonious monosemic ap- proach to the advantage of the polysemy position (see Geeraerts 1993). According to this approach, homonymy, polysemy and vagueness form a continuum. 15 The place on the continuum depends on two factors as formulated by Tuggy (1993): (i) the presence of a subsuming schema and (ii) the relative conceptual distance of such a schema from the structures. A token example of English homonymy such as in the Bank of England and river bank can be said to be subsumed by the well- entrenched thing schema but the instantiations are, as Tuggy proposes, fairly distant from each other, both conceptually and from the point of view of elabo- ration. Vagueness, also called ‘‘systematic polysemy,’’ ‘‘(partial) segment profiling,’’ or ‘‘allosemy’’ (Deane 1988), on the other hand, involves meanings which are not well entrenched, such as the gender distinction (female/male) in the English word student, but whose schematic meaning is relatively well entrenched and elabora- tively close. 4.2. Comparing the Representational Formats In the course of the previous pages, we have come across three different models of lexical semantic structure that are current in Cognitive Linguistics: the overlapping sets (or family resemblance) model, the radial set model, and the schematic net- 154 barbara lewandowska-tomaszczyk work model. Following Geeraerts (1995), we will now present a comparison of the three models. By way of example, let us start from the following meanings of bird: i. Any member of the class Aves ii. A clay disk thrown as a flying target iii. Shuttlecock as used in badminton iv. A rocket, guided missile, satellite, or airplane v. A young woman The overlapping sets model is illustrated by figure 6.1, reprinted from Geeraerts (1995: 25). Early applications may be found in studies such as Geeraerts (1990), Cuyckens (1991), and Schmid (1993). The basic elements in this representational format are the members of a category (such as the types of birds in figure 6.1), or, in some cases, instances of use of the category as found in a text corpus. These basic elements are grouped together on the basis of the features that they share or the senses that they exemplify. Each grouping is typographically represented by means of a Venn-diagram. The different groupings may overlap; the area in the figure where the sets overlap maximally constitutes the prototypical center of the category. The radial set model was introduced in Lakoff (1987), as described in the previous pages. Early examples may be found in the work of Brugman (1981), Janda (1990), Nikiforidou (1991), Goldberg (1992), and others. The basic elements in a radial set representation are the meanings or senses of a category; these are connected by means of relational links that indicate how one reading is an extension of an other. In the bird example, as represented by figure 6.2, all links from the central bio- logical reading to the peripheral readings are motivated by metaphorical similarity. (The motivational link is not the same, though. In senses [ii], [iii], and [iv], the ‘flying thing’ aspect is dominant, while the metaphor behind sense [v] would Figure 6.1. The overlapping set structure of the category bird polysemy, prototypes, and radial categories 155 rather be something like ‘pretty, lively thing’, perhaps with the overtone of serving as prey.) The typographical distribution of the various readings on the page il- lustrates the prototypical structure of the category: the prototypical sense is si- tuated roughly in the middle of the figure, while the extensions that emanate from this central sense are grouped radially around it. The schematic network model is described in detail by Langacker (1987, 1991). Early illustrations may be found in the work of Rudzka-Ostyn (1985, 1989), Tuggy (1987, 1993), Taylor (1992), Casad (1992), Schulze (1993), and others. The basic elements in the schematic network model may be meanings or members of a category. As in the radial set model, these elements are connected by means of relational links, but a systematic distinction is maintained between two kinds of links: links of schematization and links of extension. Schematicity involves the relationship between a subordinate node and a superordinate node in a tax- onomical hierarchy. The category bird, for instance, is schematic with regard to robin, sparrow, ostrich, and other types of birds. Extension, on the other hand, involves partial schematicity: assuming that the subset comprising robins, spar- rows, and blackbirds (among others) constitutes the prototypical center of the category ‘bird’, the subset comprising chickens is an extension from that proto- type. Chickens do not fall within the prototypical subset, but the concept ‘chicken’ can be seen as an extension (based on a relationship of similarity) of the proto- typical sense. (And the same holds, obviously, for ‘kiwi’, ‘ostrich’, and ‘penguin’.) Precisely because the example involves similarity, the relation is one of partial schematicity. Figure 6.2. An abstract representation of a radial set 156 barbara lewandowska-tomaszczyk We will not present an example of a schematic network as it is usually drawn; ample illustrations will be found in Tuggy (this volume, chapter 4). Given our example, though, it will be easy to appreciate that the schematic network repre- sentation is able to combine the overlapping sets representation and the radial network representation. In the radial network presentation of figure 6.2, reading (i) is schematic with regard to the analysis presented in figure 6.1: the prototype-based, family resemblance representation in figure 6.1 is an analysis of reading (i) in figure 6.2, at a higher level of granularity than what is presented in the radial network presentation of figure 6.2. A schematic network representation intends to capture both levels at the same time. An informal representation (informal in the sense that it does not use the typographical conventions specifically developed for schematic networks; again, see Tuggy, this volume, chapter 4) of the levels in the schematic network and the relationship between them might look like figure 6.3, where the lowest level presents the family resemblance analysis of figure 6.1 and where the higher level corresponds with figure 6.2. It will be clear, then, that the representational formats are not incompatible, but rather focus on different aspects of semantic structure as discussed in the previous pages: the overlapping sets representation deals primarily with the ‘‘standard version’’ of prototypicality, in Kleiber’s terms. The radial set represen- tation is well suited for the extended version of prototypicality, while the schematic network representation adds the recognition that the level of abstractedness at which categories are conceptualized is contextually flexible. Figure 6.3. A schematic network as combining the radial set model and the overlapping sets model polysemy, prototypes, and radial categories 157 5. Further Research Let us summarize. Cognitive models of polysemy reveal that vagueness, polysemy, and homonymy represent a cline of diminishing schematicity and increasing in- stance salience. Polysemy is an instance of categorization, and category members form a user-dependent chain of related senses. They are built around centers which share relevant information, where contrasting information is taken as irrelevant. Categorization is not static, given once and for all, but it is dynamic and creative. These facts direct present and future research toward refining the cognitively based concept of lexical meaning. There is, however, still much to be learned about the exact identification and characterization of linguistic meaning. In this concluding paragraph, we will identify three topics that are likely to be high on the agenda for future research. First, Prototype Theory, as well as the concept of prototype itself, has given rise to numerous controversies since the time it was first proposed (see, e.g., Osherson and Smith 1981 ). The inherent dynamism of the concept prototype is, for example, captured in a different manner by MacLaury’s Vantage Theory (MacLaury 1992; Taylor and MacLaury 1995), which is one of the possible reformulations of the theory of prototypes. Other contemporary theories of concepts extend and re- fine other aspects of the prototype theory or resort to and modify classical theo- ries of concepts (see Laurence and Margolis 1999; Margolis and Laurence 1999 for the presentation and analyses of Neoclassical Theories, the Theory-Theory, and Conceptual Atomism). The systematic comparison of theoretical models, then, should be an essential concern for the further development of semantics in Cog- nitive Linguistics. Second, another pertinent issue in Cognitive Linguistics is related to the mech- anisms of ‘‘online’’ meaning construction involving dynamic categorization and re- categorization (see, e.g., Coulson 2001). Current accounts of polysemy require fur- ther elaboration along these lines. In all those questions, more experimentation and neurobiological evidence of neural activity is welcome (see Coulson 2004), based on such measures as, for instance, the event-related brain potential (ERP) derived from the encephalogram. Some issues relevant to polysemy are discussed in the papers on ERP elicited by lexical ambiguities (Van Petten and Kutas 1987, 1991). Measures of brain activity that implement the cognitive processes, together with a description of language based on authentic language data (namely, Corpus Linguistics method- ology; see Lewandowska-Tomaszczyk 1997), are likely to present more convincing arguments for the theoretical constructs proposed by cognitive linguists. Third, the major task for Cognitive Linguistics remains the search for estab- lishing cognitive reality ofdifferentkinds of schemas governing the presence ofmean- ing relatedness among identical linguistic forms, as well as the examination of possible conceptual constraints on the number and type of polysemic senses. Apart from individual introspection and intuition, then, linguists look for various kinds of evidence. First of all, there is a substantial body of linguistic evidence to examine 158 barbara lewandowska-tomaszczyk (see Langacker 1987: 157). Furthermore, one has to resort to experimental findings and acquisitional data (as in Dowker 2003 or Nerlich, Todd, and Clarke 2003). There exist numerous empirical techniques worth mentioning here. Sandra and Rice (1995), for instance, used sorting tasks, which show the relatedness between words and sentences at different levels of granularity by means of hierarchical clustering analysis, similarity judgments involving a scale between ‘‘completely different’’ and ‘‘absolutely identical,’’ and acceptability judgments. There are also attempts to use eye-tracking techniques to determine what representation people initially access at the word processing level, as well as important psychological findings on salience in literal and nonliteral uses (see Giora 1997; Giora and Gur 2003). 16 Geeraerts, Grondelaers, and Bakema (1994) use referential analysis rather than an experimental empirical technique. Ambiguity and polysemy have also been at the center of attention of computational linguists, who study word senses and propose models of semantic tagging (e.g., Rayson 1995) and word sense disam- biguation (e.g., Pustejovsky 1991). In her doctoral dissertation on systematic po- lysemy, Lapata (2000) uses statistical methodology to disambiguate polysemic word combinations and proposes a probabilistic model for selecting the dominant meaning. The presence of elements of synchrony in diachrony and diachrony in synchrony justifies the use of historical linguistic methodology in cognitive linguistic analyses (see Tyler and Evans 2003: 108 for the concept of a primary sense in their analysis of propositional polysemy), enriched by cross-language comparisons and variationist studies. However, no convincing evidence has yet been forthcoming on the adequacy of different methods in determining the complex nature of a predominant, pri- mary, or sanctioning sense, and we still have to find out which particular instance of a lexical form more exactly counts as a distinct sense and which of the two—that is, a partial or full-specification approach to polysemy—has a higher cognitive reality. Even though, as we have recently been reminded by Tyler and Evans, ‘‘all linguistic analysis is to some extent subjective’’; more rigorous methods and tools are needed in Cognitive Linguistics to secure ‘‘replicability of findings, a prereq- uisite for any theoretically rigorous study’’ (2003: 104). NOTES 1. The purpose of the semantic description included in early Transformational Grammar (see Katz and Fodor 1963) was to account for ambiguity—in the sense of homonymy—(see, e.g., I observed the ball, Postal 1969: 32). Some researchers within the generative framework investigated the nature of the lexicon and lexical categories (see, e.g., Fillmore 1970, ‘‘The grammar of hitting and breaking’’) or made attempts to answer the question concerning the status of word meanings (Perlmutter 1970). It may be noted that an interest in semantics existed outside linguistics: researchers outside linguistics pointed to a significant role the study of polysemy can bring to illuminate the mechanisms of human cognition (cf. Brown and Witkowski 1983). polysemy, prototypes, and radial categories 159 . Brugman 199 0, Lakoff 199 0, and Turner 199 0 for the discussion of the Invariance Hypothesis). The schemas supposedly preserve their Gestalt configuration across diverse polysemic senses of the same lexical. Vantage Theory (MacLaury 199 2; Taylor and MacLaury 199 5), which is one of the possible reformulations of the theory of prototypes. Other contemporary theories of concepts extend and re- fine other. illustrations may be found in the work of Rudzka-Ostyn (198 5, 198 9), Tuggy (198 7, 199 3), Taylor (199 2), Casad (199 2), Schulze (199 3), and others. The basic elements in the schematic network model