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