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construal and perspectivization 81
chapter 4

SCHEMATICITY

david tuggy
1. Introduction

One of the most intellectually fertile concepts of Cognitive Grammar has been that
of schemas.
1
The aim of this chapter will be to characterize this concept, relate it to
some of the other concepts discussed in the surrounding chapters of this book, and
illustrate some of the many ways it is used under Cognitive Grammar. Particular

attention is given to how it allows Cognitive Grammar to explicate such traditional
concepts as polysemy, syntactic categories, rules, analogy, figurative language, head-
ship and valence, and composition, in useful and intuitively satisfying ways. These
phenomena under other models must be handled by separate mechanisms, but
recognizing them as manifestations of schematicity allows Cognitive Grammar to
handle them in an integrated manner.
The concept in itself is not a novelty attributable to Cognitive Grammar, but
some of its applications are, and especially novel is the theoretical unification it
affords. In particular, Cognitive Grammar handles, by this single cognitive mech-
anism, both phenomena which are linguistic in the strict sense (the categories and
generalizations in speakers’ minds which constitute part of languages) and meta-
linguistic phenomena (such as the categories linguists use to talk about language
and languages).
2. TheNatureofSchematicity

2.1. The Basic Idea
The use of the term in Cognitive Grammar has numerous historical roots,
2
but the
basic idea is an ancient, commonsensical one. Briefly, a schema is a superordinate
concept, one which specifies the basic outline common to several, or many, more
specific concepts. The specific concepts, which are called elaborations or instan-
tiations or subcases of the schema, fill in that outline in varying, often contrastive
ways. Both Langacker’s and Lakoff’s usages of the term have been quite influen-
tial in Cognitive Linguistics circles; they will be examined briefly in the next two
sections.
2.2. Langacker’s Characterization
Langacker considers the ability to generalize, which he equates with the extraction
of schemas, to be one of the most central human cognitive capabilities. It involves
the recognition of core commonalities, abstracting away from less important (for

the cognitive task at hand) details which may differ from one concept or cognitive
experience to another. This ability may be operative in any domain or combination
of domains of cognition (Langacker 1987a: 132), and it in fact pervades our thought
relative to them all. The relationships of schematicity thus established are one of
the main kinds of relationships that structure the ‘‘inventory of conventional lin-
guistic units’’ which constitutes a language (73–75).
3
The notion of schematicity pertains to level of specificity, i.e. the fineness of detail
with which something is characterized; the notion always pertains, primarily if
not solely, to precision of specification along one or more parameters, hence to
the degree of restriction imposed on possible values along these parameters. A
schema is thus abstract relative to its elaborations in the sense of providing less
information and being compatible with a wider range of options. The differ-
ence is akin to that between representing a structure by plotting it on a fine grid
(where even minor features show up) and on a coarse grid (where only gross
features are preserved). Our cognitive ability to conceptualize situations at
varying levels of schematicity is undeniable. It is manifested, for instance,
linguistically in the existence of terms for superordinate as well as subordi-
nate terms. The linguistic significance of this ability is hard to overstate.
(Langacker 1987a: 132–35)
Schemas are constituted as such by virtue of their relationship to their elabo-
rations, the specific subcases that give the same information at a higher level of
detail. It does not make sense to call a concept a ‘‘schema’’ or say it is ‘‘schematic’’
schematicity 83
except in the context of specific cases relative to which it is abstract or whose
information it represents at a coarser level of detail. Similarly, it makes no sense to
speak of an ‘‘elaboration’’ except in the context of a concept which is schematic
for it.
All human concepts are schematic in some degree, abstracting away from the
differences in the particular experiences or thoughts on which they are based.

4
They ‘‘allow a range of variation rather than pinning things down to an exact value.
Without this inherent imprecision and the flexibility it affords, language could
hardly have become a viable instrument of thought and communication’’ (Lan-
gacker 1987a: 132–33). The ‘‘terminal nodes’’ or most specific concepts we can ex-
press are not different in kind, but only in degree, from the relatively abstract and
even very highly abstract concepts with which we think and which we commu-
nicate on a day-to-day basis.
Since schematicity is a relative matter and all concepts communicated lin-
guistically are schematic in some degree, it should not surprise us to find hierar-
chies of schematicity, with one concept schematic relative to others, but itself
serving as an elaboration of yet more highly schematic concepts. Thus, Langacker
gives tall ? over six feet tall ? about six feet five inches tall ? exactly
six feet five and one-half inches tall,orthing ? animal ? mammal ?
rodent ? squirrel ? ground squirrel,ormove ? locomote ? run ?
sprint (1987a: 132–35).
5
An arrow is used to graphically represent the schematicity relationship, with
the schema at the tail and its elaboration at the head of the arrow; thus ? can be
read as ‘is schematic for’, and / as ‘is an elaboration of’. At each step, alterna-
tive elaborations are possible; for instance, instead of locomote above we might
have had contract or wave or fall; instead of run we might have had walk or
crawl or (purposely) roll; instead of sprint we might have had jog or trot.
Note also that schematicity is a ‘‘transitive’’ concept, in the logical sense: A ? B
and B ? C logically necessitates that A ? C; thus move ? sprint and ground
squirrel / thing.
6
In sum, for Langacker any concept that abstracts away from differences among
similar subcases may be properly called a schema.
2.3. Lakoffian ‘‘Image Schemas’’

Lakoff rarely speaks of schemas in this general sense, but often uses the related term
‘‘image schema’’ (which he credits Langacker with helping to elucidate; Lakoff 1987:
68) in a more restricted sense.
Image schemas are relatively simple structures that constantly recur in our
everyday bodily experience: containers, paths, links, forces, balance, and
in various orientations and relations: up-down, front-back, part-whole,
center-periphery, etc. These structures [image-schematic together with ‘‘basic-
84 david tuggy
level’’] are directly meaningful, first, because they are directly and repeatedly
experienced because of the nature of the body and its mode of functioning in
our environment. (Lakoff 1987: 267–68)
These are certainly schemas in the Langackerian sense, but perhaps the only
characteristic necessary for making them so is that they are ‘‘relatively simple.’’ The
characteristics that draw Lakoff’s attention are things like their constant recur-
rence, their basis in bodily experience and thus their direct meaningfulness, their
gestaltish nature (1987: 272), their ‘‘preconceptual structuring’’ (292–93), their uni-
versality in human experience (302, 312), and their ubiquity in language use (272),
particularly as structuring concepts for the metaphors so central to human un-
derstanding (283). Thus, for Lakoff, image schemas are ‘‘central truths’’ (296).
Many, doubtless most, Langackerian schemas will not exhibit these qualities to any
high degree: there are multitudinous concepts in the minds of speakers of every
language under the sun which are simple relative to other concepts but recur
relatively rarely, are not based in bodily experience, are not directly meaningful, are
limited to one or a few cultures, and so on. They also are well worth investigating
and considering—Lakoff agrees, saying of such ‘‘noncentral truths’’ that ‘‘to me,
this is the most interesting kind of truth’’ (297).
In the rest of this chapter, we will follow the Langackerian definition. This is
not to discount in any way the importance of the concepts that Lakoff is exam-
ining, the subset of schemas which are in fact experientially basic, directly mean-
ingful, and so on. They are in fact the theme of Oakley (this volume, chapter 9). But

the commonality of these with all other direct abstractions is significant and worth
discussing.
2.4. The Ubiquity of Schematicity
As noted above, many particular schemas, under the Langackerian definition, are
far from universal. For instance, the concept of an opening, in chess-nuts’ usage, is
a schema including king-pawn and queen-pawn openings (along with such less
common ones as king’s knight or queen’s rook–pawn openings) and such
cross-classifying concepts as gambit; and each of these is schematic over many
different families of openings (e.g., queen-pawn opening ? queen’s gambit ?
queen’s gambit declined ? cambridge springs defense, etc.), and each of
these in turn has many subpatterns over which it schematizes. None of these
schemas can be expected to exist in all the world’s languages, much less among
all the speakers of all those languages (though, of course, as the culture of chess
spreads, they may be expected to spread with it).
What is ubiquitous in the world’s languages is this kind of relationship: that is,
schematicity itself. Every language will have some concepts which are relatively
specific and others which designate the same sort of entity but are less specific as to
details. The following discussion will serve to illustrate this contention.
schematicity 85
3. Schematicity and Similarity;
Full and Partial Schematicity

Schematicity relations arise when cognizers compare mental structures and per-
ceive similarities between them. The act of comparison is asymmetrical, comparing
a target structure to a standard. The resulting judgment of similarity or nonsimi-
larity can be thought of as a sort of vector relationship, in which the degree to which
the standard can be recognized in the target is a major parameter of magnitude
along which different comparisons may differ. The human cognitive apparatus is
apparently of such a nature that as this degree approaches complete recognition,
the system experiences a state of heightened excitation; we notice (whether con-

sciously or not) when the standard’s specifications are entirely preserved in the
target concept.
It follows for the same reasons that schematicity at a smaller elaborative dis-
tance, where the schema has many specifications which are recognized and the
target structure adds few details, is likely to be more salient (produce higher ex-
citation) than an elaboratively distant schematicity. Thus, for example, rodent ?
squirrel will naturally be a more salient schematicity relation than thing ?
squirrel.
Full schematicity (represented by the previously mentioned solid arrow from
standard to target, S ? T) occurs in just the case when all the standard’s features
are preserved in the target, that is, when there is 100 percent coincidence. When
there is not such full coincidence, where there is omission, contravention, or
distortion of the standard’s specifications, some degree of partial schematicity or
extension obtains (represented by a dashed-line arrow, S
"
T). Most comparisons,
obviously, yield judgments of partial rather than full schematicity; very many
involve so much distortion that there is little reason to talk of even partial sche-
maticity. But as they approach the limiting case of full schematicity, their cognitive
(and linguistic) importance increases.
7
Nothing prohibits a simultaneous or subsequent converse comparison, taking
the erstwhile target as standard and the erstwhile standard as target. When there is
partial schematicity in one direction, there may well be the same in the other (A
"
B and B
"
A may both obtain). Where there is full schematicity (A ? B), the
converse comparison predictably yields partial schematicity (B
"

A) except in
the limiting case of identity or correspondence, where each concept’s specifications
are fully exhibited in the other. Thus, since run ? sprint and the two concepts are
not identical, it is predictable that a converse comparison will yield the judgment
sprint
"
run: some of sprint’s specifications are omitted from run.
As mental comparisons and schematicity judgments of these sorts are repeated,
especially repeated saliently (forcefully), in a person’s thinking, they become en-
trenched in his or her mind, and their ease of reactivation is thereby enhanced. As
usage events that presuppose or even assert them occur, their conventionality is
86 david tuggy
established, and they become part of that subset of the person’s cognitive repertoire
which constitutes the language he or she shares with other speakers; see the dis-
cussion of entrenchment and salience in Schmid (this volume, chapter 5).
Consequently, nonlinguistic cognitive structures start to become linguistic as
soon as they are used as part of a phonological or semantic structure, that is, the
minute language users start to talk about or with them. They are unlike more cen-
tral structures only in their lesser degree of entrenchment and/or conventionali-
zation. (They cannot be conventionalized without being entrenched, though they
can be entrenched without being conventionalized.)
Langacker points out (1987a: 372–75) that any act of comparison which yields
a judgment of partial schematicity necessarily involves activation of the specifi-
cations that the compared entities have in common. To the extent that those
specifications form a coherent concept, it will tend to be schematic for both the
compared entities, and to the extent that it recurs, and especially as it proves
useful in other contexts, it will become cognitively entrenched and conven-
tionalized. In this way, the relationship A
"
B tends strongly to facilitate the

establishment of C, the schema subsuming A and B, in the cognitive network
which constitutes the language.
8
And, of course, the establishment of C facili-
tates its use for communicative purposes, which in turn establishes its conven-
tionality and further entrenches it. By repeated occurrences of this sort of pro-
cess, quite extensive and complex subnetworks can be built up (see section 4.1,
figure 4.3a).
Schemas have the important and paradoxical property of being immanent to
their elaborations. Since all the specifications of C are, by definition, fulfilled in A
and in B, whenever A or B is activated, C is being activated as well. (Any time
language users think or speak of a squirrel, they are thinking of or mentioning
a rodent,amammal,ananimal, etc.) Thus, the representation in figure 4.1b,
where the curved and dashed lines of correspondence indicate identity, is entailed by
4.1a. This renders obvious an awkwardness or inaccuracy of diagrams using the
arrow conventions. For analytic purposes, we are representing in separate boxes
(using the container metaphor, in fact), on a piece of paper, structures which are
not as discrete as the representation might suggest, whose link to each other is
much more like identity. It is important not to let this analytic convenience unduly
influence the way we understand the relationship. Langacker’s comments in chap-
ter 17, page 433, though prompted by the specific issue of polysemy, are apropos for
all schematic networks.
It is also important to remember that the arrows used in diagrams of this sort
are a notational summary over correspondences between the structures involved.
A more complete (and potentially more confusing) version of figures 4.1a and 4.1b
would be like figure 4.1c,
9
where specifications x, y, z, and q correspond in all three
boxes, but A and B have other specifications which are not matched in each other
or in C. For many purposes, notably for teasing out the specifics of blending

mechanisms (see section 4.12), it may be necessary to attend carefully to those
individual correspondences or noncorrespondences.
schematicity 87
4. Functions of Schemas in the
Cognitive Grammar Model

A number of phenomena which other theories treat in quite disparate ways are
claimed, within Cognitive Grammar, to be manifestations of schematicity. This
fundamental insight of Cognitive Grammar, that all these phenomena are, at bot-
tom, the same thing, affords a conceptual unification that is an attractive feature of
the model.
4.1. Categorization: ‘‘Classical’’
and Prototype-Based Categories
The relationship of schematicity is central to the characterization of categories of
any sort in the Cognitive Grammar model.
‘‘Classical’’ categorization (to use Taylor’s 1995: 21–37 term for it) has, since
Aristotle’s day, assumed categories with fairly rigid and predictable boundaries, in-
cluding all and only those structures which meet their definitions. They are defined
either by a single abstract characterization or, in some versions, by a combination of
abstract features. Thus, the category man (i.e., human) can be defined as consisting
of all and only featherless bipeds, or, nearly equivalently, all and only those entities
which exhibit the combination of features [–feathered] and [þbiped].
Figure 4.1. Extension tends to facilitate establishment of schemas
88 david tuggy
Such categories can be easily modeled using schemas. All that is necessary is to
restrict one’s attention to relations of full schematicity and ignore relations of
extension. Thus, in figure 4.2a, the relations of full schematicity from C to A and B
mean they are members of the classical category defined by C, while the relations of
partial schematicity from C to D and E mean they are not. In figure 4.2b, the two
schemas C and C' are the functional equivalents of features: each defines a classical

category, and A and B would be in the classical category defined by the overlap of
the two categories they define.
10
Classical categories have no gradations of membership: all members have equal
claim to their status as such (Taylor 1995: 24). This again can be modeled in, or read
off, structures such as those in figure 4.2. However, as Schmid indicates in chapter 5
(this volume), structures are expected under Cognitive Grammar to vary in their
degree of salience or cognitive prominence (i.e., the energy with which they occur
in the mind, generally closely paralleling the degree of their entrenchment). This
parameter of differentiation means that when a category is activated, some mem-
bers of it are likely to be more strongly or inevitably activated than others.
In our diagrams, we will represent differences of salience by increasing the
thickness of the box lines for cases of relatively high salience and by the use of
dashed lines for cases of relatively low salience. Thus, in figure 4.1, A is more salient
than B, which is more salient than C. Ignoring such differences, as the represen-
tation in figure 4.2 does, gives a ‘‘flat’’ structure like that assumed by classical cat-
egorizations; including them means that some members are more highly entren-
ched, and thus more salient, than others.
It is natural for comparisons to be made from what is familiar to what is less so;
it is therefore quite common for a strongly entrenched and highly salient concept
to anchor many relations of full or partial schematicity. In such cases, this strongly
entrenched concept serves as the center of a category constructed on the prototype
model (see Lewandowska-Tomaszczyk, this volume, chapter 6). By repeated ap-
plications of the process represented in figure 4.1, there may come to be a single
schema uniting the whole or a small number of schemas covering large overlapping
parts of the category, but they will tend not to be as salient as the prototype and will
thus be less important cognitively and linguistically. This will be despite the nat-
ural salience that they gain from the fact that the relationships they anchor are
Figure 4.2. Classical categories modeled by schemas
schematicity 89