relationships of full (as opposed to partial) schematicity. Figure 4.3a exemplifies this sort of structure, with P as prototype and S as highest-level schema. 11 By raising the threshold of salience in figure 4 .3 a to such a degree that the schemas in dashed-line and thin-line boxes are ignored, the structure in 4.3b will result. This structure is essentially equivalent (except for retaining the relatively salient schemas S 1 and S 4 and the elaborate structures h and i) to the prototype- based ‘‘radial’’ category structures proposed by Lakoff and others (Lakoff 1987: 84; Lewandowska-Tomaszczyk, this volume, chapter 6; note the common use of di- agrams such as the one in Aitchison 1990: 54). Categorization by schema and cat- egorization by prototype are, accordingly, not incompatible, but rather can be seen as different views of or readings off the same complex cognitive structures. Part of the nature of such structures as figure 4.3a is the possibility of layers of categories, the idea that higher-order categories and subcategories are natural in human cognition and thus in language. Positing a category which consists of S (with its subcases) does not preclude the existence or minimize the possible im- portance of such subcategories as S 3 , which in turn does not preclude or down- grade S 1 or S 2 , which in their turn do not by their existence eliminate or denigrate a and P, and so forth. Linguistic categories of all sorts, whether those in speakers’ minds or in lin- guists’, will be represented, under Cognitive Grammar, in these ways. An obvious kind of example are the semantic poles of lexical items (see note 11), where the complexity of the structure will be the record of the lexical item’s polysemy. Other linguistic categories will also fit the model, including syntactic categories with their subcategories and sub-subcategories, functional categories of all sorts, other seman- tically based categories besides the semantic poles of lexical items, phonological categories, and so on. This way of viewing categories gives ease to certain theoretical or analytic problems of long standing. As one example, the traditional, commonsensical def- Figure 4.3. A prototype in a schematic network 90 david tuggy inition of a noun as a word designating a ‘person, place, or thing’ has been rejected by many linguists because it would exclude many, even—if thing is understood in its prototypical sense of ‘(inanimate) physical object’—most, nouns. None of the four (or six) nouns in the first sentence of this paragraph fits the definition at all well, for instance. Many have therefore concluded that the category ‘noun’ can have no semantic basis, but must be characterized only in terms of the syntac- tic environments words are allowed to occur in (e.g., possible co-occurrence with the, ability to head a noun phrase which can be subject or object of a verb, etc.). 12 Assuming for the moment that this is true of the category as a whole (though another possibility is presented in section 4.2), it is quite possible under Cog- nitive Grammar to represent this in a schema. Syntactic behavior is, to be sure, an extrinsic rather than intrinsic quality of lexical items, much as the combina- tory behavior of chemicals is a quality extrinsic rather than intrinsic to them, but such extrinsic qualities can be a part of or practically make up the whole of the content of a schema. The syntactic nature of the extrinsic relations in this case does not make them different in kind from other extrinsic specifications. Given such a highest-level schema, it remains clear that under Cognitive Grammar it can per- fectly well coexist with a prototype or set of prototypical subcases, such as human being, spatial location (¼ place), and inanimate physical object, which presumably all would agree are defined on semantic grounds. The traditional def- inition ‘a person, place, or thing’ can therefore be seen as a good rough-and-ready approximation to or useful handle on the prototypical center of the category. One can see both why it worked as well as it did and why it was incomplete. One is forced neither to the intuitively dubious conclusion that the category has no se- mantic basis, nor to the clearly wrong claim that all nouns do, or should in prin- ciple, share all the semantic characteristics of the most prototypical ones. Figure 4.4 is an (obviously incomplete) representation of some of the concepts in the thing category and their relationships. 4.2. Superordinate Concepts and the Substantive Nature of Schemas Classical categories have sometimes been portrayed as by nature void of intrinsic content or substance, as constituted only by essentially arbitrary inclusions and exclusions. 13 Thus, in Figure 4.2a, the claim would be that from the point of view of linguistic theory there is, or at least need be, no commonality between A and B for them to be includable in a category C. The Cognitive Grammar claim is rather that, if there is a schema C which subsumes A and B, that schema must by definition include what is common to them, and will, to that extent, be substantive, having that nonarbitrary content. It is, of course, cognitively possible for an extremely heterogeneous category to be set up in which the only common quality is the highly schematicity 91 extrinsic and ad hoc quality of having been selected to be in the category: that selectedness would then be construed as the content of the schema C characterizing the class (see Langacker 1987a: 199–200). Doubtless, there are categories in which a comparably extrinsic specification is a part of the nature of C. The schema thing in figure 4.4 would, if characterized solely in terms of syntactic behavior, be such a category, and there are other kinds of categories defined by common syntactic behavior or morphological marking for which more intrinsic semantic character- izations are highly elusive. However, in the nature of things, such schemas will be less likely to be communicatively useful or easy to maintain as conventional over time. The vast majority of useful categories will have more specifications, and par- ticularly more intrinsic specifications, which characterize the commonality of the subcases and therefore will be part of the schema subsuming them. In short, al- though it is possible under Cognitive Grammar for completely arbitrary categories to be set up, they are very much the exceptional case, and substantive character- ization of the schemas defining important categories is a very important theoretical endeavor. Categories, then, are typically defined by schemas which express the com- monality of their subcases. Such schemas are precisely what are traditionally la- beled superordinate, or hyperonymous, concepts. As such concepts are named (linked symbolically to a phonological structure) to form lexical items; they will enter into lexical hierarchies such as those in sections 2.2 or 2.4. But other kinds of superordinate concepts that linguists use are also schematic in nature. For instance, consider the hierarchy consonant ? stop ? voiceless stop ? /p/ ? [p h ]. This, as it occurs in a linguist’s mind, fits the definition for Figure 4.4. The thing category 92 david tuggy a relationship of schematicity at each step. (Each step also corresponds to a cat- egory including other structures beyond just the one subcase represented, of course, but that is not the point here.) A major difference between such superordinate concepts as consonant or voiceless stop and those in a lexical hierarchy is that these, for many speakers, do not function as the semantic pole of any commonly used word or other lexical structure. However, they may function in other ways in the language, for instance as part of the structure of entrenched generalizations (rules). In any case, for the group that knows and uses the terms, the naming of them (as consonant, voiceless stop, etc.) makes them indeed the semantic pole of a lexical item. Metalanguage is language, and the meanings of its words are not different in kind from those of other words. 14 Schematic hierarchies can be posited for other concepts with a long history of linguistic utility. For instance, in a sequence such as Hilary Rodham Clinton / Woman’s Name / Name / Noun, 15 or be running / Continuous Action Verb / Imperfective Verb / Verb, the notions Woman’s Name, Name, and Noun, are superordinate concepts which might be posited by a linguist. If so, they are sche- mas occurring in the linguist’s mind, and, again, as soon as they are named they begin to be entrenched as semantic structures of the corresponding phonologi- cal (or graphical) forms, and as they become entrenched in other speakers’ minds, they become part of the language. They may also, however, correspond to structures already entrenched in speak- ers’ minds, and the more pervasive and useful ones are likely to be so. Linguists’ categories which do not correspond to speakers’ categories are a naturally occur- ring phenomenon that can be modeled in Cognitive Grammar, but only those which in fact do correspond to speakers’ categories are likely to be valuable for building the theory, enhancing our understanding of what is actually happening in speakers’ minds. Langacker has argued extensively (1987b, 1991: 13–50) that the meanings of the basic terms noun and verb can be characterized by schemas which are almost cer- tainly linguistically universal, grounded in the nature of our cognitive apparatus (thus image schemas of the Lakoffian type; see section 2.3). The cognitive schema for the semantic pole of noun (i.e., noun), which he calls thing, 16 is characterized as ‘‘a region in some cognitive domain,’’ where ‘‘region’’ is ‘‘a set of interconnected entities’’ (1987a: 189, 198; 1991 : 15). That of verb he characterizes as process, which involves tracking a relation or cognitive interconnection through conceived time. 17 Similarly, other ‘‘basic syntactic categories’’ would be characterized by high- level schemas, as in figure 4.5 (see Langacker 1987a: 249). Reference to these ca- tegories in more complex generalizations (e.g., syntactic rules; see section 4.3) will be a matter of reference to these schemas. Insofar as this view is correct, the ubiq- uity, if not universality, of these categories is accounted for, the different behavior of nouns and verbs reflects the differences in those cognitive constructs, and cases of referential overlap (e.g., where the same situation can be described by a noun and a verb) are allowed for. Langacker’s superschema entity, which perhaps may schematicity 93 be thought of as the semantic pole of the word concept, neutralizes the distinction between these and is schematic for them and every other cognitive structure one might wish to talk about. Whether one agrees with all the details of these proposals or not, it is clear that if these are to be viable theoretical constructs within Cognitive Grammar, they will have to be of this nature, that is, they will have to be schemas. What all this means is that under Cognitive Grammar, when we speak of nouns, verbs, modifiers, and so forth, or consonants, syllables, phonemes, and so on, we are not dealing with empty, arbitrary, node, or category labels. We are employing cognitive structures which, although highly schematic, consist of positive, substan- tial content which characterizes the essential commonality of the structures which elaborate them. 18 4.3. Generalizations: Rules, Patterns, and Constructions Superordinate concepts (the semantic poles of superordinate terms) are one kind of generalization, but there are many others. All of them will, under Cognitive Grammar, exist in the mind as schemas. Just about anything that is called a ‘‘rule,’’ a pattern,’’ or a ‘‘template’’ in other linguistic theories will be handled within Cognitive Grammar by positing a schema (or schemas). This will include syntactic rules, phonological rules, diachronic rules, semantic rules, syllabic or word-level or phrasal rules, lexical rules, morphological rules and templates, phonological tem- plates or patterns, case frames, and other such constructs. 19 For each of these, it will be in principle an empirical matter whether it actually forms part of speakers’ linguistic systems or not; if it does it will be a schema in speakers’ minds, other- wise only in the linguist’s. Figure 4.5. Schematic hierarchy of major syntactic classes 94 david tuggy For instance, the classic ‘‘phrase-structure rule’’ S ? NP VP (Chomsky 1957: 26, 111) can be viewed as an expression of a schematic relationship, where S would be the schema generalizing over sentences, NP VP would be the schema general- izing over sentences consisting of a subject and verb-phrasal predicate, and the arrow would be reinterpreted as representing the schematicity relationship itself. 20 NP VP is itself, of course, a high-level schema, which could be further elaborated by relatively specific patterns, such as those represented in figures 4.6a.ii and 4.6a.iii (of which only the latter is a pronounceable sentence, of course). 21 Simi- larly, for the classic ‘‘transformational rule’’ of Passive [NP i Aux V NP j ] " [NP j Aux be V-en by NP i ] (Chomsky 1957: 43, 112), one could posit schemas for the active and passive structures, but in this case certain specifications of the active structure are contravened by specifications of the passive structure. Therefore, the arrow connecting them would not be a solid arrow representing full schematicity, but rather a dashed arrow of partial schematicity or extension; that is, the rule would be something like 4.6b.i. As in the other case, this schema can be elaborated by more specific structures such as 4.6b.ii and 4.6b.iii, of which only the latter is a pronounceable sentence. Although these and other ‘‘rules’’ can be expressed as schemas, some im- portant differences between these schemas and other theories’ rules need to be emphasized. a. There is no presumption that schemas must, should, or will be in any way absolute or exceptionless. A schema generalizes over the cases it generalizes over, and the fact that there may be similar structures that contravene its specifications is neither surprising nor problematic. There is only a difference in degree, not a difference in kind, between ‘‘major’’ and ‘‘minor rules’’; there is neither reason nor expectation that a class of exceptionless generalizations should exist, much less that it should form a coherent subpart of a language, amenable to description apart from the more normal schematic structures. Exceptionless generalizations are not ipso facto more important in the language than those that do have exceptions. b. Many have thought that once a rule (generalization) was made, the par- ticulars were thereby rendered redundant and theoretically objectionable and should be excised from the grammar. In the 1960s and 1970s, when simplicity was almost universally held up as the indispensable criterion for deciding between competing models, the phrase ‘‘listing the particu- lars means losing the generalization’’ became almost a mantra. Cognitive Grammar emphatically states that if the particulars are learned (entrenched and conventional), they are part of the language and cannot be omitted from a complete description, regardless of whether they could be predicted or built starting from other structures. In fact, all things being equal, lower- level generalizations (at least down as far as a relevant basic level; see Schmid, this volume, chapter 5) are more likely than high-level schemas to schematicity 95 be cognitively useful and therefore entrenched. This, together with the natural salience of elaboratively close schematic relationships (see section 3) has the result that high-level schemas (and categories) can be expected, a priori, not to be as salient in speakers’ minds as low-level schemas (and their categories). In this way, the configuration of figure 4.2a is typical. Schemas do not, in general, explain away their elaborations. It is not the case that the schema is the linguistically ‘‘real’’ or ‘‘basic’’ element and the elaboration (necessarily) only contingent, computed, or derived but not itself part of the linguistic system. c. One aspect of this refusal to give unquestioned pre-eminence to schemas is that rules couched in the ‘‘process metaphor’’ fit at best uncomfortably within Cognitive Grammar. To say that A ‘‘becomes’’ B, ‘‘is rewritten as’’ B, and so on, while not impossible within Cognitive Grammar, makes it hard to see B as other than contingent, completely dependent for its ex- istence on the more ‘‘basic’’ A. Such a relationship should not be assumed unless good reason can be found for it. d. As previously observed, generalizations which exist in linguists’ minds but are not entrenched in other people’s cognitive systems are at best mar- ginally part of the language. The fact that a rule may elegantly cover and in some degree account for a large amount of data does not of itself guar- antee it a place in the grammar. e. Schemas which are part of the language are (it has been claimed) subject to the content requirement (Langacker 1987a: 53 –54): they either must be themselves directly used in linguistic expressions or they must be fully schematic for structures that are. Thus, linguists’ generalizations that vi- olate this constraint are, if Cognitive Grammar is right on this point, not linguistic in the sense of being part of the language. This is related to the contention urged in section 4.2 that schemas are substantive. Figure 4.6. Syntactic rules as schemas 96 david tuggy Among the types of rules and templates posited by linguists, the constructions of the construction-grammar approaches (Croft 2001; this volume, chapter 18)show an especially close affinity to the Cognitive Grammar conception of syntactic (and other) rules. Constructions are clearly schemas, and Cognitive Grammar can be classed as a kind of construction grammar (Langacker, this volume, chapter 17, section 1; Croft, this volume, chapter 18, section 5.3). 4.4. Interpretation of Classes: Coherence and the Gradation between One and Two As emphasized above, schemas do not explain away their elaborations. One aspect of this is that a structure may perfectly well elaborate more than one schema at the same time. In other words, it may be a member of more than one category or an example of more than one rule or pattern, and to have found a rule that accounts for it or a category that includes it does not mean that it is thereby fully charac- terized or accounted for. And, diachronically, new schemas, implying new simi- larities, can be extracted from particular elaborate structures that are already es- tablished as subcases of older schemas. This is a point on which schematic hierarchies such as the one represented in figure 4.4 differ from taxonomic hierarchies, which they resemble and with which they have sometimes been confused. In a well-behaved taxonomic hierarchy, the lines from superordinate to subordinate categories do not cross, and each daughter category has only one mother category. Once bats, butterflies, and bullfinches have been classified into the three different categories of mammal, insect, and bird, it is superfluous and even objectionable to introduce a cross- cutting category of fliers into the classification scheme. In Cognitive Grammar, it is entirely natural. If speakers of a language do indeed make (and conventionalize) a cross-cutting generalization, that generalization is a schema, and a complete description of the language must include it. Investigation indicates that overlapping, cross-cutting categorial structures like that of figure 4.4 are extremely common. The hierarchy in figure 4.5, for instance, leaves out an important schema atemporal entity, which would cross-classify thing and atemporal relation together, in contrast to process. And, of course, the lower reaches of that schematic network can be expected to have many cross-classifying schemas, such as those in the thing subcategory as already represented in figure 4.4. Further, Langacker argues (1987a: 258–61) that important schemas unite the countable thing schema with the perfective process subcategory of verbs, and mass thing with imperfective process. These cross-cutting classificatory schemas are represented in figure 4.7. One kind of classification which traditionally was expected to manifest such cross-categorization was classification by features (see the discussion of figure 4.2b). In theory, all values of all features might be expected to coincide in particular subcategories, and at times substantial weight was given to the theoretical beauty schematicity 97 or economy of an analysis which utilized all the possibilities. Thus, two binary features could be expected to define four subclasses, and three would define eight (2 3 ) subclasses. Such cases can easily be modeled by schematic hierarchies, but the concept of the schematic hierarchy does not lead one to expect a priori that all combinations must occur. If a particular subcase can be shown to be established, and it elaborates more than one schema, that is fine, but the fact that two schemas might coincide in some subcase does not mean that they necessarily do so. So in figure 4 .7 , one might logically expect there to be subcases of the atemporal re- lation schema which would manifest the bounded-unbounded distinction so prominent in the thing and process categories, but there is under Cognitive Grammar no strong pressure for this to be the case. All of this leads to the observation that schema-based classifications typically rather than exceptionally involve interpenetrating classes, and a classification that is rendered salient in one context may be backgrounded and another emphasized in a different context. The term ‘‘network’’ is a natural one for describing a col- lection of schematic-elaborative relationships because it suggests this interpen- etration and multiplicity of relationships. A category achieves coherence ‘‘to the extent that its members are densely linked by categorizing relationships [i.e., full or partial schematic-elaborative relationships] of minimal distance’’ (Langacker 1987a: 388). But coherence is a matter of degree. A lexical item, for instance, is a kind of coherent category, existing ‘‘to the extent that a semantic network with common symbolization approximates a coherent category the definition al- lows a single network to be divided into lexical items in multiple and mutu- ally inconsistent ways. I regard this as a realistic characterization of the phenomena in question’’ (388). This grading of categories into each other, combined with differences of sa- lience among the cohering structures, allows for a gradual rather than an abrupt Figure 4.7. Fuller hierarchy of major syntactic classes 98 david tuggy distinction between a single category and two or more separate categories. The gradation represented in figure 4.8 has been used to represent the gradation be- tween ambiguity (two separate, noncohering meanings; figure 4.8e) via polysemy (separable but coherent meanings; figure 4.8c) to vagueness (one coherent mean- ing; figure 4.8a) (see also Tuggy 1993; Lewandowska-Tomaszczyk, this volume, chapter 6), but it finds application in many other areas of linguistic categoriza- tion as well. 22 In particular, diachronic changes involving a single category (figure 4.8a) splitting into two (figure 4.8e)—or two categories converging into one—are easily represented as gradual under such a model. 4.5. Sanction: the Mechanism of Generativity An important insight of Cognitive Grammar is that the schematicity relation- ship confers legitimacy, that to the extent that a schema is a legitimate (entrenched and conventionalized) part of the grammar of a language, its subcases are sanc- tioned by it and share in its legitimacy. More technically, (i) sanction varies directly with the degree of conventional entrenchment of the schema; (ii) a relationship of full schematicity provides full, or direct sanction, but relationships of partial sche- maticity provide only weaker, partial sanction (whose strength increases as the re- lationship approaches full schematicity); and (iii) the strength of sanction also varies inversely with the elaborative distance (see section 3) between the schema and the subcase (Langacker 1987a: 66–71). Any structure sanctions itself to the degree that it is established in the language—i.e., that it is entrenched and conventionalized (point (i) above). It le- gitimizes itself fully (point (ii) above), and it does so at the minimum possible elaborative distance, namely zero (point (iii) above). If another well-established structure is schematic to it, the self-sanctioning structure receives additional sanc- tion from that relationship, making it even more firmly a part of the language. Often, however, speakers will construct novel structures, which, since they are not conventionally entrenched, are not self-sanctioning. Such nonestablished structures will be judged as well formed to the degree that they are sanctioned by structures that are well established. Figure 4.8. The gradation between one and two (by way of three) schematicity 99 . seen as different views of or readings off the same complex cognitive structures. Part of the nature of such structures as figure 4.3a is the possibility of layers of categories, the idea that higher-order. represented, under Cognitive Grammar, in these ways. An obvious kind of example are the semantic poles of lexical items (see note 11), where the complexity of the structure will be the record of the lexical. can be a part of or practically make up the whole of the content of a schema. The syntactic nature of the extrinsic relations in this case does not make them different in kind from other extrinsic