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As an introduction, I want to contrast two approaches to formal semantics: one realistic and one cognitive. The fundamental difference concerns what kind of entities are the meanings of words. According to the realistic approach to semantics the meaning of an expression is something out there in the world. Cognitive semantics, on the other hand, identifies meanings of expressions with mental entities.
Realistic semantics comes in two flavors: extensional and intensional. In the extensional type of semantics, one starts out from a language L, which may or may not be defined in formal terms, and maps the constitutents of L onto a "world." Names are mapped onto objects, predicates are mapped onto sets of objects or relations between objects, etc. By compositions of these mappings, sentences end up being mapped onto truth values. The main objective of this kind of semantics is to determine truth conditions for the sentences in L. A consequence of this approach is that the meaning of an expression is independent of how individual users understand it.
As an account of natural language, the extensional theory of reference implicit in this kind of semantics was soon found to be wanting. In order to handle some of the problems, so called intensional semantics was developed by philosophers, logicians and linguists. In this kind of semantics, the language L is mapped onto a set of possible worlds instead of only a single world. Still, the goal of the semantics is to provide truth conditions for the sentences in L. The meaning of a sentence is taken to be a proposition, which is identified with a set of possible worlds - the set of worlds where the sentence is true. The classic form of this semantics is Kripke's (1959) semantics for modal logics. With respect to natural language, Montague's (1974) work has provided a lot of inspiration for intensional semantics.
The second paradigm of semantics is cognitivistic. The core idea of this approach is that meanings of expressions are mental. A semantics is seen as a mapping from the linguistic expressions to cognitive structures. Language itself is seen as part of the cognitive structure, and not an entity with independent standing. Within cognitive semantics the emphasis is on lexical meaning rather than on the meaning of sentences. This kind of semantics will be presented further in the following section.
It is interesting to note that if de Saussure is read properly, he proposes a cognitive analysis of the signification relation. The following excerpt from the first paragraphs of the first chapter illustrates this (de Saussure 1966: 65-66):
"for some people a language, reduced to its essentials, is a nomenclature: a list of terms corresponding to a list of things. [ ] This conception is open to a number of objections. It assumes that ideas already exist independently of words [ ]. It does not clarify whether the name is a vocal or psychological entity [ ]. Furthermore, it leads one to assume that the link between a name and a thing is something quite unproblematic, which is far from being the case. None the less, this naive view contains one element of truth, which is that linguistic units are dual in nature, comprising two elements.
[ ] the two elements involved in the linguistic sign are both psychological and are connected in the brain by an associative link. This is a point of major importance.
A linguistic sign is not a link between a thing and a name, but between a concept and a sound pattern."
However, it should be emphasized that even if de Saussure presents concepts as major elements in his definition of a sign, it does not follow that he would have endorsed the cognitive approaches to semantics and grammar that have been developed during later years.
My first aim in this paper is to present some of the main tenets of cognitive semantics. I will contrast these tenets with traditional types of semantics, but my goal is not primarily to criticize these kinds of semantics. In the third section, I will present the bare bones of a formal cognitive semantics.
One limitation of cognitive semantics as it has developed is that it focuses on individuals' meanings of words. However, there are several social aspects of language that should also be accounted for within a cognitivistic program, and in the fourth section, I will depart from an example of Putnam's for a discussion of how a social meaning can be determined on the basis of individual meanings.
I shall give a programmatic presentation of cognitive semantics in the form of six tenets together with some comments. The approach of a cognitively oriented semantics will be contrasted with the "realistic" view. Prime examples of works in the cognitive tradition are Lakoff's (1987) and Langacker's (1987). Related versions of cognitive semantics can be found in the writings of Jackendoff (1983, 1990), Fauconnier (1985), Talmy (1988), Sweetser (1990) and many others. There is also a French semiotic tradition, exemplified by Desclés (1985) and Petitot-Cocorda (1985), which shares many features with the American (mainly Californian) group.
I. Meaning is conceptualization in a cognitive model (not truth conditions in possible worlds).
The prime slogan for cognitive semantics is: Meanings are in the head. More precisely, a semantics for a language is seen as a mapping from the expressions of the language to some mental entities. A consequence of the cognitivist position that puts it in conflict with many philosophical semantic theories is that no form of truth conditions of an expression is necessary to determine its meaning. The truth of expressions is considered to be secondary, since truth concerns the relation between the mental structure and the world. To put it tersely: Meaning comes before truth.
II. Cognitive models are mainly perceptually determined (meaning is not independent of perception).
Since the cognitive structures in our heads are connected to our perceptual mechanisms, directly or indirectly, it follows that meanings are, at least partly, perceptually grounded. This, again, is in contrast to traditional realistic versions of semantics which claim that since meaning is a mapping between the language and the external world (or several worlds), meaning has nothing to do with perception.
We can talk about what we see and hear. Conversely, we can create pictures, mental or real, of what we read or listen to. This means that we can translate between the visual form of representation and the linguistic code. A central hypothesis of cognitive semantics is that the way we store perceptions in our memories has the same form as the meanings of words.
III. Semantic elements are based on spatial or topological objects (not symbols that can be composed according to some system of rules).
In contrast to the Mentalese of Fodor and others, the mental structures applied in cognitive semantics are the meanings of the linguistic expressions; there is no further step of translating conceptual structure to something outside the mind. Furthermore, instead of being a symbolic system having syntactic structure like Mentalese, the conceptual schemes that are used to represent meanings are often based on geometric or spatial constructions.
As a framework for a geometric structure used in describing a cognitive semantics, I have proposed (Gärdenfors 1988, 1991, to appear a, to appear b, to appear c) the notion of a conceptual space. A conceptual space consists of a number of quality dimensions. Examples of quality dimensions are: color, pitch, temperature, weight, and the three ordinary spatial dimensions. Some of the dimensions are closely related to what is produced by our sensory receptors, but there are also quality dimensions that are of an abstract non-sensory character.
The notion of a dimension should be understood literally. It is assumed that each of the quality dimensions is endowed with certain topological or metric structures. For example, "time" is a one-dimensional structure which we conceive of as being isomorphic to the line of real numbers. Similarly, "weight" is one-dimensional with a zero point, isomorphic to the half-line of non-negative numbers. Some quality dimensions have a discrete structure, i.e., they merely divide objects into classes, e.g., the sex of an individual.
Some of the quality dimensions seem to be innate and to some extent hardwired in our nervous system, as for example color, pitch, and probably also ordinary space. Other dimensions are presumably learned. Learning new concepts often involves expanding one's conceptual space with new quality dimensions. Functional properties used for describing artifacts may be an example here. Still other dimensions may be culturally dependent. "Time" is a good example - in contrast to our linear conception of time, some cultures conceive of time as circular so that the world keeps returning to the same point in time, and in other cultures it is hardly meaningful at all to speak of time as a dimension. Finally, some quality dimensions are introduced by science (see Gärdenfors 1993b).
There is a strong similarity between the notion of a conceptual space and the domains as used in Langacker's (1987) semantic theory. The following quotation from Langacker (1987: 5) concerning his notion of "domains" strongly supports this thesis:
"What occupies the lowest level in conceptual hierarchies? I am neutral in regard to the possible existence of conceptual primitives. It is however necessary to posit a number of 'basic domains,' that is, cognitively irreducible representational spaces or fields of conceptual potential. Among these basic domains are the experience of time and our capacity for dealing with two- and three-dimensional spatial configurations. There are basic domains associated with various senses: color space (an array of possible color sensations), coordinated with the extension of the visual field; the pitch scale; a range of possible temperature sensations (coordinated with positions on the body); and so on. Emotive domains must also be assumed. It is possible that certain linguistic predications are characterized solely in relation to one or more basic domains, for example time for (BEFORE), color space for (RED), or time and the pitch scale for (BEEP). However, most expressions pertain to higher levels of conceptual organization and presuppose nonbasic domains for their semantic characterization."
IV. Cognitive models are primarily image-schematic (not propositional). Image-schemas are transformed by metaphoric and metonymic operations (which are treated as exceptional features on the traditional view).
The most important semantic structure in cognitive semantics is that of an image schema. Image schemas have an inherent spatial structure. Lakoff (1987) and Johnson (1987) argue that schemas such as "container," "source-path-goal" and "link" are among the most fundamental carriers of meaning. They also claim that most image schemas are closely connected to kinesthetic experiences.
Metaphors and metonymies have been notoriously difficult to handle within realist semantic theories. In these theories such linguistic figures have been treated as a deviant phenomenon that has been ignored or incorporated via special stylistic rules. In contrast, they are given key positions within cognitive semantics.
V. Semantics is primary to syntax and partly determines it (syntax cannot be described independently of semantics).
This thesis is anathema to the Chomskian tradition within linguistics. Within Chomsky's school, grammar is a formal calculus, which can be described via a system of rules, where the rules are formulated independently of the meaning of the linguistic expressions. Semantics is something that is added, as a secondary independent feature, to the grammatical rule system. Similar claims are made for the pragmatic aspects of language.
Within cognitive linguistics, semantics is the primary component (which, in the form of perceptual representations, existed before language was fully developed). The structure of the semantic schemas puts constraints on the possible grammars that can be used to represent those schemas. To give a trivial example of how semantics constrains syntax, consider the role of tenses. In a Western culture where time is conceived of as a line, it is meaningful to talk about three basic kinds of time: past, present and future. This is reflected in the grammar of tenses in most languages. However, in cultures where time has a circular structure, or where time cannot be given any spatial structure at all, it is not meaningful to make a distinction between, say, past and future. And there are languages which have radically different tense structures, which reflect a different underlying conceptual structuring of time.
The Chomskian tradition within linguistics has been dominated by syntactic studies. Since grammars are represented by formal rules, they are suitable for computer implementations. This kind of work has indeed been the main focus of computational linguistics.
Within cognitive semantics, computer friendly representations are much more rare. One notable exception is Holmqvist (1993, 1994, to appear), who develops implementable representations of image schemas and other concepts from the cognitive linguists. To some extent, he is inspired by Langacker's compositional image schemas and Lang's spatial models (see Lang, Carstensen and Simmons 1991), but he extends their formalisms to a much richer computational structures. In his (1994), he also utilizes an old idea of Behaghel to generate grammatical structure solely from the valence expectations of different lexical items. The result is something that looks like a rule-governed syntax, albeit there is no single explicit syntactic rule in the system.
VI. Concepts show prototype effects (instead of following the Aristotelian paradigm based on necessary and sufficient conditions).
The classical account of concepts within philosophy is Aristotle's theory of necessary and sufficient conditions. However, one very often encounters problems when trying to apply the Aristotelian theory to concepts represented in natural language. As a result of a growing dissatisfaction with the classical theory of concept theory, prototype theory was developed within cognitive psychology.
Within cognitive semantics, one attempts to account for prototype effects of concepts. A concept is often represented in the form of an image schema and such schemas can show variations just like concepts normally do. This kind of phenomenon is much more difficult to model using traditional symbolic structures.
Here, I will only outline the first steps in developing a cognitive semantics based on conceptual spaces. According to the cognitive view, semantics is a relation between langauge and a cognitive structure, and I submit here that the appropriate framework for the cognitive structure is a conceptual space. On this assumption, formulating a semantics for a specific language can be broken down into two major steps: (1) To specify the mapping between the lexicon of the language and the appropriate conceptual spaces. (2) To describe the operations on the image schemas (which are defined with the aid of the conceptual space) that correspond to different syntactic formation rules. In this section, I will discuss only the first step.
Following the technical style of philosophical semantics, one can define an interpretation for a language L as a mapping of the components of L onto a conceptual space. As a first element of such a mapping, individual names are assigned vectors (i.e., points in the conceptual space) or partial vectors (i.e., points with some arguments undetermined). In this way each name (referring to an individual) is allocated a specific color, spatial position, weight, temperature, etc. Following Stalnaker (1981: 347), a function which maps the individuals onto a conceptual space will be called a location function.
The fundamental lexical hypothesis is then the following: Predicates in natural languages generally denote connected regions in some conceptual space. For instance, I conjecture that all color terms in natural languages express connected regions with respect to the psychological representation of the three color dimensions. It is well-known that different languages carve up the color circle in different ways, but all carvings seem to be done in terms of connected sets.
Technically, as a second element of the interpretation mapping, the basic predicates of the language are assigned regions in the conceptual space. Such a predicate is satisfied by an individual only when the location function locates the individual at one of the points included in the region assigned to a predicate.
Some of the so called intensional predicates, like "tall," "former" or "alleged," are not basic, but "secondary" in the sense that their regions cannot be described independently of other predicates. There is no class of all "tall" objects. Rather, "tall" requires a contrast class, like "tall woman" or "a tall tower" in order to be well defined. In Gärdenfors (to appear c), I provide an analysis in terms of conceptual spaces of the role of contrast classes in determining the reference of certain such secondary predicates.
If we assume that an individual is completely determined by its set of properties, then all points in the conceptual space can be taken to represent possible individuals. On this account, a possible individual is a cognitive notion that need not have any form of reference in the external world. This construction will avoid many of the problems that have plagued other accounts of possible individuals. A point in a conceptual space will always have an internally consistent set of properties - since e.g., "blue" and "yellow" are disjoint predicates in the color space, it is not possible that any individual will be both blue and yellow (all over). There is no need for meaning postulates in order to exclude such contradictory predicates.
One important contrast to the traditional intensional semantics is that the cognitive semantics outlined here does not presume the concept of a possible world. However, different location functions describe alternative ways that individuals may be located in a conceptual space. Consequently, these location functions can be given the same role as possible worlds in the traditional semantics. This means that we can define the notion of a possible world as a possible location function and this can be done without introducing any new semantical primitives to the theory.
A heavy attack against the very possibility of cognitivistic semantics has been launched by Putnam (1975, 1988). He contends that meanings can't be in the head. His argument starts from the following assumptions about meaning and mental representations, all of which seem to be accepted by the cognitive semanticists (Putnam 1988: 19):
1. Every word the speaker uses is associated in his mind with a certain mental representation.
2. Two words are synonymous (have the same meaning) only when they are associated with the same mental representation by the speakers who use those words.
3. The mental representation determines what the word refers to, if anything.
Putnam claims that these three conditions cannot be simultaneously satisfied. The reason is that we "cannot individuate concepts and beliefs without reference to the environment" (1988: 73). A central part of his argument can be illustrated by the following example (Putnam 1975: 226-227):
"Suppose you are like me and cannot tell an elm from a beech tree. We still say that the extension of 'elm' in my idiolect is the same as the extension of 'elm' in anyone else's, viz., the set of all elm trees, and that the set of all beech trees is the extension of 'beech' in both of our idiolects. Thus 'elm' in my idiolect has a different extension from 'beech' in your idiolect (as it should). Is it really credible that this difference in extension is brought about by some difference in our concepts? My concept of an elm tree is exactly the same as my concept of a beech tree (I blush to confess). (This shows that the identification of meaning 'in the sense of intension' with concept cannot be correct, by the way). [ ] Cut the pie any way you like, meanings just ain't in the head!"
The upshot seems to be that meanings must refer to something non-cognitive. A related argument has been presented by Burge (1979).
In my opinion, the lesson to be learned from Putnam's argument is not that cognitive semantics is impossible, but that it has generally forgotten about the social structure of language. In Gärdenfors (1993a), I argue that the social meanings of the expressions of a language are indeed determined from their individual meanings, i.e., the meanings the expressions have for the individuals, together with the structure of linguistic power that exists in the community. In contrast to Putnam and others, I claim that no reference to the external world is needed to handle the problem he presents.
The question of linguistic power concerns who decides on what is the "correct meaning" of an expression in a society. In other words, who are the masters of meaning? Given some rather weak assumptions concerning how the meaning of a word is determined, it can be shown that there are two basic types of power structures: oligarchial and democratic. An oligarchial (or dictatorial) power structure would arise when the social meanings of words are determined by a group of linguistic experts writing dictionaries, encyclopedias, handbooks, etc. When a language user is in doubt about the meaning of a locution that falls under the realm of the oligarchy, he would rely on the judgments of these experts.
In contrast, a democratic power structure would control those parts of the language where linguistic meaning is identified with "common usage." For such parts of the language, a dictator or a small group of speakers cannot, by themselves, change the meaning of an expression; for this, the consent of almost all language users is required. This is analogous to prices in a free market - a single agent cannot decide to change the price of a good.
I do not claim that all parts of the semantics of a language are governed by the same power structure. A more realistic description is to say that a language is a conglomerate of several sublanguages, each with its own conditions of linguistic power. The semantics of the language of lawyers is determined by criteria that are different from those of the language of entomologists; which in turn are different from those used for slang expressions. For lawyers' and entomologists' expressions, the power structures may very well be oligarchial, while the use of slang is a more democratic business. In support of this, it seems as if hedge words like "technically" can be used for expressions that are governed by an oligarchial power structure, but not for those the meaning of which are determined democratically: "Technically, a spider is not an insect" is correct, but "Technically, a hooker is a prostitute" sounds odd.
Putnam (1975: 227-229) describes something very much like an oligarchial power structure in his hypothesis about the "division of linguistic labor." This hypothesis maintains that every linguistic community "[ ] possesses at least some terms whose associated "criteria" are known only to a subset of the speakers who acquire the terms, and whose use by the other speakers depends upon a structured cooperation between them and the speakers in the relevant subsets" (1975: 228).
He claims that the hypothesis accounts for the failures of the assumptions that knowing the meaning of a locution is just a matter of being in a certain psychological state and that the meaning of a term determines its extension. Putnam's argument for this is that "[w]henever a term is subject to the division of linguistic labor, the "average" speaker who acquires it does not acquire anything that fixes its extension. In particular his individual psychological state certainly does not fix its meaning; it is only the sociolinguistic state of the collective linguistic body to which the speaker belongs that fixes the extension" (1975: 229). The last remark indicates that Putnam thinks of the fixation of social meaning in much the same way as in my analysis. However, it seems as if he misses the possibility of democratic power structures, which is a different way of determining social meaning.
In a more recent book, Putnam (1988) also discusses "conceptual role" semantics, in particular in relation to natural-kind terms. He argues that the meaning of such terms cannot be given in terms of their conceptual roles only, but "once we have identified a word as a natural-kind term, then we determine whether it is synomous with another natural-kind term primarily on the basis of the extensions of the two words" (1988: 50). Here, extension is, of course the set of things in the world that the word applies to. So natural-kind terms presume a realistic component for their semantics according to Putnam.
But, how do we know when something is a natural-kind term? Putnam is aware of the problem:
"Some words which were intended to be natural-kind terms turn out not to refer to natural kinds. "Phlogiston" was intended to be the name of a natural kind, but it turned out that there was no such natural kind. And similarly for "ether" and "caloric". In these cases it does seem that something like conceptual role is the dominant factor in meaning, for obvious reasons; we don't want to say that the words "ether" and "caloric" and "phlogiston" are synonomous just because they have the same (empty) extension. [ ] Indeed the conceptual role theory comes closest to being true in the case of words with an empty extension." (1988: 50)
However, here he seems to rely on some form of realist essentialism. If "phlogiston" could turn out not to be a natural-kind term, so can "water" and "gold," unless one assumes that natural kinds exist independently of language and cognition. And this is the kind of essentialist assumption Putnam needs to make in order to argue against the cognitive approach. But this is putting the cart before the horse: He assumes that a term is defined in terms of realist notions in order to show that it cannot be given a purely conceptual meaning.
In contrast to Putnam, I claim that the meaning of natural-kind terms like "gold" and "water" do change because of changes in the linguistic power structure (see Langacker (1987: 154-166)). I believe that this kind of meaning change is common in science in connection with scientific revolutions. For example, before the Copernican revolution "the earth" meant something that did not move, and before Einstein "mass" was something that was constant of an object. Perhaps even clearer examples are found in the social sciences. In particular Foucault's "archeological" investigations of the terminologies in various areas ("madness" for instance) show how modifications in the power structure in a society can result in radical changes of the language.
Let me finally turn to another aspect of semantics that, in my opinion, requires taking social interactions into account. From the early works of Kripke and on, one of the major successes of intensional semantics was that it provided a formal semantics for modal expressions. However, the modals being analysed were of an abstract philosophical nature and hardly any attention was paid to linguistic data about modal expressions.
Within cognitive semantics, there are now several works on modals, where perhaps Talmy's (1988) work on "force dynamics" and Sweetser's (1990) extension to the "epistemic" use of modals have been the most influential. In Talmy's analysis, physical forces are seen as more fundamental than the social for describing the semantics of modals. By metaphorical extension, the expressions used to express physical forces are used in the "psychological, social, inferential, discourse, and mental-model domains of reference and conception" (Talmy 1988:49, the abstract).
In a recent study (Winter and Gärdenfors 1994), a cognitive semantics (or rather pragmatics) is proposed that covers the whole field of (Swedish) modal verbs. In contrast to Talmy's physically oriented forces, the basic notions in the analysis are, firstly, the power relations between the speaker and the hearer (and sometimes a third party), and secondly, the expectations of the actors with respect to the action governed by the modal verb.
In the analysis of Winter and Gärdenfors (1994), the central elements of the speaker's and the listener's mental representations are the social power relations that hold between various agents. The objects of power are actions, for example the action of blasting a safe. I can blast it myself, but if I have power over you, I can also command you to do it. The second important factor of a speech situation is the agents' attitudes to the relevant actions. For example, I may want to blast the safe, while you may want that this action not be performed.
To give an example of how these notions are applied to modals, let us consider the expression "want to p," where p is an action. The expression occurs typically when the speaker wants p but is uncertain whether the hearer has the same attitude. Thus, if the speaker is the subordinate of the two, and the hearer the one in power, the speaker can say "I want to p" to mark his attitude and to signal that he is uncertain of the hearer's attitude. Or, in the reverse power relation, the speaker can, instead of directly exerting his power, say "Do you want to p?" when he expects that the hearer does not know his attitude. The speaker will then, by conversational implicature, expect that the hearer will understand the speaker's attitude (and, consequently, perform the action p).
Another example is the use of "shall." The typical use of this modal occurs in situations where the speaker is in power, when the speaker wants p, he expects that the hearer does not want p, and he does not expect the hearer to have a correct expectation of his, i.e., the speaker's, attitude. In this situation, "You shall p!" is used to inform the hearer about the speaker's attitude, and to remind him of the power relation.
Thus, also this analysis of modal expressions is an example of a cognitive model containing a social element. In brief, it is proposed that the primary meaning of modals is to express power relations.
Within the philosophical tradition, earlier analyses of modal expressions have, almost exclusively, been based on possible worlds and relations between worlds as semantic primitives. Indeed, the first modal notions to be analysed were those of necessity and possibility. However, there is nothing in the structure of possible worlds semantics that is suitable for describing social power relations, but such features must be added by more or less ad hoc means.
Cognitive semantics is still rather undeveloped. Its most detailed applications have been areas where language is tightly connected to perception, as for example in spatial prepositions. Cognitive semantics has also offered new insights in the mechanisms of metaphors. Its strength lies mainly in the analysis of lexical items, even though there are interesting attempts to explain syntactic features by cognitive means (e.g., Langacker 1987, Holmqvist 1993, 1994).
In this paper, I have tried to summarize the foundations of cognitive semantics in the form of six general tenets and I have presented the skeleton of a formal cognitive semantics based on conceptual spaces. This kind of semantics has been put in contrast to the more traditional extensional and intensional types of semantics.
Putnam has argued that a pure cognitive semantics, which puts meanings in the heads of individual speakers, is impossible. I have attempted to refute his arguments by pointing out that if the social aspects of language, in particular different kinds of power relations, are taken into account, Putnam's arguments are no longer valid.
There are areas where traditional semantics is strongly developed and where cognitive semantics is weak, for example, quantifiers and modal expression. However, I have presented a recent undertaking to supply a cognitive analysis of modals, again in a social setting including power relations. Furthermore, a cognitively oriented analysis of quantifiers has recently been proposed by Moxey and Sanford (1993).
Research for this paper has been supported by the Swedish Council for Research in the Humanities and Social Sciences. The second and third sections draw partly on Gärdenfors (to appear b), and section 4 borrows an argument from Gärdenfors (1993a).
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