The elements from which propositional thought is constructed, thus providing a means of understanding the world, concepts are used to interpret our current experience by classifying it as being of a particular kind, and hence relating it to prior knowledge. The concept of "concept" is central to many of the cognitive sciences. In cognitive psychology, conceptual or semantic encoding effects occur in a wide range of phenomena in perception, ATTENTION, language comprehension, and MEMORY. Concepts are also fundamental to reasoning in both machine systems and people. In AI, concepts are the symbolic elements from which KNOWLEDGE REPRESENTATION systems are built in order to provide machine-based expertise. Concepts are also often assumed to form the basis for the MEANING of nouns, verbs and adjectives (see COGNITIVE LINGUISTICS and SEMANTICS). In behaviorist psychology, a concept is the propensity of an organism to respond differentially to a class of stimuli (for example a pigeon may peck a red key for food, ignoring other colors). In cultural anthropology, concepts play a central role in constituting the individuality of each social group. In comparing philosophy and psychology, it is necessary to distinguish philosophical concepts understood as abstractions, independent of individual minds, and psychological concepts understood as component parts of MENTAL REPRESENTATIONS of the world (see INDIVIDUALISM).
Philosophy distinguishes NARROW CONTENT, which is the meaning of a concept in an individual's mental representation of the world, from broad content, in which the meaning of a concept is also partly determined by factors in the external world. There has been much debate on the question of how to individuate the contents of different concepts, and whether this is possible purely in terms of narrow content (Fodor 1983; Kripke 1972), and how concepts as purely internal symbols in the mind relate to classes of entities in the external world.
Concepts are considered to play an "intensional" and an "extensional" role (FREGE 1952). There are different technical ways to approach this distinction. One philosophical definition is that the extension is the set of all objects in the "actual" world which fall under the concept, whereas the intension is the set of objects that fall under the concept in "all possible worlds." In cognitive science a less strict notion of intension has been operationalized as the set of propositional truths associated with a proper understanding of the concept -- for example that chairs are for sitting on. It resembles a dictionary definition, in that each concept is defined by its relation to others. Intensions permit inferences to be drawn, as in "This is a chair, therefore it can be sat upon," although, as the example illustrates, these inferences may be fallible. The extension of a concept is the class of objects, actions or situations in the actual external world which the concept represents and to which the concept term therefore refers (Frege's "reference"). Frege argued that intension determines extension; thus the extension is the class of things in the world for which the intension is a true description. This notion of concepts leads to a research program for the analysis of relevant concepts (such as "moral" or "lie") in which proposed intensional analyses of concepts are tested against intuitions of the extension of the concept, either real or hypothetical. Fodor (1994) has advanced arguments against this program. To avoid the circularity found in dictionaries, the intension of a concept must be expressed in terms of more basic concepts (the "symbol grounding problem" in cognitive science). The problems involved in grounding concepts have led Fodor to propose a strongly innatist account of concept acquisition, according to which all simple concepts form unanalyzable units, inherited as part of the structure of the brain. Others have explored ways to ground concepts in more basic perceptual symbolic elements (Barsalou 1993).
In the psychology of concepts, there are three main research traditions. First, the "cognitive developmental" tradition, pioneered by PIAGET (1967), seeks to describe the ages and stages in the growing conceptual understanding of children. Concepts are schemas. Through self-directed action and experience the assimilation of novel experiences or situations to a schema leads to corresponding accommodation of the schema to the experience, and hence to CONCEPTUAL CHANGE and development. Piaget's theory of adult intelligence has been widely criticized for overestimating the cognitive capacities of most adults. His claims about the lack of conceptual understanding in young children have also been challenged in the literature on conceptual development (Carey 1985; Keil 1989). Research in this tradition has also had a major influence on theories of adult concepts developed within the lexical semantics tradition.
The second research tradition derives from behaviorist psychology, for which concepts involve the ability to classify the world into categories (see also CATEGORIZATION and MACHINE LEARNING). Animal discrimination learning paradigms have been used to explore how people learn and represent new concepts. A typical experiment involves a controlled stimulus set, usually composed of arbitrary and meaningless elements, such as line segments, geometric symbols, or letters, which has to be classified into two or more classes. The stimuli in the set are created by manipulating values on a number of stimulus dimensions (for example, shape or color). A particular value on a particular dimension constitutes a stimulus feature. The distribution of stimuli across the classes to be learned constitutes the structure of the concept. Training in these experiments typically involves using trial-and-error learning with feedback. In a subsequent transfer or generalization phase, novel stimuli are presented for classification without feedback, to test what has been learned. Three types of model have been explored in this paradigm. "Rule-based" learning models propose that participants try to form hypotheses consistent with the feedback in the learning trials (see for example Bruner, Goodnow, and Austin 1956). "Prototype" learning models propose that participants form representations of the average or prototypical stimulus for each class, and classify these by judging how similar the new stimulus is to each prototype. "Exemplar" models propose that participants store individual exemplars and their classification in memory, and base the classification on the relative average similarity of a stimulus to the stored exemplars in each class, with a generally assumed exponential decay of similarity as distance along stimulus dimensions increases (Nosofsky 1988). Exemplar models typically provide the best fits to experimental data, although rules and prototypes may also be used when the experimental conditions are favorable to their formation. NEURAL NETWORK models of category learning capture the properties of both prototype and exemplar models because they abstract away from individual exemplar representations, but at the same time are sensitive to patterns of co-occurrence of particular stimulus features.
The study of categorization learning in the behaviorist tradition has generated powerful models of fundamental learning processes with an increasing range of application, although the connection to other traditions in the psychology of concepts (for example, cognitive development or lexical semantics) is still quite weak. As in much behaviorist-inspired experimental research, the desire to have full control over the stimulus structure has led to the use of stimulus domains with low meaningfulness and hence poor ECOLOGICAL VALIDITY.
The third research tradition derives from the application of psychological methods to lexical semantics, the representation of word meaning, where concepts are studied through their expression in commonly used words. Within the Fregean branch of this tradition, interest has focused on how the intensions of concepts are related to their extensions. Tasks have been devised to examine each of these two aspects of people's everyday concepts. Intensions are typically studied through feature-listing tasks, where people are asked to list relevant aspects or attributes of a concept which might be involved in categorization, and then to judge their importance to the definition of the concept. Extensions are studied by asking people either to generate or to categorize lists of category members. The use of superordinate concepts (for example, birds or tools) allows instances to be named with single words. Extensions may also be studied through the classification of hypothetical or counterfactual examples, or through using pictured objects.
Five broad classes of model have been proposed within the lexical semantics tradition. The "classical" model assumes that concepts are clearly defined by a conjunction of singly necessary and jointly sufficient attributes (Armstrong, Gleitman, and Gleitman 1983; Osherson and Smith 1981). The first problem for this model is that the attributes people list as true or relevant to a concept's definition frequently include nonnecessary information that is not true of all category members (such as that birds can fly), and often fail to provide the basis of a necessary and sufficient classical definition. Second, there are category instances which show varying degrees of disagreement about their classification both between individuals and for the same individuals on different occasions (McCloskey and Glucksberg 1978). Third, clear category members differ in how "typical" they are judged to be of the category (Rosch 1975). The classical view was therefore extended by proposing two kinds of attribute in concept representations -- defining features, which form the core definition of the class, and characteristic features, which are true of typical category members only and which may form the basis of a recognition procedure for quick categorization. Keil and Batterman (1984) reported a development with age from the use of characteristic to defining features. Nevertheless, the extended classical model is still incompatible with the lack of clearly expressible definitions for most everyday concept terms.
In the second or "prototype" model, concepts are represented by a prototype with all the most common attributes of the category, which includes all instances sufficiently similar to this prototype (Rosch and Mervis 1975). The typicality of an instance in a category depends on the number of attributes which an instance shares with other category members. Prototype representations lead naturally to non-defining attri-butes and to the possibility of unstable categorization at the category borderline. Such effects have been demonstrated in a range of conceptual domains. A corollary of the prototype view is that the use of everyday concepts may show nonlogical effects such as intransivity of categorization hierarchies, and nonintersective conjunctions (Hampton 1982, 1988). Associated with prototype theory is the theory of basic levels in concept hierarchies. Rosch, Simpson, and Miller (1976) proposed that the SIMILARITY structure of the world is such that we readily form a basic level of categorization -- typically, that level corresponding to high-frequency nouns such as chair, apple, or car -- and presented evidence that both adults and children find thinking to be easier at this level of generality (as opposed to superordinate levels such as furniture or fruit, or subordinate levels such as armchair or McIntosh). This intuitive notion has, however, proved hard to formalize in a rigorous way, and the evidence for basic levels outside the well-studied biological and artifact domains remains weak. Attempts to model the combination of prototype concept classes with FUZZY LOGIC (Zadeh 1965) has also proved to be ill founded (Osherson and Smith 1981), although they have led to the development of more general research in conceptual combination (Hampton 1988).
In the third or "exemplar" model, which is only weakly represented in the lexical semantic research tradition, lexical concepts are based not on a prototype but on a number of different exemplar representations. For example, small metal spoons and large wooden spoons are considered more typical than small wooden spoons and large metal spoons (Medin and Shoben 1988). This fact could be evidence for representation through stored exemplars, although it could also be explained by a disjunctive prototype representation. Formally, explicit exemplar models are generally underpowered for representing lexical concepts, having no means to represent intensional information for stimulus domains that do not have a simple dimensional structure. As a result, they have no way to derive logical entailments based on conceptual meaning (for example, that all robins are birds).
The fourth model is the "theory-based" model (Murphy and Medin 1985), which has strong connections with the COGNITIVE DEVELOPMENT tradition. Concepts are embedded in theoretical understanding of the world. While a prototype representation of the concept bird would consist of a list of unconnected attributes, the theory-based representation would also represent theoretical knowledge about the relation of each attribute to others in a complex network of causal and explanatory links, represented in a structured frame or schema. Birds have wings in order to fly, which allows them to nest in trees, which they do to escape predation, and so forth. According to this view, objects are categorized in the class which best explains the pattern of attributes they possess (Rips 1989).
The fifth and final model, psychological ESSENTIALISM (Medin and Ortony 1989), is a development of the classical and theory-based models, and attempts to align psychological models with the philosophical intuitions of Putnam and others. The model argues for a classical "core" definition of concepts, but one which may frequently contain an empty "place holder." People believe that there is a real definition of what constitutes a bird (an essence of the category), but they do not know what it is. They are therefore forced to use available information to categorize the world, but remain willing to yield to more expert opinion. Psychological essentialism captures Putnam's intuition (1975) that people defer to experts when it comes to classifying biological or other technical kinds (for example, gold). However, it has not been shown that the model applies well to concepts beyond the range of biological and scientific terms (Kalish 1995) or even to people's use of natural kind terms such as water (Malt 1994).
The proliferation of different models for concept representation reflects the diversity of research traditions, the many different kinds of concepts we possess, and the different uses we make of them.
Armstrong, S. L., L. R. Gleitman, and H. Gleitman. (1983). What some concepts might not be. Cognition 13:263-308.
Barsalou, L. W. (1993). Structure, flexibility and linguistic vagary in concepts: Manifestations of a compositional system of perceptual symbols. In A. C. Collins, S. E. Gathercole, and M. A. Conway, Eds., Theories of Memory. Hillsdale, NJ: Erlbaum.
Bruner, J. S., J. J. Goodnow, and G. A. Austin. (1956). A Study of Thinking. New York: Wiley.
Carey, S. (1985). Conceptual Change in Childhood. Cambridge, MA: MIT Press.
Fodor, J. A. (1983). The Modularity of Mind. Cambridge, MA: MIT Press.
Fodor, J. A. (1994). Concepts -- a pot-boiler. Cognition 50:95-113.
Frege, G. (1952). On sense and reference. In P. Geach and M. Black, Eds., Translations from the Philosophical Writings of Gottlob Frege. Oxford: Blackwell.
Hampton, J. A. (1982). A demonstration of intransitivity in natural categories. Cognition 12:151-164.
Hampton, J. A. (1988). Overextension of conjunctive concepts: Evidence for a unitary model of concept typicality and class inclusion. Journal of Experimental Psychology: Learning, Memory and Cognition 14:12-32.
Kalish, C. W. (1995). Essentialism and graded membership in animal and artifact categories. Memory and Cognition 23:335-353.
Keil, F. C. (1989). Concepts, Kinds and Cognitive Development. Cambridge, MA: MIT Press.
Keil, F. C., and N. Batterman. (1984). A characteristic-to-defining shift in the development of word meaning. Journal of Verbal Learning and Verbal Behavior 23:221-236.
Kripke, S. (1972). Naming and necessity. In D. Davidson and G. Harman, Eds., Semantics of Natural Language. Dordrecht: Reidel.
Malt, B. C. (1994). Water is not H2O. Cognitive Psychology 27:41-70.
McCloskey, M., and S. Glucksberg. (1978). Natural categories: Well-defined or fuzzy sets? Memory and Cognition 6:462-472.
Medin, D. L., and A. Ortony. (1989). Psychological essentialism. In S. Vosniadou and A. Ortony, Eds., Similarity and Analogical Reasoning. Cambridge: Cambridge University Press, pp. 179-195.
Medin, D. L., and E. J. Shoben. (1988). Context and structure in conceptual combination. Cognitive Psychology 20:158-190.
Murphy, G. L., and D. L. Medin. (1985). The role of theories in conceptual coherence. Psychological Review 92:289-316.
Nosofsky, R. M. (1988). Exemplar-based accounts of relations between classification, recognition and typicality. Journal of Experimental Psychology: Learning, Memory and Cognition 14:700-708.
Osherson, D. N., and E. E. Smith. (1981). On the adequacy of prototype theory as a theory of concepts. Cognition 11:35-58.
Piaget, J. (1967). Piaget's theory. In J. Mussen, Ed., Carmichael's Manual of Child Psychology, vol. 1. New York: Basic Books.
Putnam, H. (1975). The meaning of "meaning." In Mind, Language, and Reality, vol. 2, Philosophical Papers. Cambridge: Cambridge University Press,
Rips, L. J. (1989). Similarity, typicality and categorization. In S. Vosniadou and A. Ortony, Eds., Similarity and Analogical Reasoning. Cambridge: Cambridge University Press, pp. 21-59.
Rosch, E. (1975). Cognitive representations of semantic categories. Journal of Experimental Psychology: General 104:192-232.
Rosch, E., and C. B. Mervis. (1975). Family resemblances: Studies in the internal structure of categories. Cognitive Psychology 7:573-605.
Rosch, E., C. Simpson, and R. S. Miller. (1976). Structural bases of typicality effects. Journal of Experimental Psychology: Human Perception and Performance 2:491-502.
Zadeh, L. (1965). Fuzzy sets. Information and control 8:338-353.
Hampton, J. A. (1997). Psychological representation of concepts. In M. A. Conway and S. E. Gathercole, Eds., Cognitive Models of Memory. Hove, England: Psychology Press, pp. 81-110.
Lakoff, G. (1987). Women, Fire and Dangerous Things. Chicago: University of Chicago Press.
Millikan, R. (1984). Language, Thought, and Other Biological Categories. Cambridge, MA: MIT Press.
Neisser, U., Ed. (1993). Concepts and Conceptual Development: Ecological and Intellectual Bases of Categories. Cambridge: Cambridge University Press.
Rey, G. (1983). Concepts and stereotypes. Cognition 15:237-262.
Rips, L. J. (1995). The current status of research on concept combination. Mind and Language 10:72-104.
Rosch, E., and B. B. Lloyd, Eds. (1978). Cognition and Categorization. Hillsdale, NJ: Erlbaum.
Schwanenflugel, P., Ed. (1991). The Psychology of Word Meanings. Hillsdale, NJ: Erlbaum.
Smith, E. E., and D. L. Medin. (1981). Categories and Concepts. Cambridge, MA: Harvard University Press.
van Mechelen, I., J. A. Hampton, R. S. Michalski, and P. Theuns, Eds. (1993). Categories and Concepts: Theoretical Views and Inductive Data Analysis. London: Academic Press.
Ward, T. B., S. M. Smith, and J. Viad, Eds. (1997). Conceptual Structures and Processes: Emergence Discovery and Change. Washington, DC: American Psychological Association .
Copyright © 1999 Massachusetts Institute of Technology