Isolated and interrelated concepts 1 Isolated and Interrelated Concepts

A continuum between purely isolated and purely interrelated concepts is described. A concept is interrelated to the extent that it is influenced by other concepts. Methods for manipulating and identiying a concept’s degree of interrelatedness are introduced. Relatively isolated concepts are empirically identified by a relatively large use of nondiagnostic features, and by better categorization performance for a concept’s prototype than for a caricature of the concept. Relatively interrelated concepts are identified by minimal use of nondiagnostic features, and by better categorization performance for a caricature than a prototype. A concept is likely to be relatively isolated when: subjects are instructed to create images for their concepts rather than find discriminating features, concepts are given unrelated labels, and the categories that are displayed alternate rarely between trials. The entire set of manipulations and measurements supports a graded distinction between isolated and interrelated concepts. The distinction is applied to current models of category learning, and a connectionist framework for interpreting the empirical results is presented. Isolated and interrelated concepts 3 Isolated and Interrelated Concepts Modern research on concept representation and learning has evolved from two traditions. One tradition connects concept acquisition with language in general and word learning in specific (Lakoff, 1986; Saussure, 1915/1959). Concepts are approximately equated with single words or phrases. In this tradition, for example, evidence that a child has acquired the adult concept of dog comes from the child’s use of the word “dog” to designate dogs. The other tradition connects concept acquisition with object recognition (Biederman, 1987). From this perspective, concept learning involves learning to correctly categorize perceptual inputs into classes. These two approaches, linking concepts to language and perception respectively, are not mutually exclusive, and a full account of the nature of conceptual representation will most likely borrow from both approaches. Still, the approaches emphasize different methods for representing and processing concepts. The three aims of this paper are: to describe these different characterizations, to develop empirical methods for distinguishing between them, and to devise a framework that integrates both characterizations into a single formal framework. Much of the work that ties concepts to language is concerned with the presence of (McNamara & Miller, 1989; Saussure, 1915/1959) or absence (Fodor, Garret, Walker, & Parkes, 1980) of interconceptual connections. Conversely, much of the work that ties concepts to object recognition is concerned with the links between concepts and perceptual inputs rather than between concepts. Indeed, concepts seem to be cognitively self-contained bundles of knowledge on the one hand, and intricately interconnected entities on the other. Concepts appear to be isolated from each other, each acting as an independent detector polling the world (Selfridge, 1959), and yet also seem to influence each other in an interacting network (Collins & Quillian, 1969). For example, while certain shapes seem to be directly recognized as examples of dog, the concept dog also appears to be closely associated with and influenced by other concepts such as mammal, tail and domesticated . Most models of concept representation and use try to account for one or the other of these types of conceptual behavior. The central purpose of this paper is to make a case for considering a continuum of interrelatedness in concept characterizations. The characterization of a concept refers to the way the concept is described, and the members that belong to it. A concept’s characterization will depend both on its representation, and the cognitive processes that operate on that representation. A concept is Isolated and interrelated concepts 4 interrelated to the extent that its characterization is influenced by other concepts. A concept is isolated to the extent that its characterization is not influenced by other concepts. The proposed continuum of interrelatedness is supported by results of five experiments that systematically affect the degree of interrelatedness of laboratory-acquired concepts by human subjects. Three manipulations of conceptual interrelatedness and two empirical indicators of conceptual interrelatedness are evaluated. In addition, a computational simulation of concept learning is presented. The simulation demonstrates how degrees of conceptual interrelation can be modeled in a formal network. In the model, the use of a concept can reflect intermediate degrees of interrelation, depending upon the strength of the connections that other concepts have to it. Such links are potentially determined both by the context of concept acquisition and the nature of the current processing demands. In order to understand the continuum of conceptual interrelatedness, idealized concepts at the extreme poles of the continuum are first considered individually. Interrelated Concepts There are several ways in which the characterization of concepts might be influenced by other concepts (Goldstone, 1991). First, a concept might be characterized as a modified version of another previously acquired concept. Such modifications could include adding or deleting properties, increasing or decreasing the quantity of a property, or rearranging properties. For example, one’s concept of toy poodle might be a modified version of one’s concept of standard poodle, with a modification to size. Or consider the concept unicorn . At first pass, one might think of unicorns as horses, with the addition of the features magical and horns. If unicorn is characterized by its relation to the concept horse then altering one’s concept of horse would likely also alter one’s concept of unicorn. For example, if a new fact were learned about horses (e.g. the pad in the middle of a horse’s hoof is called a “frog”), then it might be incorporated into the unicorn concept as well (Potts, St. John, & Kirson, 1989). At the very least, it would be difficult for a person in this culture to have a full concept of unicorn without also possessing a horse concept (cf. Stich, 1983). A second way that concepts can be influenced by other concepts is suggested by the work of Barr and Caplan (1987; Caplan & Barr, 1991). These researchers report evidence from feature-listing tasks that Isolated and interrelated concepts 5 people’s concepts typically contain both intrinsic and extrinsic features. Intrinsic features refer to parts or properties of the concept under scrutiny. Extrinsic features are “represented as the relationship between two or more entities” (p. 398). For example, an extrinsic feature of hammer is that it is “used to strike nails. ” This feature refers to a concept other than hammer. If this feature is part of one’s concept of hammer, then one cannot possess a hammer concept without also possessing nail. In all of the above examples of interrelatedness among concepts, the intension, or internally represented meaning (see Johnson-Laird, 1983), of a concept is influenced by other concepts in the system. The extension of a concept is the set of items that is covered by the concept. In arguing for complete interrelatedness among concepts, Saussure (1915/1959) stated that “concepts are purely differential and defined not in terms of their positive content but negatively by their relations with other terms in the system” (p. 117). That is, he contended that all concepts are “negatively defined,” or defined solely in terms of other concepts. Several current theories of word and concept representation from linguistics and computer science similarly assume that concepts’ meanings are interrelated. In semantic network representations (Collins & Quillian, 1972), concepts are represented by their relations (e.g. part-of, is-a, and has-a relations) to other concepts. For example, the meaning of cat is represented by its has-a relation to claw, its is-a relation to pet and animal, and its part-of relation to household (see McNamara and Miller (1989) for a review of evidence for theories of conceptual representation that posit interrelations between concepts). And in linguistics, there is a widespread notion that the lexicon is organized as a semantic field, in which words applicable to a common conceptual domain are organized by relations of similarity and contrast (Grandy, 1987; Lerher & Kittay, 1992; Lyons, 1963; Martin & Billman, 1994). Thus, the semantic relations that a word enters into at least partially constitute the meaning of that word. For example, one’s understanding of walk is influenced by one’s possessions of the concepts jog, skip, run, and drive. The reported experiments and simulations do not evaluate all the varieties of interrelated concepts. The research does not consider concepts that are interrelated by their semantic associations, or by their cohabitation in a single theory or system (Field, 1978; Fodor, 1983). Rather, the research focuses on artificial, laboratory-created concepts that are interrelated because they are mutually exclusive categories, and consequently, membership in one category prevents membership in the other. Although visual concepts were used in the experiments to be reported, linguists have discussed this relation of mutual Isolated and interrelated concepts 6 exclusivity between concepts. In linguistic theory, a mutually exclusive set of terms that are organized under an inclusive covering term is called a contrast set (Grandy, 1987; Lehrer & Kittay, 1992; Martin & Billman, 1994). For example, Sunday, Monday, and Tuesday belong to a common contrast set: days of the week. Concepts within a contrast set evoke each other, and once evoked, influence each others’ interpretation. In Saussure’s example (1915/1959), mutton is influenced by the presence of other neighboring concepts