Recent Views of Conceptual Structure

ness. Second, every attribute specified for a concept is shared by more than one instance of the concept. Thus, the information contained in a concept is an abstraction across instances of the concept. The overlapping networks of shared attributes thus formed hold conceptual categories together. In this respect, the family resemblance view is like the classical view: Both maintain that the instances of a concept cohere because they are similar to one another by virtueof sharing certain attributes. Weighted attributes. An object that shares attributes with many members of a category bears greater family resemblance to that category than an object that shares attributes with few members. This suggests that attributes that are shared by many members confer a greater degree of family resemblance than those that are shared by a few. A third characteristic of the family resemblance view is that it assumes that concept attributes are "weighted" according to their relevance for conferring family resemblance to the category. In general, that relevance is taken to be a function of the number of category instances (and perhaps noninstances) that share the attribute. Presumably, if the combined relevance weights of the attributes of some novel object exceed a certain level (what might be called the membership threshold or criterion), that object will be 2 Here and throughout, I use relevance to include both relevance and salience as used by Ortony, Vondruska, Foss, and Jones (1985). 504 LLOYD K. KOMATSU considered an instance of the category (Medin, 1983; Rosch & Mervis, 1975; E. E. Smith & Medin, 1981). The greater the degree to which the combined relevance weights exceed the threshold, the more typical an instance it is (see also Shafir, Smith, & Osherson, 1990). By this measure, an object must have a large number of heavily weighted attributes to be judged highly typical of a given category. Because such heavily weighted attributes are probably shared by many category instances and relatively few noninstances, an object highly typical of a category is likely to lie near the central tendencies of the category (see Retention of Central Tendencies, below), and is not likely to be typical of or lie near the central tendencies of any other category. Independence and additive combination of weights: Linear separability. Attribute weights can be combined using a variety of methods (cf. Medin & Schaffer, 1978; Reed, 1972). In the method typically associated with the family resemblance view (adapted from Tversky's, 1977, contrast model of similarity), attribute weights are assumed to be independent and combined by adding (Rosch & Mervis, 1975; E. E. Smith & Medin, 1981). This leads to a fourth characteristic of the (modal) family resemblance view: It predicts that instances and noninstances of a concept can be perfectly partitioned by a linear discriminant function (i.e., if one was to plot a set of objects by the combined weights of their attributes, all instances would fall to one side of a line, and all noninstances would fall on the other side; Medin & SchafFer, 1978; Medin & Schwanenflugel, 1981; Nakamura, 1985; Wattenmaker, Dewey, Murphy, & Medin, 1986). Thus the (modal) family resemblance view predicts that concepts are "linearly separable." Retention of central tendencies. The phrase family resemblance is used in two ways. In the sense that I have focused on until now, the family resemblance of an object to a category increases as the similarity between that object and all other members of the category increases and the similarity between that object and all nonmembers of the category decreases. This use of family resemblance (probably the use more reflective of Wittgenstein's, 1953, original ideas) has an extensional emphasis: It describes a relationship among objects and makes no assumptions about how the category of objects is represented mentally (i.e., about the intension of the word or what I have been calling the concept). In the second sense, family resemblance increases as the similarity between an object and the central tendencies of the category increases (Hampton, 1979). This use of family resemblance has an intentional emphasis: It describes a relationship between objects and a mental representation (of the central tendencies of a category). Although these two ways of thinking about family resemblance, average similarity to all instances and similarity to a central tendency, are different (cf. Reed, 1972), Barsalou (1985, 1987) points out that they typically yield roughly the same outcome, much as the average difference between a number and a set of other numbers is roughly the same as the difference between that number and the average of that set of other numbers. (For example, consider the number 2 and the set of numbers 3, 5, and 8. The average difference between 2 and 3, 5, and 8 is 3.33, and the difference between 2 and the average of 3,5, and 8 is 3.33.) Barsalou argues that although for most purposes the two ways of thinking about family resemblance are equivalent (one of the reasons the exemplar and family resemblance views are often difficult to distinguish empirically; see below), computation in terms of central tendencies may be more plausible psychologically (because fewer comparisons are involved in comparing an object with the central tendencies of a concept than with every instance and noninstance of the concept; see also Barresi, Robbins, & Shain, 1975). This suggests a fifth characteristic of the family resemblance view: A concept provides a summary of a category in terms of the central tendencies of the members of that category rather than in terms of the representations of individual instances. Economy, Informativeness, Coherence, and Naturalness Both the classical and the family resemblance views explain conceptual coherence in terms of the attributes shared by the members of a category (i.e., the similarity among the instances of a concept). The critical difference between the two views lies in the constraints placed on the attributes shared. In the classical view, all instances are similar in that they share a set of necessary and sufficient attributes (i.e., the definition). The family resemblance view relaxes this constraint and requires only that every attribute specified by the concept be shared by more than one instance. Although this requirement confers a certain amount of economy to the family resemblance view (every piece of information applies to several instances), removing the definitional constraint allows family resemblance representations to include nondefinitional information. In particular, concepts are likely to specify information beyond that true of all instances or beyond that strictly needed to understand what Medin and Smith (1984) call linguistic meaning (the different kinds of relations that hold among words such as synonymy, antynomy, hyponomy, anomaly, and contradiction as usually understood; cf. Katz, 1972; Katz & Fodor, 1963) to include information about how the objects referred to may relate to one another and to the world. It is not clear whether this loss in economy results in a concomitant increase in informativeness: Although in the family resemblance view more information may be associated with a concept than in the classical, not all of that information applies to every instance of the concept. In the family resemblance view, attributes can be inferred to inhere in different instances only with some level of probability. Thus the informativeness of the individual attributes specified is somewhat compromised. With no a priori constraint on the nature (or level) of similar3 There are several different ways to approach the representation of the central tendencies of a category. E. E. Smith and Medin (1981), for example, identified three approaches to what they called the probablistic view: the featural, the dimensional, and the holistic. E. E. Smith and Medin provided ample evidence for rejecting the holistic approach on both empirical and theoretical grounds (see also McNamara & Miller, 1989). They also argued that the similarities between the featural and dimensional approaches suggest that they might profitably be combined into a single position that could be called the "component" approach (E. E. Smith & Medin, 1981, p. 164) and concluded that the component approach is the only viable variant. RECENT VIEWS OF CONCEPTS 505 ity shared by the instances of a concept, the family resemblance view has difficulty specifying which similarities count and which do not when it comes to setting the boundaries between concepts. A Great Dane and a Bedlington terrier appear to share few similarities, but they share enough so that both are dogs. But a Bedlington terrier seems to share as many similarities with a lamb as it does with a Great Dane. Why is a Bedlington terrier a dog and not a lamb? Presumably, the family resemblance view would predict that the summed weights of Bedlington terrier attributes lead to its being more similar to other dogs than to lambs and result in its being categorized as a dog rather than a lamb. But to determine those weights, we need to know how common those attributes are among dogs and lambs. This implies that the categorization of Bedlington terriers must be preceded by the partitioning of the world into dog and lamb. Without that prior partitioning, the dog versus lamb weights of Bedlington terrier attributes cannot be determined. To answer the question of what privileges the categorization of a Bedlington terrier with the Great Dane rather than the lamb requires answering what privileges the partitioning of the world into dogs and lambs. Rosch (Rosch, 1978; Rosch & Mervis, 1975) argues that certain partitionings of the world (including, presumably, into dogs and lambs) are privileged, more immediate or direct, and arise naturally from the interaction of our perceptual apparatus and the environment. Thus whereas the classical view stresses the coherence of conceptual categories without addressing naturalness, the family resemblance view stresses naturalness with coherence emerging as a by-product (Neisser, 1987). Whereas the classical view constrains concepts through an abstract specification of the attributes that constitute a concept (i.e., that they are individually necessary and collectively sufficient), the family resemblance view suggests that concepts are constrained (at least at the basic level of abstraction) ecologically, reflecting the natural partitioning of objects in the real world by our perceptual systems. (See Anderson, 1990,1991 a, 1991 b for a closely related, and more fully developed, view of human categorization as adaptive.) A second constraint on concepts operates in the (modal) family resemblance view: linear separability. The assumption that weights are combined by summing allows the family resemblance view to describe only those categories that linearly partition the attribute space. In some sense, therefore, this view claims that category boundaries are linear discriminant functions (Murphy & Medin, 1985); items cohere by virtue of falling on the same side of some such function. Notice that unlike the ecological constraint, linear separability addresses coherence but does not address naturalness (because any arbitrary set of attributes may be used to define the attribute space). But presumably, the ecological constraint may favor certain discriminant functions over others. Thus the ecological and linear separability constraints may work together to allow the family resemblance view to explain why some categories are privileged over others. Ascendence of the Family Resemblance View Although there is a certain degree of vagueness in the family resemblance view," it is clear that it holds a great deal of promise for explaining a variety of phenomena that are difficult for the classical view to accommodate. For example, because the family resemblance view rejects the notion that the attributes specified by a concept are necessary and sufficient, it explains the failure of subjects to give necessary and sufficient definitions and attributes in a very straightforward manner: There are none to be given. Explaining typicality effects is another strong suit of the family resemblance view. In fact, E. E. Smith and Medin (1981, p. 69) argue that typicality effects follow so naturally from the family resemblance view that such effects can be considered to be support for this view. Furthermore, because the family resemblance view explains both typicality and category membership in terms of the values obtained by combining attribute relevance weights, it has a natural means of explaining fuzzy boundaries between instances and noninstances: Any noise or variability in the relevance weights of any attribute would lead to a fuzzy boundary. Because of the wealth of empirical data demonstrating the pervasive fuzziness of concepts and the wide range of results predicted by typicality judgments, the family resemblance view rapidly gained acceptance among cognitive psychologists (cf. textbooks by Bourne, Dominowski, & Loftus, 1979; Glass, Holyoak, & Santa, 1979; Klatzky, 1980). Soon, family resemblance analyses (usually called prototype analyses) were being applied not only to object concepts but also to emotions (Fehr, 1988; Fehr & Russell, 1984; Shaver, Schwartz, Kirson, & O'Connor, 1987), trait and person concepts (Cantor & Mischel, 1977; Mayer & Bower, 1986), psychological situations (Cantor, Mischel, & Schwartz, 1982; see Lingle, Altom, & Medin, 1984, for general discussion about the application of prototype analyses to social psychological categories), and clinical categories or categories of abnormal behavior (Cantor, Smith, French, & Mezzich, 1980; Genero & Cantor, 1987; Horowitz, Wright, Lowenstein, & Parad, 1981), as well as to styles of painting (Hartley & Homa, 1981) and musical themes (Welker, 1982). Dissatisfaction With the Family Resemblance View Unfortunately, it soon became clear that rejecting the classical constraint of necessity and sufficiency led the family resemblance view into some difficulty. For example, how are complex concepts (e.g., pet fish or "the center dunked the basketball") constructed out of simple(r) concepts (e.g., pet and fish)? The classical account built on set theory and described complex concepts as the union of the necessary and sufficient attribute sets of the constituent simple concepts. Because sets of necessary and sufficient attributes do not exist in the family resemblance view, that account cannot be directly adopted. 4 For example, one can assume in this view either that conceptual representations include information about the central tendencies of all attributes displayed by the instances of a category or of only some (unspecified) subset of attributes (typically, those that are most relevant or heavily weighted). The former position (which might be called the prototype approach) argues that concepts represent potential instantiations, whereas the latter (which might be called the duster approach) does not (see also Kelley & Krueger, 1984; Reed, 1972; E. E. Smith & Medin, 1981). 506 LLOYD K. KOMATSU Initially, supporters of the family resemblance view appealed to logics that were based on fuzzy sets. The idea was that the extension of most everyday terms were fuzzy sets (Hersh & Caramazza, 1976; Rosch & Mervis, 1975) and fuzzy-set logic would therefore predict the properties of combinations of such terms. Unfortunately, such accounts were found to be inadequate (Cohen & Murphy, 1984; Johnson-Laird, 1983; Osherson & Smith, 1981, 1982; but see Zadeh, 1982). Later work suggested that a family resemblance approach focusing on the subjective weightings of attributes that characterize instances of a concept may be able to deal with conceptual combination without appealing to fuzzy-set theory (e.g., Hampton, 1987, 1988; Shafir et al, 1990; E. E. Smith, 1988; E. E. Smith & Osherson, 1984; E. E. Smith, Osherson, Rips, & Keane, 1988; but see Medin & Shoben, 1988; Murphy, 1988). A second strength of the classical view lost by the family resemblance view is in accounting for linguistic meaning (Katz, 1972; Katz & Fodor, 1963; Medin & Smith, 1984). Although some progress has been made recently in explicating inductive reasoning within the family resemblance view (Osherson, Smith, Wilkie, Lopez, & Shafir, 1990; Rips, 1975), the family resemblance view still finds it difficult to account for certain forms of linguistic relations. A third problem for the family resemblance view is that people (or at least people in literate societies) have strong intuitions that words have necessary and sufficient definitions, despite the fact that they cannot articulate those definitions (cf. McNamara & Sternberg, 1983). This intuition, in fact, may be the main reason that the classical view held sway for so long. People also seem to have the intuition that the boundaries for most everyday categories are clear-cut, although those intuitions may not be terribly pervasive or strong (cf. Armstrong et al., 1983). Fourth, explaining naturalness and coherence in terms of the interaction between the human perceptual system and the environment means that the family resemblance view accounts for these characteristics only in perceptually based concepts (e.g., the domain of color). But even as he argues for the importance of an ecological constraint, Neisser (1987) notes that a perception-based account of concepts is ultimately inadequate; few adult concepts rely exclusively on perceptual similarity. Finally, subsequent research has indicated that typicality effects in themselves do not clearly dictate the nature of conceptual structure. In particular, they do not provide good justification for rejecting necessity and sufficiency. For example, Armstrong et al. (1983; Gleitman et al., 1983; see also Bourne, 1982) found that typicality judgments can be obtained for concepts with clear definitions (e.g., odd number) and that such judgments will predict reaction times in the usual tasks. Although typicality effects may indicate that the classical view is not adequate for capturing all conceptual phenomena, they do not rule out the possibility that the classical view may describe at least some aspects of many concepts. A possible fix: Combining the classical and family resemblance views. The various inadequacies of the family resemblance view led a number of psychologists (e.g., Landau, 1982; Miller & Johnson-Laird, 1976; Neimark, 1983; Rosch, 1983; E. E. Smith, 1988; E. E. Smith & Medin, 1981) to propose hybrid or dual-representational models that include both classical and family resemblance representations. Most of the details of how classical and family resemblance representations would divide and coordinate the labor of accounting for different conceptual phenomena have not been worked out. In most such cases (Landau, 1982; Miller, 1978; Miller & Johnson-Laird, 1976; Osherson & Smith, 1981; E. E. Smith, 1988; E. E. Smith & Medin, 1981), the family resemblance representation is argued to be the basis for identifying instances of the concept, whereas the classical representation is the basis for reasoning about concepts (sometimes called the core/identification procedure approach). In others, the two representations map onto a distinction between competence and performance (Neimark, 1983) or between logical and reference point (in effect, a kind of analogical) reasoning (Rosch, 1983). For a dual-representational approach to work, each aspect must hold up its own end of the explanatory burden. But the family resemblance view appears to be unable to account for several results that such hybrids assume it explains. These failures stem primarily from two built-in limitations of the view: Limiting concepts to those that are linearly separable. Independence of attribute weights and combination of weights through summing are usually assumed in the family resemblance view. These assumptions mean that the family resemblance view only describes linearly separable concepts. This implies that linearly separable artificial categories are somewhat more natural and should be easier to learn than nonlinearly separable ones. But the available evidence (Kemler Nelson, 1984; Medin & Schwanenflugel, 1981; Nakamura, 1985) does not support this prediction. In fact, under certain instructional conditions, linearly separable categories may be more difficult to learn (Wattenmaker, Nakamura, & Medin, 1988). An easy fix for this problem would be to surrender the assumption of additive combinations of attribute weights. Using alternative combination methods (e.g., multiplicative; cf. Medin & Schaffer, 1978) would allow the family resemblance view to account for both linearly and nonlinearly separable categories. Because this assumption is not critical to the characterization 5 However, this problem may be more apparent than real. It is possible that at least some of the phenomena of linguistic meaning that are most problematic for the family resemblance view (i.e., those that assume logical entailment) simply do not exist. Quine (1953), for example, argues that so-called analytic statements can be revised and are not true (as usually described) by definition. Such statements resist revision only because their revision would require the revision of many other statements. For example, it is not necessarily true that given a line and a point not on that line, it is possible to draw one and only one line through the point that is parallel to the first. But to revise that statement (i.e., to revise the notion of parallel lines) would require revising many other statements about geometry. Baker (1974), echoing Wittgenstein (1953), argued that the notion of criteria should be substituted for logical necessity. The criterion relationship is one that is established by convention. It is therefore somewhat stronger (i.e., more definite) than a simple empirical generalization that is based on probabilities (i.e., an induction) but not as definite as the relationship of logical entailment conveyed by necessity (Johnson-Laird, 1983). Therefore, although linguistic meaning poses a problem for the family resemblance view (and, as it turns out, the exemplar view) for now, future work on the notions of criteria and differential revisability may provide an adequate account of what have traditionally been interpreted as the empirical consequences of logical entailment. RECENT VIEWS OF CONCEPTS 507 of the family resemblance view, such a modification seems acceptable. Limiting concepts to information about central tendencies and attribute weights. More critical to the family resemblance view is the assumption that a concept only represents information about the central tendencies and relative weights of the attributes that characterize the instances of the category. But subjects who learn a category also seem to have information about the variability of the instances of the category (Barresi et al, 1975; Homa & Vosburgh, 1976) and about the correlations among the attributes of the instances in the category (Malt & Smith, 1984; Medin, Altom, Edelson, & Freko, 1982). Similarly problematic for the family resemblance view are the effects expectations regarding the distributions of instances have on category formation (Flannagan, Fried, & Holyoak, 1986) and the fact that subjects learn about categories in a sorting task when given no feedback about the correctness of their sorts (Fried & Holyoak, 1984; but see Homa, Burruel, & Field, 1987; Homa & Cultice, 1984, for other results and interpretations). There is also good evidence that similarity to central tendencies does not fully explain typicality effects for all categories. In the case of ad hoc, goal-derived categories (e.g., "things to take from one's home during a fire"; Barsalou, 1983,1985) or certain abstract categories (e.g., a belief or an instinct; Hampton, 1981), similarity to central tendencies seems to play very little role in determining typicality. In such cases, similarity to an ideal or frequency of instantiation seems to be a more powerful determinant (Barsalou, 1985). In some cases in which similarity to central tendency clearly does play a role (e.g., birds), similarity to an ideal and frequency of instantiation may contribute to typicality as well (Barsalou, 1985; Nosofsky, 1988b). Finally, although the fuzziness of concept boundaries (McCloskey & Glucksberg, 1978) may explain some inconsistencies in typicality judgments both within and between subjects (Barsalou, 1987; Barsalou & Sewell, 1984 [cited in Barsalou, 1989]), it cannot explain why typicality judgments vary systematically with context (Barsalou, 1985; Roth & Shoben, 1983) and points of view (Barsalou, 1987). In general, because the representations described by the family resemblance view are context free, they cannot explain how levels of family resemblance or relevance weights of attributes (hence typicality judgments) are affected by context. A possible fix: Multiple family resemblance representations. These problems might be explained by proposing multiple representations for each concept in a fashion somewhat akin to disjunctive concepts in the classical view. Instead of bird being linked to a single representation, there may be one (family resemblance) representation for birds of prey, a second for song birds, a third for fowl, and so on. Instability and sensitivity to context or point of view could then be explained by different subjects' calling up different bird representations under different circumstances. Such a multiple-representation approach is sometimes assumed implicitly in family resemblance discussions (e.g., Rosch, 1978). But consider the following: Suppose one wishes to determine whether a particular object is an instance of a bird. According to the family resemblance view, to do that one must determine the birdness-establishing relevance weights of the object's attributes. Suppose the object flies. The multiple-representation approach does not give a single weight for flying. It gives different weights depending on the particular representation (bird of prey, fowl, and so on) accessed. With a multiple-representation account of the concept bird, what is really decided is whether the object is an instance of bird of prey or fowl, not whether it is a bird as such. To decide whether an object is a bird takes two steps: First, determine whether the object is an instance of bird of prey or fowl, and if it is, then, second, infer that it is also an instance of (the superordinate category) bird. The crucial point here is that the multiple-representation account of bird does not provide a family-resemblance-based account of bird, but only one for specific types of birds. A multiple-representation account of bird is better understood as an example of the exemplar rather than the family resemblance view (E. E. Smith & Medin, 1981).