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CHAPTER 8

Categorization and Concepts

ROBERT L. GOLDSTONE, ALAN KERSTEN, AND PAULO F. CARVALHO

INTRODUCTION Issues related to concepts and catego- rization are nearly ubiquitous in psychology Concepts are the building blocks of thought. because of people’s natural tendency to They are critically involved when we rea- perceive a thing as something. We have a son, make inferences, and try to generalize powerful impulse to interpret our world. our previous experiences to new situations. This act of interpretation, an act of “seeing Behind every word in every language lies something as X” rather than simply seeing it a concept, although there are concepts, like (Wittgenstein, 1953), is fundamentally an act the small plastic tubes attached to the ends of categorization. of shoelaces, that we are familiar with and The attraction of research on concepts is k k can think about even if we do not know that an extremely wide variety of cognitive that they are called aglets. Concepts are acts can be understood as categorizations indispensable to human cognition because (Kurtz, 2015; Murphy, 2002). Identifying the they take the “blooming, buzzing confu- person sitting across from you at the breakfast sion” (James, 1890, p. 488) of disorganized table involves categorizing something as your sensory experiences and establish order spouse. Diagnosing the cause of someone’s through mental categories. These mental illness involves a disease categorization. categories allow us to make sense of the Interpreting a painting as a Picasso, an arti- world and predict how worldly entities will fact as Mayan, a geometry as non-Euclidean, behave. We see, hear, interpret, remember, a fugue as baroque, a conversationalist as understand, and talk about our world through charming, a wine as a Bordeaux, and a gov- our concepts, and so it is worthy of reflec- ernment as socialist are categorizations at tion time to establish where concepts come various levels of abstraction. The typically from, how they work, and how they can unspoken assumption of research on concepts best be learned and deployed to suit our is that these cognitive acts have something cognitive needs. in common. That is, there are principles that explain many or all acts of categorization. AQ1 We are grateful to Brian Rogosky, Robert Nosofsky, John This assumption is controversial (see Medin, Kruschke, Linda Smith, and David Landy for helpful Lynch, & Solomon, 2000), but is perhaps comments on earlier drafts of this chapter. This research justified by the potential payoff of discover- was funded by National Science Foundation REESE grant DRL-0910218, and Department of Education IES ing common principles governing concepts grant R305A1100060. in their diverse manifestations.

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The desirability of a general account of each other, and assigning values of 0 and 1 to concept learning has led the field to focus a dimension is arbitrary. For example, for a its energy on what might be called generic color dimension, red may be assigned a value concepts. Experiments typically involve arti- of 0 and blue a value 1. The exact category ficial categories that are hopefully unfamiliar structure of Table 8.1 has been used in at least to the subject. Formal models of concept 30 studies (reviewed by J. D. Smith & Minda, learning and use are constructed to be able to 2000) and instantiated by stimuli as diverse handle any kind of concept irrespective of its as geometric forms, yearbook photographs, content. Although there are exceptions to this cartoons of faces (Medin & Schaffer, 1978), general trend (Malt, 1994; Ross & Murphy, and line drawings of rocket ships. These 1999), much of the mainstream empirical researchers are not particularly interested and theoretical work on concept learning is in the category structure of Table 8.1 and concerned not with explaining how particular are certainly not interested in the catego- concepts are created, but with how concepts rization of rocket ships per se. Instead, they in general are represented and processed. choose their structures and stimuli so as to be One manifestation of this approach is that (a) unfamiliar (so that learning is required), the members of a concept are often given (b) well controlled (dimensions are approx- an abstract symbolic representation. For imately equally salient and independent), example, Table 8.1 shows a typical notation (c) diagnostic with respect to theories of used to describe the stimuli seen by a subject category learning, and (d) potentially gen- in a psychological experiment or presented eralizable to natural categories that people to a formal model of concept learning. Nine learn. Work on generic concepts is valuable k objects belong to two categories, and each if it turns out that there are domain-general k object is defined by its value along four principles underlying human concepts that binary dimensions. In this notation, objects can be discovered. Still, there is no a pri- from Category A typically have values of 1 ori reason to assume that all concepts will on each of the four dimensions and objects follow the same principles, or that we can from Category B usually have values of 0. generalize from generic concepts to naturally The dimensions are typically unrelated to occurring concepts.

Table 8.1 A Common Category Structure WHAT ARE CONCEPTS?

Dimension Concepts, Categories, and Internal Category Stimulus D1 D2 D3 D4 Representations A11110 A21010A good starting place is Edward Smith’s Category A A31011(1989) characterization that a concept is “a A41101mental representation of a class or individual A50111and deals with what is being represented and B11100how that information is typically used during Category B B20110 B30001the categorization” (p. 502). It is common to B40000distinguish between a concept and a category. A concept refers to a mentally possessed idea Source: From Medin and Schaffer (1978). Copy- right 1978 by the American Psychological Association. or notion, whereas a category refers to a Reprinted with permission. set of entities that are grouped together.

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The concept dog is whatever psychological particular objects belong, and how well, to state signifies thoughts of dogs. The category the concept’s extension. dog consists of all the entities in the real world that are appropriately categorized as Equivalence Classes dogs. The question of whether concepts determine categories or vice versa is an Another important aspect of concepts is that important foundational controversy. On the they are equivalence classes. In the classical one hand, if one assumes the primacy of notion of an equivalence class, distinguish- external categories of entities, then one will able stimuli come to be treated as the same tend to view concept learning as the enter- thing once they have been placed in the prise of inductively creating mental structures same category (Sidman, 1994). This kind of that predict these categories. One extreme equivalence is too strong when it comes to version of this view is the exemplar model human concepts because even when we place of concept learning (Estes, 1994; Medin & two objects into the same category, we do not Schaffer, 1978; Nosofsky, 1984), in which treat them as the same thing for all purposes. one’s internal representation of a concept is Some researchers have stressed the intrinsic nothing more than the set of all of the exter- variability of human concepts—variability nally supplied examples of the concept to that makes it unlikely that a concept has the which one has been exposed. If, on the other same sense or meaning each time it is used hand, one assumes the primacy of internal (Barsalou, 1987; Connell & Lynott, 2014; mental concepts, then one tends to view exter- Thelen & Smith, 1994). Still, the extent to nal categories as the end product of using which perceptually dissimilar things can k these internal concepts to organize observed be treated equivalently given the appropri- k entities. Some practitioners of a “concepts ate conceptualization is impressive. To the first” approach argue that the external world biologist armed with a strong “mammal” does not inherently consist of rocks, dogs, concept, even whales and dogs may be and tables; these are mental concepts that treated as commensurate in many situations organize an otherwise unstructured exter- related to biochemistry, child rearing, and nal world (Lakoff, 1987). Recent research thermoregulation. indicates that concepts’ extensions (the class Equivalence classes are relatively imper- of items to which the concept applies) and vious to superficial similarities. Once one intensions (the features that distinguish that has formed a concept that treats all skunks class of items) do not always cohere with as equivalent for some purposes, irrelevant each other (Hampton & Passanisi, 2016). variations among skunks can be greatly For example, dolphins and whales are often de-emphasized. When people are told a story judged to have many of the features charac- in which scientists discover that an animal teristic of an internal representation of fish that looks exactly like a raccoon actually con- (e.g., swims, lives in oceans, and has fins), tains the internal organs of a skunk and has but are still placed in the extensional set of skunk parents and skunk children, they often mammals rather than fish. The implication categorize the animal as a skunk (Keil, 1989; is that a complete model of concepts may Rips, 1989). When people classify objects require at least partially separate represen- into familiar, labeled categories such as chair, tations for intensions and extensions, rather then their memory for the individuating infor- than a more parsimonious model in which mation about the objects is markedly worse a concept’s intension determines whether (Lupyan, 2008a). People may never be able

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to transcend superficial appearances when elements in the sense of existing without categorizing objects (Goldstone, 1994b), being learned and without being constructed nor is it clear that they would want to (S. S. out of other concepts. Some theorists have Jones & Smith, 1993). Still, one of the most argued that concepts such as bachelor, kill, powerful aspects of concepts is their ability and house are primitive in this sense (Fodor, to make superficially different things alike Garrett, Walker, & Parkes, 1980), but a (Sloman, 1996). If one has the concept things considerable body of evidence suggests that to remove from a burning house, even chil- concepts typically are acquired elements that dren and jewelry become similar (Barsalou, are themselves decomposable into semantic 1983). The spoken phonemes /d/ /o/ /g/, the elements (McNamara & Miller, 1989). French word chien, the written word dog, and Once a concept has been formed, it can a picture of a dog can all trigger one’s concept enter into compositions with other concepts. of dog (Snodgrass, 1984), and although they Several researchers have studied how novel may trigger slightly different representations, combinations of concepts are produced and much of the core information will be the comprehended. For example, how does one same. Concepts are particularly useful when interpret buffalo paper when one first hears we need to make connections between things it? Is it paper in the shape of a buffalo, paper that have different apparent forms. used to wrap buffaloes presented as gifts, an essay on the subject of buffaloes, coarse paper, or is it like flypaper but used to catch WHAT DO CONCEPTS DO FOR US? bison? Interpretations of word combinations are often created by finding a relation that Fundamentally, concepts function as filters. connects the two concepts. In Murphy’s k We do not have direct access to our external k (1988) concept-specialization model, one world. We only have access to our world interprets noun–noun combinations by find- as filtered through our concepts. Concepts ing a variable that the second noun has are useful when they provide informative or that can be filled by the first noun. By this diagnostic ways of structuring this world. An account, a robin snake might be interpreted excellent way of understanding the mental as a snake that eats robins once robin is used world of an individual, group, scientific to the fill the eats slot in the snake concept. community, or culture is to find out how they In addition to promoting creative thought, organize their world into concepts (Lakoff, the combinatorial power of concepts is 1987; Malt & Wolff, 2010; Medin & Atran, required for cognitive systematicity (Fodor & 1999; Ojalehto & Medin, 2015). Pylyshyn, 1988). The notion of systematicity is that a system’s ability to entertain com- Components of Thought plex thoughts is intrinsically connected to Concepts are cognitive elements that com- its ability to entertain the components of bine together to generatively produce an those thoughts. In the field of conceptual infinite variety of thoughts. Just as an endless combination, this has appeared as the issue variety of architectural structures can be of whether the meaning of a combination constructed out of a finite set of building of concepts can be deduced on the basis of blocks, so concepts act as building blocks the meanings of its constituents. However, for an endless variety of complex thoughts. there are some salient violations of this type Claiming that concepts are cognitive ele- of systematicity. When adjective and noun ments does not entail that they are primitive concepts are combined, there are sometimes

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emergent interactions that cannot be pre- that could be stood on to reach a lightbulb), dicted by the main effects of the concepts and abstract schemas or metaphors (e.g., themselves. For example, the concept gray events in which a kind action is repaid with hair is more similar to white hair than black cruelty, metaphorical prisons, problems that hair,butgray cloud is more similar to black are solved by breaking a large force into parts cloud than white cloud (Medin & Shoben, that converge on a target). For the latter cat- 1988). Wooden spoons are judged to be fairly egories, members need not have very much large (for spoons), even though this property in common at all. An unrewarding job and a is not generally possessed by wood objects relationship that cannot be ended may both or spoons (Medin & Shoben, 1988). Still, be metaphorical prisons, but the situations there have been successes in predicting how may share little other than this. well an object fits a conjunctive description Unlike ad hoc and metaphor-base cate- based on how well it fits the individual gories, most natural kinds and many artifacts descriptions that comprise the conjunction are characterized by members that share (Hampton, 1997). A reasonable reconcilia- many features. In a series of studies, Rosch tion of these results is that when concepts (Rosch, 1975; Rosch & Mervis, 1975) has combine together, the concepts’ meanings shown that the members of natural kind systematically determine the meaning of and artifact “basic level” categories, such the conjunction, but emergent interactions as chair, trout, bus, apple, saw, and guitar, and real-world plausibility also shape the are characterized by high within-category conjunction’s meaning. overall similarity. Subjects listed features for basic level categories, as well as for broader superordinate (e.g., furniture) and narrower k Inductive Predictions k subordinate (e.g., kitchen chair) categories. Concepts allow us to generalize our expe- An index of within-category similarity was riences with some objects to other objects obtained by tallying the number of features from the same category. Experience with one listed by subjects that were common to items slobbering dog may lead one to suspect that in the same category. Items within a basic an unfamiliar dog may have the same pro- level category tend to have several features clivity. These inductive generalizations may in common, far more than items within a be wrong and can lead to unfair stereotypes superordinate category and almost as many if inadequately supported by data, but if an as items that share a subordinate categoriza- organism is to survive in a world that has tion. Rosch (Rosch & Mervis, 1975; Rosch, some systematicity, it must “go beyond the Mervis, Gray, Johnson, & Boyes-Braem, information given” (Bruner, 1973) and gen- 1976) argues that categories are defined by eralize what it has learned. The concepts we family resemblance; category members need use most often are useful because they allow not all share a definitional feature, but they many properties to be inductively predicted. tend to have several features in common. Fur- To see why this is the case, we must digress thermore, she argues that people’s basic level slightly and consider different types of con- categories preserve the intrinsic correlational cepts. Categories can be arranged roughly in structure of the world. All feature combina- order of their grounding by similarity: natu- tions are not equally likely. For example, in ral kinds (dog, oak tree), man-made artifacts the animal kingdom, flying is correlated with (hammer, airplane, chair), ad hoc categories laying eggs and possessing a beak. There (things to take out of a burning house, things are “clumps” of features that tend to occur

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together. Some categories do not conform to we possess are those that maximize induc- these clumps (e.g., ad hoc categories), but tive potential (Anderson, 1991; Goodman, many of our most natural-seeming categories Tenenbaum, Feldman, & Griffiths, 2008; do. Neural network models have been pro- Tenenbaum, 1999). An implication of this posed that take advantage of these clumps approach is that there are degrees of concept- to learn hierarchies of categories (Rogers & hood, with concepts falling on a continuum of Patterson, 2007). inductive power (Wixted, personal communi- These natural categories also permit many cation, November 2016). Most psychologists inductive inferences. If we know something studying concept learning do not believe that belongs to the category dog, then we know most of our everyday concepts are defined that it probably has four legs and two eyes, by rules or discrete boundaries (see Rules eats dog food, is somebody’s pet, pants, section below), but we may well be guilty barks, is bigger than a breadbox, and so on. of treating the concept concept as more rule Generally, natural kind objects, particularly based than it actually is. If concepts vary those at Rosch’s basic level, permit many crucially in terms of their inductive power, inferences. Basic level categories allow many they are very likely to be fuzzy and graded inductions because their members share sim- rather than discrete objects that people either ilarities across many dimensions/features. do or do not possess. Ad hoc categories and highly metaphorical categories permit fewer inductive inferences, Communication but in certain situations the inferences they Communication between people is enor- allow are so important that the categories mously facilitated if the people can count are created on an “as needed” basis. One k upon a set of common concepts being shared. k interesting possibility is that all concepts By uttering a simple sentence such as “Ed is are created to fulfill an inductive need, and a football player,” one can transmit a wealth that standard taxonomic categories, such as of information to a colleague, dealing with bird and hammer, simply become automati- the probabilities of Ed being strong, having cally triggered because they have been used violent tendencies, being a college physics often, whereas ad hoc categories are only or physical education major, and having a created when specifically needed (Barsalou, history of steroid use. Markman and Makin 1982, 1991). In any case, evaluating the (1998) have argued that a major force in inductive potential of a concept goes a long shaping our concepts is the need to efficiently way toward understanding why we have the communicate. They find that people’s con- concepts that we do. The concept peaches, cepts become more consistent and systematic llamas, telephone answering machines, or over time in order to unambiguously establish Ringo Starr is an unlikely concept because reference for another individual with whom belonging in this concept predicts very they need to communicate (see also Garrod & little. Researchers have empirically found Doherty, 1994). that the categories that we create when we strive to maximize inferences are different Cognitive Economy from those that we create when we strive to sort the objects of our world into clearly We can discriminate far more stimuli than separate groups (Yamauchi & Markman, we have concepts. For example, estimates 1998). Several researchers have been for- suggest that we can perceptually discriminate mally developing the notion that the concepts at least 10,000 colors from each other, but

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we have far fewer color concepts than this. From an information theory perspective, Dramatic savings in storage requirements can storing a category in memory rather than a be achieved by encoding concepts rather than complete description of an individual is effi- entire raw (unprocessed) inputs. A classic cient because fewer bits of information are study by Posner and Keele (1967) found required to specify the category. For example, that subjects code letters such as “A” in a Figure 8.1 shows a set of objects (shown by detailed, perceptually rich code, but that circles) described along two dimensions. this code rapidly (within 2 seconds) gives Rather than preserving the complete descrip- way to a more abstract conceptual code that tion of each of the 19 objects, one can create “A” and “a” share. Huttenlocher, Hedges, a reasonably faithful representation of the and Vevea (2000) developed a formal model distribution of objects by just storing the in which judgments about a stimulus are positions of the four triangles in Figure 8.1. based on both its category membership and In addition to conserving memory storage its individuating information. As predicted requirements, an equally important econo- by the model, when subjects are asked to mizing advantage of concepts is to reduce reproduce a stimulus, their reproductions the need for learning (Bruner, Goodnow, & reflect a compromise between the stimulus Austin, 1956). An unfamiliar object that has itself and the category to which it belongs. not been placed in a category attracts atten- When a delay is introduced between seeing tion because the observer must figure out the stimulus and reproducing it, the contri- how to think about it. Conversely, if an object bution of category-level information relative can be identified as belonging to a preestab- to individual-level information increases lished category, then typically less cognitive k (Crawford, Huttenlocher, & Engebretson, processing is necessary. One can simply treat k 2000). Together with studies showing that, the object as another instance of something over time, people tend to preserve the gist that is known, updating one’s knowledge of a category rather than the exact mem- slightly if at all. The difference between bers that comprise it (e.g., Posner & Keele, events that require altering one’s concepts 1970), these results suggest that by pre- and those that do not was described by Piaget serving category-level information rather (1952) in terms of accommodation (adjust- than individual-level information, efficient ing concepts on the basis of a new event) long-term representations can be main- and assimilation (applying already known tained. In fact, it has been argued that our perceptions of an object represent a nearly optimal combination of evidence based on the object’s individuating information and the categories to which it belongs (N. H. Feldman, Griffiths, & Morgan, 2009). By Y using category-level information, one will occasionally overgeneralize and make errors. Rattlesnakes may be dangerous in general, X but one may stumble upon a congenial one in the Arizona desert. One makes an error Figure 8.1 Alternative proposals have suggested that categories are represented by the individual when one is unduly alarmed by its presence, exemplars in the categories (the circles), the proto- but it is an error that stems from a healthful, types of the categories (the triangles), or the cate- life-sustaining generalization. gory boundaries (the lines dividing the categories).

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concepts to an event). This distinction has cat and fox concepts are represented. One also been incorporated into computational needs to know how the information in these models of concept learning that determine representations is integrated together to make whether an input can be assimilated into a the final categorization. Does one wait for the previously learned concept, and if it can- amount of confirmatory evidence for one of not, then reconceptualization is triggered the animals to rise above a certain threshold (Grossberg, 1982). When a category instance (Fific, Little, & Nosofsky, 2010)? Does one is consistent with a simple category descrip- compare the evidence for the two animals and tion, then people are less likely to store choose the more likely (Luce, 1959)? Is the a detailed description of it than if it is an information in the candidate animal concepts exceptional item (Palmeri & Nosofsky, accessed simultaneously or successively? 1995), consistent with the notion that people Probabilistically or deterministically? These simply use an existing category description are all questions about the processes that use when it suffices. In general, concept learning conceptual representations. One reaction to proceeds far more quickly than would be the insufficiency of representations alone to predicted by a naïve associative learning pro- account for concept use has been to dispense cess. Our concepts accelerate the acquisition with all reference to independent representa- of object information at the same time that tions, and instead frame theories in terms of our knowledge of objects accelerates concept dynamic processes alone (Thelen & Smith, formation (Griffiths & Tenenbaum, 2009; 1994; van Gelder, 1998). However, others Kemp & Tenenbaum, 2009). feel that this is a case of throwing out the baby with the bath water, and insist that rep- k resentations must still be posited to account k HOW ARE CONCEPTS for enduring, organized, and rule-governed REPRESENTED? thought (Markman & Dietrich, 2000).

Much research on concepts and cate- Rules gorization revolves around the issue of how concepts are mentally represented. There is considerable intuitive appeal to the As with all discussion of representations, notion that concepts are represented by some- the standard caveat must be issued—mental thing like dictionary entries. By a rule-based representations cannot be determined or account of concept representation, to possess used without processes that operate on these the concept cat is to know the dictionary entry representations. Rather than discussing the for it. A person’s cat concept may differ from representation of a concept such as cat,we Webster’s dictionary’s entry: “A carnivorous should discuss a representation-process pair mammal (Felis catus) long domesticated and that allows for the use of this concept. Empir- kept by man as a pet or for catching rats and ical results interpreted as favoring a particular mice.” Still, this account claims that a concept representation format should almost always is represented by some rule that allows one be interpreted as supporting a particular to determine whether or not an entity belongs representation given particular processes that within the category. use the representation. As a simple example, The most influential rule-based approach when trying to decide whether a shadowy to concepts may be Bruner et al.’s (1956) figure briefly glimpsed was a cat or afox, hypothesis-testing approach. Their theorizing one needs to know more than how one’s was, in part, a reaction against behaviorist

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approaches (Hull, 1920), in which concept competitive activity with winners and losers learning involved the relatively passive acqui- is adequate to identify Frisbee, professional sition of an association between a stimulus baseball, and roulette as games, while simul- (an object to be categorized) and a response taneously excluding wars, debates, television (such as a verbal response, key press, or viewing, and leisure walking from the game labeling). Instead, Bruner et al. argued that category. Even a seemingly well-defined con- concept learning typically involves active cept such as bachelor seems to involve more hypothesis formation and testing. In a typ- than its simple definition of unmarried male. ical experiment, their subjects were shown The counterexample of a 5-year-old child flash cards that had different shapes, colors, (who does not really seem to be a bachelor) quantities, and borders. The subjects’ task may be fixed by adding in an adult precon- was to discover the rule for categorizing dition, but an indefinite number of other the flash cards by selecting cards tobe preconditions are required to exclude a man tested and by receiving feedback from the in a long-term but unmarried relationship, the experimenter indicating whether the selected Pope, and a 80-year-old widower with four card fit the categorizing rule or not. The children (Lakoff, 1987). Wittgenstein argued researchers documented different strategies that instead of equating knowing a concept for selecting cards, and a considerable body with knowing a definition, it is better to think of subsequent work showed large differences of the members of a category as being related in how easily acquired are different cate- by family resemblance. A set of objects gorization rules (e.g., Bourne, 1970). For related by family resemblance need not have example, a conjunctive rule such as white any particular feature in common, but will k and square is more easily learned than a have several features that are characteristic k conditional rule such as if white then square, or typical of the set. which is in turn more easily learned than a Second, the category membership for biconditional rule such as white if and only some objects is not clear. People disagree on if square. whether or not a starfish is a fish, a camel isa The assumptions of these rule-based vehicle, a hammer is a weapon, and a stroke models have been vigorously challenged is a disease. By itself, this is not too problem- for several decades now. Douglas Medin atic for a rule-based approach. People may and Edward Smith (Medin & Smith, 1984; use rules to categorize objects, but different E. E. Smith & Medin, 1981) dubbed this people may have different rules. However, rule-based approach “the classical view,” and it turns out that people not only disagree characterized it as holding that all instances with each other about whether a bat is mam- of a concept share common properties that mal. They also disagree with themselves! are necessary and sufficient conditions for McCloskey and Glucksberg (1978) showed defining the concept. At least three criticisms that people give surprisingly inconsistent have been levied against this classical view. category-membership judgments when asked First, it has proven to be very difficult the same questions at different times. There to specify the defining rules for most con- is either variability in how to apply a cat- cepts. Wittgenstein (1953) raised this point egorization rule to an object, or people with his famous example of the concept spontaneously change their categorization game. He argued that none of the candidate rules, or (as many researchers believe) people definitions of this concept, such as activity simply do not represent objects in terms of engaged in for fun, activity with certain rules, clear-cut rules.

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Third, even when a person shows consis- average responses. A strong version of a tency in placing objects in a category, people rule-based model predicts that people create do not treat the objects as equally good mem- categories that have the minimal possible bers of the category. By a rule-based account, description length (J. Feldman, 2006). one might argue that all objects that match One approach to making the rule-governed a category rule would be considered equally approach to concepts more psychologically good members of the category (but see plausible is to discard the assumption that Bourne, 1982). However, when subjects are rule-governed implies deterministic. The past asked to rate the typicality of animals such as few years have seen a new crop of rule-based robin and eagle for the category bird,orchair models that are intrinsically probabilistic and hammock for the category furniture,they (Piantadosi & Jacobs, 2016; Piantadosi, reliably give different typicality ratings for Tenenbaum, & Goodman, 2016; Tenenbaum, different objects. Rosch and Mervis (1975) Kemp, Griffiths, & Goodman, 2011). These were able to predict typicality ratings with models work by viewing categorization as the respectable accuracy by asking subjects to result of integrating many discrete rules, each list properties of category members and of which may be imperfect predictors on its measuring how many properties possessed own. A remaining challenge for these models by a category member were shared by other is that there often is a psychological con- category members. The magnitude of this nection between rule use and determinism. so-called family-resemblance measure is Rules, particularly ones that involve relations positively correlated with typicality ratings. between elements, are often very difficult Despite these strong challenges to the to learn when they are probabilistic rather k classical view, the rule-based approach is than applied without exception (Jung & k by no means moribund. In fact, in part Hummel, 2015). In addition, even formal due to the perceived lack of constraints in concepts such as triangle have graded and neural network models that learn concepts flexible structures—structures that are tied by gradually building up associations, the less to strict definitions when the concepts rule-based approach experienced a rekindling are activated by their labels (Lupyan, 2017). of interest in the 1990s after its low point In defending a role for rule-based rea- in the 1970s and 1980s (Marcus, 1998). soning in human cognition, E. E. Smith, Nosofsky and Palmeri (Nosofsky & Palmeri, Langston, and Nisbett (1992) proposed eight 1998; Palmeri & Nosofsky, 1995) have pro- criteria for determining whether or not people posed a quantitative model of human concept use abstract rules in reasoning. These criteria learning that learns to classify objects by include “performance on rule-governed items forming simple logical rules and remember- is as accurate with abstract as with concrete ing occasional exceptions to those rules. This material,” “performance on rule-governed work is reminiscent of earlier computational items is as accurate with unfamiliar as with models of human learning that created rules familiar material,” and “performance on such as If white and square, then Category a rule-governed item or problem deterio- 1 from experience with specific examples rates as a function of the number of rules (Anderson, Kline, & Beasley, 1979; Medin, that are required for solving the problem.” Wattenmaker, & Michalski, 1987). The mod- Based on the full set of criteria, they argue els have a bias to create simple rules, and are that rule-based reasoning does occur, and able to predict entire distributions of subjects’ that it may be a mode of reasoning distinct categorization responses rather than simply from association-based or similarity-based

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reasoning. Similarly, Pinker (1991) argued the passive stimulus–response association for distinct rule-based and association-based approach, so the prototype model was devel- modes for determining linguistic categories. oped as a reaction against what was seen Neurophysiological support for this dis- as the overly analytic, rule-based classical tinction comes from studies showing that view. Central to Eleanor Rosch’s devel- rule-based and similarity-based categoriza- opment of prototype theory is the notion tions involve anatomically separate brain that concepts are organized around family regions (Ashby, Alfonso-Reese, Turken, & resemblances rather than features that are Waldron, 1998; E. E. Smith, Patalano, & individually necessary and jointly sufficient Jonides, 1998). for categorization (Mervis & Rosch, 1981; In developing a similar distinction Rosch, 1975; Rosch & Mervis, 1975). The between similarity-based and rule-based prototype for a category consists of the most categorization, Sloman (1996) introduced the common attribute values associated with the notion that the two systems can simultane- members of the category and can be empir- ously generate different solutions to a reason- ically derived by the previously described ing problem. For example, Rips (1989; see method of asking subjects to generate a list of also Rips & Collins, 1993) asked subjects to attributes for several members of a category. imagine a three-inch, round object, and then Once prototypes for a set of concepts have asked whether the object was more similar to been determined, categorizations can be pre- a quarter or a pizza, and whether the object dicted by determining how similar an object was more likely to be a pizza or a quarter. is to each of the prototypes. The likelihood There is a tendency for the object to be judged of placing an object into a category increases k as more similar to a quarter but as more likely as it becomes more similar to the category’s k to be a pizza. The rule that quarters must not prototype and less similar to other category be greater than 1 inch plays a larger role in the prototypes (Rosch & Mervis, 1975). categorization decision than in the similarity This prototype model can naturally deal judgment, causing the two judgments to dis- with the three problems that confronted the sociate. By Sloman’s analysis, the tension we classical view. It is no problem if defining feel about the categorization of the three-inch rules for a category are difficult or impossible object stems from the two different systems, to devise. If concepts are organized around indicating incompatible categorizations. prototypes, then only characteristic, not nec- Sloman argues that the rule-based system essary or sufficient, features are expected. can suppress the similarity-based system Unclear category boundaries are expected if but cannot completely suspend it. When objects are presented that are approximately Rips’ experiment is repeated with a richer equally similar to prototypes from more than description of the object to be categorized, one concept. Objects that clearly belong to categorization again tracks similarity, and a category may still vary in their typicality people tend to choose the quarter for both the because they may be more similar to the cate- categorization and similarity choices (E. E. gory’s prototype than to any other category’s Smith & Sloman, 1994). prototype, but they still may differ in how similar they are to the prototype. Prototype models do not require “fuzzy” boundaries Prototypes around concepts (Hampton, 1993), but proto- Just as the active hypothesis-testing approach type similarities are based on commonalities of the classical view was a reaction against across many attributes and are consequently

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graded, and lead naturally to categories with Posner and Keele’s (1968) classic dot-pattern graded membership. stimuli consisted of nine dots positioned A considerable body of data has been randomly or in familiar configurations on amassed that suggests that prototypes have a30× 30 invisible grid. Each prototype cognitively important functions. The simi- was a particular configuration of dots, but larity of an item to its category prototype (in during categorization training subjects never terms of featural overlap) predicts the results saw the prototypes themselves. Instead, they from several converging tasks. Somewhat saw distortions of the prototypes obtained obviously, it is correlated with the average by shifting each dot randomly by a small rating the item receives when subjects are amount. Categorization training involved asked to rate how good an example the item is subjects seeing dot patterns, guessing their of its category (Rosch, 1975). It is correlated category assignment, and receiving feedback with subjects’ speed in verifying statements indicating whether their guesses were cor- of the form, “An [item] is a [category name]” rect or not. During a transfer stage, Posner (E. E. Smith, Shoben, & Rips, 1974). It is and Keele found that subjects were better correlated with the frequency and speed able to categorize the never-before-seen of listing the item when asked to supply category prototypes than they were in cate- members of a category (Mervis & Rosch, gorizing new distortions of those prototypes. 1981). It is correlated with the probability In addition, subjects’ accuracy in categoriz- of inductively extending a property from the ing distortions of category prototypes was item to other members of the category (Rips, strongly correlated with the proximity of 1975). Taken in total, these results indicate those distortions to the never-before-seen k that different members of the same category prototypes. The authors interpreted these k differ in how typical they are of the category, results as suggesting that prototypes are and that these differences have a strong extracted from distortions, and used as a cognitive impact. Many natural categories basis for determining categorizations. seem to be organized not around definitive boundaries, but by graded typicality to the Exemplars category’s prototype. The prototype model described above Exemplar models deny that prototypes are generates category prototypes by finding explicitly extracted from individual cases, the most common attribute values shared stored in memory, and used to categorize among category members. An alternative new objects. Instead, in exemplar models, conception views prototypes as the central a conceptual representation consists only tendency of continuously varying attributes. of the actual individual cases that one has If the four observed members of a lizard observed. The prototype representation for category had tail lengths of 3, 3, 3, and 7 the category bird consists of the most typical inches, the former prototype model would bird, or an assemblage of the most common store a value of 3 (the modal value) as the attribute values across all birds, or the central prototype’s tail length, whereas the central tendency of all attribute values for observed tendency model would store a value of 4 birds. By contrast, an exemplar model repre- (the average value). The central tendency sents the category bird by representing all of approach has proven useful in modeling the instances (exemplars) that belong to this categories composed of artificial stimuli that category (L. R. Brooks, 1978; Estes, 1994; vary on continuous dimensions. For example, Hintzman, 1986; Kruschke, 1992; Lamberts,

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2000; Logan, 1988; Medin & Schaffer, 1978; instances by their similarity to old instances Nosofsky, 1984, 1986). maximizes the likelihood of categorizing the While the prime motivation for these new instances correctly (Ashby & Maddox, models has been to provide good fits to 1993; McKinley & Nosofsky, 1995; Ripley, results from human experiments, computer 1996). Furthermore, if information becomes scientists have pursued similar models with available at a later point that specifies what the aim of exploiting the power of storing properties are useful for generalizing appro- individual exposures to stimuli in a rela- priately, then preserving entire instances tively raw, unabstracted form. The exemplar, will allow these properties to be recovered. instance-based (Aha, 1992), view-based Such properties might be lost and unrecov- (Tarr & Gauthier, 1998), case-based (Schank, erable if people were less “lazy” in their 1982), nearest neighbor (Ripley, 1996), generalizations from instances. configural cue (Gluck & Bower, 1990), and Given these considerations, it is under- vector quantization (Kohonen, 1995) models standable why people often use all of the all share the fundamental insight that novel attributes of an object even when a task patterns can be identified, recognized, or demands the use of specific attributes. categorized by giving the novel patterns the Doctors’ diagnoses of skin disorders are same response that was learned for similar, facilitated when they are similar to previously previously presented patterns. By creating presented cases, even when the similarity is representations for presented patterns, not based on attributes that are known to be only is it possible to respond to repetitions irrelevant for the diagnosis (L. R. Brooks, of these patterns, it is also possible to give Norman, & Allen, 1991). Even when people k responses to novel patterns that are likely know a simple, clear-cut rule for a percep- k to be correct by sampling responses to old tual classification, performance is better on patterns, weighted by their similarity to the frequently presented items than rare items novel pattern. Consistent with these models, (Allen & Brooks, 1991). Consistent with psychological evidence suggests that people exemplar models, responses to stimuli are show good transfer to new stimuli in per- frequently based on their overall similarity to ceptual tasks just to the extent that the new previously exposed stimuli. stimuli superficially resemble previously The exemplar approach to categorization learned stimuli (Palmeri, 1997). raises a number of questions. First, once The frequent inability of human general- one has decided that concepts are to be ization to transcend superficial similarities represented in terms of sets of exemplars, might be considered as evidence of either the obvious question remains: How are the human stupidity or laziness. To the contrary, exemplars to be represented? Some exem- if a strong theory about what stimulus fea- plar models use a featural or attribute-value tures promote valid inductions is lacking, the representation for each of the exemplars strategy of least commitment is to preserve (Hintzman, 1986; Medin & Schaffer, 1978). the entire stimulus in its full richness of detail Another popular approach is to represent (L. R. Brooks, 1978). That is, by storing exemplars as points in a multidimen- entire instances and basing generalizations sional psychological space. These points on all of the features of these instances, one are obtained by measuring the subjective can be confident that one’s generalizations are similarity of every object in a set to every not systematically biased. It has been shown other object. Once an n × n matrix of simi- that in many situations, categorizing new larities among n objects has been determined

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by similarity ratings, perceptual confusions, the prototype, the cumulative effect of many spontaneous sortings, or other methods, exemplars in an exemplar model can create a statistical technique called multidimen- an emergent, epiphenomenal advantage for sional scaling (MDS) finds coordinates for the prototype. the objects in a d-dimensional space that Given the exemplar model’s account of allow the n × n matrix of similarities to be prototype categorization, one might ask reconstructed with as little error as possible whether predictions from exemplar and pro- (Nosofsky, 1992). Given that d is typically totype models differ. In fact, they typically smaller than n, a reduced representation is do, in large part because categorizations in created in which each object is represented exemplar models are not simply based on in terms of its values on d dimensions. summed similarity to category exemplars, Distances between objects in these quan- but to similarities weighted by the proximity titatively derived spaces can be used as of an exemplar to the item to be categorized. the input to exemplar models to determine In particular, exemplar models have mech- item-to-exemplar similarities. These MDS anisms to bias categorization decisions so representations are useful for generating that they are more influenced by exemplars quantitative exemplar models that can be that are similar to items to be categorized. fit to human categorizations and similarity In Medin and Schaffer’s (1978) context judgments, but these still beg the question model, this is achieved by computing the of how a stand-alone computer program or similarity between objects by multiplying a person would generate these MDS repre- rather than adding the similarities in each sentations. Presumably there is some human of their features. In Hintzman’s (1986) k process that computes object representations MINERVA 2 model, this is achieved by k and can derive object-to-object similarities raising object-to-object similarities to a from them, but this process is not currently power of 3 before summing them together. modeled by exemplar models (for steps in In Nosofsky’s generalized context model this direction, see Edelman, 1999). (1986), this is achieved by basing object-to- A second question for exemplar models object similarities on an exponential function is, If exemplar models do not explicitly of the objects’ distance in an MDS space. extract prototypes, how can they account for With these quantitative biases for close exem- results that concepts are organized around plars, the exemplar model does a better job of prototypes? A useful place to begin is by con- predicting categorization accuracy for Posner sidering Posner and Keele’s (1968) result that and Keele’s (1968) experiment than the the never-before-seen prototype is catego- prototype model because it can also predict rized better than new distortions based on the that familiar distortions will be categorized prototype. Exemplar models have been able more accurately than novel distortions that to model this result because a categorization are equally far removed from the prototype of an object is based on its summed similarity (Shin & Nosofsky, 1992). to all previously stored exemplars (Medin & A third question for exemplar models Schaffer, 1978; Nosofsky, 1986). The proto- is, In what way are concept representations type of a category will, on average, be more economical if every experienced exemplar similar to the training distortions than are is stored? It is certainly implausible with new distortions, because the prototype was large real-world categories to suppose that used to generate all of the training distortions. every instance ever experienced is stored Without positing the explicit extraction of in a separate trace. However, more realistic

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exemplar models may either store only represents categories by their periphery, not part of the information associated with an their center. One recurring empirical result exemplar (Lassaline & Logan, 1993) or only that provides some prima facie evidence for some exemplars (Aha, 1992; Palmeri & representing categories in terms of bound- Nosofsky, 1995). One particularly interesting aries is that oftentimes the most effectively way of conserving space that has received categorized object is not the prototype of empirical support (Barsalou, Huttenlocher, & a category, but rather is a caricature of the Lamberts, 1998) is to combine separate category (Davis & Love, 2010; Goldstone, events that all constitute a single individ- 1996; Goldstone, Steyvers, & Rogosky, ual into a single representation. Rather 2003; Heit & Nicholson, 2010). A caricature than passively register every event as dis- is an item that is systematically distorted tinct, people seem to naturally consolidate away from the prototype for the category in events together that refer to the same indi- the direction opposite to the boundary that vidual. If an observer fails to register the divides the category from another category. difference between a new exemplar and a An interesting phenomenon to consider previously encountered exemplar (e.g., two with respect to whether centers or periph- similar-looking Chihuahuas), then he or she eries of concepts are representationally may combine the two together, resulting in an privileged is categorical perception.Due exemplar representation that is a blend of two to this phenomenon, people are better able instances (Love, Medin, & Gureckis, 2004). to distinguish between physically different stimuli when the stimuli come from different categories than when they come from the Category Boundaries k same category (see Harnad, 1987 for several k Another notion is that a concept repre- reviews of research). The effect has been best sentation describes the boundary around a documented for speech phoneme categories. category. The prototype model would repre- For example, Liberman, Harris, Hoffman, sent the four categories of Figure 8.1 in terms and Griffith (1957) generated a continuum of the triangles. The exemplar model would of equally spaced consonant-vowel syllables, represent the categories by the circles. The going from /be/ to /de/. Observers listened category boundary model would represent the to three sounds—A followed by B followed categories by the four dividing lines between by X—and indicated whether X was identi- the categories. This view has been most cal to A or B. Subjects performed the task closely associated with the work of Ashby more accurately when the syllables A and B and his colleagues (Ashby, 1992; Ashby belonged to different phonemic categories et al, 1998; Ashby & Gott, 1988; Ashby & than when they were variants of the same Maddox, 1993; Ashby & Townsend, 1986; phoneme, even when physical differences Maddox & Ashby, 1993). It is particularly were equated. interesting to contrast the prototype and Categorical perception effects have been category boundary approaches, because their observed for visual categories (Calder, representational assumptions are almost per- Young, Perrett, Etcoff, & Rowland, 1996) fectly complementary. The prototype model and for arbitrarily created laboratory cat- represents a category in terms of its most egories (Goldstone, 1994a). Categorical typical member—the object in the center perception could emerge from either proto- of the distribution of items included in the type or boundary representations. An item category. The category boundary model to be categorized might be compared to

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the prototypes of two candidate categories. information is more likely to be represented Increased sensitivity at the category bound- when two highly similar categories must be ary would be because people represent items frequently discriminated and there is a salient in terms of the prototype to which they are reference point for the boundary. closest. Items that fall on different sides of Different versions of the category bound- the boundary would have very different rep- ary approach, illustrated in Figure 8.2, have resentations because they would be closest to been based on different ways of partitioning different prototypes (Liberman et al., 1957). categories (Ashby & Maddox, 1998). With Alternatively, the boundary itself might be independent decision boundaries, categories represented as a reference point, and as pairs boundaries must be perpendicular to a dimen- of items move closer to the boundary it sional axis, forming rules such as Category A becomes easier to discriminate between them items are larger than 3 centimeters, irrespec- because of their proximity to this reference tive of their color. This kind of boundary is point (Pastore, 1987). appropriate when the dimensions that make Computational models have been devel- up a stimulus are hard to integrate (Ashby & oped that operate on both principles. Gott, 1988). With minimal distance bound- Following the prototype approach, Harnad, aries, a Category A response is given if and Hanson, and Lubin (1995) describe a neural only if an object is closer to the Category network in which the representation of an A prototype than the Category B prototype. item is “pulled” toward the prototype of the The decision boundary is formed by finding category to which it belongs. Following the the line that connects the two categories’ pro- boundaries approach, Goldstone, Steyvers, totypes and creating a boundary that bisects k Spencer-Smith, and Kersten (2000) describe k a neural network that learns to strongly A A represent critical boundaries between cat- A A A A A A egories by shifting perceptual detectors to A A A A A A Y A B Y A B these regions. Empirically, the results are B B B B B B B B B B mixed. Consistent with prototypes being B B B B B B B B B B represented, some researchers have found X X particularly good discriminability close to a Independent decisions Minimal distance familiar prototype (Acker, Pastore, & Hall, 1995; McFadden & Callaway, 1999). Consis- A A A A A tent with boundaries being represented, other A A A A A A A A A researchers have found that the sensitivity Y A B Y A B B B B B peaks associated with categorical perception B B B B B B B B B B B B B B heavily depend on the saliency of perceptual B B cues at the boundary (Kuhl & Miller, 1975). X X Optimal boundaries General quadratic Rather than being arbitrarily fixed, category boundaries are most likely to occur at a Figure 8.2 The notion that categories are repre- location where a distinctive perceptual cue, sented by their boundaries can be constrained in such as the difference between an aspirated several ways. Boundaries can be constrained to be and unaspirated speech sound, is present. perpendicular to a dimensional axis, to be equally A possible reconciliation is that information close to prototypes for neighboring categories, to produce optimal categorization performance, about either the center or periphery of a cat- or may be loosely constrained to be a quadratic egory can be represented, and that boundary function.

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and is orthogonal to this line. The optimal whether it is a cat or not, but this is done by boundary is the boundary that maximizes the comparing the evidence in favor of the object likelihood of correctly categorizing an object. being a cat to its being something else. If the two categories have the same patterns of variability on their dimensions, and people Theories use information about variance to form their boundaries, then the optimal boundary will The representation approaches thus far con- be a straight line. If the categories differ in sidered all work irrespectively of the actual their variability, then the optimal boundary meaning of the concepts. This is both an will be described by a quadratic equation advantage and a liability. It is an advantage (Ashby & Maddox, 1993, 1998). A general because it allows the approaches to be uni- quadratic boundary is any boundary that can versally applicable to any kind of material. be described by a quadratic equation. They share with inductive statistical tech- One difficulty with representing a concept niques the property that they can operate on by a boundary is that the location of the any data set once the data set is formally boundary between two categories depends described in terms of numbers, features, or on several contextual factors. For example, coordinates. However, the generality of these Repp and Liberman (1987) argue that cat- approaches is also a liability if the meaning egories of speech sounds are influenced by or semantic content of a concept influences order effects, adaptation, and the surround- how it is represented. While few would argue ing speech context. The same sound that is that statistical T-tests are only appropriate halfway between pa and ba will be catego- for certain domains of inquiry (e.g., testing k rized as pa if preceded by several repetitions political differences, but not disease differ- k of a prototypical ba sound, but categorized ences), many researchers have argued that the as ba if preceded by several pa sounds. use of purely data-driven, inductive methods For a category boundary representation to for concept learning are strongly limited and accommodate this, two category boundaries modulated by the background knowledge one would need to be hypothesized—a relatively has about a concept (Carey, 1985; Gelman & permanent category boundary between ba Markman, 1986; Keil, 1989; Medin, 1989; and pa, and a second boundary that shifts Murphy & Medin, 1985). depending upon the immediate context. The People’s categorizations seem to depend relatively permanent boundary is needed on the theories they have about the world because the contextualized boundary must be (for reviews, see Komatsu, 1992; Medin, based on some earlier information. In many 1989). Theories involve organized systems cases, it is more parsimonious to hypothesize of knowledge. In making an argument for representations for the category members the use of theories in categorization, Murphy themselves and view category boundaries and Medin (1985) provide the example of as side effects of the competition between a man jumping into a swimming pool fully neighboring categories. Context effects are clothed. This man may be categorized as then explained simply by changes to the drunk because we have a theory of behav- strengths associated with different cate- ior and inebriation that explains the man’s gories. By this account, there may be no action. Murphy and Medin argue that the reified boundary around one’s cat concept categorization of the man’s behavior does that causally affects categorizations. When not depend on matching the man’s features asked about a particular object, we can decide to the category drunk’s features. It is highly

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unlikely that the category drunk would have looks like an insect is judged by subjects such a specific feature as jumps into pools to be more similar to an insect, but is also fully clothed. It is not the similarity between judged to be a bird still. Again, the category the instance and the category that determines judgment seems to depend on biological, the instance’s classification; it is the fact that genetic, and historical knowledge, while the our category provides a theory that explains similarity judgments seems to depend more the behavior. on gross visual appearance. Other researchers have empirically sup- Researchers have explored the importance ported the dissociation between theory- of background knowledge in shaping our derived categorization and similarity. In concepts by manipulating this knowledge one experiment, Carey (1985) observes that experimentally. Concepts are more easily children choose a toy monkey over a worm learned when a learner has appropriate back- as being more similar to a human, but that ground knowledge, indicating that more than when they are told that humans have spleens, “brute” statistical regularities underlie our are more likely to infer that the worm has a concepts (Pazzani, 1991). Similarly, when spleen than that the toy monkey does. Thus, the features of a category can be connected the categorization of objects into spleen and through prior knowledge, category learning no spleen groups does not appear to depend is facilitated (Murphy & Allopenna, 1994; on the same knowledge that guides similarity Spalding & Murphy, 1999). Even a single judgments. Carey argues that even young instance of a category can allow people to children have a theory of living things. Part form a coherent category if background of this theory is the notion that living things knowledge constrains the interpretation of k have self-propelled motion and rich internal this instance (Ahn, Brewer, & Mooney, k organizations. Children as young as 3 years of 1992). Concepts are disproportionately rep- age make inferences about an animal’s prop- resented in terms of concept features that are erties on the basis of its category label, even tightly connected to other features (Sloman, when the label opposes superficial visual Love, & Ahn, 1998). similarity (Gelman & Markman, 1986). Forming categories on the basis of Using different empirical techniques, Keil data-driven, statistical evidence, and forming (1989) has come to a similar conclusion. them based upon knowledge-rich theories In one experiment, children are told a story of the world seem like strategies fundamen- in which scientists discover that an animal tally at odds with each other. Indeed, this is that looks exactly like a raccoon actually probably the most basic difference between contains the internal organs of a skunk and theories of concepts in the field. However, has skunk parents and skunk children. With these approaches need not be mutually exclu- increasing age, children increasingly claim sive. Even the most outspoken proponents that the animal is a skunk. That is, there is of theory-based concepts do not claim that a developmental trend for children to cate- similarity-based or statistical approaches are gorize on the basis of theories of heredity not also needed (Murphy & Medin, 1985). and biology rather than visual appearance. Moreover, some researchers have suggested In a similar experiment, Rips (1989) shows integrating the two approaches. Theories an explicit dissociation between categoriza- in the form of prior knowledge about a tion judgments and similarity judgments in domain are recruited in order to account for adults. An animal that is transformed (by empirically observed categorizations, and toxic waste) from a bird into something that one mechanism for this is the process of

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subjects trying to form explanations for the what concepts they will use experimentally. observations (Williams & Lombrozo, 2013; Evidence for rule-based categories tends to Williams, Lombrozo, & Rehder, 2013). Heit be found with categories that are created (1994, 1997) describes a similarity-based, from simple rules (Bruner et al., 1956). Evi- exemplar model of categorization that incor- dence for prototypes tends to be found for porates background knowledge by storing categories made up of members that are dis- category members as they are observed (as tortions around single prototypes (Posner & with all exemplar models), but also storing Keele, 1968). Evidence for exemplar models never-seen instances that are consistent with is particular strong when categories include the background knowledge. Choi, McDaniel, exceptional instances that must be individu- and Busemeyer (1993) described a neural ally memorized (Nosofsky & Palmeri, 1998; network model of concept learning that does Nosofsky, Palmeri, & McKinley, 1994). not begin with random or neutral connections Evidence for theories is found when cat- between features and concepts (as is typical), egories are created that subjects already but begins with theory-consistent connec- know something about (Murphy & Kaplan, tions that are relatively strong. Rehder and 2000). The researcher’s choice of represen- Murphy (2003) propose a bidirectional neural tation seems to determine the experiment network model in which observations affect, that is conducted rather than the experiment and are affected by, background knowledge. influencing the choice of representation. Hierarchical Bayesian models allow theories, There may be a grain of truth to this incorporated as prior probabilities on specific cynical conclusion, but our conclusions are structural forms, to guide the construction instead that people use multiple representa- k of knowledge, oftentimes forming knowl- tional strategies (Weiskopf, 2009) and can k edge far more rapidly than predicted if each flexibly deploy these strategies based upon observation needed to be separately learned the categories to be learned. From this per- (Kemp & Tenenbaum, 2008, 2009; Lucas & spective, representational strategies should Griffiths, 2010). All of these computational be evaluated according to their trade-offs, approaches allow domain-general category and for their fit to the real-world categories learners to also have biases toward learn- and empirical results. For example, exemplar ing categories consistent with background representations are costly in terms of storage knowledge. demands, but are sensitive to interactions between features and adaptable to new cat- egorization demands. There is a growing Summary to Representation consensus that at least two kinds of repre- Approaches sentational strategies are both present but One cynical conclusion to reach from the separated—rule-based and similarity-based preceding alternative approaches is that a processes (Erickson & Kruschke, 1998; researcher starts with a theory, and tends to Pinker, 1991; Sloman, 1996). There is even find evidence consistent with the theory—a recent evidence for reliable individual dif- result that is meta-analytically consistent ferences in terms of these strategies, with with a theory-based approach! Although this different groups of people naturally inclined state of affairs is typical throughout psychol- toward either rule-based or exemplar learn- ogy, it is particularly rife in concept-learning ing processes (McDaniel, Cahill, Robbins, & research because researchers have a sig- Wiener, 2014). Other researchers have argued nificant amount of flexibility in choosing for separate processes for storing exemplars

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and extracting prototypes (Knowlton & This may be a useful simplifying assumption, Squire, 1993; J. D. Smith & Minda, 2000, allowing a researcher to test theories of how 2002). Some researchers have argued for features are combined to form concepts. a computational rapprochement between There is mounting evidence, however, that exemplar and prototype models in which conceptual processes may act directly on prototypes are formed around statistically modality-specific perceptual information, supported clusters of exemplars (Love et al., eliminating the need to first transduce that 2004). Even if one holds out hope for a uni- information into amodal feature lists before fied model of concept learning, it is important categorization can begin. to recognize these different representational Evidence for a role of perceptual infor- strategies as special cases that must be mation in conceptual processes comes achievable by the unified model given the from research relating to Barsalou’s (1999, appropriate inputs. 2008) theory of perceptual symbol systems. According to this theory, sensorimotor areas of the brain that are activated during the ini- CONNECTING CONCEPTS tial perception of an event are reactivated at a later time by association areas, serving as a Although knowledge representation appro- representation of one’s prior perceptual expe- aches have often treated conceptual sys- rience. Rather than preserving a verbatim tems as independent networks that gain record of what was experienced, however, their meaning by their internal connections association areas only reactivate certain (Lenat & Feigenbaum, 1991), it is important aspects of one’s perceptual experience, to remember that concepts are connected namely those that received attention. Because k to both perception and language. Concepts’ k these reactivated aspects of experience may connections to perception serve to ground be common to a number of different events, them (Goldstone & Rogosky, 2002; Harnad, they may be thought of as symbols, represent- 1990), and their connections to language ing an entire class of events. Because they allow them to transcend direct experience are formed around perceptual experience, and to be easily transmitted. however, they are perceptual symbols, unlike the amodal symbols typically employed in Connecting Concepts to Perception symbolic theories of cognition. Concept formation is often studied as though In support of this theory, neuroimaging it were a modular process (in the sense of research has revealed that conceptual pro- Fodor, 1983). For example, participants in cessing leads to activation in sensorimotor category learning experiments are often pre- regions of the brain, even when that acti- sented with verbal feature lists representing vated information is not strictly necessary to the objects to be categorized. The use of perform the conceptual task. For example, this method suggests an implicit assumption Simmons, Martin, and Barsalou (2005) that the perceptual analysis of an object revealed in a functional magnetic resonance into features is complete before one starts imaging (fMRI) study that pictures of appe- to categorize that object. Categorization tizing foods led to activation in areas associ- processes can then act upon the features that ated with the perception of taste, even though result from this analysis, largely unconcerned the task simply involved visual matching with the specific perceptual information that and thus taste was irrelevant. This suggests led to the identification of those features. that food concepts may be represented by

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activation in a variety of areas representing occurs early in the process of concept the different sensory modalities associated access, rather than reflecting later visual with those concepts. Furthermore, Simmons imagery processes. et al. (2007) revealed that brain areas respon- Although neuroimaging studies with sive to color information in a visual task were fMRI and ERP reveal that activation of per- also activated by judgments of color prop- ceptual areas is associated with conceptual erties associated with concepts, even though processing, these are correlational methods, the concepts and properties were presented and thus it still remains possible that acti- only in verbal form. Representing the various vation of perceptual areas does not play a properties associated with a concept appar- direct causal role in concept access and use. ently recruits the same brain mechanisms For example, on the basis of these results that are involved in directly perceiving those alone, it remains possible that presentation properties, consistent with the theory of of a word leads one to access an amodal perceptual symbol systems. symbolic representation of the associated Although findings such as these demon- concept, but that perceptual areas are also strate that perceptual representations are activated via a separate pathway. These per- activated when a concept is instantiated, they ceptual representations would thus have no leave open the possibility that the concepts causal role in accessing or representing the themselves are represented in amodal for- concept. To establish causality, it is necessary mat, and that the activation of perceptual to manipulate activation of perceptual areas representations reflects visual imagery pro- and demonstrate an effect on concept access. cesses subsequent to the identification of An example of such a manipulation was k a concept. This account remains possible carried out by Vermeulen, Corneille, and k because the coarse temporal resolution of Niedenthal (2008). They presented partici- fMRI makes unclear the exact sequence pants with a memory load presented either in of neural events leading to successful task the visual or auditory modality. While main- performance. To address this concern, Kiefer, taining these items, participants were given Sim, Herrnberger, Grothe, and Hoenig (2008) a property verification task in which either examined the activation of perceptual rep- a visual or an auditory property of a concept resentations using not only fMRI but also had to be verified. Participants were slower event-related potentials (ERPs), a brain- to verify visual properties while simultane- imaging technique with much better tem- ously maintaining a visual memory load, poral resolution. Neuroimaging with fMRI whereas they were slower to verify auditory revealed that auditory areas were activated properties while simultaneously maintaining in response to visual presentation of words an auditory memory load. These results sug- referring to objects with strongly associated gest that concept access involves activating acoustic features (e.g., telephone). Moreover, various modalities of sensorimotor informa- results with ERP suggested that these audi- tion associated with the concept, and thus tory areas were activated within 150 ms that simultaneous processing of other unre- of stimulus presentation, quite similar to lated perceptual information within the same durations previously established for access- modality can interfere with concept access ing meanings for visually presented words (see also Witt, Kemmerer, Linkenauger, & (e.g., Pulvermüller, Shtyrov, & Ilmoniemi, Culham, 2010). 2005). This combination of results suggests The results described so far in this section that activation of perceptual representations suggest that concepts are represented not in

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terms of amodal symbols transduced from In particular, the phonemes of language perceptual experience, but rather in terms of may have evolved to reflect the sensitivities perceptual information itself. The specific of the human perceptual system. Evidence patterns of perceptual information that one consistent with this viewpoint comes from has experienced when learning about a con- the fact that chinchillas are sensitive to many cept may thus influence the representation of of the same sound contrasts as are humans, that concept (e.g., see Kiefer, Sim, Liebich, even though chinchillas obviously have no Hauk, & Tanaka, 2007), possibly even for language (Kuhl & Miller, 1975). There is putatively abstract concepts that one may evidence, however, that the phonemes to not expect to be associated with percep- which a listener is sensitive can be modi- tual information, such as truth and freedom fied by experience. In particular, although (Barsalou & Wiemer-Hastings, 2005). More- newborn babies appear to be sensitive to all over, if there is overlap in perceptual and of the sound contrasts present in all of the conceptual representations, then not only world’s languages, a 1-year-old can only may perceptual information affect concept hear those sound contrasts present in his access and use, but one’s concepts may also or her linguistic environment (Werker & influence one’s perceptual sensitivities, with Tees, 1984). Thus, children growing up in concept activation leading to top-down influ- Japan lose the ability to distinguish between ences on perceptual discrimination abilities the /l/ and /r/ phonemes, whereas children (Brooks & Freeman, Chapter 13 in Volume growing up in the United States retain this 4ofthisHandbook; Lupyan, 2008b; but ability (Miyawaki, 1975). The categories of see Firestone & Scholl, 2016 for skepticism language thus influence one’s perceptual sen- k regarding top-down effects). The relationship sitivities, providing evidence for an influence k between perceptual and conceptual processes of concepts on perception. may thus be bidirectional (Goldstone & Although categorical perception was Barsalou, 1998), with the identification of originally demonstrated in the context of perceptual features influencing the catego- auditory perception, similar phenomena have rization of an object, and the categorization since been discovered in vision (Goldstone & of an object influencing the perception of Hendrickson, 2010). For example, Goldstone features (Bassok, 1996). (1994a) trained participants to make a cate- Classic evidence for an influence of con- gory discrimination either in terms of the size cepts on perception comes from research or brightness of an object. He then presented on the previously described phenomenon those participants with a same/different task, of categorical perception. Listeners are in which two briefly presented objects were much better at perceiving contrasts that are either the same or varied in terms of size or representative of different phoneme cate- brightness. Participants who had earlier cat- gories (Liberman, Cooper, Shankweiler, & egorized objects on the basis of a particular Studdert-Kennedy, 1967). For example, lis- dimension were found to be better at telling teners can hear the difference in voice onset objects apart in terms of that dimension than time between bill and pill, even when this were control participants who had been given difference is no greater than the difference no prior categorization training. Moreover, between two /b/ sounds that cannot be dis- this sensitization of categorically relevant tinguished. One may argue that categorical dimensions was most evident at those values perception simply provides further evidence of the dimension that straddled the boundary of an influence of perception on concepts. between categories.

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These findings thus provide evidence of as an example of object categorization, that the concepts that one has learned influ- with the goal of the process being to identify ence one’s perceptual sensitivities, in the what kind of object one is observing. Unlike visual as well as in the auditory modality theories of categorization, theories of object (see also Ozgen & Davies, 2002). Other recognition place strong emphasis on the research has shown that prolonged experi- role of perceptual information in identifying ence with domains such as dogs (Tanaka & an object. Taylor, 1991), cars and birds (Gauthier, Interestingly, some of the theories that Skudlarski, Gore, & Anderson, 2000), faces have been proposed to account for object (Levin & Beale, 2000; O’Toole, Peterson, & recognition have characteristics in com- Deffenbacher, 1995) or even novel “Greeble” mon with theories of categorization. For stimuli (Gauthier, Tarr, Anderson, Skud- example, structural description theories of larski, & Gore, 1999) leads to a perceptual object recognition (e.g., Biederman, 1987; system that is tuned to these domains. Gold- Hummel & Biederman, 1992) are similar to stone et al. (2000; Goldstone, Landy, & prototype theories of categorization in that Son, 2010) and Lupyan (2015) review other a newly encountered exemplar is compared evidence for conceptual influences on visual to a summary representation of a category in perception. Concept learning appears to be order to determine whether or not the exem- effective both in combining stimulus proper- plar is a member of that category. In contrast, ties together to create perceptual chunks that multiple views theories of object recognition are diagnostic for categorization (Goldstone, (e.g., Edelman, 1998; Riesenhuber & Poggio, 2000), and in splitting apart and isolating per- 1999; Tarr & Bülthoff, 1995) are similar to k ceptual dimensions if they are differentially exemplar-based theories of categorization in k diagnostic for categorization (Goldstone & that a newly encountered exemplar is com- Steyvers, 2001; M. Jones & Goldstone, pared to a number of previously encountered 2013). In fact, these two processes can be exemplars stored in memory. The categoriza- unified by the notion of creating perceptual tion of an exemplar is determined either by units in a size that is useful for relevant the exemplar in memory that most closely categorizations (Goldstone, 2003). matches it or by computing the similarities The evidence reviewed in this section sug- of the new exemplar to each of a number of gests that there is a strong interrelationship stored exemplars. between concepts and perception, with per- The similarities in the models proposed ceptual information influencing the concepts to account for categorization and object that one forms and conceptual information recognition suggest that there is consid- influencing how one perceives the world. erable opportunity for cross talk between Most theories of concept formation fail these two domains. For example, theories of to account for this interrelationship. They categorization could potentially be adapted instead take the perceptual attributes of a to provide a more complete account for stimulus as a given and try to account for object recognition. In particular, they may be how these attributes are used to categorize able to provide an account of not only the that stimulus. recognition of established object categories, One area of research that provides an but also the learning of new ones, a problem exception to this rule is research on object not typically addressed by theories of object recognition. As pointed out by Schyns recognition. Furthermore, theories of object (1998), object recognition can be thought recognition could be adapted to provide

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a better account of the role of perceptual categories, on the other hand, may be less information in concept formation and use straightforward. The nature of prelinguistic (Palmeri, Wong, & Gauthier, 2004). The event categories is not very well understood, rapid recent developments in object recog- but the available evidence suggests that nition research, including the development they are structured quite differently from of detailed computational, neurally based verb meanings. For example, research by models (e.g., Jiang et al., 2006; Yamins & Kersten and Billman (1997) demonstrated DiCarlo, 2016), suggest that a careful consid- that when adults learned event categories in eration of the role of perceptual information the absence of category labels, they formed in categorization can be a profitable research those categories around a rich set of corre- strategy. lated properties, including the characteristics of the objects in the event, the motions of those objects, and the outcome of the event. Connecting Concepts to Language Research by Casasola (2005, 2008) has simi- Concepts also take part in a bidirectional larly demonstrated that 10- to 14-month-old relationship with language. In particular, infants form unlabeled event categories one’s repertoire of concepts may influence around correlations among different aspects the types of word meanings that one learns, of an event, in this case involving particular whereas the language that one speaks may objects participating in particular spatial influence the types of concepts that one relationships (e.g., containment, support) forms. with one another. These unlabeled event The first of these two proposals is the categories learned by children and adults k less controversial. It is widely believed that differ markedly from verb meanings. Verb k children come into the process of vocabu- meanings tend to have limited correlational lary learning with a large set of unlabeled structure, instead picking out only one or concepts. These early concepts may reflect a small number of properties of an event the correlational structure in the environment (Huttenlocher & Lui, 1979; Talmy, 1985). of the young child, as suggested by Rosch For example, the verb collide involves two et al. (1976). For example, a child may form objects moving into contact with one another, a concept of dog around the correlated prop- irrespective of the objects involved or the erties of four legs, tail, wagging, slobbering, outcome of the collision. and so forth. The subsequent learning of a It may thus be difficult to directly map word meaning should be relatively easy to verbs onto existing event categories. Instead, the extent that one can map that word onto language-learning experience may be nec- one of these existing concepts. essary to determine which aspects of an Different kinds of words may vary in event are relevant and which aspects are the extent to which they map directly onto irrelevant to verb meanings. Perhaps as a existing concepts, and thus some types of result, children learning a variety of different words may be learned more easily than languages have been found to learn verbs others. For example, Gentner (1981, 1982; later than nouns (Bornstein et al., 2004; Gentner & Boroditsky, 2001) has proposed Gentner, 1982; Gentner & Boroditsky, 2001; that nouns can be mapped straightforwardly Golinkoff & Hirsh-Pasek, 2008; but see onto existing object concepts, and thus nouns Gopnik & Choi, 1995 and Tardif, 1996 for are learned relatively early by children. possible exceptions). More generally, word The relation of verbs to prelinguistic event meanings should be easy to learn to the

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extent that they can be mapped onto existing Related findings come from Chin-Parker concepts. and Ross (2002, 2004). They compared cate- There is greater controversy regarding the gory learning in the context of a classification extent to which language may influence one’s task, in which the goal of the participant concepts. Some influences of language on was to predict the category label associated concepts are fairly straightforward, however. with an exemplar, to an inference-learning As one example, words in a language provide task, in which the goal of the participant convenient “handles” for referring to patterns was to predict a missing feature value. When of correlated features that would otherwise the members of a category shared multiple be overwhelmingly complex (Lupyan, 2012). feature values, one of which was diagnos- As a second example, whether a concept is tic of category membership and others of learned in the presence or absence of lan- which were nondiagnostic (i.e., they were guage (e.g., a category label) may influence also shared with members of the contrasting the way in which that concept is learned. category), participants who were given a When categories are learned in the pres- classification task homed in on the feature ence of a category label in a supervised that was diagnostic of category membership, classification task, a common finding is failing to learn the other feature values that one of competition among correlated cues were representative of the category but were for predictive strength (Gluck & Bower, nondiagnostic (see also Yamauchi, Love, & 1988; Shanks, 1991). In particular, more Markman, 2002). In contrast, participants salient cues may overshadow less salient who were given an inference-learning task cues, causing the concept learner to fail to were more likely to discover all of the feature k notice the predictiveness of the less salient values that were associated with a given k cue (Gluck & Bower, 1988; Kruschke, 1992; category, even those that were nondiagnostic. Shanks, 1991). There is thus evidence that the presence When categories are learned in the absence of language influences the way in which a of category labels in unsupervised or obser- concept is learned. A more controversial sug- vational categorization tasks, on the other gestion is that the language that one speaks hand, there is facilitation rather than competi- may influence the types of concepts that tion among correlated predictors of category one learns. This suggestion, termed the lin- membership (Billman, 1989; Billman & guistic relativity hypothesis, was first made Knutson, 1996, Kersten & Billman, 1997). by Whorf (1956), on the basis of apparent The learning of unlabeled categories can be dramatic differences between English and measured in terms of the learning of corre- Native American languages in their expres- lations among attributes of a stimulus. For sions of ideas such as time, motion, and color. example, one’s knowledge of the correlation For example, Whorf proposed that the Hopi between a wagging tail and a slobbering make no distinction between the past and mouth can be used as a measure of one’s present because the Hopi language provides knowledge of the category dog. Billman and no mechanism for talking about this distinc- Knutson (1996) used this unsupervised cate- tion. Many of Whorf’s linguistic analyses gorization method to examine the learning of have since been debunked (see Pinker, 1994, unlabeled categories of novel animals. They for a review), but his theory remains a source found that participants were more likely to of controversy. learn the predictiveness of an attribute when Early experimental evidence suggested other correlated predictors were also present. that concepts were relatively impervious

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to linguistic influences. In particular, categories penetrate visual processing Heider’s (1972) classic finding that speakers (Lupyan, 2008b). Thus, at the very least, one of Dani, a language with only two color may expect that a concept will be more likely words, learned new color concepts in a to be learned when it is labeled in a language similar fashion to English speakers sug- than when it is unlabeled. Although this gested that concepts were determined by may seem obvious, further predictions are perception rather than by language. More possible when this finding is combined with recently, however, Roberson and colleagues the evidence for influences of concepts on (Roberson, Davidoff, Davies, & Shapiro, perception reviewed earlier. In particular, on 2005; Roberson, Davies, & Davidoff, 2000) the basis of the results of Goldstone (1994a), attempted to replicate Heider’s findings with one may predict that when a language makes other groups of people with limited color reference to a particular dimension, thus vocabularies, namely speakers of Berinmo causing people to form concepts around in New Guinea and speakers of Himba in that dimension, people’s perceptual sensi- Namibia. In contrast to Heider’s findings, tivities to that dimension will be increased. Roberson et al. (2000) found that the Berinmo Kersten, Goldstone, and Schaffert (1998) speakers did no better at learning a new color provided evidence for this phenomenon and category for a color that was easy to name referred to it as attentional persistence. This in English than for a hard to name color. attentional persistence, in turn, would make Moreover, speakers of Berinmo and Himba people who learn this language more likely did no better at learning a category discrimi- to notice further contrasts along this dimen- nation between green and blue (a distinction sion. Thus, language may influence people’s k not made in either language) than they did concepts indirectly through one’s perceptual k at learning a discrimination between two sensitivities. shades of green. This result contrasted with This proposal is consistent with L. B. the results of English-speaking participants Smith and Samuelson’s (2006) account of who did better at the green/blue discrim- the apparent shape bias in children’s word ination. It also contrasted with superior learning. They proposed that children learn- performance in Berinmo and Himba speakers ing languages such as English discover over on discriminations that were present in their the course of early language acquisition that respective languages. These results suggest the shapes of objects are important in distin- that the English division of the color spec- guishing different nouns. As a result, they trum may be more a function of the English attend more strongly to shape in subsequent language and less a function of human color word learning, resulting in an acceleration in physiology than was originally believed. subsequent shape word learning. Consistent Regardless of one’s interpretation of the with this proposal, children learning English Heider (1972) and Roberson et al. (2000, come to attend to shape more strongly and 2005) results, there are straightforward rea- in a wider variety of circumstances than do sons to expect at least some influence of speakers of Japanese, a language in which language on one’s concepts. Research dating shape is marked less prominently and other back to Homa and Cultice (1984) has demon- cues, such as material and animacy, are more strated that people are better at learning prominent (Imai & Gentner, 1997; Yoshida & concepts when category labels are provided Smith, 2003). as feedback. Verbally labeling a visual target Although languages differ to some extent exaggerates the degree to which conceptual in the ways they refer to object categories,

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languages differ perhaps even more dra- English speakers, monolingual Spanish matically in their treatment of less concrete speakers, and Spanish/English bilinguals domains, such as time (Boroditsky, 2001), performed quite similarly when the path of number (Frank, Everett, Fedorenko, & an alien creature was diagnostic of category Gibson, E., 2008), space (Levinson, Kita, membership. Differences emerged when a Haun, & Rasch, 2002), motion (Gentner & novel manner of motion of a creature (i.e., the Boroditsky, 2001; Kersten, 1998a, 1998b, way it moved its legs in relation to its body) 2003), and blame (Fausey & Boroditsky, was diagnostic, however, with monolingual 2010, 2011). For example, when describ- English speakers performing better than ing motion events, languages differ in the monolingual Spanish speakers. Moreover, particular aspects of motion that are most Spanish/English bilinguals performed differ- prominently labeled by verbs. In English, the ently depending upon the linguistic context most frequently used class of verbs refers in which they were tested, performing like to the manner of motion of an object (e.g., monolingual English speakers when tested running, skipping, sauntering), or the way in an English language context but per- in which an object moves around (Talmy, forming like monolingual Spanish speakers 1985). In other languages (e.g., Spanish), when tested in a Spanish language context however, the most frequently used class of (see also Lai, Rodriguez, & Narasimhan, verbs refers to the path of an object (e.g., 2014). Importantly, the same pattern of entering, exiting), or its direction with respect results was obtained regardless of whether to some external reference point. In these lan- the concepts to be learned were given novel guages, manner of motion is relegated to an linguistic labels or were simply numbered, k adverbial, if it is mentioned at all. If language suggesting an influence of native language k influences one’s perceptual sensitivities, itis on nonlinguistic concept formation. possible that English speakers and Spanish Thus, although the notion that language speakers may differ in the extent to which influences concept use remains controver- they are sensitive to motion attributes such as sial, there is a growing body of evidence the path and manner of motion of an object. that speakers of different languages perform Initial tests of English and Spanish speak- differently in a variety of different catego- ers’ sensitivities to manner and path of motion rization tasks. Proponents of the universalist (e.g., Gennari, Sloman, Malt, & Fitch, 2002; viewpoint (e.g., Li, Dunham, & Carey, 2009; Papafragou, Massey, & Gleitman, 2002) Pinker, 1994) have argued that such findings only revealed differences between the two simply represent attempts by research partic- groups when they were asked to describe ipants to comply with experimental demands, events in language. These results thus pro- falling back on overt or covert language use vide evidence only of an influence of one’s to help them solve the problem of “What prior language-learning history on one’s does the experimenter want me to do here?” subsequent language use, rather than an According to these accounts, speakers of influence of language on one’s nonlinguistic different languages all think essentially the concept use. More recently, however, Kersten same way when they leave the laboratory. et al. (2010) revealed effects of one’s lan- Unfortunately, we do not have very good guage background on one’s performance in a methods for measuring how people think supervised classification task in which either outside of the laboratory, so it is difficult manner of motion or path served as the diag- to test these accounts. Rather than arguing nostic attribute. In particular, monolingual about whether a given effect of language

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observed in the laboratory is sufficiently one instance is studied at a time. Moreover, if large and sufficiently general to count asa the instances being studied (even if individu- Whorfian effect, perhaps a more constructive ally) include a high level of variation along approach may be to document the various the irrelevant dimensions, learners are gen- conditions under which language does and erally more likely to transfer their learning does not influence concept use. This strategy to novel situations (e.g., Ben-Zeev & Star, may lead to a better understanding of the 2001; Chang, Koedinger, & Lovett, 2003; bidirectional relationship between concepts Braithwaite & Goldstone, 2015; H. S. Lee, and language, and the three-way relationship Betts, & Anderson, 2015). One explanation among concepts, language, and perception for this benefit is that studying a superficially (Winawer et al., 2007). diverse set of items allows the learner to notice and extrapolate the common prop- erties, central to the concept being learned HOW TO IMPROVE CATEGORY (Belenky & Schalk, 2014; Day & Goldstone, LEARNING? 2012; Gentner, 1983; Gick & Holyoak, 1983). However, item variability has also A diverse set of research has shown that there been shown to have no effect on learning are many factors that influence the effective- effectiveness (e.g., Reed, 1989). Braithwaite ness of category learning. A central question and Goldstone (2015) have presented empir- in this research is how to best configure a ical evidence and computational modeling category-learning context to promote the showing that learners with a lower initial acquisition of the relevant concept and the knowledge level benefit from less variation k ability to apply that knowledge to new exem- among study items, while learners with high k plars or situations where that knowledge is levels of prior knowledge benefit from work- useful. As an example, students and teachers ing through examples with more variability in every school, university, and training (see also Novick, 1988). center struggle to make learning efficient and Similarly, Elio and Anderson (1984) generalizable. Proposals for how to optimize proposed that learning should start with category learning range from selecting the low-variability items (e.g., items that do not appropriate type of examples to be studied differ much from one another or from the cen- (Gibson, Rogers, & Zhu, 2013), choosing the tral tendency of the category), and items with right type of task, and shifting how a student greater variability should be introduced later should approach the task. (for similar evidence with young learners An important way to promote learning see Sandhofer & Doumas, 2008). However, and transfer of concepts is by establishing not all learners benefit from this approach. comparisons between similar items and The authors also show that if the learners’ making use of analogical reasoning while approach to the task is to consciously gen- learning. When learners study two or more erate hypotheses for category membership, instances of the same concept side by side, the pattern of results is reversed (Elio & transfer to more remote instances (e.g., Anderson, 1984). One possibility is that Gick & Holyoak, 1983; Meagher, Carvalho, how the learner approaches the task changes Goldstone, & Nosofsky, 2017; Omata & what type of information gets encoded and, Holyoak, 2012; Quilici & Mayer, 2002) or consequently, what information is most rel- acquisition of a new category (e.g., Gentner & evant (Elio & Anderson, 1984). It has also Namy, 1999) is more likely than when only been suggested that for optimal transfer of

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category learning, the study situation should the goal is to acquire an independent charac- emphasize items that promote a coherent terization of each concept, presenting several generalization based on the properties that examples of the same category in close suc- frequently occur (Elio & Anderson, 1981). cession improves transfer to a greater degree Moreover, in situations where one needs to than frequent alternation (Carpenter & learn several items that promote different Mueller, 2013; Carvalho & Goldstone, 2014, types of generalizations, the best learning 2015; Zulkiply & Burt, 2013). Moreover, is achieved by studying items that promote because greater delays between presenta- similar generalizations close in time (Elio & tions make it harder to retrieve previous Anderson, 1981; Mathy & Feldman, 2009). encounters, spaced presentation of items From the brief survey just provided a of a single category can promote learning question surfaces: Should learning start with and constitute a desirable difficulty (Bjork, difficult items and progress toward easier 1994). Consistent with this idea, Birnbaum ones or the other way around? In general, et al. (2013) showed that while introducing a research seems to indicate that learning ben- temporal delay between successive presenta- efits from study with examples organized in tions of different categories hindered learning increasing order of complexity or difficulty, and transfer, increasing the temporal delay that is, from the easiest and simplest to between successive presentations of items the hardest and more complex (Ahissar & of the same category improved it (see also Hochstein, 1997; Baddeley, 1992; Hull, 1920; Kang & Pashler, 2012). Similarly, research Terrace, 1964; Wilson, Baddeley, Evans, & with young children has shown that category Shiel, 1994). However, this might be the generalization benefits from play periods k case only for categories requiring integration between successive presentations of items k across different dimensions (Spiering & of the same category (Vlach, Sandhofer, & Ashby, 2008), but the reverse may hold for Kornell, 2008), and from study with increas- categories organized around a clear rule. ingly greater temporal delays between Consistent with this latter provision, E. S. successive repetitions of the same category Lee, MacGregor, Bavelas, and Mirlin (1988) (Vlach, Sandhofer, & Bjork, 2014). showed that learners who start by studying Finally, an increasingly important issue is examples that other learners classified incor- whether category learning can be improved rectly made fewer errors during classification by just leaving it in the hands of those who tests than learners who studied the examples might care the most about it—the learn- in the opposite order. ers themselves. Is self-regulated learning When it is not possible to change type of better than being given the best study for- examples, their difficulty, or the task, cate- mat and organization as determined by an gory learning can nonetheless be improved informed teacher? On the one hand, it has by a careful sequential organization of the been shown that learners are often unaware examples (Carvalho & Goldstone, 2015). of how to improve concept learning and It has been shown before that alternat- fall victim to a series of biases (Bjork, ing presentation of items from different Dunlosky, & Kornell, 2013). On the other hard-to-discriminate categories improves hand, self-regulated study is often relatively category learning and transfer (Birnbaum, effective. For example, learners deciding Kornell, Bjork, & Bjork, 2013; Carvalho & how to sample information outperform Goldstone, 2014; Rohrer, Dedrick, & those who receive a random sampling of Stershic, 2015). On the other hand, when examples or who are yoked to the selections

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of another learner in a categorization is independent of others. For example, one task (e.g., Markant & Gureckis, 2014) or a can list the exemplars that are included in recognition memory task (Markant, DuBrow, the concept bird, or describe its central ten- Davachi, & Gureckis, 2014). The mechanism dency, without making recourse to any other behind this advantage is still an open ques- concepts. However, it is likely that all of our tion. It might be the result of efficient sam- concepts are embedded in a network where pling of information given the data available, each concept’s meaning depends on other the process of sampling itself, the greater concepts, as well as perceptual processes and effort afforded by actively learning, or deci- linguistic labels. The proper level of analysis sional processes (Gureckis & Markant, 2012). may not be individual concepts as many Understanding how concept learning can researchers have assumed, but systems of be optimized will contribute to designing concepts. The connections between concepts better instructional techniques and sys- and perception on the one hand and between tems (Koedinger, Booth, & Klahr, 2013). concepts and language on the other hand Furthermore, it will also contribute to reveal an important dual nature of concepts. our foundational understanding of the Concepts are used both to recognize objects mechanisms underlying concept learning and to ground word meanings. Working (Carvalho & Goldstone, 2015). Methods out the details of this dual nature will go a for constructing optimal sets of training long way toward understanding how human items given a known learning algorithm and thinking can be both concrete and symbolic. well-defined educational goal have proven A second direction is the development of informative for understanding both human more sophisticated formal models of concept k and machine learning, their commonalities, learning. One important recent trend in math- k and their differences (Zhu, 2015). ematical models has been the extension of rational models of categorization (Anderson, 1991) to Bayesian models that assume that CONCLUSION categories are constructed to maximize the likelihood of making legitimate inferences The field of concept learning and represen- (Goodman et al., 2008; Griffiths & Tenen- tation is noteworthy for its large number of baum, 2009; Kemp & Tenenbaum, 2009). directions and perspectives. While the lack of In contrast to this approach, other researchers closure may frustrate some outside observers, are continuing to pursue neural network it is also a source of strength and resilience. models that offer process-based accounts of With an eye toward the future, we describe concept learning on short and long timescales some of the most important avenues for future (M. Jones, Love, & Maddox, 2006; Rogers & progress in the field. McClelland, 2008), and still others chas- First, as the last section suggests, we tise Bayesian accounts for inadequately believe that much of the progress of research describing how humans learn categories in on concepts will be to connect concepts to an incremental and memory-limited fashion other concepts (Goldstone, 1996; Landauer & (M. Jones & Love, 2011). Progress in neural Dumais, 1997), to the perceptual world, and networks, mathematical models, statistical to language. One of the risks of viewing models, and rational analyses can be gauged concepts as represented by rules, prototypes, by several measures: goodness of fit to human sets of exemplars, or category boundaries is data, breadth of empirical phenomena accom- that one can easily imagine that one concept modated, model constraint and parsimony,

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and autonomy from human intervention. The factors that impact the ease of learning and current crop of models is fairly impressive in transferring conceptual knowledge. The liter- terms of fitting specific data sets, but there ature contains excellent suggestions on how is much room for improvement in terms to manipulate category labels, presentation of their ability to accommodate rich sets order, learning strategies, stimulus format, of concepts, and process real-world stimuli and category variability in order to optimize without relying on human judgments or hand the efficiency and likelihood of concept coding (Goldstone & Landy, 2010). attainment. Putting these suggestions to use A third direction for research is to in classrooms, computer-based tutorials, and tackle more real-world concepts rather multimedia instructional systems could have than laboratory-created categories, which a substantial positive impact on pedagogy. are often motivated by considerations of This research can also be used to develop controlled construction, ease of analysis, and autonomous computer diagnosis systems, fit to model assumptions. Some researchers user models, information visualization sys- have, instead, tried to tackle particular con- tems, and databases that are organized in a cepts in their subtlety and complexity, such manner consistent with human conceptual as the concepts of food (Ross & Murphy, systems. Given the importance of concepts 1999), water (Malt, 1994), and political party for intelligent thought, it is not unreasonable (Heit & Nicholson, 2010). Others have made to suppose that concept-learning research the more general point that how a concept will be equally important for improving is learned and represented will depend on thought processes. how it is used to achieve a benefit while k interacting with the world (Markman & k Ross, 2003; Ross, Wang, Kramer, Simons, & REFERENCES Crowell, 2007). Still others have worked to develop computational techniques that Acker, B. E., Pastore, R. E., & Hall, M. D. can account for concept formation when (1995). Within-category discrimination of musi- provided with large-scale, real-world data cal chords: Perceptual magnet or anchor? Per- ception and Psychophysics, 57, 863–874. sets, such as library catalogs or corpuses of one million words taken from encyclopedias Aha, D. W. (1992). Tolerating noisy, irrelevant and novel attributes in instance-based learning algo- (Glushko, Maglio, Matlock, & Barsalou, rithms. International Journal of Man-Machine 2008; Griffiths, Steyvers, & Tenenbaum, Studies, 36, 267–287. 2007; Landauer & Dumais, 1997). All of Ahissar, M., & Hochstein, S. (1997). Task diffi- these efforts share a goal of applying our the- culty and the specificity of perceptual learning. oretical knowledge of concepts to understand Nature, 387, 401–406. how specific conceptual domains of interest Ahn, W-K, Brewer, W. F., & Mooney, R. J. (1992). are learned and organized, and in the process Schema acquisition from a single example. of so doing, challenging and extending our Journal of Experimental Psychology: Learning, theoretical knowledge. Memory, and Cognition, 18, 391–412. A final important direction will beto Allen, S. W., & Brooks, L. R. (1991). Specializ- apply psychological research on concepts. ing the operation of an explicit rule. Journal of Perhaps the most important and relevant Experimental Psychology: General, 120, 3–19. application is in the area of educational Anderson, J. R. (1991). The adaptive nature of reform. Psychologists have amassed a large human categorization. Psychological Review, amount of empirical research on various 98, 409–429.

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