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CHAPTER 8

Categorization and Concepts

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

INTRODUCTION

Concepts are the building blocks of thought.They are critically involved when we rea-son, make inferences, and try to generalizeour previous experiences to new situations.Behind every word in every language liesa concept, although there are concepts, likethe small plastic tubes attached to the endsof shoelaces, that we are familiar with andcan think about even if we do not knowthat they are called aglets. Concepts areindispensable to human cognition becausethey take the “blooming, buzzing confu-sion” (James, 1890, p. 488) of disorganizedsensory experiences and establish orderthrough mental categories. These mentalcategories allow us to make sense of theworld and predict how worldly entities willbehave. We see, hear, interpret, remember,understand, and talk about our world throughour concepts, and so it is worthy of reflec-tion time to establish where concepts comefrom, how they work, and how they canbest be learned and deployed to suit ourcognitive needs.

We are grateful to Brian Rogosky, Robert Nosofsky, JohnAQ1Kruschke, Linda Smith, and David Landy for helpfulcomments on earlier drafts of this chapter. This researchwas funded by National Science Foundation REESEgrant DRL-0910218, and Department of Education IESgrant R305A1100060.

Issues related to concepts and catego-rization are nearly ubiquitous in psychologybecause of people’s natural tendency toperceive a thing as something. We have apowerful impulse to interpret our world.This act of interpretation, an act of “seeingsomething as X” rather than simply seeing it(Wittgenstein, 1953), is fundamentally an actof categorization.

The attraction of research on concepts isthat an extremely wide variety of cognitiveacts can be understood as categorizations(Kurtz, 2015; Murphy, 2002). Identifying theperson sitting across from you at the breakfasttable involves categorizing something as yourspouse. Diagnosing the cause of someone’sillness involves a disease categorization.Interpreting a painting as a Picasso, an arti-fact as Mayan, a geometry as non-Euclidean,a fugue as baroque, a conversationalist ascharming, a wine as a Bordeaux, and a gov-ernment as socialist are categorizations atvarious levels of abstraction. The typicallyunspoken assumption of research on conceptsis that these cognitive acts have somethingin common. That is, there are principles thatexplain many or all acts of categorization.This assumption is controversial (see Medin,Lynch, & Solomon, 2000), but is perhapsjustified by the potential payoff of discover-ing common principles governing conceptsin their diverse manifestations.

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276 Categorization and Concepts

The desirability of a general account ofconcept learning has led the field to focusits energy on what might be called genericconcepts. Experiments typically involve arti-ficial categories that are hopefully unfamiliarto the subject. Formal models of conceptlearning and use are constructed to be able tohandle any kind of concept irrespective of itscontent. Although there are exceptions to thisgeneral trend (Malt, 1994; Ross & Murphy,1999), much of the mainstream empiricaland theoretical work on concept learning isconcerned not with explaining how particularconcepts are created, but with how conceptsin general are represented and processed.

One manifestation of this approach is thatthe members of a concept are often givenan abstract symbolic representation. Forexample, Table 8.1 shows a typical notationused to describe the stimuli seen by a subjectin a psychological experiment or presentedto a formal model of concept learning. Nineobjects belong to two categories, and eachobject is defined by its value along fourbinary dimensions. In this notation, objectsfrom Category A typically have values of 1on each of the four dimensions and objectsfrom Category B usually have values of 0.The dimensions are typically unrelated to

Table 8.1 A Common Category Structure

Dimension

Category Stimulus D1 D2 D3 D4

A1 1 1 1 0A2 1 0 1 0

Category A A3 1 0 1 1A4 1 1 0 1A5 0 1 1 1

B1 1 1 0 0Category B B2 0 1 1 0

B3 0 0 0 1B4 0 0 0 0

Source: From Medin and Schaffer (1978). Copy-right 1978 by the American Psychological Association.Reprinted with permission.

each other, and assigning values of 0 and 1 toa dimension is arbitrary. For example, for acolor dimension, red may be assigned a valueof 0 and blue a value 1. The exact categorystructure of Table 8.1 has been used in at least30 studies (reviewed by J. D. Smith & Minda,2000) and instantiated by stimuli as diverseas geometric forms, yearbook photographs,cartoons of faces (Medin & Schaffer, 1978),and line drawings of rocket ships. Theseresearchers are not particularly interestedin the category structure of Table 8.1 andare certainly not interested in the catego-rization of rocket ships per se. Instead, theychoose their structures and stimuli so as to be(a) unfamiliar (so that learning is required),(b) well controlled (dimensions are approx-imately equally salient and independent),(c) diagnostic with respect to theories ofcategory learning, and (d) potentially gen-eralizable to natural categories that peoplelearn. Work on generic concepts is valuableif it turns out that there are domain-generalprinciples underlying human concepts thatcan be discovered. Still, there is no a pri-ori reason to assume that all concepts willfollow the same principles, or that we cangeneralize from generic concepts to naturallyoccurring concepts.

WHAT ARE CONCEPTS?

Concepts, Categories, and InternalRepresentations

A good starting place is Edward Smith’s(1989) characterization that a concept is “amental representation of a class or individualand deals with what is being represented andhow that information is typically used duringthe categorization” (p. 502). It is common todistinguish between a concept and a category.A concept refers to a mentally possessed ideaor notion, whereas a category refers to aset of entities that are grouped together.


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What Are Concepts? 277

The concept dog is whatever psychologicalstate signifies thoughts of dogs. The categorydog consists of all the entities in the realworld that are appropriately categorized asdogs. The question of whether conceptsdetermine categories or vice versa is animportant foundational controversy. On theone hand, if one assumes the primacy ofexternal categories of entities, then one willtend to view concept learning as the enter-prise of inductively creating mental structuresthat predict these categories. One extremeversion of this view is the exemplar modelof concept learning (Estes, 1994; Medin &Schaffer, 1978; Nosofsky, 1984), in whichone’s internal representation of a concept isnothing more than the set of all of the exter-nally supplied examples of the concept towhich one has been exposed. If, on the otherhand, one assumes the primacy of internalmental concepts, then one tends to view exter-nal categories as the end product of usingthese internal concepts to organize observedentities. Some practitioners of a “conceptsfirst” approach argue that the external worlddoes not inherently consist of rocks, dogs,and tables; these are mental concepts thatorganize an otherwise unstructured exter-nal world (Lakoff, 1987). Recent researchindicates that concepts’ extensions (the classof items to which the concept applies) andintensions (the features that distinguish thatclass of items) do not always cohere witheach other (Hampton & Passanisi, 2016).For example, dolphins and whales are oftenjudged to have many of the features charac-teristic of an internal representation of fish(e.g., swims, lives in oceans, and has fins),but are still placed in the extensional set ofmammals rather than fish. The implicationis that a complete model of concepts mayrequire at least partially separate represen-tations for intensions and extensions, ratherthan a more parsimonious model in whicha concept’s intension determines whether

particular objects belong, and how well, tothe concept’s extension.

Equivalence Classes

Another important aspect of concepts is thatthey are equivalence classes. In the classicalnotion of an equivalence class, distinguish-able stimuli come to be treated as the samething once they have been placed in thesame category (Sidman, 1994). This kind ofequivalence is too strong when it comes tohuman concepts because even when we placetwo objects into the same category, we do nottreat them as the same thing for all purposes.Some researchers have stressed the intrinsicvariability of human concepts—variabilitythat makes it unlikely that a concept has thesame sense or meaning each time it is used(Barsalou, 1987; Connell & Lynott, 2014;Thelen & Smith, 1994). Still, the extent towhich perceptually dissimilar things canbe treated equivalently given the appropri-ate conceptualization is impressive. To thebiologist armed with a strong “mammal”concept, even whales and dogs may betreated as commensurate in many situationsrelated to biochemistry, child rearing, andthermoregulation.

Equivalence classes are relatively imper-vious to superficial similarities. Once onehas formed a concept that treats all skunksas equivalent for some purposes, irrelevantvariations among skunks can be greatlyde-emphasized. When people are told a storyin which scientists discover that an animalthat looks exactly like a raccoon actually con-tains the internal organs of a skunk and hasskunk parents and skunk children, they oftencategorize the animal as a skunk (Keil, 1989;Rips, 1989). When people classify objectsinto familiar, labeled categories such as chair,then their memory for the individuating infor-mation about the objects is markedly worse(Lupyan, 2008a). People may never be able


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to transcend superficial appearances whencategorizing objects (Goldstone, 1994b),nor is it clear that they would want to (S. S.Jones & Smith, 1993). Still, one of the mostpowerful aspects of concepts is their abilityto make superficially different things alike(Sloman, 1996). If one has the concept thingsto remove from a burning house, even chil-dren and jewelry become similar (Barsalou,1983). The spoken phonemes /d/ /o/ /g/, theFrench word chien, the written word dog, anda picture of a dog can all trigger one’s conceptof dog (Snodgrass, 1984), and although theymay trigger slightly different representations,much of the core information will be thesame. Concepts are particularly useful whenwe need to make connections between thingsthat have different apparent forms.

WHAT DO CONCEPTS DO FOR US?

Fundamentally, concepts function as filters.We do not have direct access to our externalworld. We only have access to our worldas filtered through our concepts. Conceptsare useful when they provide informative ordiagnostic ways of structuring this world. Anexcellent way of understanding the mentalworld of an individual, group, scientificcommunity, or culture is to find out how theyorganize their world into concepts (Lakoff,1987; Malt & Wolff, 2010; Medin & Atran,1999; Ojalehto & Medin, 2015).

Components of Thought

Concepts are cognitive elements that com-bine together to generatively produce aninfinite variety of thoughts. Just as an endlessvariety of architectural structures can beconstructed out of a finite set of buildingblocks, so concepts act as building blocksfor an endless variety of complex thoughts.Claiming that concepts are cognitive ele-ments does not entail that they are primitive

elements in the sense of existing withoutbeing learned and without being constructedout of other concepts. Some theorists haveargued that concepts such as bachelor, kill,and house are primitive in this sense (Fodor,Garrett, Walker, & Parkes, 1980), but aconsiderable body of evidence suggests thatconcepts typically are acquired elements thatare themselves decomposable into semanticelements (McNamara & Miller, 1989).

Once a concept has been formed, it canenter into compositions with other concepts.Several researchers have studied how novelcombinations of concepts are produced andcomprehended. For example, how does oneinterpret buffalo paper when one first hearsit? Is it paper in the shape of a buffalo, paperused to wrap buffaloes presented as gifts,an essay on the subject of buffaloes, coarsepaper, or is it like flypaper but used to catchbison? Interpretations of word combinationsare often created by finding a relation thatconnects the two concepts. In Murphy’s(1988) concept-specialization model, oneinterprets noun–noun combinations by find-ing a variable that the second noun hasthat can be filled by the first noun. By thisaccount, a robin snake might be interpretedas a snake that eats robins once robin is usedto the fill the eats slot in the snake concept.

In addition to promoting creative thought,the combinatorial power of concepts isrequired for cognitive systematicity (Fodor &Pylyshyn, 1988). The notion of systematicityis that a system’s ability to entertain com-plex thoughts is intrinsically connected toits ability to entertain the components ofthose thoughts. In the field of conceptualcombination, this has appeared as the issueof whether the meaning of a combinationof concepts can be deduced on the basis ofthe meanings of its constituents. However,there are some salient violations of this typeof systematicity. When adjective and nounconcepts are combined, there are sometimes


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What Do Concepts Do for Us? 279

emergent interactions that cannot be pre-dicted by the main effects of the conceptsthemselves. For example, the concept grayhair is more similar to white hair than blackhair, but gray cloud is more similar to blackcloud than white cloud (Medin & Shoben,1988). Wooden spoons are judged to be fairlylarge (for spoons), even though this propertyis not generally possessed by wood objectsor spoons (Medin & Shoben, 1988). Still,there have been successes in predicting howwell an object fits a conjunctive descriptionbased on how well it fits the individualdescriptions that comprise the conjunction(Hampton, 1997). A reasonable reconcilia-tion of these results is that when conceptscombine together, the concepts’ meaningssystematically determine the meaning ofthe conjunction, but emergent interactionsand real-world plausibility also shape theconjunction’s meaning.

Inductive Predictions

Concepts allow us to generalize our expe-riences with some objects to other objectsfrom the same category. Experience with oneslobbering dog may lead one to suspect thatan unfamiliar dog may have the same pro-clivity. These inductive generalizations maybe wrong and can lead to unfair stereotypesif inadequately supported by data, but if anorganism is to survive in a world that hassome systematicity, it must “go beyond theinformation given” (Bruner, 1973) and gen-eralize what it has learned. The concepts weuse most often are useful because they allowmany properties to be inductively predicted.To see why this is the case, we must digressslightly and consider different types of con-cepts. Categories can be arranged roughly inorder of their grounding by similarity: natu-ral kinds (dog, oak tree), man-made artifacts(hammer, airplane, chair), ad hoc categories(things to take out of a burning house, things

that could be stood on to reach a lightbulb),and abstract schemas or metaphors (e.g.,events in which a kind action is repaid withcruelty, metaphorical prisons, problems thatare solved by breaking a large force into partsthat converge on a target). For the latter cat-egories, members need not have very muchin common at all. An unrewarding job and arelationship that cannot be ended may bothbe metaphorical prisons, but the situationsmay share little other than this.

Unlike ad hoc and metaphor-base cate-gories, most natural kinds and many artifactsare characterized by members that sharemany features. In a series of studies, Rosch(Rosch, 1975; Rosch & Mervis, 1975) hasshown that the members of natural kindand artifact “basic level” categories, suchas chair, trout, bus, apple, saw, and guitar,are characterized by high within-categoryoverall similarity. Subjects listed features forbasic level categories, as well as for broadersuperordinate (e.g., furniture) and narrowersubordinate (e.g., kitchen chair) categories.An index of within-category similarity wasobtained by tallying the number of featureslisted by subjects that were common to itemsin the same category. Items within a basiclevel category tend to have several featuresin common, far more than items within asuperordinate category and almost as manyas items that share a subordinate categoriza-tion. Rosch (Rosch & Mervis, 1975; Rosch,Mervis, Gray, Johnson, & Boyes-Braem,1976) argues that categories are defined byfamily resemblance; category members neednot all share a definitional feature, but theytend to have several features in common. Fur-thermore, she argues that people’s basic levelcategories preserve the intrinsic correlationalstructure of the world. All feature combina-tions are not equally likely. For example, inthe animal kingdom, flying is correlated withlaying eggs and possessing a beak. Thereare “clumps” of features that tend to occur


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together. Some categories do not conform tothese clumps (e.g., ad hoc categories), butmany of our most natural-seeming categoriesdo. Neural network models have been pro-posed that take advantage of these clumpsto learn hierarchies of categories (Rogers &Patterson, 2007).

These natural categories also permit manyinductive inferences. If we know somethingbelongs to the category dog, then we knowthat it probably has four legs and two eyes,eats dog food, is somebody’s pet, pants,barks, is bigger than a breadbox, and so on.Generally, natural kind objects, particularlythose at Rosch’s basic level, permit manyinferences. Basic level categories allow manyinductions because their members share sim-ilarities across many dimensions/features.Ad hoc categories and highly metaphoricalcategories permit fewer inductive inferences,but in certain situations the inferences theyallow are so important that the categoriesare created on an “as needed” basis. Oneinteresting possibility is that all conceptsare created to fulfill an inductive need, andthat standard taxonomic categories, such asbird and hammer, simply become automati-cally triggered because they have been usedoften, whereas ad hoc categories are onlycreated when specifically needed (Barsalou,1982, 1991). In any case, evaluating theinductive potential of a concept goes a longway toward understanding why we have theconcepts that we do. The concept peaches,llamas, telephone answering machines, orRingo Starr is an unlikely concept becausebelonging in this concept predicts verylittle. Researchers have empirically foundthat the categories that we create when westrive to maximize inferences are differentfrom those that we create when we striveto sort the objects of our world into clearlyseparate groups (Yamauchi & Markman,1998). Several researchers have been for-mally developing the notion that the concepts

we possess are those that maximize induc-tive potential (Anderson, 1991; Goodman,Tenenbaum, Feldman, & Griffiths, 2008;Tenenbaum, 1999). An implication of thisapproach is that there are degrees of concept-hood, with concepts falling on a continuum ofinductive power (Wixted, personal communi-cation, November 2016). Most psychologistsstudying concept learning do not believe thatmost of our everyday concepts are definedby rules or discrete boundaries (see Rulessection below), but we may well be guiltyof treating the concept concept as more rulebased than it actually is. If concepts varycrucially in terms of their inductive power,they are very likely to be fuzzy and gradedrather than discrete objects that people eitherdo or do not possess.

Communication

Communication between people is enor-mously facilitated if the people can countupon a set of common concepts being shared.By uttering a simple sentence such as “Ed isa football player,” one can transmit a wealthof information to a colleague, dealing withthe probabilities of Ed being strong, havingviolent tendencies, being a college physicsor physical education major, and having ahistory of steroid use. Markman and Makin(1998) have argued that a major force inshaping our concepts is the need to efficientlycommunicate. They find that people’s con-cepts become more consistent and systematicover time in order to unambiguously establishreference for another individual with whomthey need to communicate (see also Garrod &Doherty, 1994).

Cognitive Economy

We can discriminate far more stimuli thanwe have concepts. For example, estimatessuggest that we can perceptually discriminateat least 10,000 colors from each other, but


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What Do Concepts Do for Us? 281

we have far fewer color concepts than this.Dramatic savings in storage requirements canbe achieved by encoding concepts rather thanentire raw (unprocessed) inputs. A classicstudy by Posner and Keele (1967) foundthat subjects code letters such as “A” in adetailed, perceptually rich code, but thatthis code rapidly (within 2 seconds) givesway to a more abstract conceptual code that“A” and “a” share. Huttenlocher, Hedges,and Vevea (2000) developed a formal modelin which judgments about a stimulus arebased on both its category membership andits individuating information. As predictedby the model, when subjects are asked toreproduce a stimulus, their reproductionsreflect a compromise between the stimulusitself and the category to which it belongs.When a delay is introduced between seeingthe stimulus and reproducing it, the contri-bution of category-level information relativeto individual-level information increases(Crawford, Huttenlocher, & Engebretson,2000). Together with studies showing that,over time, people tend to preserve the gistof a category rather than the exact mem-bers that comprise it (e.g., Posner & Keele,1970), these results suggest that by pre-serving category-level information ratherthan individual-level information, efficientlong-term representations can be main-tained. In fact, it has been argued that ourperceptions of an object represent a nearlyoptimal combination of evidence based onthe object’s individuating information andthe categories to which it belongs (N. H.Feldman, Griffiths, & Morgan, 2009). Byusing category-level information, one willoccasionally overgeneralize and make errors.Rattlesnakes may be dangerous in general,but one may stumble upon a congenial onein the Arizona desert. One makes an errorwhen one is unduly alarmed by its presence,but it is an error that stems from a healthful,life-sustaining generalization.

From an information theory perspective,storing a category in memory rather than acomplete description of an individual is effi-cient because fewer bits of information arerequired to specify the category. For example,Figure 8.1 shows a set of objects (shown bycircles) described along two dimensions.Rather than preserving the complete descrip-tion of each of the 19 objects, one can createa reasonably faithful representation of thedistribution of objects by just storing thepositions of the four triangles in Figure 8.1.

In addition to conserving memory storagerequirements, an equally important econo-mizing advantage of concepts is to reducethe need for learning (Bruner, Goodnow, &Austin, 1956). An unfamiliar object that hasnot been placed in a category attracts atten-tion because the observer must figure outhow to think about it. Conversely, if an objectcan be identified as belonging to a preestab-lished category, then typically less cognitiveprocessing is necessary. One can simply treatthe object as another instance of somethingthat is known, updating one’s knowledgeslightly if at all. The difference betweenevents that require altering one’s conceptsand those that do not was described by Piaget(1952) in terms of accommodation (adjust-ing concepts on the basis of a new event)and assimilation (applying already known

X

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Figure 8.1 Alternative proposals have suggestedthat categories are represented by the individualexemplars in the categories (the circles), the proto-types of the categories (the triangles), or the cate-gory boundaries (the lines dividing the categories).


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concepts to an event). This distinction hasalso been incorporated into computationalmodels of concept learning that determinewhether an input can be assimilated into apreviously learned concept, and if it can-not, then reconceptualization is triggered(Grossberg, 1982). When a category instanceis consistent with a simple category descrip-tion, then people are less likely to storea detailed description of it than if it is anexceptional item (Palmeri & Nosofsky,1995), consistent with the notion that peoplesimply use an existing category descriptionwhen it suffices. In general, concept learningproceeds far more quickly than would bepredicted by a naïve associative learning pro-cess. Our concepts accelerate the acquisitionof object information at the same time thatour knowledge of objects accelerates conceptformation (Griffiths & Tenenbaum, 2009;Kemp & Tenenbaum, 2009).

HOW ARE CONCEPTSREPRESENTED?

Much research on concepts and cate-gorization revolves around the issue ofhow concepts are mentally represented.As with all discussion of representations,the standard caveat must be issued—mentalrepresentations cannot be determined orused without processes that operate on theserepresentations. Rather than discussing therepresentation of a concept such as cat, weshould discuss a representation-process pairthat allows for the use of this concept. Empir-ical results interpreted as favoring a particularrepresentation format should almost alwaysbe interpreted as supporting a particularrepresentation given particular processes thatuse the representation. As a simple example,when trying to decide whether a shadowyfigure briefly glimpsed was a cat or a fox,one needs to know more than how one’s

cat and fox concepts are represented. Oneneeds to know how the information in theserepresentations is integrated together to makethe final categorization. Does one wait for theamount of confirmatory evidence for one ofthe animals to rise above a certain threshold(Fific, Little, & Nosofsky, 2010)? Does onecompare the evidence for the two animals andchoose the more likely (Luce, 1959)? Is theinformation in the candidate animal conceptsaccessed simultaneously or successively?Probabilistically or deterministically? Theseare all questions about the processes that useconceptual representations. One reaction tothe insufficiency of representations alone toaccount for concept use has been to dispensewith all reference to independent representa-tions, and instead frame theories in terms ofdynamic processes alone (Thelen & Smith,1994; van Gelder, 1998). However, othersfeel that this is a case of throwing out thebaby with the bath water, and insist that rep-resentations must still be posited to accountfor enduring, organized, and rule-governedthought (Markman & Dietrich, 2000).

Rules

There is considerable intuitive appeal to thenotion that concepts are represented by some-thing like dictionary entries. By a rule-basedaccount of concept representation, to possessthe concept cat is to know the dictionary entryfor it. A person’s cat concept may differ fromWebster’s dictionary’s entry: “A carnivorousmammal (Felis catus) long domesticated andkept by man as a pet or for catching rats andmice.” Still, this account claims that a conceptis represented by some rule that allows oneto determine whether or not an entity belongswithin the category.

The most influential rule-based approachto concepts may be Bruner et al.’s (1956)hypothesis-testing approach. Their theorizingwas, in part, a reaction against behaviorist


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approaches (Hull, 1920), in which conceptlearning involved the relatively passive acqui-sition of an association between a stimulus(an object to be categorized) and a response(such as a verbal response, key press, orlabeling). Instead, Bruner et al. argued thatconcept learning typically involves activehypothesis formation and testing. In a typ-ical experiment, their subjects were shownflash cards that had different shapes, colors,quantities, and borders. The subjects’ taskwas to discover the rule for categorizingthe flash cards by selecting cards to betested and by receiving feedback from theexperimenter indicating whether the selectedcard fit the categorizing rule or not. Theresearchers documented different strategiesfor selecting cards, and a considerable bodyof subsequent work showed large differencesin how easily acquired are different cate-gorization rules (e.g., Bourne, 1970). Forexample, a conjunctive rule such as whiteand square is more easily learned than aconditional rule such as if white then square,which is in turn more easily learned than abiconditional rule such as white if and onlyif square.

The assumptions of these rule-basedmodels have been vigorously challengedfor several decades now. Douglas Medinand Edward Smith (Medin & Smith, 1984;E. E. Smith & Medin, 1981) dubbed thisrule-based approach “the classical view,” andcharacterized it as holding that all instancesof a concept share common properties thatare necessary and sufficient conditions fordefining the concept. At least three criticismshave been levied against this classical view.

First, it has proven to be very difficultto specify the defining rules for most con-cepts. Wittgenstein (1953) raised this pointwith his famous example of the conceptgame. He argued that none of the candidatedefinitions of this concept, such as activityengaged in for fun, activity with certain rules,

competitive activity with winners and losersis adequate to identify Frisbee, professionalbaseball, and roulette as games, while simul-taneously excluding wars, debates, televisionviewing, and leisure walking from the gamecategory. Even a seemingly well-defined con-cept such as bachelor seems to involve morethan its simple definition of unmarried male.The counterexample of a 5-year-old child(who does not really seem to be a bachelor)may be fixed by adding in an adult precon-dition, but an indefinite number of otherpreconditions are required to exclude a manin a long-term but unmarried relationship, thePope, and a 80-year-old widower with fourchildren (Lakoff, 1987). Wittgenstein arguedthat instead of equating knowing a conceptwith knowing a definition, it is better to thinkof the members of a category as being relatedby family resemblance. A set of objectsrelated by family resemblance need not haveany particular feature in common, but willhave several features that are characteristicor typical of the set.

Second, the category membership forsome objects is not clear. People disagree onwhether or not a starfish is a fish, a camel is avehicle, a hammer is a weapon, and a strokeis a disease. By itself, this is not too problem-atic for a rule-based approach. People mayuse rules to categorize objects, but differentpeople may have different rules. However,it turns out that people not only disagreewith each other about whether a bat is mam-mal. They also disagree with themselves!McCloskey and Glucksberg (1978) showedthat people give surprisingly inconsistentcategory-membership judgments when askedthe same questions at different times. Thereis either variability in how to apply a cat-egorization rule to an object, or peoplespontaneously change their categorizationrules, or (as many researchers believe) peoplesimply do not represent objects in terms ofclear-cut rules.


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Third, even when a person shows consis-tency in placing objects in a category, peopledo not treat the objects as equally good mem-bers of the category. By a rule-based account,one might argue that all objects that matcha category rule would be considered equallygood members of the category (but seeBourne, 1982). However, when subjects areasked to rate the typicality of animals such asrobin and eagle for the category bird, or chairand hammock for the category furniture, theyreliably give different typicality ratings fordifferent objects. Rosch and Mervis (1975)were able to predict typicality ratings withrespectable accuracy by asking subjects tolist properties of category members andmeasuring how many properties possessedby a category member were shared by othercategory members. The magnitude of thisso-called family-resemblance measure ispositively correlated with typicality ratings.

Despite these strong challenges to theclassical view, the rule-based approach isby no means moribund. In fact, in partdue to the perceived lack of constraints inneural network models that learn conceptsby gradually building up associations, therule-based approach experienced a rekindlingof interest in the 1990s after its low pointin the 1970s and 1980s (Marcus, 1998).Nosofsky and Palmeri (Nosofsky & Palmeri,1998; Palmeri & Nosofsky, 1995) have pro-posed a quantitative model of human conceptlearning that learns to classify objects byforming simple logical rules and remember-ing occasional exceptions to those rules. Thiswork is reminiscent of earlier computationalmodels of human learning that created rulessuch as If white and square, then Category1 from experience with specific examples(Anderson, Kline, & Beasley, 1979; Medin,Wattenmaker, & Michalski, 1987). The mod-els have a bias to create simple rules, and areable to predict entire distributions of subjects’categorization responses rather than simply

average responses. A strong version of arule-based model predicts that people createcategories that have the minimal possibledescription length (J. Feldman, 2006).

One approach to making the rule-governedapproach to concepts more psychologicallyplausible is to discard the assumption thatrule-governed implies deterministic. The pastfew years have seen a new crop of rule-basedmodels that are intrinsically probabilistic(Piantadosi & Jacobs, 2016; Piantadosi,Tenenbaum, & Goodman, 2016; Tenenbaum,Kemp, Griffiths, & Goodman, 2011). Thesemodels work by viewing categorization as theresult of integrating many discrete rules, eachof which may be imperfect predictors on itsown. A remaining challenge for these modelsis that there often is a psychological con-nection between rule use and determinism.Rules, particularly ones that involve relationsbetween elements, are often very difficultto learn when they are probabilistic ratherthan applied without exception (Jung &Hummel, 2015). In addition, even formalconcepts such as triangle have graded andflexible structures—structures that are tiedless to strict definitions when the conceptsare activated by their labels (Lupyan, 2017).

In defending a role for rule-based rea-soning in human cognition, E. E. Smith,Langston, and Nisbett (1992) proposed eightcriteria for determining whether or not peopleuse abstract rules in reasoning. These criteriainclude “performance on rule-governed itemsis as accurate with abstract as with concretematerial,” “performance on rule-governeditems is as accurate with unfamiliar as withfamiliar material,” and “performance ona rule-governed item or problem deterio-rates as a function of the number of rulesthat are required for solving the problem.”Based on the full set of criteria, they arguethat rule-based reasoning does occur, andthat it may be a mode of reasoning distinctfrom association-based or similarity-based


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reasoning. Similarly, Pinker (1991) arguedfor distinct rule-based and association-basedmodes for determining linguistic categories.Neurophysiological support for this dis-tinction comes from studies showing thatrule-based and similarity-based categoriza-tions involve anatomically separate brainregions (Ashby, Alfonso-Reese, Turken, &Waldron, 1998; E. E. Smith, Patalano, &Jonides, 1998).

In developing a similar distinctionbetween similarity-based and rule-basedcategorization, Sloman (1996) introduced thenotion that the two systems can simultane-ously generate different solutions to a reason-ing problem. For example, Rips (1989; seealso Rips & Collins, 1993) asked subjects toimagine a three-inch, round object, and thenasked whether the object was more similar toa quarter or a pizza, and whether the objectwas more likely to be a pizza or a quarter.There is a tendency for the object to be judgedas more similar to a quarter but as more likelyto be a pizza. The rule that quarters must notbe greater than 1 inch plays a larger role in thecategorization decision than in the similarityjudgment, causing the two judgments to dis-sociate. By Sloman’s analysis, the tension wefeel about the categorization of the three-inchobject stems from the two different systems,indicating incompatible categorizations.Sloman argues that the rule-based systemcan suppress the similarity-based systembut cannot completely suspend it. WhenRips’ experiment is repeated with a richerdescription of the object to be categorized,categorization again tracks similarity, andpeople tend to choose the quarter for both thecategorization and similarity choices (E. E.Smith & Sloman, 1994).

Prototypes

Just as the active hypothesis-testing approachof the classical view was a reaction against

the passive stimulus–response associationapproach, so the prototype model was devel-oped as a reaction against what was seenas the overly analytic, rule-based classicalview. Central to Eleanor Rosch’s devel-opment of prototype theory is the notionthat concepts are organized around familyresemblances rather than features that areindividually necessary and jointly sufficientfor categorization (Mervis & Rosch, 1981;Rosch, 1975; Rosch & Mervis, 1975). Theprototype for a category consists of the mostcommon attribute values associated with themembers of the category and can be empir-ically derived by the previously describedmethod of asking subjects to generate a list ofattributes for several members of a category.Once prototypes for a set of concepts havebeen determined, categorizations can be pre-dicted by determining how similar an objectis to each of the prototypes. The likelihoodof placing an object into a category increasesas it becomes more similar to the category’sprototype and less similar to other categoryprototypes (Rosch & Mervis, 1975).

This prototype model can naturally dealwith the three problems that confronted theclassical view. It is no problem if definingrules for a category are difficult or impossibleto devise. If concepts are organized aroundprototypes, then only characteristic, not nec-essary or sufficient, features are expected.Unclear category boundaries are expected ifobjects are presented that are approximatelyequally similar to prototypes from more thanone concept. Objects that clearly belong toa category may still vary in their typicalitybecause they may be more similar to the cate-gory’s prototype than to any other category’sprototype, but they still may differ in howsimilar they are to the prototype. Prototypemodels do not require “fuzzy” boundariesaround concepts (Hampton, 1993), but proto-type similarities are based on commonalitiesacross many attributes and are consequently


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graded, and lead naturally to categories withgraded membership.

A considerable body of data has beenamassed that suggests that prototypes havecognitively important functions. The simi-larity of an item to its category prototype (interms of featural overlap) predicts the resultsfrom several converging tasks. Somewhatobviously, it is correlated with the averagerating the item receives when subjects areasked to rate how good an example the item isof its category (Rosch, 1975). It is correlatedwith subjects’ speed in verifying statementsof the form, “An [item] is a [category name]”(E. E. Smith, Shoben, & Rips, 1974). It iscorrelated with the frequency and speedof listing the item when asked to supplymembers of a category (Mervis & Rosch,1981). It is correlated with the probabilityof inductively extending a property from theitem to other members of the category (Rips,1975). Taken in total, these results indicatethat different members of the same categorydiffer in how typical they are of the category,and that these differences have a strongcognitive impact. Many natural categoriesseem to be organized not around definitiveboundaries, but by graded typicality to thecategory’s prototype.

The prototype model described abovegenerates category prototypes by findingthe most common attribute values sharedamong category members. An alternativeconception views prototypes as the centraltendency of continuously varying attributes.If the four observed members of a lizardcategory had tail lengths of 3, 3, 3, and 7inches, the former prototype model wouldstore a value of 3 (the modal value) as theprototype’s tail length, whereas the centraltendency model would store a value of 4(the average value). The central tendencyapproach has proven useful in modelingcategories composed of artificial stimuli thatvary on continuous dimensions. For example,

Posner and Keele’s (1968) classic dot-patternstimuli consisted of nine dots positionedrandomly or in familiar configurations ona 30 × 30 invisible grid. Each prototypewas a particular configuration of dots, butduring categorization training subjects neversaw the prototypes themselves. Instead, theysaw distortions of the prototypes obtainedby shifting each dot randomly by a smallamount. Categorization training involvedsubjects seeing dot patterns, guessing theircategory assignment, and receiving feedbackindicating whether their guesses were cor-rect or not. During a transfer stage, Posnerand Keele found that subjects were betterable to categorize the never-before-seencategory prototypes than they were in cate-gorizing new distortions of those prototypes.In addition, subjects’ accuracy in categoriz-ing distortions of category prototypes wasstrongly correlated with the proximity ofthose distortions to the never-before-seenprototypes. The authors interpreted theseresults as suggesting that prototypes areextracted from distortions, and used as abasis for determining categorizations.

Exemplars

Exemplar models deny that prototypes areexplicitly extracted from individual cases,stored in memory, and used to categorizenew objects. Instead, in exemplar models,a conceptual representation consists onlyof the actual individual cases that one hasobserved. The prototype representation forthe category bird consists of the most typicalbird, or an assemblage of the most commonattribute values across all birds, or the centraltendency of all attribute values for observedbirds. By contrast, an exemplar model repre-sents the category bird by representing all ofthe instances (exemplars) that belong to thiscategory (L. R. Brooks, 1978; Estes, 1994;Hintzman, 1986; Kruschke, 1992; Lamberts,


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2000; Logan, 1988; Medin & Schaffer, 1978;Nosofsky, 1984, 1986).

While the prime motivation for thesemodels has been to provide good fits toresults from human experiments, computerscientists have pursued similar models withthe aim of exploiting the power of storingindividual exposures to stimuli in a rela-tively raw, unabstracted form. The exemplar,instance-based (Aha, 1992), view-based(Tarr & Gauthier, 1998), case-based (Schank,1982), nearest neighbor (Ripley, 1996),configural cue (Gluck & Bower, 1990), andvector quantization (Kohonen, 1995) modelsall share the fundamental insight that novelpatterns can be identified, recognized, orcategorized by giving the novel patterns thesame response that was learned for similar,previously presented patterns. By creatingrepresentations for presented patterns, notonly is it possible to respond to repetitionsof these patterns, it is also possible to giveresponses to novel patterns that are likelyto be correct by sampling responses to oldpatterns, weighted by their similarity to thenovel pattern. Consistent with these models,psychological evidence suggests that peopleshow good transfer to new stimuli in per-ceptual tasks just to the extent that the newstimuli superficially resemble previouslylearned stimuli (Palmeri, 1997).

The frequent inability of human general-ization to transcend superficial similaritiesmight be considered as evidence of eitherhuman stupidity or laziness. To the contrary,if a strong theory about what stimulus fea-tures promote valid inductions is lacking, thestrategy of least commitment is to preservethe entire stimulus in its full richness of detail(L. R. Brooks, 1978). That is, by storingentire instances and basing generalizationson all of the features of these instances, onecan be confident that one’s generalizations arenot systematically biased. It has been shownthat in many situations, categorizing new

instances by their similarity to old instancesmaximizes the likelihood of categorizing thenew instances correctly (Ashby & Maddox,1993; McKinley & Nosofsky, 1995; Ripley,1996). Furthermore, if information becomesavailable at a later point that specifies whatproperties are useful for generalizing appro-priately, then preserving entire instanceswill allow these properties to be recovered.Such properties might be lost and unrecov-erable if people were less “lazy” in theirgeneralizations from instances.

Given these considerations, it is under-standable why people often use all of theattributes of an object even when a taskdemands the use of specific attributes.Doctors’ diagnoses of skin disorders arefacilitated when they are similar to previouslypresented cases, even when the similarity isbased on attributes that are known to beirrelevant for the diagnosis (L. R. Brooks,Norman, & Allen, 1991). Even when peopleknow a simple, clear-cut rule for a percep-tual classification, performance is better onfrequently presented items than rare items(Allen & Brooks, 1991). Consistent withexemplar models, responses to stimuli arefrequently based on their overall similarity topreviously exposed stimuli.

The exemplar approach to categorizationraises a number of questions. First, onceone has decided that concepts are to berepresented in terms of sets of exemplars,the obvious question remains: How are theexemplars to be represented? Some exem-plar models use a featural or attribute-valuerepresentation for each of the exemplars(Hintzman, 1986; Medin & Schaffer, 1978).Another popular approach is to representexemplars as points in a multidimen-sional psychological space. These pointsare obtained by measuring the subjectivesimilarity of every object in a set to everyother object. Once an n × n matrix of simi-larities among n objects has been determined


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by similarity ratings, perceptual confusions,spontaneous sortings, or other methods,a statistical technique called multidimen-sional scaling (MDS) finds coordinates forthe objects in a d-dimensional space thatallow the n × n matrix of similarities to bereconstructed with as little error as possible(Nosofsky, 1992). Given that d is typicallysmaller than n, a reduced representation iscreated in which each object is representedin terms of its values on d dimensions.Distances between objects in these quan-titatively derived spaces can be used asthe input to exemplar models to determineitem-to-exemplar similarities. These MDSrepresentations are useful for generatingquantitative exemplar models that can befit to human categorizations and similarityjudgments, but these still beg the questionof how a stand-alone computer program ora person would generate these MDS repre-sentations. Presumably there is some humanprocess that computes object representationsand can derive object-to-object similaritiesfrom them, but this process is not currentlymodeled by exemplar models (for steps inthis direction, see Edelman, 1999).

A second question for exemplar modelsis, If exemplar models do not explicitlyextract prototypes, how can they account forresults that concepts are organized aroundprototypes? A useful place to begin is by con-sidering Posner and Keele’s (1968) result thatthe never-before-seen prototype is catego-rized better than new distortions based on theprototype. Exemplar models have been ableto model this result because a categorizationof an object is based on its summed similarityto all previously stored exemplars (Medin &Schaffer, 1978; Nosofsky, 1986). The proto-type of a category will, on average, be moresimilar to the training distortions than arenew distortions, because the prototype wasused to generate all of the training distortions.Without positing the explicit extraction of

the prototype, the cumulative effect of manyexemplars in an exemplar model can createan emergent, epiphenomenal advantage forthe prototype.

Given the exemplar model’s account ofprototype categorization, one might askwhether predictions from exemplar and pro-totype models differ. In fact, they typicallydo, in large part because categorizations inexemplar models are not simply based onsummed similarity to category exemplars,but to similarities weighted by the proximityof an exemplar to the item to be categorized.In particular, exemplar models have mech-anisms to bias categorization decisions sothat they are more influenced by exemplarsthat are similar to items to be categorized.In Medin and Schaffer’s (1978) contextmodel, this is achieved by computing thesimilarity between objects by multiplyingrather than adding the similarities in eachof their features. In Hintzman’s (1986)MINERVA 2 model, this is achieved byraising object-to-object similarities to apower of 3 before summing them together.In Nosofsky’s generalized context model(1986), this is achieved by basing object-to-object similarities on an exponential functionof the objects’ distance in an MDS space.With these quantitative biases for close exem-plars, the exemplar model does a better job ofpredicting categorization accuracy for Posnerand Keele’s (1968) experiment than theprototype model because it can also predictthat familiar distortions will be categorizedmore accurately than novel distortions thatare equally far removed from the prototype(Shin & Nosofsky, 1992).

A third question for exemplar modelsis, In what way are concept representationseconomical if every experienced exemplaris stored? It is certainly implausible withlarge real-world categories to suppose thatevery instance ever experienced is storedin a separate trace. However, more realistic


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exemplar models may either store onlypart of the information associated with anexemplar (Lassaline & Logan, 1993) or onlysome exemplars (Aha, 1992; Palmeri &Nosofsky, 1995). One particularly interestingway of conserving space that has receivedempirical support (Barsalou, Huttenlocher, &Lamberts, 1998) is to combine separateevents that all constitute a single individ-ual into a single representation. Ratherthan passively register every event as dis-tinct, people seem to naturally consolidateevents together that refer to the same indi-vidual. If an observer fails to register thedifference between a new exemplar and apreviously encountered exemplar (e.g., twosimilar-looking Chihuahuas), then he or shemay combine the two together, resulting in anexemplar representation that is a blend of twoinstances (Love, Medin, & Gureckis, 2004).

Category Boundaries

Another notion is that a concept repre-sentation describes the boundary around acategory. The prototype model would repre-sent the four categories of Figure 8.1 in termsof the triangles. The exemplar model wouldrepresent the categories by the circles. Thecategory boundary model would represent thecategories by the four dividing lines betweenthe categories. This view has been mostclosely associated with the work of Ashbyand his colleagues (Ashby, 1992; Ashbyet al, 1998; Ashby & Gott, 1988; Ashby &Maddox, 1993; Ashby & Townsend, 1986;Maddox & Ashby, 1993). It is particularlyinteresting to contrast the prototype andcategory boundary approaches, because theirrepresentational assumptions are almost per-fectly complementary. The prototype modelrepresents a category in terms of its mosttypical member—the object in the centerof the distribution of items included in thecategory. The category boundary model

represents categories by their periphery, nottheir center. One recurring empirical resultthat provides some prima facie evidence forrepresenting categories in terms of bound-aries is that oftentimes the most effectivelycategorized object is not the prototype ofa category, but rather is a caricature of thecategory (Davis & Love, 2010; Goldstone,1996; Goldstone, Steyvers, & Rogosky,2003; Heit & Nicholson, 2010). A caricatureis an item that is systematically distortedaway from the prototype for the category inthe direction opposite to the boundary thatdivides the category from another category.

An interesting phenomenon to considerwith respect to whether centers or periph-eries of concepts are representationallyprivileged is categorical perception. Dueto this phenomenon, people are better ableto distinguish between physically differentstimuli when the stimuli come from differentcategories than when they come from thesame category (see Harnad, 1987 for severalreviews of research). The effect has been bestdocumented for speech phoneme categories.For example, Liberman, Harris, Hoffman,and Griffith (1957) generated a continuumof equally spaced consonant-vowel syllables,going from /be/ to /de/. Observers listenedto three sounds—A followed by B followedby X—and indicated whether X was identi-cal to A or B. Subjects performed the taskmore accurately when the syllables A and Bbelonged to different phonemic categoriesthan when they were variants of the samephoneme, even when physical differenceswere equated.

Categorical perception effects have beenobserved for visual categories (Calder,Young, Perrett, Etcoff, & Rowland, 1996)and for arbitrarily created laboratory cat-egories (Goldstone, 1994a). Categoricalperception could emerge from either proto-type or boundary representations. An itemto be categorized might be compared to


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the prototypes of two candidate categories.Increased sensitivity at the category bound-ary would be because people represent itemsin terms of the prototype to which they areclosest. Items that fall on different sides ofthe boundary would have very different rep-resentations because they would be closest todifferent prototypes (Liberman et al., 1957).Alternatively, the boundary itself might berepresented as a reference point, and as pairsof items move closer to the boundary itbecomes easier to discriminate between thembecause of their proximity to this referencepoint (Pastore, 1987).

Computational models have been devel-oped that operate on both principles.Following the prototype approach, Harnad,Hanson, and Lubin (1995) describe a neuralnetwork in which the representation of anitem is “pulled” toward the prototype of thecategory to which it belongs. Following theboundaries approach, Goldstone, Steyvers,Spencer-Smith, and Kersten (2000) describea neural network that learns to stronglyrepresent critical boundaries between cat-egories by shifting perceptual detectors tothese regions. Empirically, the results aremixed. Consistent with prototypes beingrepresented, some researchers have foundparticularly good discriminability close to afamiliar prototype (Acker, Pastore, & Hall,1995; McFadden & Callaway, 1999). Consis-tent with boundaries being represented, otherresearchers have found that the sensitivitypeaks associated with categorical perceptionheavily depend on the saliency of perceptualcues at the boundary (Kuhl & Miller, 1975).Rather than being arbitrarily fixed, categoryboundaries are most likely to occur at alocation where a distinctive perceptual cue,such as the difference between an aspiratedand unaspirated speech sound, is present.A possible reconciliation is that informationabout either the center or periphery of a cat-egory can be represented, and that boundary

information is more likely to be representedwhen two highly similar categories must befrequently discriminated and there is a salientreference point for the boundary.

Different versions of the category bound-ary approach, illustrated in Figure 8.2, havebeen based on different ways of partitioningcategories (Ashby & Maddox, 1998). Withindependent decision boundaries, categoriesboundaries must be perpendicular to a dimen-sional axis, forming rules such as Category Aitems are larger than 3 centimeters, irrespec-tive of their color. This kind of boundary isappropriate when the dimensions that makeup a stimulus are hard to integrate (Ashby &Gott, 1988). With minimal distance bound-aries, a Category A response is given if andonly if an object is closer to the CategoryA prototype than the Category B prototype.The decision boundary is formed by findingthe line that connects the two categories’ pro-totypes and creating a boundary that bisects

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Optimal boundaries General quadratic

Figure 8.2 The notion that categories are repre-sented by their boundaries can be constrained inseveral ways. Boundaries can be constrained to beperpendicular to a dimensional axis, to be equallyclose to prototypes for neighboring categories,to produce optimal categorization performance,or may be loosely constrained to be a quadraticfunction.


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and is orthogonal to this line. The optimalboundary is the boundary that maximizes thelikelihood of correctly categorizing an object.If the two categories have the same patternsof variability on their dimensions, and peopleuse information about variance to form theirboundaries, then the optimal boundary willbe a straight line. If the categories differ intheir variability, then the optimal boundarywill be described by a quadratic equation(Ashby & Maddox, 1993, 1998). A generalquadratic boundary is any boundary that canbe described by a quadratic equation.

One difficulty with representing a conceptby a boundary is that the location of theboundary between two categories dependson several contextual factors. For example,Repp and Liberman (1987) argue that cat-egories of speech sounds are influenced byorder effects, adaptation, and the surround-ing speech context. The same sound that ishalfway between pa and ba will be catego-rized as pa if preceded by several repetitionsof a prototypical ba sound, but categorizedas ba if preceded by several pa sounds.For a category boundary representation toaccommodate this, two category boundarieswould need to be hypothesized—a relativelypermanent category boundary between baand pa, and a second boundary that shiftsdepending upon the immediate context. Therelatively permanent boundary is neededbecause the contextualized boundary must bebased on some earlier information. In manycases, it is more parsimonious to hypothesizerepresentations for the category membersthemselves and view category boundariesas side effects of the competition betweenneighboring categories. Context effects arethen explained simply by changes to thestrengths associated with different cate-gories. By this account, there may be noreified boundary around one’s cat conceptthat causally affects categorizations. Whenasked about a particular object, we can decide

whether it is a cat or not, but this is done bycomparing the evidence in favor of the objectbeing a cat to its being something else.

Theories

The representation approaches thus far con-sidered all work irrespectively of the actualmeaning of the concepts. This is both anadvantage and a liability. It is an advantagebecause it allows the approaches to be uni-versally applicable to any kind of material.They share with inductive statistical tech-niques the property that they can operate onany data set once the data set is formallydescribed in terms of numbers, features, orcoordinates. However, the generality of theseapproaches is also a liability if the meaningor semantic content of a concept influenceshow it is represented. While few would arguethat statistical T-tests are only appropriatefor certain domains of inquiry (e.g., testingpolitical differences, but not disease differ-ences), many researchers have argued that theuse of purely data-driven, inductive methodsfor concept learning are strongly limited andmodulated by the background knowledge onehas about a concept (Carey, 1985; Gelman &Markman, 1986; Keil, 1989; Medin, 1989;Murphy & Medin, 1985).

People’s categorizations seem to dependon the theories they have about the world(for reviews, see Komatsu, 1992; Medin,1989). Theories involve organized systemsof knowledge. In making an argument forthe use of theories in categorization, Murphyand Medin (1985) provide the example ofa man jumping into a swimming pool fullyclothed. This man may be categorized asdrunk because we have a theory of behav-ior and inebriation that explains the man’saction. Murphy and Medin argue that thecategorization of the man’s behavior doesnot depend on matching the man’s featuresto the category drunk’s features. It is highly


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unlikely that the category drunk would havesuch a specific feature as jumps into poolsfully clothed. It is not the similarity betweenthe instance and the category that determinesthe instance’s classification; it is the fact thatour category provides a theory that explainsthe behavior.

Other researchers have empirically sup-ported the dissociation between theory-derived categorization and similarity. Inone experiment, Carey (1985) observes thatchildren choose a toy monkey over a wormas being more similar to a human, but thatwhen they are told that humans have spleens,are more likely to infer that the worm has aspleen than that the toy monkey does. Thus,the categorization of objects into spleen andno spleen groups does not appear to dependon the same knowledge that guides similarityjudgments. Carey argues that even youngchildren have a theory of living things. Partof this theory is the notion that living thingshave self-propelled motion and rich internalorganizations. Children as young as 3 years ofage make inferences about an animal’s prop-erties on the basis of its category label, evenwhen the label opposes superficial visualsimilarity (Gelman & Markman, 1986).

Using different empirical techniques, Keil(1989) has come to a similar conclusion.In one experiment, children are told a storyin which scientists discover that an animalthat looks exactly like a raccoon actuallycontains the internal organs of a skunk andhas skunk parents and skunk children. Withincreasing age, children increasingly claimthat the animal is a skunk. That is, there isa developmental trend for children to cate-gorize on the basis of theories of heredityand biology rather than visual appearance.In a similar experiment, Rips (1989) showsan explicit dissociation between categoriza-tion judgments and similarity judgments inadults. An animal that is transformed (bytoxic waste) from a bird into something that

looks like an insect is judged by subjectsto be more similar to an insect, but is alsojudged to be a bird still. Again, the categoryjudgment seems to depend on biological,genetic, and historical knowledge, while thesimilarity judgments seems to depend moreon gross visual appearance.

Researchers have explored the importanceof background knowledge in shaping ourconcepts by manipulating this knowledgeexperimentally. Concepts are more easilylearned when a learner has appropriate back-ground knowledge, indicating that more than“brute” statistical regularities underlie ourconcepts (Pazzani, 1991). Similarly, whenthe features of a category can be connectedthrough prior knowledge, category learningis facilitated (Murphy & Allopenna, 1994;Spalding & Murphy, 1999). Even a singleinstance of a category can allow people toform a coherent category if backgroundknowledge constrains the interpretation ofthis instance (Ahn, Brewer, & Mooney,1992). Concepts are disproportionately rep-resented in terms of concept features that aretightly connected to other features (Sloman,Love, & Ahn, 1998).

Forming categories on the basis ofdata-driven, statistical evidence, and formingthem based upon knowledge-rich theoriesof the world seem like strategies fundamen-tally at odds with each other. Indeed, this isprobably the most basic difference betweentheories of concepts in the field. However,these approaches need not be mutually exclu-sive. Even the most outspoken proponentsof theory-based concepts do not claim thatsimilarity-based or statistical approaches arenot also needed (Murphy & Medin, 1985).Moreover, some researchers have suggestedintegrating the two approaches. Theoriesin the form of prior knowledge about adomain are recruited in order to account forempirically observed categorizations, andone mechanism for this is the process of


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subjects trying to form explanations for theobservations (Williams & Lombrozo, 2013;Williams, Lombrozo, & Rehder, 2013). Heit(1994, 1997) describes a similarity-based,exemplar model of categorization that incor-porates background knowledge by storingcategory members as they are observed (aswith all exemplar models), but also storingnever-seen instances that are consistent withthe background knowledge. Choi, McDaniel,and Busemeyer (1993) described a neuralnetwork model of concept learning that doesnot begin with random or neutral connectionsbetween features and concepts (as is typical),but begins with theory-consistent connec-tions that are relatively strong. Rehder andMurphy (2003) propose a bidirectional neuralnetwork model in which observations affect,and are affected by, background knowledge.Hierarchical Bayesian models allow theories,incorporated as prior probabilities on specificstructural forms, to guide the constructionof knowledge, oftentimes forming knowl-edge far more rapidly than predicted if eachobservation needed to be separately learned(Kemp & Tenenbaum, 2008, 2009; Lucas &Griffiths, 2010). All of these computationalapproaches allow domain-general categorylearners to also have biases toward learn-ing categories consistent with backgroundknowledge.

Summary to RepresentationApproaches

One cynical conclusion to reach from thepreceding alternative approaches is that aresearcher starts with a theory, and tends tofind evidence consistent with the theory—aresult that is meta-analytically consistentwith a theory-based approach! Although thisstate of affairs is typical throughout psychol-ogy, it is particularly rife in concept-learningresearch because researchers have a sig-nificant amount of flexibility in choosing

what concepts they will use experimentally.Evidence for rule-based categories tends tobe found with categories that are createdfrom simple rules (Bruner et al., 1956). Evi-dence for prototypes tends to be found forcategories made up of members that are dis-tortions around single prototypes (Posner &Keele, 1968). Evidence for exemplar modelsis particular strong when categories includeexceptional instances that must be individu-ally memorized (Nosofsky & Palmeri, 1998;Nosofsky, Palmeri, & McKinley, 1994).Evidence for theories is found when cat-egories are created that subjects alreadyknow something about (Murphy & Kaplan,2000). The researcher’s choice of represen-tation seems to determine the experimentthat is conducted rather than the experimentinfluencing the choice of representation.

There may be a grain of truth to thiscynical conclusion, but our conclusions areinstead that people use multiple representa-tional strategies (Weiskopf, 2009) and canflexibly deploy these strategies based uponthe categories to be learned. From this per-spective, representational strategies shouldbe evaluated according to their trade-offs,and for their fit to the real-world categoriesand empirical results. For example, exemplarrepresentations are costly in terms of storagedemands, but are sensitive to interactionsbetween features and adaptable to new cat-egorization demands. There is a growingconsensus that at least two kinds of repre-sentational strategies are both present butseparated—rule-based and similarity-basedprocesses (Erickson & Kruschke, 1998;Pinker, 1991; Sloman, 1996). There is evenrecent evidence for reliable individual dif-ferences in terms of these strategies, withdifferent groups of people naturally inclinedtoward either rule-based or exemplar learn-ing processes (McDaniel, Cahill, Robbins, &Wiener, 2014). Other researchers have arguedfor separate processes for storing exemplars


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and extracting prototypes (Knowlton &Squire, 1993; J. D. Smith & Minda, 2000,2002). Some researchers have argued fora computational rapprochement betweenexemplar and prototype models in whichprototypes are formed around statisticallysupported clusters of exemplars (Love et al.,2004). Even if one holds out hope for a uni-fied model of concept learning, it is importantto recognize these different representationalstrategies as special cases that must beachievable by the unified model given theappropriate inputs.

CONNECTING CONCEPTS

Although knowledge representation appro-aches have often treated conceptual sys-tems as independent networks that gaintheir meaning by their internal connections(Lenat & Feigenbaum, 1991), it is importantto remember that concepts are connectedto both perception and language. Concepts’connections to perception serve to groundthem (Goldstone & Rogosky, 2002; Harnad,1990), and their connections to languageallow them to transcend direct experienceand to be easily transmitted.

Connecting Concepts to Perception

Concept formation is often studied as thoughit were a modular process (in the sense ofFodor, 1983). For example, participants incategory learning experiments are often pre-sented with verbal feature lists representingthe objects to be categorized. The use ofthis method suggests an implicit assumptionthat the perceptual analysis of an objectinto features is complete before one startsto categorize that object. Categorizationprocesses can then act upon the features thatresult from this analysis, largely unconcernedwith the specific perceptual information thatled to the identification of those features.

This may be a useful simplifying assumption,allowing a researcher to test theories of howfeatures are combined to form concepts.There is mounting evidence, however, thatconceptual processes may act directly onmodality-specific perceptual information,eliminating the need to first transduce thatinformation into amodal feature lists beforecategorization can begin.

Evidence for a role of perceptual infor-mation in conceptual processes comesfrom research relating to Barsalou’s (1999,2008) theory of perceptual symbol systems.According to this theory, sensorimotor areasof the brain that are activated during the ini-tial perception of an event are reactivated ata later time by association areas, serving as arepresentation of one’s prior perceptual expe-rience. Rather than preserving a verbatimrecord of what was experienced, however,association areas only reactivate certainaspects of one’s perceptual experience,namely those that received attention. Becausethese reactivated aspects of experience maybe common to a number of different events,they may be thought of as symbols, represent-ing an entire class of events. Because theyare formed around perceptual experience,however, they are perceptual symbols, unlikethe amodal symbols typically employed insymbolic theories of cognition.

In support of this theory, neuroimagingresearch has revealed that conceptual pro-cessing leads to activation in sensorimotorregions of the brain, even when that acti-vated information is not strictly necessary toperform the conceptual task. For example,Simmons, Martin, and Barsalou (2005)revealed in a functional magnetic resonanceimaging (fMRI) study that pictures of appe-tizing foods led to activation in areas associ-ated with the perception of taste, even thoughthe task simply involved visual matchingand thus taste was irrelevant. This suggeststhat food concepts may be represented by


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Connecting Concepts 295

activation in a variety of areas representingthe different sensory modalities associatedwith those concepts. Furthermore, Simmonset al. (2007) revealed that brain areas respon-sive to color information in a visual task werealso activated by judgments of color prop-erties associated with concepts, even thoughthe concepts and properties were presentedonly in verbal form. Representing the variousproperties associated with a concept appar-ently recruits the same brain mechanismsthat are involved in directly perceiving thoseproperties, consistent with the theory ofperceptual symbol systems.

Although findings such as these demon-strate that perceptual representations areactivated when a concept is instantiated, theyleave open the possibility that the conceptsthemselves are represented in amodal for-mat, and that the activation of perceptualrepresentations reflects visual imagery pro-cesses subsequent to the identification ofa concept. This account remains possiblebecause the coarse temporal resolution offMRI makes unclear the exact sequenceof neural events leading to successful taskperformance. To address this concern, Kiefer,Sim, Herrnberger, Grothe, and Hoenig (2008)examined the activation of perceptual rep-resentations using not only fMRI but alsoevent-related potentials (ERPs), a brain-imaging technique with much better tem-poral resolution. Neuroimaging with fMRIrevealed that auditory areas were activatedin response to visual presentation of wordsreferring to objects with strongly associatedacoustic features (e.g., telephone). Moreover,results with ERP suggested that these audi-tory areas were activated within 150 msof stimulus presentation, quite similar todurations previously established for access-ing meanings for visually presented words(e.g., Pulvermüller, Shtyrov, & Ilmoniemi,2005). This combination of results suggeststhat activation of perceptual representations

occurs early in the process of conceptaccess, rather than reflecting later visualimagery processes.

Although neuroimaging studies withfMRI and ERP reveal that activation of per-ceptual areas is associated with conceptualprocessing, these are correlational methods,and thus it still remains possible that acti-vation of perceptual areas does not play adirect causal role in concept access and use.For example, on the basis of these resultsalone, it remains possible that presentationof a word leads one to access an amodalsymbolic representation of the associatedconcept, but that perceptual areas are alsoactivated via a separate pathway. These per-ceptual representations would thus have nocausal role in accessing or representing theconcept. To establish causality, it is necessaryto manipulate activation of perceptual areasand demonstrate an effect on concept access.An example of such a manipulation wascarried out by Vermeulen, Corneille, andNiedenthal (2008). They presented partici-pants with a memory load presented either inthe visual or auditory modality. While main-taining these items, participants were givena property verification task in which eithera visual or an auditory property of a concepthad to be verified. Participants were slowerto verify visual properties while simultane-ously maintaining a visual memory load,whereas they were slower to verify auditoryproperties while simultaneously maintainingan auditory memory load. These results sug-gest that concept access involves activatingvarious modalities of sensorimotor informa-tion associated with the concept, and thusthat simultaneous processing of other unre-lated perceptual information within the samemodality can interfere with concept access(see also Witt, Kemmerer, Linkenauger, &Culham, 2010).

The results described so far in this sectionsuggest that concepts are represented not in


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terms of amodal symbols transduced fromperceptual experience, but rather in terms ofperceptual information itself. The specificpatterns of perceptual information that onehas experienced when learning about a con-cept may thus influence the representation ofthat concept (e.g., see Kiefer, Sim, Liebich,Hauk, & Tanaka, 2007), possibly even forputatively abstract concepts that one maynot expect to be associated with percep-tual information, such as truth and freedom(Barsalou & Wiemer-Hastings, 2005). More-over, if there is overlap in perceptual andconceptual representations, then not onlymay perceptual information affect conceptaccess and use, but one’s concepts may alsoinfluence one’s perceptual sensitivities, withconcept activation leading to top-down influ-ences on perceptual discrimination abilities(Brooks & Freeman, Chapter 13 in Volume4 of this Handbook; Lupyan, 2008b; butsee Firestone & Scholl, 2016 for skepticismregarding top-down effects). The relationshipbetween perceptual and conceptual processesmay thus be bidirectional (Goldstone &Barsalou, 1998), with the identification ofperceptual features influencing the catego-rization of an object, and the categorizationof an object influencing the perception offeatures (Bassok, 1996).

Classic evidence for an influence of con-cepts on perception comes from researchon the previously described phenomenonof categorical perception. Listeners aremuch better at perceiving contrasts that arerepresentative of different phoneme cate-gories (Liberman, Cooper, Shankweiler, &Studdert-Kennedy, 1967). For example, lis-teners can hear the difference in voice onsettime between bill and pill, even when thisdifference is no greater than the differencebetween two /b/ sounds that cannot be dis-tinguished. One may argue that categoricalperception simply provides further evidenceof an influence of perception on concepts.

In particular, the phonemes of languagemay have evolved to reflect the sensitivitiesof the human perceptual system. Evidenceconsistent with this viewpoint comes fromthe fact that chinchillas are sensitive to manyof the same sound contrasts as are humans,even though chinchillas obviously have nolanguage (Kuhl & Miller, 1975). There isevidence, however, that the phonemes towhich a listener is sensitive can be modi-fied by experience. In particular, althoughnewborn babies appear to be sensitive to allof the sound contrasts present in all of theworld’s languages, a 1-year-old can onlyhear those sound contrasts present in hisor her linguistic environment (Werker &Tees, 1984). Thus, children growing up inJapan lose the ability to distinguish betweenthe /l/ and /r/ phonemes, whereas childrengrowing up in the United States retain thisability (Miyawaki, 1975). The categories oflanguage thus influence one’s perceptual sen-sitivities, providing evidence for an influenceof concepts on perception.

Although categorical perception wasoriginally demonstrated in the context ofauditory perception, similar phenomena havesince been discovered in vision (Goldstone &Hendrickson, 2010). For example, Goldstone(1994a) trained participants to make a cate-gory discrimination either in terms of the sizeor brightness of an object. He then presentedthose participants with a same/different task,in which two briefly presented objects wereeither the same or varied in terms of size orbrightness. Participants who had earlier cat-egorized objects on the basis of a particulardimension were found to be better at tellingobjects apart in terms of that dimension thanwere control participants who had been givenno prior categorization training. Moreover,this sensitization of categorically relevantdimensions was most evident at those valuesof the dimension that straddled the boundarybetween categories.


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These findings thus provide evidencethat the concepts that one has learned influ-ence one’s perceptual sensitivities, in thevisual as well as in the auditory modality(see also Ozgen & Davies, 2002). Otherresearch has shown that prolonged experi-ence with domains such as dogs (Tanaka &Taylor, 1991), cars and birds (Gauthier,Skudlarski, Gore, & Anderson, 2000), faces(Levin & Beale, 2000; O’Toole, Peterson, &Deffenbacher, 1995) or even novel “Greeble”stimuli (Gauthier, Tarr, Anderson, Skud-larski, & Gore, 1999) leads to a perceptualsystem that is tuned to these domains. Gold-stone et al. (2000; Goldstone, Landy, &Son, 2010) and Lupyan (2015) review otherevidence for conceptual influences on visualperception. Concept learning appears to beeffective both in combining stimulus proper-ties together to create perceptual chunks thatare diagnostic for categorization (Goldstone,2000), and in splitting apart and isolating per-ceptual dimensions if they are differentiallydiagnostic for categorization (Goldstone &Steyvers, 2001; M. Jones & Goldstone,2013). In fact, these two processes can beunified by the notion of creating perceptualunits in a size that is useful for relevantcategorizations (Goldstone, 2003).

The evidence reviewed in this section sug-gests that there is a strong interrelationshipbetween concepts and perception, with per-ceptual information influencing the conceptsthat one forms and conceptual informationinfluencing how one perceives the world.Most theories of concept formation failto account for this interrelationship. Theyinstead take the perceptual attributes of astimulus as a given and try to account forhow these attributes are used to categorizethat stimulus.

One area of research that provides anexception to this rule is research on objectrecognition. As pointed out by Schyns(1998), object recognition can be thought

of as an example of object categorization,with the goal of the process being to identifywhat kind of object one is observing. Unliketheories of categorization, theories of objectrecognition place strong emphasis on therole of perceptual information in identifyingan object.

Interestingly, some of the theories thathave been proposed to account for objectrecognition have characteristics in com-mon with theories of categorization. Forexample, structural description theories ofobject recognition (e.g., Biederman, 1987;Hummel & Biederman, 1992) are similar toprototype theories of categorization in thata newly encountered exemplar is comparedto a summary representation of a category inorder to determine whether or not the exem-plar is a member of that category. In contrast,multiple views theories of object recognition(e.g., Edelman, 1998; Riesenhuber & Poggio,1999; Tarr & Bülthoff, 1995) are similar toexemplar-based theories of categorization inthat a newly encountered exemplar is com-pared to a number of previously encounteredexemplars stored in memory. The categoriza-tion of an exemplar is determined either bythe exemplar in memory that most closelymatches it or by computing the similaritiesof the new exemplar to each of a number ofstored exemplars.

The similarities in the models proposedto account for categorization and objectrecognition suggest that there is consid-erable opportunity for cross talk betweenthese two domains. For example, theories ofcategorization could potentially be adaptedto provide a more complete account forobject recognition. In particular, they may beable to provide an account of not only therecognition of established object categories,but also the learning of new ones, a problemnot typically addressed by theories of objectrecognition. Furthermore, theories of objectrecognition could be adapted to provide


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a better account of the role of perceptualinformation in concept formation and use(Palmeri, Wong, & Gauthier, 2004). Therapid recent developments in object recog-nition research, including the developmentof detailed computational, neurally basedmodels (e.g., Jiang et al., 2006; Yamins &DiCarlo, 2016), suggest that a careful consid-eration of the role of perceptual informationin categorization can be a profitable researchstrategy.

Connecting Concepts to Language

Concepts also take part in a bidirectionalrelationship with language. In particular,one’s repertoire of concepts may influencethe types of word meanings that one learns,whereas the language that one speaks mayinfluence the types of concepts that oneforms.

The first of these two proposals is theless controversial. It is widely believed thatchildren come into the process of vocabu-lary learning with a large set of unlabeledconcepts. These early concepts may reflectthe correlational structure in the environmentof the young child, as suggested by Roschet al. (1976). For example, a child may forma concept of dog around the correlated prop-erties of four legs, tail, wagging, slobbering,and so forth. The subsequent learning of aword meaning should be relatively easy tothe extent that one can map that word ontoone of these existing concepts.

Different kinds of words may vary inthe extent to which they map directly ontoexisting concepts, and thus some types ofwords may be learned more easily thanothers. For example, Gentner (1981, 1982;Gentner & Boroditsky, 2001) has proposedthat nouns can be mapped straightforwardlyonto existing object concepts, and thus nounsare learned relatively early by children.The relation of verbs to prelinguistic event

categories, on the other hand, may be lessstraightforward. The nature of prelinguisticevent categories is not very well understood,but the available evidence suggests thatthey are structured quite differently fromverb meanings. For example, research byKersten and Billman (1997) demonstratedthat when adults learned event categories inthe absence of category labels, they formedthose categories around a rich set of corre-lated properties, including the characteristicsof the objects in the event, the motions ofthose objects, and the outcome of the event.Research by Casasola (2005, 2008) has simi-larly demonstrated that 10- to 14-month-oldinfants form unlabeled event categoriesaround correlations among different aspectsof an event, in this case involving particularobjects participating in particular spatialrelationships (e.g., containment, support)with one another. These unlabeled eventcategories learned by children and adultsdiffer markedly from verb meanings. Verbmeanings tend to have limited correlationalstructure, instead picking out only one ora small number of properties of an event(Huttenlocher & Lui, 1979; Talmy, 1985).For example, the verb collide involves twoobjects moving into contact with one another,irrespective of the objects involved or theoutcome of the collision.

It may thus be difficult to directly mapverbs onto existing event categories. Instead,language-learning experience may be nec-essary to determine which aspects of anevent are relevant and which aspects areirrelevant to verb meanings. Perhaps as aresult, children learning a variety of differentlanguages have been found to learn verbslater than nouns (Bornstein et al., 2004;Gentner, 1982; Gentner & Boroditsky, 2001;Golinkoff & Hirsh-Pasek, 2008; but seeGopnik & Choi, 1995 and Tardif, 1996 forpossible exceptions). More generally, wordmeanings should be easy to learn to the


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extent that they can be mapped onto existingconcepts.

There is greater controversy regarding theextent to which language may influence one’sconcepts. Some influences of language onconcepts are fairly straightforward, however.As one example, words in a language provideconvenient “handles” for referring to patternsof correlated features that would otherwisebe overwhelmingly complex (Lupyan, 2012).As a second example, whether a concept islearned in the presence or absence of lan-guage (e.g., a category label) may influencethe way in which that concept is learned.When categories are learned in the pres-ence of a category label in a supervisedclassification task, a common finding isone of competition among correlated cuesfor predictive strength (Gluck & Bower,1988; Shanks, 1991). In particular, moresalient cues may overshadow less salientcues, causing the concept learner to fail tonotice the predictiveness of the less salientcue (Gluck & Bower, 1988; Kruschke, 1992;Shanks, 1991).

When categories are learned in the absenceof category labels in unsupervised or obser-vational categorization tasks, on the otherhand, there is facilitation rather than competi-tion among correlated predictors of categorymembership (Billman, 1989; Billman &Knutson, 1996, Kersten & Billman, 1997).The learning of unlabeled categories can bemeasured in terms of the learning of corre-lations among attributes of a stimulus. Forexample, one’s knowledge of the correlationbetween a wagging tail and a slobberingmouth can be used as a measure of one’sknowledge of the category dog. Billman andKnutson (1996) used this unsupervised cate-gorization method to examine the learning ofunlabeled categories of novel animals. Theyfound that participants were more likely tolearn the predictiveness of an attribute whenother correlated predictors were also present.

Related findings come from Chin-Parkerand Ross (2002, 2004). They compared cate-gory learning in the context of a classificationtask, in which the goal of the participantwas to predict the category label associatedwith an exemplar, to an inference-learningtask, in which the goal of the participantwas to predict a missing feature value. Whenthe members of a category shared multiplefeature values, one of which was diagnos-tic of category membership and others ofwhich were nondiagnostic (i.e., they werealso shared with members of the contrastingcategory), participants who were given aclassification task homed in on the featurethat was diagnostic of category membership,failing to learn the other feature values thatwere representative of the category but werenondiagnostic (see also Yamauchi, Love, &Markman, 2002). In contrast, participantswho were given an inference-learning taskwere more likely to discover all of the featurevalues that were associated with a givencategory, even those that were nondiagnostic.

There is thus evidence that the presenceof language influences the way in which aconcept is learned. A more controversial sug-gestion is that the language that one speaksmay influence the types of concepts thatone learns. This suggestion, termed the lin-guistic relativity hypothesis, was first madeby Whorf (1956), on the basis of apparentdramatic differences between English andNative American languages in their expres-sions of ideas such as time, motion, and color.For example, Whorf proposed that the Hopimake no distinction between the past andpresent because the Hopi language providesno mechanism for talking about this distinc-tion. Many of Whorf’s linguistic analyseshave since been debunked (see Pinker, 1994,for a review), but his theory remains a sourceof controversy.

Early experimental evidence suggestedthat concepts were relatively impervious


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to linguistic influences. In particular,Heider’s (1972) classic finding that speakersof Dani, a language with only two colorwords, learned new color concepts in asimilar fashion to English speakers sug-gested that concepts were determined byperception rather than by language. Morerecently, however, Roberson and colleagues(Roberson, Davidoff, Davies, & Shapiro,2005; Roberson, Davies, & Davidoff, 2000)attempted to replicate Heider’s findings withother groups of people with limited colorvocabularies, namely speakers of Berinmoin New Guinea and speakers of Himba inNamibia. In contrast to Heider’s findings,Roberson et al. (2000) found that the Berinmospeakers did no better at learning a new colorcategory for a color that was easy to namein English than for a hard to name color.Moreover, speakers of Berinmo and Himbadid no better at learning a category discrimi-nation between green and blue (a distinctionnot made in either language) than they didat learning a discrimination between twoshades of green. This result contrasted withthe results of English-speaking participantswho did better at the green/blue discrim-ination. It also contrasted with superiorperformance in Berinmo and Himba speakerson discriminations that were present in theirrespective languages. These results suggestthat the English division of the color spec-trum may be more a function of the Englishlanguage and less a function of human colorphysiology than was originally believed.

Regardless of one’s interpretation of theHeider (1972) and Roberson et al. (2000,2005) results, there are straightforward rea-sons to expect at least some influence oflanguage on one’s concepts. Research datingback to Homa and Cultice (1984) has demon-strated that people are better at learningconcepts when category labels are providedas feedback. Verbally labeling a visual targetexaggerates the degree to which conceptual

categories penetrate visual processing(Lupyan, 2008b). Thus, at the very least, onemay expect that a concept will be more likelyto be learned when it is labeled in a languagethan when it is unlabeled. Although thismay seem obvious, further predictions arepossible when this finding is combined withthe evidence for influences of concepts onperception reviewed earlier. In particular, onthe basis of the results of Goldstone (1994a),one may predict that when a language makesreference to a particular dimension, thuscausing people to form concepts aroundthat dimension, people’s perceptual sensi-tivities to that dimension will be increased.Kersten, Goldstone, and Schaffert (1998)provided evidence for this phenomenon andreferred to it as attentional persistence. Thisattentional persistence, in turn, would makepeople who learn this language more likelyto notice further contrasts along this dimen-sion. Thus, language may influence people’sconcepts indirectly through one’s perceptualsensitivities.

This proposal is consistent with L. B.Smith and Samuelson’s (2006) account ofthe apparent shape bias in children’s wordlearning. They proposed that children learn-ing languages such as English discover overthe course of early language acquisition thatthe shapes of objects are important in distin-guishing different nouns. As a result, theyattend more strongly to shape in subsequentword learning, resulting in an acceleration insubsequent shape word learning. Consistentwith this proposal, children learning Englishcome to attend to shape more strongly andin a wider variety of circumstances than dospeakers of Japanese, a language in whichshape is marked less prominently and othercues, such as material and animacy, are moreprominent (Imai & Gentner, 1997; Yoshida &Smith, 2003).

Although languages differ to some extentin the ways they refer to object categories,


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languages differ perhaps even more dra-matically in their treatment of less concretedomains, such as time (Boroditsky, 2001),number (Frank, Everett, Fedorenko, &Gibson, E., 2008), space (Levinson, Kita,Haun, & Rasch, 2002), motion (Gentner &Boroditsky, 2001; Kersten, 1998a, 1998b,2003), and blame (Fausey & Boroditsky,2010, 2011). For example, when describ-ing motion events, languages differ in theparticular aspects of motion that are mostprominently labeled by verbs. In English, themost frequently used class of verbs refersto the manner of motion of an object (e.g.,running, skipping, sauntering), or the wayin which an object moves around (Talmy,1985). In other languages (e.g., Spanish),however, the most frequently used class ofverbs refers to the path of an object (e.g.,entering, exiting), or its direction with respectto some external reference point. In these lan-guages, manner of motion is relegated to anadverbial, if it is mentioned at all. If languageinfluences one’s perceptual sensitivities, it ispossible that English speakers and Spanishspeakers may differ in the extent to whichthey are sensitive to motion attributes such asthe path and manner of motion of an object.

Initial tests of English and Spanish speak-ers’ sensitivities to manner and path of motion(e.g., Gennari, Sloman, Malt, & Fitch, 2002;Papafragou, Massey, & Gleitman, 2002)only revealed differences between the twogroups when they were asked to describeevents in language. These results thus pro-vide evidence only of an influence of one’sprior language-learning history on one’ssubsequent language use, rather than aninfluence of language on one’s nonlinguisticconcept use. More recently, however, Kerstenet al. (2010) revealed effects of one’s lan-guage background on one’s performance in asupervised classification task in which eithermanner of motion or path served as the diag-nostic attribute. In particular, monolingual

English speakers, monolingual Spanishspeakers, and Spanish/English bilingualsperformed quite similarly when the path ofan alien creature was diagnostic of categorymembership. Differences emerged when anovel manner of motion of a creature (i.e., theway it moved its legs in relation to its body)was diagnostic, however, with monolingualEnglish speakers performing better thanmonolingual Spanish speakers. Moreover,Spanish/English bilinguals performed differ-ently depending upon the linguistic contextin which they were tested, performing likemonolingual English speakers when testedin an English language context but per-forming like monolingual Spanish speakerswhen tested in a Spanish language context(see also Lai, Rodriguez, & Narasimhan,2014). Importantly, the same pattern ofresults was obtained regardless of whetherthe concepts to be learned were given novellinguistic labels or were simply numbered,suggesting an influence of native languageon nonlinguistic concept formation.

Thus, although the notion that languageinfluences concept use remains controver-sial, there is a growing body of evidencethat speakers of different languages performdifferently in a variety of different catego-rization tasks. Proponents of the universalistviewpoint (e.g., Li, Dunham, & Carey, 2009;Pinker, 1994) have argued that such findingssimply represent attempts by research partic-ipants to comply with experimental demands,falling back on overt or covert language useto help them solve the problem of “Whatdoes the experimenter want me to do here?”According to these accounts, speakers ofdifferent languages all think essentially thesame way when they leave the laboratory.Unfortunately, we do not have very goodmethods for measuring how people thinkoutside of the laboratory, so it is difficultto test these accounts. Rather than arguingabout whether a given effect of language


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observed in the laboratory is sufficientlylarge and sufficiently general to count as aWhorfian effect, perhaps a more constructiveapproach may be to document the variousconditions under which language does anddoes not influence concept use. This strategymay lead to a better understanding of thebidirectional relationship between conceptsand language, and the three-way relationshipamong concepts, language, and perception(Winawer et al., 2007).

HOW TO IMPROVE CATEGORYLEARNING?

A diverse set of research has shown that thereare many factors that influence the effective-ness of category learning. A central questionin this research is how to best configure acategory-learning context to promote theacquisition of the relevant concept and theability to apply that knowledge to new exem-plars or situations where that knowledge isuseful. As an example, students and teachersin every school, university, and trainingcenter struggle to make learning efficient andgeneralizable. Proposals for how to optimizecategory learning range from selecting theappropriate type of examples to be studied(Gibson, Rogers, & Zhu, 2013), choosing theright type of task, and shifting how a studentshould approach the task.

An important way to promote learningand transfer of concepts is by establishingcomparisons between similar items andmaking use of analogical reasoning whilelearning. When learners study two or moreinstances of the same concept side by side,transfer to more remote instances (e.g.,Gick & Holyoak, 1983; Meagher, Carvalho,Goldstone, & Nosofsky, 2017; Omata &Holyoak, 2012; Quilici & Mayer, 2002) oracquisition of a new category (e.g., Gentner &Namy, 1999) is more likely than when only

one instance is studied at a time. Moreover, ifthe instances being studied (even if individu-ally) include a high level of variation alongthe irrelevant dimensions, learners are gen-erally more likely to transfer their learningto novel situations (e.g., Ben-Zeev & Star,2001; Chang, Koedinger, & Lovett, 2003;Braithwaite & Goldstone, 2015; H. S. Lee,Betts, & Anderson, 2015). One explanationfor this benefit is that studying a superficiallydiverse set of items allows the learner tonotice and extrapolate the common prop-erties, central to the concept being learned(Belenky & Schalk, 2014; Day & Goldstone,2012; Gentner, 1983; Gick & Holyoak,1983). However, item variability has alsobeen shown to have no effect on learningeffectiveness (e.g., Reed, 1989). Braithwaiteand Goldstone (2015) have presented empir-ical evidence and computational modelingshowing that learners with a lower initialknowledge level benefit from less variationamong study items, while learners with highlevels of prior knowledge benefit from work-ing through examples with more variability(see also Novick, 1988).

Similarly, Elio and Anderson (1984)proposed that learning should start withlow-variability items (e.g., items that do notdiffer much from one another or from the cen-tral tendency of the category), and items withgreater variability should be introduced later(for similar evidence with young learnerssee Sandhofer & Doumas, 2008). However,not all learners benefit from this approach.The authors also show that if the learners’approach to the task is to consciously gen-erate hypotheses for category membership,the pattern of results is reversed (Elio &Anderson, 1984). One possibility is thathow the learner approaches the task changeswhat type of information gets encoded and,consequently, what information is most rel-evant (Elio & Anderson, 1984). It has alsobeen suggested that for optimal transfer of


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How to Improve Category Learning? 303

category learning, the study situation shouldemphasize items that promote a coherentgeneralization based on the properties thatfrequently occur (Elio & Anderson, 1981).Moreover, in situations where one needs tolearn several items that promote differenttypes of generalizations, the best learningis achieved by studying items that promotesimilar generalizations close in time (Elio &Anderson, 1981; Mathy & Feldman, 2009).

From the brief survey just provided aquestion surfaces: Should learning start withdifficult items and progress toward easierones or the other way around? In general,research seems to indicate that learning ben-efits from study with examples organized inincreasing order of complexity or difficulty,that is, from the easiest and simplest tothe hardest and more complex (Ahissar &Hochstein, 1997; Baddeley, 1992; Hull, 1920;Terrace, 1964; Wilson, Baddeley, Evans, &Shiel, 1994). However, this might be thecase only for categories requiring integrationacross different dimensions (Spiering &Ashby, 2008), but the reverse may hold forcategories organized around a clear rule.Consistent with this latter provision, E. S.Lee, MacGregor, Bavelas, and Mirlin (1988)showed that learners who start by studyingexamples that other learners classified incor-rectly made fewer errors during classificationtests than learners who studied the examplesin the opposite order.

When it is not possible to change type ofexamples, their difficulty, or the task, cate-gory learning can nonetheless be improvedby a careful sequential organization of theexamples (Carvalho & Goldstone, 2015).It has been shown before that alternat-ing presentation of items from differenthard-to-discriminate categories improvescategory learning and transfer (Birnbaum,Kornell, Bjork, & Bjork, 2013; Carvalho &Goldstone, 2014; Rohrer, Dedrick, &Stershic, 2015). On the other hand, when

the goal is to acquire an independent charac-terization of each concept, presenting severalexamples of the same category in close suc-cession improves transfer to a greater degreethan frequent alternation (Carpenter &Mueller, 2013; Carvalho & Goldstone, 2014,2015; Zulkiply & Burt, 2013). Moreover,because greater delays between presenta-tions make it harder to retrieve previousencounters, spaced presentation of itemsof a single category can promote learningand constitute a desirable difficulty (Bjork,1994). Consistent with this idea, Birnbaumet al. (2013) showed that while introducing atemporal delay between successive presenta-tions of different categories hindered learningand transfer, increasing the temporal delaybetween successive presentations of itemsof the same category improved it (see alsoKang & Pashler, 2012). Similarly, researchwith young children has shown that categorygeneralization benefits from play periodsbetween successive presentations of itemsof the same category (Vlach, Sandhofer, &Kornell, 2008), and from study with increas-ingly greater temporal delays betweensuccessive repetitions of the same category(Vlach, Sandhofer, & Bjork, 2014).

Finally, an increasingly important issue iswhether category learning can be improvedby just leaving it in the hands of those whomight care the most about it—the learn-ers themselves. Is self-regulated learningbetter than being given the best study for-mat and organization as determined by aninformed teacher? On the one hand, it hasbeen shown that learners are often unawareof how to improve concept learning andfall victim to a series of biases (Bjork,Dunlosky, & Kornell, 2013). On the otherhand, self-regulated study is often relativelyeffective. For example, learners decidinghow to sample information outperformthose who receive a random sampling ofexamples or who are yoked to the selections

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of another learner in a categorizationtask (e.g., Markant & Gureckis, 2014) or arecognition memory task (Markant, DuBrow,Davachi, & Gureckis, 2014). The mechanismbehind this advantage is still an open ques-tion. It might be the result of efficient sam-pling of information given the data available,the process of sampling itself, the greatereffort afforded by actively learning, or deci-sional processes (Gureckis & Markant, 2012).

Understanding how concept learning canbe optimized will contribute to designingbetter instructional techniques and sys-tems (Koedinger, Booth, & Klahr, 2013).Furthermore, it will also contribute toour foundational understanding of themechanisms underlying concept learning(Carvalho & Goldstone, 2015). Methodsfor constructing optimal sets of trainingitems given a known learning algorithm andwell-defined educational goal have proveninformative for understanding both humanand machine learning, their commonalities,and their differences (Zhu, 2015).

CONCLUSION

The field of concept learning and represen-tation is noteworthy for its large number ofdirections and perspectives. While the lack ofclosure may frustrate some outside observers,it is also a source of strength and resilience.With an eye toward the future, we describesome of the most important avenues for futureprogress in the field.

First, as the last section suggests, webelieve that much of the progress of researchon concepts will be to connect concepts toother concepts (Goldstone, 1996; Landauer &Dumais, 1997), to the perceptual world, andto language. One of the risks of viewingconcepts as represented by rules, prototypes,sets of exemplars, or category boundaries isthat one can easily imagine that one concept

is independent of others. For example, onecan list the exemplars that are included inthe concept bird, or describe its central ten-dency, without making recourse to any otherconcepts. However, it is likely that all of ourconcepts are embedded in a network whereeach concept’s meaning depends on otherconcepts, as well as perceptual processes andlinguistic labels. The proper level of analysismay not be individual concepts as manyresearchers have assumed, but systems ofconcepts. The connections between conceptsand perception on the one hand and betweenconcepts and language on the other handreveal an important dual nature of concepts.Concepts are used both to recognize objectsand to ground word meanings. Workingout the details of this dual nature will go along way toward understanding how humanthinking can be both concrete and symbolic.

A second direction is the development ofmore sophisticated formal models of conceptlearning. One important recent trend in math-ematical models has been the extension ofrational models of categorization (Anderson,1991) to Bayesian models that assume thatcategories are constructed to maximize thelikelihood of making legitimate inferences(Goodman et al., 2008; Griffiths & Tenen-baum, 2009; Kemp & Tenenbaum, 2009).In contrast to this approach, other researchersare continuing to pursue neural networkmodels that offer process-based accounts ofconcept learning on short and long timescales(M. Jones, Love, & Maddox, 2006; Rogers &McClelland, 2008), and still others chas-tise Bayesian accounts for inadequatelydescribing how humans learn categories inan incremental and memory-limited fashion(M. Jones & Love, 2011). Progress in neuralnetworks, mathematical models, statisticalmodels, and rational analyses can be gaugedby several measures: goodness of fit to humandata, breadth of empirical phenomena accom-modated, model constraint and parsimony,


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and autonomy from human intervention. Thecurrent crop of models is fairly impressive interms of fitting specific data sets, but thereis much room for improvement in termsof their ability to accommodate rich setsof concepts, and process real-world stimuliwithout relying on human judgments or handcoding (Goldstone & Landy, 2010).

A third direction for research is totackle more real-world concepts ratherthan laboratory-created categories, whichare often motivated by considerations ofcontrolled construction, ease of analysis, andfit to model assumptions. Some researchershave, instead, tried to tackle particular con-cepts in their subtlety and complexity, suchas the concepts of food (Ross & Murphy,1999), water (Malt, 1994), and political party(Heit & Nicholson, 2010). Others have madethe more general point that how a conceptis learned and represented will depend onhow it is used to achieve a benefit whileinteracting with the world (Markman &Ross, 2003; Ross, Wang, Kramer, Simons, &Crowell, 2007). Still others have workedto develop computational techniques thatcan account for concept formation whenprovided with large-scale, real-world datasets, such as library catalogs or corpuses ofone million words taken from encyclopedias(Glushko, Maglio, Matlock, & Barsalou,2008; Griffiths, Steyvers, & Tenenbaum,2007; Landauer & Dumais, 1997). All ofthese efforts share a goal of applying our the-oretical knowledge of concepts to understandhow specific conceptual domains of interestare learned and organized, and in the processof so doing, challenging and extending ourtheoretical knowledge.

A final important direction will be toapply psychological research on concepts.Perhaps the most important and relevantapplication is in the area of educationalreform. Psychologists have amassed a largeamount of empirical research on various

factors that impact the ease of learning andtransferring conceptual knowledge. The liter-ature contains excellent suggestions on howto manipulate category labels, presentationorder, learning strategies, stimulus format,and category variability in order to optimizethe efficiency and likelihood of conceptattainment. Putting these suggestions to usein classrooms, computer-based tutorials, andmultimedia instructional systems could havea substantial positive impact on pedagogy.This research can also be used to developautonomous computer diagnosis systems,user models, information visualization sys-tems, and databases that are organized in amanner consistent with human conceptualsystems. Given the importance of conceptsfor intelligent thought, it is not unreasonableto suppose that concept-learning researchwill be equally important for improvingthought processes.

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