Cambridge Handbook of Thinking and Reasoning

The Cambridge Handbook of Thinking and Reasoning


Edited by

Keith J. Holyoak and Robert G. Morrison

cambridge university press Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, São Paulo Cambridge University Press The Edinburgh Building, Cambridge cb2 2ru, UK Published in the United States of America by Cambridge University Press, New York www.cambridge.org Information on this title: www.cambridge.org/9780521824170 © Cambridge University Press 2005 This book is in copyright. Subject to statutory exception and to the provision of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press. First published in print format 2005 isbn-13 isbn-10

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The editors gratefully dedicate this volume to Patricia Wenjie Cheng (from KJH) and Deborah Lee Morrison (from RGM)

Contents

Preface Contributors

page ix xi

p a r t ii REASONING

5. The Problem of Induction 1 . Thinking and Reasoning: A Reader’s Guide

1

Keith J. Holyoak Robert G. Morrison

6. Analogy 7. Causal Learning

13

9. Mental Models and Thought

1 69

1 85

P. N. Johnson-Laird

1 0. Visuospatial Reasoning 37

Douglas L. Medin Lance J. Rips

Leonidas A. A. Doumas John E. Hummel

8. Deductive Reasoning Jonathan St. B. T. Evans

Robert L. Goldstone Ji Yun Son

4. Approaches to Modeling Human Mental Representations: What Works, What Doesn’t, and Why

1 43

Marc J. Buehner Patricia W. Cheng

THE NATURE OF HUMAN CONCEPTS

3. Concepts and Categories: Memory, Meaning, and Metaphysics

117

Keith J. Holyoak

pa r t i

2 . Similarity

95

Steven A. Sloman David A. Lagnado

209

Barbara Tversky

p a r t iii

JUDGMENT AND DECISION MAKING 73

1 1 . Decision Making

243

Robyn A. LeBoeuf Eldar B. Shafir vii

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1 2 . A Model of Heuristic Judgment

267

Daniel Kahneman Shane Frederick

1 3. Motivated Thinking

ONTOGENY, PHYLOGENY, LANGUAGE, AND CULTURE 295

Daniel C. Molden E. Tory Higgins

2 3. Mathematical Cognition

2 4. Effects of Aging on Reasoning 3 21

351

Robert J. Sternberg Todd I. Lubart James C. Kaufman Jean E. Pretz

3 71

401

43 1

663

685

Phoebe C. Ellsworth

705

Kevin Dunbar Jonathan Fugelsang

30. Thinking and Reasoning in Medicine

45 7

727

Vimla L. Patel Jos´e F. Arocha Jiajie Zhang

31 . Intelligence

75 1

Robert J. Sternberg

475 32 . Learning to Think: The Challenges of Teaching Thinking

Vinod Goel

Peter Bachman Tyrone D. Cannon

63 3

p a r t vii THINKING IN PRACTICE

2 9. Scientific Thinking and Reasoning

Robert G. Morrison

2 1 . Cognitive and Neuroscience Aspects of Thought Disorder

2 7. Paradigms of Cultural Thought

2 8. Legal Reasoning

pa r t v COGNITIVE AND NEURAL CONSTRAINTS ON HUMAN THOUGHT

2 0. Cognitive Neuroscience of Deductive Reasoning

607

Josep Call Michael Tomasello

Patricia M. Greenfield

Leib Litman Arthur S. Reber

1 9. Thinking in Working Memory

5 89

Lila Gleitman Anna Papafragou

Marsha C. Lovett John R. Anderson

1 8. Implicit Cognition and Thought

2 5. Reasoning and Thinking in Nonhuman Primates

2 6. Language and Thought

Michelene T. H. Chi Stellan Ohlsson

1 7. Thinking as a Production System

559

Timothy A. Salthouse

Laura R. Novick Miriam Bassok

1 6. Complex Declarative Learning

5 29

C. R. Gallistel Rochel Gelman

PROBLEM SOLVING AND COMPLEX LEARNING

1 5. Creativity

2 2 . Development of Thinking Graeme S. Halford

p a r t iv

1 4. Problem Solving

p a r t vi

493

775

Ron Ritchhart David N. Perkins

Index

803

Preface

A few decades ago, when the science of cognition was in its infancy, the early textbooks on cognition began with perception and attention and ended with memory. Socalled higher-level cognition – the mysterious, complicated realm of thinking and reasoning – was simply left out. Things have changed – any good cognitive text (and there are many) devotes several chapters to topics such as categorization, inductive and deductive reasoning, judgment and decision making, and problem solving. What has still been missing, however, is a true handbook for the field of thinking and reasoning – a book meant to be kept close “at hand” by those involved in the field. Such a book would bring together top researchers to write chapters, each of which summarizes the basic concepts and findings for a major topic, sketches its history, and provides a sense of the directions in which research is currently heading. This handbook would provide quick overviews for experts in each topic area, and more importantly for experts in allied topic areas (because few researchers can keep up with the scientific literature over the full breadth of the field of thinking and rea-

soning). Even more crucially, this handbook would provide an entry point into the field for the next generation of researchers by providing a text for use in classes on thinking and reasoning designed for graduate students and upper-level undergraduates. The Cambridge Handbook of Thinking and Reasoning is intended to be this previously missing handbook. The project was first conceived at the meeting of the Cognitive Science Society in Edinburgh, Scotland, during the summer of 2001 . The contents of the volume are sketched in Chapter 1 . Our aim is to provide comprehensive and authoritative reviews of all the core topics of the field of thinking and reasoning, with many pointers for further reading. Undoubtedly, there are still omissions, but we have included as much as we could realistically fit in a single volume. Our focus is on research from cognitive psychology, cognitive science, and cognitive neuroscience, but we also include work related to developmental, social, and clinical psychology; philosophy; economics; artificial intelligence; linguistics; education; law; and medicine. We hope that scholars and students in all these ix

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fields and others will find this to be a valuable collection. We have many to thank for their help in bringing this endeavor to fruition. Philip Laughlin, our editor at Cambridge University Press, gave us exactly the balance of encouragement and patience we needed. It is fitting that a handbook of thinking and reasoning should bear the imprint and indeed the name of this illustrious press, with its long history reaching back to the origins of scientific inquiry. Michie Shaw, Senior Project Manager at TechBooks, provided us with close support throughout the arduous editing process. At UCLA, Christine Vu did a great deal of organizational work in her role as our editorial assistant for the entire project. During this period, our own efforts were supported by grants R3 05 H03 01 41 from the Institute of Education Sciences and SES-00803 75 from the National Science Foundation to KJH, and from Xunesis and National Service Research Award MH-064244 from the National Institute of Mental Health to RGM. Then there are the authors. (It would seem a bit presumptuous to call them “our” authors!) People working on tough intellec-

tual problems sometimes experience a moment of insight – a sense that although many laborious steps may lay ahead, the basic elements of a solution are already in place. Such fortunate people work on happily, confident that ultimate success is assured. In preparing this handbook, we also had our moment of “insight.” It came when all these outstanding researchers agreed to join our project. Before the first chapter was drafted, we knew the volume was going to be of the highest quality. Along the way, our distinguished authors graciously served as each other’s critics as we passed drafts around, working to make the chapters as integrated as possible, adding in pointers from one to another. Then the authors all changed hats again and went back to work revising their own chapters in light of the feedback their peers had provided. We thank you all for making our own small labors a great pleasure. KEITH J. HOLYOAK University of California, Los Angeles ROBERT G. MORRISON Xunesis, Chicago October 2 004

Contributors

John R. Anderson Carnegie Mellon University Department of Psychology Pittsburgh, PA 1 5 21 3 -3 890 [email protected] Jose´ F. Arocha Department of Health Studies & Gerontology University of Waterloo 200 University Ave. W. Waterloo, Ontario Canada N2L 3 G1 [email protected] Peter Bachman University of California, Los Angeles Department of Psychology Franz Hall Los Angeles, CA 90095 -1 5 63 [email protected] Miriam Bassok University of Washington Department of Psychology Box 3 5 1 5 25 Seattle, WA 981 95 -1 5 25 [email protected]

Marc J. Buehner School of Psychology Cardiff University Tower Building Park Place Cardiff, CF1 0 3 AT Wales, UK [email protected] Josep Call Max Planck Institute for Evolutionary Anthropology Deutscher Platz 6 D-041 03 Leipzig, Germany [email protected] Tyrone D. Cannon University of California, Los Angeles Department of Psychology Franz Hall Los Angeles, CA 90095 -1 5 63 [email protected] Patricia W. Cheng University of California, Los Angeles Department of Psychology Franz Hall Los Angeles, CA 90095 -1 5 63 [email protected]

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Michelene T. H. Chi University of Pittsburgh Learning Research and Development Center 3 93 9 O’Hara Street Pittsburgh, PA 1 5 260 [email protected] Leonidas A. A. Doumas University of California, Los Angeles Department of Psychology Franz Hall Los Angeles, CA 90095 -1 5 63 [email protected] Kevin Dunbar Dartmouth College Department of Psychological & Brain Sciences Hanover, NH 03 75 5 [email protected] Phoebe C. Ellsworth University of Michigan Department of Psychology 5 25 East University Ann Arbor, MI 481 09-1 1 09 [email protected] Jonathan St. B. T. Evans University of Plymouth Centre for Thinking and Language School of Psychology Plymouth PL4 8AA UK [email protected] Shane Frederick Massachusetts Institute of Technology Sloan School of Management Room E5 6-3 1 7 3 8 Memorial Drive Cambridge, MA 021 42-1 3 07 [email protected]

Rochel Gelman Rutgers University Psychology and Rutgers Center for Cognitive Science 1 5 2 Frelinghuysen Road Piscataway, NJ 0885 4-8020 [email protected] Lila Gleitman University of Pennsylvania Departments of Psychology and Linguistics Institute for Research in Cognitive Science 3 401 Walnut St. – 4th floor Philadelphia, PA 1 91 04 [email protected] Vinod Goel York University Department of Psychology Toronto, Ontario Canada M3 J 1 P3 [email protected] Robert L. Goldstone Indiana University Psychology Department Psychology Building 1 1 01 E 1 0th St. Bloomington, IN 47405 -7007 [email protected] Patricia M. Greenfield University of California, Los Angeles Department of Psychology Franz Hall Los Angeles, CA 90095 -1 5 63 [email protected]

Jonathan Fugelsang Dartmouth College Department of Psychological & Brain Sciences Hanover, NH 03 75 5 [email protected]

Graeme S. Halford University of Queensland School of Psychology Brisbane Queensland 4072 Australia [email protected]

Charles R. Gallistel Rutgers University Psychology and Rutgers Center for Cognitive Science 1 5 2 Frelinghuysen Road Piscataway, NJ 0885 4-8020 [email protected]

E. Tory Higgins Columbia University Department of Psychology 401 D Schermerhorn Mail Code 5 5 01 New York, NY 1 0027-5 5 01 [email protected]

contributors Keith J. Holyoak – editor University of California, Los Angeles Department of Psychology Franz Hall Los Angeles, CA 90095 -1 5 63 [email protected] John E. Hummel University of California, Los Angeles Department of Psychology Franz Hall Los Angeles, CA 90095 -1 5 63 [email protected] P. N. Johnson-Laird Princeton University Department of Psychology 3 -C-3 Green Hall Princeton, NJ 085 44 [email protected] Daniel Kahneman Princeton University Woodrow Wilson School 3 24 Wallace Hall Princeton, NJ 085 44 [email protected] James C. Kaufman California State University, San Bernardino Department of Psychology 5 5 00 University Parkway San Bernardino, CA 92407 [email protected] David A. Lagnado Department of Psychology University College London Gower Street London, UK WC1 E 6BT [email protected] Robyn A. LeBoeuf University of Florida Warrington College of Business Marketing Department PO Box 1 1 71 5 5 Gainesville, FL 3 261 1 -71 5 5 [email protected] Leib Litman Brooklyn College of CUNY Department of Psychology 2900 Bedford Avenue Brooklyn, NY 1 1 21 0 [email protected]

Marsha C. Lovett Carnegie Mellon University Department of Psychology Pittsburgh, PA 1 5 21 3 -3 890 [email protected] Todd I. Lubart Laboratoire Cognition et Developpement ´ Institut de Psychologie – Universite´ Paris 5 71 , avenue Edouard Vaillant 92774 Boulogne-Billancourt cedex France [email protected] .fr Douglas L. Medin Northwestern University Department of Psychology 2029 Sheridan Road Evanston, IL 60208 [email protected] Daniel C. Molden Northwestern University Department of Psychology 2029 Sheridan Road Evanston, IL 60208 [email protected] Robert G. Morrison – editor Xunesis P.O. Box 2691 87 Chicago, IL 60626-91 87 [email protected] Laura R. Novick Vanderbilt University Department of Psychology & Human Development Peabody College #5 1 2 23 0 Appleton Place Nashville, TN 3 7203 -5 721 [email protected] Stellan Ohlsson University of Illinois, Chicago Department of Psychology Chicago, IL 60607-71 3 7 [email protected] Anna Papafragou University of Pennsylvania Institute for Research in Cognitive Science 3 401 Walnut Street, Suite 400A Philadelphia, PA 1 91 04 [email protected]

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Vimla L. Patel Columbia University Department of Biomedical Informatics and Psychiatry Vanderbilt Clinic-5 622 West 1 68th Street New York, NY 1 0003 [email protected]

Eldar B. Shafir Princeton University Department of Psychology and the Woodrow Wilson School of Public Affairs Green Hall Princeton, NJ 085 44 [email protected]

David N. Perkins Harvard Graduate School of Education Project Zero 3 1 5 Longfellow Hall, Appian Way Cambridge, MA 021 3 8 david [email protected]

Steven A. Sloman Brown University Cognitive & Linguistic Sciences Box 1 978 Providence, RI 0291 2 Steven [email protected]

Jean E. Pretz Department of Psychology Illinois Wesleyan University P.O. Box 2900 Bloomington, IL 61 702-2900 [email protected]

Ji Yun Son Indiana University Psychology Department Psychology Building 1 1 01 E 1 0th St. Bloomington, IN 47405 -7007 [email protected]

Arthur S. Reber Brooklyn College of CUNY Department of Psychology 2900 Bedford Avenue Brooklyn, NY 1 1 21 0 [email protected]

Robert J. Sternberg PACE Center Yale University P.O. Box 2083 5 8 New Haven, CT 065 20-83 5 8 [email protected]

Lance J. Rips Northwestern University Department of Psychology 2029 Sheridan Road Evanston, IL 60208 [email protected]

Michael Tomasello Max Planck Institute for Evolutionary Anthropology Deutscher Platz 6 D-041 03 Leipzig, Germany [email protected]

Ron Ritchhart Harvard Graduate School of Education Project Zero 1 24 Mount Auburn Street Cambridge, MA 021 3 8 ron [email protected]

Barbara Tversky Stanford University Department of Psychology Building 420 Stanford, CA 943 05 -21 3 0 [email protected]

Timothy A. Salthouse University of Virginia Department of Psychology Charlottesville, VA 22904-4400 [email protected]

Jiajie Zhang School of Health Information Sciences University of Texas at Houston 7000 Fannin, Suite 600 Houston, TX 7703 0 [email protected]

CHAPTER 1

Thinking and Reasoning: A Reader’s Guide Keith J. Holyoak Robert G. Morrison

“Cogito, ergo sum,” the French philosopher Rene´ Descartes famously declared, “I think, therefore I am.” Every normal human adult shares a sense that the ability to think, to reason, is a part of their fundamental identity. A person may be struck blind or deaf, yet we still recognize his or her core cognitive capacities as intact. Even loss of language, the gift often claimed as the sine qua non of homo sapiens, does not take away a person’s essential humanness. Unlike language ability, which is essentially unique to our species, the rudimentary ability to think and reason is apparent in nonhuman primates (see Call & Tomasello, Chap. 25 ); and yet it is thinking, not language, that lies closest to the core of our individual identity. A person who loses language but can still make intelligent decisions, as demonstrated by actions, is viewed as mentally intact. In contrast, the kinds of brain damage that rob an individual of the capacity to think and reason are considered the harshest blows that can be struck against a sense of personhood. Cogito, ergo sum.

What Is Thinking? We can start to answer this question by looking at the various ways the word “thinking” is used in everyday language. “I think that water is necessary for life” and “George thinks the Pope is a communist” both express beliefs (of varying degrees of apparent plausibility), that is, explicit claims of what someone takes to be a truth about the world. “Anne is sure to think of a solution” carries us into the realm of problem solving, the mental construction of an action plan to achieve a goal. The complaint “Why didn’t you think before you went ahead with your half-baked scheme?” emphasizes that thinking can be a kind of foresight, a way of “seeing” the possible future.1 “What do you think about it?” calls for a judgment, an assessment of the desirability of an option. Then there’s “Albert is lost in thought,” where thinking becomes some sort of mental meadow through which a person might meander on a rainy afternoon, oblivious to the world outside.

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Rips and Conrad (1 989) elicited judgments from college students about how various mentalistic terms relate to one another. Using statistical techniques, the investigators were able to summarize these relationships in two diagrams, shown in Figure 1 .1 . Figure 1 .1 (A) is a hierarchy of kinds, or categories. Roughly, people believe planning is a kind of deciding, which is a kind of reasoning, which is a kind of conceptualizing, which is a kind of thinking. People also believe that thinking is part of conceptualizing, which is part of remembering, which is part of reasoning, and so on [Figure 1 .1 (B)]. The kinds ordering and the parts ordering are similar; most strikingly, “thinking” is the most general term in both orderings – the grand superordinate of mental activities, which permeates all the others. It is not easy to make the move from the free flow of everyday speech to scientific definitions of mental terms, but let us nonetheless offer a preliminary definition of thinking to suggest what this book is about: Thinking is the systematic transformation of mental representations of knowledge to characterize actual or possible states of the world, often in service of goals. Obviously, our definition introduces a plethora of terms with meanings that beg to be unpacked, but at which we can only hint. A mental representation of knowledge is an internal description that can be manipulated to form other descriptions. To count as thinking, the manipulations must be systematic transformations governed by certain constraints. Whether a logical deduction or a creative leap, what we mean by thinking is more than unconstrained associations (with the caveat that thinking may indeed be disordered; see Bachman & Cannon, Chap. 21 ). The internal representations created by thinking describe states of some external world (a world that may include the thinker as an object of self-reflection) – that world might be our everyday one, or perhaps some imaginary construction obeying the “laws” of magical realism. Often (not always – the daydreamer, and indeed the night dreamer, are also thinkers), thinking is directed toward achieving some desired

state of affairs, some goal that motivates the thinker to perform mental work. Our definition thus includes quite a few stipulations, but notice also what is left out. We do not claim that thinking necessarily requires a human (higher-order primates, and perhaps some other species on this or other planets, have a claim to be considered thinkers) (see Call & Tomasello, Chap. 25 ) or even a sentient being. (The field of artificial intelligence may have been a disappointment in its first half-century, but we are reluctant to define it away as an oxymoron.) Nonetheless, our focus in this book is on thinking by hominids with electrochemically powered brains. Thinking often seems to be a conscious activity of which the thinker is aware (cogito, ergo sum); however, consciousness is a thorny philosophical puzzle, and some mental activities seem pretty much like thinking, except for being implicit rather than explicit (see Litman & Reber, Chap. 1 8). Finally, we do not claim that thinking is inherently rational, optimal, desirable, or even smart. A thorough history of human thinking will include quite a few chapters on stupidity. The study of thinking includes several interrelated subfields that reflect slightly different perspectives on thinking. Reasoning, which has a long tradition that springs from philosophy and logic, places emphasis on the process of drawing inferences (conclusions) from some initial information (premises). In standard logic, an inference is deductive if the truth of the premises guarantees the truth of the conclusion by virtue of the argument form. If the truth of the premises renders the truth of the conclusion more credible but does not bestow certainty, the inference is called inductive.2 Judgment and decision making involve assessment of the value of an option or the probability that it will yield a certain payoff ( judgment) coupled with choice among alternatives (decision making). Problem solving involves the construction of a course of action that can achieve a goal. Although these distinct perspectives on thinking are useful in organizing the field

thinking and reasoning: a reader’s guide

3

Figure 1 .1 . People’s conceptions of the relationships among terms for mental activities. A, Ordering of “kinds.” B, Ordering of “parts.” (Adapted from Rips & Conrad, 1 989, with permission.)

(and this volume), these aspects of thinking overlap in every conceivable way. To solve a problem, one is likely to reason about the consequences of possible actions and make decisions to select among alternative actions. A logic problem, as the name implies, is a problem to be solved (with the goal of deriving or evaluating a possible conclusion). Making a decision is often a problem that requires reasoning. These subdivisions of the field, like our preliminary definition of thinking, should be treated as guideposts, not destinations.

A Capsule History Thinking and reasoning, long the academic province of philosophy, have over the past century emerged as core topics of empirical investigation and theoretical analysis in the modern fields known as cognitive psychology, cognitive science, and cognitive neuroscience. Before psychology was founded, the

eighteenth-century philosophers Immanuel Kant (in Germany) and David Hume (in Scotland) laid the foundations for all subsequent work on the origins of causal knowledge, perhaps the most central problem in the study of thinking (see Buehner & Cheng, Chap. 7). If we were to choose one phrase to set the stage for modern views of thinking, it would be an observation of the British philosopher Thomas Hobbes, who, in 1 65 1 , in his treatise Leviathan, proposed, “Reasoning is but reckoning.” “Reckoning” is an odd term today, but in the seventeenth century it meant computation, as in arithmetic calculations.3 It was not until the twentieth century that the psychology of thinking became a scientific endeavor. The first half of the century gave rise to many important pioneers who in very different ways laid the foundations for the emergence of the modern field of thinking and reasoning. Foremost were the Gestalt psychologists of Germany, who provided deep insights into the nature of problem solving (see Novick & Bassok, Chap. 1 4).

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Most notable of the Gestaltists were Karl Duncker and Max Wertheimer, students of human problem solving, and Wolfgang Kohler, a keen observer of problem solv¨ ing by great apes (see Call & Tomasello, Chap. 25 ). The pioneers of the early twentieth century also include Sigmund Freud, whose complex and ever-controversial legacy includes the notions that forms of thought can be unconscious (see Litman & Reber, Chap. 1 8) and that “cold” cognition is tangled up with “hot” emotion (see Molden & Higgins, Chap. 1 3 ). As the founder of clinical psychology, Freud’s legacy also includes the ongoing integration of research on normal thinking with studies of thought disorders, such as schizophrenia (see Bachman & Cannon, Chap. 21 ). Other early pioneers in the early and mid-twentieth century contributed to various fields of study that are now embraced within thinking and reasoning. Cognitive development continues to be influenced by the early theories developed by the Swiss psychologist Jean Piaget (see Halford, Chap. 22) and the Russian psychologist Lev Vygotsky (see Greenfield, Chap. 27). In the United States, Charles Spearman was a leader in the systematic study of individual differences in intelligence (see Sternberg, Chap. 3 1 ). In the middle of the century, the Russian neurologist Alexander Luria made immense contributions to our understanding of how thinking depends on specific areas of the brain, anticipating the modern field of cognitive neuroscience (see Goel, Chap. 20). Around the same time, in the United States, Herbert Simon argued that the traditional rational model of economic theory should be replaced with a framework that accounted for a variety of human resource constraints such as bounded attention and memory capacity and limited time (see LeBoeuf & Shafir, Chap. 1 1 , and Morrison, Chap. 1 9). This was one of the contributions that in 1 978 earned Simon the Nobel Prize in Economics. In 1 943 , the British psychologist Kenneth Craik sketched the fundamental notion that a mental representation provides a kind of model of the world that can be “run” to make

predictions (much like an engineer might use a physical scale model of a bridge to anticipate the effects of stress on the actual bridge intended to span a river).4 In the 1 960s and 1 970s, modern work on the psychology of reasoning began in Britain with the contributions of Peter Wason and his collaborator Philip Johnson-Laird (see Evans, Chap. 8). The modern conception of thinking as computation became prominent in the 1 970s. In their classic treatment of human problem solving, Allen Newell and Herbert Simon (1 972) showed that the computational analysis of thinking (anticipated by Alan Turing, the father of computer science) could yield important empirical and theoretical results. Like a program running on a digital computer, a person thinking through a problem can be viewed as taking an input that represents initial conditions and a goal, and applying a sequence of operations to reduce the difference between the initial conditions and the goal. The work of Newell and Simon established computer simulation as a standard method for analyzing human thinking. Their work also highlighted the potential of production systems (see Novick & Bassok, Chap. 1 4), which were subsequently developed extensively as cognitive models by John Anderson and his colleagues (see Lovett & Anderson, Chap. 1 7). The 1 970s saw a wide range of major developments that continue to shape the field. Eleanor Rosch, building on earlier work by Jerome Bruner (Bruner, Goodnow, & Austin, 1 95 6), addressed the fundamental question of why people have the categories they do, and not other logically possible groupings of objects (see Medin & Rips, Chap. 3 ). Rosch argued that natural categories often have fuzzy boundaries (a whale is an odd mammal) but nonetheless have clear central tendencies or prototypes (people by and large agree that a bear makes a fine mammal). The psychology of human judgment was reshaped by the insights of Amos Tversky and Daniel Kahneman, who identified simple cognitive strategies, or heuristics, that people use to make judgments of frequency and probability. Often quick and accurate, these

thinking and reasoning: a reader’s guide

strategies can in some circumstances lead to nonnormative judgments. After Tversky’s death in 1 996, this line of work was continued by Kahneman, who was awarded the Nobel Prize in Economics in 2002. The current view of judgment, which has emerged from 3 0 years of research, is summarized by Kahneman and Frederick (Chap. 1 2; also see LeBoeuf & Shafir, Chap. 1 1 ). (Goldstone and Son, Chap. 2, review Tversky’s influential theory of similarity judgments.) In 1 982, a young vision scientist, David Marr, published a book called Vision. Largely a technical treatment of visual perception, the book includes an opening chapter that lays out a larger vision – a vision of how the science of mind should proceed. Marr distinguished three levels of analysis, which he termed the level of computation, the level of representation and algorithm, and the level of implementation. Each level, according to Marr, addresses different questions, which he illustrated with the example of a physical device, the cash register. At Marr’s most abstract level, computation (not to be confused with computation of an algorithm on a computer), the basic questions are “What is the goal that the cognitive process is meant to accomplish?” and “What is the logic of the mapping from the input to the output that distinguishes this mapping from other input–output mappings?” A cash register, viewed at this level, is used to achieve the goal of calculating how much is owed for a purchase. This task maps precisely onto the axioms of addition (e.g., the amount owed should not vary with the order in which items are presented to the sales clerk, a constraint that precisely matches the commutativity property of addition). It follows that, without knowing anything else about the workings of a particular cash register, we can be sure (if it is working properly) that it will be performing addition (not division). The level of representation and algorithm, as the name implies, deals with the questions, “What is the representation of the input and output?” and “What is the algorithm for transforming the former into the latter?” Within a cash register, addition

5

might be performed using numbers in either decimal or binary code, starting with either the leftmost or rightmost digit. Finally, the level of implementation addresses the question, “How are the representation and algorithm realized physically?” The cash register could be implemented as an electronic calculator, a mechanical adding machine, or even a mental abacus in the mind of the clerk. In his book, Marr stressed the importance of the computational level of analysis, arguing that it could be seriously misleading to focus prematurely on the more concrete levels of analysis for a cognitive task without understanding the goal or nature of the mental computation.5 Sadly, Marr died of leukemia before Vision was published, and so we do not know how his thinking about levels of analysis might have evolved. In very different ways, Marr’s conception of a computational level of analysis is reflected in several chapters in this book (see especially Doumas & Hummel, Chap. 4; Buehner & Cheng, Chap. 7; Lovett & Anderson, Chap. 1 7). In the most recent quarter-century, many other springs of research have fed into the river of thinking and reasoning, including the field of analogy (see Holyoak, Chap. 6), neural network models (see Doumas & Hummel, Chap. 4; Halford, Chap. 22), and cognitive neuroscience (see Goel, Chap. 20). The chapters of this handbook collectively paint a picture of the state of the field at the dawn of the new millennium.

Overview of the Handbook This volume brings together the contributions of many of the leading researchers in thinking and reasoning to create the most comprehensive overview of research on thinking and reasoning that has ever been available. Each chapter includes a bit of historical perspective on the topic and ends with some thoughts about where the field seems to be heading. The book is organized into seven sections.

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Part I: The Nature of Human Concepts

Part III: Judgment and Decision Making

The three chapters in Part I address foundational issues related to the representation of human concepts. Chapter 2 by Goldstone and Son reviews work on the core concept of similarity – how people assess the degree to which objects or events are alike. Chapter 3 by Medin and Rips considers research on categories and how concepts are organized in semantic memory. Thinking depends not only on representations of individual concepts, such as dogs and cats, but also on representations of the relationships among concepts, such as the fact that dogs often chase cats. In Chapter 4, Doumas and Hummel evaluate different computational approaches to the representation of relations.

We then turn to topics related to judgment and decision making. In Chapter 1 1 , LeBoeuf and Shafir set the stage with a general review of work on decision making. Then, in Chapter 1 2, Kahneman and Frederick present an overarching model of heuristic judgment. In Chapter 1 3 , Molden and Higgins review research revealing the ways in which human motivation and emotion influence judgment.

Part II: Reasoning Chapters 5 to 1 0 deal with varieties of the core topic of reasoning. In Chapter 5 , Sloman and Lagnado set the stage by laying out the issues surrounding induction – using what is known to generate plausible, although uncertain, inferences. Then, in Chapter 6, Holyoak reviews the literature on reasoning by analogy, an important variety of inductive reasoning that is critical for learning. The most classic aspect of induction is the way in which humans and other creatures acquire knowledge about causal relations, which is critical for predicting the consequences of actions and events. In Chapter 7, Buehner and Cheng discuss research and theory on causal learning. Then, in Chapter 8, Evans reviews work on the psychology of deductive reasoning, the form of thinking with the closest ties to logic. In Chapter 9, Johnson-Laird describes the work that he and others have performed using the framework of mental models to deal with various reasoning tasks, both deductive and inductive. Mental models have close connections to perceptual representations that are visuospatial in Chapter 1 0, Barbara Tversky reviews work on the role of visuospatial representations in thinking.

Part IV: Problem Solving and Complex Learning The five chapters that comprise this section deal with problem solving and allied issues concerning how people learn in problemsolving situations. In Chapter 1 4, Novick and Bassok provide a general overview of the field of human problem solving. Problem solving has close connections to the topic of creativity, the focus of Chapter 1 5 by Sternberg, Lubart, Kaufman, and Pretz. Beyond relatively routine problem solving, there are occasions when people need to restructure their knowledge in complex ways to generate deeper understanding. How such complex learning takes place is the topic of Chapter 1 6 by Chi and Ohlsson. In Chapter 1 7, Lovett and Anderson review work on thinking that is based on a particular formal approach rooted in work on problem solving, namely, production systems. Finally, in Chapter 1 8, Litman and Reber consider research suggesting that some aspects of thinking and learning depend on implicit mechanisms that operate largely outside of awareness. Part V: Cognitive and Neural Constraints on Human Thought High-level human thinking cannot be fully understood in isolation from fundamental cognitive processes and their neural substrates. In Chapter 1 9, Morrison reviews the wealth of evidence indicating that thinking and reasoning depend critically on what is known as “working memory,” that is, the system responsible for short-term maintenance

thinking and reasoning: a reader’s guide

and manipulation of information. Current work is making headway in linking thought processes to specific brain structures such as the prefrontal cortex; in Chapter 20, Goel discusses the key topic of deductive reasoning in relation to its neural substrate. Brain disorders, notably schizophrenia, produce striking disruptions of normal thought processes, which can shed light on how thinking takes place in normal brains. In Chapter 21 , Bachman and Cannon review research and theory concerning thought disorder. Part VI: Ontogeny, Phylogeny, Language, and Culture Our understanding of thinking and reasoning would be gravely limited if we restricted investigation to young adult English speakers. The six chapters in Part VI deal with the multifaceted ways in which aspects of thinking vary across the human lifespan, across species, across speakers of different languages, and across cultures. In Chapter 22, Halford provides an overview of the development of thinking and reasoning over the course of childhood. In Chapter 23 , Gallistel and Gelman discuss mathematical thinking, a special form of thinking found in rudimentary form in nonhuman animals that undergoes development in children. In Chapter 24, Salthouse describes the changes in thinking and reasoning brought on by the aging process. The phylogeny of thinking – thinking and reasoning as performed by apes and monkeys – is discussed in Chapter 25 by Call and Tomasello. One of the most controversial topics in the field is the relationship between thinking and the language spoken by the thinker; in Chapter 26, Gleitman and Papafragou review the hypotheses and evidence concerning the connections between language and thought. In Chapter 27, Greenfield considers the ways in which modes of thinking may vary in the context of different human cultures. Part VII: Thinking in Practice In cultures ancient and modern, thinking is put to particular use in special cultural practices. Moreover, there are individual dif-

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ferences in the nature and quality of human thinking. This section includes three chapters focusing on thinking in particular practices and two chapters that deal with variations in thinking ability. In Chapter 28, Ellsworth reviews what is known about thinking in the field of law. In Chapter 29, Dunbar and Fugelsang discuss thinking and reasoning as manifested in the practice of science. In Chapter 3 0, Patel, Arocha, and Zhang discuss reasoning in a field – medicine – in which accurate diagnosis and treatment are literally everyday matters of life and death. Then, in Chapter 3 1 , Sternberg reviews work on the concept of intelligence as a source of individual differences in thinking and reasoning. Finally, Chapter 3 2 by Ritchhart and Perkins concludes the volume by reviewing one of the major challenges for education – finding ways to teach people to think more effectively.

Examples of Chapter Assignments for a Variety of Courses This volume offers a comprehensive treatment of higher cognition. As such, it serves as an excellent source for courses on thinking and reasoning, both at the graduate level and for upper-level undergraduates. Although instructors for semester-length graduate courses in thinking and reasoning may opt to assign the entire volume as a textbook, there are a number of other possibilities (including using chapters from this volume as introductions for various topics and then supplementing with readings from the primary literature). Here are a few examples of possible chapter groupings tailored to a variety of possible course offerings: Introduction to Thinking and Reasoning

Chapter 1 Chapter 2 Chapter 3

Thinking and Reasoning: A Reader’s Guide Similarity Concepts and Categories: Memory, Meaning, and Metaphysics

8

Chapter 5 Chapter 6 Chapter 7 Chapter 8 Chapter 9 Chapter 1 0 Chapter 1 1 Chapter 1 2 Chapter 1 4 Chapter 1 5 Chapter 1 6 Chapter 1 8

the cambridge handbook of thinking and reasoning

The Problem of Induction Analogy Causal Learning Deductive Reasoning Mental Models and Thought Visuospatial Reasoning Decision Making A Model of Heuristic Judgment Problem Solving Creativity Complex Declarative Learning Implicit Cognition and Thought

Chapter 7 Chapter 9 Chapter 2 2 Chapter 1 7

Applied Thought

Chapter 1 4 Chapter 1 0 Chapter 2 3 Chapter 2 6 Chapter 1 5 Chapter 3 1 Chapter 1 3 Chapter 2 7

Development of Thinking

Chapter 1 6

Chapter 2 Chapter 3

Chapter 1 8

Chapter 2 2 Chapter 2 3 Chapter 2 6 Chapter 2 4 Chapter 2 5 Chapter 1 9 Chapter 3 1 Chapter 3 2

Similarity Concepts and Categories: Memory, Meaning, and Metaphysics Development of Thinking Mathematical Thinking Language and Thought Effects of Aging on Reasoning Reasoning and Thinking in Nonhuman Primates Thinking in Working Memory Intelligence Learning to Think: The Challenges of Teaching Thinking

Chapter 2 8 Chapter 2 9 Chapter 3 0

Chapter 3 1 Chapter 1 5 Chapter 1 9 Chapter 2 1

Modeling Human Thought

Chapter 4

Chapter 6

Similarity Concepts and Categories: Memory, Meaning, and Metaphysics Approaches to Modeling Human Mental Representations: What Works, What Doesn’t, and Why Analogy

Problem Solving Visuospatial Reasoning Mathematical Thinking Language and Thought Creativity Intelligence Motivated Thinking Paradigms of Cultural Thought Complex Declarative Learning Implicit Cognition and Thought Legal Reasoning Scientific Thinking and Reasoning Reasoning in Medicine

Differences in Thought

Chapter 2 2 Chapter 2 5 Chapter 2 Chapter 3

Causal Learning Mental Models and Thought Development of Thinking Thinking as a Production System

Chapter 2 4 Chapter 2 6 Chapter 1 3 Chapter 2 7 Chapter 2 9 Chapter 3 2

Intelligence Creativity Thinking in Working Memory Cognitive and Neuroscience Aspects of Thought Disorder Development of Thinking Reasoning and Thinking in Nonhuman Primates Effects of Aging on Reasoning Language and Thought Motivated Thinking Paradigms of Cultural Thought Scientific Thinking and Reasoning Learning to Think: The Challenges of Teaching Thinking

thinking and reasoning: a reader’s guide

Acknowledgments Preparation of this chapter was supported by grants R3 05 H03 01 41 from the Institute of Education Sciences and SES-00803 75 from the National Science Foundation to Holyoak, and by Xunesis (www.xunesis.org) and a National Institute of Mental Health National Service Research Award (MH064244) to Morrison. The authors thank Miriam Bassok and Patricia Cheng for comments on an earlier draft of this chapter.

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tive reasoning.” In an old Western movie, a hero in a tough spot might venture, “I reckon we can hold out till sun-up,” illustrating how calculation has crossed over to become a metaphor for mental judgment. 4. See Johnson-Laird, Chap. 9, for a current view of thinking and reasoning that owes much to Craik’s seminal ideas. 5 . Indeed, Marr criticized Newell and Simon’s approach to problem solving for paying insufficient attention to the computational level in his sense.

References Notes 1 . Notice the linguistic connection between “thinking” and “seeing,” and thought and perception, which was emphasized by the Gestalt psychologists of the early twentieth century. 2. The distinction between deduction and induction blurs in the study of the psychology of thinking, as we see in Part II of this volume. 3 . There are echoes of the old meaning of “reckon” in such phrases as “reckon the cost.” As a further aside, the term “dead reckoning,” a procedure for calculating the position of a ship or aircraft, derives from “deduc-

Bruner, J. S., Goodnow, J. J., & Austin, G. A. (1 95 6). A study of thinking. New York: Wiley. Craik, K. (1 943 ). The nature of explanation. Cambridge, UK: Cambridge University Press. Hobbes, T. (1 65 1 /1 968). Leviathan. London: Penguin Books. Marr, D. (1 982). Vision. San Francisco: W. H. Freeman. Newell, A., & Simon, H. A. (1 972). Human problem solving. Englewood Cliffs, NJ: Prentice Hall. Rips, L. J., & Conrad, F. G. (1 989). Folk psychology of mental activities. Psychological Review, 96, 1 87–207.

Part I

THE NATURE OF HUMAN CONCEPTS




CHAPTER 2

Similarity Robert L. Goldstone Ji Yun Son

Introduction Human assessments of similarity are fundamental to cognition because similarities in the world are revealing. The world is an orderly enough place that similar objects and events tend to behave similarly. This fact of the world is not just a fortunate coincidence. It is because objects are similar that they will tend to behave similarly in most respects. It is because crocodiles and alligators are similar in their external form, internal biology, behavior, diet, and customary environment that one can often successfully generalize from what one knows of one to the other. As Quine (1 969) observed, “Similarity, is fundamental for learning, knowledge and thought, for only our sense of similarity allows us to order things into kinds so that these can function as stimulus meanings. Reasonable expectation depends on the similarity of circumstances and on our tendency to expect that similar causes will have similar effects” (p. 1 1 4). Similarity thus plays a crucial role in making predictions because similar things usually behave similarly.

From this perspective, psychological assessments of similarity are valuable to the extent that they provide grounds for predicting as many important aspects of our world as possible (Holland, Holyoak, Nisbett, & Thagard, 1 986; see Dunbar & Fugelsang, Chap. 29). Appreciating the similarity between crocodiles and alligators is helpful because information learned about one is generally true of the other. If we learned an arbitrary fact about crocodiles, such as they are very sensitive to the cold, then we could probably infer that this fact is also true of alligators. As the similarity between A and B increases, so does the probability of correctly inferring that B has X upon knowing that A has X (Tenenbaum, 1 999). This relation assumes we have no special knowledge related to property X. Empirically, Heit and Rubinstein (1 994) showed that if we do know about the property, then this knowledge, rather than a one-size-fits-all similarity, is used to guide our inferences. For example, if people are asked to make an inference about an anatomical property, then anatomical similarities have more influence than 13

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behavioral similarities. Boars are anatomically but not behaviorially similar to pigs, and this difference successfully predicts that people are likely to make anatomical but not behavioral inferences from pigs to boars. The logical extreme of this line of reasoning (Goodman, 1 972; Quine, 1 977) is that if one has complete knowledge about the reasons why an object has a property, then general similarity is no longer relevant to generalizations. The knowledge itself completely guides whether the generalization is appropriate. Moonbeams and melons are not very similar generally speaking, but if one is told that moonbeams have the property that the word begins with Melanie’s favorite letter, then one can generalize this property to melons with very high confidence. By contrasting the cases of crocodiles, boars, and moonbeams, we can specify the benefits and limitations of similarity. We tend to rely on similarity to generate inferences and categorize objects into kinds when we do not know exactly what properties are relevant or when we cannot easily separate an object into separate properties. Similarity is an excellent example of a domain-general source of information. Even when we do not have specific knowledge of a domain, we can use similarity as a default method to reason about it. The contravening limitation of this domain generality is that when specific knowledge is available, then a generic assessment of similarity is no longer as relevant (Keil, 1 989; Murphy, 2002; Murphy & Medin, 1 985 ; Rips, 1 989; Rips & Collins, 1 993 ). Artificial laboratory experiments in which subjects are asked to categorize unfamiliar stimuli into novel categories invented by the experimenter are situations in which similarity is clearly important because subjects have little else to use (Estes, 1 994; Nosofsky, 1 984, 1 986). However, similarity is also important in many real world situations because our knowledge does not run as deep as we think it does (Rozenblit & Keil, 2002) and because a general sense of similarity often has an influence even when more specific knowledge ought to overrule it (Allen & Brooks, 1 991 ; Smith & Sloman, 1 994).

Another argument for the importance of similarity in cognition is simply that it plays a significant role in psychological accounts of problem solving, memory, prediction, and categorization. If a problem is similar to a previously solved problem, then the solution to the old problem may be applied to the new problem (Holyoak & Koh, 1 987; Ross, 1 987, 1 989). If a cue is similar enough to a stored memory, the memory may be retrieved (Raaijmakers & Shiffrin, 1 981 ). If an event is similar enough to a previously experienced event, the stored event’s outcome may be offered as a candidate prediction for the current event (Sloman, 1 993 ; Tenenbaum & Griffiths, 2001 ). If an unknown object is similar enough to a known object, then the known object’s category label may be applied to the unknown object (Nosofsky, 1 986). The act of comparing events, objects, and scenes and establishing similarities between them is of critical importance for the cognitive processes we depend on. The utility of similarity for grounding our concepts has been rediscovered in all the fields comprising cognitive science (see Medin & Rips, Chap. 3 ). Exemplar (Estes, 1 994; Kruschke, 1 992; Lamberts, 2000; Medin & Schaffer, 1 978; Nosofsky, 1 986), instance-based (Aha, 1 992), viewbased (Tarr & Gauthier, 1 998), case-based (Schank, 1 982), nearest neighbor (Ripley, 1 996), configural cue (Gluck & Bower, 1 990), and vector quantization (Kohonen, 1 995 ) models share the underlying strategy of giving responses learned from similar, previously presented patterns to novel patterns. Thus, a model can respond to repetitions of these patterns; it can also give responses to novel patterns that are likely to be correct by sampling responses to old patterns weighted by their similarity to the novel pattern. Consistent with these models, psychological evidence suggests that people show good transfer to new stimuli in perceptual tasks to the extent that the new stimuli resemble previously learned stimuli (Kolers & Roediger, 1 984; Palmeri, 1 997). Another common feature of these approaches is that they

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similarity

represent patterns in a relatively raw, unprocessed form. This parallels the constraint described previously on the applicability of similarity. Both raw representations and generic similarity assessments are most useful as a default strategy when one does not know exactly what properties of a stimulus are important. One’s best bet is to follow the principle of least commitment (Marr, 1 982) and keep mental descriptions in a relatively raw form to preserve information that may be needed at a later point. Another reason for studying similarity is that it provides an elegant diagnostic tool for examining the structure of our mental entities and the processes that operate on them. For example, one way to tell that a physicist has progressed beyond the novice stage is that he or she sees deep similarities between problems that require calculation of force even though the problems are superficially dissimilar (Chi, Feltovich, & Glaser, 1 981 ; see Novick & Bassok, Chap. 1 4). Given that psychologists have no microscope with direct access to people’s representations of their knowledge, appraisals of similarity provide a powerful, if indirect, lens onto representation/process assemblies (see also Doumas & Hummel, Chap. 4). A final reason to study similarity is that it occupies an important ground between perceptual constraints and higherlevel knowledge system functions. Similarity is grounded by perceptual functions. A tone of 200 Hz and a tone of 202 Hz sound similar (Shepard, 1 987), and the similarity is cognitively impenetrable (Pylyshyn, 1 985 ) – enough that there is little that can be done to alter this perceived similarity. However, similarity is also highly flexible and dependent on knowledge and purpose. By focusing on patterns of motion and relations, even electrons and planets can be made to seem similar (Gentner, 1 983 ; Holyoak & Thagard, 1 989; see Holyoak, Chap. 6). A complete account of similarity will make contact both with Fodor’s (1 983 ) isolated and modularized perceptual input devices and the “central system” in which everything a person knows may be relevant.

A Survey of Major Approaches to Similarity There have been a number of formal treatments that simultaneously provide theoretical accounts of similarity and describe how it can be empirically measured (Hahn, 2003 ). These models have had a profound practical impact in statistics, automatic pattern recognition by machines, data mining, and marketing (e.g., online stores can provide “people similar to you liked the following other items . . . ”). Our brief survey is organized in terms of the following models: geometric, feature based, alignment based, and transformational. Geometric Models and Multidimensional Scaling Geometric models of similarity have been among the most influential approaches to analyzing similarity (Carroll & Wish, 1 974; Torgerson, 1 95 8, 1 965 ). These approaches are exemplified by nonmetric multidimensional scaling (MDS) models (Shepard, 1 962a, 1 962b). MDS models represent similarity relations between entities in terms of a geometric model that consists of a set of points embedded in a dimensionally organized metric space. The input to MDS routines may be similarity judgments, dissimilarity judgments, confusion matrices, correlation coefficients, joint probabilities, or any other measure of pairwise proximity. The output of an MDS routine is a geometric model of the data, with each object of the data set represented as a point in an ndimensional space. The similarity between a pair of objects is taken to be inversely related to the distance between two objects’ points in the space. In MDS, the distance between points i and j is typically computed by  r1
n  r |Xik − X jk| dissimilarity(i, j) = k=1

(2.1 ) where n is the number of dimensions, X ik is the value of dimension k for item i, and r is a parameter that allows different spatial

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metrics to be used. With r = 2, a standard Euclidean notion of distance is invoked, whereby the distance between two points is the length of the straight line connecting the points. If r = 1 , then distance involves a city-block metric where the distance between two points is the sum of their distances on each dimension (“shortcut” diagonal paths are not allowed to directly connect points differing on more than one dimension). An Euclidean metric often provides a better fit to empirical data when the stimuli being compared are composed of integral, perceptually fused dimensions such as the brightness and saturation of a color. Conversely, a city-block metric is often appropriate for psychologically separated dimensions such as brightness and size (Attneave, 1 95 0). Richardson’s (1 93 8) fundamental insight, which is the basis of contemporary use of MDS, was to begin with subjects’ judgments of pairwise object dissimilarity and work backward to determine the dimensions and dimension values that subjects used in making their judgments. MDS algorithms proceed by placing entities in an n-dimensional space such that the distances between the entities accurately reflect the empirically observed similarities. For example, if we asked people to rate the similarities [on a scale from 1 (low similarity) to 1 0 (high similarity)] of Russia, Cuba, and Jamaica, we might find Similarity (Russia, Cuba) = 7 Similarity (Russia, Jamaica) = 1 Similarity (Cuba, Jamaica) = 8 An MDS algorithm would try to position the three countries in a space such that countries that are rated as being highly similar are very close to each other in the space. With nonmetric scaling techniques, only ordinal similarity relations are preserved. The interpoint distances suggested by the similarity ratings may not be simultaneously satisfiable in a given dimensional space. If we limit ourselves to a single dimension (we place the countries on a “number line”), then

we cannot simultaneously place Russia near Cuba (similarity = 7) and place Russia far away from Jamaica (similarity = 1 ). In MDS terms, the “stress” of the one-dimensional solution would be high. We could increase the dimensionality of our solution and position the points in two-dimensional space. A perfect reconstruction of any set of proximities among a set of n objects can be obtained if a high enough dimensionality (specifically, n − 1 dimensions) is used. One of the main applications of MDS is to determine the underlying dimensions comprising the set of compared objects. Once the points are positioned in a way that faithfully mirrors the subjectively obtained similarities, it is often possible to give interpretations to the axes or to rotations of the axes. In the previous example, dimensions may correspond to “political affiliation” and “climate.” Russia and Cuba would have similar values on the former dimension; Jamaica and Cuba would have similar values on the latter dimension. A study by Smith, Shoben, and Rips (1 974) illustrates a classic use of MDS (Figure 2.1 ). They obtained similarity ratings from subjects on many pairs of birds. Submitting these pairwise similarity ratings to MDS analysis, they hypothesized underlying features that were used for representing the birds. Assigning subjective interpretations to the geometric model’s axes, the experimenters suggested that birds were represented in terms of their values on dimensions such as “ferocity” and “size.” It is important to note that the proper psychological interpretation of a geometric representation of objects is not necessarily in terms of its Cartesian axes. In some domains, such as musical pitches, the best interpretation of objects may be in terms of their polar coordinates of angle and length (Shepard, 1 982). More recent work has extended geometric representations still further, representing patterns of similarities by generalized, nonlinear manifolds (Tenenbaum, De Silva, & Lanford, 2000). MDS is also used to create a compressed representation that conveys relative similarities among a set of items. A set of n items requires n(n − 1 )/2 numbers to express

similarity

17

Figure 2 .1 . Two multidimensional scaling (MDS) solutions for sets of birds (A) and animals (B). The distances between words in the MDS space reflect their psychology dissimilarity. Once an MDS solution has been made, psychological interpretations for the dimensions may be possible. In these solutions, the horizontal and vertical dimensions may represent size and domesticity, respectively. (Reprinted from Rips, Shoben, & Smith, 1 974, by permission.)

all pairwise distances among the items, if it is assumed that any object has a distance of 0 to itself and distances are symmetric. However, if an MDS solution fits the distance data well, it can allow these same distances to be reconstructed using only ND numbers, where D is the number of dimensions of the MDS solution. This compression may be psychologically very useful. One of the main goals of psychological representation is to create efficient codes for representing a set of objects. Compressed representations can facilitate encoding, memory, and processing. Shimon Edelman (1 999) proposed that both people and machines efficiently code their world by creating geometric spaces for objects with much lower dimensionality than the objects’ physical descriptions (see also Gardenfors, 2000). A third use of MDS is to create quantitative representations that can be used in mathematical and computational models of cognitive processes. Numeric representations, namely coordinates in a psychological space, can be derived for stories, pictures, sounds, words, or any other stimuli

for which one can obtain subjective similarity data. Once constructed, these numeric representations can be used to predict people’s categorization accuracy, memory performance, or learning speed. MDS models have been successful in expressing cognitive structures in stimulus domains as far removed as animals (Smith, Shoben, & Rips, 1 974), Rorschach ink blots (Osterholm, Woods, & Le Unes, 1 985 ), chess positions (Horgan, Millis, & Neimeyer, 1 989), and air flight scenarios (Schvaneveldt, 1 985 ). Many objects, situations, and concepts seem to be psychologically structured in terms of dimensions, and a geometric interpretation of the dimensional organization captures a substantial amount of that structure. Featural Models In 1 977, Amos Tversky brought into prominence what would become the main contender to geometric models of similarity in psychology. The reason given for proposing a feature-based model was that subjective assessments of similarity did not always

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satisfy the assumptions of geometric models of similarity.

problems with the standard geometric model

Three assumptions of standard geometric models of similarity are Minimality: D(A,B) ≥ D(A,A ) = 0 Symmetry: D(A,B) = D(B,A ) Triangle Inequality: D(A,B) + D(B,C) ≥ D(A,C ) where D(A,B) is interpreted as the dissimilarity between items A and B. According to the minimality assumption, all objects are equally (dis)similar to themselves. Some violations of this assumption are found (Nickerson, 1 972) when confusion rates or RT measures of similarity are used. First, not all letters are equally similar to themselves. For example, in Podgorny and Garner (1 979), if the letter S is shown twice on a screen, subjects are faster to correctly say that the two tokens are similar (i.e., they come from the same similarity defined cluster) than if the twice-shown letter is W. By the reaction time measure of similarity, the letter S is more similar to itself than the letter W is to itself. Even more troublesome for the minimality assumption, two different letters may be more similar to each other than a particular letter is to itself. The letter C is more similar to the letter O than W is to itself, as measured by interletter confusions. In Gilmore, Hersh, Caramazza, and Griffin (1 979), the letter M is more often recognized as an H ( p = .3 91 ) than as an M ( p = .1 80). This is problematic for geometric representations because the distance between a point and itself should be zero. According to the symmetry assumption, (dis)similarity should not be affected by the ordering of items because the distance from point A to B is equal to the distance from B to A. Contrary to this presumed symmetry, similarity is asymmetric on occasion (Tversky, 1 977). In one of Tversky’s examples, North Korea is judged to be more similar to Red China than Red China is to North Korea. Often, a nonprominent item is more

similar to a prominent item than vice versa. This is consistent with the result that people judge their friends to be more similar to themselves than they themselves are to their friends (Holyoak & Gordon, 1 983 ), under the assumption that a person is highly prominent to him- or herself. More recently, Polk et al. (2002) found that when the frequency of colors is experimentally manipulated, rare colors are judged to be more similar to common colors than common colors are to rare colors. According to the triangle inequality assumption (Figure 2.2), the distance/ dissimilarity between two points A and B cannot be more than the distance between A and a third point C plus the distance between C and B. Geometrically speaking, a straight line connecting two points is the shortest path between the points. Tversky and Gati (1 982) found violations of this assumption when it is combined with an assumption of segmental additivity [D(A,B) + D(B,C) = D(A,C), if A, B, and C lie on a straight line]. Consider three items in multidimensional space, A, B, and C, falling on a straight line such that B is between A and C. Also consider a fourth point, E, that forms a right triangle when combined with A and C. The triangle inequality assumption cum segmental additivity predicts that D(A,E) ≥ D(A,B) and D(E,C) ≥ D(B,C) or D(A,E) ≥ D(B,C) and D(E,C) ≥ D(A,B) Systematic violations of this prediction are found such that the path going through the corner point E is shorter than the path going through the center point B. For example, if the items are instantiated as A= B= C= E=

White, 3 inches Pink, 4 inches Red, 5 inches Red, 3 inches

then people’s dissimilarity ratings indicate that D(A,E) < D(A,B) and D(E,C) < D(B,C). Such an effect can be modeled by

similarity 6

C

5

B

size

4 3

E

A

2 1 0 redness

Figure 2 .2 . The triangle inequality assumption requires the path from A to C going through B to be shorter than the path going through E.

geometric models of similarity if r in Eq. 2.1 is given a value less than 1 . However, if r is less than 1 , then dissimilarity does not satisfy a power metric, which is often considered a minimal assumption for geometric solutions to be interpretable. The two assumptions of a power metric are (1 ) distances along straight lines are additive, and (2) the shortest path between points is a straight line. Other potential problems with geometric models of similarity are (1 ) they strictly limit the number of nearest neighbors an item can have (Tversky & Hutchinson, 1 986), (2) MDS techniques have difficulty describing items that vary on a large number of features (Krumhansl, 1 978), and (3 ) standard MDS techniques do not predict that adding common features to items increases their similarity (Tversky & Gati, 1 982). On the first point, MDS models consisting of two dimensions cannot predict that item X is the closest item to 1 00 other items. There would be no way of placing those 1 00 items in two dimensions such that X would be closer to all of them than any other item. For human data, a superordinate term (e.g., fruit) is often the nearest neighbor of many of its exemplars (apples, bananas, etc.), as measured by similarity ratings. On the second point, although there is no logical reason why geometric models cannot represent items of any number of dimensions (as long as the number of dimensions is less than number of items minus one), geometric models tend to

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yield the most satisfactory and interpretable solutions in low-dimensional space. MDS solutions involving more than six dimensions are rare. On the third point, the addition of the same feature to a pair of items increases their rated similarity (Gati & Tversky, 1 984), but this is incompatible with simple MDS models. If adding a shared feature corresponds to adding a dimension in which the two items under consideration have the same value, then there will be no change to the items’ dissimilarity because the geometric distance between the points remains the same. MDS models that incorporate the dimensionality of the space could predict the influence of shared features on similarity, but such a model would no longer relate similarity directly to an inverse function of interitem distance. One research strategy has been to augment geometric models of similarity in ways that solve these problems. One solution, suggested by Carol Krumhansl (1 978), has been to model dissimilarity in terms of both interitem distance in a multidimensional space and spatial density in the neighborhoods of the compared items. The more items there are in the vicinity of an item, the greater the spatial density of the item. Items are more dissimilar if they have many items surrounding them (their spatial density is high) than if they have few neighboring items. By including spatial density in an MDS analysis, violations of minimality, symmetry, and the triangle inequality can potentially be accounted for, as well as some of the influence of context on similarity. However, the empirical validity of the spatial density hypothesis is in some doubt (Corter, 1 987, 1 988; Krumhansl, 1 988; Tversky & Gati, 1 982). Robert Nosofsky (1 991 ) suggested another potential way to save MDS models from some of the previous criticisms. He introduces individual bias parameters in addition to the inter-item relation term. Similarity is modeled in terms of inter-item distance and biases toward particular items. Biases toward items may be due to attention, salience, knowledge, and frequency of items. This revision handles asymmetric similarity results and the result

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that a single item may be the most similar item to many other items, but it does not directly address several of the other objections. the contrast model

In light of the previous potential problems for geometric representations, Tversky (1 977) proposed to characterize similarity in terms of a feature-matching process based on weighting common and distinctive features. In this model, entities are represented as a collection of features and similarity is computed by S(A, B) = θ f (A ∩ B) − a f (A − B) − b f (B − A) (2.2) The similarity of A to B is expressed as a linear combination of the measure of the common and distinctive features. The term (A ∩ B) represents the features that items A and B have in common. (A − B) represents the features that A has but B does not. (B − A) represents the features of B that are not in A. θ , a, and b are weights for the common and distinctive components. Common features, as compared with distinctive features, are given relatively more weight for verbal as opposed to pictorial stimuli (Gati & Tversky, 1 984), cohesive as opposed to noncohesive stimuli (Ritov, Gati, & Tversky, 1 990), similarity as opposed to difference judgments (Tversky, 1 977), and entities with a large number of distinctive as opposed to common features (Gati & Tversky, 1 984). There are no restrictions on what may constitute a feature. A feature may be any property, characteristic, or aspect of a stimulus. Features may be concrete or abstract (i.e., “symmetric” or “beautiful”). The contrast model predicts asymmetric similarity because a is not constrained to equal b and f(A − B) may not equal f(B − A). North Korea is predicted to be more similar to Red China than vice versa if Red China has more salient distinctive features than North Korea, and a is greater than b. The contrast model can also account for nonmirroring between similarity and difference judgments. The common features term

(A ∩ B) is hypothesized to receive more weight in similarity than difference judgments; the distinctive features term receives relatively more weight in difference judgments. As a result, certain pairs of stimuli may be perceived as simultaneously being more similar to and more different from each other compared with other pairs (Tversky, 1 977). Sixty-seven percent of a group of subjects selected West Germany and East Germany as more similar to each other than Ceylon and Nepal. Seventy percent of subjects also selected West Germany and East Germany as more different from each other than Ceylon and Nepal. According to Tversky, East and West Germany have more common and more distinctive features than Ceylon and Nepal. Medin, Goldstone, and Gentner (1 993 ) presented additional evidence for nonmirroring between similarity and difference, exemplified in Figure 2.3 . When two scenes share a relatively large number of relational commonalities (e.g., scenes T and B both have three objects that have the same pattern), but also a large number of differences on specific attributes (e.g., none of the patterns in scene T match any of the patterns in B), then the scenes tend to be judged as simultaneously very similar and very different. A number of models are similar to the contrast model in basing similarity on features and in using some combination of the (A ∩ B), (A − B), and (B − A) components. Sjoberg (1 972) proposed that similarity is defined as f (A ∩ B)/f (A ∪ B). Eisler and Ekman (1 95 9) claimed that similarity is proportional to f (A ∩ B)/ (f (A) + f(B)). Bush and Mosteller (1 95 1 ) defined similarity as f (A ∩ B)/f (A). These three models can all be considered specializations of the general equation f (A ∩ B)/[f (A ∪ B) + af (A − B) + bf (B − A)]. As such, they differ from the contrast model by applying a ratio function as opposed to a linear contrast of common and distinctive features. The fundamental premise of the contrast model, that entities can be described in terms of constituent features, is a powerful idea in cognitive psychology. Featural

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T

A

B

Figure 2 .3. The set of objects in B is selected as both more similar to, and more different from, the set of objects in T relative to the set of objects in A. From Medin, Goldstone, and Gentner (1 990). Reprinted by permission.

analyses have proliferated in domains of speech perception (Jakobson, Fant, & Halle, 1 963 ), pattern recognition (Neisser, 1 967; Treisman, 1 986), perception physiology (Hubel & Wiesel, 1 968), semantic content (Katz & Fodor, 1 963 ), and categorization (Medin & Schaffer, 1 978; see Medin & Rips, Chap. 3 ). Neural network representations are often based on features, with entities being broken down into a vector of ones and zeros, where each bit refers to a feature or “microfeature.” Similarity plays a crucial role in many connectionist theories of generalization, concept formation, and learning. The notion of dissimilarity used in these systems is typically the fairly simple function “Hamming distance.” The Hamming distance between two strings is simply their cityblock distance; that is, it is their (A − B) + (B − A) term. “1 0 0 1 1 ” and “1 1 1 1 1 ” would have a Hamming distance of 2 because they differ on two bits. Occasionally, more sophisticated measures of similarity

in neural networks normalize dissimilarities by string length. Normalized Hamming distance functions can be expressed by [(A − B) + (B − A)]/[ f (A ∩ B)]. similarities between geometric and feature-based models

Although MDS and featural models are often analyzed in terms of their differences, they also share a number of similarities. More recent progress has been made on combining both representations into a single model, using Bayesian statistics to determine whether a given source of variation is more efficiently represented as a feature or dimension (Navarro & Lee, 2003 ). Tversky and Gati (1 982) described methods of translating continuous dimensions into featural representations. Dimensions that are sensibly described as being more or less (e.g., loud is more sound than soft, bright is more light than dim, and large is more size than small) can be represented by sequences of nested

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feature sets. That is, the features of B include a subset of A’s features whenever B is louder, brighter, or larger than A. Alternatively, for qualitative attributes such as shape or hue (red is not subjectively “more” than blue), dimensions can be represented by chains of features such that if B is between A and C on the dimension, then (A ∩ B) ⊃ (A ∩ C) and (B ∩ C) ⊃ (A ∩ C). For example, if orange lies between red and yellow on the hue dimension, then this can be featurally represented if orange and red share features that orange and yellow do not share. An important attribute of MDS models is that they create postulated representations, namely dimensions, that explain the systematicities present in a set of similarity data. This is a classic use of abductive reasoning; dimensional representations are hypothesized that, if they were to exist, would give rise to the obtained similarity data. Other computational techniques share with MDS the goal of discovering the underlying descriptions for items of interest but create featural rather than dimensional representations. Hierarchical cluster analysis, such as MDS, takes pairwise proximity data as input. Rather than output a geometric space with objects as points, hierarchical cluster analysis outputs an invertedtree diagram with items at the root-level connected with branches. The smaller the branching distance between two items, the more similar they are. Just as the dimensional axes of MDS solutions are given subjective interpretations, the branches are also given interpretations. For example, in Shepard’s (1 972) analysis of speech sounds, one branch is interpreted as voiced phonemes, whereas another branch contains the unvoiced phonemes. In additive cluster analysis (Shepard & Arabie, 1 979), similarity data are transformed into a set of overlapping item clusters. Items that are highly similar will tend to belong to the same clusters. Each cluster can be considered as a feature. More recent progress has been made on efficient and mathematically principled models that find such featural representations for large databases (Lee, 2002a, 2002b; Tenenbaum, 1 996).

Another commonality between geometric and featural representations, one that motivates the next major class of similarity models that we consider, is that both use relatively unstructured representations. Entities are structured as sets of features or dimensions with no relations between these attributes. Entities such as stories, sentences, natural objects, words, scientific theories, landscapes, and faces are not simply a “grab bag” of attributes. Two kinds of structure seem particularly important: propositional and hierarchical. A proposition is an assertion about the relation between informational entities (Palmer, 1 975 ). For example, relations in a visual domain might include above, near, right, inside, and larger than, which take informational entities as arguments. The informational entities might include features such as square and values on dimensions such as 3 inches. Propositions are defined as the smallest unit of knowledge that can stand as a separate assertion and have a truth value. The order of the arguments in the predicate is critical. For example, above (triangle, circle) does not represent the same fact as above (circle, triangle). Hierarchical representations involve entities that are embedded in one another. Hierarchical representations are required to represent the fact that X is part of Y or that X is a kind of Y. For example, in Collins and Quillian’s (1 969) propositional networks, labeled links (“Is-a” links) stand for the hierarchical relation between canary and bird. Some quick fixes to geometric and featural accounts of similarity are possible, but they fall short of a truly general capacity to handle structured inputs. Hierarchical clustering does create trees of features, but there is no guarantee that there are relationships, such as Is-a or Part-of, between the subtrees. However, structure might exist in terms of features that represent conjunctions of properties. For example, using the materials in Figure 2.4, 20 undergraduates were shown triads consisting of A, B, and T and were asked to say whether scene A or B was more similar to T. The strong tendency to choose A over B in the first panel suggests that

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Figure 2 .4. The sets of objects T are typically judged to be more similar to the objects in the A sets than the B sets. These judgments show that people pay attention to more than just simple properties such as “black” or “square” when comparing scenes.

the feature “square” influences similarity. Other choices indicated that subjects also based similarity judgments on the spatial locations and shadings of objects as well as their shapes. However, it is not sufficient to represent the leftmost object of T as {left, square, black} and base similarity on the number of shared and distinctive features. In the second panel, A is again judged to be more similar to T than is B. Both A and B have the features “black” and “square.” The only difference is that for A and T, but not B, the “black” and “square” features belong to the same object. This is only compatible with feature set representations if we include the possibility of conjunctive features in addition to simple features such as “black” and “square” (Gluck, 1 991 ; Hayes-Roth & Hayes-Roth, 1 977). By including the conjunctive feature “black-square,” possessed by both T and A, we can explain, using feature sets, why T is more similar to A than B. The third panel demonstrates the need for a “black-left” feature, and other data indicate a need for a “square-left” feature. Altogether, if we want to explain the similarity judgments that people make, we need a feature set representation that includes six features (three simple and three complex) to represent the square of T.

However, there are two objects in T, bringing the total number of features required to at least two times the six features required for one object. The number of features required increases still further if we include feature triplets such as “left-blacksquare.” In general, if there are O objects in a scene and each object has F features, then there will be OF simple features. There will be O conjunctive features that combine two simple features (i.e., pairwise conjunctive features). If we limit ourselves to simple and pairwise features to explain the pattern of similarity judgments in Figure 2.3 , we still will require OF(F + 1 )/2 features per scene, or OF(F + 1 ) features for two scenes that are compared with one another. Thus, featural approaches to similarity require a fairly large number of features to represent scenes that are organized into parts. Similar problems exist for dimensional accounts of similarity. The situation for these models becomes much worse when we consider that similarity is also influenced by relations between features such as “black to the left of white” and “square to the left of white.” Considering only binary relations, there are O2 F2 R -OFR relations within a scene that contains O objects, F features per object, and R different types of relations between features. Although more

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sophisticated objections have been raised about these approaches by Hummel and colleagues (Holyoak & Hummel, 2000; Hummel, 2000, 2001 ; Hummel & Biederman, 1 992; Hummel & Holyoak, 1 997, 2003 ; see Doumas & Hummel, Chap. 4), at the very least, geometric and featural models apparently require an implausibly large number of attributes to account for the similarity relations between structured, multipart scenes. Alignment-Based Models Partly in response to the difficulties that the previous models have in dealing with structured descriptions, a number of researchers have developed alignment-based models of similarity. In these models, comparison is not just matching features but determining how elements correspond to, or align with, one another. Matching features are aligned to the extent that they play similar roles within their entities. For example, a car with a green wheel and a truck with a green hood both share the feature green, but this matching feature may not increase their similarity much because the car’s wheel does not correspond to the truck’s hood. Drawing inspiration from work on analogical reasoning (Gentner, 1 983 ; Holyoak & Thagard, 1 995 ; see Holyoak, Chap. 6), in alignment-based models, matching features influence similarity more if they belong to parts that are placed in correspondence, and parts tend to be placed in correspondence if they have many features in common and are consistent with other emerging correspondences (Goldstone, 1 994a; Markman & Gentner, 1 993 a). Alignment-based models make purely relational similarity possible (Falkenhainer, Forbus, & Gentner, 1 989). Initial evidence that similarity involves aligning scene descriptions comes from Markman and Gentner’s (1 993 a) result that when subjects are asked to determine corresponding objects, they tend to make more structurally sound choices when they have first judged the similarity of the scenes that contain the objects. For example, in Figure 2.5 , subjects could be asked which object in the bottom set corresponds to the leftmost

object in the top set. Subjects who had rated the similarity of the sets were more likely to choose the rightmost object – presumably because both objects were the smallest objects in their sets. Subjects who did not first assess similarity had a tendency to select the middle object because its size exactly matched the target object’s size. These results are predicted if similarity judgments naturally entail aligning the elements of two scenes. Additional research has found that relational choices such as “smallest object in its set” tend to influence similarity judgments more than absolute attributes like “3 inches” when the overall amount of relational coherency across sets is high (Goldstone, Medin, & Gentner, 1 991 ), the scenes are superficially sparse rather than rich (Gentner & Rattermann, 1 991 ; Markman & Gentner, 1 993 a), subjects are given more time to make their judgments (Goldstone & Medin, 1 994), the judges are adults rather than children (Gentner & Toupin, 1 986), and abstract relations are initially correlated with concrete relations (Kotovsky & Gentner, 1 996). Formal models of alignment-based similarity have been developed to explain how feature matches that belong to well-aligned elements matter more for similarity than matches between poorly aligned elements (Goldstone, 1 994a; Love, 2000). Inspired by work in analogical reasoning (Holyoak & Thagard, 1 989), Goldstone’s (1 994a) SIAM model is a neural network with nodes that represent hypotheses that elements across two scenes correspond to one another. SIAM works by first creating correspondences between the features of scenes. Once features begin to be placed into correspondence, SIAM begins to place objects into correspondence that are consistent with the feature correspondences. Once objects begin to be put in correspondence, activation is fed back down to the feature (mis)matches that are consistent with the object alignments. In this way, object correspondences influence activation of feature correspondences at the same time that feature correspondences influence the activation of object correspondences. Activation between nodes spreads

similarity

Target

Size match Relation match

Figure 2 .5. The target from the gray circles could match either the middle black object because they are the same size, or the rightmost object because both objects are the smallest objects in their sets.

in SIAM by two principles: (1 ) nodes that are consistent send excitatory activation to each other, and (2) nodes that are inconsistent inhibit each another (see also Holyoak, Chap. 6). Nodes are inconsistent if they create two-to-one alignments – if two elements from one scene would be placed into correspondence with one element of the other scene. Node activations affect similarity via the equation n ∗ (match valuei Ai ) similarity = i=1 n , i=1 Ai (2.3 ) where n is the number of nodes in the system, Ai is the activation of node i, and the match value describes the physical similarity between the two features placed in correspondence according to the node i. By this equation, the influence of a particular matching or mismatching feature across two scenes is modulated by the degree to which the features have been placed in alignment. Consistent with SIAM, (1 ) aligned feature matches tend to increase similarity more than unaligned feature matches (Goldstone, 1 994a); (2) the differential influence between aligned and unaligned feature matches increases as a function of processing time (Goldstone & Medin, 1 994); (3 ) this same differential influence increases

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with the clarity of the alignments (Goldstone, 1 994a); and (4) under some circumstances, adding a poorly aligned feature match can actually decrease similarity by interfering with the development of proper alignments (Goldstone, 1 996). Another empirically validated set of predictions stemming from an alignment-based approach to similarity concerns alignable and nonalignable differences (Markman & Gentner, 1 993 b). Nonalignable differences between two entities are attributes of one entity that have no corresponding attribute in the other entity. Alignable differences are differences that require the elements of the entities first be placed in correspondence. When comparing a police car with an ambulance, a nonalignable difference is that police cars have weapons in them, but ambulances do not. There is no clear equivalent of weapons in the ambulance. Alignable differences include the following: police cars carry criminals to jails rather than carrying sick people to hospitals, a police car is a car whereas ambulances are vans, and police car drivers are policemen rather than emergency medical technicians. Consistent with the role of structural alignment in similarity comparisons, alignable differences influence similarity more than nonalignable differences (Markman & Gentner, 1 996) and are more likely to be encoded in memory (Markman & Gentner, 1 997). Alignable differences between objects also play a disproportionately large role in distinguishing between different basic-level categories (e.g., cats and dogs) that belong to the same superordinate category (e.g., animals) (Markman & Wisniewski, 1 997). In short, knowing these correspondences affects not only how much a matching element increases similarity (Goldstone, 1 994a), but also how much a mismatching element decreases similarity. Thus far, much of the evidence for structural alignment in similarity has used somewhat artificial materials. Often, the systems describe how “scenes” are compared, with the underlying implication that the elements comprising the scenes are not as tightly connected as elements comprising objects. Still, if the structural alignment account proves

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to be fertile, it will be because it is applicable to naturally occurring materials. Toward this goal, researchers have considered structural accounts of similarity in language domains. The confusability of words depends on structural analyses to predict that “stop” is more confusable with “step” than “pest” (the “st” match is in the correct location with “step” but not “pest”), but more confusable with “pest” than “best” (the “p” match counts for something even when it is out of place). Substantial success has been made on the practical problem of determining the structural similarity of words (Bernstein, Demorest, & Eberhardt, 1 994; Frisch, Broe, & Pierrehumbert, 1 995 ). Structural alignment has also been implicated when comparing more complex language structures such as sentences (Bassok & Medin, 1 997). Likewise, structural similarity has proven to be a useful notion in explaining consumer preferences of commercial products, explaining, for example, why new products are viewed more favorably when they improve over existing products along alignable rather than unalignable differences (Zhang & Markman, 1 998). Additional research has shown that alignment-based models of similarity provide a better account of category-based induction than feature-based models (Lassaline, 1 996). Still other researchers have applied structural accounts of similarity to the legal domain (Hahn & Chater, 1 998; Simon & Holyoak, 2002). This area of application is promising because the U.S. legal system is based on cases and precedents, and cases are structurally rich and complex situations involving many interrelated parties. Retrieving a historic precedent and assessing its relevance to a current case almost certainly involves aligning representations that are more sophisticated than assumed by geometric or featural models. Transformational Models A final historic approach to similarity that has been more recently resuscitated is that the comparison process proceeds by transforming one representation into the other. A critical step for these models is to spec-

ify what transformational operations are possible. In an early incarnation of a transformational approach to cognition broadly construed, Garner (1 974) stressed the notion of stimuli that are transformationally equivalent and are consequently possible alternatives for each other. In artificial intelligence, Shimon Ullman (1 996) argued that objects are recognized by being aligned with memorized pictorial descriptions. Once an unknown object has been aligned with all candidate models, the best match to the viewed object is selected. The alignment operations rotate, scale, translate, and topographically warp object descriptions. For rigid transformations, full alignment can be obtained by aligning three points on the object with three points on the model description. Unlike recognition strategies that require structural descriptions (e.g., Biederman, 1 987; Hummel, 2000, 2001 ), Ullman’s alignment does not require an image to be decomposed into parts. In transformational accounts that are explicitly designed to model similarity data, similarity is usually defined in terms of transformational distance. In Wiener-Ehrlich, Bart, and Millward’s (1 980) generative representation system, subjects are assumed to possess an elementary set of transformations and invoke these transformations when analyzing stimuli. Their subjects saw linear pairs of stimuli such as {ABCD, DABC} or twoAB DA dimensional stimuli such as { CD , BC }. Subjects were required to rate the similarity of the pairs. The researchers determined transformations that accounted for each subject’s ratings from the set {rotate 90 degrees, rotate 1 80, rotate 270, horizontal reflection, vertical reflection, positive diagonal reflection, negative diagonal reflection}. Similarity was assumed to decrease monotonically as the number of transformations required to make one sequence identical to the other increased. Imai (1 977) made a similar claim. The stimuli used were sequences such as XXOXXXOXXXOX, where Xs represent white ovals and Os represent black ovals. The four basic transformations were mirror

similarity

image (XXXXXOO → OOXXXXX), phase shift (XXXXXOO → XXXXOOX), reversal (XXXXXOO → OOOOOXX), and wavelength (XXOOXXOO → XOXOXOXO). The researcher found that sequences that are two transformations removed (e.g., XXXOXXXOXXXO and OOXOOOXOOOXO require a phase shift and a reversal to be equated) are rated to be less similar than sequences that can be made identical with one transformation. In addition, sequences that can be made identical by more than one transformation (XOXOXOXO and OXOXOXOX can be made identical by mirror image, phase shift, or reversal transformations) are more similar than sequences that have only one identityproducing transformation. More recent work has followed up on Imai’s research and generalized it to stimulus materials, including arrangements of Lego bricks, geometric complexes, and sets of colored circles (Hahn, Chater, & Richardson, 2003 ). According to these researchers’ account, the similarity between two entities is a function of the complexity required to transform the representation of one into the representation of the other. The simpler the transformation, the more similar they are assumed to be. The complexity of a transformation is determined in accord with Kolmogorov complexity theory (Li & Vitanyi, 1 997), according to which the complexity of a representation is the length of the shortest computer program that can generate that representation. For example, the conditional Kolmogorov complexity between the sequence 1 2 3 4 5 6 7 8 and 2 3 4 5 6 7 8 9 is small because the simple instructions add 1 to each digit and subtract 1 from each digit suffice to transform one into the other. Experiments by Hahn et al. (2003 ) demonstrate that once reasonable vocabularies of transformation are postulated, transformational complexity does indeed predict subjective similarity ratings. It is useful to compare and contrast alignment-based and transformational accounts of similarity. Both approaches place scene elements into correspondence. Whereas the correspondences are explicitly

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stated in the structural alignment method, they are implicit in transformational alignment. The transformational account often does produce globally consistent correspondences – for example, correspondences that obey the one-to-one mapping principle; however, this consistency is a consequent of applying a patternwide transformation and is not enforced by interactions between emerging correspondences. It is revealing that transformational accounts have been applied almost exclusively to perceptual stimuli, whereas structural accounts are most often applied to conceptual stimuli such as stories, proverbs, and scientific theories (there are also notable structural accounts in perception, i.e., Biederman, 1 987; Hummel, 2000; Hummel & Biederman, 1 992; Marr & Nishihara, 1 978). Defining a set of constrained transformations is much more tenable for perceptual stimuli. The conceptual similarity between an atom and the solar system could possibly be discovered by transformations. As a start, a miniaturization transformation could be applied to the solar system. However, this single transformation is not nearly sufficient; a nucleus is not simply a small sun. The transformations that would turn the solar system into an atom are not readily forthcoming. If we allow transformations such as an “earth-becomes-electron” transformation, then we are simply reexpressing the structural alignment approach and its part-by-part alignment of relations and objects. Some similarity phenomena that are well explained by structural alignment are not easily handled by transformations. To account for the similarity of “BCDCB” and “ABCDCBA” we could introduce the fairly abstract transformation “add the leftmost letter’s predecessor to both sides of string.” However, the pair “LMN” and “KLMNK” do not seem as similar as the earlier pair, even though the same transformation is applied. A transformation of the form “if the structure is symmetric, then add the preceding element in the series to both ends of the string” presupposes exactly the kind of analysis in defining “symmetric” and “preceding” that are the bread and butter of propositional

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representations and structural alignment. For this reason, one fertile research direction would be to combine alignmentbased accounts’ focus on representing the internal structure within individual scenes with the constraints that transformational accounts provide for establishing psychologically plausible transformations (Hofstadter, 1 997; Mitchell, 1 993 ).

Conclusions and Further Directions To provide a partial balance to our largely historic focus on similarity, we conclude by raising some unanswered questions for the field. These questions are rooted in a desire to connect the study of similarity to cognition as a whole. Is Similarity Flexible Enough to Provide Useful Explanations of Cognition? The study of similarity is typically justified by the argument that so many theories in cognition depend on similarity as a theoretical construct. An account of what makes problems, memories, objects, and words similar to one another often provides the backbone for our theories of problem solving, attention, perception, and cognition. As William James put it, “This sense of Sameness is the very keel and backbone of our thinking” (James, 1 890/1 95 0, p. 45 9). However, others have argued that similarity is not flexible enough to provide a sufficient account, although it may be a necessary component. There have been many empirical demonstrations of apparent dissociations between similarity and other cognitive processes, most notably categorization. Researchers have argued that cognition is frequently based on theories (Murphy & Medin, 1 985 ), rules (Sloman, 1 996; Smith & Sloman, 1 994), or strategies that go beyond “mere” similarity. To take an example from Murphy and Medin (1 985 ), consider a man jumping into a swimming pool fully clothed. This man may be categorized as drunk because we have a theory of behavior and inebriation that explains the man’s action.

Murphy and Medin argued that the categorization of the man’s behavior does not depend on matching the man’s features to the category drunk’s features. It is highly unlikely that the category drunk would have such a specific feature as “jumps into pools fully clothed.” It is not the similarity between the instance and the category that determines the instance’s classification; it is the fact that our category provides a theory that explains the behavior. Developmental psychologists have argued that even young children have inchoate theories that allow them to go beyond superficial similarities in creating categories (Carey, 1 985 ; Gelman & Markman, 1 986; Keil, 1 989). For example, Carey (1 985 ) observed that children choose a toy monkey over a worm as being more similar to a human, but that when they are told that humans have spleens are more likely to infer that the worm has a spleen than that the toy monkey does. Thus, the categorization of objects into “spleen” and “no spleen” groups does not appear to depend on the same knowledge that guides similarity judgments. Adults show similar dissociations between similarity and categorization. In an experiment by Rips (1 989), an animal that is transformed (by toxic waste) from a bird into something that looks like an insect is judged by subjects to be more similar to an insect but is still judged to be a bird. Again, the category judgment seems to depend on biological, genetic, and historic knowledge, whereas the similarity judgments seems to depend more on gross visual appearance (see also Keil, 1 989; Rips & Collins, 1 993 ). Despite the growing body of evidence that similarity appraisals do not always track categorization decisions, there are still some reasons to be sanguine about the continued explanatory relevance of similarity. Categorization itself may not be completely flexible. People are influenced by similarity despite the subjects’ intentions and the experimenters’ instructions (Smith & Sloman, 1 994). Allen and Brooks (1 991 ) gave subjects an easy rule for categorizing cartoon animals into two groups. Subjects were then transferred to the animals that looked very

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similar to one of the training stimuli but belonged in a different category. These animals were categorized more slowly and less accurately than animals that were equally similar to an old animal but also belonged in the same category as the old animal. Likewise, Palmeri (1 997) showed that even for the simple task of counting the number of dots, subjects’ performances are improved when a pattern of dots is similar to a previously seen pattern with the same numerosity and worse when the pattern is similar to a previously seen pattern with different numerosity. People seem to have difficulty ignoring similarities between old and new patterns even when they know a straightforward and perfectly accurate categorization rule. There may be a mandatory consideration of similarity in many categorization judgments (Goldstone, 1 994b), adding constraints to categorization. At the same time, similarity may be more flexible and sophisticated than commonly acknowledged (Jones & Smith, 1 993 ) and this may also serve to bridge the gap between similarity and highlevel cognition. Krumhansl (1 978) argued that similarity between objects decreases when they are surrounded by many close neighbors that were also presented on previous trials (also see Wedell, 1 994). Tversky (1 977) obtained evidence for an extension effect according to which features influence similarity judgments more when they vary within an entire set of stimuli. Items presented within a particular trial also influence similarity judgments. Perhaps the most famous example of this is Tversky’s (1 977) diagnosticity effect according to which features that are diagnostic for relevant classifications will have disproportionate influence on similarity judgments. More recently, Medin, Goldstone, and Gentner (1 993 ) argued that different comparison standards are created, depending on the items that are present on a particular trial. Other research has documented intransitivities in similarity judgments situations in which A is judged to be more similar to T than is B, B is more similar to T than is C, and C is more similar to T than is A (Goldstone, Medin, & Halberstadt, 1 997). This kind of result also suggests

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that the properties used to assess the similarity of objects are determined, in part, by the compared objects themselves. Similarity judgments not only depend on the context established by recently exposed items, simultaneously presented items, and inferred contrast sets, but also on the observer. Suzuki, Ohnishi, and Shigemasu (1 992) showed that similarity judgments depend on level of expertise and goals. Expert and novice subjects were asked to solve the Tower of Hanoi puzzle and judge the similarity between the goal and various states. Experts’ similarity ratings were based on the number of moves required to transform one position to the other. Less expert subjects tended to base their judgments on the number of shared superficial features. Similarly, Hardiman, Dufresne, and Mestre (1 989) found that expert and novice physicists evaluate the similarity of physics problems differently, with experts basing similarity judgments more on general principles of physics than on superficial features (see Sjoberg, 1 972, for other expert/novice differences in similarity ratings). The dependency of similarity on observer-, task-, and stimulus-defined contexts offers the promise that it is indeed flexible enough to subserve cognition. Is Similarity Too Flexible to Provide Useful Explanations of Cognition? As a response to the skeptic of similarity’s usefulness, the preceding two paragraphs could have the exact opposite of their intended effect. The skeptic might now believe that similarity is much too flexible to be a stable ground for cognition. In fact, Nelson Goodman (1 972) put forth exactly this claim, maintaining that the notion of similarity is either vague or unnecessary. He argued that “when to the statement that two things are similar we add a specification of the property that they have in common . . . we render it [the similarity statement] superfluous” (p. 445 ). That is, all the potential explanatory work is done by the “with respect to property Z” clause and not by the similarity statement. Instead of saying “this object

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belongs to category A because it is similar to A items with respect to the property ‘red’,” we can simplify matters by removing any notion of similarity with “this object belongs to category A because it is red.” There are reasons to resist Goodman’s conclusion that “similarity tends under analysis either to vanish entirely or to require for its explanation just what it purports to explain” (p. 446). In most cases, similarity is useful precisely because we cannot flesh out the “respect to property Z” clause with just a single property. Evidence suggests that assessments of overall similarity are natural and perhaps even “primitive.” Evidence from children’s perception of similarity suggests that children are particularly likely to judge similarity on the basis of many integrated properties rather than analysis into dimensions. Even dimensions that are perceptually separable are treated as fused in similarity judgments (Smith & Kemler, 1 978). Children younger than 5 years of age tend to classify on the basis of overall similarity and not on the basis of a single criterial attribute (Keil, 1 989; Smith, 1 989). Children often have great difficulty identifying the dimension along which two objects vary, even though they can easily identify that the objects are different in some way (Kemler, 1 983 ). Smith (1 989) argued that it is relatively difficult for young children to say whether two objects are identical on a particular property but relatively easy for them to say whether they are similar across many dimensions. There is also evidence that adults often have an overall impression of similarity without analysis into specific properties. Ward (1 983 ) found that adult subjects who tended to group objects quickly also tended to group objects like children by considering overall similarity across all dimensions instead of maximal similarity on one dimension. Likewise, Smith and Kemler (1 984) found that adults who were given a distracting task produced more judgments by overall similarity than subjects who were not. To the extent that similarity is determined by many properties, it is less subject to drastic context-driven changes. Furthermore, inte-

grating multiple sources of information into a single assessment of similarity becomes particularly important. The four approaches to similarity described in the previous section provide methods for integrating multiple properties into a single similarity judgment and, as such, go significantly beyond simply determining a single “property Z” to attend. A final point to make about the potential overflexibility of similarity is that, although impressions of similarity can change with context and experience, automatic and “generic” assessments of similarity typically change slowly and with considerable inertia. Similarities that were once effortful and strategic become second nature to the organism. Roughly speaking, this is the process of perceiving what was once a conceptual similarity. At first, the novice mycologist explicitly uses rules for perceiving the dissimilarity between the pleasing Agaricus Bisporus mushroom and the deadly Amanita Phalloides. With time, this dissimilarity ceases to be effortful and rule based and becomes perceptual and phenomenologically direct. When this occurs, the similarity becomes generic and default and can be used as the ground for new strategic similarities. In this way, our cognitive abilities gradually attain sophistication by treating territory as level ground that once made for difficult mental climbing. A corollary of this contention is that our default impression of similarity does not typically mislead us; it is explicitly designed to lead us to see relations between things that often function similarly in our world. People, with good reason, expect their default similarity assessments to provide good clues about where to uncover directed, nonapparent similarities (Medin & Ortony, 1 989). Should “Similarity” Even Be a Field of Study Within Cognitive Science? This survey has proceeded under the convenient fiction that it is possible to tell a general story for how people compare things. One reason to doubt this is that the methods used for assessing similarity have large effects on the resulting similarity viewed.

similarity

Similarity as measured by ratings is not equivalent to similarity as measured by perceptual discriminability. Although these measures correlate highly, systematic differences are found (Podgorny & Garner, 1 979; Sergent & Takane, 1 987). For example, Beck (1 966) found that an upright T is rated as more similar to a tilted T than an upright L but that it is also more likely to be perceptually grouped with the upright Ls. Previously reviewed experiments indicate the nonequivalence of assessments that use similarity versus dissimilarity ratings, categorization versus forced-choice similarity judgments, or speeded versus leisurely judgments. In everyday discourse we talk about the similarity of two things, forgetting that this assessment depends on a particular task and circumstance. Furthermore, it may turn out that the calculation of similarity is fundamentally different for different domains (see Medin, Lynch, & Solomon, 2000, for a thoughtful discussion of this issue). To know how to calculate the similarity of two faces, one would need to study faces specifically and the eventual account need not inform researchers interested in the similarity of words, works of music, or trees. A possible conclusion is that similarity is not a coherent notion at all. The term similarity, similar to the bug or family values, may not pick out a consolidated or principled set of things. Although we sympathize with the impulse toward domain-specific accounts of similarity, we also believe in the value of studying general principles of comparison that potentially underlie many domains. Although we do not know whether general principles exist, one justification for pursuing them is the large payoff that would result from discovering these principles if they do exist. A historically fruitful strategy, exemplified by Einstein’s search for a law to unify gravitational and electromagnetic acceleration and Darwin’s search for a unified law to understand the origins of humans and other animals, has been to understand differences as parametric variations within a single model. Finding differences across tasks does not necessarily point to the in-

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coherency of similarity. An alternative perspective would use these task differences as an illuminating source of information in developing a unified account. The systematic nature of these task differences should stimulate accounts that include a formal description not only of stimulus components but also of task components. Future success in understanding the task of comparison may depend on comparing tasks.

Acknowledgments This research was funded by NIH grant MH5 6871 and NSF grant 01 25 287. Correspondence concerning this chapter should be addressed to [email protected] or Robert Goldstone, Psychology Department, Indiana University, Bloomington, Indiana 47405 . Further information about the laboratory can be found at http://cognitrn.psych. indiana.edu

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CHAPTER 3

Concepts and Categories: Memory, Meaning, and Metaphysics Douglas L. Medin Lance J. Rips

Introduction The concept of concepts is difficult to define, but no one doubts that concepts are fundamental to mental life and human communication. Cognitive scientists generally agree that a concept is a mental representation that picks out a set of entities, or a category. That is, concepts refer, and what they refer to are categories. It is also commonly assumed that category membership is not arbitrary, but rather a principled matter. What goes into a category belongs there by virtue of some lawlike regularities. However, beyond these sparse facts, the concept CONCEPT is up for grabs. As an example, suppose you have the concept TRIANGLE represented as “a closed geometric form having three sides.” In this case, the concept is a definition, but it is unclear what else might be in your triangle concept. Does it include the fact that geometry books discuss them (although some don’t) or that they have 1 80 degrees (although in hyperbolic geometry none do)? It is also unclear how many concepts have definitions or what substitutes for definitions in ones that do not.

Our goal in this chapter is to provide an overview of work on concepts and categories in the last half-century. There has been such a consistent stream of research during this period that one reviewer of this literature, Gregory Murphy (2002), was compelled to call his monograph, The Big Book of Concepts. Our task is eased by recent reviews, including Murphy’s aptly named one (e.g., Medin, Lynch, & Solomon, 2000; Murphy, 2002; Rips, 2001 ; Wisniewski, 2002). Their thoroughness gives us the luxury of writing a review focused on a single perspective or “flavor” – the relation between concepts, memory, and meaning. The remainder of this chapter is organized as follows. In the rest of this section, we briefly describe some of the tasks or functions that cognitive scientists have expected concepts to perform. This will provide a road map to important lines of research on concepts and categories. Next, we return to developments in the late 1 960s and early 1 970s that raised the exciting possibility that laboratory studies could provide deep insights into both concept representations and the organization of (semantic) 37

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memory. Then we describe the sudden collapse of this optimism and the ensuing lines of research that, however intriguing and important, essentially ignored questions about semantic memory. Next, we trace a number of relatively recent developments under the somewhat whimsical heading, “Psychometaphysics.” This is the view that concepts are embedded in (perhaps domain-specific) theories. This will set the stage for returning to the question of whether research on concepts and categories is relevant to semantics and memory organization. We use that question to speculate about future developments in the field. In this review, we use all caps to refer to concepts and quotation marks to refer to linguistic expressions. Functions of Concepts For purposes of this chapter, we collapse the many ways people can use concepts into two broad functions: categorization and communication. The conceptual function that most research has targeted is categorization, the process by which mental representations (concepts) determine whether some entity is a member of a category. Categorization enables a wide variety of subordinate functions because classifying something as a category member allows people to bring their knowledge of the category to bear on the new instance. Once people categorize some novel entity, for example, they can use relevant knowledge for understanding and prediction. Recognizing a cylindrical object as a flashlight allows you to understand its parts, trace its functions, and predict its behavior. For example, you can confidently infer that the flashlight will have one or more batteries, will have some sort of switch, and will normally produce a beam of light when the switch is pressed. Not only do people categorize in order to understand new entities, but they also use the new entities to modify and update their concepts. In other words, categorization supports learning. Encountering a member of a category with a novel property – for example, a flashlight that has a siren for emer-

gencies – can result in that novel property being incorporated into the conceptual representation. In other cases, relations between categories may support inference. For example, finding out that flashlights can contain sirens may lead you to entertain the idea that cell phones and fire extinguishers might also contain sirens. Hierarchical conceptual relations support both inductive and deductive reasoning. If all trees contain xylem and hawthorns are trees, then one can deduce that hawthorns contain xylem. In addition, finding out that white oaks contain phloem provides some support for the inductive inference that other kinds of oaks contain phloem. People also use categories to instantiate goals in planning (Barsalou, 1 983 ). For example, a person planning to do some night fishing might create an ad hoc concept, THINGS TO BRING ON A NIGHT FISHING TRIP, which would include a fishing rod, tackle box, mosquito repellent, and flashlight. Concepts are also centrally involved in communication. Many of our concepts correspond to lexical entries, such as the English word “flashlight.” For people to avoid misunderstanding each other, they must have comparable concepts in mind. If A’s concept of cell phone corresponds with B’s concept of flashlight, it will not go well if A asks B to make a call. An important part of the function of concepts in communication is their ability to combine to create an unlimited number of new concepts. Nearly every sentence you encounter is new – one you have never heard or read before – and concepts (along with the sentence’s grammar) must support your ability to understand it. Concepts are also responsible for more ad hoc uses of language. For example, from the base concepts of TROUT and FLASHLIGHT, you might create a new concept, TROUT FLASHLIGHT, which in the context of our current discussion would presumably be a flashlight used when trying to catch trout (and not a flashlight with a picture of a trout on it, although this may be the correct interpretation in some other context). A major research challenge is to

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understand the principles of conceptual combination and how they relate to communicative contexts (see Fodor, 1 994, 1 998; Gleitman & Papafragou, Chap. 26 ; Hampton, 1 997; Partee, 1 995 ; Rips, 1 995 ; Wisniewski, 1 997).

Overview So far, we have introduced two roles for concepts: categorization (broadly construed) and communication. These functions and associated subfunctions are important to bear in mind because studying any one in isolation can lead to misleading conclusions about conceptual structure (see Solomon, Medin, & Lynch, 1 999, for a review bearing on this point). At this juncture, however, we need to introduce one more plot element into the story we are telling. Presumably everything we have been talking about has implications for human memory and memory organization. After all, concepts are mental representations, and people must store these representations somewhere in memory. However, the relation between concepts and memory may be more intimate. A key part of our story is what we call “the semantic memory marriage,” the idea that memory organization corresponds to meaningful relations between concepts. Mental pathways that lead from one concept to another – for example, from ELBOW to ARM – represent relations like IS A PART OF that link the same concepts. Moreover, these memory relations may supply the concepts with all or part of their meaning. By studying how people use concepts in categorizing and reasoning, researchers could simultaneously explore memory structure and the structure of the mental lexicon. In other words, the idea was to unify categorization, communication (in its semantic aspects), and memory organization. As we will see, this marriage was somewhat troubled, and there are many rumors about its breakup. However, we are getting ahead of our story. The next section begins with the initial romance.

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A Minihistory Research on concepts in the middle of the last century reflected a gradual easing away from behaviorist and associative learning traditions. The focus, however, remained on learning. Most of this research was conducted in laboratories using artificial categories (a sample category might be any geometric figure that is both red and striped) and directed at one of two questions: (1 ) Are concepts learned by gradual increases in associative strength, or is learning all or none (Levine, 1 962; Trabasso & Bower, 1 968)?, and (2) Which kinds of rules or concepts (e.g., disjunctive, such as RED OR STRIPED, versus conjunctive, such as RED AND STRIPED) are easiest to learn (Bourne, 1 970; Bruner, Goodnow, & Austin, 1 95 6; Restle, 1 962)? This early work tended either to ignore real world concepts (Bruner et al., 1 95 6, represent something of an exception here) or to assume implicitly that real world concepts are structured according to the same kinds of arbitrary rules that defined the artificial ones. According to this tradition, category learning is equivalent to finding out the definitions that determine category membership. Early Theories of Semantic Memory Although the work on rule learning set the stage for what was to follow, two developments associated with the emergence of cognitive psychology dramatically changed how people thought about concepts. turning point 1: models of memory organization

The idea of programming computers to do intelligent things (artificial intelligence or AI) had an important influence on the development of new approaches to concepts. Quillian (1 967) proposed a hierarchical model for storing semantic information in a computer that was quickly evaluated as a candidate model for the structure of human memory (Collins & Quillian, 1 969).

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Figure 3 .1 provides an illustration of part of a memory hierarchy that is similar to what the Quillian model suggests. First, note that the network follows a principle of cognitive economy. Properties true of all animals, such as eating and breathing, are stored only with the animal concept. Similarly, properties that are generally true of birds are stored at the bird node, but properties distinctive to individual kinds (e.g., being yellow) are stored with the specific concept nodes they characterize (e.g., CANARY). A property does not have to be true of all subordinate concepts to be stored with a superordinate. This is illustrated in Figure 3 .1 , where CAN FLY is associated with the bird node; the few exceptions (e.g., flightlessness for ostriches) are stored with particular birds that do not fly. Second, note that category membership is defined in terms of positions in the hierarchical network. For example, the node for CANARY does not directly store the information that canaries are animals; instead, membership would be “computed” by moving from the canary node up to the bird node and then from the bird node to the animal node. It is as if a deductive argument is being constructed of the form, “All canaries are birds and all birds are animals and therefore all canaries are animals.” Although these assumptions about cognitive economy and traversing a hierarchical structure may seem speculative, they yield a number of testable predictions. Assuming traversal takes time, one would predict that the time needed for people to verify properties of concepts should increase with the network distance between the concept and the property. For example, people should be faster to verify that a canary is yellow than to verify that a canary has feathers and faster to determine that a canary can fly than that a canary has skin. Collins and Quillian found general support for these predictions. turning point 2: natural concepts and family resemblance

The work on rule learning suggested that children (and adults) might learn concepts

by trying out hypotheses until they hit on the correct definition. In the early 1 970s, however, Eleanor Rosch and her associates (e.g., Rosch, 1 973 ; Rosch & Mervis, 1 975 ) argued that most everyday concepts are not organized in terms of the sorts of necessary and sufficient features that would form a (conjunctive) definition for a category. Instead, such concepts depend on properties that are generally true but need not hold for every member. Rosch’s proposal was that concepts have a “family resemblance” structure: What determines category membership is whether an example has enough characteristic properties (is enough like other members) to belong to the category. One key idea associated with this view is that not all category members are equally “good” examples of a concept. If membership is based on characteristic properties and some members have more of these properties than others, then the ones with more characteristic properties should better exemplify the category. For example, canaries but not penguins have the characteristic bird properties of flying, singing, and building a nest, so one would predict that canaries would be more typical birds than penguins. Rosch and Mervis (1 975 ) found that people do rate some examples of a category to be more typical than others and that these judgments are highly correlated with the number of characteristic features an example possesses. They also created artificial categories conforming to family resemblance structures, and produced typicality effects on learning and on goodnessof-example judgments. Rosch and her associates (Rosch, Mervis, Gray, Johnson, & Boyes-Braem, 1 976) also argued that the family resemblance view has important implications for understanding concept hierarchies. Specifically, they suggested that the correlational structure of features (instances that share some features tend to share others) creates natural “chunks” or clusters of instances that correspond to what they referred to as basic-level categories. For example, having feathers tends to correlate with nesting in trees (among other features) in the animal

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concepts and categories

Animal

Has wings Can fly Has feathers

Bird

Canary

Can sing Is yellow

Ostrich

Has long, thin legs Is tall , Can t fly

Has skin Can move around Eats Breathes

Fish

Has fins Can swim Has gills

Shark

Salmon

Can bite Is dangerous

Is pink Is edible Swims upstream to lay eggs

Figure 3.1 . A semantic network.

kingdom, and having gills with living in water. The first cluster tends to isolate birds, whereas the second picks out fish. The general idea is that these basic-level categories provide the best compromise between maximizing within-category similarity (birds tend to be quite similar to each other) and minimizing between-category similarity (birds tend to be dissimilar to fish). Rosch et al. showed that basic-level categories are preferred by adults in naming objects, are learned first by children, are associated with the fastest categorization reaction times, and have a number of other properties that indicate their special conceptual status. Turning points 1 and 2 are not unrelated. To be sure, the Collins and Quillian model, as initially presented, would not predict typicality effects (but see Collins & Loftus, 1 975 ), and it was not obvious that it contained anything that would predict the importance of basic-level categories. Nonetheless, these conceptual breakthroughs led to an enormous amount of research premised on the notion that memory groups concepts

according to their similarity in meaning, where similarity is imposed by correlated and taxonomic structure (see Anderson & Bower, 1 973 , and Norman & Rumelhart, 1 975 , for theories and research in this tradition, and Goldstone & Son, Chap. 2, for current theories of similarity). Fragmentation of Semantics and Memory Prior to about 1 980, most researchers in this field saw themselves as investigating “semantic memory” – the way that long-term memory organizes meaningful information. Around 1 980, the term itself became passe, ´ at least for this same group of researchers, and the field regrouped under the banner of “Categories and Concepts” (the title of Smith & Medin’s, 1 981 , synthesis of research in this area). At the time, these researchers may well have seen this change as a purely nominal one, but we suspect it reflected a retreat from the claim that semantic memory research had much to say about either semantics or memory. How did this change come about?

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memory organization

Initial support for a Quillian-type memory organization came from Quillian’s own collaboration with Allan Collins (Collins & Quillian, 1 969), which we mentioned earlier. Related evidence also came from experiments on lexical priming: Retrieving the meaning of a word made it easier to retrieve the meaning of semantically related words (e.g., Meyer & Schvanevelt, 1 971 ). In these lexical decision tasks, participants viewed a single string of letters on each trial and decided, under reaction time instructions, whether the string was a word (“daisy”) or a nonword (“raisy”). The key result was that participants were faster to identify a string as a word if it followed a semantically related item rather than an unrelated one. For example, reaction time for “daisy” was faster if, on the preceding trial, the participant had seen “tulip” rather than “steel.” This priming effect is consistent with the hypothesis that activation from one concept spreads through memory to semantically related ones. Later findings suggested, however, that the relation between word meaning and memory organization was less straightforward. For example, the typicality findings (see turning point 2) suggested that time to verify sentences of the form An X is a Y (e.g., “A finch is a bird”) might be a function of the overlap in the information that participants knew about the meaning of X and Y rather than the length of the pathway between these concepts. The greater the information overlap – for example, the greater the number of properties that the referents of X and Y shared – the faster the time to confirm a true sentence and the slower the time to disconfirm a false one. For example, if you know a lot of common information about finches and birds but only a little common information about ostriches and birds, you should be faster to confirm the sentence “A finch is a bird” than “An ostrich is a bird.” Investigators proposed several theories along these lines that made minimal commitments to the way memory organized its mental concepts (McCloskey & Glucksberg, 1 979; Smith, Shoben, & Rips, 1 974; Tversky, 1 977). Rosch’s (1 978) theory like-

wise studiously avoided a stand on memory structure. Evidence from priming in lexical decision tasks also appeared ambiguous. Although priming occurs between associatively related words (e.g., “bread” and “butter”), it is not so clear that there is priming between semantically linked words in the absence of such associations. It is controversial whether, for example, there is any automatic activation between “glove” and “hat” despite their joint membership in the clothing category (see Balota, 1 994, for a discussion). If memory is organized on a specifically semantic basis – on the basis of word meanings – then there should be activation between semantically related words even in the absence of other sorts of associations. A meta-analysis by Lucas (2000) turned up a small effect of this type, but as Lucas noted, it is difficult to tell whether the semantically related pairs in these experiments are truly free of associations. The idea that memory organization mimics semantic organization is an attractive one, and memory researchers attempted to modify the original Quillian approach to bring it into line with the results we have just reviewed (e.g., Collins & Loftus, 1 975 ). The data from the sentence verification and lexical decision experiments, however, raised doubts about these theories. Later in this chapter, we consider whether newer techniques can give us a better handle on the structure of memory, but for now let’s turn to the other half of the memory equals meaning equation.

semantics

Specifying the meaning of individual words is one of the goals of semantics, but only one. Semantics must also account for the meaning of phrases, sentences, and longer units of language. One problem in using a theory like Quillian’s as a semantic theory is how to extend its core idea – that the meaning of a word is the coordinates of a node in memory structure – to explain how people understand meaningful phrases and sentences. Of course, Quillian’s theory and its successors

concepts and categories

can tell us how we understand sentences that correspond to preexisting memory pathways. We have already seen how the model can explain our ability to confirm sentences such as “A daisy is a flower.” However, what about sentences that do not correspond to preexisting connections – sentences such as “Fred placed a daisy in a lunchbox”? The standard approach to sentence meaning in linguistics is to think of the meaning of sentences as built from the meaning of the words that compose them, guided by the sentence’s grammar (e.g., Chierchia & McConnell-Ginet, 1 990). We can understand sentences that we have never heard or read before, and because there are an enormous number of such novel sentences, we cannot learn their meaning as single chunks. It therefore seems quite likely that we compute the meaning of these new sentences. However, if word meaning is the position of a node in a network, it is hard to see how this position could combine with other positions to produce sentence meanings. What is the process that could take the relative network positions for FRED, PLACE, DAISY, IN, and LUNCHBOX and turn them into a meaning for “Fred placed a daisy in a lunchbox”? If you like the notion of word meaning as relative position, then one possible solution to the problem of sentence meaning is to connect these positions with further pathways. Because we already have an array of memory nodes and pathways at our disposal, why not add a few more to encode the meaning of a new sentence? Perhaps the meaning of “Fred placed a daisy in the lunchbox” is given by a new set of pathways that interconnect the nodes for FRED, PLACE, DAISY, and so on, in a configuration corresponding to the sentence’s structure. This is the route that Quillian and his successors took (e.g., Anderson & Bower, 1 973 ; Norman & Rumelhart, 1 975 ; Quillian, 1 969), but it comes at a high price. Adding new connections changes the overall network configuration and thereby alters the meaning of the constituent terms. (Remember: Meaning is supposed to be relative position.) However, it is far from obvious that encoding incidental facts alters

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word meaning. It seems unlikely, for example, that learning the sentence about Fred changes the meaning of “daisy.” Moreover, because meaning is a function of the entire network, the same incidental sentences change the meaning of all words. Learning about Fred’s daisy placing shifts the meaning of seemingly unrelated words such as “hippopotamus” if only a bit. Related questions apply to other psychological theories of meaning in the semantic memory tradition. To handle the typicality results mentioned earlier, some investigators proposed that the mental representation of a category such as daisies consists of a prototype for that category – for example, a description of a good example of a daisy (e.g., Hampton, 1 979; McCloskey & Glucksberg, 1 979). The meaning of “daisy” in these prototype theories would thus include default characteristics, such as growing in gardens, that apply to most, but not all, daisies. We discuss prototype theories in more detail soon, but the point for now is that prototype representations for individual words are difficult to combine to obtain a meaning for phrases that contain them. One potential way to combine prototypes – fuzzy set theory (Zadeh, 1 965 ) – proved vulnerable to a range of counterexamples (Osherson & Smith, 1 981 , 1 982). In general, the prototypes of constituent concepts can differ from the prototypes of their combinations in unpredictable ways (Fodor, 1 994). The prototype of BIRDS THAT ARE PETS (perhaps a parakeet-like bird) may differ from the prototypes of both BIRDS and PETS (see Storms, de Boeck, van Mechelen, & Ruts, 1 998, for related evidence). Thus, if word meanings are prototypes, it is hard to see how the meaning of phrases could be a compositional function of the meaning of their parts. Other early theories proposed that category representations consist of descriptions of exemplars of the category in question. For example, the mental representation of DAISY would include descriptions of specific daisies that an individual had encoded (e.g., Hintzman, 1 986; Medin & Schaffer, 1 978; Nosofsky, 1 986). However, these

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theories have semantic difficulties of their own (see Rips, 1 995 ). For example, if by chance the only Nebraskans you have met are chiropractors and the only chiropractors you have met are Nebraskans, then exemplar models appear to mispredict that “Nebraskan” and “chiropractor” will be synonyms for you. To recap briefly, we have found that experimental research on concepts and categories was largely unable to confirm that global memory organization (as in Quillian’s semantic memory) conferred word meaning. In addition, neither the global theories that initiated this research nor the local prototype or exemplar theories that this research produced were able to provide insight into the basic semantic problem of how we understand the meaning of novel sentences. This left semantic memory theory in the unenviable position of being unable to explain either semantics or memory.

Functions and Findings Current research in this field still focuses on categorization and communication, but without the benefit of a framework that gives a unified explanation for the functions that concepts play in categorizing, reasoning, learning, language understanding, and memory organization. In this section, we survey the state of the art, and in the following one, we consider the possibility of reuniting some of these roles. Category Learning and Inference One nice aspect of Rosch and Mervis’s (1 975 ) studies of typicality effects is that they used both natural language categories and artificially created categories. Finding typicality effects with natural (real world) categories shows that the phenomenon is of broad interest; finding these same effects with artificial categories provides systematic control for potentially confounding variables (e.g., exemplar frequency) in a way that cannot be done for lexical concepts. This general strategy linking the natural to the artificial

has often been followed over the past few decades. Although researchers using artificial categories have sometimes been guilty of treating these categories as ends in themselves, there are enough parallels between results with artificial and natural categories that each area of research informs the other (see Medin & Coley, 1 998, for a review). prototype versus exemplar models

One idea compatible with Rosch’s family resemblance hypothesis is the prototype view. It proposes that people learn the characteristic features (or central tendency) of categories and use them to represent the category (e.g., Reed, 1 972). This abstract prototype need not correspond to any experienced example. According to this theory, categorization depends on similarity to the prototypes. For example, to decide whether some animal is a bird or a mammal, a person would compare the (representation of ) that animal to both the bird and the mammal prototypes and assign it to the category whose prototype it most resembled. The prototype view accounts for typicality effects in a straightforward manner. Good examples have many characteristic properties of their category and have few characteristics in common with the prototypes of contrasting categories. Early research appeared to provide striking confirmation of the idea of prototype abstraction. Using random dot patterns as the prototypes, Posner and Keele (1 968, 1 970) produced a category from each prototype. The instances in a category were “distortions” of the prototype generated by moving constituent dots varying distances from their original positions. Posner and Keele first trained participants to classify examples that they created by distorting the prototypes. Then they gave a transfer test in which they presented both the old patterns and new low or high distortions that had not appeared during training. In addition, the prototypes, which the participants had never seen, were presented during transfer. Participants had to categorize these transfer patterns, but unlike the training procedure, the transfer test gave participants no feedback about the

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correctness of their responses. The tests either immediately followed training or appeared after a 1 -week delay. Posner and Keele (1 970) found that correct classification of the new patterns decreased as distortion (distance from a category prototype) increased. This is the standard typicality effect. The most striking result was that a delay differentially affected categorization of prototypic versus old training patterns. Specifically, correct categorization of old patterns decreased over time to a reliably greater extent than performance on prototypes. In the immediate test, participants classified old patterns more accurately than prototypes; however, in the delayed test, accuracy on old patterns and prototypes was about the same. This differential forgetting is compatible with the idea that training leaves participants with representations of both training examples and abstracted prototypes but that memory, for examples, fades more rapidly than memory for prototypes. The Posner and Keele results were quickly replicated by others and constituted fairly compelling evidence for the prototype view. However, this proved to be the beginning of the story rather than the end. Other researchers (e.g., Brooks, 1 978; Medin & Schaffer, 1 978) put forth an exemplar view of categorization. Their idea was that memory for old exemplars by itself could account for transfer patterns without the need for positing memory for prototypes. On this view, new examples are classified by assessing their similarity to stored examples and assigning the new example to the category that has the most similar examples. For instance, some unfamiliar bird (e.g., a heron) might be correctly categorized as a bird not because it is similar to a bird prototype, but rather because it is similar to flamingos, storks, and other shore birds. In general, similarity to prototypes and similarity to stored examples will tend to be highly correlated (Estes, 1 986). Nonetheless, for some category structures and for some specific exemplar and prototype models, it is possible to develop differential predictions. Medin and Schaffer (1 978), for ex-

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ample, pitted the number of typical features against high similarity to particular training examples and found that categorization was more strongly influenced by the latter. A prototype model would make the opposite prediction. Another contrast between exemplar and prototype models revolves around sensitivity to within-category correlations (Medin, Altom, Edelson, & Freko, 1 982). A prototype representation captures what is on average true of a category, but is insensitive to within-category feature distributions. For example, a bird prototype could not represent the impression that small birds are more likely to sing than large birds (unless one had separate prototypes for large and small birds). Medin et al. (1 982) found that people are sensitive to within-category correlations (see also Malt & Smith, 1 984, for corresponding results with natural object categories). Exemplar theorists were also able to show that exemplar models could readily predict other effects that originally appeared to support prototype theories – differential forgetting of prototypes versus training examples, and prototypes being categorized as accurately or more accurately than training examples. In short, early skirmishes strongly favored exemplar models over prototype models. Parsimony suggested no need to posit prototypes if stored instances could do the job. Since the early 1 980s, there have been a number of trends and developments in research and theory with artificially constructed categories, and we give only the briefest of summaries here.

new models

There are now more contending models for categorizing artificial stimuli, and the early models have been extensively elaborated. For example, researchers have generalized the original Medin and Schaffer (1 978) exemplar model to handle continuous dimensions (Nosofsky, 1 986), to address the time course of categorization (Lamberts, 1 995 ; Nosofsky & Palmeri, 1 997a; Palmeri, 1 997), to generate probability estimates in inference tasks (Juslin & Persson, 2002), and

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to embed it in a neural network (Kruschke, 1 992). Three new kinds of classification theories have been added to the discussion: rational approaches, decision-bound models, and neural network models. Anderson (1 990, 1 991 ) proposed that an effective approach to modeling cognition in general and categorization in particular is to analyze the information available to a person in the situation of interest and then to determine abstractly what an efficient, if not optimal, strategy might be. This approach has led to some new sorts of experimental evidence (e.g., Anderson & Fincham, 1 996; Clapper & Bower, 2002) and pointed researchers more in the direction of the inference function of categories. Interestingly, the Medin and Schaffer exemplar model corresponds to a special case of the rational model, and Nosofsky (1 991 ) discussed the issue of whether the rational model adds significant explanatory power. However, there is also some evidence undermining the rational model’s predictions concerning inference (e.g., Malt, Ross, & Murphy, 1 995 ; Murphy & Ross, 1 994; Palmeri, 1 999; Ross & Murphy, 1 996). Decision-bound models (e.g., Ashby & Maddox, 1 993 ; Maddox & Ashby, 1 993 ) draw their inspiration from psychophysics and signal detection theory. Their primary claim is that category learning consists of developing decision bounds around the category that will allow people to categorize examples successfully. The closer an item is to the decision bound the harder it should be to categorize. This framework offers a new perspective on categorization in that it may lead investigators to ask questions such as How do the decision bounds that humans adopt compare with what is optimal? and What kinds of decision functions are easy or hard to acquire? Researchers have also directed efforts to distinguish decisionbound and exemplar models (e.g., Maddox, 1 999; Maddox & Ashby, 1 998; McKinley & Nosofsky, 1 995 ; Nosofsky, 1 998; Nosofsky & Palmeri, 1 997b). One possible difficulty with decision-bound models is that they contain no obvious mechanism by which stimulus familiarity can affect performance,

contrary to empirical evidence that it does (Verguts, Storms, & Tuerlinckx, 2001 ). Neural network or connectionist models are the third type of new model on the scene (see Knapp & Anderson, 1 984, and Kruschke, 1 992, for examples, and Doumas & Hummel, Chap. 4, for further discussion of connectionism). It may be a mistake to think of connectionist models as comprising a single category because they take many forms, depending on assumptions about hidden units, attentional processes, recurrence, and the like. There is one sense in which neural network models with hidden units may represent a clear advance on prototype models: They can form prototypes in a bottom-up manner that reflects withincategory structure (e.g., Love, Medin, & Gureckis, 2004). That is, if a category comprises two distinct clusters of examples, network models can create a separate hidden unit for each chunk (e.g., large birds versus small birds) and thereby show sensitivity to within-category correlations. mixed models and multiple categorization systems

A common response to hearing about various models of categorization is to suggest that all the models may be capturing important aspects of categorization and that research should determine in which contexts one strategy versus another is likely to dominate. One challenge to this divide and conquer program is that the predictions of alternative models tend to be highly correlated, and separating them is far from trivial. Nonetheless, there is both empirical research (e.g., Johansen & Palmeri, 2002; Nosofsky, Clark, & Shin, 1 989; Reagher & Brooks, 1 993 ) and theoretical modeling that support the idea that mixed models of categorization are useful and perhaps necessary. Current efforts combine rules and examples (e.g., Erickson & Kruschke, 1 998; Nosofsky, Palmeri, & McKinley, 1 994), as well as rules and decision bounds (Ashby, Alfonso-Reese, Turken, & Waldron, 1 998). Some models also combine exemplars and prototypes (e.g., Homa, Sterling, & Trepel, 1 981 ; Minda & Smith, 2001 ; Smith & Minda,

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1 998, 2000; Smith, Murray, & Minda, 1 997), but it remains controversial whether the addition of prototypes is needed (e.g., Busemeyer, Dewey, & Medin, 1 984; Nosofsky & Johansen, 2000; Nosofsky & Zaki, 2002; Stanton, Nosofsky, & Zaki, 2002). The upsurge of cognitive neuroscience has reinforced the interest in multiple memory systems. One intriguing line of research by Knowlton, Squire, and associates (Knowlton, Mangels, & Squire, 1 996; Knowlton & Squire, 1 993 ; Squire & Knowlton, 1 995 ) favoring multiple categorization systems involves a dissociation between categorization and recognition. Knowlton and Squire (1 993 ) used the Posner and Keele dot pattern stimuli to test amnesic and matched control patients on either categorization learning and transfer or a new–old recognition task (involving five previously studied patterns versus five new patterns). The amnesiacs performed very poorly on the recognition task but were not reliably different from control participants on the categorization task. Knowlton and Squire took this as evidence for a two-system model, one based on explicit memory for examples and one based on an implicit system (possibly prototype abstraction). On this view, amnesiacs have lost access to the explicit system but can perform the classification task using their intact implicit memory. These claims have provoked a number of counterarguments. First, Nosofsky and Zaki (1 998) showed that a single system (exemplar) model could account for both types of data from both groups (by assuming the exemplar-based memory of amnesiacs was impaired but not absent). Second, investigators have raised questions about the details of Knowlton and Squire’s procedures. Specifically, Palmeri and Flanery (1 999) suggested that the transfer tests themselves may have provided cues concerning category membership. They showed that undergraduates who had never been exposed to training examples (the students believed they were being shown patterns subliminally) performed above chance on transfer tests in this same paradigm. The debate is far from resolved, and there are strong

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advocates both for and against the multiple systems view (e.g., Filoteo, Maddox, & Davis, 2001 ; Maddox, 2002; Nosofsky & Johansen, 2000; Palmeri & Flanery, 2002; Reber, Stark, & Squire, 1 998a, 1 998b). It is safe to predict that this issue will receive continuing attention.

inference learning

More recently, investigators have begun to worry about extending the scope of category learning studies by looking at inference. Often, we categorize some entity to help us accomplish some function or goal. Ross (1 997, 1 999, 2000) showed that the category representations people develop in laboratory studies depend on use and that use affects later categorization. In other words, models of categorization ignore inference and use at their peril. Other work suggests that having a cohesive category structure is more important for inference learning than it is for classification (Yamauchi, Love, & Markman, 2002; Yamauchi & Markman, 1 998, 2000a, 2000b; for modeling implications see Love, Markman, & Yamauchi, 2000; Love et al., 2004). More generally, this work raises the possibility that diagnostic rules based on superficial features, which appear so prominently in pure categorization tasks, may not be especially relevant for contexts involving multiple functions or more meaningful stimuli (e.g., Markman & Makin, 1 998; Wisniewski & Medin, 1 994).

feature learning

The final topic on our “must mention” list for work with artificial categories is feature learning. It is a common assumption in both models of object recognition and category learning that the basic units of analysis or features remain unchanged during learning. There is increasing evidence and supporting computational modeling that indicate this assumption is incorrect. Learning may increase or decrease the distinctiveness of features and may even create new features (see Goldstone, 1 998, 2003 ; Goldstone, Lippa, & Shriffin, 2001 ; Goldstone & Stevyers, 2001 ;

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Schyns, Goldstone, & Thibaut, 1 998; Schyns & Rodet, 1 997). Feature learning has important implications for our understanding of the role of similarity in categorization. It is intuitively compelling to think of similarity as a causal factor supporting categorization – things belong to the same category because they are similar. However, this may have things backward. Even standard models of categorization assume learners selectively attend to features that are diagnostic, and the work on feature learning suggests that learners may create new features that help partition examples into categories. In that sense, similarity (in the sense of overlap in features) is the by-product, not the cause, of category learning. We take up this point again in discussing the theory theory of categorization later in this review. reasoning

As we noted earlier, one of the central functions of categorization is to support reasoning. Having categorized some entity as a bird, one may predict with reasonable confidence that it builds a nest, sings, and can fly, although none of these inferences is certain. In addition, between-category relations may guide reasoning. For example, from the knowledge that robins have some enzyme in their blood, one is likely to be more confident that the enzyme is in sparrows than in raccoons. The basis for this confidence may be that robins are more similar to sparrows than to raccoons or that robins and sparrows share a lower-rank superordinate category than do robins and raccoons (birds versus vertebrates). We do not review this literature here because Sloman and Lagnado (Chap. 5 ) summarize it nicely. summary

Bowing to practicalities, we have glossed a lot of research and skipped numerous other relevant studies. The distinction between artificially created and natural categories is itself artificial – at least in the sense that it has no clear definition or marker. When we take up the idea that concepts may be

organized in terms of theories, we return to some laboratory studies that illustrate this fuzzy boundary. For the moment, however, we shift attention to the more language-like functions of concepts. Language Functions Most investigators in the concepts and categories area continue to assume that, in addition to their role in recognition and category learning, concepts also play a role in understanding language and in thinking discursively about things. In addition to determining, for example, which perceptual patterns signal the appearance of a daisy, the DAISY concept also contributes to the meaning of sentences such as our earlier example, “Fred placed a daisy in a lunchbox.” We noted that early psychological research on concepts ran into problems in explaining the meaning of linguistic units larger than single words. Most early theories posited representations, such as networks, exemplars, or prototypes, that did not combine easily and, thus, complicated the problem of sentence meaning. Even if we reject the idea that sentence meanings are compositional functions of word meaning, we still need a theory of sentence meanings, and no obvious contenders are in sight. In this section, we return to the role that concepts play in language understanding to see whether new experiments and theories have clarified this relationship. concepts as positions in memory structures

One difficulty with the older semantic memory view of word meaning is that memory seems to change with experience from one person to another, whereas meaning must be more or less constant. The sentences you have encoded about daisies may differ drastically from those we have encoded because your conversation, reading habits, and other verbal give and take can diverge in important ways from ours. If meaning depends on memory for these sentences, then your meaning for “daisy” should likewise differ from ours. This raises the question of how you could possibly understand the

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sentences in this chapter in the way we intend or how you could meaningfully disagree with us about some common topic (see Fodor, 1 994). It is possible that two people – say, Calvin and Martha – might be able to maintain mutual intelligibility as long as their conceptual networks are not too different. It is partly an empirical question as to how much their networks can vary while still allowing Calvin’s concepts to map correctly into Martha’s. To investigate this issue, Goldstone and Rogosky (2002) carried out some simulations that try to recover such a mapping. The simulations modeled Calvin’s conceptual system as the distance between each pair of his concepts (e.g., the distance between DOG and CAT in Calvin’s system might be one unit, whereas the distance between DOG and DAISY might be six units). Martha’s conceptual system was represented in the same way (i.e., by exactly the same interconcept distances) except for random noise that Goldstone and Rogosky added to each distance to simulate the effect of disparate beliefs. A constraint-satisfaction algorithm then applied to Calvin’s and Martha’s systems that attempted to recover the original correspondence between the concepts – to map Calvin’s DOG to Martha’s DOG, Calvin’s DAISY to Martha’s DAISY, and so on. The results of the stimulations show that with 1 5 concepts in each system (the maximum number considered and the case in which the model performed best) and with no noise added to Martha’s system, the algorithm was always able to find the correct correspondence. When the simulation added to each dimension of the interconcept distance in Martha a small random increment (drawn from a normal distribution with mean 0 and standard deviation equal to .004 times the maximum distance), the algorithm recovered the correspondence about 63 % of the time. When the standard deviation increased to .006 times the maximum distance, the algorithm succeeded about 1 5 % of the time (Goldstone & Rogosky, 2002, Figure 2). What should one make of the Goldstone and Rogosky results? Correspondences may be recovered for small amounts of noise,

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but performance trailed off dramatically for larger amounts of noise. Foes of the meaningas-relative-position theory might claim that the poor performance under the .6% noise condition proves their contention. Advocates would point to the successful part of the simulations and note that their ability to detect correct correspondences usually improved as the number of points increased (although there are some nonmonotonicities in the simulation results that qualify this finding). Clearly, this is only the beginning of the empirical side of the debate. For example, the differences between Martha and Calvin are likely to be not only random, but also systematic, as in the case in which Martha grew up on a farm and Calvin was a city kid.

concept combination

Let’s look at attempts to tackle head-on the problem of how word-level concepts combine to produce the meanings of larger linguistic units. There is relatively little research in this tradition on entire sentences (see Conrad & Rips, 1 986; Rips, Smith, & Shoben, 1 978), but there has been a fairly steady research stream devoted to noun phrases, including adjective-noun (“edible flowers”), noun-noun (“food flowers”), and noun-relative clause combinations (“flowers that are foods”). We’ll call the noun or adjective parts of these phrases components and distinguish the main or head noun (“flowers” in each of our examples) from the adjective or noun modifier (“edible” or “food”). The aim of the research in question is to describe how people understand these phrases and, in particular, how the typicality of an instance in these combinations depends on the typicality of the same instance in the components. How does the typicality of a marigold in the category of edible flowers depend on the typicality of marigolds in the categories of edible things and flowers? As we already noticed, this relationship is far from straightforward (parakeets are superbly typical as pet birds but less typical pets and even less typical birds). There is an optimistic way of looking at the results of this research program and a

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pessimistic way as well (for more recent, mostly optimistic, reviews of this work, see Hampton, 1 997; Murphy, 2002; Rips, 1 995 ; and Wisniewski, 1 997). The optimistic angle is that interesting phenomena have turned up in investigating the typicality structure of combinations. The pessimistic angle, which is a direct result of the same phenomena, is that little progress has been made in figuring out a way to predict the typicality of a combination from the typicality of its components. This difficulty is instructive – in part because all psychological theories of concept combination posit complex, structured representations, and they depict concept combination either as rearranging (or augmenting) the structure of the head noun by means of the modifier (Franks, 1 995 ; Murphy, 1 988; Smith, Osherson, Rips, & Keane, 1 988) or as fitting both head and modifier into a larger relational complex (Gagne´ & Shoben, 1 997). Table 3 .1 summarizes what is on offer from these theories. Earlier models (at the top of the table) differ from later ones mainly in terms of the complexity of the combination process. Smith et al. (1 988), for example, aimed at explaining simple adjective-noun combinations (e.g., “white vegetable”) that, roughly speaking, refer to the intersection of the sets denoted by modifier and head (white vegetables are approximately the intersection of white things and vegetables). In this theory, combination occurs when the modifier changes the value of an attribute in the head noun (changing the value of the color attribute in VEGETABLE to WHITE) and boosts the importance of this attribute in the overall representation. Later theories attempted to account for nonintersective combinations (e.g., “criminal lawyers,” who are often not both criminals and lawyers). These combinations call for more complicated adjustments – for example, determining a relation that links the modifier and head (a criminal lawyer is a lawyer whose clients are in for criminal charges) or extracting a value from the modifier that can then be assigned to the head (e.g., a panther lawyer might be one who is especially vicious or tenacious). So why no progress? One reason is that many of the combinations that investiga-

tors have studied are familiar or, at least, have familiar referents. Some people have experience with edible flowers, for example, and know that they include nasturtiums, are sometimes used in salads, are often brightly colored, are peppery tasting, and so on. We learn many of these properties by direct or indirect observation (by what Hampton, 1 987, called “extensional feedback”), and they are sometimes impossible to learn simply by knowing the meaning of “edible” and “flower.” Because these properties can affect the typicality of potential instances, the typicality of these familiar combinations will not be a function of the typicality of their components. This means that if we are going to be able to predict typicality in a compositional way, we will have to factor out the contribution of these directly acquired properties. Rips (1 995 ) refered to this filtering as the “no peeking principle” – no peeking at the referents of the combination. Of course, you might be able to predict typicality if you already know the relevant real-world facts in addition to knowing the meaning of the component concepts. The issue about understanding phrases, however, is how we are able to interpret an unlimited number of new ones. For this purpose, people need some procedure for computing new meanings from old ones that is not restricted by the limited set of facts they happened to have learned (e.g., through idiosyncratic encounters with edible flowers). Another reason for lack of progress is that some of the combinations used in this research may be compounds or lexicalized phrases [e.g., “White House” (accent on “White”) = the residence of the President] rather than modifier-head constructions [e.g., “white house” (accent on “house”) = a house whose color is white]. Compounds are often idiomatic; their meaning is not an obvious function of their parts (see Gleitman & Gleitman’s, 1 970, distinction between phrasal and compound constructions; and Partee, 1 995 ). There is a deeper reason, however, for the difficulty in predicting compound typicality from component typicality. Even if we adhere to the no peeking principle and

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concepts and categories Table 3.1 . Some Theories of Concept Combination Model

Domain

Representation of Head Noun

Schemas Noun-Noun and (attribute-value lists Noun-Relativewith attributes Clause NPs varying in (conjunctive NPs, importance) e.g., sports that are also games) Schemas Smith, Osherson, Rips, Simple (attribute-value lists & Keane (1 988) Adjective-Noun NPs with distributions of (e.g., red apple) values and weighted attributes) Schemas (lists of slots Murphy (1 988) Adj-Noun and and fillers) Noun-Noun NPs (esp. nonpredicating NPs, e.g., corporate lawyer) Schemas Franks (1 995 ) Adj-Noun and (attribute-value Noun-Noun NPs structures with (esp. privatives, e.g., default values for fake gun) some attributes) Gagne´ & Shoben Noun-Noun NPs Lexical representations (1 997) containing distributions of relations in which nouns figure Wisniewski (1 997) Noun-Noun NPs Schemas (lists of slots and fillers, including roles in relevant events) Hampton (1 987)

stick to clear modifier-head constructions, the typicality of a combination can depend on “emergent” properties that are not part of the representation of either component (Hastie, Schroeder, & Weber, 1 990; Kunda, Miller, & Claire, 1 990; Medin & Shoben, 1 988; Murphy, 1 988). For example, you may never have encountered, or even thought

Modification Process Modifier and head contribute values to combination on the basis of importance and centrality Adjective shifts value on relevant attribute in head and increases weight on relevant dimension Modifier fills relevant slot; then representation is “cleaned up” on the basis of world knowledge Attribute-values of modifier and head are summed with modifier potentially overriding or negating head values Nouns are bound as arguments to relations (e.g., flu virus = virus causing flu) 1 . Modifier noun is bound to role in head noun (e.g., truck soap = soap for cleaning trucks) 2. Modifier value is reconstructed in head noun (e.g., zebra clam = clam with stripes) 3 . Hybridization (e.g., robin canary = cross between robin and canary)

about, a smoky apple (so extensional feedback does not inform your conception of the noun phrase), but nevertheless it is plausible to suppose that smoky apples are not good tasting. Having a bad taste, however, is not a usual property of (and is not likely to be stored as part of a concept for) either apples or smoky things; on the contrary,

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many apples and smoky things (e.g., smoked meats, cheese, fish) are often quite good tasting. If you agree with our assessment that smoky apples are likely to be bad tasting, that is probably because you imagine a way in which apples could become smoky (being caught in a kitchen fire, perhaps) and you infer that under these circumstances the apple would not be good to eat. The upshot is that the properties of a combination can depend on complex inductive or explanatory inferences (Johnson & Keil, 2000; Kunda et al., 1 990). If these properties affect the typicality of an instance with respect to the combination, then there is little hope of a simple model of this phenomenon. No current theory comes close to providing an adequate and general account of these processes. inferential versus atomistic concepts

Research on the typicality structure of noun phrases is of interest for what it can tell us about people’s inference and problemsolving skills. However, because these processes are quite complex – drawing on general knowledge and inductive reasoning to produce emergent information – we can not predict noun phrase typicality in other than a limited range of cases. For much the same reason, typicality structure does not appear very helpful in understanding how people construct the meaning of a noun phrase while reading or listening. By themselves, emergent properties do not rule out the possibility of a model that explains how people derive the meaning of a noun phrase from the meaning of its components. Compositionality does not require that all aspects of the noun phrase’s meaning are parts of the components’ meanings. It is sufficient to find some computable function from the components to the composite that is simple enough to account for people’s understanding (see Partee, 1 995 , for a discussion of types of composition). The trouble is that if noun phrases’ meanings require theory construction and problem solving, such a process is unlikely to explain the ease and speed with which we usually understand them in ongoing speech.

Of course, we have only considered the role of schemas or prototypes in concept combination, but it is worth noting that many of the same problems with semantic composition affect other contemporary theories, such as latent semantic analysis (Landauer & Dumais, 1 997), which take a global approach to meaning. Latent semantic analysis takes as input a table of the frequencies with which words appear in specific contexts. In one application, for example, the items comprise about 60,000 word types taken from 3 0,000 encyclopedia entries, and the table indicates the frequency with which each word appears in each entry. The analysis then applies a technique similar to factor analysis to derive an approximately 3 00-dimensional space in which each word appears as a point and in which words that tend to co-occur in context occupy neighboring regions in the space. Because this technique finds a best fit to a large corpus of data, it is sensitive to indirect connections between words that inform their meaning. However, the theory has no clear way to derive the meaning of novel sentences. Although latent semantic analysis could represent a sentence as the average position of its component words, this would not allow it to capture the difference between, say, The financier dazzled the movie star versus The movie star dazzled the financier, which depend on sentence structure. In addition, the theory uses the distance between two words in semantic space to represent the relation between them, and so the theory has trouble with semantic relations that, unlike distances, are asymmetric. It is unclear, for example, how it could cope with the fact that father implies parent but parent does not imply father. On the one hand, online sentence understanding is a rapid, reliable process. On the other hand, the meaning of even simple adjective-noun phrases seems to require heady inductive inferences. Perhaps we should distinguish, then, between the interpretation of a phrase or sentence and its comprehension (Burge, 1 999). On this view, comprehension gives us a more or less

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immediate understanding of novel phrases based primarily on the word meaning of the components and syntactic/semantic structure. Interpretation, by contrast, is a potentially unlimited process relying on the result of comprehension plus inference and general knowledge. The comprehension/interpretation distinction may be more of a continuum than a dichotomy, but the focus on the interpretation end of the continuum means that research on concepts is difficult to apply to comprehension. As we have just noticed, it is hard, if not impossible, to compute the typicality structure of composites. So if we want something readily computable in order to account for comprehension, we have to look to something simpler than typicality structures (and the networks, prototypes, schemas, or theories that underlie them). One possibility (Fodor, 1 994, 1 998) is to consider a representation in which word meanings are mental units not much different from the words themselves, and whose semantic values derive from (unrepresented) causal connections to their referents. generic noun phrases

Even if we abandon typicality structures as accounts of comprehension, however, it does not follow that these structures are useless in explaining all linguistic phenomena. More recent research on two fronts seems to us to hold promise for interactions between psychological and linguistic theories. First, there are special constructions in English that, roughly speaking, describe default characteristics of members of a category. For example, “Lions have manes” means (approximately) that having a mane is a characteristic property of lions. Bare plural noun phrases (i.e., plurals with no preceding determiners) are one way to convey such a meaning as we have just noticed, but indefinite singular sentences (“A lion has a mane”) and definite singular sentences (“The lion – Panthera leo – has a mane”) can also convey the same idea in some of their senses. These generic sentences seem to have normative content. Unlike “Most lions have manes,”

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generic sentences seem to hold despite the existence of numerous exceptions; “Lions have manes” seems to be true even though most lions (e.g., female and immature lions) do not have manes (see Krifka et al., 1 995 , for an introduction to generic sentences). There is an obvious relation between the truth or acceptability of generic sentences and the typicality structure of categories because the typical properties of a category are those that appear in true generic sentences. Of course, as Krifka et al. noted, this may simply be substituting one puzzle (the truth conditions of generic sentences) for another (the nature of typical properties), but this may be one place where linguistic and cognitive theories might provide mutual insight. Research by Susan Gelman and her colleagues (see Gelman, 2003 , for a thorough review) suggests that generic sentences are a frequent way for caregivers to convey category information to children. Four-yearolds differentiate sentences with bare plurals (“Lions have manes”) from those explicitly quantified by “all” or “some” in comprehension, production, and inference tasks (Gelman, Star, & Flukes, 2002; Hollander, Gelman, & Star, 2002). It would be of interest to know, however, at what age, and in what way, children discriminate generics from accidental generalizations – for example, when they first notice the difference between “Lions have manes” and “Lions frequently have manes” or “Most lions have manes.” polysemy

A second place to look for linguistic-cognitive synergy is in an account of the meanings of polysemous words. Linguists (e.g., Lyons, 1 977, Chap. 1 3 ) traditionally distinguish homonyms such as “mold,” which have multiple unrelated meanings (e.g., a form into which liquids are poured vs. a fungus), from polysemous terms such as “line,” which have multiple related meanings (e.g., a geometric line vs. a fishing line vs. a line of people, etc.). What makes polysemous terms interesting to psychologists in this area is that the relations among their meanings often possess a kind of typicality structure of their

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own. This is the typicality of the senses of the expression rather than the typicality of the referents of the expression and is thus a type of higher-level typicality phenomenon. Figure 3 .2 illustrates such a structure for the polysemous verb “crawl,” as analyzed by Fillmore and Atkins (2000). A rectangle in the figure represents each sense or use and includes both a brief label indicating its distinctive property and an example from British corpuses. According to Fillmore and Atkins, the central meanings for crawl have to do with people or creatures moving close to the ground (these uses appear in rectangles with darker outlines in the figure). But there are many peripheral uses – for example, time moving slowly (“The hours seemed to crawl by”) and creatures teeming about (“The picnic supplies crawled with ants”). The central meanings are presumably the original ones with the peripheral meanings derived from these by a chaining process. Malt, Sloman, Gennari, Shi, and Wang (1 999) observed similar instances of chaining in people’s naming of artifacts, such as bottles and bowls, and it is possible that the gerrymandered naming patterns reflect the polysemy of the terms (e.g., “bottle”) rather than different uses of the same meaning. As Figure 3 .2 shows, it is not easy to distinguish different related meanings (polysemy) from different uses of the same meaning (contextual variation) and from different unrelated meanings (homonymy). Some research has attacked the issue of whether people store each of the separate senses of a polysemous term (Klein & Murphy, 2002) or store only the core meaning, deriving the remaining senses as needed for comprehension (Caramazza & Grober, 1 976; Franks, 1 995 ). Conflicting evidence in this respect may be due to the fact that some relations between senses seem relatively productive and derivable (regular polysemy, such as the relationship between terms for animals and their food products, e.g., the animal meaning of “lamb” and its menu meaning), whereas other senses seem ad hoc (e.g., the relation between “crawl” = moving close to the ground and “crawl” =

teeming with people in Figure 3 .2). Multiple mechanisms are likely to be at work here. summary

We do not mean to suggest that the only linguistic applications of psychologists’ “concepts” are in dealing with interpretation, generic phrases, and polysemy – far from it. There are many areas, especially in developmental psycholinguistics, that hold the promise of fruitful interactions but that we cannot review here. Nor are we suggesting that investigators in this area give up the attempt to study the use of concepts in immediate comprehension. However, concepts for comprehension seem to have different properties from the concepts that figure in the other functions we have discussed, and researchers need to direct more attention to the interface between them.

Theories, Modules, and Psychometaphysics We have seen, so far, some downward pressure on cognitive theories to portray human concepts as mental entities that are as simple and streamlined as possible. This pressure comes not only from the usual goal of parsimony but also from the role that concepts play in immediate language comprehension. However, there is also a great deal of upward pressure – pressure to include general knowledge about a category as part of its representation. For example, the presence of emergent properties in concept combinations suggests that people use background knowledge in interpreting these phrases. Similarly, people may bring background knowledge and theories to bear in classifying things even when they know a decision rule for the category. Consider psychodiagnostic classification. Although DSM-IV (the official diagnostic manual of the American Psychological Association) is atheoretical and organized in terms of rules, there is clear evidence that clinicians develop theories of disorders and, contra DSM-IV, weight causally central symptoms more than causally peripheral symptoms (e.g., Kim & Ahn, 2002a).

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Figure 3.2 . The meanings of crawl: Why it is difficult to distinguish different related meanings (polysemy) from different uses of the same meaning (contextual variation) and from different unrelated meanings (homonymy). Adapted from Fillmore & Alking (2000) by permission of Oxford University Press.

The same holds for laypersons (e.g., Furnham, 1 995 ; Kim & Ahn, 2002b). In this section, we examine the consequences of expanding the notion of a concept to include theoretical information about a category. In the case of the natural categories, this information is likely to be causal because people probably view physical causes as shaping and maintaining these categories. For artifacts, the relevant information may be the intentions of the person creating the object (e.g., Bloom, 1 996). The issues we raise here concern the content and packaging of these causal beliefs. The first of these issues focuses on people’s beliefs about the locus of these causal forces – what we called “psychometaphysics.” At one extreme, people may believe that each natural category is associated with a single source, concentrated within a

category instance, that controls the nature of that instance. The source could determine, among other things, the instance’s typical properties, its category membership, and perhaps even the conditions under which it comes into and goes out of existence. Alternatively, people may believe that the relevant causal forces are more like a swarm – not necessarily internal to an instance, nor necessarily emanating from a unitary spot – but shaping the category in aggregate fashion. The second issue has to do with the cognitive divisions that separate beliefs about different sorts of categories. People surely believe that the causes that help shape daisies differ in type from those that shape teapots. Lay theories about flowers and other living things include at least crude information about specifically biological properties,

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whereas lay theories of teapots and other artifacts touch instead on intended and actual functions. However, how deep do these divisions go? On the one hand, beliefs about these domains could be modular (relatively clustered, relatively isolated), innate, universal, and local to specific brain regions. On the other hand, they may be free floating, learned, culturally specific, and distributed across cortical space. This issue is important to us because it ultimately affects whether we can patch up the “semantic memory” marriage. Essentialism and Sortalism psychological essentialism

What’s the nature of people’s beliefs about the causes of natural kinds? One hypothesis is that people think there is something internal to each member of the kind – an essence – that is responsible for its existence, category membership, typical properties, and other important characteristics (e.g., Atran, 1 998; Gelman & Hirschfeld, 1 999; Medin & Ortony, 1 989). Of course, it is unlikely that people think that all categories of natural objects have a corresponding essence. There is probably no essence of pets, for example, that determines an animal’s pet status. However, for basic-level categories, such as dogs or gold or daisies, it is tempting to think that something in the instance determines crucial aspects of its identity. Investigators who have accepted this hypothesis are quick to point out that the theory applies to people’s beliefs and not to the natural kinds themselves. Biologists and philosophers of science agree that essentialism will not account for the properties and variations that real species display, in part because the very notion of species is not coherent (e.g., Ghiselin, 1 981 ; Hull, 1 999). Chemical kinds, for example, gold, may conform much more closely to essentialist doctrine (see Sober, 1 980). Nevertheless, expert opinion is no bar to laypersons’ essentialist views on this topic. In addition, psychological essentialists have argued that people probably do not have a fully fleshed out explanation of what the essence is. What they have, on this hypothesis, is an

IOU for a theory: a belief that there must be something that plays the role of essence even though they can not supply a description of it (Medin & Ortony, 1 989). Belief in a hypothetical, minimally described essence may not seem like the sort of thing that could do important cognitive work, but psychological essentialists have pointed out a number of advantages that essences might afford, especially to children. The principal advantage may be induction potential. Medin (1 989) suggested that essentialism is poor metaphysics but good epistemology in that it may lead people to expect that members of a kind will share numerous, unknown properties – an assumption that is sometimes correct. In short, essences have a motivational role to play in getting people to investigate kinds’ deeper characteristics. Essences also explain why category instances seem to run true to type – for example, why the offspring of pigs grow up to be pigs rather than cows. They also explain the normative character of kinds (e.g., their ability to support inductive arguments and their ability to withstand exceptions and superficial changes) as well as people’s tendency to view terms for kinds as well defined. Evidence for essentialism tends to be indirect. There are results that show that children and adults do in fact hold the sorts of beliefs that essences can explain. By the time they reach first or second grade, children know that animals whose insides have been removed are no longer animals, that baby pigs raised by cows grow up to be pigs rather than cows (Gelman & Wellman, 1 991 ), and that cosmetic surgery does not alter basic-level category membership (Keil, 1 989). Research on adults also shows that “deeper” causes – those that themselves have few causes but many effects – tend to be more important in classifying than shallower causes (Ahn, 1 998; Sloman, Love, & Ahn, 1 998). However, results like these are evidence for essence only if there are no better explanations for the same results, and it seems at least conceivable that children and adults make room for multiple types and sources

concepts and categories

of causes that are not yoked to an essence. According to Strevens (2000), for example, although people’s reasoning and classifying suggest that causal laws govern natural kinds, it may be these laws alone, rather than a unifying essence, that are responsible for the findings. According to essentialists, people think there is something (an essence) that is directly or indirectly responsible for the typical properties of a natural kind. According to Strevens’ minimalist alternative, people think that for each typical property there is something that causes it and that something may vary for different properties. It is important to settle this difference – the presence or absence of a unique central cause – if only because the essentialist claim is the stronger one. Essentialists counter that both children and adults assume a causal structure consistent with essence (see Braisby, Franks, & Hampton, 1 996; Diesendruck & Gelman, 1 999; and Kalish, 1 995 , 2002, for debate on this issue). One strong piece of evidence for essentialism is that participants who have successfully learned artificial, family resemblance categories (i.e., those in which category members have no single feature in common) nevertheless believe that each category contained a common, defining property (Brooks & Wood, as cited by Ahn et al., 2001 ). Other studies with artificial “natural” kinds have directly compared essentialist and nonessentialist structures but have turned in mixed results (e.g., Rehder & Hastie, 2001 ). It is possible that explicit training overrides people’s natural tendency to think in terms of a common cause. In the absence of more direct evidence for essence, the essentialist-minimalist debate is likely to continue (see Ahn et al., 2001 ; Sloman & Malt, 2003 ; and Strevens, 2001 , for the latest salvos in this dispute). Indeed, the authors of this chapter are not in full agreement. Medin finds minimalism too unconstrained, whereas Rips opines that essentialism suffers from the opposite problem. Adding a predisposition toward parsimony to the minimalist view seems like a constructive move, but such a move would shift minimalism considerably closer to es-

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sentialism. Ultimately, the issue boils down to determining to what extent causal understandings are biased toward the assumption of a unique, central cause for a category’s usual properties. sortalism

According to some versions of essentialism, an object’s essence determines not only which category it belongs to but also the object’s very identity. According to this view, it is by virtue of knowing that Fido is a dog that you know (in principle) how to identify Fido over time, how to distinguish Fido from other surrounding objects, and how to determine when Fido came into existence and when he will go out of it. In particular, if Fido happens to lose his dog essence, then Fido not only ceases to be a dog, but he also ceases to exist entirely. As we noted in discussing essentialism, not all categories provide these identity conditions. Being a pet, for example, doesn’t lend identity to Fido because he may continue to survive in the wild as a nonpet. According to one influential view (Wiggins, 1 980), the critical identity-lending category is the one that answers the question What is it? for an object, and because basic-level categories are sometimes defined in just this way, basic-level categories are the presumed source of the principles of identity. (Theories of this type usually assume that identity conditions are associated with just one category for each object because multiple identity conditions lead to contradictions; see Wiggins, 1 980). Contemporary British philosophy tends to refer to such categories as sortals, however, and we adopt this terminology here. Sortalism plays an important role in current developmental psychology because developmentalists have used children’s mastery of principles of identity to decide whether these children possess the associated concept. In some well-known studies, Xu and Carey (1 996) staged for infants a scene in which a toy duck appears from one side of an opaque screen and then returns behind it. A toy truck next emerges from the other side of the screen and then returns to its hidden position. Infants habituate after

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a number of encores of this performance, at which time the screen is removed to reveal both the duck and truck (the scene that adults expect) or just one of the objects (duck or truck). Xu and Carey reported that younger infants (e.g., 1 0-month-olds) exhibit no more surprise at seeing one object than at seeing two, whereas older infants (and adults) show more surprise at the oneobject tableau. Xu and Carey also showed in control experiments that younger and older infants perform identically if they see a preview of the two starring objects together before the start of the performance. The investigators infer that the younger infants lack the concepts DUCK and TRUCK because they are unable to use a principle of identity for these concepts to discern that a duck cannot turn into a truck while behind the screen. Xu and Carey’s experiments have sparked a controversy about whether the experimental conditions are simple enough to allow babies to demonstrate their grip on object identity (see Wilcox & Baillargeon, 1 998; Xu, 2003 ), but for present purposes what is important is the assumption that infants’ inability to reidentify objects over temporal gaps implies lack of the relevant concepts. Sortal theories impose strong constraints on some versions of essentialism. We noted that one of essentialism’s strong points is its ability to explain some of the normative properties of concepts – for example, the role concepts play in inductive inferences. However, sortalism places some restrictions on this ability. Members of sortal categories can not lose their essence without losing their existence, even in counterfactual circumstances. This means that if we are faced with a premise such as Suppose dogs can bite through wire . . . , we cannot reason about this supposition by assuming the essence of dogs has changed in such a way as to make dogs stronger. A dog with changed essence is not a superdog, according to sortalism, but rather has ceased to exist (see Rips, 2001 ). For the same reason, it is impossible to believe without contradiction both that basic-level categories are sortals and that objects can shift from one basic-level category to another.

These consequences of sortalism may be reasonable ones, but it is worth considering the possibility that sortalism – however well it fares as a metaphysical outlook – incorrectly describes people’s views about object identity. Although objects typically do not survive a leap from one basic-level category to another, it may not be impossible for them to do so. Blok, Newman, and Rips (in press) and Liittschwager (1 995 ) gave participants scenarios that described novel transformations that sometimes altered the basic-level category. In both studies, participants were more likely to agree that the transformed object was identical to the original if the transformational distance was small. However, these judgments could not always be predicted by basic-level membership. Results from these sci-fi scenarios should be treated cautiously, but they suggest that people think individual objects have an integrity that does not necessarily line up with their basic-level category. Although this idea may be flawed metaphysics, it is not unreasonable as psychometaphysics. People may think that individuals exist as the result of local causal forces – forces that are only loosely tethered to basic-level kinds. As long as these forces continue to support the individual’s coherence, it can exist even if it finds itself in a new basic-level category. Of course, not all essentialists buy into this link between sortalism and essentialism. For example, people might believe that an individual has both a category essence and a history and other characteristics that make it unique. Gutheil and Rosengren (1 996) hypothesized that objects have two difference essences, one for membership and another for identity. Just how individual identity and kind identity play out under these scenarios could then be highly variable. Domain Specificity The notion of domain specificity has served to organize a great deal of research on conceptual development. For example, much of the work on essentialism has been conducted in the context of exploring children’s na¨ıve biology (see also Au, 1 994; Carey, 1 995 ; Gopnik & Wellman, 1 994; Spelke, Phillips,

concepts and categories

& Woodward, 1 995 ). Learning in a given domain may be guided by certain skeletal principles, constraints, and (possibly innate) assumptions about the world (see Gelman, 2003 ; Gelman & Coley, 1 990; Keil, 1 981 ; Kellman & Spelke, 1 983 ; Markman, 1 990; Spelke, 1 990). Carey’s (1 985 ) influential book presented a view of knowledge acquisition as built on framework theories that entail ontological commitments in the service of a causal understanding of real-world phenomena. Two domains can be distinguished from one another if they represent ontologically distinct entities and sets of phenomena and are embedded within different causal explanatory frameworks. These ontological commitments serve to organize knowledge into domains such as naive physics (or mechanics), naive psychology, or naive biology (e.g., see Au, 1 994; Carey, 1 995 ; Gelman & Koenig, 2001 ; Gopnik & Wellman, 1 994; Hatano & Inagaki, 1 994; Keil, 1 994; Spelke et al., 1 995 ; Wellman & Gelman, 1 992). In the following, we focus on one candidate domain, na¨ıve biology.

folk biology and universals

There is fairly strong evidence that all cultures partition local biodiversity into taxonomies whose basic level is that of the “generic species” (Atran, 1 990; Berlin et al., 1 973 ). Generic species often correspond to scientific species (e.g., elm, wolf, robin); however, for the large majority of perceptually salient organisms (see Hunn, 1 999), such as vertebrates and flowering plants, a scientific genus frequently has only one locally occurring species (e.g., bear, oak). In addition to the spontaneous division of local flora and fauna into generic species, cultures seem to structure biological kinds into hierarchically organized groups, such as white oak/oak/tree. Folk biological ranks vary little across cultures as a function of theories or belief systems (see Malt, 1 994, for a review). For example, in studies with Native American and various U.S. and Lowland Maya groups, correlations between folk taxonomies and classical evolutionary taxonomies of the local fauna and flora average r = .75 at the generic species level

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and about 0.5 with higher levels included (Atran, 1 999; Bailenson et al., 2002; Medin et al., 2002). Much of the remaining variance owes to obvious perceptual biases (Itza’ Maya group bats with birds in the same life form) and local ecological concerns. Contrary to received notions about the history and cross-cultural basis for folk biological classification, utility does not appear to drive folk taxonomies (cf. Berlin et al., 1 973 ). These folk taxonomies also appear to guide and constrain reasoning. For example, Coley, Medin, and Atran (1 997) found that both Itza’ Maya and U.S. undergraduates privilege the generic species level in inductive reasoning. That is, an inference from swamp white oak to all white oaks is little if any stronger than an inference from swamp white oak to all oaks. Above the level of oak, however, inductive confidence takes a sharp drop. In other words, people in both cultures treat the generic level (e.g., oak) as maximizing induction potential. The results for undergraduates are surprising because the original Rosch et al. (1 976) basic-level studies had suggested that a more abstract level (e.g., TREE) acted as basic for undergraduates and should have been privileged in induction. That is, there is a discrepancy between results with undergraduates on basicness in naming, perceptual classification, and feature listing, on the one hand, and inductive inference, on the other hand. Coley et al. (1 997) suggested that the reasoning task relies on expectations associated with labeling rather than knowledge and that undergraduates may know very little about biological kinds (see also Wolff, Medin, & Pankratz, 1 999). Medin and Atran (in press) cautioned against generalizing results on biological thought from undergraduates because most have relatively little first-hand experience with nature.

interdomain differences

One of the most contested domain distinctions, and one that has generated much research, is that between psychology and biology (e.g., Au & Romo, 1 996, 1 999; Carey, 1 991 ; Coley, 1 995 ; Gelman, 2003 ; Hatano

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& Inagaki, 1 996, 2001 ; Inagaki, 1 997; Inagaki & Hatano, 1 993 , 1 996; Johnson & Carey, 1 998; Keil, 1 995 ; Keil, Levin, Richman, G. Gutheil, 1 999; Rosengren et al., 1 991 ; Springer & Keil, 1 989, 1 991 ). Carey (1 985 ) argued that children initially understand biological concepts such as ANIMAL in terms of folk psychology, treating animals as similar to people in having beliefs and desires. Others (e.g., Keil, 1 989) argued that young children do have biologically specific theories, albeit more impoverished than those of adults. For example, Springer and Keil (1 989) showed that preschoolers think biological properties are more likely to be passed from parent to child than are social or psychological properties. They argued that this implies that the children have a biology-like inheritance theory. The evidence concerning this issue is complex. On the one hand, Solomon, Johnson, Zaitchik, and Carey (1 996) claimed that preschoolers do not have a biological concept of inheritance because they do not have an adult’s understanding of the biological causal mechanism involved. On the other hand, there is growing cross-cultural evidence that 4to 5 -year-old children believe (like adults) that the category membership of animals and plants follows that of their progenitors regardless of the environment in which the progeny matures (e.g., progeny of cows raised with pigs, acorns planted with apple seeds) (Atran et al., 2001 ; Gelman & Wellman, 1 991 ; Sousa et al., 2002). Furthermore, it appears that Carey’s (1 985 ) results on psychology versus biology may only hold for urban children who have little intimate contact with nature (Atran, et al., 2001 ; Ross et al., 2003 ). Altogether, the evidence suggests that 4- to 5 -year-old children do have a distinct biology, although perhaps one without a detailed model of causal mechanisms (see Rozenbilt & Keil, 2002, for evidence that adults also only have a superficial understanding of mechanisms). domains and brain regions

Are these hypothesized domains associated with dedicated brain structure? There is intriguing evidence concerning category-

specific deficits in which patients may lose their ability to recognize and name category members in a particular domain of concepts. For example, Nelson (1 946) reported a patient who was unable to recognize a telephone, a hat, or a car but could identify people and other living things (the opposite pattern is also observed and is more common). These deficits are consistent with the idea that anatomically and functionally distinct systems represent living versus nonliving things (Sartori & Job, 1 988). An alternative claim (e.g., Warrington & Shallice, 1 984) is that these patterns of deficits are due to the fact that different kinds of information aid in categorizing different kinds of objects. For example, perceptual information may be relatively more important for recognizing living kinds and functional information more important for recognizing artifacts (see Devlin et al., 1 998; Farah & McClelland, 1 991 , for computational implementations of these ideas). Although the weight of evidence appears to favor the kinds of information view (see Damasio et al., 1 996; Forde & Humphreys, in press; Simmons & Barsalou, 2003 ), the issue continues to be debated (see Caramazza & Shelton, 1 998, for a strong defense of the domain specificity view). domains and memory

The issue of domain specificity returns us to one of earlier themes: Does memory organization depend on the meaning? We have seen that early research on semantic memory was problematic in this respect because many of the findings that investigators used to support meaning-based organization had alternative explanations. Generalpurpose decision processes could produce the same pattern of results even if the information they operated on was haphazardly organized. Of course, in those olden days, semantic memory was supposed to be a hierarchically organized network like that in Figure 3 .1 ; the network clustered concepts through shared superordinates and properties but was otherwise undifferentiated. Modularity and domain specificity offer a new take on semantic-based memory structure – a partition of memory space into

concepts and categories

distinct theoretical domains. Can large-scale theories like these support memory organization in a more adequate fashion than homogeneous networks? One difficulty in merging domain specificity with memory structure is that domain theories do not taxonomize categories – they taxonomize assumptions. What differentiates domains is the set of assumptions or warrants they make available for thinking and reasoning (see Toulmin, 1 95 8, for one such theory), and this means that a particular category of objects usually falls in more than one domain. To put it another way, domain-specific theories are “stances” (Dennett, 1 971 ) or “construals” (Keil, 1 995 ) that overlap in their instances. Take the case of people. The naive psychology domain treats people as having beliefs and goals that lend themselves to predictions about actions (e.g., Leslie, 1 987; Wellman, 1 990). The naive physics domain treats people as having properties such as mass and velocity that warrant predictions about support and motion (e.g., Clement, 1 983 ; McCloskey, 1 983 ). The naive law school domain treats people as having properties, such as social rights and responsibilities, that lead to predictions about obedience or deviance (e.g., Fiddick, Cosmides, & Tooby, 2000). The naive biology domain (at least in the Western adult version) treats people as having properties such as growth and self-animation that lead to expectations about behavior and development. In short, each ordinary category may belong to many domains. If domains organize memory, then longterm memory will have to store a concept in each of the domains to which it is related. Such an approach makes some of the difficulties of the old semantic memory more perplexing. Recall the issue of identifying the same concept across individuals (see “Concepts as Positions in Memory Structures”). Memory modules have the same problem, but they add to it the dilemma of identifying concepts within individuals. How do you know that PEOPLE in your psychology module is the same concept as PEOPLE in your physics module and PEOPLE in your law school module? Similarity is out (be-

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cause the modules will not organize them in the same way), spelling is out (both concepts might be tied to the word “people” in an internal dictionary, but then fungi and metal forms are both tied to the word “mold”), and interconnections are out (because they would defeat the idea that memory is organized by domain). We can not treat the multiple PEOPLE concepts as independent either because it is important to get back and forth between them. For example, the rights and responsibilities information about people in your law school module has to get together with the goals and desires information about people in your psychology module in case you have to decide, together with your fellow jury members, whether the killing was a hate crime or was committed with malice aforethought. It is reasonable to think that background theories provide premises or grounds for inferences about different topics, and it is also reasonable to think that these theories have their “proprietary concepts.” However, if we take domain-specific modules as the basis for memory structure – as a new semantic memory – we also have to worry about nonproprietary concepts. We have argued that there must be such concepts because we can reason about the same thing with different theories. Multiple storage is a possibility if you are willing to forego memory economy and parsimony and if you can solve the identifiability problem that we discussed in the previous paragraph. Otherwise, these domain-independent concepts have to inhabit a memory space of their own, and modules can not be the whole story. summary

We seem to be arriving at a skeptical position with respect to the question of whether memory is semantically organized, but we need to be clear about what is and what is not in doubt. What we doubt is that there is compelling evidence that long-term memory is structured in a way that mirrors lexical structure as in the original semantic memory models. We do not doubt that memory reflects meaningful relations among concepts, and it is extremely plausible that these

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relations depend to some extent on word meanings. For example, there may well be a relation in memory that links the concept TRUCKER with the concept BEER, and the existence of this link is probably due in part to the meaning of “trucker” and “beer.” What is not so clear is whether memory structure directly reflects the sort of relations that, in linguistic theory, organizes the meaning of words (where, e.g., “trucker” and “beer” are probably not closely connected). We note, too, that we have not touched (and we do not take sides on) two related issues, which are themselves subjects of controversy. One of these residual issues is whether there is a split in memory between (1 ) general knowledge and (2) personally experienced information that is local to time and place. Semantic memory (Tulving, 1 972) or generic memory (Hintzman, 1 978) is sometimes used as a synonym for general knowledge in this sense, and it is possible that memory is partitioned along the lines of this semantic/episodic difference, even though the semantic side is not organized by lexical content. The controversy in this case is how such a dual organization can handle learning of “semantic” information from “episodic” encounters (see Tulving, 1 984, and his critics in the same issue of Behavioral and Brain Sciences, for the ins and outs of this debate). The second issue that we are shirking is whether distributed brands of connectionist models can provide a basis for meaningbased memory. One reason for shirking is that distributed organization means that concepts such as DAISY and CUP are not stored according to their lexical content. Instead, parts of the content of each concept are smeared across memory in overlapping fashion. It is possible, however, that at a subconcept level – at the level of features or hidden units – memory has a semantic dimension, and we must leave this question open.

Conclusions and Future Directions Part of our charge was to make some projections about the future of research on

concepts. We do not recommend a solemn attitude toward our predictions. However, there are several trends that we have identified and, barring unforeseen circumstances (never a safe assumption), these trends should continue. One property our nominations share is that they uniformly broaden the scope of research on concepts. Here’s our shortlist. Sensitivity to Multiple Functions The prototypical categorization experiment involves training undergraduates for about an hour and then giving transfer tests to assess what they have learned. This practice is becoming increasingly atypical, even among researchers studying artificially constructed categories in the lab. More recently, researchers have studied functions other than categorization, as well as interactions across functions. (See also Solomon et al., 1 999.) Broader Applications of Empirical Generalizations and Computational Models As a wider range of conceptual functions comes under scrutiny, new generalizations emerge and computational models face new challenges (e.g., Yamauchi et al., 2002). Both developments set the stage for better bridging to other contexts and applications. This is perhaps most evident in the area of cognitive neuroscience, where computational models have enriched studies of multiple categorization and memory systems (and vice versa). Norman, Brooks, Coblenz, and Babcock (1 992) provided a nice example of extensions from laboratory studies to medical diagnosis in the domain of dermatology. Greater Interactions between Work on Concepts and Psycholinguistic Research We have pressed the point that research on concepts has diverged from psycholinguistics because two different concepts of concepts seem to be in play in these fields. However, it cannot be true that the concepts we use in online sentence understanding are unrelated to the concepts we employ in

concepts and categories

reasoning and categorizing. There is an opportunity for theorists and experimenters here to provide an account of the interface between these functions. One possibility, for example, is to use sentence comprehension techniques to track the way that the lexical content of a word in speech or text is transformed in deeper processing (see Pinango, Zurif, & Jackendoff, 1 999, for one effort in this direction). Another type of effort at integration is Wolff and Song’s (2003 ) work on causal verbs and people’s perception of cause in which they contrast predictions derived from cognitive linguistics with those from cognitive psychology. Greater Diversity of Participant Populations Although research with U.S. undergraduates at major universities will probably never go out of style (precedent and convenience are two powerful staying forces), we expect the recent increase to continue in the use of other populations. Work by Nisbett and his associates (e.g., Nisbett & Norenzayan, 2002; Nisbett, Peng, Choi, & Norenzayan, 2001 ) has called into question the idea that basic cognitive processes are universal, and categories and conceptual functions are basic cognitive functions. In much of the work by Atran, Medin, and their associates, undergraduates are the “odd group out” in the sense that their results deviate from those of other groups. In addition, cross-linguistic studies are often an effective research tool for addressing questions about the relationship between linguistic and conceptual development (e.g., Waxman, 1 999). More Psychometaphysics An early critique of the theory theory is that it suffered from vagueness and imprecision. As we have seen in this review, however, this framework has led to more specific claims (e.g., Ahn’s causal status hypothesis) and the positions are clear enough to generate theoretical controversies (e.g., contrast Smith, Jones, & Landau, 1 996 with Gelman, 2000, and Booth & Waxman, 2002, in press, with Smith, Jones, Yoshida, & Colunga, 2003 ). It

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is safe to predict even greater future interest in these questions. All of the Above in Combination Concepts and categories are shared by all the cognitive sciences, and so there is very little room for researchers to stake out a single paradigm or subtopic and work in blissful isolation. Although the idea of a semantic memory uniting memory structure, lexical organization, and categorization may have been illusory, this does not mean that progress is possible by ignoring the insights on concepts that these perspectives (and others) provide. We may see further fragmentation in the concepts of concepts, but it will still be necessary to explore the relations among them. Our only firm prediction is that the work we will find most exciting will be research that draws on multiple points of view.

Acknowledgments Preparation of this chapter was supported by grants NSF SBR 9983 260 and NSF SES9907424. The authors also want to thank Serge Blok, Rob Goldstone, Keith Holyoak, Ji Son, and Sandra Waxman for comments on an earlier version of the chapter.

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CHAPTER 4

Approaches to Modeling Human Mental Representations: What Works, What Doesn’t, and Why Leonidas A. A. Doumas John E. Hummel

Relational Thinking A fundamental aspect of human intelligence is the ability to acquire and manipulate relational concepts. Examples of relational thinking include our ability to appreciate analogies between seemingly different objects or events (e.g., Gentner, 1 983 ; Gick & Holyoak, 1 980, 1 983 ; Holyoak & Thagard, 1 995 ; see Holyoak, Chap. 6), our ability to apply abstract rules in novel situations (e.g., Smith, Langston, & Nisbett, 1 992), our ability to understand and learn language (e.g., Kim, Pinker, Prince, & Prasada, 1 991 ), and even our ability to appreciate perceptual similarities (e.g., Goldstone, Medin, & Gentner, 1 991 ; Hummel, 2000; Hummel & Stankiewicz, 1 996; Palmer, 1 978; see Goldstone & Son, Chap. 2). Relational thinking is ubiquitous in human cognition, underlying everything from the mundane (e.g., the thought “the mug is on the desk”) to the sublime (e.g., Cantor’s use of set theory to prove that the cardinal number of the reals is greater than the cardinal number of the integers).

Relational thinking is so commonplace that it is easy to assume the psychological mechanisms underlying it are relatively simple. They are not. The capacity to form and manipulate relational representations appears to be a late evolutionary development (Robin & Holyoak, 1 995 ) closely tied to the increase in the size and complexity of the frontal cortex in the brains of higher primates, especially humans (Stuss & Benson, 1 986). Relational thinking also develops relatively late in childhood (see, e.g., Smith, 1 989; Halford, Chap. 22). Along with language, the human capacity for relational thinking is the major factor distinguishing human cognition from the cognitive abilities of other animals (