Rational Constructivism in Cognitive Development

430 Pages·2012·3.879 MB·1-428\430

by  Fei Xu and Tamar Kushnir (Eds.)

Contributors to This Volume
Luca L. Bonatti Natasha Z. Kirkham
E. Bonawitz Tamar Kushnir
Sophie Bridgers Jeff Loucks
Daphna Buchsbaum James Negen
Nicolo Cesana-Arlotti Marjorie Rhodes
Colin R. Dawson Barbara W. Sarnecka
Stephanie Denison Laura Schulz
S. Denison Elizabeth Seiver
Baxter S. Eaves David M. Sobel
Gyorgy Gergely Jessica A. Sommerville
LouAnn Gerken Erno Téglas
Alison Gopnik Michaela B. Upshaw
T.L. Griffiths Fei Xu
Pierre Jacob
VOLUME FORTY THREE
RATIONAL
CONSTRUCTIVISM
IN COGNITIVE
DEVELOPMENT
Volume Editors
FEI XU
Professor, Department of Psychology,
3423 Tolman Hall, University of California,
Berkeley, CA 94720-1650
TAMAR KUSHNIR
Assistant Professor, Department of Human Development,
Cornell University, M Van Rensselaer Hall,
Room G62B, Ithaca, NY 14853-4401
Serial Editor
JANETTE B. BENSON
Department of Psychology,
University of Denver,
Denver, Colorado, USA
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CONTRIBUTORS
Luca L.Bonatti
ICREA, Universitat Pompeu Fabra, Barcelona, Espan~a
E.Bonawitz
DepartmentofPsychology,UniversityofCaliforniaatBerkeley,Berkeley,California,USA
Sophie Bridgers
Institute of HumanDevelopment, Department of Psychology, University of California
at Berkeley,Tolman Hall, Berkeley,CA 94720,USA
Daphna Buchsbaum
Institute of HumanDevelopment, Department of Psychology, University of California
at Berkeley,Tolman Hall, Berkeley,CA 94720,USA
Nicolo(cid:2) Cesana-Arlotti
ICREA, Universitat Pompeu Fabra, Barcelona, Espan~a
Colin R.Dawson
School of information: Science, Technology, and Arts 1040E.4th StreetUniversity of
Arizona, Tucson, AZ 85721-0077, USA
Stephanie Denison
DepartmentofPsychology,UniversityofCalifornia,Berkeley,Berkeley,CA,94720,USA
S.Denison
DepartmentofPsychology,UniversityofCaliforniaatBerkeley,Berkeley,California,USA
Baxter S.Eaves Jr.
Department ofPsychological and BrainSciences 317Life Sciences Building,University of
Louisville, Louisville, Ky40292,USA
Gyo€rgy Gergely
Department of Cognitive Science,Cognitive Development Center, CentralEuropean
University, 1015Budapest, Hattyu(cid:3) u.14,Hungary
LouAnn Gerken
Department of Psychology 1503E University Blvd.University of Arizona, Tucson,
AZ 85721-0068, USA
Alison Gopnik
Institute of HumanDevelopment, Department of Psychology, University of California at
Berkeley, TolmanHall, Berkeley, CA 94720,USA
T. L.Griffiths
DepartmentofPsychology,UniversityofCaliforniaatBerkeley,Berkeley,California,USA
Pierre Jacob
InstitutJeanNicod,UMR8129,CNRS/ENS/EHESS,ecoleNormaleSupérieure,29,rue
d’Ulm,75005 Paris,France
j
ix
x Contributors
Natasha Z. Kirkham
Centre for Brain and Cognitive Development, BirkbeckCollege, University of London,
London,England, UK
Tamar Kushnir
Department of HumanDevelopment, Cornell University,Ithaca, NY 14853
JeffLoucks
Department of Psychology &Center forChild andFamily Well-being, University of
Washington, Campus Box351525, Seattle, WA98195
JamesNegen
Department of Cognitive Sciences,University of California, Irvine,CA 92697-5100
Marjorie Rhodes
Department of Psychology, New YorkUniversity, NewYork, NY 10003
Barbara W.Sarnecka
Department of Cognitive Sciences,University of California, Irvine,CA 92697-5100
Laura Schulz
Department of Brain and CognitiveSciences, Massachusetts Instituteof Technology,
Boston,Massachusetts
Elizabeth Seiver
Institute ofHuman Development, Department of Psychology, University of California at
Berkeley, TolmanHall, Berkeley, CA94720, USA
Patrick Shafto
Department ofPsychological andBrain Sciences 317Life SciencesBuilding, Universityof
Louisville, Louisville, Ky40292,USA
David M.Sobel
Department of Cognitive, Linguistic, andPsychological Sciences, BrownUniversity,
Providence, Rhode Island,USA
JessicaA.Sommerville
Department of Psychology &Center forChild andFamily Well-being, University of
Washington, Campus Box351525, Seattle, WA98195
Erno Tégl(cid:3)as
CognitiveDevelopmentCentre,CentralEuropeanUniversity,H-1015Budapest,Hungary
Michaela B. Upshaw
Department of Psychology &Center forChild andFamily Well-being, University of
Washington, Campus Box351525, Seattle, WA98195
Fei Xu
DepartmentofPsychology,UniversityofCalifornia,Berkeley,Berkeley,CA,94720,USA
PREFACE
Fei Xu1 and Tamar Kushnir2
1UniversityofCalifornia,Berkeley
2CornellUniversity
What Is Rational Constructivism?
The main goal of this volume is to compile a set of papers synthesizing
new research from the last few years, under the umbrella term “a rational
constructivistapproach”tothestudyofcognitivedevelopment.Thepapers
come in three flavors: syntheses of a body of empirical work and its theo-
reticalunderpinnings,explicationsofhowcomputationalmodels(especially
Bayesian models) may help us understand cognitive development, and
philosophical reflections on the research enterprise.
Muchofthisworkwasmotivatedbytheideathatweneedanapproach
to cognitive development that is neither extreme empiricism nor extreme
nativism. Nativist theories have primarily focused on specifying innate
concepts and core knowledge systems, and how abstract, symbolic repre-
sentations underpin notonly ourmature conceptualsystem butalsothat of
infants and young children (Chomsky, 1988; Fodor, 1975; Pinker, 1994;
Spelke, 1994), whereas empiricist theories have focused on specifying
associative learning mechanisms and the graded nature of our learning and
representations (Elman et al., 1996; Karmiloff-Smith, 1992; Smith, 2001).
The inadequacy of both extreme nativist and extreme empiricist views has
led researchers to try to find a substantive middle ground (e.g. Johnson,
2010; Newcombe, 2010).
The new perspective on cognitive development represented in this
volume has been dubbed “rational constructivism” (e.g. Xu, 2007; Xu,
Dewar, & Perfors, 2009; Xu & Griffiths, 2011), as it blends elements of
a constructivist account of development with the account of learning as
rational statistical inference that underlies probabilistic models of cognition
(Chater&Oaksford,2008;Griffiths,Chater,Kemp,Perfors,&Tenenbaum,
2010; Tenenbaum, Kemp, Griffiths, & Goodman 2011). Although the
workisstillquitenewandopinionsdiffer,herearesometenetsthatwethink
unite the rational constructivist approach.
(cid:129) Humanlearning is best describedas a form of rational Bayesian
inference: the learner starts with some prior probability
j
xi
xii Preface
distributionoverasetofhypotheses,andcomputestheposterior
probabilities of these hypotheses given the strength of the
evidence as given by Bayes rule. This is a computational level
characterization; that is, it describes the inferential process
without making a priori commitments to how that process is
instantiated at the algorithmic level (Marr, 1982).
(cid:129) Hypotheses can be represented as probability distributions.
Inferences are probabilistic and graded, so hypotheses are not
simply ruled in or out. Instead, learners may be more or less
confident about the various hypotheses.
(cid:129) Learners represent the world not just by forming associations
andcorrelations,butbyconstructingabstract,causal,generativemodels.
(cid:129) Learners acquire new concepts and biases in the course of
development; the newly acquired knowledge becomes part of
the prior and thus constrains subsequent learning.
(cid:129) Domain-generallearningmechanismsmaygiverisetodomain-
specific knowledge.
(cid:129) Representations may differ in their strengths; some support
predictions, actions, and explanations, while others may not.
(cid:129) Learners are actively engaged in the learning process, from
infancy to adulthood.
How Is the Rational Constructivist View Different
from Other Views
Weareintheearlydaysofdevelopinganewtheory,andourthinkingisstill
evolving. In terms of how to characterize human knowledge, rational
constructivism fully endorses the view that human knowledge is best
characterized by symbols and rules (see e.g. Fodor & Pylyshyn, 1988;
Marcus, 2001; Pinker & Prince, 1988) and human learning is best captured
by inferential mechanisms, not just associative learning mechanisms. At the
same time, rational constructivism endorses the view that early learning is
statistical: the inferences and representations may be graded and partial,
much like what has been instantiated in neural networks (e.g. Elman et al.,
1996; Colunga & Smith, 2005; Karmiloff-Smith, 1992).
This view also departs from the traditional Piagetian view of develop-
ment (Piaget, 1954), in at least two waysddevelopment does not progress
throughstages,drivenbyqualitativechangesinthechild’slogicalcapacities,
and development does not start with sensorimotor primitives and a lack of
Preface xiii
differentiation between the child and the world (see Carey, 2009, for
discussion). Instead, the construction of new concepts and new learning
biases are driven by a rational inferential learning process. It remains to be
seen how these inferential learning mechanisms account for the rapidly
developing domain knowledge in infants and how we might want to
rethink the issue of characterizing the initial state.
Some Answers, More Questions
The chapters in this book investigate the nature, power, and limits of these
earlyinductivelearningmechanisms.Theyareatestamenttotheremarkable
progress that has been made, as well as to the number of unanswered
questions that remain. These questions are posed, and answers and specu-
lations are offered by many contributors:
1) Howsophisticatedareinfantsandyoungchildren’sprobabilistic
inferencemechanisms?Whatarethelimits?Thisquestionisthe
mainfocusofChapters1,2,and4,allofwhichprovideevidence
for early rational inferential (as opposed to associative) learning.
2) Bayesian models provide good analyses of many aspects of
cognitivedevelopmentatthecomputationallevel,butwhatare
the algorithms and how are they implemented in the neural
hardware? Chapter 6 offers a Bayesian account of the general
learning processes; Chapters 8 and 11 present Bayesian models
on social learning and number.
3) If infants are engaged in hypothesis testing, where do the
hypotheses come from? How do they construct the hypothesis
space?Chapters3and13takeuptheseissuesfromdifferentperspectives.
4) Inmanycases,childrenexhibitwhatseemstobequiteirrational
behavior, and they make systematic errors in reasoning, at least
fromtheadultperspective.Cansomeofthedifferencesbetween
children’s reasoning and adults’ be viewed through the lens of
rational constructivist learning? Chapters 7, 8, 9 provide
examplesofhowitmightbepossibletoanswerthisquestionin
three different conceptual domains.
5) Social learning in infants and children has received much
attentioninrecentyears.Chapters5,11,and12addressissuesin
this domain: is social learning rational? How can a rational
constructivist framework help explain social learning?
xiv Preface
6) Lastly, with limited amounts of evidence, infants and young
children can revise their beliefs and acquire new concepts. But
much learning in childhood takes place on a much larger
time-scale, and the conceptual change that results from such
learningismuchmoreprofound.Itisanopenquestionwhether
the same underlying process can explain these long-term
changes and developments. Chapter 10 discusses these issues.
REFERENCES
Carey, S.(2009). The originsof concepts. OxfordUniversity Press.
Chater,N.,&Oaksford,M.(Eds.).(2008).Theprobabilisticmind:prospectsforBayesiancognitive
science.Oxford: Oxford University Press.
Chomsky, N. (1988). Language andthe problem of knowledge.Cambridge, MA:MIT Press.
Colunga,E.,&Smith,L.B.(2005).Fromthelexicontoexpectationsaboutkinds:therole
of associative learning. Psychological Review, 112,347–382.
Elman, J., Bates, E., Johnson, M., Karmiloff-Smith, A., Parisi, D., & Plunkett, K. (1996).
Rethinking innateness: A connectionist perspective on development. Cambridge, MA: MIT
Press.
Fodor,J. (1975). The language ofthought.Cambridge, MA: Harvard University Press.
Fodor,J.,&Pylyshyn,Z.(1988).Connectionismandcognitivearchitecture.Cognition,28,
3–71.
Griffiths,T.L.,Chater,N.,Kemp,C.,Perfors,A.,&Tenenbaum,J.B.(2010).Probabilistic
modelsofcognition:exploringrepresentationsandinductivebiases.TrendsinCognitive
Sciences, 14, 357–364.
Johnson, S. (2010). Neoconstructivism.New York: OxfordUniversity Press.
Karmiloff-Smith, A. (1992). Beyond modularity.Cambridge, MA:MIT Press.
Marcus, G.(2001). The algebraic mind. Cambridge,MA: MITPress.
Marr, D.(1982). Vision.Cambridge, MA:MITPress.
Newcombe, N. (2010). What is neoconstructivism? In S. Johnson (Ed.), Neoconstructivism
New York: OxfordUniversity Press.
Pinker,S. (1994). The language instinct.WilliamMorrow.
Pinker, S., & Prince, A. (1988). On language and connectionism: analysis of a parallel
distributed processing modelof language acquisition. Cognition, 28, 73–193.
Smith, L. B. (2001). How domain-general processes may create domain-specific biases. In
M. Bowerman, & S. Levinson (Eds.), Language acquisition and conceptual development.
Cambridge University Press.
Spelke, E.S. (1994). Initial knowledge:six suggestions. Cognition, 50,431–445.
Tenenbaum, J. B., Kemp, C., Griffiths, T. L., & Goodman, N. D. (2011). How to grow
a mind:statistics, structure, and abstraction. Science, 331,1279–1285.
Xu, F. (2007). Rational statistical inference and cognitive development. In Carruthers, P,
Laurence,S.,&Stich,S.(Eds.).(2007).Theinnatemind:Foundationsandthefuture,Vol.3
(pp. 199–215). OxfordUniversity Press.
Xu, F., Dewar, K., & Perfors, A. (2009). Induction, overhypotheses, and the shape bias:
someargumentsandevidenceforrationalconstructivism.InB.M.Hood,&L.Santos
(Eds.), The originsof objectknowledge (pp. 263–284). OxfordUniversity Press.
Xu, F., & Griffiths, T. (2011). Probabilistic models of cognitive development: towards
arationalconstructivistapproachtothestudyoflearninganddevelopment.Cognition,
120,299–301.
CHAPTER ONE
The Probable and the Possible
at 12 Months: Intuitive Reasoning
about the Uncertain Future
Nicolo(cid:1) Cesana-Arlotti*, Erno Tégl(cid:3)as**, and Luca L. Bonatti*,1
*ICREA,UniversitatPompeuFabra,Barcelona,Espan~a
**CognitiveDevelopmentCentre,CentralEuropeanUniversity,H-1015Budapest,Hungary
1Addresscorrespondenceto:LucaL.Bonatti,ICREA,UniversitatPompeuFabra,C.RocBoronat,138,
EdificiTanger,55.110,08018Barcelona,Espan~a.Email:[email protected]
Contents
1. Introduction 2
2. CanHumansReasonabouttheProbableandthePossible? 3
3. Infants’ReasoningAbilities:Domain-SpecificMechanisms,GeneralSystems 7
ofInferences,andFuturePredictions
4. ATheoryofProbabilisticReasoning:FromLogicalRepresentations 10
toSingle-CaseProbabilities
5. Infants’ExpectationsabouttheProbableFuture 12
6. IntuitiveStatisticsandLogicalIntuitionsofProbabilities:Conflicting 15
orComplementaryExplanations?
7. InfantRationalityandSimulations:YetaThirdAlternative? 18
8. Whatabout“ExperiencedFrequencies”? 20
9. TheFutureofPredictionsabouttheFuture 22
Acknowledgments 22
References 23
Abstract
How do infants predict the next future event, when such a prediction requires esti-
matingtheevent’sprobability?Theliteraturesuggeststhatadulthumansoftenfailthis
taskbecausetheirprobabilityestimatesareaffectedbyheuristicsandbiasesorbecause
theycanreasonaboutthefrequencyofclassesofeventsbutnotabouttheprobability
ofsingle events.Recentevidencesuggests insteadthatalready at12monthsinfants
haveanintuitivenotionofprobabilitythatappliestosingle,neverexperiencedevents
and that they may use it to predict what will happen next. We present a theory
accordingtowhichinfants’intuitivegraspoftheprobability offutureeventsderives
fromtheirrepresentationoflogicallyconsistentfuturepossibilities.Wecompareitand
other theories against the currently available data. Although the evidence does not
speakuniquelyinfavorofonetheory,theresultspresentedandthetheoriescurrently
being developed to account for them suggest that infants have surprisingly
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