RATIONALITY IN CHILDREN: THE FIRST STEPS

Andrew WOODFIELD[1]

ABSTRACT: Not all categorization is conceptual. Many of the experimental findings concerning infant and animal categorization invite the hypothesis that the subjects form abstract perceptual representations, mental modelsor cognitive maps thatare notcomposedof concepts. The paper is a reflection upon the idea that conceptual categorization involves the ability to make categorical judgements under the guidance of norms of rationality. These include a norm of truth-seeking and a norm of good evidence. Acceptance of thesenorms implieswillingnesstodefer to cognitive authorities, unwillingness tocommit oneself to contradictions, and knowledgeof how to reorganize one's representational system upon discovering that one has made a mistake. lt is proposed that the cognitive architecture required for basic rationality is similar to that which underlies pretend-play. The representational system must be able to rTl4ke roomfor separate 'mental spaces in which alternatives to the actual worldareentertained.Thesamefeature underlies the ability to understand modalities, time, the appearance-reality distinction, other minds, and ethics. Each area of understanding admits of degrees, and mastery (up to normal adult levei) takes years. Butrational concept-management, at least in its most rudimentary form,does not require a capacity to form second-order representations. lt requires knowledge of how to operate upon, and compare, the contents of diferent mental spaces.

KEYWORDS: The roots of rationality; conceptual categorization; perceptual representations; mental models; cognitive maps; common-sense psychology; cognitive capacities; representation of absent objects.

I. INTRODUCTION

Are children naturally rational, or do they have to learn to be rational? At what age do they start being rational? Questions like these were raised in the times of the Ancient Greeks and probably before. Every mother and father in human history has probably wondered about these matters, especially at times when the child was behaving badly. It is only in the twentieth century that people have begun to investigate these questions in a scientific way. I say 'scientific' with due caution. Although developmental psychologists aspire to this honorific title, it has to be recognized that their domain is not a hard science like chemistry. In some ways, our knowledge about the intellectual development of the child is pre-scientific; there are philosophical and methodological problems which have not yet been solved. The notion of rationality is partly normative; so the standards of rationality need to be dermed (and our choice of standards should be justified). Rationality is not a direct1y observable characteristic, so we need some operational tests of it. lnterpreting the behaviour of the child can present problems. Given that the child moved her body in such and such a way, there is still the question of identifying her intention. If she produced apparent speech sounds, what did she mean by them? We should not simply take for granted that she meant what the words conventionally mean.

Rationality is not a single quality. It has many components. No one would claim to have a complete list of these. But I suppose that any list would include the following:

1. Means-end rationality. The capacity to act appropriately in the light one's desires and beliefs.

2. Rationality in belief-formation. Weighing appropriately the information provided by perceptions and by other people's utterances.

3. lnferential rationality. There are at least two types (deductive and inductive), and perhapsother (e.g. abductive, analogical). All have to do with transitions from premisses to conclusions. Deductive rationality includes drawing out the more obvious logical consequencesofone's thoughts and noticing contradictions. lnductiverationalityincludesthe ability to form generalizations and hypothesisthatarewell-foundedin beliefs about individual cases.

4. Rationality in the Management of Stored Beliefs. Unwillingness to remain for very long with an incompatible set of beliefs. S tries to drop one (or more) of the beliefs, taking into account the balance of evidence and also the overall coherence with background beliefs.

In general, being rational is a good strategy for ariving at true beliefs, and for maintaining a store of beliefs that are true; both being worthwhile goals. If you fonn only empirical beliefs that are well supported, you will maximize the number of beliefs that correspond to empirical reality. However, success is not guaranteed. The relation between evidential justification and truth is complex; the former is not sufficient for the latter, nor is it necessary.

It is impossibletodo justicetoalI aspects in one paper. I want to concentrate upon the roots of rationality, the very rrrst signs of rational thinking, and the area I focus upon is conceptual categorization. On the whole, the literature on infant categorization fails to address theissueofrationality,andthisreflectsa widespread reluctance amongst psychologist torecognizehowmuchweightis caried by the word 'concept'. Categorization at the conceptual leveI is a far more complex matter than mere stimulus-generalization. But may cognitive psychologists use the terms 'concept' and 'category' interchangeably, thus making it hard for themselves to keepinmind that not alI categorizationisconceptual,andat the same time obliterating the absolutely crucial distinction between ontological theory and psychological theory.

11 .PERCEPTUAL CATEGORIZATION IN INFANTS AND ANIMALS

Developmental psychologists want to know how children of various ages classify things. The older the child, the more likely it is that she will group things in the same categories as her parents, because she will have had more time in which to learn what the parents do.A child who is old enough to speak and who knows a kind name 'K' must already possess some knowledge of the parents' use of that name. But the pre-verbal phase (from O to 12 months) is of great interest. If pre-verbal babies categorize their experiences at alI, their classifications are more likely to be innate.

Data about infants, and especially about new-born babies, willprovide the best material to test for this. Accordingly, many researchers havespeculatedabout whether the newborn's criteria of similarity coincide with adult criteria and whether babies see the world in the same way as grown-ups.

Until recent1y,good evidence of neonate classification was hard to obtain. Babies do not have sufficierit motor control to indicate their cognitive responses by reliable limb movements. But in the late 70's and 80's, developmentalists made increasing use of the technique know as 'habituation-dishabituation by looking', and obtained results which were interpreted as evidence about the baby's ways of categorizing stimuli. Neonates can control where they look, and how long they look. The experimenter, by noting the baby's looking patterns, can telI what the baby finds interesting. When presented with a static display, the baby gets bored with it after a while and shifts her gaze to something else. If a novel stimulus is introduced, the directed babys's attention will be directed toward that stimulus. The technique exploitsthese facts.The babyissubjected to a series of habituation-trials in which an object or set of objects is presented and the baby is allowed to look for as long as she likes. If the displays on successive trial are perceived as similar, the length of time spent looking at them goes down. The baby becomes habituated to those objects. The experimenter decides upon a criterion of habituation, that is, a length of time such that, if the baby does not look at a stimulus for more than that time, the baby is said to have habituated to the stimulus. For example, the criterion may be half the looking-time that occurred on the first trial. After habituation comes a test trial. The baby is given a pair of objects to look at and the duration of her gaze at each object is measured. If she finds one of the objects novel, she will look at it for longer. If she gazes at an object for a relatively short time this is a sign that she assimilates it to the set of the objects which she became familiar on the habituation trials. Clearly, the experimenter can manipulate manyvariableswithinthis framework, while controlling for individual differences andrandom1yfluctuating causes of looking or failing to look. Careful experimental designs yield results whose most plausible explanation is that thesubjects perceive distinctionsof kindand quality amongst the stimuli. The technique reveals whether the test-stimuli are expected or unexpected, against the background context of the training stimuli.

Thanks to this technique, many fascinating facts have been discoveredabout infants' perceptions of objects, events, and similarities. Very young children can and do see objects as possessing quite 'deep' objective properties, as well as possessing superficial properties such as colour and shape. They se the external object as an externaI object, because they are sensitive to such properties as : the unity of the object (the fact that its parts stay together and move together), spatial boundedness (the fact that the object occupies a demarcated place in a three dimensional space), its substantialness (the fact that it impedes other objects from occupying the same place at the same time), and its spatio-temporal continuity (that is, the fact that it persists even though it may be temporarily hidden from view). Even the youngest infants see the world in terms of three-dimensionalsolid objects, and not asa series of fleeting two-dimensional colour-patterns. These discoveries, many of which are duetoElizabethSpelke(andsumzedinSpelke(1 2)) , challengetheearlier doctrines of Piaget, who held that infants perceived the world egocentrically, as a sequence of evanescent sense-data. According to Piaget, children do not perceive independent1y existing solid objects in objective space until they have formed the object-concept, and it takes them at least two years to do so.

If properties such as depth, unity, substantialness, permanence and so on are not 'given' to the subject in the proximal stimuli that impinge on the retina, the subject must in some sense'construct' the objective three-dimensional world by'supplying' the missing properties. Piaget accepts this, and he then makes the further step of assuming that the way in which the mind objectifies the flux of experience is by subsuming the experiences under concepts. Piaget is, in this respect, a follower of Kant. He holds that the ability to perceive the environment as containing solid, substantial objects requires that the subject already possess certain concepts, such as the concepts solid, substantial, and whatever other concepts maybe logically implied by the concept object.

Piaget saw no evidence that the infant under two years of age perceived the world thus. Indeed he had great deal of evidence that seemed to show that infants fail to perceive the world oft enduring solid objects (e. g. the of replicated and reliable evidence of certain kinds of errors that are made by infants at various stages between O and 24 months). He was led, therefore, to hypothesize (a) that infants do not see the world as adults do, and (b) that the reason for that is that infants lack the necessary concepts.

IfPiaget had beenalive today, it would have been interesting to know his reaction to Spelke's experiments. Her results, like his, have been replicated many times. It is possible that Piaget would have accepted that infants perceive the world in terms of enduring,solid,three-dimensionalobjects right from the earliest days of life, and accepted that his stage 1 through stage 6 errors are probably due to non-perceptual in the infanto If he were to revise hypothesis (a) in the light of the new data, he would undoubtedly also reject (b) as well. He would draw the conclusion that Spelke herself draws, namely that children possess the object concept much earlier than the age of two, indeed that they probably possess it at birth.

However, there is a weak link in the reasoning, the link connecting hypothesis (a) with hypothesis (b). It is the assumption that a person must have the concept of object m order to perceive something as an object. It depends what one means by 'concept' ,ofcourse,butsurelythereexiststhepossibilitythatasubjectmight experience thedepth,substantiality,and'object-hood'of objectswit}zout conceptualizing them as three-dimensional, substantial objects. Not alI mental representations are conceptual, after alI. Some are images.And some are more like maps or models.

There are several reasons for favouring the alternative view that babies have representations of objects, and ways of categorizing objects into groups, which are nonconceptual.

In Spelke (12), no satisfactory criterion of the conceptual is given. Several criteria are hinted at, but none stands up too wel1. For example, she suggests that a representation of a quality Q is perceptual if quality Q is present in the proximal stimulus, conceptual if Q is not a property of the proximal stimulus. This is no good as a definition, for there are qualities such as colour and shape which are both present in the proximal stimulus and conceptualizable by adults. Since any quality can be represented in different fonnats, is impossible to defme a form of representation (such as 'concept' or 'percept') just by specifying which qualities it represents. But even to use this as an operationalcriterion is unsatisfactory, because it begs the question against the hypothesis that depth, permanence, solidity, etc. can be represented in a purely perceptual way. Such a hypothesis taken seriously in the infonnation pick-up' approach (see Gibson (4» , but it is compatible also with an 'information-processing' approach that assumes that such properties are neither present nor 'specified' in the proximal stimulus.

David Mar's theory of vision(1 1) andFodor'stheory of modular input-systems (1) both adopt the cognitivist 'infonnation-processing' approach. For them, a perceptual system is a mechanism that takes proximal stimuli as input and produces as output representations of the distal stimulus (the external object). The system performs a series of computational transfonnations upon the input, guided by built-in 'assumptions' about the physical world and the properties of .light. For example, if there is a sudden change in the texture gradient along a line in the retinal image, the visual system 'assumes' that there are ' two surfaces outthereoriented in different planes with respect to the eye. This is not anassumption mode by the viewing subject.It is simply a hard-wired principIe by which the mechanism operates. The fact that animais possess input-processing mechanisms that use such principIes is due to natural selection ; a mechanism sensitive to texture gradient-changes is well-adapted to the terrestrial environment in wbich such changes normally are correlated with changes in surface-orientation. The perceptions that we enjoy, the outputs of our special-purpose input-systems, are largely independent of our beliefs and thoughts.Even asolipsist who believed that the world was an illusion would still have visual experiences presenting an apparent wodd of solid objects in 3-D space. The solipsist cannot prevent bis visual system from producing such experiences. Equally, it is probable that babies have visual experiences of a 3-D external world from the earliest age, as soon as their input-systems start to work.

Another criterion proposed by Spelke is that a representation is conceptual if it is amodal. She conducted a series of habituation experiments upon children aged 4 months, in which the infants were allowed to touch two rings, one in each hand, under a cloth which concealed the rings from view. One group was giventworings connected rigidly together by a metal bar, in fact, a single object shaped like a dumb-bell. The other group was given two independently movablerings joined together by a cord. Each infant was habituated to one of these two stimuli and was then shown alternating visualdisplaysof a pair of rigidly connected rings and a pair of rings joined by string. Those who were habituated to the feel of the rigidly connected rings looked longer at the string-joined rings. This is evidence that they saw the latter as something different from the object they had touched. The infants who had been tactuallyhabituated to the movable rings looked longer at the rigidly joined rings, again showing that they regarded the latter as being different from what they had touched. Spelke concludes that the child's expectations about the unity and boundaries of stimulus objects generalize from the haptic mode to the visual mode. The four month old child forms an amodal (or multi-modal) representation of the stimulus object.

This fascinating result fits in well with thetheorythatinfantsconstructa cognitive map of their environment, locating bounded objects at positions within a spatial layout, and endowing those objects with many of the primary qualities. The experimentsuggeststhat information obtained through different sensory channels gets pooled intoa single, modality-independent map.But amodality is notsufficient to prove that the information is conceptualized. The common representational format which encodes information from different senses couldbenon-conceptual.And surely, if the subjects had been lower animals instead of human babies, the latter hypothesis would have seemed preferable.

The idea, perhaps originating with Tolman , that rats constructageometric cognitive map of their local environment has been conÍmned by a wealth of experiments (seeGallistel (3,chap.6)for a review).Suppose it were shown that other species, much less intelligent than rats, also did so. We would be faced with a choice between saying that those animals possess concepts, and saying that concepts are not required in order for an animal to construct amodal representations of objects laid out in space.To justifyour choice either way, it would be necessary to deÍme more precisely what makes a representation count as conceptual.

Let us return to thecategorizationofvisualstimuli.Herrnstein'sworkhas shown beyonddoubt that pigeonssee theworld in terms of a three-dimensional space containing objects, though their representations are not quite so rich in depth information as ours,andalsothat pigeonsclassify objectsinto groups, and that their groupings can bemade to coincide with categories such as tree, car, human being, and so on.But itseemsfar-fetched to say that a pigeon,with itssmall central nervous system, can acquire concepts.LloydMorgan'scanon('Donot ascribe more mental apparatus to animals than is strictlynecessaryin order to account for their behaviour') recommends the second option:pigeonscategorize things non-conceptually. Current cognitive science implicitly recognizes that stimulus-generalizationis not the same as conceptual categorization, for there exists arrowing body of ethological and computational research perceptual categorization (or 'categorical perception') in animaIs and humans, which is defacto independent of the tradition of work in cognitive and developmental psychology. Its main concems are to discover the discriminatory capacities of different species, and to propose models of possible mechanisms which would account for the discovered functional capacities.

In a well-known experiment,Hemstein(6)showed pigeons80 colour slides each day. 40 were photographs of trees, trees in full view, treespartiallyhidden,under various lightingconditionsandat variousdistancesfrom thecamera.These 40 were the positive instances. If a pigeon pecked at a key inresponsetosuchaslide,it received a foodreward.Theother40 slidesshowednotrees,and pigeonsreceived no reward if they pecked in responsetothem.Eachslidewasprojectedfor 45 seconds. After 5 days even the slowest pigeon was discriminating the trees ata statistically significant leveI. The three fastest werediscriminatingbythesecond session, havingseentheslidesonlyonce before. Evidently they found the task easy. Not onlydo pigeons have thecapacitytoseetreesassimilar tooneanother,they also readily exercisethiscapacity if givenan incentive.Theywould readily dosoin the wild, then,ifnatureprovidedthemwithanincentive.Indeed,theysurelydo have natural incentives for discriminating treesfrom other objectssuchas telegraph poles and chimneys, since trees are better places to perch, and feed, and build nests.

In another experiment (8), pigeons ieamed to sort underwater photographs of fishes (which were of various species taken from many different angles) from photographs of turtles, shrimp, starfish and scuba diverso In the wild, pigeons never encounter any underwater creatures, so grouping alI fish together would not be naturally useful. Yet pigeons have the capacity to do this, and they can easily be induced to exercise the capacity, if any reward depends upon it. Other discriminations that pigeonscan,and will make, inincreasing order of difficulty,are: oak leaves vs leaves of other kinds (very easy); photographs of a particular woman in various orientations, contexts, and clothing-styles vs. photographs of other people (easy); pictures of Charlie Brown vs. pictures of other characters from the Peanuts cartoon (difficult) ; computer-generated tine drawings of cubes and other solid forms vs. computer-generated distortions of such drawings which failed to represent solid forms (very difficult). The work is reviewed in Hermstein (7).

From an evolutionary perspective it is plausible that aspecies highly dependent upon vision and widely dispersed across the globe should be innately endowed with a tlexible capacity to leam to make discriminations on the basis of alI sorts of visual cues. The discriminations that an individual pigeon actually ls are those that are useful to it in itsparticular environment. Theset of useful discriminations amounts to a tinysubset of the set of possible discriminations that the pigeon can leam. Some will be harder to leam than others, of course (for an interesting discussion of the idea thatanimaIsare programed to leam certain things easily,see Gould and Marler (5)).

It is als.o plausible that certain habits .ofgroupingwillbe useful in every envir.onment,f.orexample,thetendencyt.oc1assifypercepti.ons.of asingle. object viewed from different angles. Such tendencies might well be innate in pige.ons.

AlI .of the ab.ove remarks are probably br.oadly true .of human infants , th.ough the discriminati.ons that c.ome easily t.o birds may n.ot be the same as the .ones that c.ome easily t.o human beings. H.owever, facts ab.out natural tendencies t.o generalize tell us evidence little .or n.othing ab.out concepts. The evidence .of perceptual categ.orizati.on in infants is n.ot .of the right s.ort t.osh.ow that infants p.ossess the object c.oncept, n.or d.oes it support the hypothesis that they have any specific c1assificat.ory c.oncepts, suchas cat,human face,or Mama.S.o what s.orts .of evidence w.ould be relevant? I shall focus a small area, and try t.o establish a link between c.oncept-p.ossessi.on and very rudimentary f.orm .of raponality. The starting p.oint is c.ommon-sense psych.ol.ogy, and m.ore specifically , the c.omm.on-sense view .ofjudgements.

IH. JUDGING THAT AN OBJECT BELONGS TO A CATEGORY

C.oncepts are n.orma1ly taken t.o be representati.ons that figures in judgements and inferences.C.onsider a physical kind c.oncept K, where K stands f.or a kind like cat, d.og, .or caro Among its vari.ous .other roles, a K-c.oncept plays a predicative r.ole in categ.orical judgements.Oneimp.ortant type.of categ.orical judgement is .of the f.orm 'This is a K', where ' This' is a dem.onstrative referring t.o a current1y perceived .object. In .order t.o make such a categ.orical judgement y.ou need two representati.ons.

Y.ouneedapercept.ofthe.object,andy.ouneedageneralrepresentati.on.of the categoryK,andtheny.oumustc.ombine the tw.o predicatively t.o f.orm a c.omplete th.ought.Asalreadymenti.oned,y.our percept .of the .object already categ.orizes it, in the sense that it represents it as having certain properties, inc1uding s.ome quite deep pr.operties. T.o judge that the perceived .object is a K requires als.o that y.ou m.obilize a K-c.oncept and apply it t.o that .object.Every act .of judging inv.olves exercising s.ome c.oncept in the predicative part, and hence requires that the judge sh.ould already p.ossess that c.oncept. S.o judgements depend upon c.oncepts. B ut I als.o want t.o c1aim thatpossessi.on.of theconceptKispartlydefinedinterms.of theability t.o make rati.onal K-judgements. The tw.o are mutually interdependent, the c.oncept K and the ability t.o make rati.onal judgements about K-h.o.od. There is a partial circularity here, but n.ot a vici.ous circularity, because we can ground b.oth the.oretical terms simultane.ously. Als.o it is n.ot a c1.osed circle, because c.oncepts have .other r.oles as wellastheir role in judgements, and they may be partlydefmed in terms.of these .other r.oles.

An.other assumpti.on made by c.omm.on-sense is that judging is a mental act regulated by norms. Tw.o important n.ormative principIes are:

(i) that judgements about empírical matters sh.ould aim at truth;

(ti) that empírical judgements sh.ould be justifiable by reas.ons.

In the case of a categorical j udgementabouta perceived object based on the object' s appearance, S's perception should normally furnish good reason for the judgement.

A sophisticated judge makes a cognitive commitment, knowing that his or her act is potentially subject to evaluation and critical scrutiny in the light of norms (i) and (ü). A being who is capable of making judgements must understand not only that judgements can be either true or false, but also that false judgements are incorrect when assessed against principIe (i). Such a being must appreciate also that hasty, groundless judgementsare bad according to norm (ü), even they happen byluck to be true. I am talking here about a being who has fully mastered the art of j udging, a competent participant in the game of rational inquiry. A young child who has not yet acquired fuII mastery will not fully appreciate that her categorical thoughts are evaluable by these two standards. But in order for her thoughts to count as judgements at alI, she should be able to recognize in a rudimentary way the existence of intellectual values. She. must appreciate that there is a difference between intellectual right and wrong.

Conceptual categorization, then, is a mental act governed by a norm of truth and a norm of evidential j ustification. Accepting that these norms guideone'smental activity, voluntarily submitting oneself to their authority, is a basickindof rationality. Full concept-possession demands that the subject should possess at least that kind of rationality.

Let us examine what goes on in categorization tasks whenthesubjectisa competent, rational concept-user. The proper description of the adult case is essential, before we considerthequestionof children.We need to describe the competences to be acquired, in order to identify the states of the child which approximate to those competences. In categorization research, there are several quitedistinctparadigms. There is the 'free-sorting' task beloved of Inhelder andPiaget,the 'forced choice on triads' task, the discrimination-Iearning' task wherestimuliare presented one at a time, and many other types of tasks. There might be no feedback about the result of a trial, or there might be feedback. In the latter case, feedback informationcantake various forms: it might be a reward, or the reply 'correct' or 'incorrect', or even an explanation of why one's action on the trial was correct or incorrect. It is important to specify the experimental paradigm, for the subject's strategies will be adapted to the demands of that particular paradigm as he perceives them.

In the paradigmIwishto consider,Sispresentedwith one object on each trial, and there is a predetermined category K such that S has to decidewhetherthe presented object is a K. S knows which category is the relevant one; S possesses the conceptK, andSknowsthat he is supposed to decide whether the object isa K. S may choose between three types of response(e.g.there are three buttonsto press): one means 'Yes', one means 'No', and the third means'I don't know'. This task is far easier than theoneinwhichtheexperimenter has a certain definite category in mind as the one which fixes the standards of correct and incorrect responses, but where S is ignoraot of which category that is. On the latter task, S tries to guess the category, using the infonnation that gradually accumulates about the correctness or incorctness of his responses so faro Under the 'ignorance' condition , the task is two-fold. The general problem across a whole series of trials is to find out which category fixes the criterion of correctness. The specific problem on each trial is to decide 'Is this object before me a member of category X?', where X is the category that S is currently supposing to be the relevant category. No algorithm exists for solving the general problem, because the infonnation available to S, however long he sits at it, always underdetermines the choice of hypothesis as to which category is the right one. But although it is theoreticaUy impossible to guarantee that a person or a machine will solve the problem, in fact people often succeed in guessing the category that the experimenter had in mind. S's homing-process is highly constrained; one hypothesis is sometimes much more salient than alI its rivals.

But we shall focus upon the easier task, where S does know which category is in questiono Suppose the category is oak tree. The task is, essentially, a test of S's skill at recognizing oak trees on the basis of their visual appearance.

There are many concepts that I possess which I cannot reliablyor confidently apply to perceived objects. I do not know much about the appearance of instances of the foUowing concepts:chlorophyU,cholesterol, maple tree, capibara. If you present me with furry animals that are not dogs, cats or any other kind that I aro familiar with and ask me on a series of forced-choice trials if they are capibaras, my perfonnance wiU be poor. But I do possess the concept capibara (I know that capibaras are South American rodents, and that they are the biggest rodents in the world), and I would exercise that concept on each trial, in an affirmative or a negative judgement. If I aro forced to say defmitely yes or no, even in cases where I prefer to say 'I don't know', I will expect a low success rate. Similarly, some people are poor at recognizing oak trees. Poor perfonnance by S does not show that S was not trying to put the objects in the right category. On the contrary, on every trialS exercises the relevant concept oak tree. But anobserver might not beable to teU that S is employing the concept oak tree at all.

Conversely, consider the response pattem of a different subject attempting to judge whether the same stimulus objf'..ctsarebeechtrees. And suppose that thisman isapoorjudgeofbeechtrees.Hisresponsesmaycoincideexactlywiththe responses produced by a good judge of oaktrees.Evena100% correctresponse profile for the oak tree task would not prove that this man had been employing the concept oak tree in his judgements. Perfect perfonnance is not sufficient proof, just as poor perfonnance is not sufficient disproof.

Another important point is that S's success-rate depends upon how difficult the stimulus-materialsare. Itdepends,forinstance,uponthedegreeof contrast between the positive stimuli and the negative stimuli. A blurred photograph of part of an oak tree at a great distance is more difficult to interpret as an oak tree than a clear picture of an oak tree in sunlight at 20 metres. If alI the positive stimuli are blurred, then even askilled oak: tree-recognizer will not score very bigh on a forced choice task. For similar reasons, the success-rate will be lower if the negativestimuli are similar in appearance to oak: tres, bigher if the negative stimuli look very unlikeoak: trees. A person who is not good at recognizing oak: trees will score as high as an expert botanist, if the task is simply to see the difference between oak: trees and cars.

Being good at recognizing oak: trees is a comparative attribute. It means being better than the average person. Here, 'average' is relative to á contextually given reference class. The average farmer in Europe is better at recognizing oak: trees than the average computer programmer in Hong Kong. But the Hong Kong programers and the European farmers are all thinking about the same category, and their judgements are subject to the same standards of truth and falsity.

In a set-up like ours, where S has the option of saying 'I don't know', rational subjects will adapt their responses to suit their skill, in the light of how difficult the stimulus materials are. An expert botanist will say 'I don't know' less often than a novice.Of course, people differ in their temperaments. Confident subjects are happy to tak:e risks. Others are cautious. A cautious person will say 'I don't know' more often than a risk-tak:er even when the two have the same leveI of expertise. However, a rational person realizes that there are limits to caution, and also limitsto confidence. A person who knows very little about how oak: trees look, and who knows that he knows very little, should not mak:e firm commitments on every trial. Heshouldrealizethathecannotalwaysmak:eadefmitecommitment.l.amingthis is part of learning how to judge. And it is part of what it is to possess the concept . oak tree, or any other kind-concept. Concept-possession in -..general entails lalowing how to manage your concepts sensibly, in a variety of contexts.

Suppose S leams, after bis responseon each trial, whether the object presenteei is or is not an oak:tre. How might tbis feedback after bis performance over the medium to long term? Suppose that the stimuli are clear and easily discriminable, and suppose that at time t, after a number of trials, S becomes aware that bis responses have been correct only 70% of the time., S may reflect as follows: 'My success rate is rather poor. I may be under some misapprehension as to the diagnostic features of oak trees. I shall therefore modify the criteria I am using, and see if my performance improves '.S tak:es a garnble. By altering bis criteria he runs the risk of a decline in performance rather than animprovement.But if he does get worse, and takes note of the fact ; he will be free to revert totheoriginal criteria, or to experiment with another modiflcation. Any improvement in performance will cause him to retain the changed criterion. Over a long run of trials, and with a bit of luck, S's performance should improve. The constant trial by trial feedback gives him the opportunity to leam how to recognize oak: trees better.

Yet the identity of the concept does not change. It is still the concept oak tree after 500 trials, just as it was on the frrst trial. The changes that occur are changes in S's criteria for applying that concept observationally. Suppose that some criteria for visual recognition areincluded in S's concept. S hasa partly observation-based concept of oaktrees.ThenitistruethatS's concept undergoesinternaldevelopment, if bis criteriaof recognitionchange.Butitsreferentialcontentstays the saroe:it is stilI the concept oak tree.

Improvement in performance can go only so faro There will be an asymptotic leveI at wbich S is exploiting alI the visual features wbich it is witbin bis power to exploit. But remember, some categories have very few distinctive visual characteristics , and so the asymptote will be quite low for these. For example, powdered chalk, salt and magnesium chloride alI look pretty much the saroe. A rational person regulates bis practice according to how much he knows about the appearance of K's, but alsoaccording to howdistinctive in appearance he thinks the category K objectively is.

Enough has beensaid to establish that thereexists no uniquebehavioural profile, no particular performance-pattern , such that everybody who possesses the concept oak tree will exbibit j ust that patern profile, on a series of open choice trials with feedback. Whatonewould expect isthata rational person faced with this task will adj ust bis or her responsesinthelightof multiple considerations tailored to his or her own personal knowledge and skilI.

IV. COGNITIVE CAPACITIES REQUIRED FOR JUDGING

What underlying cognitive capacities must S have, in order to make rational categorical judgements? The questionseemstodemand a top-downanalysisof a very global ability. The whole capacity gets subdivided into sub-capacities, the sub-capacities in their turn get subdivided, and so on , until we arve at a set of capacities that are taken as primitives.A fulI top-down analysis gives the structure of a bierarchy of capacities and identifies every node in the bierarchy. It is beyond the scope of this paper to attempt a complete analysis, but let us at least make a start.

As a first step, we isolate two components involved in S's general understanding thata responsemaybe either correct or incorrect.What does it mean to say that an act of pressing a button in response to a visual stimulus is correct? The act isnot correct in virtue of its intrinsic properties. Nor is it correct in virtue of the fact that it leads to a reward or to any confrnng feedback.Theoutwardactelicitsthat feedback only because the act is interpreted as the sign of a correct judgement. The judgementisan internaI act mediating between perception and outward behaviour. The subject needs to understand, therefore, that it is the mental statewbichis evaluated as correct, in the first instance. The behaviour iscorrectonlyina derivative sense. So the first component is an ability to isolate, to identify, that particular part of the whole cognitive process which is evaluated. Smustbe understand that the response was rewarded only because the judgement was correct. This component may be called 'ability to locate the primary object of evaluation'.

The second component is understanding why the judgement was favourably evaluated. S must know that the criterion of evaluation is simultaneous with the judgement, and notforward-looking.That is, the correctness of the judgement does not consist in its being instrumental in producing good consequences. Rather the converse is the case: the judgement produces good consequences because it was correct at the time when it was made. Why was it correct at that time? An adult can answer this question by saying 'Because it matched rea1ity. It corresponded to the fact that the object was a member of category K. In short, the judgement was correct in the sense that it was true'. 'It is hardly likely that a young child would produce such a sophisticated answer. Yet the child must, in my view, have some inchoate grasp of the notion of truth. To appreciate fully that the judgement's correctness consists in its corresponding to an independently existing fact, S needs to be able to think thoughts of the forros 'My recent judgement that o is a K was correct because (asI now leam)oreallyisa K', and thougths of the forro 'My recent judgement that o is a K was wrong because (as I now leam) o is not a K'. Thoughts of these two require Sto compare his previous judgement with his current updated judgement and to give precedence to the latter. To do this, S must remember his own earlier judgement. That is, S must represents the content of his earlier judgement as a content that he judged earlier, but without committing himself to it the second time round.

The two components both imply that S needs to be able to reflect upon his own representations. This capacity, in turn, can be subdivided into components. Also it admits of degrees.Conscious, explicit representations of one's representations would be the highest degree, but, as I shall shortly show, there existlower degrees of reflective ability.

Reflection issomeforro or other liesat the core of rational concept-management. It plays a role, for instance, in the process of deciding to respond 'I don't know'. A rational decision to abstain is the upshot of thinking 'I don't have enough evidence to judgethatthisobjectisaK,butequallyI don't haveenoughevidenceto judge that it is not a K'. This thought is about the relationship between current evidence and a possible future judgement, andhenceitisnotavailabletoanybeingwhocannot think about possible future judgements. A child of two perhaps cannot dothis.But perhaps a child of two can think about hisownactual past judgements, ones that he remembers making. This is an empirical questiono At the moment,since we engaged in a top-down analysis of the adult capacity, our next step ought to be separate the various components of the ability to reflect critically upon one's ownactualor possible judgements. This ability is probably one aspect of a more general ability to reflect upon one's own desires, intentions, hopes, fears, and other first-oroer mental states. And self-reflection is probablyjustaspecialcaseofanevenmore. wide-ran ging capacity to thinkaboutmental statesand representations of al sorts, not only one's own but also those of other people.

Suppose we call thismost general capacity'meta-representation'. It contains at least two components: the ability to forrosecond-order representations,andthe ability to do things with them in thought, comparing a meta-representation with a frrst-order representation and drawing some conc1usion from the comparison. To analyse these two components would be an extremely interesting, exceedingly intricate exercise, which would tak:e a whole book. So Iproposetocurtail my analysis at this point in order to tak:e stock of the situation and relate it to the case of young children.

V. EVIDENCE OF SUCH CAPACITIES IN CIDLDREN

Top-down analysis is like reverse engineering. You take a system that works and you dissect it to Ímd out how it works, what its components are, how they fit together. A description of the structure of a fully developed system is synchronic. But it has diachronic implications regarding the process of manufacturing such a system. When you do forward engineering, you will be well advised to adopt Herbert Simon's 'watchmaker' principIe: 'First tak:e the smallest components and build some small, easy to handle, sub-systems. Next join the sub-systems together. Don't try to build the whole system directly out of the smallest components, or you will get lost'. Nature generally follows this principle. So an analysis of what is involved in adult conceptual categorization does have developmental implications. If a high-level ability presupposes a set of lower-level abilities, we may infer that the lower-level abilitiesmust be established at an earlier point in time than the high ones. After the low ones are in place, it becomes possible to synthesize the higher ability. Before they are in place, synthesis is impossible.

At what age do children start reflecting upon their own thoughts, and what stages lead up to this? Instead of working backwards let us now adopt a more natural chronological perspective and look at some of the relevant phenomena in the order in which they appear.

Activating Representations ofAbsent pbjects

By 9 months, children can update their memory of the location of absent objects. Mandler (10), cites the example of the little girl who goes directly to the top drawer where she last discovered her ribbons, instead of to the bottom drawer where she knew they had been previously kept. Children of this age have a large store of memories about familiar objects in their home which they can update as necessary. These representations, when mobilized in the course of planning, are not confused with perceptions. They are activated not in 'perceiving' mode, but in 'remembering' mode. 9 months old children can process representations that are detached or 'decoupled' from input-processingwhile they are processing input. Thissimple fact already implies that there are at least two leveIs of processing going on simultaneously. Both are on-line, but only one of them operates directly upon sensory input.

Constructing Possible Worlds

According to Forguson and Gopnik (2), among the Írrst phrases that English-speaking children learn (at around 12-18 months) are 'Al gone' and 'There'.

The former is used when an interesting scene disappears from view (e.g. when there is no food left on the plate). The exclarnation 'There' is uttered when the child successfuUy caries out an action that she had antecedently intended. It is an expression of satisfaction that things went according to plan o An intention framed in advance of action is, of course, a representation of a non-actual state of affairs. It may never become actual, and may not have been actual in the pasto So by this age, children can construct possibilities, as well as remember past actualities.The utterances 'All gone' and 'There' suggest that the child ismakinga comparison between the curntly perceived state of affairs andanotherrepresentedstateof affairs. With 'Allgone', the latter is the statein which an object is present. With 'There', it is the state of affairs envisaged and desired. In the former case, the child recognises that the two states are not thesame: the world has changed.In the latter, she recognises that they are the same, though they used not be. Again, the world has changed. It seems, then, that a one and a half year old can two representations entertained in different modes. She canextractinformationfromacomparison cared out in her head.

Pretend P/ay

By the age of two, most children engage in'pretend-play'.Theyconstruct imaginary scenarios within which they carry out routines on play objects which are normallyperformed onseriousobjects.The toy telephone rings,and the child picks it up and pretendsto listen.Or inAlan Leslie's example,a banana is help up to the ear as if it were a telephone.

Leslie, who has studied pretend play in depth, believes that it provides the earliest evidence of meta-representation. In an experiment described in Leslie (9), he and the child jointly construct a scenario in which toy animaIs pour 'water' into cups, 'drink' from the cups, and play around with the 'water'. In reality there is no water. The experimenter takes a jug and pretends to fllltwo cups withwater.He then picks up one of these cupsand turns it upside down. He replaces the cup on the table and asks the child which of the two cupsis empty.The child points to the cup that was upturned. The experimenter upturns theother cupontothehead of ananimal,and the child is asked to explain what hashappened.Thechild repliesthat the animal is alI wet. This behaviour shows that the child not only constructs an imaginary world using real objects as props, but she also makes inferences about what is happening in that imaginary world,usinggeneral knowledge derived from her experienceof the real world. For example, the child keeps track of the consequences of actions in the pretend world (the animal is wet), and at the same time knows that the animal is not really wet. AsLeslie putsit, the childmust be able to create two mental spaces, one for the real world, one for the pretend world, and in each mental space there are representationsrelated to one another in a coherent way. In both spaces, the same causal laws hold &Ild the same roles of logical inference apply. The child will neither judge nor pretend that a cup is both fuU and empty at the same time. A contradiction is impossible in any world. But the child can represent the cup as empty, while at the same time entertaining a representation of the empty cup as being fuH. 5he can keeps both in mind at the same time provided the second representation is activated in 'pretend' space.

Of course, this talk of mental spaces is metaphorical. Although it will eventually need to be cashed out,in the present state of theorizing this metaphor, like many others, can be a useful tool for describing the child's mind. I think it offers us a good way to characterize the child's inchoate grasp of the fact that she has categorized an object incorrectly. In pretend-play, the child represents real objects as having certain properties in a 'pretend world'. This possible world is created inside its own dedicated mental space, with the same representational building blocks, be they models, images, prototypes or symbols in the language of thought, as are used in the space where the 5 represents the actual world. In rational categorizing, the child keeps a record of real world commitments that she has previously made so as to create a'previous world', that is, a world of the facts as she has conceived them from her earlier point of view. The 'previous world' is kept inside its own designated mental space.

The space which contains her 'previous' world is separate from the space in which she holds representations to which she is currently committed. 50 there is room in her mind for the content expressed by 'o is a K' to appear twice. One token of that representation-type figures in her 'Then' space and another token of the same type appears in her 'Now' space.And normally there will be two such tokens of any given type that she has committed herself to, for her standard procedure is to make a copy of every judgement she makes and insert it in her 'Then' space, while retaining the original in her 'Now' space.

The distinctness of the two spaces does make it possible, however, for to represent that o is a K in her previous world without representing this in her current world. When this happens, she detaches her previous commitment from her current commitments.

The child approximates to the adult meta-representational state of thinking 'I have judgethato isa K', in so far as she represents o asbeinga K from her previous point of view.Thisis like representing the cup as containing water from a pretend point of view. Doing this is not the same as mentally denying that o is a K; it remains open whether she is or is not committed currently to o's being a K.

5 is normally loyal to her previous judgements. But individual judgements can be overridden .,Thishappenswhensherespondsinacertainwaytothesignal'No'or 'Incorrect' immediately foHowing an outward manifestation of theindividual judgement in questiono 5 interprets the signal as an instruction to retracther judgement. 5uch understanding is a complex disposition to engage in the following operations .

(a) 5defers tothe'authority'of the feedbacksignal.5he gets ready to car out some energy-consuming internal reorganization, in such a way as to make her representations conform better to a rule imposed from outside.

(b) S deletes 'o is a K' from her 'Now' space while retaining it in her 'Then' space .

(c) S inserts 'o is not a K' in her 'Now' space.

(d) S compares the token of 'o is a K' which is in her 'Then' space with the token of 'o is not a K' which is inher'Now'space, andshe notes their logical incompatibility.

(e) Asa result of (d),S blocksanoperationthatshewouldnormally be disposed to make, namely, ,moving a token of 'ois a K' from 'Then' , space down to her 'Now' space. She is not willing henceforth to judge that o is a K, unless some new experience leads her to override the canceIlation.

As well as making these changes to her current representational state, S changes the implicit criteria she wiIl use to decide whether future objects are or are not K's. The set of features possessed by o, which she regarded as a sign that o was a K, will no longer be taken as a reliable sign of K-ness. If an object qualitatively identical to o is presented to her in the future, S is likely to judge that this object is not a K. The mechanism by which her criteria get retumed is a matter for empirical investigation. But one possible mechanism is that S compares the look of new objects with the appearances of previously seen objects that she has judgedto beK's.This assumes, of course, that she remembers the appearances of those individual objects, and also that shekeepsa recordof whetheror not her judgement about them were confirmed. If the new object is more like objects in the 'confirmed' class than like objects in the 'disconfirmed' class, S categorizes the new object as a K. This way her criteria wiIl change automatically as a result of any corrections she makes, because part of what she does when she corrects is to bring about a change in the composition of the two remembered classes.

It is crucial to the picture just sketched there should be a causal relation between step (d) and step (e). S blocks a normal functional property of herprevious judgement because she registers that itcontradictsher curnt judgement.That is how shc manifests that shc regards the previous judgements as falsc. Indeed, it could be said that hcr primitive conception of thc falsity of á proposition p consists in hcr being reluctant to accept p for the reason that p is incompatible with a proposition to which she is currently committed. Note that this primitive conception of falsity aIlows her to attribute falsity only to one of her previous beliefs. It does not apply to her current judgements and beliefs. Falsity of current beliefs is an undefined notion for S. A two years old does not understand, cannot entertain the thought, that his or her own current beliefs might be false. Ability to combine the notion of false belief with epistemic modalities such as 'might' and 'possible' comes a good deal later, perhaps around age four, if my picture is right, the stage at which the child begins to understand what mistaken judgements are comes fairly early, around the same time as the emergence of pretend-play (two to two and a half, according to Leslie).

A great advantage of 'mental spaces' talk is that it expresslyrefrainsfrom ascribing second-order representations. My hypothesis, for example, does not claim that atwo yearsold hasthoughtsof the fonu'Iused to think that o was a K'. To ascribe such thoughtswould,1think,betoexaggerate the intellectualcapacityof such a young child. First-order representations in mental spaces are a substitute for, indeed are precursors of, representations that have other representations embedded within them. Thechildhasan implicit understanding thatshe usedto think that p, just as she implicitly grasps that she is only pretending that the cup is full. 'lmplicit understanding' is explained in terms of the functional roles ofrepresentationsin different mental spaces and in terms of proceduresthatthechildispreparedto perfonu upon these.

Later, perhaps at age 3 but this is controversial, the child starts to meta-represento A natural explanation of this development would be that the child.who already has separate mental spaces starts beingable to embed one space inside another.She keeps them separate while also letting them intermingle and interpenetrate.

If 1 am right that rational concept-management requires at least these two mental spaces plus procedures for manipulating representations within and across them, it follows that run-of-the-mill conceptual categorization of the physical environment is intimately linked with other mental operations which depend upon the creation and comparison of mental spaces. And there are plenty of them. Juggling mental spaces is required not only for pretend-play but also for representing time, 8.lethic possibility, epistemic possibility, counterfactuality, potentiality, powers, the appearance-reality distinction, moral right and wrong, as well as for understanding other minds. All are interconnected: the roots of rationality coincide with the roots of knowledge of objectivity, morality and psychology. The mark that distinguishes conceptual categorization from other kinds of categorization js that a conceptualizer interprets theactual in termsof at least one alternative possible world, the world as he or she has (once) conceived it. The structure of such a mind is very different from the functional structure of a connectionist leaming system, eventhoughboth systems, after a respectively appropriate number of training trials, come to reflect objective patterns that are present in the world.

. 1shall end by summarizing the main points cited insupportofmy claim that conceptual thinking is intimately connected to a rudimentary kind of rationality:

(1) Smust realize that the primaryobject of evaluation is a mental state. This requires an ability to monitor one's own cognitive processes.

(2) S must be trained to defer to outside authority. Toacceptcorrection involves an ability to operate upon already existing representations,to dismantle internal structures that have been previously set up.

(3) S must notice a logical incompatibility and cancel a previous representation because of it. She updates the contents of her 'Now' space in such a way as to maintain consistency amongst them.

(4) S modifies her criteria for making future judgements in the light of lessons she leams from feedback. She makes use of remembered knowledge in the service of future categorizing. Theprocedure is not as simpleas back-propagation,where error-signals modify the connection-strengths between the units responsible for the most recent response.

WOODFIELD, A. Racionalidade nas crianças: os primeiros passos. Trans/Forml Ação, São Paulo, v. 14, p. 53-72, 1991.

RESUMO: Nem toda categorização é conceitual. Muitas das descobertas experimentais sobre o processo de categorização nas crianças e animais sugerem a hipótese segundo a qual os sujei tos formam representações perceptuais abstratas, modelos mentais ou mapas cognitivos que não são compostos de conceitos. Este artigo é            reflexão acerca da idéia de que categorização conceitual envolve a habilidade de fazer julgamentos categoriais, tendo- como guia as normas de racionalidade. Estas incluem norma de busca da verdade e norma de evidência ade quada. A aceitação dessas normas implica boa vontade em respeitar as autoridades cognitivas, o desejo de evitar as contradições e o conhecimento de como reorganizar seu sistema representa cional após descobrir que se cometeu um erro. Sugere-se que a arquitetura cognitiva requerida pela racionalidade básica é semelhante àquela subjacente ao jogo do "faz de conta". O sistema representacional deve ser capaz de arrumar lugar para "espaços mentais", nos quais alternativas para o mundo real são consideradas. A mesma caracterfstica subjaz à habilidade de compreender modalidades, tempo, a distinção entre aparência e realidade, outras mentes e éticas. Cada área de compreensão admite graus, e o seu dorntnio (alcançado pelo adulto normal) leva anos. Contu do a manipulação racional de conceitos, pelo menos na sua forma mais rudimentar, não requer a capacidade de formar representações de segunda ordem. Ela requer conhecimento do procedi mento de como operar e comparar os conteúdos dos diferentes espaços mentais.

UNITERMOS: As ra(zes da racionalidade; categorização conceitual e não-conceitual; repre sentações perceptuais; modelos mentais; mapas cognitivos; psicologia do senso-comum; capaci dades cognitivas; representação de objetos ausentes.

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[1] Department of Philosophy -Universíty of Brístol.