The Principle Features of Child Logic
Excerpts from the works of Jean Piaget
Judgment and Reasoning in the Child
Reasoning ignorant of the logic of relations, of logical classes (juxtaposition being constantly chosen in preference to hierarchical arrangement).
Thought proceeds neither by amplifying induction nor by an appeal to general proposition, but, instead, moves from particular to particular by means of a reasoning process which never bears the character of logical necessity.
Logical activity is not the whole of intelligence. One can be intelligent without being particularly logical. The main functions of intelligence, that of inventing solutions, and that of verifying them, do not necessarily involve one another. The first partakes of imagination, the second alone is properly logical. Demonstration, search for truth, is therefore the true function of logic. "Ludistic" tendencies, the inability to distinguish between fabulation and truth and immediate belief in his own ideas are inherent in children. The child assimilates everything he hears to his own point of view and has the greatest difficulty in entering into anyone else’s point of view.
The child sees things in terms of the momentary perception which is taken as absolute. He therefore makes no attempt to find the intrinsic relations existing between things. Explanation takes on the character of a narrative. Appeal to a general proposition is lacking. The child seeks neither to establish a proposition by means of successive inductions, nor to postulate it for the purposes of deduction. (Moreover) if we are to make him aware of a general rule, we shall find that it is by no means the rule for which we were prepared.
Understanding undergoes a process which is unanalytic. A sentence heard is not broken up into distinct terms, but gives rise to a general schema which is vague and indissociable. Any two phenomena perceived at the same moment become caught up in a schema which the mind will not allow to become dissociated, and which will be appealed to whenever a problem arises in connection with either of these two phenomena. The relationship of cause and effect is distorted.
The sun does not fall down "because it is very high up". If one asks why the water has risen, the explanation given will often be a simple description of what has happened; but because of syncretism this description will possess explanatory value.
For by the term "reasoning"should be understood the work of verifying and proving hypothesis, which work alone creates conscious implications among judgments. Claparède has distinguished with great clarity three distinctly separate moments in intellectual activity: question, the invention of hypothesis, and verification. Now, the question is only the manifestations of a desire; the hypothesis is framed by the imagination to fill up the gap created by the desire. Reasoning, therefore appears only at the moment when the hypothesis is verified. Up till then there has been no logical activity. The sole function of this level of thought is to give immediate and unlimited satisfaction to desire and interests by deforming reality so as to adapt it to the ego. For reality is infinitely plastic for the ego.
For adults...it is chiefly in relation to other people that we are obliged to verify our beliefs, and to place ourselves in different planes those that are not compatible with each other or that we gradually build up within ourselves a plane of reality, a plane of possibility, a plane of fiction, and so on. The hierarchy of these planes is therefore determined by their degree of objectivity.
The child’s egocentric thought processes do not lead him to try to prove whether such or such of his ideas do or do not correspond to reality. When the question is put to him, he evades it. It does not interest him.
Between the years 7-8 and 11-12, there is awareness of implications when reasoning rests upon beliefs and not upon assumptions. The child cannot reason from premises without believing in them. Or, even if he reasons implicitly, from assumptions which he makes on his own, he cannot do so from those which are proposed to him. For what prevents the child from reasoning from data that he does not agree to but is asked simply to "assume", is that he is untutored in the art of entering into other people’s point of view. For him, there is only one comprehensible point of view - his own.
Many adults are still egocentric to their way of thinking. Such people interpose between themselves and reality an imaginary or mystical world, and they reduce everything to this individual point of view. Unadapted to ordinary conditions, they seem to be immersed in an inner life that is all the more intense. Does this make them more conscious of themselves? Does egocentrism point the way to a truer introspection? On the contrary, it can easily be seen that there is a way of living in oneself that develops a great wealth of inexpressible feelings, of personal images and schemas, while at the same time in impoverishes analysis and consciousness of self. In short, the claim is not too bold that we become conscious of ourselves to the extent that we are adapted to other people Our discovery that other people do not spontaneously understand us nor we them is the gauge of the efforts we make to mould our language out of the thousand and one accidents created by this lack of adaption and the measure of our aptitude for the simultaneous analysis of others and of ourselves.
For the construction of the objective world and the elaboration of strict reasoning both consist in a gradual reduction of egocentricity in favor of the progressive socialization of thought. In favor, that is to say, of objectivization and reciprocity of viewpoint. Truth - empirical truth or formal truth such as forms the subject matter of argument - is obscured by the ego. This level of thought is transductive... that is to say, it is ignorant of the logic of relations. .As soon as logical thought breaks away from transduction and becomes deductive, the idea of reality also breaks away from all these forms of primitive realism.
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Synthetic Incapacity: |
Juxtaposition
...There is a tendency in childish reasoning to juxtapose classes and propositions rather than to establish their exact hierarchy. We went into this in connection with the difficulties raised by logical multiplication [Journ. de Psych, 19 (1922: 222.} The child is given, for example, a test of the form: "If this animal has long ears it is a mule or a donkey; if it has a thick tail it is a mule or a horse. Well, this animal has long ears and a thick tail. What is it." Instead of finding the exact intersection of the two classes and saying that the animal in question is a mule, boys, even of 10 or 11 years old, add up the conditions and juxtapose the classes instead of excluding the unwanted elements. In this way, they reach the conclusion that the animal might just as well be a horse, a donkey or a mule. This shows the true nature of the phenomenon of juxtapostion. The child begins by considering the existence of long ears, and concludes that the animal must be a donkey or a mule. He then considers the existence of the thick tail. If this new condition were made to interfere with the preceding one, the child would eliminate the donkey since it has not got a thick tail. But the child considers this new condition separately, he juxtaposes it instead of contrasting it with the former condition, and he concludes that the animal may be a horse or a mule. Each judgment is therefore juxtaposed and not assimilated to the judgment that precedes it. Finally, the child merges these two judgments into a single whole, but this whole constitutes a mere juxtaposition, not a hierarchy. For the child comes to the conclusion that all three cases are possible. He therefore eliminates nothing. He juxtaposes without choosing. In a sense then, this is synthetic incapacity, since all synthesis implies choice and hierarchy, and differs from mere juxtaposition (J.R. Chap. IV, § 2)....
But the tendency to juxtapose instead of synthesizing is not to be found only in the schematism of judgments as in the preceding examples, it also characterizes implication itself. What is meant by this was shown by our study of the conjunctions of logical and causal relation (because) and of the conjunctions of discordance (although) (J.R. Chap. I,) In his language, the child frequently omits from between his successive judgments such relations as we would expect to find, and is content to juxtapose these judgments without any conjunctions or place between children (L.T. Chap. III, § 1) there are hardly any explicit causal relations. Explanation takes on the character of a narrative. Relations are only indicated by "and then" and even in connection with mechanical phenomena. This is why, when a child of 7-8 is asked to complete a sentence containing "because," he will sometimes do so correctly and sometimes invert the relation indicated by "because." For example, "The man fell off his bicycle because he was ill afterwards." The word "because" is often used correctly by the child to indicate psychological relations (such as motivation: "because Daddy won't let me"). But instances of "because" indicating relations of physical causality or logical relations are almost completely absent from the spontaneous talk of the child, and when their use is induced, mistakes such as those we have quoted tend to occur. For a long time, finally the word "therefore" (donc) does not exist in child language. It is replace by the term "and then" (alors); but for a considerable period this term only indicates succession in time and not the relation of consequence.
All these facts agree in proving a certain synthetic incapacity in the thought of the child, and show that this incapacity bears primarily upon the schematism of judgment or upon the relations existing between judgments. But does this mean that the mind of the child is peopled with a multitude of juxtaposed ideas and judgments unconnected by any bond, as appears to the the case to the outsider? In other words, has the child himself a feeling of chaos and discontinuity? It is obvious that nothing could be farther from the truth, and that for any deficiency in objective relations there is a corresponding excess of subjective relations. This is shown to be the case by the phenomenon of syncretism which seems to be the opposite, but is really the complement of juxtaposition.
There is one particular feature in the structure of childish ideas which serves as a transition between juxtaposition and syncretism; we mean the relation which unites terms that have been separated by synthetic incapacity. When there is no occasion, such as drawing or language, for the child to break up objects by analysis, these are, as will be shown in a moment, perceived syncretically. But once they have been broken up and that synthetic incapacity renders their synthesis impossible, what is the relation which gathers the juxtaposed elements into a group? Luquet has noted with great truth that it is a relation of membership and not of inclusion, by which he means (no regard being paid to the logical meaning of these terms) that an arm drawn alongside of a manikin is conceived by the child as "going with" the manikin not as "forming part of" his body. We have often come across this relation in the ideas of children, and have given it the name of relation of property, so as to avoid confusion with the vocabulary of logic. This is how in the expression "A part of my posy" the term "of" indicates neither a partitive nor an attributive relation, but, as it were, a mixture of the two: "the part that is with my posy," such is the translation which a child gave us. And it is in the same way that our young Genevans, though they knew for the most part that Geneva is in Switzerland, yet declare themselves to be Genevan and not Swiss, because they cannot imagine being both at the same time (J.R. Chap. III, § 6). For them, Geneva "goes with" Switzerland, but they see no sign here of a part and a whole, and make no attempt to define the spatial contacts. Finally - if comparison may be made between heterogeneous cases - this is how judgments of juxtaposition come to be accompanied by a "feeling of juxtaposition," although this feeling never becomes an awareness of causality or of implication. Children who draw a bicycle chain alongside of a gear wheel and a pedal know that these things "go together"; but if they are urged to be more precise in their statements, they will sometimes say that gear wheel sets the dogged chain in motion, sometimes that it is the other way about. These two statements coexist within the same individual, and prove very clearly that in this case the consciousness of causality does not go beyond a simple feeling of relation."
Juxtaposition and synthetic incapacity do not therefore stand for disharmony. These phenomena are accompanied by relational feelings, either static (relation of property) or dynamic (feeling of causal relation), feelings of which the explanation is supplied by our analysis of syncretism. For they constitute a substitute for syncretism when the unity which the latter supplied has been broken up, and no fresh unity has been built up again.
Syncretism
Syncretism is related to nearly all the phenomena we have been calling to mind. In the first place, as we said a moment ago, it seems like the contrary but is really the complement of juxtaposition. For if childish perception considers objects in their immediate, fragmentary, and unrelated aspect, and if either in language or in drawing these objects are simply juxtaposed instead of being arranged in a hierarchy, it is perhaps because these objects, before being broken up by the exigencies of drawing or conversation, were too intimately related to one another, too deeply sunk in comprehensive schemas, and too thoroughly implcated in one another to be broken up with impunity. The reason why this relatedness given in the original perception of objects offers so little resistance to the disintegrating effects of drawing or conversation is perhaps that it was exaggerated and, consequently, subjective. Now to say that child thought is syncretistic means precisely this, that childish ideas arise through comprehensive schemas and through subjective schemas, i.e., schemas that do not correspond to analogies or causal relations that can be verified by everybody. If, therefore, the child possesses neither the logic of relations nor the synthetic capacity which would enable him to conceive of things as objectively related to one another, it must be because his way of thinking is syncretistic. For in the mind of the child everything is connected with everything else, everything can be justified by means of unforseen allusions and implications. But we have no suspicion of this wealth of relations, precisely because this very syncretism which causes it is without the means of expression that would render it communicable.
This last remark leads one to suppose that syncretism, besides being bound up with the phenomenon of juxtaposition and with inability to handle the logic of relations, is also the direct outcome of childish egocentrism. Egocentric thought is necessarily syncretic.... Syncretism is the expression of this perpetual assimilation of all things to subjective schemas and to schemas that are comprehensive because they are unadapted.
Syncretism therefore permeates the thought of the child. Claparède has pinted out its importance in perception. Cousinet has described, under the name of "immediate analogy," the prompt and unhesitating process by which the child identifies new objects with old schemas. In the meantime, we have discovered in the understanding and reasoning of the child under 7-8 and in the understanding and verbal thought of the child between 8 and 11-12, a tendency which is common to all syncretism. On the one hand, childish understanding undergoes a process which is completely unanalytic. A sentence heard is not broken up into distinct terms, but gives rise to a general schema which is vague and indissociable. On the other hand the child does not reason by explicit inferences, but by projecting these schemas into one another, and by fusing images according to laws which are more often those of "condensation" than of logic. Let us recall [briefly] how syncretism makes its appearance before the age of 7-8, then what it becomes once it has been shifted onto the verbal plane between 7-8 and 11-12. Before the age of 7-8, syncretism may be said to be bound up with all mental events and with nearly all the judgments that are made. For any two phenomena perceived at the same moment become caught up in a schema which the mind will not allow to become dissociated, and which will be appealed to whenever a problem arises in connection with either of these two phenomena...
Here are some examples: The sun does not fall down "because it is hot. The sun stops there. - How? - Because it is yellow" (Leo, age 6). "And the moon, how does it stop there? - The same as the sun, because it is lying down on the sky" (Leo). "Because it is very high up, because there is no (no more) sun, because it is very high up" (Bèa, age 5), etc. Or again, if one shows the child a glass of water and if, after putting a small pebble into it so as to make the level of the water rise, one asks the child why the water has risen, the only explanation given will often be a simple description of what has happened; but because of syncretism, this description will possess explanatory value for the child. In Tor's opinion (age 7 1/2) the water rises because the pebble is heavy. When wood is used, the water rises because the wood is light, and so on.... What is most remarkable is that two contradictory reasons can be invoked by the same subject. Either such facts as these are due to the n'importe quisme of which Binet and Simon have spoken (and this would hardly apply to cases where the child is interested in the experiment in which he is taking part), or else description has a greater explanatory value for the child than for us, because features bound together within the raw material of observation seem to him to be related to one another by causal connections. This immediate relation is what constitutes syncretism.
In all these cases - and they are without number - syncretism seems to describe the following course. First of all two objects or two features are given simultaneously in perception. Henceforth the child perceives or conceives them as connected or rather as fused within a single schema. Finally, the schema acquires the strength of reciprocal implication, which means that if one of the features is isolated from the whole, and the child is asked for its reason, he will simply appeal to the existence of the other features by way of explanation or justification.
This facility in connecting everything with everything else, or to speak more accurately, this inability on the part of childish perception and understanding to isolate the elements of [global] schemas, is to be found again on the verbal plane after the age of 7-8. For after this age perception becomes more analytical, causal explanation begins to play its part in a mentality which up till then was precausal (see p. 105 and sel. 15); in short, syncretism tends to disappear from the subject's view of the external world. But on the verbal plane, which, with the increasing mental intercourse between children and between children and adults, becomes the habitual sphere of reasoning, the old difficulties survive and even reappear in new forms. For sentences and statements heard in the mouth of other people give rise to a mass of syncretistic verbal manifestations which are due, as before, to analytical weakness, and the tendency to connect everything with everything else...
Another and very different case of syncretism which we discovered is equally suggestive from the point of view of the analytical weakness shown by the child whenever there is any question of connecting propositions or even of understanding words independently of the schemas in which they are enveloped (L.T. Chap. IV). The child is given a certain number of easy proverbs and a certain number of corresponding sentences jumbled together, but each meaning the same thing as one of the given proverbs. He is then asked to find the corresponding sentence more or less at random, or at any rate by means of accidental and purely superficial analogies. But the significant thing is that at the moment of choosing the corresponding sentence the child fuses proverb and sentence into a single schema which subsumes them both and justifies the correspondence. We have here a syncretistic capacity which at first sight seems due to pure invention; but analysis shows that it comes from the child's inability to dissociate comprehensive perceptions or to restrain the tendency that wants to simplify and condense everything. For instance, a child of 9 assimilates the proverb "White dust will ne'er come out of a sack of coal," to the corresponding sentence, "People who waste their time neglect their business." According to him, these two propositions mean "the same thing," because coal is black and can be cleaned. Similarly, people who waste their time neglect their children, who then become black and can no longer be cleaned. The uniformity shown by these answers to which we need not return at this point, excludes the hypothesis of invention. It shows how universal is the tendency of the child to create comprehensive schemas in his imagination, and to condense various images into each other.
Such, then, is syncretism: immediate fusion of heterogeneous elements, and unquestioning belief in the objective interimplication of elements condensed in this way. Syncretism is therefore necessarily accompanied by a tendency to justify things at any price. Now this is exactly what the facts show to be the case. The child can always find a reason, whatever may happen to be in question.
Transduction, and Insensibility to Contradiction
Does reasoning in the child obey the laws of adult logic? Above all, does it obey the law of contradiction? If it be borne in mind, in the first place, that child thought is ignorant of the logic of relations, that addition and multiplication of logical classes are unknown to it (juxtaposition being constantly chosen in preference to hierarchical arrangement): if it be remembered, moreover, that the various relations created by syncretism are comprehensive and do not admit of analysis, then nothing will prevent us from concluding that the process of reasoning in the child is, as Stern has put it, neither inductive nor deductive, but transductive. By this Stern means that child thought proceeds neither by an amplifying induction nor by an appeal to general propositions which are designed to prove particular propositions, but that it moves from particular to particular by means of a reasoning process which never bears the character of logical necessity. For instance, a child of 7 who is asked whether the sun is alive, answers: "Yes. - Why? - Because it moves (moves along)." But he never says that "All things that move are alive." This appeal ot a general proposition has not yet come into being. The child seems neither to establish such a proposition by means of successive inductions, nor to postulate it for the purposes of deduction. [Moreover], if we try to make him aware of a general rule, we shall find that it is by no means the rule for which we were prepared.
What seems to us the distinguishing feature of transduction is therefore its lack of logical necessity; the fact that this type of reasoning deals only with individual cases is certainly important, but cannot be said to be fundamental. As a result of his egocentrism, the child does not as yet feel any desire for demonstration; he makes no attempt to connect his judgments with bonds that bear the mark of necessity... What welds these momentary judgments together is some one aim, external to the act of judging or some one action carried out upon the world of reality. But outside such extrinsic systematization there exist between these judgments no conscious implication and no demonstrative links. The psychologist will certainly succeed in finding the logical reason for a child's judgment, but the child himself looks for no such filiation between his propositions. At this stage, therefore, implication constitutes a motor rather than a mental phenomenon, and it is no exaggeration in this sense to say that there is no logical reasoning before the age of 7-8. For the justifications arising out of syncretism are devoid of logical necessity. As to the motor implications which have produced the reasoning process, they are still below the level of consciousness.
For by the term "reasoning" should be understood the work of [verifying] and proving hypotheses, which work alone creates conscious implications among judgments. Claparède has distinguished with great clarity three distinctly separate moments in intellectual activity: questioning, invention of hypothesis, and [verification]. Now, the question is only the manifestation of a desire; the hypothesis is framed by the imagination to fill up the gap created by this desire. Reasoning, therefore appears only at the moment when the hypothesis is verified. Up till then there has been no logical activity.
How then does the [verification] take place? To use the current formula, by means of a mental experiment. But this formula is slightly ambiguous and there are, in our opinion, three genetically distinct types of mental experiment: that which we find in the child before the age of 7-8, that which we find between 7-8 and 11-12, and finally, that of the adult. We also believe it necessary to point out that this third type of mental experiment is accompanied by an experiment which might be called "logical experiment"....
Mental experiment is a reproduction in thought of events as they actually succeed one another in the course of nature; or again, it is an imagined account of events in the order which they would follow in the course of an experiment which one would actually carry out, if it were technically possible to do so. As such, mental experiment knows nothing of the problem of contradiction; it simply declares that a given result is possible or actual, if we start from a given point, but it never reaches the conclusion that two judgments are contradictory of each other. Consequently, mental experiment, like actual physical experiment, is irreversible, which means that, starting from a and finding b, it will not necessarily be able to find a again, or if it does so, it will not be able to prove that what it has found is really a and not a become a'. Similarly, if it finds b again after starting from c or from d, and not from a, it will have no means of proving that what it has found is really b and not b become b'. And these defects in mental experiment are the same as those which characterize childish reasoning, for the latter is content to imagine or to reproduce mentally actual physical experiments or external sequences of fact.
The logical experiment which intervenes from the age of 11-12 is certainly derivative from this process and has no other material than that of the mental experiment itself. It also deals mostly with individual cases, and does no more than combine the different relations existing between things, with or without the aid of syllogisms. But this logical experiment which comes as the completion of mental experiment and which alone confers upon it the quality of true "experiment," introduces, nevertheless, a new element which is of fundamental importance: it is an experiment upon the subject himself as a thinking-subject, an experiment analogous to those which one makes upon oneself in regulating one's moral conduct. It is therefore an attempt to become conscious of one's own operations (and not only of their results), and to see whether they imply, or whether they contradict one another.
In this sense, logical experiment is very different from mental experiment. The first is the construction of reality and the awareness of the construction. Now this ordering, which is the mark of logical experiment, has a considerable effect upon mental experiment: it makes it reversible. This means that the subject is led to lay down only such premises as are capable of entertaining reciprocal relation to each other and of remaining each identical with themselves throughout during the mental experiment. (This feature is one whose importance may not be evident to introspection, but is nevertheless fundamental from the genetic point of view, because it appears very late and is in no way implied in the mechanism of mental experiment pure and simple.) Premises which are the necessary requisite of logical experiment will therefore contain decisive judgments, which means that they will necessitate the use of conventional definitions, of assumptions, and so on, and that they will consequently extend beyond the sphere of mere fact and observation. This is the price of reversibility in mental experiment. Logical experiment is therefore an experiment carried out on oneself for the detection of contradiction. This process is undoubtedly founded on mental experiment, but on mental experiment which it fashions for itself, and which differs from primitive mental experiment as widely as does the work of the physicist from the observations of the man in the street. The necessity resulting from mental experiment is a necessity of fact; that which results from logical experiment is due to the implications existing between the various operations: it is a moral necessity due to the obligation of remaining true to oneself.
We are now in a position to understand how this first stage of childish reasoning is to be distinguished from logical reasoning proper. We were saying just now that the judgments of children before the age of 7-8 do not imply each other, but simply follow one another, after the manner of successive actions or perceptions which are psychologically determined without being logically necessitated by each other. For transduction is nothing but a mental experiment unaccompanied by logical experiment. It is either a simple account of events in succession, or a sequence of thoughts grouped together by one and the same aim or by one and the same action; it is not yet a reversible system of judgments, such that each will be found to have remained identical with itself after no matter what kind of transformation.
The irreversibility of primitive reasoning may be recognized by the further circumstance (J.R. Chap. VI, §§ 4-5) that the subject cannot keep a premise identical with itself throughout a mental experiment. This is because while he is "constructing" by means of this premise a whole series of new results, he has no means (unless he takes the decisions that regulate the experiment itself) of knowing whether this premise has varied or not in the course of the mental experiment. Or again, there is no means of knowing whether a concept to which one has been led by different paths is really the same under these different forms, and does not contain any contradictions. In reality, neither of these questions exists for the child before the age of 7-8, and his habit of reasoning only about individual cases, of applying judgments which, though universal in appearance are particular in fact, leaves him in almost complete ignorance of the problem.
... For instance, we can take a list of objects specially selected so as to avoid suggestion, and ask children of 7-8 whether such and such an object is alive, or has force, and so on. We shall then immediately realize that a concept like that of "life" is frequently determined by two or three heterogeneous components. For example, the same child will agree that the sun, the moon, wind, and fire are alive, because they "move." but that neither streams, nor lakes, nor clouds are alive, because the wind pushes them and they consequently have no movement on their own. On the other hand, clouds are alive, because they "make rain," the lake, because it "runs"; both, in short, because they perform some activity which is useful to man. Thus the two components "self-movement" and "useful activity" define between them the concept of life. But owing to the schematism of childish judgment which we have described, these components do not multiply, or to put it differently, they do not interfere, but remain juxtaposed without synthesis in such a way that they only act one at a time, and make the child say, for instance, sometimes that the lake is alive, and sometimes that it is not. The idea of force, again, is defined by movement, by solidity and by activity, all of them components that define the adult idea of force, but which in the child remain thrown together without any hierarchical order. It is in this sense that childish reasoning is irreversible. According to the turn taken by the mental experiment, the child will discover on the way, facts which will cause him to alter his definitions, modify his premises, and which will completely change the nature of one and the same concept by reason of the path taken to reach it... On the one hand, the logic of relations is foreign to the child along with all the adult habits of logical multiplication, of hierarchical arrangement of classes and of propositions. This is one cause of irreversibility. The child can certainly reach a conclusion from given premises, but he cannot perform the return journey without deviating from his path. On the other hand syncretism, which makes the child connect everything with everything else, and prevents him from making the excisions and distinctions necessary to analytical thought, will have the natural consequences of making him concentrate heterogeneous elements within a single word. We have here a second cause of irreversibility. The concepts of children are systems which are not in equilibrium, to borrow a term from chemistry. They have a pseudo-equilibrium, which means that their seeming immobility is simply due to their viscosity. In consequence of this they do not remain identical, but vary imperceptibly throughout a reasoning process.
We can now lay our finger upon the real cause of contradiction in the child. There can be no doubt that up to the age of 7-8, child thought teems with contradictions.... And as these contradictions to which the child seems completely [insensitive] are of two kinds, it is important to distinguish very clearly between them.
To begin with, there is what may be called contradiction "by amnesia." which incidentally has no particular interest for us. The child has two contradictory opinions about one object, and hesitates between them. When he is questioned he will affirm one of these, but a moment later he will forget what he has said, and affirm the other, and so on. For instance, a child believes that rivers are dug out and made entirely by the hand of man. Then he learns that the water coming from their sources has been sufficient to produce them. But for a long time he fluctuates between these two explanations, neither of which he finds completely satisfactory, so that when questioned, he will give first one, then the other, forgetting each time what he has previously asserted.
The second type of contradiction, on the other hand, strikes us as peculiarly characteristic of child thought. It is what might be called contradiction "by condensation." The child, unable to choose between two contradictory explanations of one and the same phenomenon, agrees to both simultaneously and even fuses them into each other. Nor must it be thought that this is any way an attempt at synthesis. The child is never in the presence of two terms which are first conceived as separate and then condensed, faute de mieux. It is rather a certain lack of restraint that allows new elements to be constantly heaped on the old ones, regardless of synthesis. Such schemes inherit their character from these syncretistic habits of thought which lead the subject to simply add up and condense his impressions instead of synthesizing them. And this is the immediate consequence of what we were saying just now about the irreversibility of child thought. For one and the same concept being different according to the path along which the child has reached it, the various components of which this concept is the product are bound to be heterogeneous and to lead to incessant contradictions.
Let us recall an example. A boy of 7 1/2 tells us that boats float because they are light. As to big boats, they float because they are heavy, thought of as strong and supporting the boat, in the second case the boat is thought of as strong and supporting itself. But as a matter of fact, the child is not aware of this opposition. He is subject to contradiction because he is unable to resolve this condensation of heterogeneous explanations.
We may also conclude that transductive reasoning, insofar as it consists purely in mental experiment, is still irreversible and consequently powerless to detect contradiction. The reason for this is quite simple. Consciousness of contradiction arises from an awareness of mental operations, and not from observation of nature, whether this observation be actual or imaginary. Now, up to the age of 7-8, childish judgments entail each other without any awareness of implications. They succeed, but do not justify each other. It is therefore perfectly natural that contradictory judgments should be added straightaway to the pile by simple condensation. Only if the child became conscious of the definitions he has adopted or of the steps by which his reasoning proceeds, would these judgments seem to him to contradict one another.
After the age of 7-8, however, comes a stage lasting till about the age of 11-12, and during which the following fundamental changes take place. Little by little the child becomes conscious of the definition of the concepts he is using, and acquires a partial aptitude for introspecting his own mental experiments. Henceforward, a certain awareness of implications is created in his mind, and this gradually renders these experiments reversible, removing at least such contradictions as are the fruit of condensation. Does this mean that these are finally disposed of, and that the child is now fit to reason formally, i.e., from given or merely hypothetical premises? We have shown that this is not the case, and that formal thought does not appear till about the age of 11-12. From 7-8 till 11-12 syncretism, contradiction by condensation, etc., all reappear independently of observation, upon the plane of verbal reasoning, in virtue of the law of shifting. It is therefore not until about the age of 11-12 that we can really talk of "logical experiment." The age of 7-8, nevertheless, marks a considerable advance, for logical forms have entered upon the scene of the mind in perception.
Within the sphere of direct observation the child becomes capable of amplifying induction and of necessary deduction.
It is not without interest to recall that these advances in logic are connected with the definite diminution of egocentrism at the age of 7-8. The result of this last phenomenon is on the one hand to give birth to the need for proof and verification, and on the other to induce a relative awareness of the way thought moves. We have here a remarkable instance of the influence of social factors on the functioning of thought.
Schema: (plural, SCHEMAS or SCHEMATA), A mental structure or pattern of behavior arising out of the integration of simpler, more primitive units into en enlarged and more complex whole.
Frederick Bartlett (1932, 1958) is credited with first proposing the concept of schema (plural: schemata). He arrived at the concept from studies of memory he conducted in which subjects recalled details of stories that were not actually there. He suggested that memory takes the form of schema which provide a mental framework for understanding and remembering information.
According to Bartlett, in Remembering: A Study in Experimental and Social Psychology, incoming meaningful information the child assimilates into schema, defined in terms of an active organization of past experiences. That is, schema is another name for units of previous knowledge. Schema always operate in any well-adaped cognitive response. Active schema allow the person to transform and to reconstruct imput, skills using both past knowledge and the material being read. While Bartlett's conception of schema remains sketchy, the concept of cognitive structures as an organized representation of experience is compatible with results of experiments on comprehension and useful in explaining what it means to comprehend.
Mandler (1984) and Rumelhart (1980) further developed the schema concept. Schema have received significant empirical support from studies in psycholinguistics. For example, the experiments of Bransford & Franks (1971) involved showing people pictures and asking them questions about what the story depicted; people would remember different details depending upon the nature of the picture. Schema are also considered to be important components of cultural differences in cognition (e.g., Quinn & Holland, 1987). Research on novice versus expert performance (e.g., Chi et al., 1988) suggests that the nature of expertise is largely due to the possession of schemas that guide perception and problem-solving.
Egocentrism: Lack of awareness of anything outside the realm of one's immediate experience. It is evidenced most learly in infants, who are unaware even of their own hands and feet as living parts of their bodies and do not realize that objects exist when they can no longer be seen. Egocentric thinking persists throughout childhood, as shown by the child's unawareness of points of view other than his own, and projection of his own wishes, fears, and desires onto the world around him.
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A Short Biography of Jean Piaget
The Jean Piaget Archives
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