Jean Piaget (1955)
§ 3. From Sensori-motor Universe to Representation of the Child’s World
1. Space and Object
The understanding of spatial relations is a particularly clear first example of the parallelism with temporal displacement between the sensorimotor acquisitions and those of representative thought.
We recall how, starting with purely practical and quasi-physiological groups, the child begins by elaborating subjective groups, then arrives at objective groups, and only then becomes capable of representative groups. But the groups of this last type, if they constitute the culminating point of practical space and thus insert in sensorimotor spatial relations the representation of displacements not occurring within the direct perceptual field, are far from marking the beginning of a complete representation of space, that is, a representation completely detached from action. What will happen when the child is called upon, apart from any current action, to represent to himself a group of displacements or a system of coherent perspectives? It is from this decisive moment that we witness, on the plane of thought properly so called, a repetition of the evolution already accomplished on the sensorimotor plane.
Take, for example, the following problem. The child is presented with a model, about one square meter in size, representing three mountains in relief; he is to reconstruct the different perspectives in which a little doll views them in varying positions that follow a given order. No technical or verbal difficulty impedes the child, for he may simply point with his finger to what the doll sees, or choose from among several pictures showing the possible perspectives, or construct with boxes symbolising mountains the photograph the doll could take from a given point of view. Moreover, the problem posed to the child consists in representing to himself the simplest of all the spatial relations which transcend direct action and perception, that is, to represent to himself what he would see if he were in the successive positions suggested to him. At first it would seem as though the child’s answers would merely extend the acquisitions of the sixth stage of sensorimotor space and arrive immediately at the correct representations.
But interestingly enough the youngest of the children capable of understanding the problem of the mountains and of responding without difficulties of a verbal or technical kind reveal an attitude which, instead of extending the objective and representative groups of our sixth stage, on the contrary, regresses to the integral egocentrism of the subjective groups. Far from representing the various scenes which the doll contemplates from different viewpoints, the child always considers his own perspective as absolute and thus attributes it to the doll without suspecting this confusion. In other words, when he is asked what the doll sees from a particular position the child describes what he himself sees from his own position without taking into account the obstacles which prevent the doll from seeing the same view. When he is shown several pictures from among which he is to choose the one which corresponds to the doll’s perspective, he chooses the one which represents his own. Finally, when he is to reconstruct with boxes the photograph the doll might take from its place, the child again reproduces his own view of things.
Then, when the child disengages himself from this initial egocentrism and masters the relationships involved in these problems, we witness a totality of transitional phases. Either the child who begins to understand that the perspective differs according to the doll’s position effects various mixtures between those perspectives and his own perspective ("pre-relations"), or else he takes into account only one relation at a time (left-right or before-behind, etc.) and does not succeed in multiplying the interrelations. These transitions correspond to the limited groups of displacements belonging to the fourth of the sensorimotor stages. Finally, complete relativity is attained, corresponding to stages V-VI of the same series.
How then can this temporal displacement be explained, as-well as this return to the phases which have already been transcended on the plane of sensorimotor space? To act in space the child is certainly obliged to understand little by little that the things which surround him have a trajectory independent of himself and that their displacements are thus grouped in objective systems. From a purely practical point of view the child is therefore led to emerge from an initial egocentrism, in which things are considered to depend solely on his personal activity, and to master a relativity which is established between displacements successively perceived or even between certain perceived moments and others which have simply been represented. But the egocentrism and objective relativity in question here concern only the relationships between the child and things, and nothing in sensorimotor action forces him to leave this narrow realm. So long as the problem is not to represent to himself reality in itself, but simply to use it or to exert an influence upon it, there is no need to go beyond the system of relations established between objects and self or among objects as such in the field of personal perspective; there is no need to assume the existence of other perspectives and to interconnect them in including his own among them. To be sure, the act by which one confers an objectivity on the displacements of things already implies an enlargement of the initial egocentric perspective and it is in this sense that, apropos of the fifth and sixth sensorimotor stages, we have been able to speak of a change in perspective and the mastery of a universe in which the subject locates himself instead of bringing the universe illusively to him. But this is only the first step, and even in this objective, practical universe, everything is related to a single frame of reference which is that of the subject and not that of other possible subjects. Hence there is objectivity and even relativity, but within the limits of a realm which is always considered absolute, because nothing yet induces the subject to transcend it. If we may be permitted to make a somewhat daring comparison, the completion of the objective practical universe resembles Newton’s achievements as compared to the egocentrism of Aristotelian physics, but the absolute Newtonian time and space themselves remain egocentric from the point of view of Einstein’s relativity because they envisage only one perspective on the universe among many other perspectives which are equally possible and real. On the contrary, from the time when the child seeks no longer merely to act upon things, but to represent them to himself in themselves and independently of the immediate action, this single perspective, in the midst of which he had succeeded in introducing objectivity and relativity, no longer suffices and has to be coordinated with the others.
This is true for two reasons, one relating to the subject’s intention in his attempt at representation, the other to the requirements of representation. Why at a given moment in his mental evolution does the subject try to represent spatial relations to himself instead of simply acting upon them? Obviously in order to communicate to someone else or to obtain from someone else some information on a fact concerning space. Outside of this social relation there is no apparent reason why pure representation should follow action. The existence of multiple perspectives relating to various individuals is therefore already involved in the child’s effort to represent space to himself. Moreover, to represent to himself space or objects in space is necessarily to reconcile in a single act the different possible perspectives on reality and no longer to be satisfied to adopt them successively. Take, for example, a box or some object upon which the child acts. At the end of his sensorimotor evolution he becomes perfectly capable of turning the box over in all directions, of representing to himself its reverse side as well as its visible parts, its contents as well as its exterior. But do these representations connected with practical activity, with the "concrete active behaviour" of which Gelb and Goldstein have spoken in their fine studies on space, suffice to constitute a total representation of the box, a pattern of "formal conceptive behaviour?" Surely not, for to achieve that the box must be seen from all sides at once, that is, it must be located in a system of perspectives in which one can represent it to oneself from any point of view whatever and transfer it from one to the other point of view without recourse to action. Now, if it is possible for the child to imagine himself as occupying several positions at one time, it is obvious that it is rather by representing to himself the perspective of another person and by coordinating it with his own that he will solve such a problem in concrete reality. In this sense one can maintain that pure representation detached from personal activity presupposes adaptation to others and social coordination.
Therefore we understand why, in the problem of the mountains which is typical in this respect, the child four to six years of age still reveals an egocentrism reminiscent of the beginnings of sensorimotor intelligence and the most elementary subjective groups; it is because, on the plane of pure representation to which this experiment pertains, the subject must compare various points of view with his own, and as yet nothing has prepared him for this operation. Besides, the attitudes which have already been transcended in the relations between things and himself reappear when connections are established with other persons. Social egocentrism follows sensorimotor egocentrism and reproduces its phases, but as the social and the representative are interdependent there appears to be regression here, whereas the mind simply wages the same battles on a new plane to make new conquests.
Moreover, this temporal displacement in comprehension, which arises when there is transition of thought from a lower to a higher plane, may combine with the temporal displacements in extension (of which we have spoken earlier), which arise when problems located on the same plane present increasing complexity. Thus, on the occasion of movements near at hand, after having constructed the groups of displacements studied above, the child finds himself confronted by analogous problems raised by the observation of more distant movements: displacements relating to bodies situated on the horizon or to celestial movements. For many years we have observed the child’s attitude toward the moon and often toward clouds, stars, etc.; until he is about seven years old he believes that he is followed by these bodies and considers their apparent movements real. From the point of view of space, this is only an extension of the behaviour patterns relating to nearby objects observed during the first sensorimotor stages. The child, by taking appearance for reality, links all displacements to himself, instead of locating them in an objective system that includes his own body without being centred on it. Similarly, we have observed in our children analogous illustrations relating to mountains, on an excursion in the Alps or in an automobile going up and down the hills. At four or five years of age the mountains still seem to be displaced and actually to change shape in connection with our own movements, exactly like the nearby objects in the subjective groups of the baby.
These last remnants of primitive space in the child of school age lead us to the temporal displacements of processes relating to the object. It is self-evident that in proportion as the groups of displacements require new constructive work on the plane of representation or of conceptual thought to complete them, the object, in its turn, cannot be considered as entirely elaborated once it has been formed on the sensorimotor plane. At the time of displacements in extension, of which we have spoken apropos of the moon and the mountains, the matter is clear. The mountains which move and change shape with our movements are not objects, since they lack permanence of form and mass. So also a moon which follows us is not "the" moon as object of simultaneous or successive perceptions of different possible observers. The proof is that at the period in which the child believes he is being followed by the stars he believes in the existence of several moons rising over and over again and capable of occupying different regions of space simultaneously.
But this difficulty in attributing substantial identity to distant objects is not the most interesting residue of the processes of objectification peculiar to the stages of sensorimotor intelligence. Or rather, it constitutes only a residue explainable by the simple mechanism of temporal displacements in extension, whereas, because of the temporal displacements in comprehension that condition the transition from the sensorimotor plane to the plane of reflective thought, the construction of the object seems to be not only a continuous process unremittingly pursued throughout the evolution of reason and still found in the most elaborate forms of scientific thought, but also a process constantly passing through phases analogous to those of the initial sensorimotor series. Thus the different principles of conservation whose progressive formation occupies the whole development of the child’s physics are only successive aspects of the objectification of the universe. For example, the conservation of matter does not seem necessary to the child three to six years old in cases of changes of state or even changes of form. Sugar melting in water is believed to be returning to the void, only taste (that is, a pure quality) being supposed to subsist and that only for a few days. So also, when one offers the child two pellets of the same weight and mass and then moulds one of them into a long cylinder, this one is considered to have lost both weight and mass. When one empties the contents of a large ,bottle of water into small bottles or tubes, the quantity of liquid is conceived as having been changed, etc. On the contrary, the child subsequently arrives at the concept of a necessary conservation of matter, independently of changes of form or of state. But having arrived at this level, he nevertheless continues to believe that the weight of bodies can change with their form; thus the pellet by becoming elongated loses weight while conserving the same quantity of matter. Around eleven or twelve years of age, on the other hand, the child is so convinced of the conservation of weight that he attributes to the particles of sugar dissolved in water the same total weight as to the initial lump.
Thus we see that, from the point of view of conservation of matter and weight, the child again, this time on the plane of conceptual and reflective thought, passes through stages analogous to those he traverses on the sensorimotor plane from the point of view of conservation of the object itself. Just as the baby begins by believing that objects return to the void when they are no longer perceived and emerge from it when they re-enter the perceptual field, so also the six-year-old child still thinks the quantity of matter augments or diminishes according to the form the object takes, and that a substance which dissolves is completely annihilated. Then, just as numerous intermediate stages exist between the level on which the baby is the victim of appearances and that on which he constructs a permanence sufficient to make him believe in objects, so also the child who talks passes over a series of steps before he is able to postulate, independently of any direct experience, the constancy of weight itself despite changes in form, and before he forms, with this objective in view, a sort of crude atomism which reconciles quantitative invariance with qualitative variations.
How then can we explain this temporal displacement; how can we explain why thought, at the moment it gathers up the work of sensori-motor intelligence and in particular the belief in permanent objects, does not at the outset attribute to objects constancy of matter and of weight? As we have seen, it is because three formative processes are necessary to the elaboration of object concept: the accommodation of the organs which makes it possible to foresee the reappearance of bodies; the coordination of schemata which makes it possible to endow each of these bodies with a multiplicity of interconnected qualities; and the deduction peculiar to sensorimotor reasoning which makes it possible to understand displacements of bodies and to reconcile their permanence with their apparent variations. These three functional factors - foresight, coordination, and deduction - change entirely in structure when they pass from the sensorimotor plane to that of speech and conceptual operations, and when systems of classes and thoughtful relations are substituted for simple practical schemata. Whereas the substantial object is a mere product of action or practical intelligence, the concepts of quantity of matter and conservation of weight presuppose on the contrary a very subtle rational elaboration. In practical object concept there is nothing more than the idea of a permanence of qualities (form, consistency, colour, etc.) independent of immediate perception. There is, however, in the concept of the conservation of matter such as sugar, the clay pellet which changes shape, or the liquid poured from a large receptacle into several small ones, a quantitative relation which as soon as it is perceived seems essential; this is the idea that despite changes of state or of form (real form and no longer merely apparent form) something is conserved. This something is not at the outset weight, but it is volume, occupied space, and only later is it weight, that is, a quality that is quantified in so far as it is considered invariant. But for their construction these qualitative relationships do not solely involve a foresight which remains practical in kind (foresight of the water level when the sugar is dissolved, of the weight of the pellet made into a cylinder, etc.); they involve primarily a coordination of classes and of logical relations as well as true deduction, for on the plane of thought foresight gradually becomes the function of deduction instead of preceding it.
In the case of the sugar which dissolves in water, how does the child succeed in postulating the permanence of matter and even in making the atomic hypothesis of invisible particles of sugar permeating the liquid, particles whose total volume equals that of the initial lump, to the point of explaining that the water level remains above the original level. From all the evidence this is not a simple lesson of experience or, as in the case of the permanence of the practical object, an intelligent structuring of experience, but rather a deduction which is primarily due to thought and in which a complex series of concepts and relations intervenes. So also, the idea that the pellet conserves its weight while becoming a cylinder is a deductive construction which experience does not suffice to explain, for the child has neither the means to perform the delicate weighing that verification of such a hypothesis would necessitate nor, above alt the curiosity to attempt such a verification, because its affirmation seems to him self-evident and because as a general rule the problem does not arise for him. What is most interesting in the child’s reaction is the fact that, having doubtless never thought about the problem, he solves it at once a priori and with such certainty that he is surprised it was raised, whereas a year or two earlier he would have solved it in precisely the opposite direction and would not have had recourse to the idea of conservation!
In short, the development of the principles of conservation can only be explained as the function of an internal progress in the child’s logic in its triple aspect of an elaboration of deductive structures, of relations, and of classes, forming a corporate system. This is the explanation of the temporal displacement under discussion here. Through speech the child arrives on the plane of representative thought, which at the same time is the plane of socialised thought; to the extent that he must now adapt himself to other persons, his spontaneous egocentrism, already overcome on the sensorimotor plane, reappears in the course of this adaptation, as we have shown with the examples concerning space. From this arises a series of consequences with regard to the structure of thought, as we have emphasised in § 2. On the one hand, in proportion as the child does not succeed in coordinating with his own perspective the perspectives peculiar to different individuals, he cannot master the logic of relationships, although he knows how to handle practical relations on the sensorimotor plane. Thus the concepts of heavy and light which directly concern the conservation of weight are conceived as absolute qualities long before they are understood as purely relative ones, because, once they have been detached from any personal frame of reference, they are applied to the egocentric point of view of immediate perception before being transformed into relations among different subjects and different objects and into relations among objects themselves. Moreover, and by virtue of this fact, the child begins by utilising only syncretic pseudo-concepts before elaborating true logical classes, because the operations formative of classes (logical addition and multiplication) require a system of definitions whose stability and generality transcend the personal point of view and its subjective attachments (definitions by usage, syncretic classifications, etc.). From this stems the conclusion that a deductive structure on the plane of reflective thought presupposes a mind freed from the personal point of view by methods of reciprocity inherent in cooperation or intellectual exchange, and that reason, dominated by egocentrism on the verbal and social plane, can only be "transductive," that is. proceeding through the fusion of pre-concepts located midway between particular cases and true generality.
If the conquest of the object on the sensorimotor plane is not at once extended on the conceptual plane through an objectification capable of insuring rational permanence, it is because the egocentrism reappearing on this new plane prevents thought from attaining at the outset the logical structures necessary for this elaboration. Let us try again to define this mechanism by analysing some examples chosen from the periods of the beginning of speech and of reflective thought; these will show us both how difficult it is at first for the child to form true logical classes and how those pseudo-concepts and primitive transductions lead us back to a stage which, from the point of view of the object, seemed to be surpassed by sensorimotor intelligence and which reappears on the conceptual plane.
First of all it is currently observed that the first generic concepts utilised by the child, when they do not designate certain ordinary objects related to daily activity but totalities properly so called, remain midway between the individual and the general. For a long time, for instance, one of my children, to whom I showed slugs on successive walks, called each new specimen encountered "the slug"; I was unable to ascertain whether he meant "the same individual" or "a new individual of the slug species." While it is impossible to furnish definitive proof, in such a case everything seems to indicate that the child himself neither succeeds in answering nor tries to answer the question and that "Slug" is for him a sort of semi-individual and semi-generic type shared by different individuals. It is the same when the child encounters "Lamb," "Dog," etc.; we are confronted by neither the individual nor the generic in the sense of the logical class but by an intermediate state which is precisely comparable on the conceptual plane to the primitive state of the sensorimotor object floating between the unsubstantial perceptual image and permanent substance.
Interpretation may seem hazardous when observations of this kind are involved because one can always attribute them to mere mistakes by the subject, but it becomes more certain when these pseudo-concepts come into operation in transductions properly so called, that is, in the analytical or classificatory reasoning proceeding by fusion of analogous cases. Let us refer, for example, to the explanations given us by the youngest of our subjects concerning the phenomenon of the shadow or the draft: the shadow produced on a table before their eyes comes, according to them, from "under the trees" or other possible sources of darkness, just as the draft from a fan emanates from the north wind which blows outside the room. The child thus likens, as we do ourselves, the shadow from a notebook to that of the trees, the draft to the wind, etc., but instead of simply placing the two analogous phenomena in the same logical class and explaining them by the same physical law, he considers the two compared terms as participants of each other from a distance and without any intelligible physical link. Consequently, here again the child’s thought wavers between the individual and the generic. The shadow of the notebook is not a pure singular object since it emanates from that of the trees, it "is" really that of trees arising in a new context. But an abstract class does not exist either, precisely since the relation between the two shadows compared is not a relation of simple comparison and common appurtenance to the same totality, but of substantial participation. The shadow perceived on the table is therefore no more an isolable object than is, on the sensorimotor plane, the watch which disappears under one cushion and which the child expects to see appear under another. But if there is thus an apparent return to the past it is for an opposite reason to that which obstructs objectification in sensorimotor intelligence; in the latter case the object is difficult to form in proportion as the child has difficulty in intercoordinating perceptual images, whereas on the plane of conceptual thought the object, already elaborated, again loses its identity to the extent that it is coordinated with other objects to construct a class or a relation.
In conclusion, in the case of the object as in that of space, from the very beginnings of verbal reflection there is a return of the difficulties already overcome on the plane of action, and there is repetition, with temporal displacements, of the stages and process of adaptation defined by the transition from egocentrism to objectivity. And in both cases the phenomenon is due to the difficulties experienced by the child, after he has reached the social plane, in inserting his sensorimotor acquisitions in a framework of relationships of logical classes and deductive structures admitting of true generalisation, that is, taking into account the point of view of others and all possible points of view as well as his own. ***
We recall how, starting with purely practical and quasi-physiological groups, the child begins by elaborating subjective groups, then arrives at objective groups, and only then becomes capable of representative groups. But the groups of this last type, if they constitute the culminating point of practical space and thus insert in sensorimotor spatial relations the representation of displacements not occurring within the direct perceptual field, are far from marking the beginning of a complete representation of space, that is, a representation completely detached from action. What will happen when the child is called upon, apart from any current action, to represent to himself a group of displacements or a system of coherent perspectives? It is from this decisive moment that we witness, on the plane of thought properly so called, a repetition of the evolution already accomplished on the sensorimotor plane.
Take, for example, the following problem. The child is presented with a model, about one square meter in size, representing three mountains in relief; he is to reconstruct the different perspectives in which a little doll views them in varying positions that follow a given order. No technical or verbal difficulty impedes the child, for he may simply point with his finger to what the doll sees, or choose from among several pictures showing the possible perspectives, or construct with boxes symbolising mountains the photograph the doll could take from a given point of view. Moreover, the problem posed to the child consists in representing to himself the simplest of all the spatial relations which transcend direct action and perception, that is, to represent to himself what he would see if he were in the successive positions suggested to him. At first it would seem as though the child’s answers would merely extend the acquisitions of the sixth stage of sensorimotor space and arrive immediately at the correct representations.
But interestingly enough the youngest of the children capable of understanding the problem of the mountains and of responding without difficulties of a verbal or technical kind reveal an attitude which, instead of extending the objective and representative groups of our sixth stage, on the contrary, regresses to the integral egocentrism of the subjective groups. Far from representing the various scenes which the doll contemplates from different viewpoints, the child always considers his own perspective as absolute and thus attributes it to the doll without suspecting this confusion. In other words, when he is asked what the doll sees from a particular position the child describes what he himself sees from his own position without taking into account the obstacles which prevent the doll from seeing the same view. When he is shown several pictures from among which he is to choose the one which corresponds to the doll’s perspective, he chooses the one which represents his own. Finally, when he is to reconstruct with boxes the photograph the doll might take from its place, the child again reproduces his own view of things.
Then, when the child disengages himself from this initial egocentrism and masters the relationships involved in these problems, we witness a totality of transitional phases. Either the child who begins to understand that the perspective differs according to the doll’s position effects various mixtures between those perspectives and his own perspective ("pre-relations"), or else he takes into account only one relation at a time (left-right or before-behind, etc.) and does not succeed in multiplying the interrelations. These transitions correspond to the limited groups of displacements belonging to the fourth of the sensorimotor stages. Finally, complete relativity is attained, corresponding to stages V-VI of the same series.
How then can this temporal displacement be explained, as-well as this return to the phases which have already been transcended on the plane of sensorimotor space? To act in space the child is certainly obliged to understand little by little that the things which surround him have a trajectory independent of himself and that their displacements are thus grouped in objective systems. From a purely practical point of view the child is therefore led to emerge from an initial egocentrism, in which things are considered to depend solely on his personal activity, and to master a relativity which is established between displacements successively perceived or even between certain perceived moments and others which have simply been represented. But the egocentrism and objective relativity in question here concern only the relationships between the child and things, and nothing in sensorimotor action forces him to leave this narrow realm. So long as the problem is not to represent to himself reality in itself, but simply to use it or to exert an influence upon it, there is no need to go beyond the system of relations established between objects and self or among objects as such in the field of personal perspective; there is no need to assume the existence of other perspectives and to interconnect them in including his own among them. To be sure, the act by which one confers an objectivity on the displacements of things already implies an enlargement of the initial egocentric perspective and it is in this sense that, apropos of the fifth and sixth sensorimotor stages, we have been able to speak of a change in perspective and the mastery of a universe in which the subject locates himself instead of bringing the universe illusively to him. But this is only the first step, and even in this objective, practical universe, everything is related to a single frame of reference which is that of the subject and not that of other possible subjects. Hence there is objectivity and even relativity, but within the limits of a realm which is always considered absolute, because nothing yet induces the subject to transcend it. If we may be permitted to make a somewhat daring comparison, the completion of the objective practical universe resembles Newton’s achievements as compared to the egocentrism of Aristotelian physics, but the absolute Newtonian time and space themselves remain egocentric from the point of view of Einstein’s relativity because they envisage only one perspective on the universe among many other perspectives which are equally possible and real. On the contrary, from the time when the child seeks no longer merely to act upon things, but to represent them to himself in themselves and independently of the immediate action, this single perspective, in the midst of which he had succeeded in introducing objectivity and relativity, no longer suffices and has to be coordinated with the others.
This is true for two reasons, one relating to the subject’s intention in his attempt at representation, the other to the requirements of representation. Why at a given moment in his mental evolution does the subject try to represent spatial relations to himself instead of simply acting upon them? Obviously in order to communicate to someone else or to obtain from someone else some information on a fact concerning space. Outside of this social relation there is no apparent reason why pure representation should follow action. The existence of multiple perspectives relating to various individuals is therefore already involved in the child’s effort to represent space to himself. Moreover, to represent to himself space or objects in space is necessarily to reconcile in a single act the different possible perspectives on reality and no longer to be satisfied to adopt them successively. Take, for example, a box or some object upon which the child acts. At the end of his sensorimotor evolution he becomes perfectly capable of turning the box over in all directions, of representing to himself its reverse side as well as its visible parts, its contents as well as its exterior. But do these representations connected with practical activity, with the "concrete active behaviour" of which Gelb and Goldstein have spoken in their fine studies on space, suffice to constitute a total representation of the box, a pattern of "formal conceptive behaviour?" Surely not, for to achieve that the box must be seen from all sides at once, that is, it must be located in a system of perspectives in which one can represent it to oneself from any point of view whatever and transfer it from one to the other point of view without recourse to action. Now, if it is possible for the child to imagine himself as occupying several positions at one time, it is obvious that it is rather by representing to himself the perspective of another person and by coordinating it with his own that he will solve such a problem in concrete reality. In this sense one can maintain that pure representation detached from personal activity presupposes adaptation to others and social coordination.
Therefore we understand why, in the problem of the mountains which is typical in this respect, the child four to six years of age still reveals an egocentrism reminiscent of the beginnings of sensorimotor intelligence and the most elementary subjective groups; it is because, on the plane of pure representation to which this experiment pertains, the subject must compare various points of view with his own, and as yet nothing has prepared him for this operation. Besides, the attitudes which have already been transcended in the relations between things and himself reappear when connections are established with other persons. Social egocentrism follows sensorimotor egocentrism and reproduces its phases, but as the social and the representative are interdependent there appears to be regression here, whereas the mind simply wages the same battles on a new plane to make new conquests.
Moreover, this temporal displacement in comprehension, which arises when there is transition of thought from a lower to a higher plane, may combine with the temporal displacements in extension (of which we have spoken earlier), which arise when problems located on the same plane present increasing complexity. Thus, on the occasion of movements near at hand, after having constructed the groups of displacements studied above, the child finds himself confronted by analogous problems raised by the observation of more distant movements: displacements relating to bodies situated on the horizon or to celestial movements. For many years we have observed the child’s attitude toward the moon and often toward clouds, stars, etc.; until he is about seven years old he believes that he is followed by these bodies and considers their apparent movements real. From the point of view of space, this is only an extension of the behaviour patterns relating to nearby objects observed during the first sensorimotor stages. The child, by taking appearance for reality, links all displacements to himself, instead of locating them in an objective system that includes his own body without being centred on it. Similarly, we have observed in our children analogous illustrations relating to mountains, on an excursion in the Alps or in an automobile going up and down the hills. At four or five years of age the mountains still seem to be displaced and actually to change shape in connection with our own movements, exactly like the nearby objects in the subjective groups of the baby.
These last remnants of primitive space in the child of school age lead us to the temporal displacements of processes relating to the object. It is self-evident that in proportion as the groups of displacements require new constructive work on the plane of representation or of conceptual thought to complete them, the object, in its turn, cannot be considered as entirely elaborated once it has been formed on the sensorimotor plane. At the time of displacements in extension, of which we have spoken apropos of the moon and the mountains, the matter is clear. The mountains which move and change shape with our movements are not objects, since they lack permanence of form and mass. So also a moon which follows us is not "the" moon as object of simultaneous or successive perceptions of different possible observers. The proof is that at the period in which the child believes he is being followed by the stars he believes in the existence of several moons rising over and over again and capable of occupying different regions of space simultaneously.
But this difficulty in attributing substantial identity to distant objects is not the most interesting residue of the processes of objectification peculiar to the stages of sensorimotor intelligence. Or rather, it constitutes only a residue explainable by the simple mechanism of temporal displacements in extension, whereas, because of the temporal displacements in comprehension that condition the transition from the sensorimotor plane to the plane of reflective thought, the construction of the object seems to be not only a continuous process unremittingly pursued throughout the evolution of reason and still found in the most elaborate forms of scientific thought, but also a process constantly passing through phases analogous to those of the initial sensorimotor series. Thus the different principles of conservation whose progressive formation occupies the whole development of the child’s physics are only successive aspects of the objectification of the universe. For example, the conservation of matter does not seem necessary to the child three to six years old in cases of changes of state or even changes of form. Sugar melting in water is believed to be returning to the void, only taste (that is, a pure quality) being supposed to subsist and that only for a few days. So also, when one offers the child two pellets of the same weight and mass and then moulds one of them into a long cylinder, this one is considered to have lost both weight and mass. When one empties the contents of a large ,bottle of water into small bottles or tubes, the quantity of liquid is conceived as having been changed, etc. On the contrary, the child subsequently arrives at the concept of a necessary conservation of matter, independently of changes of form or of state. But having arrived at this level, he nevertheless continues to believe that the weight of bodies can change with their form; thus the pellet by becoming elongated loses weight while conserving the same quantity of matter. Around eleven or twelve years of age, on the other hand, the child is so convinced of the conservation of weight that he attributes to the particles of sugar dissolved in water the same total weight as to the initial lump.
Thus we see that, from the point of view of conservation of matter and weight, the child again, this time on the plane of conceptual and reflective thought, passes through stages analogous to those he traverses on the sensorimotor plane from the point of view of conservation of the object itself. Just as the baby begins by believing that objects return to the void when they are no longer perceived and emerge from it when they re-enter the perceptual field, so also the six-year-old child still thinks the quantity of matter augments or diminishes according to the form the object takes, and that a substance which dissolves is completely annihilated. Then, just as numerous intermediate stages exist between the level on which the baby is the victim of appearances and that on which he constructs a permanence sufficient to make him believe in objects, so also the child who talks passes over a series of steps before he is able to postulate, independently of any direct experience, the constancy of weight itself despite changes in form, and before he forms, with this objective in view, a sort of crude atomism which reconciles quantitative invariance with qualitative variations.
How then can we explain this temporal displacement; how can we explain why thought, at the moment it gathers up the work of sensori-motor intelligence and in particular the belief in permanent objects, does not at the outset attribute to objects constancy of matter and of weight? As we have seen, it is because three formative processes are necessary to the elaboration of object concept: the accommodation of the organs which makes it possible to foresee the reappearance of bodies; the coordination of schemata which makes it possible to endow each of these bodies with a multiplicity of interconnected qualities; and the deduction peculiar to sensorimotor reasoning which makes it possible to understand displacements of bodies and to reconcile their permanence with their apparent variations. These three functional factors - foresight, coordination, and deduction - change entirely in structure when they pass from the sensorimotor plane to that of speech and conceptual operations, and when systems of classes and thoughtful relations are substituted for simple practical schemata. Whereas the substantial object is a mere product of action or practical intelligence, the concepts of quantity of matter and conservation of weight presuppose on the contrary a very subtle rational elaboration. In practical object concept there is nothing more than the idea of a permanence of qualities (form, consistency, colour, etc.) independent of immediate perception. There is, however, in the concept of the conservation of matter such as sugar, the clay pellet which changes shape, or the liquid poured from a large receptacle into several small ones, a quantitative relation which as soon as it is perceived seems essential; this is the idea that despite changes of state or of form (real form and no longer merely apparent form) something is conserved. This something is not at the outset weight, but it is volume, occupied space, and only later is it weight, that is, a quality that is quantified in so far as it is considered invariant. But for their construction these qualitative relationships do not solely involve a foresight which remains practical in kind (foresight of the water level when the sugar is dissolved, of the weight of the pellet made into a cylinder, etc.); they involve primarily a coordination of classes and of logical relations as well as true deduction, for on the plane of thought foresight gradually becomes the function of deduction instead of preceding it.
In the case of the sugar which dissolves in water, how does the child succeed in postulating the permanence of matter and even in making the atomic hypothesis of invisible particles of sugar permeating the liquid, particles whose total volume equals that of the initial lump, to the point of explaining that the water level remains above the original level. From all the evidence this is not a simple lesson of experience or, as in the case of the permanence of the practical object, an intelligent structuring of experience, but rather a deduction which is primarily due to thought and in which a complex series of concepts and relations intervenes. So also, the idea that the pellet conserves its weight while becoming a cylinder is a deductive construction which experience does not suffice to explain, for the child has neither the means to perform the delicate weighing that verification of such a hypothesis would necessitate nor, above alt the curiosity to attempt such a verification, because its affirmation seems to him self-evident and because as a general rule the problem does not arise for him. What is most interesting in the child’s reaction is the fact that, having doubtless never thought about the problem, he solves it at once a priori and with such certainty that he is surprised it was raised, whereas a year or two earlier he would have solved it in precisely the opposite direction and would not have had recourse to the idea of conservation!
In short, the development of the principles of conservation can only be explained as the function of an internal progress in the child’s logic in its triple aspect of an elaboration of deductive structures, of relations, and of classes, forming a corporate system. This is the explanation of the temporal displacement under discussion here. Through speech the child arrives on the plane of representative thought, which at the same time is the plane of socialised thought; to the extent that he must now adapt himself to other persons, his spontaneous egocentrism, already overcome on the sensorimotor plane, reappears in the course of this adaptation, as we have shown with the examples concerning space. From this arises a series of consequences with regard to the structure of thought, as we have emphasised in § 2. On the one hand, in proportion as the child does not succeed in coordinating with his own perspective the perspectives peculiar to different individuals, he cannot master the logic of relationships, although he knows how to handle practical relations on the sensorimotor plane. Thus the concepts of heavy and light which directly concern the conservation of weight are conceived as absolute qualities long before they are understood as purely relative ones, because, once they have been detached from any personal frame of reference, they are applied to the egocentric point of view of immediate perception before being transformed into relations among different subjects and different objects and into relations among objects themselves. Moreover, and by virtue of this fact, the child begins by utilising only syncretic pseudo-concepts before elaborating true logical classes, because the operations formative of classes (logical addition and multiplication) require a system of definitions whose stability and generality transcend the personal point of view and its subjective attachments (definitions by usage, syncretic classifications, etc.). From this stems the conclusion that a deductive structure on the plane of reflective thought presupposes a mind freed from the personal point of view by methods of reciprocity inherent in cooperation or intellectual exchange, and that reason, dominated by egocentrism on the verbal and social plane, can only be "transductive," that is. proceeding through the fusion of pre-concepts located midway between particular cases and true generality.
If the conquest of the object on the sensorimotor plane is not at once extended on the conceptual plane through an objectification capable of insuring rational permanence, it is because the egocentrism reappearing on this new plane prevents thought from attaining at the outset the logical structures necessary for this elaboration. Let us try again to define this mechanism by analysing some examples chosen from the periods of the beginning of speech and of reflective thought; these will show us both how difficult it is at first for the child to form true logical classes and how those pseudo-concepts and primitive transductions lead us back to a stage which, from the point of view of the object, seemed to be surpassed by sensorimotor intelligence and which reappears on the conceptual plane.
First of all it is currently observed that the first generic concepts utilised by the child, when they do not designate certain ordinary objects related to daily activity but totalities properly so called, remain midway between the individual and the general. For a long time, for instance, one of my children, to whom I showed slugs on successive walks, called each new specimen encountered "the slug"; I was unable to ascertain whether he meant "the same individual" or "a new individual of the slug species." While it is impossible to furnish definitive proof, in such a case everything seems to indicate that the child himself neither succeeds in answering nor tries to answer the question and that "Slug" is for him a sort of semi-individual and semi-generic type shared by different individuals. It is the same when the child encounters "Lamb," "Dog," etc.; we are confronted by neither the individual nor the generic in the sense of the logical class but by an intermediate state which is precisely comparable on the conceptual plane to the primitive state of the sensorimotor object floating between the unsubstantial perceptual image and permanent substance.
Interpretation may seem hazardous when observations of this kind are involved because one can always attribute them to mere mistakes by the subject, but it becomes more certain when these pseudo-concepts come into operation in transductions properly so called, that is, in the analytical or classificatory reasoning proceeding by fusion of analogous cases. Let us refer, for example, to the explanations given us by the youngest of our subjects concerning the phenomenon of the shadow or the draft: the shadow produced on a table before their eyes comes, according to them, from "under the trees" or other possible sources of darkness, just as the draft from a fan emanates from the north wind which blows outside the room. The child thus likens, as we do ourselves, the shadow from a notebook to that of the trees, the draft to the wind, etc., but instead of simply placing the two analogous phenomena in the same logical class and explaining them by the same physical law, he considers the two compared terms as participants of each other from a distance and without any intelligible physical link. Consequently, here again the child’s thought wavers between the individual and the generic. The shadow of the notebook is not a pure singular object since it emanates from that of the trees, it "is" really that of trees arising in a new context. But an abstract class does not exist either, precisely since the relation between the two shadows compared is not a relation of simple comparison and common appurtenance to the same totality, but of substantial participation. The shadow perceived on the table is therefore no more an isolable object than is, on the sensorimotor plane, the watch which disappears under one cushion and which the child expects to see appear under another. But if there is thus an apparent return to the past it is for an opposite reason to that which obstructs objectification in sensorimotor intelligence; in the latter case the object is difficult to form in proportion as the child has difficulty in intercoordinating perceptual images, whereas on the plane of conceptual thought the object, already elaborated, again loses its identity to the extent that it is coordinated with other objects to construct a class or a relation.
In conclusion, in the case of the object as in that of space, from the very beginnings of verbal reflection there is a return of the difficulties already overcome on the plane of action, and there is repetition, with temporal displacements, of the stages and process of adaptation defined by the transition from egocentrism to objectivity. And in both cases the phenomenon is due to the difficulties experienced by the child, after he has reached the social plane, in inserting his sensorimotor acquisitions in a framework of relationships of logical classes and deductive structures admitting of true generalisation, that is, taking into account the point of view of others and all possible points of view as well as his own. ***
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