ABSTRACT
When we ask children to explain and compare two causal situations, we find ourselves face to face with new problems. The first concerns “lawfulness.” Lawfulness is evident in functions different in nature from correspondences among arbitrary forms. This is because lawful functions consist not only in comparisons between the results of two transformations (Tf’s) 1 but also add the idea of dependency between the transformations of y and those of x. When the child discovers dependency between covariations by means of correspondences of this sort, he needs to explain them causally or, in other words, to show why such dependency is necessary. According to our previous hypotheses, casual explanation consists in assimilating the transformations observed to some sort of operations analogous to the subject’s own operations but “attributed” to the objects themselves. In causal explanations, objects are therefore considered to be operators. That being the case, the correspondences that the subject establishes between transformations he discovers deep within objects and his own operations will constitute a second problem. In other words, the correspondences that the subject finds between the processes he observes and the deductive model to which he is committed present more difficulties. It is, however, a matter of course that this second system of correspondences, while being more or less clearly manifested in notions that the child constructs, cannot be teased out by the observer. This is because the mechanisms responsible for the “attribution” in which it results are not conscious. The psychologist’s job is, therefore, to establish how the subject uses his logicomathematical, in particular his spatial and “infralogical,” operations 2 in general in order to interpret causal connections among phenomena. Contrary to some people’s opinion, it is easy for the experimenter to discern the operations the subject uses without confusing them with those of the adult theoretician. The most noteworthy way this is accomplished is by comparing the child’s operations to those of following as well as to those of preceding stages. Nevertheless, a difficulty remains with respect to the distinction of causal operations from those that the subject already employs on the plane of lawfulness. In effect, it is clear that the subject needs a logicomathematical framework even to “read” facts. In that case, however, it is only a matter of operations “applied” to objects as assimilatory instruments; it is not yet a matter of operations “attributed” to objects in the sense just defined. Even if this distinction complicates the analysis, the persisting problem is still to reconsitute the correspondences between transformations that the subject situates in reality and his own operations or conceptual schemes.
