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This latest volume in the series of translations of Piaget's valuable works was originally published in 1941 in Switzerland. This is its first appearance in English. Continuing his earlier work on language, thought, judgment, reasoning and physical causality, he resumes with a further study investigating the development of the child's operations which give rise to number, continuous quantities, to space, to intuitive and egocentric pre-logic, and rational co-ordination that will be both inductive and deductive. The procedure in this study remains, as always in Piaget's work, free conversation with the child, governed by the questions put to him and the answers received. But it is now necessary to add actual manipulation of objects—it is not just thinking in a void.
The author and his co-workers (they never work alone but in a collaborative setting) postulate that the construction of number goes together with the development of logic, and that a pre-numeral stage corresponds to a pre-logical developmental level. His observational results show that number is really organized in stages, in close connection with the gradual elaborations of “systems of inclusions” (hierarchy of logical classes) and systems of asymmetrical relations (qualitative seriations). The sequence of numbers thus results from an operational synthesis of classification and seriation. Arithmetical operations result from a generalization and fusion of logical operations that seem psychologically natural, quality generally being disregarded. When the child has to apply this operational system to sets which are qualitatively defined he is then forced to consider classes and asymmetrical relationships.
There is thus a kind of dualism of the logic of classes and asymmetrical relations. When this system is applied to sets irrespective of their qualities, the fusion of inclusion and seriation of the elements into a single operational totality takes place, and this same