Originally published in 1974, a wide and interesting set of intellectual abilities in children are examined here. Volume 1 of 4 (Organization of Length and Class Concepts: Empirical Consequences of a Piagetian Formalism) converts an axiomatization of classes and asymmetrical relationships (proper to Piaget's discipline of Genetic Epistemology) into a model of the development of these notions in children. Here may be one of the only attempts to derive predictive consequences from the more philosophically oriented writings of the Genevan School.