ABSTRACT
Throughout history the concept of infinity has played an important role in almost every branch of human knowledge. Paradoxically, very little effort has been made by the various theoretical schools in Cognitive Science to study this fascinating aspect of human mental activity. The study of subdivision offers an interesting subject matter to address the question of how the idea of infinity in the small emerge in our minds. 32 students, aged 8, 10, 12 and 14 (high and low intellectual-academic performers), participated in this study, in which a version of one of Zeno’s paradoxes was analyzed by means of individual interviews. Results suggest that between ages 10 and 12, a certain intuition of the entailments of subdivision emerges, remaining very labile afterwards and being very influenced by the context. 66% of the 12- and 14-year-old children said that the process involved in the paradox comes to an end. Less than 25% considered (with deep hesitations) the possibility that the process might continue endlessly. This suggests that the classic piagetian view that the indefinite subdivision is mastered at the period of formal operations must be reassessed. Some epistemological consequences based on an embodied-cognition oriented perspective are discussed.
