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Beyond natural geometry: on the nature of proto-geometry

ABSTRACT We discuss the thesis of universality of geometric notions and offer critical reflections on the concept of “natural geometry” employed by Spelke and others. Promoting interdisciplinary work in this field, we bring in logical results and historical evidence, turning to cognitive history and cognitive archaeology in search of clarification of what basic “proto-geometry” might be. This notion is proposed as an alternative to “natural geometry.” Moreover, we highlight the role of cognitive artifacts and external representations (e.g., pictures, diagrams) in making possible the emergence of proto-geometric notions, and we end up with a tentative characterization of “proto-geometry” that underscores its differences with Euclidean geometry. Regarding universality, we suggest that a line of argument toward such a conclusion might be based on comparative historical considerations.