Title: An enhanced argument for innate elementary geometric knowledge and its philosophical implications
Authors: De Cruz, Helen
Issue Date: 2009
Publisher: World Scientific
Host Document: New perspectives on mathematical practices. Essays in philosophy and history of mathematics pages:185-206
Conference: Perspectives on Mathematical Practice edition:2 location:Brussels date:26-28 March 2007
Abstract: The idea that formal geometry derives from intuitive notions of space has appeared in many guises, most notably in Kant’s argument from geometry. Kant claimed that an a priori knowledge of spatial relationships both allows
and constrains formal geometry: it serves as the actual source of our cognition of principles of geometry and as a basis for its further cultural development. The development of non-Euclidean geometries, however, seemed to denitely
undermine the idea that there is some privileged relationship between our spatial intuitions and mathematical theory. This paper’s aim is to look at this
longstanding philosophical issue through the lens of cognitive science. Drawing on recent evidence from cognitive ethology, developmental psychology, neuroscience and anthropology, I argue for an enhanced, more informed version of the argument from geometry: humans share with other species evolved, innate intuitions of space which serve as a vital precondition for geometry as a formal
ISBN: 978-9812812223
Publication status: published
KU Leuven publication type: IHb
Appears in Collections:Centre for Logic and Analytical Philosophy

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