In Bart Van Kerkhove (ed.), New perspectives on mathematical practices. Essays in philosophy and history of mathematics. World Scientific (2007)
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 deﬁnitely 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 science.
|Keywords||argument from geometry mathematical cognition mathematical intuition|
|Categories||categorize this paper)|
References found in this work BETA
No references found.
Citations of this work BETA
No citations found.
Similar books and articles
Two Approaches to Modelling the Universe: Synthetic Differential Geometry and Frame-Valued Sets.John L. Bell - unknown
Beyond Core Knowledge: Natural Geometry.Elizabeth Spelke, Sang Ah Lee & Véronique Izard - 2010 - Cognitive Science 34 (5):863-884.
Poincaré's Thesis of the Translatability of Euclidean and Non-Euclidean Geometries.David Stump - 1991 - Noûs 25 (5):639-657.
Poincaré, Kant, and the Scope of Mathematical Intuition.Terry F. Godlove - 2009 - Review of Metaphysics 62 (4):779-801.
Edmund Husserl on the Applicability of Formal Geometry.René Jagnow - 2006 - In Emily Carson & Renate Huber (eds.), Intuition and the Axiomatic Method. Springer. pp. 67-85.
Added to index2009-11-20
Total downloads142 ( #32,782 of 2,158,842 )
Recent downloads (6 months)2 ( #193,365 of 2,158,842 )
How can I increase my downloads?