David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jack Alan Reynolds
Learn more about PhilPapers
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)|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library|
References found in this work BETA
No references found.
Citations of this work BETA
No citations found.
Similar books and articles
John L. Bell, Two Approaches to Modelling the Universe: Synthetic Differential Geometry and Frame-Valued Sets.
Elizabeth Spelke, Sang Ah Lee & Véronique Izard (2010). Beyond Core Knowledge: Natural Geometry. Cognitive Science 34 (5):863-884.
David Stump (1991). Poincaré's Thesis of the Translatability of Euclidean and Non-Euclidean Geometries. Noûs 25 (5):639-657.
Michael Friedman (2012). Kant on Geometry and Spatial Intuition. Synthese 186 (1):231-255.
Terry F. Godlove Jr (2009). Poincaré, Kant, and the Scope of Mathematical Intuition. Review of Metaphysics 62 (4):779-801.
Jairo José Silva (2012). Husserl on Geometry and Spatial Representation. Axiomathes 22 (1):5-30.
Jairo da Silva (2012). Husserl on Geometry and Spatial Representation. Axiomathes 22 (1):5-30.
René Jagnow (2006). Edmund Husserl on the Applicability of Formal Geometry. In Emily Carson & Renate Huber (eds.), Intuition and the Axiomatic Method. Springer 67--85.
Rene Jagnow (2003). Geometry and Spatial Intuition: A Genetic Approach. Dissertation, Mcgill University (Canada)
Lisa Shabel (2004). Kant's "Argument From Geometry". Journal of the History of Philosophy 42 (2):195-215.
Added to index2009-11-20
Total downloads134 ( #26,139 of 1,789,801 )
Recent downloads (6 months)1 ( #420,681 of 1,789,801 )
How can I increase my downloads?