David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jack Alan Reynolds
Learn more about PhilPapers
Dissertation, Mcgill University (Canada) (2003)
In this thesis, I investigate the nature of geometric knowledge and its relationship to spatial intuition. My goal is to rehabilitate the Kantian view that Euclid's geometry is a mathematical practice, which is grounded in spatial intuition, yet, nevertheless, yields a type of a priori knowledge about the structure of visual space. I argue for this by showing that Euclid's geometry allows us to derive knowledge from idealized visual objects, i.e., idealized diagrams by means of non-formal logical inferences. By developing such an account of Euclid's geometry, I complete the "standard view" that geometry is either a formal system or an empirical science , which was developed mainly by the logical positivists and which is currently accepted by many mathematicians and philosophers. My thesis is divided into three parts. I use Hans Reichenbach's arguments against Kant and Edmund Husserl's genetic approach to the concept of space as a means of arguing that the "standard view" has to be supplemented by a concept of a geometry whose propositions have genuine spatial content. I then develop a coherent interpretation of Euclid's method by investigating both the subject matter of Euclid's geometry and the nature of geometric inferences. In the final part of this thesis, I modify Husserl's phenomenological analysis of the constitution of visual space in order to define a concept of spatial intuition that allows me not only to explain how Euclid's practice is grounded in visual space, but also to account for the apriority of its results
|Keywords||No keywords specified (fix it)|
|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
Michael Friedman (2012). Kant on Geometry and Spatial Intuition. Synthese 186 (1):231-255.
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.
Lisa Shabel (2004). Kant's "Argument From Geometry". Journal of the History of Philosophy 42 (2):195-215.
Helen De Cruz (2007). An Enhanced Argument for Innate Elementary Geometric Knowledge and its Philosophical Implications. In Bart Van Kerkhove (ed.), New perspectives on mathematical practices. Essays in philosophy and history of mathematics. World Scientific
Jairo da Silva (2012). Husserl on Geometry and Spatial Representation. Axiomathes 22 (1):5-30.
Jairo José Silva (2012). Husserl on Geometry and Spatial Representation. Axiomathes 22 (1):5-30.
Mirja Helena Hartimo (2008). From Geometry to Phenomenology. Synthese 162 (2):225 - 233.
Davide Rizza (2009). Abstraction and Intuition in Peano's Axiomatizations of Geometry. History and Philosophy of Logic 30 (4):349-368.
Richard Tieszen (2005). Free Variation and the Intuition of Geometric Essences: Some Reflections on Phenomenology and Modern Geometry. Philosophy and Phenomenological Research 70 (1):153–173.
Marco Panza (2012). The Twofold Role of Diagrams in Euclid's Plane Geometry. Synthese 186 (1):55-102.
Phillip John Meadows (2011). Contemporary Arguments for a Geometry of Visual Experience. European Journal of Philosophy 19 (3):408-430.
Stewart Shapiro (1996). Space, Number and Structure: A Tale of Two Debates. Philosophia Mathematica 4 (2):148-173.
Terry F. Godlove Jr (2009). Poincaré, Kant, and the Scope of Mathematical Intuition. Review of Metaphysics 62 (4):779-801.
Gary Hatfield (1984). Spatial Perception and Geometry in Kant and Helmholtz. PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1984:569 - 587.
Added to index2011-01-07
Total downloads68 ( #62,160 of 1,902,050 )
Recent downloads (6 months)4 ( #205,572 of 1,902,050 )
How can I increase my downloads?