Geometry and Spatial Intuition: A Genetic Approach

Dissertation, Mcgill University (Canada) (2003)
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Abstract

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.

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Rene Jagnow
University of Georgia

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References found in this work

Inference and Meaning.Wilfrid Sellars - 1956 - Journal of Symbolic Logic 21 (2):203-204.
Perception.Kevin Mulligan - 1995 - In Barry Smith & David Woodruff Smith (eds.), The Cambridge companion to Husserl. New York: Cambridge University Press. pp. 168-238.
Kant on Intuition in Geometry.Emily Carson - 1997 - Canadian Journal of Philosophy 27 (4):489 - 512.

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