Geometry, Formalism and Intuition: David Hilbert and the formal Axiomatic Method (1891-1905)

Abstract

The paper presents and analyzes a set of unpublished notes for lecture courses on geometry, which David Hilbert gave between 1891 and 1905. it will be argued that in these lecture courses the author elaborates the conception of geometry which underlies his axiomatic investigations in Foundations of Geometry (1899). on the one hand, it is claimed that this conception of geometry can be characterized by: i) an abstract or formal axiomatic view; ii) an empiricist stance regarding the origins of geometry and its place among the different mathematical theories. on the other hand, it is asserted that the role that Hilbert assigns to geometrical intuition in the process of the (formal) axiomatization of this theory, can be used to perceive his clear opposition with regard to (radical) formalist views which he is often identified with.