The concept of space in Veronese

Le concept de l'espace chez Veronese

Paola Cantu (1)

1 Université de Provence - Aix-Marseille 1

Giuseppe Veronese (1854-1917) is well known for his studies on hyperspaces, whereas his remarks on the foundations of geometry and mathematics have been rarely investigated in the literature. The paper investigates Veronese’s writings on the construction of a non-Archimedean geometry (several years before David Hilbert) and on the formulation of a notion of continuity that includes infinitely great ans small quantities. The author presents several central issues of Veronese’s epistemology and analyzes the relation between geometry and spatial intuition by means of a comparison of the conceptions of geometrical space developed by Helmholtz and Poincaré. According to Veronese, the geometrical space can be distinguished from the intuitive space, but both are non-Euclidean and lack a fixed number of dimensions. Thus, both a four dimensional space and a non-Archimedean continuum can be intuited.

Mots clés: continuum; space; intuition; Veronese; Helmholtz; Poincaré; hyperspaces; infinite; geometry

Domaines: Philosophie; Histoire, Philosophie et Sociologie des sciences; Histoire et perspectives sur les mathématiques [math.HO]

Paola Cantu. Le concept de l'espace chez Veronese : Une comparaison avec la conception de Helmholtz et Poincaré. Philosophia Scientiae, 2009, 13 (2), pp.129-149. ⟨10.4000/philosophiascientiae.299⟩. ⟨hal-00587737⟩