Le concept d’espace chez Veronese

Abstract

Giuseppe Veronese is known for his studies on spaces with more dimensions; less known are his “philosophical” writings, that concern the foundations of geometry and mathematics and explain the reasons for constructing a non-Archimedean geometry (several years before David Hilbert’s Grundlagen) and the formulation of a concept of continuity that admits infinitely big and small quantities. After sketching some relevant aspects of Veronese’s epis-temology, the article will analyse the relation between geometry and spatial intuition by a comparison of Veronese’s, Helmholtz’s and Poincaré’s conceptions of the geometrical space. According to Veronese, the representational space, and the geometrical space as well, are not Euclidean nor have a definite number of dimensions: that is why one can represent himself a space with four dimensions and even a non-Archimedean continuum.