The Geometrical Foundation of Federigo Enriques’ Gnoseology and Epistemology

Abstract

The purpose of this paper is to valuate the role of geometry inside Enriques’ theory of knowledge and epistemology. Our thesis is that such a role is prominent. We offer a particular interpretation of Enriques’ gnoseology, according to which geometry is the cornerstone to fully catch also the way in which he framed his conception of the history of science, of the origin of philosophy and of mathematics’ foundations. Our argumentation is divided into three sections: in the first one, we provide the reader with Enriques’ ideas on the physiological and conceptual bases of geometry. We distinguish between the primary and the secondary intuitions and expound the role Enriques ascribes to history inside the construction of human mind. In the second section, Enriques’ idea that philosophy was born as a rational geometry is expounded. In the third section we see what foundations of mathematics means in Enriques’ speculation. The reader will be in front of a thinker, whose theories are not separated one from the other, rather they are strictly connected. Geometry is the link which ties the various parts of Enriques’ theories and contributions. The Italian mathematician was an important thinker inside the European cultural milieu oriented towards scientific philosophy. In different forms, and with different ideas, mathematicians, philosophers, scientists as Mach, Poincaré, Hilbert, Painlevé—only to mention the most famous ones— were members of such a milieu, which, between the end of the 19th century and the beginning of the first world war, hoped to construct a philosophy based on science, whose value should have not been only scientific, but socio-anthropological, as well.