Les originations de la géométrie. Les problèmes posés par le singulier dans le titre de Husserl

Abstract

The programme of geometrical archaeology initiated by the last Husserlian texts merits being taken further with renewed emphasis on historical discontinuities. The revolutions that geometry has gone through have led to profound changes in meaning. The arch-foundations of geometry were not actually definitively set out at the time of the first factual institution of geometry, namely Greek geometry. Instead, the full plurality of the historical forms of geometry does not just consist of a movement to generalise axioms. It involves the reform of the archi-foundations themselves. We will show this using the example of two important revolutions: 1) the discovery of non-Euclidean geometries and 2) the transition to a differential geometry and a dynamic metric. We will also discuss the philosophical difficulties these two moments of re-origination brought up. These studies will follow an introductory section on historical phenomenology and the architecture of the original strata of geometry, the idea being to introduce the conceptual tools and vocabulary required for the studies in the final part.