Hacia una resistencia sintética en filosofía matemática

(Towards a Synthetic Resistance in Mathematical Philosophy)

Abstract

We study the concept of border/frontier under non-analytical perspectives (reverse, continuity, mediation), and we situate Riemann’s surfaces (1850), Peirce’s continuum (1890) and Grothendieck’s categorical archetypes (1960) under those three perspectives. We further present sheaf logic as a mediation between logical (analytical) and topological (synthetical) polarities, which helps to better understand some border/frontier problems, and to expand reason beyond purely linguistic constraints.