Mathematizing the Limits of Time: Heidegger, Derrida, and the Topology of Temporality

Abstract

"The mathematization of time has limits," writes Derrida in Ousia and Gramme. Taking this quote in all possible senses, this paper considers Derrida's definition of limit as gramme, trace, and aporia, and develops the mathematization of all three. I will consider the structure of mathematical limit in Fregean arithmetics, calculus, and topology. I argue that a topological approach to the concept of gramme creates a new "limit" that illustrates the map of our "commute" to the unknown, and therefore avoids the aporetic act of crossing the impassible limit between life and death. This new "limit," often referred to by mathematicians as a "cone," is a shapeless shape that offers us knowledge about time and space that we otherwise cannot know about. By redefining the limit of time through three mathematical systems -- arithmetic, calculus, and topology -- this paper offers new perspectives to couple mathematics with philosophy.