Abstract

This essay considers the ‘limit’ in Derrida's work from the early consideration of linearisation in ‘Ousia and Grammē’ to the conception of limit as aporia in Aporias. Developing Derrida's tripartite definition of the limit via a reading of Being and Time as closure, border and demarcation, the essay then considers the earlier presentation of limit in Heidegger as temporal primordiality. Developing the metaphysics of line as presentation of presence in terms of Aristotle's aporetics of time as line, the circle is then considered as representing the closed field of presence and its definition via the negation of being's other. This leads to Derrida's early, foundational definition of the law of metaphysics as submission-subtraction, and his proposal of the trace as an alternate way of thinking spatially about being, nonbeing and difference. The second half of the essay then proposes a series of alternative ways of thinking geometrically to those of the traditional metaphysics of point-line-circle topography. Thus topology is proposed as an alternate means of thinking field enclosure, similarity and difference. The figures of the double torus and mathematical limit are proposed as a potential alternative geometry for Western thought. Finally the essay concludes on the apotropaic logic of the problem which echoes that of the trace and is developed in contradistinction to the aporia. Proposing the edge as an interim state between the metaphysics of the line and the deconstructive impossibilities of the aporia, it suggests that the limits of metaphysics are to be found not merely in the apotropaic law of submission-subtraction, but also across alternate geometries which facilitate the bringing together of the two central elements of the totality of Derrida's thinking the limit: différance and singularity