VICIOUS CIRCLE AND CRITICAL REVOLUTION IN GILLES DELEUZE’S THEORY OF PROBLEMS

the Role of Algebra in Deleuze's Transcendental Philosophy

Abstract

This paper aims to shed light on the concept of “problem” developed by Gilles Deleuze in Difference and repetition by analyzing the presence in that book of the Norwegian algebraist Niels Henrik Abel. Deleuze attributes to this mathematician having invented a method that breaks the “vicious circle” which consists in tracing the problems to the image and similarity of

the solutions. We will argue that Deleuze’s interpretation is based on Jules Vuillemin’s work La philosophie de l’algèbre, which draws a parallelism between Lagrange’s algebra and Fichte’s transcendental philosophy to show a common flaw in both their methods. We will begin by characterizing the aforementioned “vicious circle”, and then go through the general characteristics of the algebraic problem and its parallel with critical philosophy, in order to show, finally, the main features that Deleuze seeks to highlight in the abelian method –presented by Vuillemin as the overcoming of Lagrange (and, consequently, of Fichte).