Hegel and Deleuze on the Metaphysical Interpretation of the Calculus

The aim of this paper is to explore the uses made of the calculus by Gilles Deleuze and G.W.F. Hegel. I show how both Deleuze and Hegel see the calculus as providing a way of thinking outside of finite representation. For Hegel, this involves attempting to show that the foundations of the calculus cannot be thought by the finite understanding, and necessitate a move to the standpoint of infinite reason. I analyse Hegel’s justification for this introduction of dialectical reason by looking at his responses to Berkeley’s criticisms of the calculus. For Deleuze, instead, I show that the differential must be understood as escaping from both finite and infinite representation. By highlighting the sub-representational character of the differential in his system I show how the differential is a key moment in Deleuze’s formulation of a transcendental empiricism. I conclude by dealing with some of the common misunderstandings which occur when Deleuze is read as endorsing a modern mathematical interpretation of the calculus.