Deleuze and the calculus

The paper investigates Deleuze’s philosophical interpretation of differential calculus, which draws upon the approaches of Maïmon, Wronski, and Bordas-Demoulin. Deleuze argues that for each of these thinkers the differential is the Idea—respectively, Leibnizian, Kantian, or Platonic. He further argues that, within the differential, three principles are combined to form a sufficient reason: the principle of determinability, which corresponds to the undetermined (dx, dy); the principle of reciprocal determination, which corresponds to the reciprocally determinable (dx/dy); and the principle of complete determination, which corresponds to the effectively determined (the singular values of dx/dy). This Deleuzian conception of the calculus is discussed in relation to his Spinozian critique of the Leibnizian, Kantian, and Platonic Idea, his deployment of a virtual ontology, which has been strongly influenced by Bergson’s notion of the élan vital, and recent developments in stochastic calculus. It is argued that, while these latter developments are mostly congruent with Deleuze’s interpretation of the calculus, Robert Rosen’s critique of mechanism raises some doubts about the adequacy and completeness of Deleuzes’s conception of the differential, especially in relation to Bergson’s élan vital.