A central claim of Deleuze's reading of Bergson is that Bergson's distinction between space as an extensive multiplicity and duration as an intensive multiplicity is inspired by the distinction between discrete and continuous manifolds found in Bernhard Riemann's 1854 thesis on the foundations of geometry. Yet there is no evidence from Bergson that Riemann influences his division, and the distinction between the discrete and continuous is hardly a Riemannian invention. Claiming Riemann's influence, however, allows Deleuze to argue that quantity, in (...) the form of ‘virtual number’, still pertains to continuous multiplicities. This not only supports Deleuze's attempt to redeem Bergson's argument against Einstein in Duration and Simultaneity, but also allows Deleuze to position Bergson against Hegelian dialectics. The use of Riemann is thereby an important element of the incorporation of Bergson into Deleuze's larger early project of developing an anti-Hegelian philosophy of difference. This article first reviews the role of discrete and continuous multiplicities or manifolds in Riemann's Habilitationsschrift, and how Riemann uses them to establish the foundations of an intrinsic geometry. It then outlines how Deleuze reinterprets Riemann's thesis to make it a credible resource for Deleuze's Bergsonism. Finally, it explores the limits of this move, and how Deleuze's later move away from Bergson turns on the rejection of an assumption of Riemann's thesis, that of ‘flatness in smallest parts’, which Deleuze challenges with the idea, taken from Riemann's contemporary, Richard Dedekind, of the irrational cut. (shrink)

This paper contributes to clarifying Deleuze’s theory of the Idea by a commentary on its technical definition: “a defined, continuous, n-dimensional multiplicity”, presented in chapter IV of Difference and Repetition. This definition implicitly intertwines Deleuze’s own metaphysical view of the Idea as a virtual problem with a series of notions taken from the differential geometry developed by the German mathematician Georg B. Riemann. To clarify this influence, we will reconstruct the fundamental elements of the Riemannian notions used by Deleuze, and (...) show how these elements are presupposed in Deleuze’s concept of Idea. (shrink)

This paper presents an interpretation of the ontology developed by Deleuze in Différence et répétition under a topological perspective. It maintains that the Deleuzian thesis concerning Being as univocal and differential is supported by a theory of expression which holds a conception of space that goes beyond the Euclidian viewpoint. I will approach this spatial dynamism from a series of mathematical notions that assist the production of Deleuze’s main ontological concepts, defining the expression and its moments by the interaction between (...) different types of multiplicities, made of heterogeneous folds. (shrink)

Why would Deleuze condemn the dialectic of the One and the Many? It is not simply to replace one set of categories with another. Rather, it is to make differential topology safe for the philosophy of time. If Deleuze affirms pure multiplicity, it is to overcome Henri Bergson's prohibition upon using mathematics to inquire into time. How else could Deleuze justify his monstrous identification of ‘continuous multiplicities’ with Riemannian manifolds?

When Gilles Deleuze, in his book on Michel Foucault, asks, ‘who would think of looking for life among the archives?’, he uncovers something particular to Foucault's philosophy, but also to his own: a commitment to the question of what it means to think, and think politically. Although Foucault and Deleuze, who first met in 1952, immediately felt fondness for each other, a growing animosity had settled into the friendship by the end of the 1970s – a rift deepened by theoretical (...) differences. Notwithstanding these difficulties, Foucault and Deleuze shared a love for Nietzsche, as well as a curious fascination with Kant. Kant's influence, which was met with more opposition, is precisely the tension I tease out in this article, showing how Foucault critiques Kant's a priori through his own concept of the historical a priori, along with regularity and resistance, while Deleuze and Guattari, if more obliquely, critique Kant's a priori by further developing Foucault's notion of the historical a priori through their own method of pragmatics, particularly in three chapters of A Thousand Plateaus, namely ‘The Geology of Morals’, ‘Postulates of Linguistics’ and ‘On Several Regimes of Signs’. What I am interested in, then, is Deleuze and Guattari's treatment of redundancy, a concept mentioned seventy times in A Thousand Plateaus. Although not one of their main or most developed concepts, redundancy is a thread that can be traced back to Deleuze's first book, Empiricism and Subjectivity. Moreover, their more developed concepts, for example the diagram, the abstract machine, becoming, micro-politics and the ritornello, as well as their political philosophy, are grounded in their understanding of redundancy, which moves their philosophy beyond mapping out the conditions of possibility and demonstrating that the historical a priori emerges as a contingent function of its own expression to the genesis of thought. (shrink)

This thesis seeks to understand the nature of and relation between science and philosophy articulated in the early work of the French philosopher Gilles Deleuze. It seeks to challenge the view that Deleuze’s metaphysical and metaphilosophical position is in important part an attempt to respond to twentieth century developments in the natural sciences, claiming that this is not a plausible interpretation of Deleuze’s early thought. The central problem identified with such readings is that they provide an insufficient explanation of the (...) nature of philosophy’s contribution to the encounter between philosophy and science that they discern in Deleuze’s work. The philosophical, as opposed to scientific, dimension of the position attributed to Deleuze remains obscure. In chapter 1, it is demonstrated that this question of philosophy’s contribution to intellectual life and of how to differentiate philosophy from the sciences is a live one in Deleuze’s early thought. An alternative, less anachronistic interpretation of the parameters of Deleuze’s early project is offered. The remaining chapters of the thesis examine the early Deleuze’s understanding of the divergence between philosophy and science. Chapter 2 gives an account of Deleuze’s metaphilosophy, alongside a reconstruction of his largely implicit early understanding of science. The divergent intellectual processes and motivating concerns that account for Deleuze’s understanding of the differentiation of science and philosophy are thus clarified. In chapter 3, Deleuze’s use of mathematical and physical concepts is examined. It is argued that these concepts are used metaphorically. In chapter 4, the association between modern science and the Deleuzian concept of immanence that has been proposed by some Deleuze scholars is examined and ultimately challenged. The thesis concludes with some reflections on the significance of Deleuze’s early work for contemporary debates concerning the future of continental philosophy and the nature of philosophy more generally. (shrink)