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)

Bergson’s critique of intensive magnitude in Time and Free Will mainly targets Kant’s “Anticipations of Perception”, in which the Kantian distinction between matter and form is lowered. Bergson pra...

There is an old but still unresolved debate pertaining to the question of Bergsonian monism or dualism. Scholars who think that Bergson is ultimately monist clash with those who claim that he has consistently maintained a dualist position. Others speak of contradiction and point out his failure to reconcile dualism with monism. What feeds on the debate is Bergson’s undeniable change of direction: while his first book is flagrantly dualist, his second book takes a sharp turn toward monism. Without denying (...) the intricacy generated by the change of direction, this paper argues that the originality of his position is overlooked every time that the problem is presented in terms of Bergson being dualist or monist. Notably, it contends that Bergson’s third book, Creative Evolution, overcomes both dualism and monism by removing their contradiction through a durational or slanted approach to Being. (shrink)