Deleuze and the History of Mathematics In Defense of the 'New' [Hardcover]

Gilles Deleuze's engagements with mathematics, replete in his work, rely upon the construction of alternative lineages in the history of mathematics, which challenge some of the self imposed limits that regulate the canonical concepts of the discipline. For Deleuze, these challenges are an opportunity to reconfigure particular philosophical problems - for example, the problem of individuation - and to develop new concepts in response to them. The highly original research presented in this book explores the mathematical construction of Deleuze's philosophy, as well as addressing the undervalued and often neglected question of the mathematical thinkers who influenced his work.

In the wake of Alain Badiou's recent and seemingly devastating attack on the way the relation between mathematics and philosophy is configured in Deleuze's work, Simon Duffy offers a robust defence of the structure of Deleuze's philosophy and, in particular, the adequacy of the mathematical problems used in its construction. By reconciling Badiou and Deleuze's seeming incompatible engagements with mathematics, Duffy succeeds in presenting a solid foundation for Deleuze's philosophy, rebuffing the recent challenges against it.

Simon Duffyis a Research Fellow in Philosophy at the University of Sydney, Australia. He is the author ofThe Logic of Expression: Quality, Quantity and Intensity in Spinoza, Hegel and Deleuze(Ashgate, 2006) and editor ofVirtual Mathematics: The Logic of Difference(Clinamen Press, 2006).

Introduction \ Part I: The Role of Mathematics in 17th and 18th Century Philosophy \ 1. Spinoza and the Problem of the infinite \ 2. Leibniz and the Infinitesimal Point of View of the Differential Calculus \ 3. Maimon and the Doctrine of the Differential \ Part II: The Role of Mathematics in Late 19th and Early 20th Century Philosophy \ 4. Bergson and the Concept of Multiplicity \ 5. Riemann and the Concept of the Manifold \ 6. Lautman and the ConceplӤ