Although Alain Badiou dedicates a number of texts to the philosophy of Benedict de Spinoza throughout his work—after all, the author of a systematic philosophy of being more geometrico must be a point of reference for the philosopher who claims that “mathematics = ontology”—the reading offered in Meditation Ten of his key work Being and Event presents the most significant moment of this engagement. Here, Badiou proposes a reading of Spinoza’s ontology that foregrounds a concept that is as central to, (...) and celebrated in, his philosophy as it is strictly excluded by Spinoza: the void. In nuce, Badiou contends that for all of Spinoza’s efforts to offer an ontology of total plenitude, the void returns in his philosophy under the (at first sight) unlikely name of infinite mode. The presence of this errant name in Spinoza’s philosophy bears witness to the failure of his most profound intellectual endeavour. However striking Badiou’s reading of Spinoza, this paper argues that it fails to adequately grasp Spinoza’s metaphysics, particularly with respect to the central concept of modal essence, a concept which does not appear at all in the Badiouian text. By introducing a consideration of this concept, it becomes able to resolve the status of infinite modes, and to account for the move across the notorious finite–infinite divide. Thus the argument turns to the reading of Spinoza offered by Gilles Deleuze for a more thorough-going and nuanced approach, much superior to Badiou’s procrustean critique. (shrink)

The collection Virtual Mathematics: the logic of difference brings together a range of new philosophical engagements with mathematics, using the work of French philosopher Gilles Deleuze as its focus. Deleuze’s engagements with mathematics rely upon the construction of alternative lineages in the history of mathematics in order to reconfigure particular philosophical problems and to develop new concepts. These alternative conceptual histories also challenge some of the self-imposed limits of the discipline of mathematics, and suggest the possibility of forging new connections (...) between philosophy and more recent developments in mathematics. This component of Deleuze’s work has, to date, been rather neglected by commentators working in the field of Deleuze studies. One of the aims of this collection is to address this critical deficit by providing a philosophical presentation of Deleuze’s relation to mathematics; one that is adequate to his project of constructing a philosophy of difference and to the exploration of some of its applications. This project developed as a result of encounters with an increasing number of researchers who have been working on the mathematical aspects of Deleuze’s work and the key role that these play in his philosophy. By bringing this work together for the first time, this collection makes an important contribution to the emerging body of work that endeavours to explore the broad range of Deleuze’s philosophy. (shrink)