Multiplicity and ontology in deleuze and badiou

This book approaches work by Gilles Deleuze and Alain Badiou through their shared commitment to multiplicity, a novel approach to addressing one of the oldest philosophical questions: is being one or many? Becky Vartabedian examines major statements of multiplicity by Deleuze and Badiou to assess the structure of multiplicity as ontological ground or foundation, and the procedures these accounts prescribe for understanding one in relation to multiplicity. Written in a clear, engaging style, Vartabedian introduces readers to Deleuze and Badiou’s key ontological commitments to the mathematical resources underpinning their accounts of multiplicity and one, and situates these as a conversation unfolding amid political and intellectual transformations

Negation, Structure, Transformation: Alain Badiou and the New Metaphysics

In this article, I discuss Alain Badiou\u27s 2008 address titled The Three Negations. Though the text was originally presented in a symposium concerning the relationship of law to Badiou\u27s theory of the event, I discuss the way this brief address offers an introduction to the broad sweep of Badiou\u27s metaphysics, outlining his accounts of being, appearing, and transformation. To do so, Badiou calls on the resources of three paradigms of negation: from classical Aristotelian logic, from Brouwer\u27s intuitionist logic, and in paraconsistent logics developed by DaCosta. I explain Badiou\u27s use of negation in the three primary areas of his metaphysics, as well as to diagnose the degrees of transformation that may have occurred in a situation. My analysis of Badiou\u27s use of negation in this text is aided by examples from his broader ontological oeuvre. I also explain the underlying requirement in Badiou\u27s work that formal considerations - mathematical or logical - get their sense by being tethered to readily-identifiable political, aesthetic, scientific, or interpersonal concerns. I conclude by addressing the foundation Badiou\u27s work establishes for pursuing a new metaphysics, and by discussing certain of the liabilities that remain in the wake of his account

Rethinking Multiplicity After Deleuze and Badiou

This dissertation is built around two questions. The first concerns a structure for analyzing Gilles Deleuze\u27s (1925-1995) work with multiplicity and Alain Badiou\u27s (1937- ) presentation of the same concept: On what grounds is it possible to understand the relationship between Badiou\u27s and Deleuze\u27s work on multiplicity and its ontological significance? I answer with Deleuze\u27s mechanism of the problem-solution couple, a framework that accommodates the affirmation of diverse solutions to any philosophical or ontological problem. Using the problem-solution couple as a framework for organizing the relationship between Deleuze and Badiou provides an alternative to the traditional positioning of these programs as opposed and incompatible. The second question identifies the problem to which these respective accounts of multiplicity are solutions: In what ways does philosophical inquiry cope with the excess presented to thought? I identify the excess present to thought in philosophical accounts of multiplicity, plurality, or manifold that require the persistence of elements beyond the reach of structure. I begin by describing the problem-solution couple and identify three precedent solutions in which multiplicity or plurality indicates an excess present to thought: Kant\u27s manifold; Merleau-Ponty\u27s presentation of wild or brute being; and the account of multiplicity in early moves of Hegel\u27s Phenomenology of Spirit. In Chapters 2 and 3, I present Badiou\u27s and Deleuze\u27s respective solutions with a particular focus on the mathematical resources they deploy: Badiou\u27s use of Cantor\u27s inconsistent multiple and the Zermelo-Fraenkel axiom system; and Deleuze\u27s invocation of Riemannian continuous multiplicity and differential calculus. Situating Badiou\u27s and Deleuze\u27s versions of multiplicity as two among a series of solutions to the broader problem of excess presented to thought reveals a number of connections between the two projects, rather than the simple opposition according to which they are typically cast. I position these solution-cases in relation to the precedent cases offered by Kant and Merleau-Ponty, and conclude by suggesting ways Hegel\u27s account offers a horizon for continued study