Rethinking Multiplicity After Deleuze and Badiou
McAnulty College and Graduate School of Liberal Arts
Alain Badiou, Gilles Deleuze, Multiplicity, Bernhard Riemann, Set Theory
This dissertation is built around two questions. The first concerns a structure for analyzing Gilles Deleuze's (1925-1995) work with multiplicity and Alain Badiou's (1937- ) presentation of the same concept: On what grounds is it possible to understand the relationship between Badiou's and Deleuze's work on multiplicity and its ontological significance? I answer with Deleuze's 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's manifold; Merleau-Ponty's presentation of wild or brute being; and the account of multiplicity in early moves of Hegel's Phenomenology of Spirit. In Chapters 2 and 3, I present Badiou's and Deleuze's respective solutions with a particular focus on the mathematical resources they deploy: Badiou's use of Cantor's inconsistent multiple and the Zermelo-Fraenkel axiom system; and Deleuze's invocation of Riemannian continuous multiplicity and differential calculus. Situating Badiou's and Deleuze's 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's account offers a horizon for continued study.
Vartabedian, B. (2015). Rethinking Multiplicity After Deleuze and Badiou (Doctoral dissertation, Duquesne University). Retrieved from https://dsc.duq.edu/etd/1535