In this article, I discuss Alain Badiou’s 2008 address titled “The Three Negations.” Though the text was originally presented in a symposium concerning the relationship of law to Badiou’s theory of the event, I discuss the way this brief address offers an introduction to the broad sweep of Badiou’s 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’s intuitionist logic, and in (...) paraconsistent logics developed by DaCosta. I explain Badiou’s 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’s use of negation in this text is aided by examples from his broader ontological oeuvre. I also explain the underlying requirement in Badiou’s 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’s work establishes for pursuing a new metaphysics, and by discussing certain of the liabilities that remain in the wake of his account. (shrink)

Jane Bennett’s vital materialism develops positive ontological commitments to lively matter and resistant vitality, articulated using notions of actant and assemblage, thing-power and the out-side. I show that these ontological commitments reveal a limit for traditional modes of human knowing, favoring an emergent epistemology that attends to the ways actants and assemblages express themselves. I then argue for an account of acting that positions humans as guests of vibrant matter. Compacts of guest-friendship in Plato’s Crito and Kant’s To Perpetual Peace (...) indicate that to be a guest is to be embedded in an asymmetrical system. The compact that binds the guest in a world of vibrant matter is the prospect of friendship with nonhuman others, a prospect I discuss following the work of Nick Bingham. I conclude by addressing Axelle Karera’s recent critique of Anthropocenean discourses, explaining the role guest-friendship can play in addressing certain of the weaknesses Karera identifies. (shrink)

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 mathematical 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, including the mathematical resources underpinning their accounts of multiplicity and one, and situates these as a conversation unfolding amid political and intellectual transformations. (shrink)