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.
Aristotle. Metaphysics. Translated by W.D. Ross. In The Complete Works of Aristotle, Volume 2: 1552-1728. Edited by Jonathan Barnes. Princeton, NJ: Princeton University Press, 1984.Search in Google Scholar
Badiou, Alain. Being and Event. Translated by Oliver Feltham. London: Continuum, 2005.Search in Google Scholar
Badiou, Alain. “The Three Negations.” Cardozo Law Review 29.5 (2008): 1877-883.Search in Google Scholar
Badiou, Alain. Logics of Worlds. Translated by Alberto Toscano. London: Continuum, 2009.Search in Google Scholar
Badiou, Alain. and Gilles Haéri. In Praise of Mathematics. Translated by Susan Spitzer. Malden, Mass.: Polity, 2016.Search in Google Scholar
Cusset, François. French Theory: How Foucault, Derrida, Deleuze & Co. Transformed the Intellectual Life of the United States. Minneapolis, MN: University of Minnesota Press, 2008.Search in Google Scholar
Fraser, Zachary. “The Law of the Subject: Alain Badiou, Luitzen Brouwer and the Kripkean Analyses of Forcing and the Heyting Calculus.” Cosmos and History: the Journal of Natural and Social Philosophy 2:1-2 (2006): 94-133.Search in Google Scholar
Gironi, Fabio. Naturalizing Badiou: Mathematical Ontology and Structural Realism. London: Palgrave Macmillan, 2015.Search in Google Scholar
Goodrich, Peter. “Symposium Law and Event Preface: (On Alain Badiou’s Handwriting).” Cardozo Law Review 29.5 (2008): 1867-1875.Search in Google Scholar
Johnston, Adrian. “Phantom of consistency: Alain Badiou and Kantian transcendental idealism,” in Continental Philosophy Review 41 (2008): 345-366. DOI 10.1007/s11007-008-9086-5.10.1007/s11007-008-9086-5Search in Google Scholar
Moore, Adrian. The Evolution of Modern Metaphysics: Making Sense of Things. Cambridge, UK: Cambridge University Press, 2012.Search in Google Scholar
Nirenberg, Ricardo L. and David Nirenberg. “Badiou’s Number: A Critique of Mathematics as Ontology.” Critical Inquiry 37:4 (Summer 2011): 583-614. DOI 10.1086/660983.10.1086/660983Search in Google Scholar
Noys, Benjamin. “On the Edge of the Negative: Badiou.” In The Persistence of the Negative: A critique of Contemporary Continental Theory: 134-159. Edinburgh: Edinburgh University Press, 2010.Search in Google Scholar
© by Becky Vartabedian, published by De Gruyter
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.