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Procedures: One, Multiple, Subtraction

  • Becky Vartabedian
Chapter

Abstract

This chapter attends to the prescribed procedures for relating one to multiple and multiplicity in Badiou’s and Deleuze’s work. I begin with the work of constructing consistent multiples in Badiou’s work, a procedure requiring attention to the void set and its mark Ø, their background in Zermelo and Bourbaki, and axioms of Zermelo-Fraenkel set theory. I attend to this procedure’s relation to Badiou’s earlier account of scission, a technique for ‘cutting’ a one from the multiple. I address one-production in Deleuze’s account by discussing the differential relation (dy/dx) and its mobilization toward the pre-individual singularity, which Deleuze develops in his account of the virtual idea. My analysis focuses on those procedures by which the relation of one to multiple is maintained, namely subtraction, apparent in the analysis of the war machine in A Thousand Plateaus and in their assessment of the cogito in “Example 1”. I show how Deleuze’s earlier concern with overturned Platonism expresses this subtractive impulse; in short, one sees that where multiplicity appears in Deleuze’s oeuvre, subtraction seems to follow.

References

  1. Aristotle. 1984. Metaphysics. Translated by W.D. Ross. In The Collected Works of Aristotle, vol. 2, edited by Jonathan Barnes, 1552–1728. Princeton, NJ: Princeton University Press.Google Scholar
  2. Badiou, Alain. 1985. Peut-on penser la politique? Paris: Seuil.Google Scholar
  3. ———. 2005. Being and Event. Translated by Oliver Feltham. London: Continuum. Originally L’être et l’événement. Paris: Éditions du Seuil, 1988. (Cited in text as BE)Google Scholar
  4. ———. 2009. Theory of the Subject. Translated and with an Introduction by Bruno Bosteels. London: Continuum. Originally Théorie du sujet. Paris: Éditions du Seuil, 1982. (Cited in text as TS)Google Scholar
  5. ———. [1965] 2012. “The (Re)Commencement of Dialectical Materialism.” In The Adventure of French Philosophy, 133–170. Translated by Bruno Bosteels. London: Verso.Google Scholar
  6. ———. [1969] 2012. “Mark and Lack.” Translated by Zachary Luke Fraser with Ray Brassier. In Concept and Form, Volume One: Key Texts from the Cahiers pour l’Analyse, edited by Peter Hallward and Knox Peden, 151–158. London: Verso.Google Scholar
  7. ———. 2012. “The Fascism of the Potato.” In The Adventure of French Philosophy, 191–201, edited and translated by Bruno Bosteels. London: Verso. Originally Georges Peyrol. “Le fascisme de la pomme de terre.” In La situation actuelle sur le front de la philosophie, 42–52. Paris: François Maspero, 1977. (Cited in text as FP)Google Scholar
  8. Badiou, Alain, and Gilles Haéri. 2016. In Praise of Mathematics. Translated by Susan Spitzer. Cambridge, UK: Polity Press. Originally Éloge des mathématiques, Paris: Flammarion, 2015.Google Scholar
  9. Badiou, Alain, and Tzuchien Tho. 2007. “The Concept of Model Forty Years Later: An Interview with Alain Badiou.” In The Concept of Model: An Introduction to the Materialist Epistemology of Mathematics, 79–104, edited and translated by Zachary Luke Fraser and Tzuchien Tho. Melbourne: re.press.Google Scholar
  10. Bartlett, A.J., and Justin Clemens. 2012. “II: Neither/Nor.” Critical Inquiry 38 (2): 365–380.  https://doi.org/10.1086/662747. Accessed 1 September 2013.
  11. Bosteels, Bruno. 2001. “Alain Badiou’s Theory of the Subject: Part I. The Recommencement of Dialectical Materialism?” Pli 12: 200–299.Google Scholar
  12. Bourbaki, Nicolas. 1968. Elements of Mathematics: Theory of Sets. Paris: Hermann.Google Scholar
  13. Boyer, Carl. 1949. The History of Calculus and Its Conceptual Development. New York: Dover.Google Scholar
  14. Brassier, Ray. 2005 “Badiou’s Materialist Epistemology of Mathematics.” Angelaki 10 (2): 135–150.CrossRefGoogle Scholar
  15. DeLanda, Manuel. 2002. Intensive Science and Virtual Philosophy. Continuum Impacts Series. London: Continuum.Google Scholar
  16. ———. 2012. “Deleuze, Mathematics, and Realist Ontology.” In The Cambridge Companion to Deleuze, edited by Henry Somers-Hall and Daniel W. Smith, 220–238. Cambridge, UK: Cambridge University Press.Google Scholar
  17. Deleuze, Gilles. 1994. Difference and Repetition. Translated by Paul Patton. New York: Columbia University Press. Originally Différence et repetition. Paris: Presses Universitaires de France, 1968. (Cited in text as DR)Google Scholar
  18. Deleuze, Gilles, and Félix Guattari. 1981. “Rhizome—Introduction.” Translated by Paul Patton. I & C 8 (Spring): 49–71. Originally Rhizome: Introduction. Paris: Les Éditions de Minuit, 1976. (Cited in text as R)Google Scholar
  19. ———. 1994. What Is Philosophy? Translated by Hugh Tomlinson and Graham Burchell. New York: Columbia University Press. Originally Qu’estce que la philosophie? Paris: Les Éditions de Minuit, 1991. (Cited in text as WP)Google Scholar
  20. Descartes, Rene. 1984. Meditations on First Philosophy. In The Complete Works of Descartes, vol. 2. Translated by John Cottingham, Robert Stoothoff, and Dugald Murdoch, 1–62. Cambridge, UK: Cambridge University Press.Google Scholar
  21. Duffy, Simon. 2013. Deleuze and the History of Mathematics: In Defense of the “New”. Bloosmbury Studies in Continental Philosophy. London: Bloomsbury.Google Scholar
  22. Feltham, Oliver. 2008. Alain Badiou: Live Theory. London: Continuum.Google Scholar
  23. Hegel, G.W.F. 2010. The Science of Logic. Translated by George di Giovanni. Cambridge, UK: Cambridge University Press.Google Scholar
  24. Kant, Immanuel. 1998. Critique of Pure Reason. Translated by Paul Guyer and Allen W. Wood. Cambridge, UK: Cambridge University Press.Google Scholar
  25. Khan, Sal. 2015. “Calculating Slope of Tangent Line Using Derivative Definition.” Khan Academy. https://www.khanacademy.org/math/ap-calculus-ab/ab-derivative-intro/ab-defining-derivative/v/calculus-derivatives-2-new-hd-version. Accessed 27 May 2015.
  26. Kline, Morris. 1967. Mathematics for the Non-mathematician. New York: Dover.Google Scholar
  27. Livingston, Paul. 2014. “Formalism and the Real: Ontology, Politics, and the Subject.” Lecture, Pittsburgh Summer Symposium in Contemporary Philosophy, Duquesne University, Pittsburgh, August 6.Google Scholar
  28. Lucretius. 1975. De Rerum Natura. Translated by W.H.D. Rouse. Loeb Classical Library, edited by Jeffrey Henderson. Cambridge, MA: Harvard University Press.Google Scholar
  29. Merzbach, Uta, and Carl Boyer. 2011. A History of Mathematics, 3rd ed. Hoboken, NJ: Wiley.Google Scholar
  30. Miller, Jacques-Alain. [1965] 2012. “Suture (Elements of the Logic of the Signifier).” Translated by Jacqueline Rose. In Concept and Form, Volume One: Key Texts from the Cahiers pour l’Analyse, edited by Peter Hallward and Knox Peden, 91–102. London: Verso.Google Scholar
  31. Miller, Jeff. 2017. “Earliest Uses of Symbols of Set Theory and Logic.” Last updated 23 June 2017. http://jeff560.tripod.com/set.html. Accessed 12 July 2017.
  32. Penrose, Roger. 2004. “Riemann Surfaces and Complex Mappings.” In The Road to Reality: A Complete Guide to the Laws of the Universe, 135–152. New York: Vintage.Google Scholar
  33. Plato. 1997. Sophist. Translated by John M. Cooper. In Plato: Complete Works, edited by John M. Cooper, 235–293. Indianapolis, IN: Hackett Publishing Company.Google Scholar
  34. Plotnitsky, Arkady. 2009. “Bernhard Riemann’s Conceptual Mathematics and the Idea of Space.” Configurations 17 (2): 105–130.  https://doi.org/10.1353/con.0.0068. Accessed 12 June 2013.
  35. Power, Nina. 2006. “Towards an Anthropology of Infinitude: Badiou and the Political Subject.” Cosmos and History: The Journal of Natural and Social Philosophy 2 (1): 186–209.Google Scholar
  36. Riemann, Bernhard. 1873. “On the Hypotheses Which Lie at the Bases of Geometry.” Translated by W.K. Clifford. Nature VIII (183–184): 14–17, 36–37.Google Scholar
  37. Riera, Gabriel. 2015. “The Question of Art: Badiou and Hegel.” In Badiou and Hegel: Infinity, Dialectics, Subjectivity, edited by Jim Vernon and Antonio Calcagno, 77–102. Lanham, MD: Lexington Books.Google Scholar
  38. Ruda, Frank. 2015. “Badiou with Hegel Preliminary Remarks on A(ny) Contemporary Reading of Hegel.” In Badiou and Hegel: Infinity, Dialectics, Subjectivity, edited by Jim Vernon and Antonio Calcagno, 105–122. Lanham, MD: Lexington Books.Google Scholar
  39. Smith, Daniel W. 2012. “The Concept of the Simulacrum: Deleuze and the Overturning of Platonism.” In Essays on Deleuze, 3–26. Edinburgh: Edinburgh University Press.Google Scholar
  40. Somers-Hall, Henry. 2010. “Hegel and Deleuze on the Metaphysical Interpretation of the Calculus.” Continental Philosophy Review 42: 555–572.  https://doi.org/10.1007/s11007-008-9120-2. Accessed 12 July 2013.
  41. Voss, Daniela. 2011. “Maïmon and Deleuze: The Viewpoint of Internal Genesis and the Concept of Differentials.” Parrhesia 11: 62–74. http://ParrhesiaJournal.org/parrhesia11/parrhesia11_voss.pdf. Accessed 14 November 2011.
  42. ———. 2013. Conditions of Thought: Deleuze and Transcendental Ideas. Edinburgh: Edinburgh University Press.Google Scholar
  43. Zermelo, Ernst. 1977. “Investigations in the Foundations of Set Theory (1908).” Translated by Stefan Bauer-Mengelberg. In From Frege to Gödel: a Sourcebook in Mathematical Logic, edited by Jean van Heijenoort, 199–215. Cambridge, MA: Harvard University Press.Google Scholar

Copyright information

© The Author(s) 2018

Authors and Affiliations

  1. 1.Regis UniversityDenverUSA

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