Advertisement

Continental Philosophy Review

, Volume 42, Issue 4, pp 555–572 | Cite as

Hegel and Deleuze on the metaphysical interpretation of the calculus

  • Henry Somers-Hall
Article

Abstract

The aim of this paper is to explore the uses made of the calculus by Gilles Deleuze and G. W. F. Hegel. I show how both Deleuze and Hegel see the calculus as providing a way of thinking outside of finite representation. For Hegel, this involves attempting to show that the foundations of the calculus cannot be thought by the finite understanding, and necessitate a move to the standpoint of infinite reason. I analyse Hegel’s justification for this introduction of dialectical reason by looking at his responses to Berkeley’s criticisms of the calculus. For Deleuze, instead, I show that the differential must be understood as escaping from both finite and infinite representation. By highlighting the sub-representational character of the differential in his system, I show how the differential is a key moment in Deleuze’s formulation of a transcendental empiricism. I conclude by dealing with some of the common misunderstandings that occur when Deleuze is read as endorsing a modern mathematical interpretation of the calculus.

Keywords

Hegel Deleuze Calculus Mathematics Representation 

References

  1. Berkeley, George. 1992. De Motu and the Analyst (trans: Jesseph, Douglas M.). Dordrecht: Kluwer.Google Scholar
  2. Boyer, Carl B. 1959. The history of the calculus and its conceptual development. London: Dover.Google Scholar
  3. Deleuze, Gilles. 1994. Difference and repetition (trans: Patton, P.). New York: Columbia University Press.Google Scholar
  4. Duffy, Simon. 2006. The logic of expression: quality, quantity, and intensity in Spinoza, Hegel and Deleuze. Aldershot: Ashgate.Google Scholar
  5. Eves, Howard Whitley. 1990. An introduction to the history of mathematics. Philadelphia: Saunders College Pub.Google Scholar
  6. Hegel, G.W.F. 1989. Hegel’s science of logic (trans: Miller, A.V.). Atlantic Highlands, NJ: Humanities Press International.Google Scholar
  7. Monk, Ray. 1997. Was Russell an analytic philosopher? In The rise of analytic philosophy, ed. H.-J. Glock, 35–50. Oxford: Blackwell.Google Scholar
  8. Newton, Sir Isaac. 1934. Mathematical principles of natural philosophy and his system of the world (trans: Cajori, Florian.). London: University of California Press.Google Scholar
  9. Newton, Sir Isaac. 1964. The mathematical works of Isaac Newton. ed. D.T. Whiteside. New York: Johnson Reprint.Google Scholar
  10. OU. History of Mathematics Course Team. 1974. History of mathematics. Milton Keynes: Open University Press.Google Scholar
  11. Russell, Bertrand. 1946. A history of western philosophy: and its connection with political and social circumstances from the earliest times to the present day. London: Allen and Unwin.Google Scholar
  12. Russell, Bertrand. 1956. Portraits from memory. London: Allen and Unwin.Google Scholar
  13. Struik, D. J. (ed.). 1986. A source book in mathematics 1200–1800. Princeton: Princeton University Press.Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  1. 1.Manchester Metropolitan UniversityManchesterUK

Personalised recommendations