Continental Philosophy Review

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

Hegel and Deleuze on the metaphysical interpretation of the calculus



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.


Hegel Deleuze Calculus Mathematics Representation 


  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