From The Art and Popular Culture Encyclopedia
Multiplicity is a philosophical concept that Edmund Husserl and Henri Bergson developed from Riemann's mathematical concept. It forms an important part of the philosophy of Gilles Deleuze, particularly in his collaboration with Félix Guattari, Capitalism and Schizophrenia (1972-80). In his Foucault (1986), Deleuze describes Michel Foucault's The Archaeology of Knowledge (1969) as "the most decisive step yet taken in the theory-practice of multiplicities."
The notion of multiplicity forms a central part of Bergson's critique of philosophical negativity and the dialectical method, Deleuze argues in his commentary, Bergsonism (1966). The theory of multiplicities, he explains, must be distinguished from traditional philosophical problems of "the One and the Multiple." By opposing "the One and the Multiple," dialectical philosophy claims "to reconstruct the real," but this claim is false, Bergson argues, since it "involves abstract concepts that are much too general."
Instead of referring to "the Multiple in general," Bergson's theory of multiplicities distinguishes between two types of multiplicity: continuous multiplicities and discrete multiplicities (a distinction that he developed from Riemann).
The features of this distinction may be tabulated as follows:
|Continuous multiplicities||Discrete multiplicities|
|differences in kind||differences in degree|
|divides only by changing in kind||divides without changing in kind|
|non-numerical - qualitative||numerical - quantitative|
|differences are virtual||differences are actual|
|qualitative discrimination||quantitative differentiation|
|subjective - subject||objective - object|
- Deleuze, Gilles. 1966. Bergsonism. Trans. Hugh Tomlinson and Barbara Habberjam. NY: Zone, 1991. ISBN 0942299078.
- ---. 1986. Foucault. Trans. Sean Hand. London: Althone, 1988. ISBN 0826457800.
- Deleuze, Gilles and Félix Guattari. 1972. Anti-Œdipus. Trans. Robert Hurley, Mark Seem and Helen R. Lane. London and New York: Continuum, 2004. Vol. 1 of Capitalism and Schizophrenia. 2 vols. 1972-1980. Trans. of L'Anti-Oedipe. Paris: Les Editions de Minuit. ISBN 0826476953.
- ---. 1980. A Thousand Plateaus. Trans. Brian Massumi. London and New York: Continuum, 2004. Vol. 2 of Capitalism and Schizophrenia. 2 vols. 1972-1980. Trans. of Mille Plateaux. Paris: Les Editions de Minuit. ISBN 0826476945.
- Foucault, Michel. 1969. The Archaeology of Knowledge. Trans. A. M. Sheridan Smith. London and New York: Routledge, 2002. ISBN 0415287537.
- Massumi, Brian. 1992. A User's Guide to Capitalism and Schizophrenia: Deviations from Deleuze and Guattari. Swerve editions. Cambridge, USA and London: MIT. ISBN 0262631431.