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Multiplicity is an assertion that there is more than one geo-historical trajectory. It is a philosophical concept that Edmund Husserl and Henri Bergson developed by analogy with Riemann's description of the 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 philosopher Jonathan Roffe describes Deleuze's concept of Multiplicity as follows: "A multiplicity is, in the most basic sense, a complex structure that does not reference a prior unity. Multiplicities are not parts of a greater whole that have been fragmented, and they cannot be considered manifold expressions of a single concept or transcendent unity. On these grounds, Deleuze opposes the dyad One/Many, in all of its forms, with multiplicity. Further, he insists that the crucial point is to consider multiplicity in its substantive form – a multiplicity – rather than as an adjective – as multiplicity of something. Everything for Deleuze is a multiplicity in this fashion."
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|
- "It was Riemann in the field of physics and mathematics who dreamed about the notion of 'multiplicity' and other different kinds of multiplicities. The philosophical importance of this notion then appeared in Husserl's Formal and Transcendental Logic, as well as in Bergson's Essay on the Immediate Given of Awareness" (Deleuze 1986, 13).
- Deleuze (1986, 14).
- The Deleuze Dictionary: the revised edition. Edinburgh: Edinburgh University Press. p. 181.
- "Multiplicity remains completely indifferent to the traditional problems of the multiple and the one, and above all to the problem of a subject who would think through this multiplicity, give it conditions, account for its origins, and so on. There is neither one nor multiple, which would at all events entail having recourse to a consciousness that would be regulated by the one and developed by the other" (Deleuze 1986, 14).
- See Deleuze (1966, 38-47); The dialectical method "compensates for the inadequacy of a concept that is too broad or too general by invoking the opposite concept, which is no less broad and general [. . .]. The concrete will never be attained by combining the inadequacy of one concept with the inadequacy of its opposite. The singular will never be attained by correcting a generality with another generality" (Deleuze 1966, 44).
- Deleuze (1966, 39).
- Husserl's philosophy
- Deleuze, Gilles. 1966. Bergsonism. Trans. Hugh Tomlinson and Barbara Habberjam. NY: Zone, 1991. ISBN 0-942299-07-8.
- ---. 1986. Foucault. Trans. Sean Hand. London: Althone, 1988. ISBN 0-8264-5780-0.
- 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 0-8264-7695-3.
- ---. 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 0-8264-7694-5.
- Foucault, Michel. 1969. The Archaeology of Knowledge. Trans. A. M. Sheridan Smith. London and New York: Routledge, 2002. ISBN 0-415-28753-7.
- Massumi, Brian. 1992. A User's Guide to Capitalism and Schizophrenia: Deviations from Deleuze and Guattari. Swerve editions. Cambridge, USA and London: MIT. ISBN 0-262-63143-1.
- Nicholas Tampio, ["Multiplicity"] "Sage Encyclopedia of Political Theory" (2010).