Multiplicity (philosophy)

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:

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