Multiplicity (French: multiplicité) is a philosophical concept developed by Edmund Husserl and Henri Bergson from Riemann's description of the mathematical concept.[1] It was later an important concept for Gilles Deleuze.

Bergson

Bergson first unpacked the difference between qualitative and quantitative multiplicity in the second chapter of his doctoral thesis, Time and Free Will. The two senses of multiplicity are radically different, and our investigation of them lead us to mathematics and abstraction, on the one hand, and metaphysics and concrete reality on the other. Qualitative multiplicity names the manifold of differences which are nevertheless together in our entire field of sense experience, or are unified by continuity in the becoming of our inner duration. Bergson selects a few examples to highlight the unique characteristics of qualitative multiplicity: sympathy, grace, and effort. Each of these, as a "given" or "fact" of immediate consciousness exhibits what we today might call a depth of temporality, earlier phases are still present, at least virtually, in the later phases and the later phases only make sense as emerging from the events that preceded them. Sympathy is at first painful, and rather than flee from this pain as we normally do, the emotion then transforms into a yearning to be with, suffer with, and care for the one with whom we sympathize. The later moments are the progression of earlier ones and the whole ensemble is a transformation which leads to a new state of the soul, a new attitude and intention. Qualitative multiplicity names this reality which is essentially temporal; we can distinguish unique phases but we cannot abstract these phases from the indivisible whole they form as a passage through differences. While we tend to translate the continuous, "multiple unity" of duration into a totality of quantities measured and represented in empty space, quantitative multiplicity is always abstract and is derivative.

In his essay The Idea of Duration, Bergson discusses multiplicity in light of the notion of unity. Whereas a unity refers to a given thing in as far as it is a whole, multiplicity refers to the "parts [of the unity] which can be considered separately."[2] Bergson distinguishes two kinds of multiplicity: one form of multiplicity refers to parts which are quantitative, distinct, and countable, and the other form of multiplicity refers to parts that are qualitative, which interpenetrate, and which each can give rise to qualitatively different perception of the whole.[3]

Multiplicity in Gilles Deleuze's philosophy

Multiplicity 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."[4]

Deleuze argues in his commentary Bergsonism (1966) that the notion of multiplicity forms a central part of Bergson's critique of philosophical negativity and the dialectical method. The theory of multiplicities, he explains, must be distinguished from traditional philosophical problems of "the One and the Multiple."[5] 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."[6] In Difference and Repetition Deleuze lists 3 major aspects to his notion of multiplicity:[7]

(1) the elements of the multiplicity must have neither sensible form nor conceptual signification, nor, therefore, any assignable function. They are not even actually existent, but inseparable from a potential or a virtuality. In this sense they imply no prior identity, no positing of a something that could be called one or the same. On the contrary, their indetermination renders possible the manifestation of difference freed from all subordination. (2) These elements must in effect be determined, but reciprocally, by reciprocal relations which allow no independence whatsoever to subsist. Such relations are precisely non-localisable ideal connections, whether they characterise the multiplicity globally or proceed by the juxtaposition of neighbouring regions. In all cases the multiplicity is intrinsically defined, without external reference or recourse to a uniform space in which it would be submerged. Spatio-temporal relations no doubt retain multiplicity, but lose inferiority; concepts of the understanding retain inferiority, but lose multiplicity, which they replace by the identity of an 'I think' or something thought. Internal multiplicity, by contrast, is characteristic of the Idea alone. (3) A multiple ideal connection, a differential relation, must be actualised in diverse spatio-temporal relationships, at the same time as its elements are actually incarnated in a variety of terms and forms. The Idea is thus defined as a structure. A structure or an Idea is a 'complex theme', an internal multiplicity - in other words, a system of multiple, non-localisable connections between differential elements which is incarnated in real relations and actual terms.

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).[8] 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
continuous discontinuous
qualitative discrimination quantitative differentiation
succession simultaneity
fusion juxtaposition
organization order
subjective - subject objective - object
duration space

See also

References

  1. ^ "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).
  2. ^ Bergson (2002, 49).
  3. ^ Bergson (2002,72-74)
  4. ^ Deleuze (1986, 14).
  5. ^ "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).
  6. ^ 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).
  7. ^ Deleuze, Gilles (2001) [1997]. Difference and Repetition. 1968, Presses Universitaires de France English translation © 1994 The Athlone Press (published 1994). p. 183. ISBN 0 8264 5957 9.
  8. ^ Deleuze (1966, 39).

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