---- by Jonathan Roffe
  'Multiplicity' is arguably Deleuze's most important concept. It is found throughout his work, and is the basis for other important concepts such as rhizome, assemblage, and 'concept' itself. It is also one of Deleuze's most difficult concepts to grasp because of the many different ways and contexts in which he puts it to work. Yet, there are some essential traits to be noted.
  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 two people whom Deleuze regularly associates with the development of the concept of multiplicity are the mathematician Georg Riemann, and the French philosopher Henri Bergson. From Riemann, Deleuze takes the idea that any situation is composed of different multiplicities that form a kind of patchwork or ensemble without becoming a totality or whole. For example, a house is a patchwork of concrete structures and habits. Even though we can list these things, there is finally no way of determining what the essence of a particular house is, because we cannot point to anything outside of the house itself to explain or to sum it up - it is simply a patchwork. This can also be taken as a good description of multiplicities themselves.
  Deleuze's debt to Bergson here is more profound. It is in Bergsonism (1966) that Deleuze first discusses multiplicity, which receives an extended elaboration in Bergson's philosophy. Deleuze notes first of all that there are two kinds of multiplicity in Bergson: extensive numerical multiplicities and continuous intensive multiplicities. The first of these characterises space for Bergson; and the second, time. The difference between extensive and intensive is perhaps the most important point here. In contrast to space, which can be divided up into parts (this is why it is called numerical), intensive multiplicity cannot be divided up without changing in nature. In other words, any alteration to an intensive multiplicity means a total change in its nature - a change in its intensive state. This is important for Deleuze because it means that there is no essence of particular multiplicities which can remain unaffected by encounters with others.
  Deleuze also makes the important link between the concept of the virtual and that of multiplicity in the context of his reading of Bergson, and it is in connection with the theme of virtual intensive multiplicity that Deleuze most palpably remains a Bergsonian. Frequently when discussing the virtual, Deleuze quotes Marcel Proust's adage in relation to memory: 'Real without being actual, ideal without being abstract'. Virtual multiplicity, then, is real without being necessarily embodied in the world. And, rather than expressing abstract alternative possibilities, virtual multiplicity forms something like the real openness to change that inheres in every particular situation.
  This is perhaps the most difficult point to grasp in Deleuze's doctrine of virtual multiplicities. While virtual multiplicities are embodied in particular states of affairs, they must not be considered to be somehow transcendent or essentially immutable. As Deleuze shows in his discussion of Gottfried Wilhelm von Leibniz in Difference and Repetition, the virtual and the actual are interrelated, and effect changes in each other. So, while the virtual is embodied in actual situations, the changes in actual situations also effect changes in the virtual multiplicity. Existence, then, is a combination of actual multiplicities - states of affairs - and virtual multiplicities - particular intensive movements of change.
  While these concepts seem particularly abstract, they offer Deleuze grounds upon which to develop a very practical picture of the world. The concept of multiplicity makes no reference to a transcendent realm of the world that contains the structures or laws of existence. Since we live among actual multiplicities (and are ourselves multiplicities), we are always elements and actors within the world. In this sense, both philosophy and human existence are eminently practical. The virtual counterparts of our actual multiplicities also make possible continued movement and change, even at the points where the world of actuality seems most rigid and oppressive.
   § concepts
   § rhizome
   § virtual / virtuality

The Deleuze Dictionary. Revised Edition. . 2015.

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