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FOUR THE VIRTUAL AND THE ACTUAL INTRODUCTION In an afterword written in 1988 to his study, Bergsonism, Deleuze calls attention to the three themes of Bergson’s work that he believes must be pursued if we are to continue to practice metaphysics. These are intuition, the relation of science and metaphysics, and the theory of multiplicities. These three themes will be the central focus of this chapter on the structure of Deleuze’s ontology, although we will also briefly look at some areas of Deleuze’s thought on aesthetics. Taking the themes in reverse order, it is the theme of the two multiplicities in Bergson’s thought that is most fundamental to Deleuze’s project of renewing metaphysics. In the last chapter, we looked at the differences Bergson posits between space, on the one hand, and duration, on the other. In making this distinction, Deleuze claims that “Bergson moves toward a distinction between two major types of multiplicities , the one discrete or discontinuous, the other continuous, the one spatial and the other temporal, the one actual, the other virtual” (B, 117). The first of these multiplicities is that of Aristotle and Russell and operates with a logic of identity, negation, and opposition, the second, which corresponds to duration in Bergson’s system, instead uses the principles of difference. In exploring the interrelations of these two multiplicities, Deleuze highlights Bergson’s “constitution of a logic of multiplicities” (B, 117). Extending and clarifying this logic will be fundamental to Deleuze’s own project. The second aspect of Bergson’s thought taken up by Deleuze is the constitution of a new relation between science and metaphysics. “Bergson did not merely criticize science as if it went no further than space, the solid, the immobile. Rather, he thought the Absolute has two ‘halves,’ to which science and metaphysics correspond” (B, 116). To properly take up the insights of Bergson therefore means, for Deleuze, not to consider science simply to be a reductionist mode of understanding the world, but to recognize that without a metaphysics it remains abstract and without sense. Thus, modern metaphysics must 91 92 HEGEL, DELEUZE, AND THE CRITIQUE OF REPRESENTATION make an understanding of modern science’s achievements possible, as well as building on these advances. Returning to the question of the two multiplicities , Deleuze’s project will involve fulfilling Bergson’s intention to “[give] multiplicities the metaphysics which their scientific treatment demands” (B, 117). Given that contemporary science, particularly the fields of chaos and complexity theory, has taken up the idea of non-classical geometrical space as a vital tool in understanding the behavior of systems, Deleuze will frequently refer to the scientific (and in particular, mathematical) treatment of continuous multiplicities in order to provide an explanation of them which gives a level of rigor unavailable at Bergson’s time of writing. We should be careful to recognize, however, that Deleuze is not himself engaged in a scientific enterprise, and while mathematics provides perhaps the easiest way to understand his project, it simply provides the paradigm case for understanding terms such as actualization, the relations of problems and solutions, and the structures of the virtual and the actual. This distinction is especially clear in his discussion of differential calculus, which will become a central tool in developing his theory of difference: “Differential calculus in the most precise sense is only a mathematical instrument which, even in its own domain, does not necessarily represent the most complete form of expression of problems and the constitution of their solution” (DR, 181). There is a wider sense to the differential calculus, however, as a calculus of difference, which will apply to all domains. “Each engendered domain, in which dialectical Ideas of this or that order are incarnated, possesses its own calculus” (DR, 181).1 The analysis of the differential calculus, and its application to nonstandard geometries should therefore be seen as the application in one domain of a calculus of difference that in the end will go beyond purely mathematical results (“mathesis universalis but also universal physics, universal psychology and universal sociology” [DR, 190]). Deleuze’s philosophy thus involves neither a reduction of science to metaphysics nor a reduction of metaphysics to science. The third aspect that Deleuze will take from Bergson is the method of intuition. Deleuze emphasizes the two functions of intuition as “a cutting up or division of reality in a given domain, according to lines of different natures and, on the other hand, an intersection of lines which are...

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