Virtual multiplicity and the concept of difference
According to Deleuze, Bergson practised a method of analysis that shares some features with Kantian transcendental analysis. Whereas Kant sought to discover the conditions of all possible experience, Bergson sought virtual conditions of real experience (Deleuze 1988a:27). However, in both cases the aim is to decompose the given into its underlying conditions. For Bergson, time understood as duration is the ultimate element in which these differences occur, and the method of analysis thus progresses from the superficial, extensive nature of things to their underlying temporal nature. Deleuze argues that Bergson’s ontological distinction between duration and extensity corresponds to a distinction between kinds of multiplicity. The extensive or objective reality of things takes the form of ‘numerical multiplicity’, where this is understood as the kind of multiplicity which divides by differences in degree and where the process of division does not involve changes in kind. Arithmetical number is an example of this kind of multiplicity: numbers are infinitely divisible but the outcome is always further numbers of the same kind. Space is another example.
By contrast, the other type of multiplicity ‘appears in pure duration: It is an internal multiplicity of succession, of fusion, of organization, of heterogeneity, of qualitative discrimination, or of difference in kind; it is a virtual and continuous multiplicity that cannot be reduced to numbers’ (Deleuze 1988a:38). These qualitative or non-numerical multiplicities change in kind as they divide. Bergson draws examples of such multiplicities from the domain of consciousness. Here, a complex multiplicity such as a feeling may contain a number of elements imperfectly perceived, but once these elements are distinctly perceived by consciousness, the feeling inevitably changes its nature as a result. Deleuze points to examples from other domains such as intensities of sound or temperature, or the movements of horses which can be divided into several qualitatively distinct gaits: walk, trot, lope, canter, etc. In all these cases, what is divided ‘changes in nature at each moment of the division, without any one of these moments entering into the composition of any other’ (Deleuze and Guattari 1987:483). The problem of distinguishing between types of multiplicity originated with Reimann and is taken up in different ways by Husserl, Meinong and Russell. Bergson transformed the problem to his own ends in arguing that qualitative multiplicity is characteristic of duration.6 As we shall see below, Deleuze transforms it further by using the Bergsonian distinction between two kinds of multiplicity as part of the logical framework for the theory of assemblages in A Thousand Plateaus (1987). The characterisation of qualitative multiplicities as virtual provides another dimension of that theory.
In Bergson’s ontology, duration as qualitative multiplicity is linked to the concept of virtuality. According to Deleuze, Bergson bases his philosophy of memory and life on the concept of the virtual, treating duration, pure memory and life or élan vital equally as virtual realities, where the concept of the virtual implies a process of actualisation or ‘differenciation’. Deleuze argues that ‘the characteristic of virtuality is to exist in such a way that it is actualised by being differenciated and is forced to differenciate itself, to create its lines of differenciation in order to be actualised’ (Deleuze 1988a: 97). Virtuality is distinguished from the concept of possibility externally by its relations to other concepts: possibility is contrasted with reality whereas virtuality is contrasted with actuality. Deleuze employs a formula from Proust to describe the virtual as ‘real without being actual, ideal without being abstract’ (Deleuze 1988a:96). Virtuality is also distinguished from the concept of possibility internally by virtue of its content: that which is possible typically resembles or prefigures the real, while the real is typically considered a subset of that which is possible. The virtual, by contrast, does not have to resemble the actual and ‘the rules of actualisation are not those of resemblance and limitation’ (Deleuze 1988a:97). The virtual is actualised by a process of differenciation in which difference is primary in two senses: there are differences between the virtual point of departure and the actual outcome, and there are differences between the
various lines along which actualisation can take place, so that, for example, life may be actualised as plant or animal, etc.
One of Deleuze’s last published texts begins with the claim that ‘Philosophy is the theory of multiplicities’ (Deleuze 1996:179).7 This is an appropriate description of his own philosophy of difference. His studies in the history of philosophy involve recurrent efforts to elucidate a vision of a world in which all things are the expression of virtual multiplicities. His descriptions of a Platonic world of simulacra, Nietzsche’s will to power and Bergson’s realm of qualitative multiplicities of duration are all examples of this metaphysics of virtual multiplicities. Even in What Is Philosophy? (1994), the pure events to which philosophical concepts give expression are understood as virtual multiplicities which may be incarnated in an indeterminate number of actual states of affairs. However, the clearest exposition of this differential metaphysics is to be found in Difference and Repetition (Deleuze 1994), where Chapter 4 outlines the theory of a transcendental field, the constituent elements of which are qualitative or pure multiplicities. These are the ‘more profound’ real elements which, Deleuze had argued in Chapter 1 of that book, must be determined as abstract and potential multiplicities in order to enable an account of a world of free differences (Deleuze 1994:50). These positive and differential elements are unique to Deleuze’s metaphysics of difference. They provide the key to his conception of difference ‘in itself and to his dynamic conception of difference as the ‘ground’ of being.
In Chapter 4 of Difference and Repetition (1994), virtual multiplicities are specified as Ideas, Problems or Structures. They are structures in the sense that these were understood by the structuralist theories of the period. That is, they are composed of purely formal elements defined by the reciprocal relations between their component elements. In the case of language, the ultimate signifying units or phonemes are defined by their reciprocal relations to other phonemes. It is the structure of these relations, prior to their actualisation in a given series of sounds or inscriptions, which defines a given language. In the case of social structures, Deleuze follows the structural Marxism of Althusser and his collaborators in taking the economic structure of society to be a system of ‘differential relations between differential elements’ (Deleuze 1994:186). These include relations of property and relations of production established between unspecified ‘supports’ of ownership and labour power. Defined in this manner, intrinsically rather than by external relations, such structures constitute ‘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’ (Deleuze 1994:183). Deleuze proposes that the relations of reciprocal determination between the elements of a given structure be understood on the model of the differential relationship dy/dx, where the progressive determination of this relationship is supposed
to generate a particular primitive function. Just as the determination of a given differential relation partially specifies the behaviour of a curve at adjoining points, so the specification of a given series of singularities or singular points determines the curve corresponding to the relation between the elements in question. For this reason, Deleuze comments in ‘How do we recognize structuralism?’, that there are two aspects to any given structure: ‘a system of differential relations according to which the symbolic elements determine themselves reciprocally, and a system of singularities corresponding to those relations and tracing the space of the structure’ (Deleuze 1998a:265).8
As we noted above, Deleuze’s structures are virtual in that they are not actual, not in the sense that they lack reality: ‘The virtual is fully real in so far as it is virtual’ (Deleuze 1994:208). The differential elements and relations, along with the singularities that correspond to them, form the real content of a given structure. They define a completely positive multiplicity which, Deleuze argues, should not be subsumed under the categories of opposition or negation since these play no part either in the constitution of structures or in their actualisation: ‘The process of difference and of differenciation is primary in relation to that of the negative and opposition’ (Deleuze 1994:207). Differenciation is the process by which Ideas become actualised in spatio-temporal events and states of affairs. The agents of differenciation are ‘spatio-temporal dynamisms’ which are internal to given fields of ideational or material intensity. The embryological example of the egg provides an example of this process of actualisation and of the sense in which the order of morphogenetic processes implies a prior ideal structure of relations embedded in the genetic structure (Deleuze 1994:214). This account of the relation between virtual structures and spatiotemporal events and states of affairs is the means by which Deleuze circumvents the philosophy of representation: bodies and states of affairs do not resemble the structures or ideal events of which they are the expression. In this sense, he argues, ‘actualisation or differenciation is always a genuine creation’ (Deleuze 1994:212).
Deleuze’s concept of difference therefore has two parts: on the one hand the determination of the virtual content of a multiplicity, which he calls differentiation, and on the other the actualisation of the multiplicity in particular species and component parts, which he calls differenciation:
Whereas differentiation determines the virtual content of the Idea as problem, differenciation expresses the actualisation of this virtual and the constitution of solutions…Differenciation is like the second part of difference, and in order to designate the integrity or the integrality of the object we require the complex notion of different/ciation.
There is therefore an important sense in which he maintains the primacy of difference over identity. Difference is the fundamental term on the basis of which the identity of all phenomena must be understood. As such, difference never refers back to a primary identity but only to further differences. Ultimately, however, difference is a process before it is a category: ‘Every object, every thing, must see its own identity swallowed up in difference, each being no more than a difference between differences. Difference must be shown differing (Deleuze 1994:56).
Deleuze describes this process of difference differing by reference to the forms of communication which take place between different physical, linguistic, psychic or other differential structures. Such communication between different systems implies the presence of an agent which he calls the ‘disparate’ or the ‘dark precursor’. The differences of electrical potential which cause a signal or flash of lightning to discharge provide one example, but in reality the identity of such ‘agents’ of communication between heterogeneous systems will vary from case to case, since it will be defined by the particular difference between the systems involved. This difference will be expressed in its effects. In this sense, like the relationship of reciprocal determination between the elements of a structure, the dark precursor may be described as a second-order difference or ‘differing difference’ (Deleuze 1994:119–20).
In apparent contrast to the account we have given of the metaphysics outlined in Difference and Repetition, Todd May argues that Deleuze is ‘not a thinker of difference at all, if by that is meant that he is a thinker who should be read as considering difference to be privileged over unity’ (May 1997:166). May does not claim that Deleuze does not privilege a concept of difference at the expense of unity, in both the ethical and metaphysical senses indicated above. On the contrary, he points out that Deleuze develops a concept of difference intended to serve a ‘positive and disruptive function’, namely that of resisting the privilege attached to forms of unity and totality within philosophy. The function of the concept of difference, he suggests, ‘is at once to attack the unifying forces that have abounded in philosophical discourse and to substitute for such forces a new perspective’ (May 1997:176). However, he argues that Deleuze cannot do this by simply positing a world of pure difference in which unities are explained only as secondary phenomena. To do so would create a number of inconsistencies within Deleuze’s philosophy. First, he points out that an attempt to describe a world of difference ‘in itself would involve claims about the nature of Being which might readily be construed as claims about a realm which is transcendent to human experience. As a result, ‘Being as difference threatens to go transcendent, to become a thing apart from our experience that structures it from the outside’ (May 1997:184). Such a relapse into transcendence is inadmissible for Deleuze, since an essential aim of his philosophy is to refuse
transcendence in all its forms. May reminds us that in What Is Philosophy? (1994) transcendence is identified as foremost among the illusions that inevitably arise from the plane of immanence on which a given philosophy is laid out (Deleuze and Guattari 1994:49). Second, he argues that Deleuze’s various characterisations of this world of difference ‘in itself, whether in terms of Bergsonian duration or pre-individual singularities, invoke a concept of the unity of the field or plane of immanence upon which these entities are described: a unity of time in the case of duration, a unity of the domain of pre-individual differences subtending all identities, and so on. If this is so, then it cannot be true that difference is prior to unity.
May is right to point out that Deleuze’s philosophy of difference cannot be understood simply in terms of the dialectical interrelations of the concepts of unity and difference. But his argument for incoherence in the Deleuzian concept of difference does not withstand closer examination. Deleuze provides many indications that his account of difference in itself should not be construed as invoking a transcendent realm. Rather, he proposes a concept of differential conditions which must be understood as transcendental but entirely immanent to real experience. As May himself points out (May 1997:186), for Deleuze as for Kant, transcendental conditions of experience are not the same as transcendent conditions. Whereas Kant proposes transcendental conditions of possible experience, Deleuze’s transcendental empiricism refers to genetic conditions of real experience. His suggestion that the transcendental field is open to quasi empirical investigation points to an appropriate response to May’s second objection. In positing time as a condition of experience, Kant does not suppose the unity of time. He does suppose the continuity and uniformity of time, but since he also argues that time is neither finite nor infinite, this uniformity does not imply unity. Similarly, Deleuze posits a uniform transcendental field, whether of duration, difference, will to power or intensities, without supposing the unity of that field.