<<TRANSMATHOME

IV Deduction II: Deleuze

‘ce qui est soustrait, amputé ou neutralisé, ce sont les éléments du Pouvoir, les éléments qui font ou représentent un système du Pouvoir’

(what is substracted, amputated or neutralized are elements of power, the elements which make or represent a system of power)’.[171]

Deleuze understands deduction eliminatively. Real critique and real creation are not differentiated, and the destruction of the image of thought and the elements constitutive of its power are immanent to the real genesis of thought. There are always two things occurring simultaneously, and the negative is always an effect of the positive, but there is no determination of signs in advance of the formation of the division: creation is not of necessity positive, anymore than destruction is of necessity negative. It is important not to confuse Deleuze’s method as prescriptive of a better future, or as claiming more truth than any other: uncovering the real conditions of the production of production is not an exercise in curing the world of its ills, but rather of describing the mechanisms implicated in its construction, and it is in this sense that Deleuze’s is a rigorously critical project.

This method of eliminative deduction complements that of selection, by stripping out  the signs of power in a writer or system or order, so allowing for a description of the development of virtual elements disguised or covered over by constructions submitting to the requirements of law and systematic unity. ‘Soustraire l’unique de la multiplicité à constituer; écrire à n-1 (subtract the unique from the multiplicity to be constitute; write at n -1 dimensions).’[172] The method is positive, in that it is not simply a case of removing arbitrary components, but of selecting elements which collapse the necessities attaching to functions of power, unity, law, the State: the negative elimination is thus a function of a positive operation. He calls the method minoritarian and it differs from majoritarian thought, which operates on a principle of recognition and law, in the following ways: majoritarian law makes doctrine from thought, facts from events and normalizes by admiration; a minor literature disengages life from culture, becoming from history, thought from doctrine, and bodies from society. Minorities are defined not in terms of their denumerable quantity - which would, for example, disclude women from minoritarian status - but ‘par l’écart qui les séparent de tel ou tel axiome constituant une majorité redondante (by the gap that separates them from this or that axiom constituting a redundant majority’[173]. As minoritarian in method, Deleuze’s deduction focusses on exposing the differential intensive elements and problematic sensations which attraction cancels by condensation into a point, an axiomatic quanta immanent to real distributions, and tracking the tactile connections of the actual continuum, generating simultaneously a radical new description of space.

In Mille Plateaux, Deleuze and Guattari describe the coexistence of mechanisms in primitive and nomadic societies, which anticipate the State in two senses, both warding off or repulsing centres of resonance, and incorporating vectors moving in their direction. Before appearing, the State

‘agit déjà sous forme de l’onde convergente ou centripète...qui s’annule précisément au point de convergence qui marquerait l’inversion des signes ou l’apparition d’Etat.

(already acts in the form of a convergent or centripetal wave...that cancels itself out precisely at the point of convergence marking the inversion of signs or the appearance of the State)’.[174]

The model fits neatly with Kant’s description of attraction as a wave-like convergence from all points on the surface of a sphere towards a point. The point made in Mille Plateaux is that this movement is anticipatory of the State, rather than effected by it, responding to it as something which does not yet exist, but which nonetheless ‘agit déjà sous une autre forme que celle de son existence (is already in action, in a different form than that of its existence)’.[175] The point of attraction is thus doubled, functioning both virtually, as a real potential to be anticipated and warded off, and actually, as concrete, effectuated. The inverse movement of a diffusive, divergent wave testifies to this actual operation, to the concrete striation of space and division of forces in terms of an order folded back over the surface of the flows, imposed from one point on all distances.

Rather than searching for the origins of the resonant central point,  the State, or giving a chronological account of its emergence from pre-State societies, Mille Plateaux divides the existence of both - state and nomadic societies - into virtual and actual potentials, arguing that both have always existed, and that virtual potentials co-exist alongside concrete machines, but cannot be described in their terms. The move is familiarly Kantian: the transcendental cannot be described from the empirical, but is its condition. Where it departs from Kant is in its refusal to generalize over the virtual, and reduce it to a possibility recognizable in its concrete instantiations, and in the positive feedback from the concrete which functions as a selective mechanism, potentiating the actualization of virtual elements. There is no Law, no lex continui in natura, no Master, no Slave and no Rebel, and the economy is not visual, but tactile, affective, a matter of sensation and intensity rather than sight and extension. Every assemblage is individuated simultaneously as both singular and collective, virtual and concrete, and only by empirical exploration of the branchings, proximities, contacts and connections into which an assemblage enters is its mode of functioning disclosed. Thus, for example, when addressing the situation of women in relation to capital, no general statement is possible which comprehends the complexities and degrees of attachment to this system, and attributes a position of women as a whole. Instead, the actual situation of individual women has to be explored, and the micro-physics of power organizing and blocking lines of becoming followed at the local level, rather than from a global perspective.

Kant defines points of contact, tactile proximities in full space in terms of relative degrees of compression, and Deleuze and Guattari focus in on this problem. Rather than uniformizing their distributions, a move which proposes both an initial and eventual equilibrium, initially that of unity, or the present, and eventually that of homogeneous entropy, or the future, each is taken as singular. So a different concept of chaos emerges, one which is not unformed and uniformly homogeneous, but which is patterned, populated by haecceities, or ‘des modes d’individuation qui ne procèdent ni par la forme ni par le sujet (modes of individuation proceeding neither by form nor by the subject’, and which is immanent to the content and expression of bodies and their languages.[176] Each plateaux describes a singularity, a concrete date which effectuates a set of virtual elements in a configuration without precedent or model, a region of chaos sufficiently massive for exploration by human methods. Unformed matter is no longer the future generality of good sense, heat death or the kingdom of ends, but ‘une matière-mouvement qui comporte des singularités (a matter-movement bearing singularities)’, the stuff of bodies, or content; and a nonformal functions diagramming a plane of consistency or abstract machine, is ‘une expressivité-mouvement qui comporte toujours une langue étrangère (an expressivity-movement always bearing a foreign tongue)’,  the stuff of language, or expression.[177]

An abstract machine is defined in terms of concrete flows on its surface, flows of air, breath, heat, food, sperm, shit, sex, words, sunbeams, money, stones, etc.: ‘continuums of intensity, blocs of becoming, emissions of particles, combinations of fluxes’.[178] The theory of assemblages or multiplicities arises from these flows, from non-formal functions, tendencies to the limit,  unformed matters and the atypical expressions of minoritarian sciences and literatures, philosophies and arts, which no longer refer to disciplines or faculties, but to the relative mix of elements composing a machine. The State is an abstract machine, and there has always been a State, Deleuze and Guattari argue, and nomadic societies, far from being precursors of the State, are always in some relation to them. Instead of separating the waves of attraction and repulsion, convergence and divergence into two separate tendencies Mille Plateaux seeks to theorize them as simultaneously concretizing different virtual tendencies, or abstract machines, so that any assemblage or multiplicity is both attached to the strata, which are State apparatus of capture, and so interior to its territory and as transversed by a vector of escape, which eludes and evades that order. Applied to Kant, this exposes a third kind of line, which is neither that of convergence or divergence, nor that which biunivocalizes relations between two bodies, which Deleuze and Guattari call a line of flight.

The surface on which forces are distributed is no longer made uniform by rectilinear lines striating space, and organized by a superstratum elevated vertically above it and functioning as a central resonator for all points on the sphere, but is instead a differential field of thresholds and gradients of intensities. This intensive space, or spatium connects with discussions in chapter one - with the given as intensive, the sufficient reason of sense  which forces thought: with Deleuze’s definition of the transcendent form of a faculty as grasping that in the world which concerns it exclusively, differentiating the transcendental: with Kant’s definition of transcendental matter as that which corresponds to sensation: with the thing-in-itself, or in-itself of difference. Deducting the assumption of unity which covers over the real problematic involved in these elements, and attaches them to a subject-based epistemology and an ontology of being, Deleuze opens up the problem of diagrammatization of this differential field, populated by spatio-temporal dynamisms, torsions, drifts and larval subjects. Rather than, as with Kant, attempting to construct a concept of quantity which could contain magnitudes of intensity, and allow for their mechanical distribution through the medium of a subject, Deleuze concentrates instead on the nature of lines, flows, connections and distributions immanent to material-forces.

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