- ---- by Alberto ToscanoA term used to define the operation of contemporary capitalism within the universal history and general semiology proposed by Deleuze and Guattari in A Thousand Plateaus. Originating in the discourse of science and mathematical set theory in particular, axiomatic denotes a method that need not provide definitions of the terms it works with, but rather orders a given domain with the adjunction or subtraction of particular norms or commands (axioms). Axioms thus operate on elements and relations whose nature need not be specified. They are indifferent to the properties or qualities of their domain of application and treat their objects as purely functional, rather than as qualitatively differentiated by any intrinsic features. Axioms are in turn accompanied by theorems, or models of realisation, which apply them to certain empirical or material situations.If we take ﬂows (and their cuts or breaks) as the basic constituents of Deleuze and Guattari's transcendental materialism, an axiomatic system differs from systems of coding and overcoding by its capacity to operate directly on decoded ﬂows. In this respect, whilst it too implies a form of capture, its degree of immanence and ubiquity is far greater than that of coding systems, all of which require an instance of externality or transcendence (e.g. the Emperor). That is why Deleuze and Guattari defend the thesis of a difference in kind between capitalist and pre-capitalist formations: the latter code ﬂows, while the former operates without coding. Within universal history the immanent axiomatic of capitalism is activated with the passing of a threshold of decoding and deterritorialisation, at the moment when, following Marx, we are confronted with 'free' labour and independent capital. The axiomatic method, as instantiated by contemporary capitalism and royal science, can be juxtaposed to schizoid practice, which is capable of combining decoded ﬂows without the insertion of axioms, as well as to the problematic method in the sciences, which is concerned with events and singular points rather than systemic consistency.One of the bolder claims made by Deleuze and Guattari is that we should not think of the axiomatic as a notion analogically exported from science to illustrate politics. On the contrary, within science itself the axiomatic collaborates with the State in the fixation of unruly ﬂows, diagrams and variations. It is an essentially stratifying or semioticising agency, which subordinates the transversal communications and conjunctions of ﬂows to a system of fixed points and constant relations. As Deleuze and Guattari indicate, the unity of an axiomatic system, and of capitalism in particular, is itself very difficult to pin down: the opportunistic character of the adjunction and subtraction of axioms opens up the question of the saturation of the system and of the independence of the axioms from one another. Moreover, though their dependence on axioms makes models of realisation isomorphic (e.g. all states in one way or another satisfy the axiom of production for the market) these models can demonstrate considerable amounts of heterogeneity and variation (e.g. socialist, imperialist, authoritarian, social-democratic, or 'failed' states). The axiomatic system is therefore not a dialectical totality, since it also generates 'undecidable propositions' that demand either new axioms or the overhaul of the system, and it is interrupted by entities (e.g. non-denumerable infinite sets) whose power is greater than that of the system, and which thus open up breaches onto an outside. It is the capacity to conjugate and control ﬂows without the introduction of a transcendent or totalising agency which makes the capitalist axiomatic the most formidable apparatus of domination.The capitalist axiomatic's ability to establish relations and connections between decoded ﬂows that are otherwise incommensurable and unrelated, and to subordinate these ﬂows to a general isomorphy (i.e. all subjects must produce for the market), leads Deleuze and Guattari to posit a resurgence - beyond citizenship, sovereignty and legitimation of a machinic enslavement which, no longer referred to an emperor or a transcendent figure, is made all the more cruel by its impersonality. Inasmuch as its mode of operation can entirely bypass subjective belief or the coding of human behaviour, such an axiomatic moves us from a society of discipline to a society of control, where power acts directly on a decoded 'dividual' matter. Not only do ﬂows continue to evade and even overpower the axiomatic, but the global and non-qualified subjectivity of capital never attains absolute deterritorialisation, and is always accompanied by forms of social subjection, in the guise of nation-states, and a panoply of territorialisations at the level of its modes of realisation.Connectives
The Deleuze dictionary. Revised Edition Edited by Adrian Parr . 2010.