Outliers, flows, and micropolitics

Hannah Arendt once complained about the methodology of statistics in use in studies such as political science, economics, sociology in this way:

“The laws of statistics are valid only where large numbers or long periods are involved, and acts or events can statistically appear only as deviations or fluctuations. The justification of statistics is that deeds and events are rare occurrences in everyday life and in history. Yet the meaningfulness of everyday relationships is disclosed not in everyday life but in rare deeds, just as the significance of a historical period shows itself only in the few events that illuminate it. The application of the law of large numbers and long periods to politics or history signifies nothing less than the willful obliteration of their very subject matter, and it is a hopeless enterprise to search for meaning in politics or significance in history when everything that is not everyday behavior or automatic trends has been ruled out as immaterial.”

Arendt, The Human Condition, 42-43.

(As will be seen, there are points of both profound agreement and profound disagreement between Arendt and contemporary theory.)

According to this view, which has only gained currency with the theme of the exception in thinkers such as Badiou, Agamben, and Zizek, the outlier is that which eludes the counting procedure of a knowledge-situation, that element which denies its elemental status, which subtracts itself from presentation. Statistics can, thus, only grasp the molar fluctions in a terrain of study and does not register the subjacent molecular flows determining those fluctions. The outlier, in a very real sense, orients the structuration of the as-one, and yet appears (to the counting procedure, the statistician) as nothing, as a scientifically uninteresting, marginal datum. Agrammaticality, infinitesimal asignifying particle, the outlier escapes the overcoding of representation and “microdetermines” the macrodecisions of actual political work, that done by legislators and politicians.

The outlier is understood by the statistician as an individual, a mere anomalous individual deviating from the distribution of the general population studied. However true this may be from the molar-representational standpoint, the essential is lost if the analysis stops here. Hence the need for a micropolitics, a microstatistics, a subrepresentational study of details, of desires and beliefs, of quantum flows. For instance, Fernand Braudel’s three-volume history of capitalism up to the 18th century follows social phenomena such as trends in clothing, edibles, spending, and so on, to formulate a theory of the formation of market and antimarket economies, general and restricted economies. Braudel is a micropolitical theorist for this reason: he follows flows and waves operating at the level of the productive unconscious, using statistics only for their cutting edges, their outliers.

In what is arguably the most important plateau (noting the irony of such a contention – it has meaning only with reference to its closest cousins, the “Treatise on Nomadology,” “The Smooth and the Striated,” and so on), Deleuze & Guattari write:

“What…is a flow? It is belief or desire (the two aspects of every assemblage); a flow is always of belief and of desire. Beliefs and desires are the basis of every society, because they are flows and as such are ‘quantifiable’; they are veritable social Quantities, whereas sensations are qualitative and representations are simple resultants. Infinitesimal imitation, opposition, and invention are therefore like flow quanta marking a propagation, binarization, or conjugation of beliefs and desires. Hence the importance of statistics, providing it concerns itself with the cutting edges and not only with the ’stationary’ zone of representations. For in the end, the difference is not at all between the social and the individual (or interindividual), but between the molar realm of representations, individual or collective, and the molecular realm of beliefs and desires in which the distinction between the social and the individual loses all meaning since flows are neither attributable to individuals nor overcodable by collective signifiers. Representations already define large-scale aggregates, or determine segments on a line; beliefs and desires, on the other hand, are flows marked by quanta, flows that are created, exhausted, or transformed, added to one another, subtracted or combined. [...]
This is how you tell the difference between the segmented line and the quantum flow. A mutant flow always implies something tending to elude or escape the codes; quanta are precisely signs or degrees of deterritorialization in the decoded flow. The rigid line, on the other hand, implies an overcoding that substitutes itself for the faltering codes; its segments are like reterritorializations on the overcoding or overcoded line.”

Deleuze & Guattari, “Micropolitics and Segmentarity,” A Thousand Plateaus, 219.

These mutant flows, emitters of asignifying sign-particles, literally “make or break” the macropolitical decisions of policymakers, legislators, and so on. If, as Deleuze & Guattari hypothesize, beliefs and desires are the basis of a modern State society (they seem to think this is true for any society), an evaluation of flows and their quanta ought to reveal the variable, fluid ‘architecture’ subtending politics and judgment in the popular sense; that is, in this realm of inquiry, we ought to find the distributions, nomadic or sedentary, of singularities organizing the macropolitical field. Perhaps the most difficult aspect of initiating such an analysis, however, is finding the correct, “molecular” means of ingress into the mass. This is the role of the outlier for minor statistics.

I wonder what the relation might be between the figure of the outlier and of what Deleuze & Guattari call power centers or central black holes. The latter function as switches in the economy of quantum flows and segmentarities, translating one into the other in a ceaseless perpetuum mobile. Power centers are chambers of resonance, causing communication between the microflows and macrosegments to commence. Every power center is thus molar and molecular, centralizing and decentralizing, coordinating and reshuffling. This is termed the “zone of indiscernibility” between flows and segmentations, the becoming-flow of segmentation and becoming-segmentation of flows – the operative microtexture of a black hole. As elsewhere, smooth and striated, mutation and overcoding, flow and segment cannot but analytically be separated. Hence, a power center is the entre-deux in the economy. As such:

“[T]he texture [of a power center] lies between the line of overcoding with rigid segments and the ultimate quantum line. It continually swings between the two, now channeling the quantum line back into the segmented line, now causing flows and quanta to escape from the segmented line. This is [the limit of power centers]. For the only purpose these centers have is to translate as best they can flow quanta into line segments (only segments are totalizable, in one way or another). But this is both the principle of their power and the basis of their impotence. Far from being opposites, power and impotence complement and reinforce each other….”

“Micropolitics and Segmentarity,” 225.

We might suspect that the figure of the outlier is a product of the impotency of power. But this is probably not accurate. The outlier rather functions as a removal from the power center, a soft subversion of the regime of signs, precisely an asignifying particle, a line of flight. The scheme produced by the statistician crosses over into, or rather opens the space of possibility for the drawing of a map from the perspective of its silent datum. The outlier is included in the scheme but excepted from the general curve. The latter sees the former as hostile – here again, Draussen ist feindlich, outside is hostile. But we receive a new image of the curve itself when we stand in the place of the outlier: perhaps that of a mountain peak, an unscalable height. Our map becomes a diagram for action, a system of creative evasion: the outlier becomes a war machine (in truth, it has never been anything but).

The space of an outlier is, in Arendt’s language, uncivilized (see her Origins of Totalitarianism, 297) or, in Deleuze & Guattari’s language, smooth. A war machine creates smoothness, seizes upon agrammaticalities, paves over striations and rigidifications. The task is always to carve out uncivilized spaces. In this sense, a war machine is universal, a stateless assemblage of universals (i.e., flows: desires, beliefs). The virtual universalism of flows is only ever embodied in particular outliers; however, it is in this way that the outlier determines the curve, curves the curve. The interactions between flows enact redistributions of singularities and relations between singularities in the universal Open (the Whole, the ungivable antitotality, connective thread), and are the objects of study, by way of the outlier, for the positive science of micropolitics – the positive science of discerning potentialities in a given historical situation.

Absolute disjunctive syntheses: contemporary music, part one

In this post, I’d like to highlight one of a number of identifiable absolute, or inclusive, disjunctive syntheses in contemporary art. In the grand scheme of things, highlighting these phenomena of the new poem may point toward a kairotic moment opening an evental site, to use the language of Badiou & Derrida: Politics, Events, and Their Time author Antonio Calcagno.[*see addendum] In that sense, my conceptual matrix for this project is heavily dependent upon Badiou’s work. However, Badiou largely provides me with only formal guidance in the overall determination of this project’s direction. When I do use his concepts as tools in analysis, moreover, I will undoubtedly run up against obstacles that require extensions of these tools beyond their breaking points and have to look to other theorists, other artifacts, and conceptual invention to capture the affects generated by these disjuncts. I think my approach is more in line with Deleuze’s method than Badiou’s, for that matter.

Broadly speaking, I understand absolute or inclusive disjunctive syntheses as propulsions into a structural impasse, direct confrontations with terminal points built into the edifice of a field of praxis or discourse. Moreover, these encounters, which thus bear upon the impossible, must be conceived as productive, edifying (heightening of power), potentially transformative operations. Foreign elements with no necessary or prescribed relation come together to break apart a sedimented, totalized-totalizing scheme of behavior. And yet, any one instance is never the necessary precursor, however dark, to an opening of lines of communication between divergent series. An amorphous, vertiginous cloud accumulates differential elements (elements with no intrinsic properties whose relations are therefore wholly exterior) and relations which do not interact and determine themselves through negation, but rather do so through affirmative, symbiotic amplification or resonance. If no resonance forms between such series, which are nevertheless synthesized or brought under a sort of vinculum in the synthesis at hand, nothing (substantial) in the structure changes and the series might dissociate (de-synthesize, dissolve) or remain non-resonantly, non-communicatively, non-productively coupled, acquiring new elements (and concomitant relations) for synthesis in future encounters. An absolute or inclusive disjunctive synthesis is thus one potential “effect” of a de/reterritorialization or erasure and reinscription of relations of exteriority pertaining to some set of differential elements. As such, finer prediction is guesswork.

I would like to take the work of Einstürzende Neubauten, a group of German pioneers of sonic metallurgy, as a muse in this and follow-up posts on contemporary music. This work is marked by a series of profound reversals, foldings-back (and foldings-forth, foldings-diagonal, etc.), and errant, unpredictable reorientations over the course of several decades. This is evidenced not only in changes in raw materials (ranging from traditional musical instruments and electronic components to specially-crafted or found objects and, importantly, found phrases) and methods of composition, but also in forms of arrangement. The latter have taken traditional or “conservative” schemes, but less frequently than they have been cast in the shape of the “revolutionary” – and we shall see that this conservative-revolutionary thematic is important for understanding Neubauten’s impact on contemporary music’s structure of behavior in itself. Neubauten has, in some counter-cultural circles, become famous for the silence-noise circuits, the conservative-revolutionary zone of indistinction, and the amplifications or swellings of singularities constituting the body of work. These, for us, highlight the shifting of the virtual landscape and the rise toward crisis points of self-enveloping quanta, which promise to reshape the actual, constituted patterns of behavior in contemporary music.

Kollaps is a natural starting point for any discussion of Neubauten’s body of work, being the first official full-length work. This post discusses, however incompletely, only this project. Few subsequent projects will have the consistency of this first; or, perhaps, we might say that this first project suffers from a lack of complexity that properly embodies Neubauten’s profound inconsistency. In either case, the sonic assault that is Kollaps has, in Zizek’s language, its space curved according to a principle of pure noise. Percussion dominates on a material level; of this there is no question. As pure, concrete noise (concrete here in the sense of musique concrete, sound as material, sound disconnected from any means of production and metonymically substituted for both its process of production and itself), however, it must not be confused with destruction. As the introductory cut (“Tanz Debil”) demonstrates, it is a dance of the mad, a “body devoted to its zenith” (Badiou, Handbook of Inaesthetics, 59). It desires to rely on no criterion outside itself to determine its movement; it wills its movement alone as itself. However, a certain ambivalence remains inscribed at the heart of the work of this period. The mad dance knows, as if proprioceptively, that it is nothing but amor fati, creation of its own immanent fate, yet expresses itself as a logic of the No. This is the meaning of the title of the cut “Negative Nein”: Kollaps thinks itself as negative-no, “three times No,” but engages with itself, materially functions as affirmation of amplification.

Nevertheless, Kollaps also enacts an unrelenting critique of capitalism, perhaps to be located on a continuum somewhere between a classical Marxist / dialectical materialist approach and a Deleuzo-Guattarian (radical trans-Marxist?) political-libidinal economic approach. That is, capitalism and its overcodifications, its microfascist-engendering chains of displacement grounded upon its floating metric (capital), are subjected to a line of interrogation calculated to extract the affective kernel: namely, greed. Greed is indissolubly linked with death, a principle and practice, a culture, of death (as the opening line of “Tanz Debil” attests: stell dich tot!). Greed and death color the entirety of Kollaps, and the fascination with these themes probably played a part in its self-conception as “negative-no,” progression according to negation and self-externalization. Greed and death culminate, in Kollaps, in the conclusion that Draussen ist feindlich, outside is hostile: go and hide with me, retreat into interiority, close off all lines of flight. Such is the subjective structure produced in a capitalist social formation (microfascism, desire’s desire of its own repression, outside is hostile: synonyms); such is the object of Kollaps, however inadequately reached it might be.

The use of found objects in art is often aligned with such a (latent or manifest) critique of capitalism. The very artifacts capitalism secretes – especially in disused or abused condition – are taken up and mobilized against its operation. Hence, in Kollaps, unidentifiable metals, plates or shards of glass, hand tools, heavy springs, and running water, among other instruments, are put to use on the body of capital, tearing away at its hard surface. Capital, as we already hinted above with our brief comments on the motif of greed, is weighty, hard, insofar as it is inextricably bound up with the spirit of gravity, is this very spirit at its core. Subjects of capitalism – all of us – “tr[y] convulsively to fly from the earth, but at the following level [we] actually rise[] above it…powered by centrifugal forces that triumph over gravity” (Paul Klee, On Modern Art, 43; quoted in Deleuze & Guattari, A Thousand Plateaus, 312). The lightness of the dance of the mad gracefully – though frenetically – strives to reshape the body of the earth, make it rotate upon an axis other than that of capital, the spirit of gravity. Yet, perhaps despite Klee’s optimism, the subject of / to capitalism is always in a sense the tarantula (Nietzsche’s figure of gravity in Thus Spoke Zarathustra), the ideologue. Trying convulsively to flee the earth of capital and succeeding in flight requires composition with the infinite forces of the outside, those centrifugal forces to which Klee alludes; however, the subject of / to capitalism is structured according to the maxim outside is hostile, and so incipit homo, commence reactive-man. The active figure of praxis is today often thought in Nietzsche’s terms as the Übermensch, the form of life that is a zone of indistinction between life and itself, that is, between life itself and its own immanent power. “The forces within man enter into a relation with forces from the outside, those of silicon which supersedes carbon, or genetic components which supersede the organism, or agrammaticalities which supersede the signifier. … What is the [Übermensch]? It is the formal compound of the forces within man and these new forces” (Deleuze, Foucault, 131-132). Agrammaticalities superseding the signifier! If this deadlock of the regime of signs (legitimizer of the signifier) yet sounds foreign to us – how can an asignifying particle, an agrammaticality, present itself as anything other than nothing? – we remain as tarantulas, tattooed with the triangle and black symbol of capital on our backs.

Segue to the next post on contemporary music: Kollaps does not, in itself, articulate a vehement, serious critical treatment of capitalism. It lacks the anarchitectural efficacy of, e.g., Haus der Lüge, with its free-zones and perplications, that Neubauten has deployed and shown to be necessary for any sustained treatment of capitalism. That is to say, Kollaps receives its truth in subsequent projects. How Kollaps plays into the synthetic act of absolute disjunction cannot be made clearer until other works have been explored.

*Addendum: You’ll note that I merely use his language; the kairological moment, for Calcagno, is the temporality of the intervention.

Of teleological suspensions

The athletic and evocative LarvalSubjects blog currently features a discussion on the aims of and possibilities of reflexivity for philosophy / critique: here and here. I’d like to wager a modest contribution in the form of a mutant Kierkegaardian-Foucaultian model. As such, shall we start with Zizek?

Somewhere in the vast archives of culture jamming extraordinaire Slavoj Zizek lies a claim to the effect that the Kierkegaardian triad, aesthetic-ethical-religious, is transposed in Lacan’s imaginary-symbolic-real knot. The consequences of this might be that the fundamental question – the parallactic question of Passage – is similarly a transposition of Kierkegaard’s fundamental question: Is there a teleological suspension of the ethical? That is, our (critical) question would be: Is there a teleological suspension of the symbolic?

It appears quite impossible. Any true rupture with the symbolic order would seem to merely institute a new symbolism, as it were, a new regime of signs. This is a question of some considerable dialogue – it is present in Freud as in Lacan, in Benjamin as in Adorno. But isn’t this impossibility precisely the “aim” or telos of philosophy as critique? This would be the impossibility of freedom, a freedom that must first be recognized as a new symbolic mediation. Freedom can, from the immersed perspective of critique, only be given as that which is not given in the symbolic. Freedom is the unpresented in presentation, the void of the situation. Subtractive freedom.

How can the symbolic be suspended, teleologically? We have many names for this most romantic figure of latter day anti-romanticisms: care of the self, celebration of awareness, traversing the fantasy (in a sense), pure Act, occupation without counting, subtraction, to skim the surface of popular alternatives. We might follow Foucault, in his lecture series on the Hermeneutics of the Subject as he painstakingly develops his notion of care of the self, to be assembled in the third volume of The History of Sexuality.

Foucault effectively claims that the teleological suspension of the symbolic can be accomplished through a set of self-displacing practices known to the ancients as epimeleia heautou, broader in scope and efficacy than gnothi seauton (and not, for that, the very same set of practices, which would be not only undesirable but impossible). Foucault says: “Attending to the self is not…just a brief preparation for life; it is a form of life,” exactly the form-of-life Agamben thematizes throughout his work on politics (the zoe that is its own bios, life that refuses separation from what it can do). This extends to (critical) pedagogy, the truest form of which would probably look something like Deleuze’s paideia or apprenticeship. For Foucault, care of the self involves a certain experimentalism, a ceaseless intensification of life, becoming a body without organs in the throes of individuation. Recall that Deleuze, for instance, celebrates the suspension of individuation we witness in the close-up in cinema – suspension here in the sense of prolongation, moving to the edge of the void without allowing the schizophrenizing-intensifying processes to bring about a collapse of cognizance, but rather to cause an excess of cognizance, a hyper-perception. This would be freedom. Philosophy requires a perpetuality of movement, an utterly ceaseless subjectification/desubjectification circuit. This is not a “leap out” of the dominant symbolic-ideological discourse. This is a productive reconfiguration of the symbolically determined structures of subjectivity, a discernment (hence “hyper-perception”) of the virtualities / potentialities available for actualization in any given social formation. “Leaping out” is impossible – it is a negation. Freedom must be produced, and produced through adjustments to the assemblage – hence my blog’s subtitle.

Small steps toward a theory of practical ensembles

The following post is the first in a rather unorganized series, an endeavor that will undoubtedly take several attempts and will certainly produce several false starts. Having just finished the recently translated lecture series on The Century by Badiou, I’m excited to put some ideas down, even in very rough fashion, regarding a development Badiou’s text produced in my thinking about such problems as community, (political, artistic, scientific, amorous) movements, and groups and the subjectivities of groups. This is something I’d been thinking about for quite some time, and so this is perhaps something I sought out in Badiou, something that many readers would find uninteresting or peripheral with respect to Badiou’s real thematic foci. Of course these readers are correct. Nevertheless.

What is a group? The aim of a micropolitical inquiry into group-formation is to propose a typology of qualitatively different groups classified by genetic history, and then to study the dynamics between the group types. Groups or we-subjects can be broadly divided into three inconsistent types on the basis of their comportment toward the real of their subjectivities: I. those that maintain a representational relation with the real (parties and states, for instance); II. those that maintain a material or presentational relation with the real (microscopic assemblages, revolutionary/inventive subjectivities); III. those that maintain an ambiguous relation with the real – and this cannot be an intermittent ambiguity, but is instead a necessary ambiguity (e.g., art movements which adhere to the principles of a manifesto or other imaginary identificatory device but at the same time continually effectuate revolutionary changes in what it is possible to do in terms of thought, praxis, etc.).

The real is inconsistent, discontinuous, fragmented multiplicity. Badiou claims that “[t]he real may be encountered, manifested, or constructed, but it is not represented.” The Century, 108. Presentational groups reflect this character of the real: they only exist in particularity, in moments of dissonance (political, artistic, etc.), leaping up from and out of the cold representationalist sea like warm-blooded, iridescent flashes. There is probably no such thing as a “presentational-group manifesto.” There is no possibility of following a pathbreaking leader, no chance of adhering to a doctrine. There is only a spark in search of a powder keg, Breton said. There where the real avails itself of an encounter stands the presentational group. The Idea itself is action, and it has, as Idea, a materiality all its own.

“A demonstration or an insurrection, and more broadly a political sequence, or even an artistic creation seized in the violence of its gesture, are in no way representable. Fraternity is not representable. As I’ve already suggested, the unwarranted appeal to large, inert, macroscopic – and therefore supposedly ‘objective’ – sets (class-in-itself, race, nation…) infects subjectivation by way of its presumed representative legitimacy. But only inertia can be represented.”

Badiou, The Century, ibid.

This is, moreover, one reason why presentational and ambiguous groups are not subject to discussion as such: by the time they’ve become “household names,” by the time it becomes possible to trade opinions about them, they’ve already become inert, qualitatively different. Deleuze, for instance, abhors discussion for this very reason.

Each typological variant has traits unique to it, insofar as some relations resist representation but acquiesce to presentation, or resist presentation but acquiesce to representation, and some cannot be pigeonholed in this way due to a constitutive ambi-valence (ambi = both, multiple; valence = capacity, power).

Badiou gives us a way of thinking about group formation, drawing from Sartre and Lacan:

“Since the being of the subject is the lack-of-being, it is only by dissolving itself into a project that exceeds him that an individual can hope to attain some subjective real. Thenceforth, the ‘we’ constructed in and by this project is the only thing that is truly real…. The individual is thus, in its very essence, the nothing that must be dissolved into a we-subject.”

Badiou, The Century, 100-101.

According to Badiou, a subject is such only insofar as a process of truth authorizes him to say ‘we.’ One can say ‘I’ only so long as one can say ‘we.’ The truth procedure to which the subject attaches and which constitutes the subject presents or represents some real, namely, the real of the we-subjectivity. The party, the state, the faith becomes worth dying for; indeed, it would be an honor. Can we not see in this a valuable insight for thinking about political and religious organizations and the ways in which power is inflected in their operations? Perhaps it is not, as Foucault prophesied, or not only, the law which has taken over the management of decisions over life and death (the quintessential function of biopower); perhaps, instead, the we-subjectivities of representational groups have usurped this responsibility. The legitimacy of saying ‘we’ is guaranteed in the real of the group; after this is secured, after the real has been accessed, the we-subject has a stake in Honor, in upholding the Law of the real, and its very identity is placed in peril in the slightest manifestation of doubt vis-a-vis the veracity of the real of the group; death becomes a way into immortality, a solidification of identity. (It might be possible to move this argument out of the general “ideology critiques” we’re so familiar with. The rudiments of the schema are only taking root.)

This line of inquiry has a history. Micropolitics (Deleuze & Guattari’s word in A Thousand Plateaus) or the politics of collective desire would probably be the correct moniker, though in the framework of the latter thinkers, this name is redundant. We see plenty of precedents in the history of modern thought: Gabriel Tarde’s micro-sociological and -criminological inquiries; Gilbert Simondon’s notion of collective individuation, however underdeveloped; Sartre’s late investigations into the praxis of practical ensembles, in the Critique of Dialectical Reason; Foucault and the microphysics of power; Jacques Donzelot in The Policing of Families, a central micropolitical text; perhaps Bourdieu, Stiegler, and DeLanda today, not to mention Badiou’s lectures here cited and undoubtedly in Logiques des mondes (my French isn’t near strong enough, so I eagerly anticipate the translation). This is a sort of offhand list of resources; I would venture the claim that a micropolitical approach to group-formation and group-activity is not a determinative focus of any of the above figures or works.

I would like to end this rather scattered, allusive, and no doubt disappointing post with a constructive, and revealing, excerpt from Badiou, once again. He writes: “From the end of the seventies onwards, the century has bequeathed to us the following question: What is a ‘we’ that is not subject to the ideal of an ‘I,’ a ‘we’ that does not pretend to be a subject?” (Badiou, The Century, 96.) He concludes this quite central essay, “Anabasis,”:

“[T]oday, everything that is not already mired in corruption raises the question of where a ‘we’ could originate that would not be prey to the ideal of the fusional, quasi-military ‘I’ that dominated the century’s adventure; a ‘we’ that would freely convey its own immanent disparity without thereby dissolving itself. What does ‘we’ mean in times of peace rather than war? How are we to move from the fraternal ‘we’ of the epic [note: where alterity is recognized only as the alterity of the adversary] to the disparate ‘we’ of togetherness [note: in Paul Celan's sense, perhaps closer to an alterity of impossible friendship], of the set, without ever giving up on the demand that there be a ‘we’? I too exist within this question.”

Badiou, The Century, 96-97.

What is a multiplicity?

A fundamental question! Philosophies of the multiple or manifold today abound, as philosophy recovers from its linguistic detour. So much has been said on the idea of the pure multiple, and yet, it seems, what really needs to be said has not been. Far be it from me to enunciate philosophy’s subject; but I think I can put forth some suggestions, if only in clarification.

Deleuze is the first true, systematic thinker of multiplicity in the philosophical / ontological sphere. For Deleuze, everything is multiplicity. Most importantly, however, “multiplicity” usually refers to a virtual Idea or problem, the unextended, creative plenum of ideality folded into the material world as we know it in a banal sense. The notion that “everything is multiplicity,” and especially in the latter sense, is what allows Deleuze to move beyond the structuralism with which he begins. (For Deleuze’s seminal ontological works, Difference & Repetition and The Logic of Sense are undoubtedly attempts to provide ontological orientation to the basic operations of structural anthropology, ethnology, and linguistics; what emerges from this attempt is a theory that supersedes structuralism tout court: “post-structuralism” might be less accurate than “genetic structuralism,” however.) Though the two works just mentioned contain much more rigorous presentations of the idea of multiplicity, it is in Deleuze & Guattari’s What is Philosophy? that we obtain the most basic insights into the nature of multiplicity. One could turn to practically any page in this text and find a slightly different “definition” of multiplicity on each one. Yet there is a constancy of thought as well, as each supplementation or erasure can be assimilated with the claims put forward in Difference & Repetition concerning multiplicities as Ideas, in the discussion that begins with an analysis of Kant (“Ideas and the Synthesis of Difference”). I will quote an excerpt that is all the more revealing in that it comes at the end of Deleuze & Guattari’s brief inquiry into Badiou’s set-theoretical ontology in Being & Event:

By starting from a neutralized base, the set, which indicates any multiplicity whatever, Badiou draws up a line that is single, although it may be very complex, on which functions and concepts will be spaced out, the latter above the former: philosophy thus seems to float in an empty transcendence, as the unconditioned concept that finds the totality of its generic conditions in the functions (science, poetry, politics, and love). Is this not the return, in the guise of the multiple, to an old conception of the higher philosophy? It seems to us that the theory of multiplicities does not support the hypothesis of any multiplicity whatever (even mathematics has had enough of set-theoreticism). There must be at least two multiplicities, two types, from the outset. This is not because dualism is better than unity but because the multiplicity is precisely what happens between the two. Hence, the two types will certainly not be one above the other but rather one beside the other, against the other, face to face, or back to back. Functions and concepts, actual states of affairs and virtual events, are two types of multiplicities that are not distributed on an errant line but related to two vectors that intersect, one according to which states of affairs actualize events and the other according to which events absord (or rather, adsorb) states of affairs.”

-Deleuze & Guattari, What is Philosophy?, 152-153. Emphasis added.

Even the One, they claim at some earlier point in this text, is a multiplicity, having multiple elements which grant it consistency (in this case, being and non-being, themselves multiplicities, and so on ad infinitum). Everything is multiplicity, but are we by that sweeping claim to understand that everything consists of smaller elements, can be broken down into component parts? Is this a new mereology? Not at all. And the reason is deceptively simple. Let us take an analytic approach and follow this thread nevertheless. Take any empirical thing or state of affairs. At the very least, it is constructed of physical components: chemical elements, protons and neutrons, etc. Now strip this physical item of all its properties, down to the single, smallest possible component particle (it does not matter what it is – quark, lepton, something smaller still). It is still a multiplicity by virtue of its relation to other quarks, leptons, whatevers. Let us take another step: strip this particle of all relation to other things. It remains a multiplicity by virtue of its genetic history and its relation to the potentials insisting in it, which are just as real as this physical particle, though non-actual, unextended. Furthermore, as any physicist will tell you, even this (purely academic) minute particle is in a state of flux, and can thereby be said to constitute a field of individuation in itself, which field can only be understood as a multiplicity in becoming (different/ciating into ever more multiplicities).

What is a multiplicity? A field of exterior relations – what I prefer to call proximities.

Deleuze & Guattari point up a competing theory of multiplicities: Badiou’s. A brief detour: Badiou takes Deleuze & Guattari’s criticism seriously, and his more recent writings on Deleuze reflect this more than does his work stamped with the proper name of his critic. The intensive, the entre-deux is appreciated as the “beyond” of the One and the Multiple: “‘[B]eyond’ clearly does not mean a synthesis or a third transcendent term. ‘Beyond’ means in the middle, wherein Being is what activates the essential falsehood of the true and virtualizes the truth of the false through the rhizomatic-network shifter between virtualization and actualization.” (Badiou, “Deleuze’s Vitalist Ontology,” Briefings on Existence, 65.) In short, as Deleuze & Guattari claim, there must be at least two types of multiplicity because there is a third.

Badiou’s idea of multiplicity, the set (which, moreover, refuses definition because to define necessitates a counting procedure, where the parts or elements of a set, pure multiples or sets themselves, can only be thought as what-will-have-been-counted), always comprises the name of the void as minimum of Being, the “point of Being” of any situation. The void or multiple of nothing subtracts itself from any presentation, unpresents itself, and hangs over as remainder, “phantom of inconsistency.” In this way, all sets or multiples are themselves multiples of multiples: even the multiple of nothing is a multiple of multiples insofar as the void “insists” but resists presentation.

What is a multiplicity? Insofar as belonging, inclusion, and subtraction are relations, a field of relations.

Badiou, unlike Deleuze & Guattari, does not suggest that all relations are exterior. Indeed, for Badiou, there are intrinsic relations that, by virtue of this thesis, expose the entire ontological theory of sets as multiples of multiples to the criticism that a dialectic of negation is operative, even if synthesis cannot ever be complete (if only because there is no set of all sets). Subtraction is not negation, to be sure. But the logic of sets is indeed a logic of contraries. After all, the unpresented grounds (abyssally, it is true) the presented and reacts in relation to the presentation of the presented, precisely by a dialectical procedure of unpresentation or subtraction. Subtraction or unpresentation itself escapes the charge of dialecticism, but its relation with presentation is unquestionably dialectical, and this because of its intrinsic predisposition to negate the presented, because it includes within itself its other as itself. The same claims hold a fortiori for the presented, for every presented implies an unpresented and a process of unpresentation.