Infinity and the Subject (Part I)

What follows will no doubt butcher the history of mathematics. My aim here is to get right to the point of Alain Badiou’s intervention in set theory and ontology, shamelessly eliding and summarising important discoveries as I go and claiming no expertise. If anyone spots something technically incorrect about this post feel free to let me know. My education in mathematics ended at age 18 and we did not part amicably, and my enthusiasm is only now being rekindled through philosophy. I’m interested in understanding the logic, not in objections to the heuristic ‘value’ of set theory. 

After the gradual replacement of infinitesimals with the definition of limit, the mathematical and philosophical context in which Georg Cantor set to work was one that held the notion of infinity as irredeemably potential, essentially inaccessible, and more or less explicitly analogous to a transcendent entity, or God. It was also a time after the discovery of various non-Euclidean geometries and the dawning realisation that geometric axioms were not the foundation of physical extensive space but each relative to a given model thereof. If mathematical truths could no longer be grounded in representations of space, then perhaps they could be grounded in number, but we return to question of the coherence of number at its ultimate ‘limit’ of infinity.

Cantor began with a distinction between the enumeration of a given quantity of collected objects in a set on the one hand (ordinal numbers), and the relative size or ‘power’ of sets on the other (cardinal numbers). With finite sets we can say that the ordinal enumeration of its parts will be identical with its cardinal power; the finite whole is the sum of its collected parts. But when we consider infinite sets we realise this ratio breaks down and a one-to-one correspondence can be made between set and subset. In the infinite succession of natural numbers, then, there are as many odd numbers (subset) as there are odd and even numbers (set). We can, furthermore, pair off every natural number with a rational number, the latter infinite denumerable set adding no further cardinality to the former. All infinite denumerable sets have the same cardinality, regardless of how large a part of the ‘original’ infinite denumerable set they include. This ‘original’ set of all denumerable natural and rational numbers was denoted by Cantor as the Hebrew letter aleph, subscript zero: ℵ0

[I had the subscript formatted in my Word document but WordPress doesn’t have the toolbar options to hand on the editor. I have neither the time nor patience to fiddle around with the toolbar, so here the subscript characters will be in normal type.]

Things get interesting when Cantor considers the already-proven existence of irrational numbers. ℵ0 clearly does not exhaust the numerical description of a linear geometric continuum (all conceivable points on a line), hence the set-theoretic discovery of a distinct and nondenumerable order of infinity over and above, so to speak, the denumerable collection of rational numbers. This nondenumerable set Cantor called c [Fraktur script]. It follows that all conceivable segments of the geometric continuum (from ℵ0-dimensional to one-dimensional) are of the same cardinal power. Moreover, the axiom of the power set allows Cantor to denote the infinite arrangements of subsets found within set ℵ0 as 2ℵ0 proceeding on with a sequence of numbers each infinitely larger than the last. Cantor’s continuum hypothesis set out to prove that the power set axiom was the key to a well-ordered transfinite realm of successive cardinal numbers; that the nondenumerable infinite set of irrational numbers was actually the power set of ℵ0 all along, that 2ℵ0=c, and that this set is the very next discrete cardinal number in an ordered sequence thereof, denoted by aleph, subscript one: ℵ1.

To Cantor’s great despair, he was unable to draw this direct link, and later Paul Cohen firmly established that there is no clear relationship between the ‘successor’ cardinal ℵ1 and the power set axiom. Cantor ultimately had to accept a distinction between the ‘consistent’ transfinite and the ‘inconsistent’ Absolute infinite inaccessible to numerical treatment, anticipating Russell’s paradox of the set of all sets (which is itself a set, etc.). To this day the precise boundary between consistent and inconsistent number remains unclear; the consequences of the power set axiom, the generation of ever further orders of cardinality, simply cannot be brought into alignment with the ordinal. The axiomatization of set theory, beginning with Ernst Zermelo, was an attempt to maintain transfinite order precisely by removing the inconsistent Absolute from the picture altogether. Definition of set would be replaced by axioms for avoiding inconsistency and paradox.

This is where many philosophers of mathematics leave the room. If axiomatic set theory cannot even define its own elementary concept, how can it be assigned any ontological authority? For Alain Badiou, however, this is precisely the place of ontology, because it does not authoritatively define its ground but instead modestly prescribes a set of procedures, marking a point where the subject can be brought into being through a decisive act. For Badiou, the continuum hypothesis is the most profound site of thought and being, the place where the two become most emphatically indistinguishable, and from which we can proceed with sound ontological investigation . . .

Continued in Part II

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The Revolutionary Micropolitics of Desire (Part IV)

 Following Marx, the critique of capitalism found in Anti-Oedipus readily acknowledges it as the most powerful force in the history of mankind with regards to the dissolution of primitive and despotic codes, sign regimes, modes of social organisation etc. The life and work of each of us is liberated from transcendent determination and overcoding by the revelation of the abstract, subjective (deterritorialised) forms of labour and libido. As we have seen, however, it is the function of the capitalist axiom to reinscribe labour onto private property towards production for production’s sake, and to relegate libido into the private family domicile. Filiation on the socius is now the sole purview of capital, producing its own surplus in perpetuity, while human reproduction no longer has any meaningful place on the social field. Capitalism is the mode of social organisation which simultaneously reveals the identical, immanent nature of social production (labour) and desiring-production (libido) whilst extricating and separating the two into different regimes more forcefully than any previous mode.

Addressing these forms of production according to two distinct regimes will necessitate the introduction of two different levels of analysis and types of psychic and social investment, termed by D&G molar and molecular. The molar essentially corresponds to ‘macro’ statistical trends, whereas the molecular operates at the level of partial objects, deeper than the individual ego, down to the ‘micro’ connections and disjunctions which coordinate a given subject-form. The molar investments are essentially paranoiac – an illegitimate use of the syntheses of consciousness – as they capture synchronic statistical aggregates in representational forms and invariably exert selective pressure on the molecular connections and disjunctions. The anti-capitalist function of schizoanalysis, then, is to invert this hierarchy and subordinate the molar representation of capital to a truly ‘free’ market of molecular transactions.

Another investment of the molar kind takes place when psychoanalysis treats myth and tragedy. Whereas historically the representations found in myth refer to a transcendent object (full body of the earth, despotic figure), mythology under capitalism is rendered abstract and subjective, recoded by psychoanalysis into an infinite, universal dream. Lacanian psychoanalysis depersonalises the Oedipal triangle, expanding the schema from literal persons to the Imaginary and Symbolic, the alienated realm of universal metaphor. This all takes on the countenance of a paradox; belief in myth is preserved without belief in myth. Belief has been privatised, stripped of objectivity and made into an element of a subjective yet universal history. A schizoanalytic approach, on the other hand, will not address representation be it mythological or familial, but will instead cut directly to the syntheses of consciousness as elaborated in the previous post.

In a political sense, the success or failure of a revolution is determined by both its degree of libidinal force/investment (revolutions are sparked firstly by desire, not duty) and its direction, molar or molecular. D&G borrow from Sartre to distinguish the two forms a collective revolutionary movement might take once it has gathered enough momentum. The ‘subjugated’ group is one that subordinates its investments to the molar aggregates, to ‘interests’ and ‘aims’ of one kind or another (the proletariat, the Aryan race) in order to instantiate a new order, a new socius to which unconscious desire and debts of surplus value are referred. The subject-group, on the other hand, refers to the inverted face of the socius, the molecular body without organs, rendering society as the surface of inscription for unconscious desire, and bringing labour and libido under a single regime of desiring-production. Historically, the capitalist axiom of reterritorialisaton has seen to it that subject groups either fizzle out with no social repercussions or are turned into subjugated groups. Writing in the wake of May ’68 it is clear that D&G (along with many of their contemporaries) view the French Communist Party in such a light.

We see here a departure from the classic Hegelian Left conception of the vanguard party representing (coding) the rights and interests of the working class as the purported subject of universal history. Deleuze and Guattari historically aligned themselves quite closely with the work of Antonio Negri of the Autonomist movement in Italy, representing the anarchist/anti-authoritarian Left and, like Deleuze, proposing a Spinozist form of materialism. Spinoza did not subordinate matter to thought as in Hegel’s idealism, but instead introduced a parallelism or coextension of matter and thought. The pursuit and practice of ‘adequate thought’ involves the avoidance of something like what D&G would call the illegitimate use of the syntheses of consciousness (imagination, ideology), moving towards the realisation and expansion of human conatus (this can be compared nicely to Nietzsche’s will to power).

~

A clear and radical directive emerges in the Anti-Oedipus: the dissolution of the nuclear family. This essentially capitalist institution is the analytic locus of modern psychological and social repression which psychoanalysis merely interprets and reinforces in the form of Oedipus, the universal dream of private man. When the investments of desire are constrained to the molar dualities of father and mother and the various metaphorical connotations and stigmas identified therein by psychoanalysis, we see the outlines of a hierarchical and segregative image of thought and the inevitability of neurosis/perversion (repetition of the same over difference) or castration in the form of asceticism. The ‘destructive task’ of schizoanalysis is thus inextricable from the positive task of producing molecular modes of individual and collective subject-forms. One example of the latter in this context, then, might be an increase in socialised, community-oriented child-rearing. In the first instance, the act of historicising Oedipus and psychoanalysis and thereby stripping it of universality staves off resignation and opens up the possibility for alternatives.

The positive criteria for the legitimate use of the syntheses of consciousness do, however, call into question forms of minority political action which advocate on the basis of exclusive disjunctions between fixed identities along the lines of gender, race, sexuality etc. Deleuze and Guattari are very explicit about this:

For example, no ‘gay liberation movement’ is possible as long as homosexuality is caught up in a relation of exclusive disjunction with heterosexuality, a relation that ascribes them both to a common Oedipal and castrating stock, charged with ensuring only their differentiation in two non-communicating series, instead of bringing to light their reciprocal inclusion and their transverse communication in the decoded flows of desire (included disjunctions, local connections, nomadic conjunctions). (Anti-Oedipus, 399)

You can substitute any minority group you like in this schema. Perhaps the finest elaboration of the illegitimate use of the syntheses of consciousness with regards to gender can be found in the works of Judith Butler, in which gender is historicised as varying performative forms of neurotic repetition of the same.

Despite all this, one must grant that capitalism, in its rampant decoding of despotic sign regimes, has indirectly provided ample opportunity for minority expression. In capitalist spaces all types of discourse lose their objective, transcendent quality and become a subjective matter of disjunctive synthesis with varying degrees of inclusivity and exclusivity. There are no doubt institutions which implicitly or explicitly recode their majoritarian aims and interests along the lines of molar subjugation, but the unstoppable waves of the capitalist axiom are continually providing opportunities for revolutionary subject-group investments of molecular unconscious desire.

The Syntheses of Consciousness (Part III)

In the previous post I made reference to the ‘syntheses’ of consciousness, describing connective synthesis and inclusive/exclusive disjunctions in relation to a critique of psychoanalysis. Here I will clarify what exactly is meant by each of the three syntheses of consciousness.

Connective synthesis of production

These essentially correspond to the Freudian drives, instincts, cathexis etc. The desiring-machine, or the ‘libidinal’ motor of human life, makes connections between partial objects: infant’s mouth to mother’s breast, eye to face, hand to hand, etc. All these connections link up to constitute a physiological or psychological effect in the manner of relays or breaks in the flow of desire. Each object in the connection is partial; it is not assigned to an englobed ego or complete object. The connection does not have to consist of two organs; in breathing, for example, we inhale through the mouth in connection with the ambient atmosphere. Each connection is multiple, heterogeneous and constitutes a linear series of ‘and . . . and then . . . and then.’ The French edition of Anti-Oedipus actually uses the Rube Goldberg machine as an illustration.

 

Disjunctive synthesis of recording [inscription, registration]

The effects or ‘products’ of linear connective syntheses are recorded/registered on a surface of inscription in the unconscious. Deleuze has always maintained that it is the enjoyment of difference which provides a disjunction from the neurosis of the Freudian pleasure principle which returns to the pleasantly familiar, a mechanical repetition of the same. In order to avoid locking the psyche into the neuroses of habit and instinct, something is required to break the relay of desire, to neutralise the libidinal investment of a given connective synthesis. The body without organs is thus proposed as an empty, dis-organised limit point, a tendency opposed to the formation of habit and neurotic repetition. It is the form of anti-production as such. On the body without organs, then, connective syntheses are recorded into memory as disjunctive codes or signs, with varying degrees of freedom, of organisation-disorganisation, on a spectrum of variation-repetition. Our unconscious psyche possesses varying degrees of freedom to relate and compare (in a logic of ‘either . . . or . . . or’) among a multiplicity of sign regimes with schizophrenic desire at one end of the scale and neurotic repetition at the other.

The form of memory and time in the unconscious is not strictly linear; it composes an image not of a single signifying chain in Lacan’s terms, stretching back into the past, but a synchronic multiplicity of substantively different signs and sign regimes (much more than mere language), a polyvocal free association of images and letters, symbols and codes, and schizophrenia is the condition of a psyche wherein no single code prevails. For Lacan, repression follows from the onset of language and the chasm opened up between signification in the unconscious and substantial, material being as a result. The reason D&G avoid this tragic existentialist condition is that, for them, there is no schism between the differential Symbolic and substantial Real in their materialist semiotics – codes and signs are produced directly by material processes. They instead engage in critique of various codes and sign regimes on terms immanent to the three syntheses; there is no ultimate incompatibility between signification and reality, only degrees of legitimacy and illegitimacy with regards to connective, disjunctive, and conjunctive synthesis (in the spirit of Kant’s critical method). D&G offer us a remarkable poststructuralist semiotics that simultaneously relativises systems of representation while providing us with pragmatic, real criteria for success and failure.

 

Conjunctive synthesis of consumption

We have said that the body without organs is the form of anti-production, the form which it takes in the psyche. One danger of anti-production, especially in a material and social context of despotism, is the persistent denial of connective syntheses and their inscription in a system of oppression-repression. This is elaborated fully in the genealogy of Oedipus. Two notable forms of subjectivity result from a systematically oppressive tension between anti-production and desiring-production – the neurotic and the pervert. On the one hand, the neurotic becomes fixated on substituting for whatever connective syntheses have been denied them, and on the other, the pervert maintains the prohibited connection which is often enjoyed all the more for it being prohibited.

It must be noted that neurotics and perverts are not so by conscious choice. For D&G, the subject is really an after-image or photograph of the given disjunctive syntheses brought to consciousness at a given moment. Subjectivity is crafted by the interplay of desire and repression, with no ideal separation of the subject from the social field. Self-recognition is always retrospective, lagging behind the material processes of the previous syntheses; ‘I am . . .’ is always-already ‘I was . . .’ The identifications made by subjectivity denote the surplus values leftover from the previous syntheses. The Self, in this sense, subsists by ‘consumption’ of surplus value. The social effect of anti-production then, to historically varying degrees, is to mandate and carry along this surplus value and distribute it on the social field.

We can trace the illusion of sovereignty along these lines: the actual process of connective synthesis is forgotten – what is inscribed in the psyche is the connected products. We mistake the disjunctive multiplicity of codes and signs for the original source of our very being when it is actually only a product of connective synthesis. We then, furthermore, mistake the consumption of surplus value in conjunctive synthesis for full ownership of consciousness, desire, and action. The sovereign subject is just one example of the idealist, illegitimate use of the conjunctive synthesis, whereas our materialist analysis views the conjunctive synthesis as a constellation of intensive states and experiences. If a subject truly believes itself to be fixed, or is repressed into fixity, then this will be borne out in neurotic or perverse behaviours, themselves producing limited connections in the first synthesis, a restriction of difference in the second, and repetitious, mechanistic experience in the last. The illusion is in sovereignty, not in the existence of forms of subjectivity which correspond to constellations of material experience.

The criteria for legitimate use of the syntheses of consciousness, then, would constitute a form of subjectivity as finely attuned to the multiplicity of the body without organs as possible whilst maintaining one’s capacity to prolong such a state long term in the actual. We cannot practically maintain a state of permanent revolution and hope to live well, but we can, for example, avoid the paralogism of extrapolation which would subject the psyche to the overcoding of a transcendent signifier. More on this later . . .

The Paralogisms of Psychoanalysis (Part II)

We departed in the previous post with the assertion that psychoanalysis is a fundamentally capitalist institution, carrying out the latter’s cynical system of anti-production, reinforcing the Oedipal structure on the unconscious towards its own perpetuation. The crux of Deleuze and Guattari’s critique of psychoanalysis lies in the overturning of prohibitions against desire which come in the form of taboo and law. The existence of an incest taboo is not empirical proof of its status at the ground of the unconscious. Generally speaking, the law does not contain knowledge of anything. It comprises a system of representation essentially corresponding to the standard poststructuralist semiotic schema; a ‘repressing representation’ as signifier, a ‘displaced represented’ as signified, and a ‘repressed representative’ as referent. The signifier of repressing representation, Oedipus, generates a distorted image of desire, a displaced represented/signified which is the corresponding complex taking place in the psyche.  The repressed representative, the referent, is desire as such, still there in the background but divorced from its own productive processes, induced by the signifier to generate the image of its own repression.

For D&G, any fixed representation, any transcendent signifier, is despotic in relation to the true productive and variant nature of unconscious desire. The key thing to note, however, is that the unconscious is utterly neutral and thus vulnerable to structuration by all kinds of despotic sign regimes. Lacan sees the unconscious as inextricably linguistic, structured upon the advent of semiotics into a given sign regime of language and thus rendering us irrevocably alienated from our bodies in the Real. D&G, however, go one step further and conclude that the unconscious is not comprised of one sign regime (language), but multiple. The schizoanalytic image of the unconscious disavows meaning much like Lacan’s, but D&G refuse to resign themselves to alienation. Having a positive image or referent of the unconscious in mind, they are able to critique various semiotics/sign regimes according to their legitimate and illegitimate uses of the syntheses of consciousness (heavily influenced here by Kant). They are not concerned, then, with the ultimate truth of the content of a given representation, but with its functional effects on the psyche, its form of structuration on an otherwise ambivalent body without organs. The critique of Oedipus is a functional, aesthetic one.

~

Oedipus was not invented by psychoanalysis, but it is reinforced in the latter’s material practice in the context of the capitalist social formation which produces what we know as the nuclear family. Here we strip the universality from Oedipus and put it in its historical place. Once we follow the implications of this historical materialism, all forms of fixed identity become quaint and technically illegitimate. Desire in the nuclear family is domesticated into identification initially with the prohibited object of desire and the agent of prohibition (the Lacanian depersonalisation of ‘mother’ and ‘father’). There is a paucity of real determination here and subjectivity increasingly seeks and admits of supplementation from the outside. It is not enough to merely identify with one or the other gender in the home; wider social investments of desire take hold in the identities of nation, race, religious sect, etc. (White, Anglo-Saxon, Protestant) The fatal mistake of psychoanalysis is to repetitively and monotonously inscribe these social investments back onto the domestic scene and the Oedipal triangle as a universal triptych of exegesis.

Deleuze and Guattari go further than Lacan in the depersonalisation of Oedipus, not content to distinguish between the Imaginary figures of daddy-mommy and the Symbolic functions of desire and prohibition. For schizoanalysis, the Imaginary and Symbolic are just so many different functions; all is function. This exclusive disjunction between Imaginary and Symbolic in Lacan gives rise to the next paralogism of the double-bind. The only choice for the subject in psychoanalysis is either to resolve Oedipus by accepting prohibition, ‘differentiating’ oneself from one’s parents and seeking Symbolic substitutes; or alternatively to remain fixated and thus undifferentiated in the realm of the Imaginary. The inclusive disjunctions of schizoanalysis, on the other hand, affirm every form of transitory individuation and subjectivity as always-already substantively different.

~

Lacan’s positioning of the phallus in the Symbolic register as signifier of desire is a prime example of the next paralogism of psychoanalysis, that of extrapolation. If the chains and flows of connective and disjunctive syntheses pertain to so-called ‘partial objects’ – for example, the breast as it relates to the infant before the latter is able to assign the former to a concrete englobed ego (mother) – then psychoanalysis specialises in extracting such partial objects and transforming them seemingly by fiat into complete signifying objects which inform the rest of the structure. In another procedure of extrapolation, Melanie Klein conceives of partial-object connections as a ‘pre-Oedipal’ stage on the way to developing an integrated global subject.

For D&G, the synthesis of partial objects into complete objects is never complete. The machines of desire are always at work in connective and (inclusive) disjunctive syntheses, fragmenting and reconfiguring, dissolving complete objects into partial objects and placing them back into the flow of desiring-production. This procedure of partial-object connections thus cannot be termed ‘pre-Oedipal’ so much as anoedipal. It is the very formulation of complete objects which introduces lack into the schema. The ego is confronted with its own real inadequacy by comparison with its Imaginary wholeness and completion, and with its relative poverty in the face of the vast Symbolic register of language and meaning. The claim of D&G is that complete objects, whilst psychologically real, are not transcendental givens but social and historical. As they show in their genealogical critique, it is the claim to universality of complete objects which is illegitimate.

~

For Lacan, the exclusive disjunction between undifferentiated Imaginary and differentiated Symbolic leaves consciousness tragically alienated from the Real. But what if our perspective was not limited to that of consciousness, fixed identity, ego, as is the psychoanalyst? Here we must go back to the third term of our poststructuralist semiotics, the repressed referent of desire. It is the connective synthesis of partial objects by the machines of desire which constitutes the Real – yes, ego can only ever hope to represent the Real, but ego is not the basis of human existence. The primacy of the ego is the repression of the Real, the latter of which designates the inextricable coextension of man and nature.

For a psychoanalytic typology this might look an awful lot like a fixation on the Imaginary, stuck in the undifferentiated. “You’re just rebelling against the law of the father and identifying incestuously with the mother! You can’t escape the double-bind!” This is why Anti-Oedipus remains so vital. Nature is not essentially feminine, even though a movement in that direction necessarily involves a rejection of the Oedipal father. Schizoanalysis diagnoses Oedipus even today. Remember, it is the extrapolation of mother and father, masculine sign and feminine nature, into complete objects as contradictory terms of a dualism that is illegitimate. But that does not mean they remain undifferentiated in schizoanalysis, on the contrary, they are made all the more substantively, gloriously different when they are placed back into the multiple flows and connections of partial objects in the syntheses of consciousness . . .

. . . everyone is bisexual, everyone has two sexes: but partitioned, noncommunicating; the man is merely the one in whom the male part, and the woman the one in whom the female part, dominates statistically. So that at the level of elementary combinations [in the statistical sense] at least two men and two women must be made to intervene to constitute the multiplicity in which transverse communications are established – connections of partial objects and flows: the male part of a man can communicate with the female part of a woman, but also with the male part of a woman, or with the female part of another man, or yet again with the male part of the other man, etc. Here all guilt ceases, for it cannot cling to such flowers as these.1

Footnote

  1. Gilles Deleuze & Felix Guattari, Anti-Oedipus, trans. by Robert Hurley, Mark Seem, and Helen R. Lane (Bloomsbury Academic, 2013), p. 87.

 

Surplus Value and the Genesis of the Oedipal Psyche (Part I)

I

Firstly, we must recognise that desire thought in terms of lack is one of the great misconceptions of Western thought. Lack and need do not produce desire – the opposite is true. Lack and need emerge as a product of primary desire and the distribution of this remainder in various forms of social organisation. Secondly, we ought to think of social organisation not principally as the fulfillment of basic needs, but on the basis of the distribution of excess. Meaning in productive activity is derived from the expenditure of what we can call surplus value, which does not necessarily come in the form of raw materials or capital, but in any kind of social investment of desire (ritual sacrifice, for example, a phenomenon that is far from diminished in relation to resource scarcity). This distribution or expenditure can be called anti-production. It is the forces and relations of anti-production which either foster or inhibit social obligations and power relations in different forms throughout history, which brings us to our most important critical principle . . .

Social formations do not ‘evolve’ in a smooth trajectory across time, broadly moving along a teleological line of development. One principle of genealogy is discontinuity, of the abrupt reconfiguration and recombination of social formations towards crucially different means and ends in each case. This would be to disagree with the structural anthropology of Claude Levi-Strauss that societies across space and time organise according to a universal principle of value exchange. There is always anti-production, but its direction and form of distribution varies, and it is in terms of these variations that we can differentiate between ideal-types of society. Surplus value must go somewhere and its constitution on the socius formulates it not in terms of exchange but as debt which is always on its way to a creditor. In primitive societies, for example, it is the full body of the earth which takes credit for production; in despotic societies it is the figure of the despot; and under capitalism it is universalised into capital as such. The socius is thus a kind of abstract quasi-cause, the basis upon which all systems of anti-production are inscribed. The debt is paid, for example, into forms of shamanism or ancestor worship in primitive societies, to the emperors and monarchs of despotic states, or to the capitalist banking system (a fact brought into stark relief in recent times).

In the primitive society, it is local social codes which determine the value of objects qua the produce of the earth. The surplus value here is in the form of code, and so reciprocity does not take place according to the exchange of equivalent goods. Anti-production takes the form of sporadic expenditures of local surplus in ritual and the payment of debt remains immanent to the social organisation of blood filiations and marriage alliances. The time of empire, then, is signalled by the total centralisation of these coding regimes of signs onto the figure of the despot. Traditions may be maintained locally, but their codes mean nothing outside of the lineages and alliances specific to them – they are rendered into an archaism. The despot encloses and envelopes the system, imposing a unity on the disparate multiplicity of tribes covering the earth and overcoding them with a transcendent signifier in the form of standardised currency. Tribes now pay perpetual tribute for the sake of the maintenance and expansion of the despotic state apparatus. The debt is no longer sporadic and deferred into immanent social organisation of filiation-alliance obligations and ritual sacrifice; as far as the despot is concerned (which is all that matters) the debt is now infinite and universal, a ‘debt of existence’ applying indefinitely and equally to all. This is the first great deterritorialisation of codes and meaning away from earthly produce, via abstract value towards a universal equivalent.

Under capitalism, however, codes and overcoding signifiers as such become an archaism (however strongly they might retain local significance). Surplus value itself becomes the object of concern, not for expenditure or distribution, but for its own sake. The deterritorialisation of the socius taking place under capitalism is away from codes and towards flows – surplus value returns from the flow of money into means of production. Anti-production, the social organisation and expenditure of surplus value, thus becomes coextensive and effectively synonymous with production. The economic axiom to produce excess functions to dissolve the old coding regimes of signs which would otherwise organise and expend excess flows of production, be they social investments of desire or the desires of the psyche (the distinction has never really existed). As long as there are heterogeneous flows of desire which can be conjoined towards the production of surplus value, capitalism will relentlessly and monotonously dissolve whatever codes exist there to distinguish them as meaningful objects. Things are no longer qualitative, all things are quantitative; everything exists as abstract quanta equated to the production of surplus value. ‘Meaning’ must now be written in scare quotes as social formulations enter into a continual process of unstable recoding of signs after each wave of the economic axiom washes in and decodes the incumbent ones.

II

With this brief history of surplus value (aka capital) out of the way we can begin to elucidate all the implications for a study of the psyche with regards to each social formation: primitive, despotic, capitalist. Interesting conclusions can be drawn when we analyse sexual reproduction in primitive societies. Firstly, as an effusion of desire, sexual reproduction is here inscribed on the socius directly as social production. It is categorically social, religious, political. We can see from the start that these terms are really synonymous. Deleuze & Guattari see no difference in nature between the desires of the psyche (desiring-production) and social production. It is different forms of anti-production which tend to extricate desire under separate regimes. We do not yet see Oedipus in primitive societies, despite the efforts of psychoanalysts to claim otherwise, because the incest taboo does not exist as a negative prohibition but as a secondary corollary of the filiation-alliance obligation. Sexual reproduction is not yet a matter of private sexual complexes.

Before we begin to imagine primitive societies as proto-hippie communes, however, we must remember that anti-production is a mode of repression; the expenditure of surplus value by definition separates us from the productions of desire, and prevents their direct enjoyment. In primitive societies, debt payments are enforced in a system of repressive cruelty. The purpose of primitive codes is to carefully, painfully, cruelly mediate access to the full body of the earth which constitutes the source of all life (food, shelter, women, Earth-Mother). Memory of this code is often enforced and imprinted directly on the flesh. This physical code takes the form of a writing that does not signify meaning so much as inscribes a position on the earth-body; a given anthropological study describes such a ritual inscription upon the body of a woman to be married. The betrothal is a payment of debt, yes, but the ritual constitutes the mediation of the womb in the filiation-alliance network, the coding of pure flows of desire from its origins to its productions (D&G here agree with the Jungian equation of earth and mother). The hand which writes, the voice which speaks (writing does not yet refer to speech), and the collective eye which witnesses, are each independent organs invested socially in a tripartite system of ritual cruelty. Even the (re)productive organs are public; nobody writes, speaks, sees, or gives birth ‘for themselves’ because there is not yet a private self to represent.

If we can call the primitive system of anti-production one of cruelty, despotic anti-production operates according to a system of terror. The despot reinscribes all the forces and agents of production upon himself, and in so doing commits an incest of the symbolic order as the abstract representation of repression (still not yet a complex of the psyche). By appropriating all the elements of the filiation-alliance network, the despot weds himself simultaneously to the mother whose womb delineates the temporal vector of filiation and the sister whose betrothal demarcates the spatial vector of alliance. Those previously immanent coded flows are directed toward the overcoding signifier who is now everyone’s father, brother, and spouse. Whereas before, the power over life and death was subject directly to nature and the positioning of the body in the system of filiation-alliance obligations, it is now subject solely to the law of the despot. The place of desire under despotism is always one of potential rebellion – the possibility that a single flow might escape overcoding. The law of the despot is thus defined by paranoia, intrinsically constructed in order to pre-empt this potential on threat of death, hence a system of terror in which the death drive looms over all as a ‘voice from on high.’

We must go on to note, then, that inasmuch as the State survives the transition from despotism to capitalism, desire has become fundamentally reactive in the Nietzschean sense. Our subjectivity is always-already in a relationship with the State, variously pacified by it or reactive towards it. The effective equivalence of the relations of anti-production and production under capitalism, however, renders the function of the capitalist State apparatus immanent to those relations. This is true of production generally, as we have said. Surplus value, instead of being expended socially or politically, be it among the tribe or toward the despot, is now privatised. In primitive societies the width and breadth of social organisation was defined by kinship and marriage alliance; and even the caste system continued to be determined by filiation and marriage albeit ultimately subordinated to the political dominion of the despot-king who could confer honour and prestige. These are now archaisms; capitalist social production is concerned only with the flow of capital, it has no concern for filiation-alliance. Capital now reproduces itself on its own line of filiation over and above the commercial exchange-relations of goods which constituted the trust-alliances of mercantile capital. Social production is thus divested from desiring-production as biological reproduction no longer has any meaningful place on the socius. Desiring-production is confined to the private domicile and its inhabitants, resulting in all the knots and complexes of the psyche that come with the real divestment and repression of desire.

As a result, the incest taboo takes on a sinister twist. The highest injunction on sexual activity precludes the investment of sexual desire precisely on the predominant figures available to it. On a broader scale, there emerges a morbid complex of child-worker/father-employer in which the worker is dependent on precarious access to the means of subsistence on the labour market in much the same way that the child is dependent on the support of the father who is also a worker. The power over life and death folds into a death drive immanent to both private and public spheres, as child-worker becomes reactive towards the law of the father, itself a de- and reterritorialization of the despotic law and a quaint reflection of the economic axioms of the market. This law functions effectively to train good ascetics (the relationship between the Protestant work ethic and the growth of capitalism is elaborated best by Max Weber).

Whereas the Oedipal triangle emerged as a result of the demotion of the family away from the social, the onset of mass media and education (each a new and heterogeneous function of the capitalist axiom) ushered in a steady encroachment of the public back into the private. This is where Deleuze and Guattari see the pernicious influence of psychoanalysis: the institutionalised recoding of behaviour in place of the decoded law of the father, except the psychoanalyst demands payment and does not provide parental love along with the conferral of behavioural discipline. For these authors, psychoanalysis is like a microcosm of the capitalist system of cynicism, reinforcing the repressive gestures of the capitalist system in their purest form in the guise of a cure for those very symptoms of neurosis and psychosis.

 

In the next essay I’ll elaborate the response of Deleuze & Guattari to this rather bleak genealogy of Oedipus and the merits of their prescriptions since the publication of Anti-Oedipus in 1972.

Notes on the Rhizome

“To attribute the book to a subject . . . is to fabricate a beneficent God to explain geological movements.”

Deleuze & Guattari, A Thousand Plateaus

 

  • The discourse of ATP is that of geology. It is a writing of the earth, with topographical lines and vectors. There is nothing outside this geology, but there is a discourse of bodies without segmentarity, strata, or territory. ATP is a deeply pragmatic geophilosophy, a profound faith in body and earth.

 

  • The machinic assemblage can be called, in Foucauldian terms, the ‘diagram’ of a thing. There is a diagram of literature, war, love, revolution. Each diagram constitutes a machine, subsumed by a general pragmatics of diagrams, the ‘abstract machine’.

 

  • The book as a ‘spiritual reality’ of its own, a signifying and subjective organic interiority, is spurious and illegitimate.

 

  • Deleuze & Guattari find the Maoist-Leninist political ideology of antagonistic contradiction, the One Divides into Two, to be “the weariest kind of thought.” Nature does not proceed by dichotomy.

 

  • Maoism is of a piece with all binary logics and images of thought, including Chomsky’s universal grammar which proceeds by dichotomy from the always-already grammatically-correct S(entence) as a principal unity, dividing into NP and VP (noun phrase and verb phrase) and so on. This principal unity is a ‘spiritual reality’, reflecting no real natural procedures or objects.

 

  • Modernity obtains a fascicular image of thought. D&G wonder if this image is not an even more comprehensive ‘secret unity, or a more extensive totality’. Principal, linear unity is shattered only to assert even more firmly a superior cyclic unity; the cyclic dimension of the sentence in Joyce, the eternal return in Nietzsche. There remains a dualism of subject-object, whereby the fragmentary subject-book reflects an image of a chaotic object-world. This mode of thought has a kind of ‘natural reality’ and is more sophisticated than ‘spiritual reality’. This critique of modernity might also implicate the authors’ prior works.

 

  • For D&G, true multiplicity is not attained by supplementing an image with more dimensions, more discourses, a proliferation of typographical, lexical, or syntactical voices. Multiplicity is attained only when unity is subtracted from the system (hence the formula n – 1). D&G prefer an open system to a complex but closed one. ATP is an open system covering its array of fields but they are all covered with a sobriety of register along geological, pragmatist lines.

 

  • Rationalist linguistics claims to make no presuppositions about language; it does not aspire to an implicit meaning behind discourse, obtaining only that which is explicit. And yet the gravity of its discourse actually implicates language towards particular modes of assemblage. The act of abstracting language from a general pragmatics of the social field (the collective assemblage of enunciation) paradoxically invests it with an attractive, microphysical power in that very field. D&G come down hard on the side of sociolinguistics.

 

  • The function of grammaticality, closing language upon itself, is to render the people impotent.

 

  • Unity signals a power takeover or subjectification proceeding. It is never immanent to the system, always supplementary to it. Unity is overcoding.

 

  • The plane of consistency denotes a plane without unities and contradictory terms. It consists only in magnitudes, dimensions, and lines.

 

  • Segmentary lines can become lines of flight, the means by which multiplicities connect with other multiplicities and constitute a new assemblage.

 

  • The line of flight does not constitute a change in signification, as in the signifying breaks separating two terms of a duality or dichotomy. A line of flight is neither good nor bad; there is always a danger of ‘Oedipal resurgences or fascist concretions’ on these lines.

 

  • Psychoanalysis constitutes a tracing of the unconscious, using an overcoding structure as its stencil. Schizoanalysis is a map of the unconscious, which is properly rhizomatic. The rhizome no doubt has impasses, blockages, points of structuration, incipient roots. The tracing however simply reproduces these points of redundancy on the map.

 

  • “The imitator always creates a model, and attracts it.” This applies as much to psychoanalysis as linguistics.

 

  • Deleuze had written previously ‘On the Superiority of Anglo-American Literature’ and one digression here is a precis of that essay. D&G again caution that the rhizome is not immune from domination by trees and the search for roots, the quest for national identity, of European ancestry, citing Kerouac’s digressions into his Breton family origins.

 

  • D&G like “the aspects of Wittfogel’s work that have not been refuted.” Whereas the Western feudal state was based on landed property negotiated through warfare, litigation and marriage, the Eastern despotic state centralised power through irrigation works.

 

  • American history, then, is a special case, an intermediary, proceeding by (often violent) flows and channels of people and capital which carry up property along with them.

 

  • One cannot write ‘in the name of’ the outside, of the rhizome, because the latter has no image, signification, or subjectivity. D&G pose instead a writing ‘with’ the outside, forming an assemblage of multiplicities.

 

  • D&G acknowledge that this mode of thought is difficult from a sedentary perspective, counter-intuitive even. It is a matter of seeing in the midst of things, in the milieu, rather than observing and judging from above or beside. What D&G hate more than anything are pretensions to transcendence and principal unity, the spiritual reality of the intellectual.

Cinema and the Powers of the False

Deleuze’s work on the arts can be characterised as an elaborate formalisation of different modes of existence, of various new and radical forms of individuation. For Deleuze, art is not a vain and disinterested form of distraction, reflection or judgment, but is directly implicated within a general pragmatics of affective subjectivity. In a four year period in the late 70s and early 80s, Deleuze published two volumes on cinema, another dedicated to painting, and a large enough portion of A Thousand Plateaus dedicated to music and literature to constitute a worthy standalone contribution to those fields. In those chapters of the cinema books dedicated to revolutionary and Third World cinema we find some of Deleuze’s most politically charged work but some of the theorisation taking place in those passages remains somewhat remote and abstract until we find a direct connection therein with Foucault’s image of thought, the ‘Thought of the Outside’. And in light of Deleuze’s monograph on the latter thinker, we can go back to those passages in the cinema books and in so doing lend them a richer formalisation, adding both specificity and wider applicability beyond the field of visual arts, and a further elaboration on the construction of problematic fields.

The most important aspect of Foucault’s thought we must bear in mind in this discussion is the profound degree to which our mode of existence, our individuation and subjectivation, is conditioned. The truth of our subjectivity, or what we might call self-knowledge, is not uncovered by discourse of confession and reflection; it is actively produced thereby. In the other direction, the urban masses are subjected by the political technology of discipline; they are ‘made’ docile and productive. Jumping ahead somewhat for the sake of time, we can say, like good empiricists, that for the most part what we consider to be true, at least when we talk about human experience, is a fictioned world, a play of simulacra. This fiction is not necessarily that of the ruling class, but a result of the pragmatic integration of everyday discourse and practice towards various aims, one of the most powerful of which in modernity is the maintenance and expansion of the state. The state here is not this or that national government but a state-form of governance as such, a mechanism of governing subjects. Even in principle, truth is not a transcendent standard subordinate to the aims of rationalism; it is, principally, a productive and conditioning discourse-practice that varies throughout history.

It is in this context that we can better understand the ‘Powers of the False’. Fiction that is directed towards ‘truth’ is fatally reverent and predetermined, perverting the true story-telling function, which is the power to ‘think otherwise’. The traditional notion of storytelling is characterised essentially by mimesis, the dualistic reflection of ‘the real world’ in some representation or imitation undertaken in narrative structure, stories, or characters. Mimesis is supposed to capture the essence of being in some manner, and in so doing contribute to our understanding of the world and our place in it. Deleuze, here following Nietzsche, formalises in cinematographic discourse a complete reversal of this tradition: the true object of storytelling is precisely that which is not true, that which is not stratified and lies outside power-knowledge. The power of the false is the thought of the outside.

~

  Traditional storytelling operated along the logical lines of cause and effect, action and reaction, problem and solution, according to a principle of efficiency and economy. Whilst it may present numerous ellipses, anomalies and detours (recollections, dreams), it remains faithful to a chronological time inferred from movement in a Euclidean geometric space. Narration under the powers of the false, however, will effectively collapse this sensory-motor schema. In new cinema, the temporal presentation is no longer derived from objective spatial movement; instead we are confronted with direct images of time in the form of non-localisable relations of sight and sound. Whereas, in the sensory-motor schema, slips and breaks in chronological time are anomalous but all the more proper to a resolution of tensions, the power of the false is to subordinate movement to a non-linear time which confronts us with contradictory and indeterminate pasts and presents as a rule.

The power of the false is not a representation of shifting forms or identities, nor is it alternating perspectives on a given form or identity; it is a programme of transformation as such. The creation acquires its own perspective and so is perpetually falsifying the preceding perspective, recurrently dislocating time from space, narration from description. Recall that Foucault theorised knowledge as the composite of discursive formations and non-discursive practices, or the strata of articulable expression and visible content, each irreducible to the other with its own form and substance, but nevertheless implicating each other in a multiplicity. This multiplicity is impinged upon through relations of force or power which constitute an outside of the strata. When elements of a particular formalised stratum, like cinema, explicitly highlight the respective content and expression of that stratum as potentials for real disjunction, those elements are actually leveraging the process of truth-production away from the production of truth. They are, so to speak, actively forcing the issue of truth by revealing its real incommensurability. The stratum ruptures and those revolutionary elements can thus access the outside from which new diagrams of power can be drawn. These are the Powers of the False that produced new cinema: step back from the conditioning formalism of the given stratum, map its methodology (bearing in mind one’s own subject position within the diagram/problematic), falsify its production of truth by differentiating content and expression, and develop a new methodology founded on this real difference.

~

What exactly does this new cinema look like? This is a difficult question to answer without going and watching some of the more obscure independent cinema Deleuze uses for examples, but I’ll do my best to infer the general method at work in these chapters. In Pasolini we find the idea of ‘free indirect discourse’ in cinema, where distinction between what the character sees subjectively and what the camera sees objectively is dissolved, and the two categories are decomposed and recomposed to constitute a ‘poetics’ of cinema, as opposed to the old novelistic style. The story is ‘simulated’ visually and sonorously rather than ‘described’ by objective images of movement.

Deleuze also analyses various examples of Direct Cinema and cinéma vérité. These movements, particularly in the documentary genre, self-consciously grapple with the affective presence of the camera in a given subjected community. Rather than pretend to a position of ‘objective observer’ attempting to excavate or interpret these communities from above or outside, they instead accept the camera as pure storytelling function, provoking its ‘real’ characters into a storytelling role free from the reverence of truth. What takes place is the real invention of a people. The storytelling function of the camera is interposed with the storytelling of the poor and both object and subject become-other in a new individuation beyond object and subject.

In due time I hope to be able  to conduct a deep dive into these volumes on the cinema and get to the specifics of these film-makers and the processes Deleuze sees at work in their films. But due to the fact that Deleuze is consciously writing both for a philosophy audience and cinema audience and so for a general non-specialist reader, we nevertheless find some of the most clear-sighted and poignant passages of his entire oeuvre. Deleuze sees in cinema a particular capacity for breaking open the strata and approaching the world without the banal fictions of truth; “it is the world which looks to us like a bad film.” We are so trapped in this banality that Deleuze even writes of a need for a new faith, a renewed belief in the link between man and world, but not a world transformed or otherwise worked upon by man, but the world as it is, freed from the conditions of knowledge. It is only when we ascend to this belief, beyond truth, that body and world can find its own immanent truth.

Knowledge, Power, and the Self (Part II)

What we find in Deleuze’s book on his late friend Michel Foucault is a remarkable alignment of some the most difficult conceptual content of A Thousand Plateaus (itself infused with Nietzsche) and Foucault’s historical genealogy of modernity. Deleuze provocatively described his monographs on other philosophers as an immaculate conception and the production of a monstrous chimeric offspring. We never get an exact reproduction, but a recuperation of useful concepts and a truly novel way of understanding both the topic of conversation (in this case, Foucault) and the prior works of Deleuze.

I

We have said that knowledge is found in that which can be seen and that which can be said. We can mirror this with D&G’s Strata, each stratum a composite of ‘content’ and ‘expression’, effectively corresponding to the two aspects of knowledge. Content denotes a form of seeing (prisons, the panopticon) populated by a substance which is seen (prisoners). Expression denotes a form of saying (penal law), and a substance of which we speak (delinquency). This all constitutes knowledge as an actual historical assemblage, made up of discursive formations (articulable expression) and non-discursive practices (visible content), each irreducible to the other but sometimes influencing the other across the threshold, and nothing else. One of Foucault’s most powerful claims is that discourse and practice hides nothing. Politics hides nothing of its cynicism and pettiness; everything is in the articulable and the visible, and the scholar need only identify the method of saying and seeing. This radical pragmatism implies that the only meaningful transgression is to realise that there is no transgression, only methodical (in)competence. There is nothing behind the curtain, which makes the tapestry all the more significant.

Turning for a moment to the non-discursive practices, our choice of words is very important. The form of content is not that of objects or bodies, but a form of visibility or a way of seeing that is a kind of mechanism. Architecture is considered not for its qualities, but in the mechanism by which it distributes qualities, objects, bodies. This is how Foucault conceives the panopticon: not merely in terms of Bentham’s design and its limited use in the penal system but as a mechanism of visibility as such which can be (and was, according to Foucault) transposed across the whole assemblage.

II

Knowledge, or the strata, is the domain of that which is formalised. Power, on the other hand, seems to traverse or skirt along the surface of the strata, manifesting itself not as formalised kinetic energy passing through formalised objects, but as force of relative action/reaction at particular strategic points of the strata. Before explaining further, let us address another misconception of power: the repressive hypothesis. Power is not a top-down tyrannical domination or the ideology of the ruling class; remember, there is nothing behind the curtain. Power does not repress the truth, it actively produces the conditions of truth particular to the historical assemblage. The repressive hypothesis itself is a mechanism of power which is the source of legitimacy for the political technology of confession and reflection. If the truth is repressed then it must be liberated by more confession and reflection, more discourse, the production of new conditions for truth. The point is not the veracity or accuracy of the discourse, the point is its method of conditioning biopower.

This is what Foucault means when he says power is ‘local and diffuse’: it traverses particular features of the assemblage, but cannot be traced to a central node. It is a relation of forces that synthesises and produces local visibilities and articulations. This is the microphysics of power, the process of integrating statements and practices into an institution. There is no ideal State, only a form of government, a mechanism of governing or conditioning subjects not constrained to particular strata, finding itself in schools, courts, markets, households, sexual relations. Power relations can be drawn as an affective map or diagram of forces derived from a dynamic plane adjacent to or alongside knowledge; not external to or separate from the strata, but the outside of the strata, flowing without form between and across each stratum, alternately like a tranquil breeze or gust of wind between the trees. Strata are arborescent, forces are rhizomatic. As Nietzscheans, we recognise that it is a mistake to think of power as an object to acquire.

III

This is where Deleuze brilliantly recuperates his own image of thought conceived at the beginning of his mature work in Difference and Repetition. True thought is to access the outside of stratified forms. As subjects we are interminably contained within the strata, but it is within our capacity to ‘think otherwise’. As a diagram, the panopticon is a map of particular power relations. This of course presupposes that there are alternative power relations, the potential to draw new maps derivative of a general field of power, the outside of strata. Resistance to particular power relations is precisely to access this field of general non-relativised power. This presents a rather more optimistic situation in Foucault than is generally considered to be the case: the narrow confines of power relations presuppose a vastly greater potentiality beyond those relations. This non-relation of power is the very being of thought. Power is affect.

This instance of thought takes on the form of a metaphysical folding of the outside, at once a pure exteriority and pure interiority. Where Difference and Repetition leaves us with the fracturing of the transcendental subject and a radically contingent image of thought, Deleuze-Foucault provides us with a more convincing practical programme of subjectivation and locates the reader with respect to his/her limitations and potentials. This is the originality Foucault identifies in the Ancient Greeks: the differentiation (not negation) of the given diagram of power-relations into a concept of power as such directed upon the Self. The students of Socrates transformed the adjective enkrates (dominant, possessive, controlling) to the noun enkrateia (self-control), the capacity for self-constitution, emerging historically as a reflection of constituting power. Self-constitution is the a priori exercise of affect, an affect of self on self. True subjectivity is derived from the actual, indeed is a kind of affirmation of the actual, but is no longer dependent.

Does this amount to an archaism? Is the solution to our problems found in the distilled wisdom of the ancients? To start with, modern science necessitates a very different conception of the actual more sympathetic to Heraclitus than Parmenides. In any case, Foucault’s genealogy means to do away with essences; in principle he isolates precisely the mode of variation of self-reflection across history. The result is a pragmatic programme which necessitates not the splendid isolation of free men but the perpetual drawing of new diagrams founded on ethical self-constitution. It amounts to a general aesthetics, and genealogy allows us to draw upon history once we wrest some short intervals of thought from the subjection of power-knowledge.