On the Question of Mastery: Is a Lacanian / Anarchist Intervention Possible?

I would like to offer two stories from my personal life.

First, while attending the European Graduate School in Switzerland I was honored to have met some of the other students of Slavoj Zizek and Alain Badiou. I quickly came to realize that these individuals took Lacan seriously. They established reading cartels that operated according to very precise principles and met regularly to engage thoroughly with the written word. I met two of these students for coffee. They asked me to articulate the relationship, as I saw it, between anarchist political philosophy and Lacanian psychoanalysis. This is a fair question. However, it occurs to me that this question was derived from an insistence that Lacan was – if anything at all – at heart a bit of a communist. Well, that’s how students of Zizek and Badiou would put it. It is simply a matter for them of demonstrating that this is the case. (To be fair, one doesn’t get the sense that Lacan is a communist in clinical circles.) The obscure relation between Lacanian psychoanalysis and Marxian theory has already been settled by students of Zizek and Badiou. It is the answer. The problem is simply to discover the proper question.

I struggled to find the connection between anarchism and Lacanian psychoanalysis. I always have struggled to find the connection. Anarchism in some way led me to Lacan’s work. However, this precisely is the value of Lacanian psychoanalysis for anarchist political philosophy: the question is not yet settled, there are no answers – there are only possibilities and impossibilities. In other words, there are still plenty of points of intervention and points of discovery. The field has not yet been overcoded. In any case, all of the valuable insights that Badiou has provided for political analyses seemed to me to be already present in a less articulated form within anarchist political philosophy – if only anarchists would see these seeds beneath their snow instead of harping on about their own moral autonomy.

Second: while attending Trent University, I was briefly under the supervision of an anarchist. In one way or another, I was also surrounded by anarchists. What passed for conversation in the class-room (some days) was: “Why is ‘X’ not included within ‘X’ theory? (where ‘X’ was a placeholder for any number of social, cultural, and political identifications). The supervisor, in front of this crowd, asked me: “How is Lacan an anarchist?” As is often the case, the question had its own answer: he wasn’t … but surely he needed to be! There is an imperative not only that Lacan be easily understandable but that his moral considerations should be worn on his sleeve.

I learned very quick that it was better to leave the question unsettled. There is no need to respond to the demand to be understood and to be a moral agent. For his part, Saul Newman (in From Bakunin to Lacan) attempted to provide an answer: he insisted that Lacan, unlike Bakunin and other anarchists, provided a privileged point of departure for political intervention through his notion of subjectivity. Without an ‘uncontaminated’ point of departure outside of power (or, if you like, outside of the symbolic chain of signifiers) politics is pointless. Of course, Newman’s reading of Lacan was not deep and faithful to Lacan. For example, the subject is not an uncontaminated point of departure – quite the reverse! The subject is absolutely contaminated; so much so that it is split between one signifier and another… the signifier is what represents a subject for another signifier. It seemed to me that Newman wanted so much a place of subjective mastery over the political field that he discovered it in the most master-less place: a place where the subject is nothing but an empty place within the system of signifiers. Newman discovered an ‘outside’ to political power that was paradoxically inherent to political power itself.

The matter was not settled. Zizek noted the problem of the desire for an uncontaminated point of departure for politics: it is as if before the political subject is capable of acting he needs some security that he is acting from the right agency, from the correct place and at the correct time. Who could secure this agency for him but the big Other, that is, a master? This is why it is important to demonstrate, as I have in my recent book, that there are all kinds of places from which one is capable of acting – and the real is not privileged here.

So, I held onto Lacan. There was more to be said. It became increasingly clear that Lacan’s value was precisely to create this disjuncture between politics and theory. Lacan never fails to interrupt interpretive or diagnostical political interventions. Lacan will not respond to the demand to be understood and to be put to political purposes. To paraphrase the punchline to a joke told to me recently from a psychoanalyst: Lacan fell asleep during our political theorization of the place of pure political agency and then woke up and said “Please . . . continue . . . ”

We must continue. With or without Lacan. For many anarchists, this will always mean without Lacan. In fact, most anarchists will fail to read an article on Lacan and anarchism except to confirm or develop an already established critical response. The anarchist needs this opposition to what they detect as a master – all the more to establish their own passive mastery. Lacan teaches us that passive mastery is an all the more cruel form of mastery. Recall the analogy of the ‘postmodern father’ developed by Zizek: the traditional father will tell you ‘go to see your grandmother!’ and if you don’t like it, you can transfer all your anger onto your father: ‘He is MAKING me go!’ The postmodern father says: ‘do you want to see your grandmother?’ Here, the ruthless authoritarian father is forcing you to be responsible for your failure to want to see your grandmother. You have failed in your moral obligation to be a good grandson.

Anarchists are the postmodern fathers of theory and practice.

There is one avenue through which we can approach the question of anarchism and Lacanian psychoanalysis — through the question of ‘mastery.’ Not so long ago the anarchist journal I manage (ADCS) started receiving articles that dealt with the question of ‘voluntary in-servitude.’ The idea put forward was that the political task was to voluntarily withdraw from oppressive and exploitative relations. Recall Gustav Landaeur’s famous suggestion that the state is a relationship and that the best way to destroy the state is therefore to change our close social relationships, to reroute them, etc. Many anarchists in Canada took this to mean that they had to disengage from the militant confrontational political work of revolution and partake in autonomous community-based organizing. The key principles were ‘groundless solidarity’ and ‘mutual aid.’ I call this the ‘long revolution’ to invoke the spirit of Raymond Williams.

By the time we’ve constructed our revolutionary communities, the master won’t even know that we cut his balls off! Ironically, this principle was first put forward by the Lacanian anarchist Richard J.F. Day in his book Gramsci is Dead. The idea was that it broke the loop-back circuit of demand. (But did it replace the loop-back circuit of the drive?)

What we soon discover is that we can only run away from the problem of mastery precisely by returning to it as a question. What anarchist studies rightfully convinces Lacanians about is that the desire to live without a master is itself an important desire. It is important because it highlights the essential question through which some knowledge might be had. Lacanian psychoanalysis teaches us that the effort to run away from the master is itself a form of passive mastery. Recall, for example, Freud’s discussion of “Little Hans” in Beyond the Pleasure Principle. Was it not the case that this little boy mastered his mother’s absence precisely by making his own little toy disappear from view? The problem of mastery is here much more pronounced because it has entered into the symbolic apparatus – one controls through the symbolic what one couldn’t control in the real.

We must become aware of the fact that mastery is not always exercised actively. More often, and this is especially the case for anarchists, mastery is exercised passively. Who reading this who calls himself an anarchist has not witnessed the attempt by other anarchists to control a situation by acting passively? We see it in consensus decision making, through calm and quiet speech, and so on. For example, I once co-owned an anarchist cafe. There was a proposal to add non-vegan muffins to the stock. It was blocked by a person during consensus decision making. At the next meeting, the proposition was raised as a negative proposal: “can we NOT include non-vegan muffins?” The proposer’s friend blocked the motion and the non-vegan muffins were added to the stock.

This attitude toward passive mastery is particularly prominent among inexperienced therapists who, like many Yoga instructors in this country, believe to be rid of the problem of mastery simply by lowering the tone and cadence of the voice. This is nothing but a pretense at liberation. During my own personal analysis I blurted out, unexpectedly: “I could be the master by pretending not to be!” Is this not my life story as an anarchist? It was a condition made particularly noticeable by an American Lacanian named Bruce Fink, who wrote: “[O]ne might have to watch out for a tendency to present oneself as a master at non-mastery like that found in certain spiritual practices, and akin to the tendency to promote oneself as the most humble of the humble in certain religious groups.” Anarchists are among the best in the political world of presenting themselves in this way.

How to avoid the problem of mastery? Confront it! Anarchists have at least this correct: they must raise the question of mastery overtly. For those who suffer from involuntary servitude it is not even a question: the difficulty is always to make these slaves aware that they are voluntarily serving a master. What, then, about the possibility of voluntary servitude? This is certainly what many Lacanians present themselves as, voluntary slaves: they choose to be ‘unfree’ and to follow the master, Lacan.

We are not yet rid of the question of mastery. In some sense, we have only avoided it by retreating into passive mastery. We must think through the end of the question of mastery, and of our implication in the situation of slavery. In addition to active and passive slavery, we must also be attentive to: (1) the mastery of death as a real intervention which can not be imagined but from which we derive some excitement, (2) the mastery of ‘figures’ and ‘bodies’ which are often incarnated in the figure of the state, in political masters, in corporations — these are the fake masters which are given more power than they in fact have, and; (3) the mastery which must be present in order for thinking and political action to occur at all (without which there is no possibility for the question of mastery to occur).

Newman was wrong, then. It is not that we need an uncontaminated point of departure for politics – the subject – for there to be any political intervention worthwhile. Rather, it is precisely the opposite: without a master, that is, without the third type of master, there is no possibility for subjectivity.

Very quick response to a friend: on non-monogamy and love

There are three positions that I am interested in exploring.

First, there is the position which claims that love is something to be shared, something which must forever be open to an encounter, and which is something that can never be pinned down to One decision. I name this position the love of the market.

It is the love of the market because we are dealing with encounters which are never made significant through the exclusion of temptation. To forever open oneself to an encounter, without recognizing that encounters are provocations, is to partake in the love one has for the products one might encounter at the supermarket. Against this, I claim that Love is not something one seeks, it is not something one can be prepared for, it is rather something that radically provokes a world already made complete. Thus, the love of the market, love which encounters any possibility as a pure possibility, is the love of anything, and thus, of everything.

Multiplicity is not enough to escape the logic of the One. Rather, it is, more than anything, the security of the logic of the One. Multiplicity, like the infinity of potential partners which one may make oneself available to (if only in the hope that this, unlike the others, might be the One), is forever put in the service of the One. We see this very clearly in the logic of number. It is infinity, the n+1, which secures the continuation of the system of numbers – it is always possible to count One more number, and to thereby extend finitude.

Love is not something that one seeks as if in a supermarket. Love is a provocation, and perhaps an unhappy one. It is a twisting of the lover’s world into a new decision and a new truth. Love by necessity is a decisive response to a provocation. One must choose to go through love, and, to the great exclusion of temptation to be in love others. Or else one rejects love. Without struggle, love is nothing. The marketplace is not a place of struggle, it is a place of many false choices. The only struggle within the marketplace is the struggle against the choices of the marketplace. And so the marketplace invites you to fall in love with one more product, and the marketplace of love invites you to fall in love with one more partner.

Love is a decision against the market, a decision to move away from temptation, and to redefine history.

Love is always the love of two.

The love of multiplicity is always also the love of One.

I should be clear. I see nothing inherently wrong with the love of One. The number one can also be thought of as a point, a new foundation for a new history between lovers. It ought not always be thought of as a contract. It can also be thought of as the coming into existence of a new way of viewing the world and oneself in it. This may very well be secured by one new idea. But the number of love is not itself one – it is always two.

The love of two does not have to mean that there are only two people involved. To be sure, two people cannot be thought of as simply two ones (eg., 1+1). The love of two is the love of the movement of the new world, the new love, inside and against the old world, which is the marketplace of love (eg., 1+0). So long as the minimal conditions are met it seems to me that the love of two could occur among any number of people. We could have a love of various scales and intensities. However, this is a love which responds to a provocation which has already happened, and not, as it were, something which could happen.

The love of a love to come, of deferred love, is the love of impossible love. Lacan was fond of claiming that the obsessional neurotic harbors an impossible desire, and so, because it is impossible, nothing can ever compare to it. And so it goes with impossible love. Impossible love may be an endless encounter with failure, one which, to be certain, sustains a certain enjoyment for all of those involved.

It seems to me that the more appropriate point of departure is unsatisfied love. Unsatisfied love is love which can always be better, can always be reorganized and reignited. Unsatisfied love is love without limits, love which desires more than anything else an entirely new meaning to come into the world.

And so the second position is the love of two.

The third position is the love of one, the marriage of love or the love of marriage. Whereas genuine love is the construction of a new possibility in the world of the sexual market, the love of marriage can only be a perverse love which forbids temptation – but in the name of a higher power. This is the great love of slaves.

Anarchism: Real Politics or Politics of the Act?

This is a bit of a response to a post made earlier this evening on Levi Bryant’s blog about anarchism. Apologies for the scattered ideas and the poor writing.

I’ve been an anarchist for more than half of my life. While I am often charged with being an “armchair anarchist,” the truth is that I spent the greater part of my life on the front lines tossing bricks, building autonomous spaces, and experimenting with different anarchist practices. I’ve been arrested, I’ve hiked the country, I’ve grown gardens, I’ve had dinner parties, I’ve worn black masks, I’ve fought with police officers, I’ve disrupted the meetings of members of the power elite, and I’ve participated in conspiracies against the government, and so on. I write this knowing very well that it marks me as a target. However, I also say it knowing very well that these are no longer practices that I find compelling as an anarchist. I suggest that these are reified forms of political activity which are every bit as recuperated as voting. As it happens, I’ve also spent a significant part of my life reading through the works of the great anarchists of our tradition. I write this so that it can be known that I am fully aware that many people will not recognize the anarchist tradition that I offer for them here. The point is that I recognize it, and, moreover, I am capable of defending it. Anarchism is a tradition, and a tradition which is well worth defending. Moreover, the point is that I see great value in thinking about our tradition, and in thinking itself as a form of direct action.

In a book I wrote many years ago now, namely After Post-Anarchism, I argued that most of anarchist thinking has centred around an influential text by Peter Kropotkin (his “Mutual Aid: A Factor of Evolution”). Kropotkin went on to write an unfinished volumes on Ethics. The importance of Kropotkin’s work can not be overstated. He is at the centred of the popular tradition, and unavoidable for thinking anarchists. Moreover, his point of departure, that is, ethics, has defined a trajectory of thought. As a result, many anarchists in this continent, including Uri Gordon, Andrej Grubacic, Simon Critcley, Richard J. F. Day, etc, have argued, in each their own way, that anarchism has been to ethics what Marxism has been to strategy. The point that I am trying to make is that Levi Bryant is correct to suggest that ethics has been central to the anarchist tradition. And so as anarchists we can make a choice: we can accept the tradition as it has been popularly read through Kropotkin, we can reject that tradition (and, perhaps, build our own), or we can reread that tradition to discover entirely new ethical orientations. In After Post-Anarchism, I attempted to do all of the above. I rejected the anarchist tradition and found that at its base it was really a nihilist ethical tradition. But I also offered new readings of the tradition, through Kropotkin and Stirner.

I have argued that anarchism is not itself an ideal form of society, and that it does not necessarily teach us how to act in the world. It does not make prescriptions about action in the world. It does not suggest that building a commune or connecting the syndicates is the way to an ideal society. Anarchists have always tried to distance themselves from lofty ideals and normative abstractions. And so I attempt to demonstrate that anarchism does not necessarily signify “without law” or even “without masters.” Both of these conceptions share a similar utopian presumption about the anarchist tradition. Some of the most interesting and ignored contemporary texts in our continent have reread Kropotkin’s work to discover something similar to what I am outlining here. For example, Brian Morris and Allan Antliff have discovered that Kropotkin was, like Stirner, against these ideals. Allan Antliff has written that Kropotkin’s ethics offer a “refusal to model individuals according to an abstract idea.” This certainly sounds like something Stirner could have written. At base, then, the abstract ideal of freedom, of life without a master, would also be subject to intense anarchist scrutiny.

Some thinkers, notably Larry Gambone, have demonstrated that Proudhon and Kropotkin were against utopia because it was restrictive of personal liberty. Utopia was something that was too violent for the individual, and even for the collective. I think that a more interesting reading would argue that Kropotkin, being against abstract normative ideals, was against utopia precisely because it wasn’t violent enough. In this understanding, the problem is not that anarchism has been understood as an ethics of living without a master but that it suffers from ignoring the properly violent and traumatic dimension of the real. And this is what a politics of the real also suffers from – the real is traumatic, and we do not want to live within it. Moreover, there are times when the symbolic dimension of life collapses into the real, hides out there, and reemerges as the zone of freedom. I recall a painting by Ad Reinhardt named Abstract Painting which presents to us what immediate appears to be pure black. I maintain that this is the space of the real, of freedom, of thinking. I also note that if one remains in front of the appearance for long enough, one might discern the various shades of black that separate and give structure to the painting (see here). Reinhardt explained: “[In this painting,] there is a black which is old and a black which is fresh. Lustrous black and dull black, black in sunlight and black in shadow.” Well, this is precisely what happens in the real. Sometimes when the distribution of the sensible gives rise to the real, the uncounted, there emerges, deep in the shadows, the hegemony of the straight line. We discover that nothing has really changed. And this is what I find so disconcerting about an anarchism which begins with the assumption that life without a master is possible.

On the contrary, we negotiate with the real. We want to work something out from it, to work through the anxiety that it produces. And we want to do so with courage and conviction. We must be prepared to do the long a difficult work of thinking, of staring at the real and discovering what within it has the structure of the old world. Finally, we must seek a new justice. We must recognize that utopian interpretations of the anarchist tradition go against a deeper and more interesting reading which argues that anarchism is about seeking out and uncovering the masters concealed from the world but which nonetheless subject us to their laws (even and especially when we believe ourselves to be free of them). But anarchism, if it is to be a political doctrine, must also forever find a way to renew a sense of the subject. As Saul Newman argued so many years ago, there is no genuine political philosophy without a point of departure, uncontaminated by power, outside. This outside could be something rather paradoxical: an outside that exists deeply on the inside. We can not lose this sense of the nothing which resists suture, which forces itself inside of the world.

Finally, Levi’s conception of anarchism is that it is always at odds with the vanguard party. On this point, I am in agreement. However, when he employs a particular reading of the Lacanian plus-one as the empty place, he seems to reintroduce the possibility for the reemergence of the vanguard party. As it happens, Jodi Dean and others have already described the vanguard party as the empty place or plus-one of politics. This is why we can not model anarchist politics on the plus-one in practice. We must instead rethink the plus-one from the standpoint of the Lacanian tradition. The first thing we notice is that the plus-one has the power of achieving a sort of direct action at the level of thought: it compels us to think of the master, of all masters, as castrated. But it does not compel us toward utopian presumptions that the master does not or can not in fact exist. The master is the minimal possibility of freedom. Without the master, nothing is permitted. Anarchists know this more than any other – they get off on interrogating the master, without whom they would have no proper existence, or identity. They require the master at the level of thought. The task of anarchism is, then, to castrate the master, and then, moreover, to discover new masters. Who are the masters today? Are they the same as yesterday? Anarchism is the process of thinking and castrating the master and not, as it were, the development of a fantasy about a world without masters.

Stirner’s Subject

For many decades the words “egoism,” “individualism,” and “nihilism,” have been used as synonyms by anarchists. This permits a fixing of the concept governing Max Stirner’s book „Der Einzige und sein Eigenthum“. These fixations determine in advance our reading of the text by accenting those words which have carried unfortunate connotations for so many decades, thus leading us to believe that there may be some unitary and transparent self at the foundation of Stirner’s Egoist thinking. This misreading is no different from the one which has cursed Cartesian philosophy for so many years, and which has permitted, quite paradoxically, a thinking which has nothing to say about existence. I state this without waiting another moment: these scholars do not think, and ought therefore not exist.

We must emphasize the nihilist moment in Stirner’s work so as to provide a counter-point to the Cartesian boogeyman erected by enemies of thought. Stirner’s self is not really the ego misleadingly translated from Freud’s work. Rather, it is the subject as we understand it in the Lacanian tradition. Stirner’s subject, his creative nothing, is grounded on something absent or missing from the normative abstractions governing daily life. It is a subject which forces its way into the appearances of the world – it makes room for itself in the world, by forcing itself as truth. It is a subject based on nothing which, at its creative moment, forces itself in opposition to the deceptive process of suturing. Stirner reminds us that we must not avoid acknowledging the subject as this creative element missing from symbolic life. Put differently, at the heart of all appearances, spooks, normative abstractions, and so on, there stands something which can not be contained or captured, something which exceeds all attempts to suture it, and something which is, from the standpoint of the world of comforting appearances, properly traumatic.

Stirner concludes his book with the radical forcing of the subject:

They say of God, “Names name thee not.” That holds good of me: no concept expresses me, nothing that is designated as my essence exhausts me; they are only names. […] In the unique one the owner himself returns into his creative nothing, of which he is born. Every higher essence above me, be it God, be it man, weakens the feeling of my uniqueness, and pales only before the sun of this consciousness. If I set my affair on myself, the unique one, then my concern rests on its transitory, mortal creator, who consumes himself, and I may say: All things are nothing to me.

‘And’ versus ‘Or’ – The Politics of Enjoyment

Two thoughts concerning recent events:

1. Today’s radical thinking seems to encourage us to have our cake and eat it too. « Qu’ils mangent de la brioche » exclaim the educated classes, most of whom seem to believe that authentic change occurs only after one has wished away political contradiction and overcome one’s own binarisms. But real political change requires one to take the difficult path, avoid temptation, avoid the pragmatism which soothes our immediate afflictions at the expense of a more global shift toward equality, liberty, and fraternity. As Badiou has put it: if you want the victory, you can have it in the end. This is the principle of perseverance.

2. In this continent today we seem to bring ourselves to the point of anxiety so that we can enjoy, and so that we can be seen enjoying. This has become a basic principle of life in America, a major political factor of recent times. If yesterday we were killed over Bread then today we are killed over skittles, coca-cola, popcorn, and so on. Today’s anxiety is whether or not we can have two cans of Coca-Cola while being black, or while being poor, or while being a woman, etc.

Anarchism, Logic, Revolution

We can learn a lot about the relationship between logic and revolution by engaging with the mainstream. Take for example Taylor Swift’s acceptance speech for best female video at the 2009 MTV music video awards. Taylor begins her speech and then Kanye West grabs the microphone and says: “Yo, Taylor Imma Let you finish but Beyonce had the best video of all time!”

Is this not the logic that anarchists have adopted in the contemporary period? It often seems that the best we can hope for is a temporary interruption of capitalist rituals, a quick shout out to communism, all the while intending to let capitalism continue functioning as it always has been.

In effect, we are saying: “Yo, capitalism, imma let you finish, but communism is the best political system of all time.”

We need to stop being the Kanye Wests of the revolution.

See: “The Three Logics of Negation”

Alain Badiou: Two Names for Infinity

What follows is a hyper-transcription of a lecture that Alain Badiou gave at the European Graduate School in 2010, called “Infinity and Set Theory: Repetition and Succession.” Until today, I have produced dozens of hyper-transcriptions, some of which are below.

Badiou begins his lecture with a diagram which looks something like the following:

Nothingness | 0, 1, 2, 3, … | Infinity

We can read the diagram from left to right in the following way: nothingness comes before the series of finite numbers which comes before infinity. At this stage of our understanding, that which is finite is always sandwiched between two negative forms of being (nothingness and infinity). On the one side there is nothingness. Nothingness can be thought of as that which is purely negative. On the other hand, infinity can be thought of as that which is without limit. In any case, there is currently, within this traditional understanding, no affirmative or positive definition of infinity. And, finally, we have the finite in the middle. The entire lecture is dedicated to exploring this understanding of numbers. If we like, we can also draw the following diagram:

Nothingness | The Finite (0, 1, 2, 3 …) | Infinity

The finite is a form of positive existence which is composed through the name of nothingness itself. To begin with, we know that 1 is not the same number as 2, and 2 is not the same number as 3. There are real differences between each unique number: there is something within the number 2 which is not within the number 1, there is something within the number 3 which is not within the number 2, and so on. This all concerns the realm of the finite, which is also the realm of differences and movement. We can describe the realm of the finite as the realm of differences and movement because what we notice is that the passage from 1 to 2 and from 2 to 3, and so on, implies that there is a continuation. This continuation manifests itself as a repetition which is without limit.

The infinite is not something which can be affirmed, rather it is the absence of limits upon something else. So this is how we can come to understand the negativity of infinity. Infinity itself has no being. It is not being, but limitation. It is not being itself but that which is the absence of a limit for a process. The infinite is the very possibility of the continuation of a process, the infinite ensures that the process continues without interruption. This is why we can refer to it as a negative determination. So, to revise our main argument: the finite is always between the negation of being (nothingness) and the negation of the limit (the infinite).

This leaves unanswered the question, how is it that finite numbers continue along their process? What is the process of this continuation? How is it that finite numbers can continue along their process without stopping? How is there an absence of limits? In other words, how is it that there is an absence of limits on the continuation of the process of finite numbers? To make sense of this, we must begin with a formalization of the question: how do we pass from the number, N, to the number, N+1?

Let be the number of terms. For example, = {0, 1, 2, 3}. Here, N = 4 because we have four numbers (0, 1, 2, and 3). A successor of is N1:

N = { 0, 1, 2, 3 }

N1 = { 0, 1, 2, 3, N }

When we want the successor of as N1 then we must take the entire set of elements from and add the previous name of that set itself. Thus, to pass from the number to the number after, N1, we must take the contents of the first as well as the name of the predecessor (where is the name of the first set of numbers). So, in the final instance, we always add the name to that which came before. For this reason, our writing is composed uniquely of names. We introduce a new unique name (N1) as a substitute for the old name (N). The operation for passing from one unique name of a number to another unique name of number is very simple: you place one element after all of the others within the new set which is uniquely the name of the set which came before.

And what is this name, in the first instance? It is a name of nothingness. In the end, the only material that we have at our disposal is a list of names. We have as our first name the proper name of nothingness and after that we have a composition of new names. For example we can decide that the following is the name of nothingness:

Ø

And we can give this a new name:

1 = { Ø }

 Here, the new name is 1. After that we can construct another new name as follows:

2 = {Ø, { Ø }}

Here, the new name is 2. Finally, we arrive at the point: only names exist, as well as nothingness. Only names and nothingness exist. The previous example looks more like this then:

Name “Two” equals Nothingness and One as the Name of Nothingness

Arithmetics is perhaps the complete understanding of the world: the world is composed of only names and nothingness. We must not forget that we give the name one only because the one is composed of nothingness {Ø}, and that we give the name two as the composition of the name of nothingness plus nothingness, and so on. So, when we pass from one number to another number we by necessity take the first number (which is a collection of names from 0 to N+1) and we put it inside of the new numbers as one of its elements. The successor is thus always, by definition, one element more. 

We can summarize this in two ways: first, we have a “primitive name” such that a name is absolutely primitive if it is the name of nothingness itself (but there is nothing before the name), and; second we have an operation (which is to succeed).

  • Primitive Name
  • Operation, S.

The operation which concerns us is an operation which moves the continuation or the process along. It is identified as an ‘S‘ because it ‘succeeds’ the line of numbers, it ensures that something comes after. So we have:

{Ø} and S

With both of these we have all of the processes required for the construction of the finite. The successor of a number is composed exactly of the contents of that number plus the previous number: S(n) = … ].

All of this is possible because the name of ‘something’ is not the same ‘thing’ as the ‘something’ itself. This is a point of contingency. For example, the name of the void is not identical to the void. If the name of the void were identical to the void then the thing would be nothing rather than something which exists. The name of a number is not identical to the number itself. The name, N, for N = { 0, 1, 2, 3 }, which is a set of names, is different from the set itself. We know this because the set does not include itself. For example, where 4 = { 0, 1, 2, 3 }, there is no number 4 within the set at all. So we must always have a name for the number which is not within the set itself. Interestingly, at this point Badiou draws a diagonal line across the right side of N, as if to “bar” the name from the set of elements inside of it.

Finally, the name introduces something new. This is an important point because it answers the question: why is the set of finite numbers not a pure repetition? The name of a set is a creation which results from an operation and introduces something new into the chain of numbers. The number two is not reducible to the number one even though the number one is within the set of the number two. And the number one is not within the set of the number one.

When we place the name of something inside of its own set of elements we are performing the operation of succession. By doing so we produce something new which is the successor of the set. It is what comes after the set: what succeeds the set and what names the new set.

Counting is a basic operation of thinking and yet we are generally not reflexive about how the operation functions. Only a philosopher is truly reflexive about all of this. We always function by putting the name of something inside of a set in order to construct something new. For example, when we write a novel we often decide on the name of a character by included all of those characteristics of this character (his hair color, eye color, personality, etc) under the novelty of a name. It is thus the collection of all of the characteristics of the person as well as his name.

So, we have the following as the name of the void:

Ø

And we have the process of succession as follows:

 Ø, S(Ø, S(Ø,S(Ø)), ….

This can be read in the following way: the name of the void, the successor of the name of the void, and the successor of the successor of the name of the void, and so on. For those who are interested, you can find a full explanation of all of this on page 160 of the newest English edition of Being & Event.

All of this is really a presentation of numbers via the operation of succession:

Ø, S(Ø), S,(S(Ø)) = 0, 1, 2

What is two? Two is the operation to ‘succeed’ twice. There are two successors for the number two. A number is therefore always the result of a repetition. But it is not the result of a pure repetition of the number itself. Rather, it is the repetition of the operation of succession. It is the successor which repeats. Three is always three times the same operation, it is three successions: the name of the void, the successor of the name of the void, the successor of the successor of the name of the void, and the successor of the successor of the successor of the name of the void. If we do this operation five times then you will have the number five as a result.

creative repetition is always a succession of numbers within the finite. It is a paradox of sorts. The new number is really different from the number which came before it – we have proof that 4 is not 3, and so on – but it is also another composition of the void which gives it a unique name. The number or the name of the number itself changes even where the operation remains the same. You go from one to two to three to four, and so on, using the exact same operation. This is why it can be annoying to count because even though the numbers change you inevitably get bored of the repetition of the operation itself.

We have a new definition: the finite is a mixture between novelty and repetition. This is why we can describe succession as creative repetition. But, we should also note that the finite is the insistence of succession. It is the succession, without limit, of repetition. The numbers always continue and this is the insistence of the repetition. As such, the finite is under the law of repetition: ‘one more, once more again, again once more again, etc’.

In French we describe this using the word Encore, which means, to succeed. This is also the title of one of Lacan’s seminars, seminar XX. In fact, within that seminar there is an entire meditation concerning the very concept of repetition. What we notice is that within concrete life, repetition exists. And this is why we are finite beings: we are always in the field of repetition. Very often, we must do the same things. There is an insistence, which is not always part of our conscious agency, to repeat. And so the subjective repetition is very often also a creative repetition. It is the same with numbers. There is something profoundly similar with respect to subjectivity and number.

Perhaps we can approach a definition of the subject in this way: the subject is always known by his repetitions. We know somebody by noting their repetitions. When we claim to know somebody we often make that claim in full awareness that there will be some creative repetitions. A person seems to always have the same behaviors or opinions, even if there is a creative element to those behaviors or opinions – even if they change a little bit here or there. The operation nonetheless insists. Finally, this finite structure can produce many differences, novelties, surprises, complexities, within the entire world. This is precisely why we can claim that the finite is under the law of encore … continue, continue…

We approach our first definition of the infinite: the infinite is the space of repetition itself. In this respect, it is logical to conclude that the space of repetition must be infinite if we can continue within it without limit. If we can endlessly repeat the operation of succession then we can say that the space of the infinite is without limits. In other words, if we know that repetition is without limits then there must be a space for that repetition which is itself without limits. And so we can not know the creative nature of repetition without claiming that there is something which is without limits. If repetition were within limits then we would think of it like a circle, or a loop. In fact, it seems to me that this was Lacan’s conception of the repetition of the drive:

Badiou claims that our understanding of the finite realm necessitates a thinking which does not close in upon itself like a boomerang. We do not always return to the same. Conversely, with number, we always have a linear continuation. We have an obligation to assume that there is something without limits, without closure, within the realm of repetition itself. This is qualified in a very precise sense by the operation of succession. The space of repetition, then, is infinite, and it is linear. It is not, like the traditional understanding of the Lacanian drive, closed in upon itself like a boomerang and circular. If there is no limit point to numbers then there is something infinite which keeps moving as if in a chain and it is this chain which is the result of a creative repetition. We never arrive at the limit point precisely because this negative notion of infinity is that there is an absence of limits. And it is this absence of limits which permits the repetition of succession to continue, infinitely.

The first name of infinity is thus virtual infinity. Virtual infinity names the position that the infinite does not exist except as an absence of limits to the finite. So the infinite exists alongside the possibility for the continuation of the finite. What exists is always finite and so the infinite, if it were to exist, would fall into the finite realm of numbers. What exists is the unlimited process of the finite. The point is that virtual infinity reduces the infinite to the absence of limits for the finite. So, finally, the infinite is always at the service of the finite and is not an affirmation of something which exists itself.

Most mathematicians do not admit that there is something like an actual or real infinite. They typically only admit the virtual infinite as that which has no limit and which is never finished within the finite realm. Badiou describes the position of virtual infinity as a compromise situation: it is a compromise between the finite and the infinite. This compromise operates in the service of the finite precisely because the infinite does not exist as a separate being. Rather, the infinite exists inside the finite as its negative necessity via the law of succession.

The infinite is an internal law of the finite.

According to this view the infinite is itself a part of nothingness. Whereas the finite is sandwiched between two forms of nothingness we can claim that the first form is pure nothingness (nothing at all) and the other form is infinity as that which does not exist. Thus, the infinite is really “No Thing” because it is not a Thing. So we have Nothing and No-Thing. The infinite is a virtual law of the finite but it is No-Thing.

If we decide that we want to go beyond this understanding of infinity then we must allow ourselves to realize that the infinite comes also in the form of a thing. There is no other possibility to overcome the problem. We must affirm the existence of something infinite and not only the infinite as the pure absence of limits in the service of the insistence of repetition within the finite realm. And so the infinite must therefore exist as a point which is beyond repetition itself – it can not be inside of the repetition. It is the repetition which is without limit. If we want to go beyond virtual infinity then we must propose something which is not a form of a law which exists inside of the repetition. The new infinity must itself be infinite. But how can we propose something like that?

We had the following:

Ø, S(Ø), S,S(Ø)), etc

0, 1, 2, N+1 …

We must begin by affirming the existence of a term which does not succeed and which is therefore not inscribed within the repetition. This term must exist after one term, like all whole numbers (N+1), but it must also exist after all numbers. But we immediately run into the problem of thinking a set of all numbers.

If we were to think about all numbers then it can not be as a consequence of the operation of succession. We can not simply at N+1 to the chain of finite numbers. There is no point where the succession produces something which is beyond succession. And so this is the paradox. We can not produce a term for infinity by using the internal law of succession because this would immediately place us back within the finite realm. So, we can not produce something infinite using succession as such.

Repetition as such can not produce any term which is infinite. That is impossible. Consequently, we must affirm the existence of something completely new: a term which does not succeed. A term which is outside the scope of the repetition. Badiou proposes the following matheme for the affirmation of a term for infinity:

¬ E(x) [(Infinite = S(x)]

There does not exist one x where the infinite is the successor of x. In other words, the infinite does not succeed at all. We shall name the infinite, “omega” using the following symbol: ω.

¬ E(x) [ω = S(x)]

Not Exist X, omega is the successor of x. This is our first possible concept of a positive infinite. However, by the use of the symbol of negation (¬) placed as it is on the existential quantifier we note immediately that this is another negative definition of infinity. However, this time our negation is not the negation of a limit. What we are dealing with this time is the negation of succession itself – a negation of the operation which sustains the creative repetition.

There is no x for which omega is the successor of x.

So it is not the without limit of the space of the succession, of the space of the repetition. But it is the negation of the repetition itself. We can claim that if something infinite exists then the first infinite – or the beginning of the infinite – is always in the form of an interruption of repetition. It is a rejection of continuation and therefore finds itself radically outside of the continuation of the operation of succession. This is omega, then: the first infinite outside of repetition. What we have with our matheme is a reversal of the first negative definition of infinity – it is a reversal of virtual infinity.

  1. Definition One: NO LIMITS AT ALL
  2. Definition To: NO SUCCESSION AT ALL

And we have the following:

  1. Virtual infinity is the name of the strength of repetition: repetition can continue without limits. It is the strength of the finite, then. The finite is stronger precisely because it can continue as virtual infinity.
  2. Real infinity is not inside of repetition and is not the result of succession. It is the weakness of the finite. It is beyond the possibility of the finite.

The point is now to examine our decision for real infinite: can we rationally accept the existence of something which is beyond the repetition? Something which is beyond the successive construction of the finite numbers? How can we do that? How rationally can we do something like that? Cantor’s greatness was to answer this question. Cantor is the father of the modern conception of the infinite. Before Cantor we only had access to the virtual form of infinity, it was the dominant conception. Cantor affirmed the existence of something entirely new: the omega which exists beyond all finite numbers, ω. How can we be beyond all finite numbers? Cantor’s idea was to claim that we can take all finite numbers and presume that they are a set (as if the repetition was finished). The idea is that we can put the set of that which is without limits as a new limitation. 

So we are between two names:

Ø & ω

We can write that omega is the name for the space of the repetition as such. The space where all numbers are defined by successive repetition.

ω = { 0, 1, 2, 3, … }

There is in fact a limit, and this limit is omega itself as the complete recollection as the total process of the collection of numbers. We have here a very obvious problem which is the notion that somehow we can close the set to produce a set of all sets. But we must understand that when we speak of the closure of the set in this instance we are actually speaking about the closure of a set which remains unlimited in terms of the operation of succession. The closure we are discussion is therefore something which is perhaps better described as a pure interruption of the operation of succession. We are simply affirming something which does not succeed. And so there is no clear contradiction then between the non-limit of succession and the name of the set which is outside the scope of the succession.

A succession operates on the name which came before it but omega deals with a ‘before’ which is not in the same sense as the ‘before’ of succession. For succession, two is before three. We know exactly what is before 3, it is 2. But with omega what comes before is the operation itself. 

For Lacan, feminine jouissance is something which is infinite. Why is it that the infinite is so often associated with the feminine? Often, woman is represented as the point where man does not understand his own limitations. Woman, according to Lacan’s graph of sexuation, is represented as being without limits of the male process. Classically, the man is on the side of the process of numbers – there is a succession. The male is the being of succession. And, classically, woman is represented as without limits according to the total space of repetition. She is an interruption of repetition itself and exists outside of the succession of numbers. This is why we sometimes claim that man is a finite number and woman is an infinite number, or that man is quantitative and woman is qualitative.