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.

Thinking Anarchism

I have lived more than half of my life as an anarchist. The majority of that time was spent learning about anarchism as a type of activism. As a result, for many years of my life I believed quite strongly that anarchism was nothing more than a particular subset of activism. You can understand this as a statement about the orientation of anarchism toward practice. Activism, for me, was something that one did in the world, it was act-based and not, as it were, thought-based. It took me at least a decade to begin to disrupt this prevailing orientation. Now I believe that it is quite the opposite: activism is something like a subset of anarchism, or, to be more precise, something which can be partially united with anarchism. But it is explicitly not something that can be entirely reduced to it. Rather, thinking, it seems to me, already has within it the possibility of acting, of, to borrow a phrase from Alejandro de Acosta, “direct action at the level of thought.”
At this point I am willing to maintain that anarchism is *not* a practice. I realize that this goes against much of the tradition that we know and love, and that, more than that, it goes against the prevailing orientation of the pro-anarchist milieu. In fact, it goes against my own previous understanding. But the point must be made, and it must be made well: anarchism is primarily a type of thinking. Already I have two concepts which deserve to be interrogated by all anarchists: act and thinking. We shall find, I have no doubt, that in order to act, and to act authentically in the world such that our results are meaningful from the perspective of revolutionary strategy, one must begin to think what it means to act. To these two concepts I would like to add another: tradition. 


At the very beginning of this blog I used the word tradition in a fairly casual way. Tradition is something we take for granted. Naive anarchists often claim that if anarchists had a tradition it would be necessary that we destroy it. In this understanding, tradition is something which is an authority, and, moreover, which coerces us, and perhaps robs us of our freedom. However, tradition also authorizes our freedom. To Dostoevsky’s point that “if God is dead, everything is permitted,” Lacan reformulated: “If God is dead, then nothing is permitted.” Well, it is the same with tradition: if tradition is dead, if it has no authority, then freedom is not permitted. This means that we have no way to transmit our experiences as anarchists to future generations. As a result, anarchism dies at fairly young age, as it always has. And so we must locate within our tradition points which make anarchism relevant for the experiences of our time, and, moreover, to the people who make use of the tradition.

The question arises: how can we locate within tradition these points? Most of us tend to believe that traditions are hard knowledges, things which do not change, as if they are hard-coded into history. The task of thinking consists of disrupting this understanding of tradition. Previously, many anarchists have been content with this understanding of tradition as hard knowledge, and this is why on the one hand, we have dogmatists whose reading of the tradition is so fixed that it no longer speaks to our experience, or, on the other hand, we have nihilists (the bad kind) who reject tradition entirely. The latter group of people do not realize that by rejecting tradition for being authoritarian one also inadvertently presumes that tradition has more power than it actual does. And so we must think. Thinking is always a practice of reading tradition for new points of departure. And through this process we find the ability to act.

To act is never to repeat, unless that repetition disrupts the prevailing orientation of the world. Tradition, in some sense, is precisely a form of repetition. And so to act is to produce a new form of repetition into the world. We produce something that can be repeated through a language that can be understood. An act is not a repetition of an old tactic that has never worked within this world. It is the construction of a new tradition within and against the coordinates of the prevailing order. An act finds what from the very beginning disrupts the present and opens up a hole in the future. As an anarchist, this has been my experience. From the very beginning I have been thinking about the possibility for acting.

And so this leads me to a plea. If, on the one hand, there are more anarchists within the university than ever before, and if, on the other hand, anarchism, as a body of thought, no longer seems to have anything holding it together in the form of a tradition – or, dare I say it, in the form of a serious journal, then the only hope we have for the future is to renew the tradition. I once described this as fortifying the troops, but that is an unfortunate idiom – the point is that we need to act now to save our tradition precisely so that an authentic act – and make no mistake about it, anarchism is *the* thinking of authentic acts, what anarchism offers politics as a form of thinking – can remain possible. There may very well be other avenues for thinking the political act, I have no doubt about it. However, I believe, as I hope many of you do, that anarchism still offers the most fertile conceptual toolkit. Our tradition has always been a thinking of the act.

‘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.

Is the Mentor supposed-to-know?

An unlikely series of proposals this week have me reflecting on the nature of mentorship.

In the first case, a young student who took a class with me began to meet me at the cafe often. She was interested in receiving scholarly advice from me and yet the discussion seldom strayed from her own personal (romantic and mental health) issues. Of course I was happy to oblige until the situation escalated and I was forced to inject some distance between us. I’m not sure to what degree this could be a case of transference.

In the second case, a woman from the other side of Canada asked me to be a mentor to her after she friended me on facebook. She refuses to reveal her identity and she speaks often of her struggle to socialize with others. She is concerned about the fact that she has no ‘spirit’ or ‘passion’. She is concerned about her own inabilities as a student and thinker, and yet she carefully crafts her sentences with expensive words. I have found some ‘spirit’ in her when I deliberately provoke her, when I confront her with her own words and plays on words.

In the third case, an older man, older than myself, who has been a facebook friend for quite some time has approached me for mentoring. He insists on paying me and on my imposing upon him a strict system of milestones. He further insists that he requires somebody to be very harsh on his writing. He wants somebody to impose a reading routine on him so that he can get his work done – he feels he needs lose something (money, time, etc) in order to progress in his work.

Here, I am prone to argue that the task of the mentor is resolutely not to impose knowledge or curricula. Neither is it to necessarily assist a student with their writing, their marketability, their know-how, and their professional development. Certainly, some degree of that is necessary, but far more important is it to regularly confront the student with their own desire.

Of the three students, I can feel, already, some ‘spirit’ coming out of the second student. This is a student I would have least suspected of change – indeed, she least suspects herself capable of change. I believe that the first student needs distance from mentors, for fear of deepening the transference beyond analytic intervention. Unfortunately, I responded to the lures much too soon and this is what accounted for the breaking of the relationship.

All of this is simply to suggest that the first responsibility of a mentor is not to be a subject supposed to know.

Suture (Elements of the Logic of the Signifier) – Unworked Notes

Presented on 24 February 1965, approximately one month after Yves Duroux’s introduction, “Psychology and Logic”.

Miller begins by noting that only those who have gone through personal analysis and gained the “precise conceptions of analysis” should concern themselves with “it”. He does not state what “it” is, but I presume that “it” is the “logic of the signifier”.

Miller asks himself a question from the perspective of the audience: if he does not have the credentials to speak about it, what is he doing here?

He then redirects the question: why are analysts here, listening to somebody without credentials, without practice. Miller seems quite amazed, almost dumb-founded, that he has an audience of analysts listening to him speak.

“The Freudian field is not representable as a closed surface” – this is what Miller claims gives him the authority to speak to an audience of analysts.

If you are situated on the inside, and Miller is outside, and the two are here speaking, then, this is because the two surfaces join up and the periphery or outer edge crosses over the circumscription.

Interested in the logic of the signifier. It is a general logic – it governs all fields of knowledge. It is a minimal logic – there is a movement, a progression, along a linear sequence.

The logic of the signifier is not only a logic for linguistic study. It can be imported into other discourses. And we should import it into psychoanalysis.

There is a relationship between the signifier’s logic and the “logician’s logic.” The signifier’s logic treats the emergence of the logician’s logic. The signifier’s logic is the logic of the origin of logic. This means that the signifier’s logic does not follow its own laws – it itself falls outside of the jurisdiction of its logic.

There is something similar being done in our method as Derrida did in his phenomenology [Edmund Husserl’s Origin of Geometry: An Introduction, by Derrida).

Miscognition finds its point of departure in the production of meaning. It is constituted on repression. To designate all of this Miller uses the name “suture”.

Suture names the relation of the subject to the chain of its discourse; it figures there as the element which is lacking, in the form of a stand-in [holding in place of, substitute]. Just because something is lacking doesn’t mean that it is purely and simply absent. Suture – which is a relation of lack to structure – is a taking the place of.

Suture is not named explicitly by Lacan, but it is there in his system.

Miller is not speaking as a philosopher, Freud, quoting Heinrich Heine, claimed that philosophers “with his nightcaps and the tatters of his dressing-gown, patching up the gaps in the structure of the universe.” Suturation is not peculiar to the philosopher. Philosophers suture universal structures. And the logician, like the linguist, also sutures at his particular level. And so does anybody who says “I”.

We must focus on the letter of a discourse and not its meaning. We are concerned with a dead letter – the meaning dies.

We are concerned with Gottlob Frege’s argument in The Foundations of Arithmetic (1953). Frege’s system puts into question natural numbers taken as primary, (1) zero, (2) number, and (3) succession.

What is it [a question of being] which functions in the series of whole natural numbers and to which we can assign their progression/succession?

Miller provides the answer up front. At this point we’ve already taken a step beyond Duroux’s short text: “in the process of the constitution of the [numeric] series, in the genesis of progression, the function of the subject, miscognized, is operative.”

Frege’s logical discourse begins with an exclusion which makes possible the passage of the thing to the unit and to the set/collection of units to the unit of number. Frege excludes the subject as the basis for this passage. The function of the subject is the support of the operations of abstraction and unification.

The unity of individual [unit?] and set only holds if we presume that the number functions as its name.

A subject – the other side of the subject is politics – is a faculty of memory necessary to close the set without any loss of any of the interchangable elements, and a faculty of repetition which operates inductively. Deciphering this: the subject is what makes possible the faculty of repetition, and the memory of that which preceded number, the passage from one number to another, for example.

But Frege excludes the subject from the start, excludes it from the field in which the concept of the number is to appear.

The subject is not reducible to the psychological – the exclusion of the subject from the field of number is assimilable to repetition.

Frege’s discourse begins with three concepts: the concept, the object, and the number. It also includes two relations: subsumption [relation of concept to object], and assignation [relation of concept to number]. A number is assigned to a concept which subsumes objects.


Subsumption [concept <> object]
Assignation [concept <> number]

Logic of Frege’s system: a concept is defined and exists solely through the relation which it maintains as subsumer with that which it subsumes [concept relation to object]. Also: object only exists insofar as it falls under a concept – the object takes its meaning from its difference to the thing integrated, to the real. Does this not imply a new concept, then? What is a thing? Miller does not say. Object is related to something which is not a concept and which is not a number – it is a thing, and it is in the real.

Miller picks this up immediately: the thing disappears from Frege’s system, it must disappear for the object to appear. The object then:

Object is thing insofar as it is One.

The thing is counted as One, it is elevated to the status of One.

So there is a redoubling: the concept is formed through the determination of subsumption [concept <> object]: the concept of identity to a concept. [concept <> object, 1 <> 1 is taken where there should be object <> thing, 1 <> 0].

So this redoubling, Miller seems to call “identity”. The concept is redoubled, induced in the concept by identity – and it effects the disappearance of the thing it gives rise to the emergence of the numerable. The thing, as 0, is erased, to give the 1.

Identity as a logic, is similar to what Duroux named equivalence – there is a correspondence, presumed, between thing and object, or, if not presumed, avoided or repressed, in favour of redoubling of the concept – in favour of the concept referring only to the concept.

Assignation of number [concept <> number]: ‘the number assigned to the concept F is the extension of the concept ‘identical to the concept F’”. All that is left to the Thing, in Frege’s system, is the support of its identity with itself. This is the support for the numerable.

Distinctive unit supports the number, unifying unit is assigned by the number.

A distinctive unit’s foundation is situated in the function of identity. The function of identity confers on each thing in the world the property of being One, whole – a unit. It also transforms the unit into an object of the logical concept. Miller therefore insists that we call this logic “identity” rather than “equality”.

Frege takes his definition from Leibniz: ‘Those things are identical of which one can be substituted for the other salva veritate, without loss of truth.’ Here is the emergence of the function of truth. What the function assumes is more important than what is expresses: that is, identity-with-itself.

A thing can not be substituted for itself – where does this therefore leave truth?

If a thing can not be substituted for itself then this subverts the field of truth, ruins it, abolishes it.

But identity-with-itself is essential if truth is to be saved – and identity-with-itself is what we connote when we pass from the thing to the object, according to Frege.

Truth is. Each thing is identical with itself.

Let: Thing, X, be in the world
Let: There is an empirical Concept of Thing X
But: Empirical Concept of Thing X is a redoubled Concept
Therefore: Concept of Thing X is identical with the Concept of Thing X.
Let: Object X fall under Concept X as a Unit.
Let: Number Assigned to Concept X be “1”

This means: The number 1, as function, is repetitive for all things of the world.

Thus: Number 1 is only the unit which constitutes the number as such, and not the 1 in its personal identity as a number with its own particular place and a proper name in a series of numbers.

The construction of the Number 1 demands that we call upon the thing in the world and yet this, according to Frege, can not be done. What is logical can therefore only be sustained through what is logical itself.

For Number 1 to pass from the repetition of 1 of the identical that of its ordered succession [eg., 2], in order for the number to gain autonomy definitively, without any reference to the real, the zero has to appear.

Zero is the number assigned to not-identical-with-itself.

So: there is a Concept, “Not identical with itself” This concept must subsume an Object – but it doesn’t, it does not subsume an Object.

Zero is supported by the proposition: truth is.
If no Object falls under the Concept “not identical with itself” then this is because truth must be saved.

The concept of not-identical-with-itself is assigned by the number zero, and it sutures logical discourse.

It has been necessary in Frege’s system, in order to exclude any reference to the real, to evoke on the level of the concept an object not-identical-with-itself which is subsequently rejected from the dimension of truth.

The zero assigned as number consummates the exclusion of this object. [an object is missing here]. The object is missing, it is lacking, and so nothing can be written there – if a 0 must be traced, it is merely in order to figure a blank, to render visible the lack.

“From the zero lack to the zero number, the non-conceptualizable is conceptualized.”

If through subsumption [concept <> object] we move from 0 to 1:

Thing = 0
Concept = Concept of 0
Object = Unit of Concept 0
Number = 1

Circulation: number 0 -> concept of 0 -> object of 0 -> number 1

The entire system is constituted with the 0 counting as 1.
The concept 0 subsumes nothing in the real but a blank. This is the support of the series of numbers – of succession.

Successor is obtained by obtaining the number following n by adding a unit to it, n’. Thus, n+1.

n … (n+1) … = n’

Frege opens n+1 to discover what is involved in the passage from n to its successor.

Successor, for Frege: the Number assigned to the Concept member of the series of natural numbers ending with n is what follows in the series of natural numbers ending after n.

For example: …member of a series ending with 3. The number assigned to this Concept is 4. The number here functions as a unifying name of a set.

The 3 subsumes 3 objects in the order of the real. In the order of number, which is that of discourse bound by truth, it is numbers which are counted: before the 3 there are 3 numbers, but with the 3 there is a fourth, the 0.

In the order of number there is the additional 0, and the 0 counts for 1.

That which in the real is pure is simple – finds itself in number noted as 0 and counted for 1.

Something is rejected by truth – an object not-identical with itself – and is sutured by discourse or annulled.

The emergence of a lack as 0, and of 0 as counted as 1, is what determines the successor.

Let: n be.
Let: 0 lack.
Let: 0 be fixed as 1
Let: n+1 absorb the 1

The 1 of n+1 counts the 0 as 1. Subsumption is this process.

The sign of “+” is somewhat unneeded then.

The 1 is the primary symbol of the emergence of lack in the field of truth. The sign “+” indicates the crossing, the transgression through which the 0 lack comes to be represented as 1 … and this allows for the name of a number to come into being, succession.

This opens up the new logic, the logic which comes before the logician’s logic.

The fact that zero is a number assures the logical dimension of its closure.

The zero is a number which sutures and stands-in for the lack.

The zero cancels out the meaning of each of the names caught up in the metonymic chain of successional progression.

0 (as lack of contradictory object) must be distinguished from that which sutures this absence in the series of numbers
1 (as the proper name of a number) must be distinguished from that which comes to fix in a trait the zero of the not-identical with itself sutured by the identity with itself. It is the law of discourse in the field of truth.

The paradox: the trait of the identical represents the non-identical, whence is deduced the impossibility of its redoubling, and from that impossibility the structure of repetition as the process of differentiation of the identical.

0 is represented and excluded in the chain of succession.

The 0 summons and rejects in order to constitute itself. The succession wants to know nothing of it, rejects it. We name this object which is rejected and which the chain wants to know nothing of, the subject.

It is excluded from the discourse is suture.

Number = signified
trait = signifier
logic of signifier = relation of lack to the trait.

relation of subject to the Other (the locus of truth) = relation the zero entertains with the identit6 of the unique as the support of truth.

Zero = not identical with itself.

The subject is excluded by the field of the Other and is represented in that field (Subject <> Other) in the form of the unit, the trait – the unit-trait. The exclusion is marked by Lacan as $<>A.

This exteriority of the subject to the Other institutes the unconscious.

Repetition is produced by the vanishing of the subject and its passage as lack. Only the unconscious can name the progression which constitutes the chain in the order of thought.

A definition of the subject: the possibility of one signifier more.

This explains the possibility of an enumerable infinity.

Lacan: sign is that which represents something for someone – signifier is that which represents the subject for another signifier. The insertion of the subject into the chain is representation. It is not necessarily an exclusion as a vanishing.

Once we have a signifier: the subject is both before and after the signifier. The subject is the effect of the signifier and the signifier is the representative of the subject.

Suture = 0
The subject flickers – a movement open and closes for the subject, in succession. It delivers up the lack in the form of 1 in order to abolish it in the successor itself.

Psychology and Logic (Yves Duroux) – Notes

This piece appears in the first volume of Form & Content. It is some variation on a presentation that Duroux gave on 27 January 1965 during Lacan’s seminar at the Ecole Normale Superieure. It was meant as an introduction to Jacques-Alain Miller’s paper on Frege’s logic, and, more specifically, The Foundations of Arithmetic (1884). In this work, we are told, Frege developed a definition of the number zero and of the whole of numbers – finally, he described something called a ‘successor function’. The ‘successor function’ deals with the question: ‘how is it that we can count from 1 to 2, and from 2 to 3, and so on. We’ve seen the same question examined by Alain Badiou in his work. We’ve seen that Badiou wants to first describe the logic of succession (of the ‘count’) and second the logic of the axiom of second infinity (which allows us to break with the logic of succession itself).

In any case, we are dealing with whole numbers. And, to repeat Duroux’s questions, we are asking: (1) what is a number (eg., what is the number 1, what is the number 2?), (2) what is zero?, and (3) what is the successor?

These are the key questions. And, really, once we come to understand the answers to these questions we begin to realize that it is all very basic. But not immediately.

First: if we assume that zero is not separate from the rest of whole numbers then the real question is: what is a number?, and how do we pass from one number to another number? Another way of stating the first question is: how do we move from a collection of real things to a numeric representation of that collection of real things?

The first is a question of “collection” and the second is a question of “addition”.

The “unit” is an undifferentiated and undetermined element of any given “set”. I’m going to diagram this:

Undifferentiated/Undetermined <– Collection

Unit <– Set

A unit can also be the name of One, the number One.

One <– 1

One, One <– 2

When we say that there is one horse and one horse and one horse – each one horse is a unit. Each is an element of a set of the three horses.

Horse, Horse, Horse <– 3 Horses

There is nothing intrinsic to the units – one horse, one horse, one horse – that allows us to use the number 3 to identify the collection. There is nothing inside the units that gives rise to the number three for the set. The only way to use the number three is to impose it on the units by force.

The following:

One Horse + One Horse + One Horse = 3 Horses

Can only be said if we make two modifications: (1) we must presume that the “one” is a number, and (2) we must transform the “and” of “one horse and one horse and one horse” into an operation, given the symbol of the plus “+”.

What we therefore discover is that by repeating “one horse” we give rise to something new. It is through the repetition that a new signification comes into existence. We get something new which is not itself a repetition. For example, one plus one plus one, are a series of ones which give us a new number not already there: three.

We must suppose a subject here, one capable of operating on the succession of numbers and giving name to them.

Frege separates the domain of representation into the psychological or subjective side and the objective side. But this separation by Frege effaces the subjective side in favor of the objective side of laws and logic. And this, as we shall see, gives rise to a strange logic, one that, it seems, Frege does not himself acknowledge.

Frege provides the example “venus has no moon” What does “no” signify here? We do not, in this sentence, according to Frege, attribute the “no” to the object moon. This is because there is no moon. A moon does not exist, so we can not negate it. But this leaves open the question of “zero”. Is zero a negation? Can it be if there was nothing there to begin with? We have a concept of a “venus moon”. And this concept is related to the object “moon”. But the relation is such that there is “no moon”. Number, for Frege, belongs to “concept”.

Object <– Concept

No Moon <– 0 Moons

This does not give us an individual number though. There is no “the” one, “the” two, “the” three. For Frege, there is only “one one”, “one two,” “one three”, and so on. The numbers are not unique – they are all only “one”.

One, One, One <– One “3”

Frege moves forward. He gives another example of planets and moons: “Jupiter has four moons.” Here the number “four” is equal to the number of moons. It is identical to the number of Jupiter’s moons. To the concept of Jupiter’s moons there is the number four.

Frege posits a primordial relation of equivalence or identity. It describes a logical relation that enables one to order objects or concepts in a one-to-one correspondence.

For example:

“Socrates” = Object
“is a philosopher” = Concept

Socrates <– a philosopher

The two are equivalent – Socrates already is a philosopher, and a philosopher already is socrates. There is nothing remaining here, the latter is a designation of what is right there – it is not imposed from the outside, it is a natural consequence of a correspondence with Socrates.

One we posit the relation of equivalence we can arrive at a second definition of number: the number that belongs to the concept f is the extension of the concept equivalent to the concept F.

For example:

“one horse, one horse, one horse” – Object (F)
“three horses” – Concept f (extension of F)

This means we have posited a determined concept F; we have determined through the relation of equivalence, all the equivalences of this concept F; we then define the number as the extension of this concept equivalent to the concept F (all the equivalences of the concept F).

So the concept, three horses, is determined by its object, in this understanding.

determination (object) <– determined (concept)

How do we obtain the number zero?

Frege thinks the idea of that which is not-identical-to-itself. Initially, Frege imagines that any contradictory statement refers to zero. For example: “Socrates is a horse” has an Object which is “Socrates” and a concept which is “Horse” and this just is not true. So the concept is zero in this case.

Socrates <– Horse = 0

Now the question of addition.

One number follows another in a series if “this number is attributed to a concept under which falls an object” So, 1 follows 0 because 1 as an object is attributed to the concept “equal to zero”.

So there is a contradiction here in the succession from 0 to 1.

0 = contradiction (Socrates <– Horse)


1 = 0


0 (Socrates <– Horse) = 1 [ = 0]

First: zero is defined as a contradiction. It is the concept for contradiction.

Second: the movement from 0 to 1 is a contradiction of contradiction.

Thus, the motor of Frege’s addition is a ‘negation of negation’.