[The following is a translation of Alain Badiou’s seminar from February 15, 2016, part of his last series of lectures on the Immanence of Truths. The video in French is here and the transcript (which I have added to in parts) here. For ease of reading, I’ve divided the text into sections:  Introduction to oppression as covering;  Finitude and constructible sets;  Infinity and non-constructible sets; and  Fundamental ethics of the Idea.]
 General Introduction to Covering
The big idea we are working with for the moment, I remind you, is that ultimately every figure of oppression comes down to an imprisonment in a finite figure of existence, right where an infinite perspective could have been upheld. In other words, we are transforming the problem of emancipation, or the process of liberating human possibilities, by no longer treating it directly under the form of an explicit contradiction between loose or separated terms like the oppressors and the oppressed. In fact, we believe that what attracts oppression upon oneself, oppression in all its figures, is always the fear, doubt, risk, or possibility that something will emerge that would be radically in excess over the order whose guardians are the masters. If the order functions without supposing its opposite, then specific methods of oppression will not even have to be used. Order itself then constitutes the oppressive figure. What we will discuss is the specific, identifiable figure of oppression that is required once order–in its own functioning, in the only machine it constitutes–no longer appears sufficient (or so it fears) to contain in the finite closure of oppression the figure that it represents.
Our intuitive point of departure is that oppression manifests itself whenever something that could extract itself from the order that contains it dares to appear. This is one possible meaning of the strong old revolutionary statement: “Where there is oppression, there is revolt.” Unfortunately, this is not quite true; it is not mechanically true. What is certain, on the contrary, is that where there is revolt, there is oppression. Where something surges up that appears to disturb the general order, that order will immediately and always put in place precise and specific figures. How is an antagonistic possibility is contained?
My hypothesis, which has an ontological character, is that the dialectic adequate for thinking this in its being is the dialectic of the finite and the infinite. The ambition of a closed order, whatever its nature might be, is to perpetuate itself, to maintain its closure as such, that is, to prevent the manifestation of something qualitatively foreign to this closure. This closed order can always be described as the maintenance of a certain type of finitude. Everything that appears as being beyond the dominant conception of finitude, everything that appears in excess of it, as deregulating this closure, is perceived as a perilous in-finitization of the situation. And, in particular, of the in-finitization of possibles. Because locking-down what is possible is the key to maintaining order. That is why, in general, order begins by saying that nothing other than itself is possible, blocking the possible itself, in a precise point, through this very fact. What we are doing is finding the deep underlying logic whereby order seeks to actually break that which appears to go beyond the norm and the rule. For this logic is even more fundamental than the system of means, which we all know so well (mechanisms of propaganda, policing, open oppression, etc.).
My second hypothesis has to do with an extremely important procedure that I call covering. At the most general level, it is the attempt to neutralize the possible emergence of a new infinity by covering it over with preexisting significations, already given in the situation, which aim to forbid its development, on the one hand, but also its internal meaning, the immanent sense of this infinite, of this excess, this new infinity. It is not a matter of declaring that it did not happen or that nothing happened, but rather that this something does not have the signification it gives to itself. It is possible, in effect, to analyze this situation in terms of oppression itself: it is to cover up in some way, as if one had put a sack over the top of it, the set of that which is said and done in the name of this novelty with old, generally stereotypical significations internal to the situation, and in such a way that the very intelligibility of what has happened is annihilated, such that even those who participate in it wind up no longer really knowing if what they are doing is truly what they say it is. For this procedure also aims at an intrinsic demoralization of the agents of the novelty, by convincing them, through numerous artifices, that what they believe is new is in fact old, and not just old, but harmfully antiquated. That is the general operation of covering. In order to cover something up, one has to plaster already-existing significations over its advent, its upsurge, its embryonic instances. In that way one kills the pioneering intensity of the upsurging or novel figure of infinity.
Now, I hold that this business of covering is very important. I think that in reality it is the most continually exerted oppression, in the most lively fields of human creation. And I insist on the fact that it does not only aim to make the threatening being of the new infinity, novelty or thing-in-rupture, disappear. More profoundly, its aim is to render it definitively unintelligible, to kill its very sense and, through the covering, to introduce in a figure of non-sense or, paradoxically, of impossibility, that which nonetheless appeared to be possible. The three political examples I give below are typical: a parasitic signification was plastered over what happened, covering it up in such a way that which was really at stake is no longer decipherable or visible–not in the future, but also for a part of those who participated in the very thing thus covered up. In these three cases, seen from the future, something obscure and undecidable is constituted through the covering which makes it so that the thing is declared to be mixed up, covered, disintensified by the disparate operations coming from the preexisting situation. It asphyxiates, annuls, disidentifies the element of rupture, inauguration, novelty and creation that it seemed to bear, not at all by negating the fact that something happened, but by substituting something else for what did happened. What happened in the vital lives of its actors is in no way what happened from the point of view of the thing once it is covered over.
And so a dark and retrospective legend is made. At the very point where something like hope or novelty appeared to infinitize the situation relative to the closed order, the covering makes a sort of formless stub appear, a thing that should not have existed, something insignificant and abominable–not at all because it is simply negated, but because it is covered over. This operation is absolutely essential because, in a certain way, at every level of collective history, as well as personal, artistic, or scientific history, it organizes the battle of significations and not just the battle of reality. It creates distinct memories, historical legends. Ultimately, it qualifies, determines, or modifies the historical meaning of what happened. From this point of view, covering is a long-range operation, a sort of poison infiltrating time. It is something that does not simply abolish what has taken place; it disfigures it in such a way that it becomes unrecognizable, and in a way that is even more intense because it is maintained as what did take place. But what took place has been transformed into something totally different.
- This is how a political event, potentially infinite in its possible consequences, is covered by common, negative places. Already the lively party of the French Revolution (1792-1794), which opened to infinity a real egalitarian process, was immediately covered by commonplaces concerning the acts of the “cold monster” Robespierre, bitter and bloodthirsty. The actors in the coup de force of Thermidor, the “thermidorians,” pushed through in this covering (which is still wielded today by reactionaries on every side) the return to tyranny of property owners and the corrupt.
- Similarly, the Cultural Revolution in China (1965-1968), an unprecedented attempt to restart the real communist movement in the space of a socialist State on its way to sclerosis through the massive and direct intervention of students and workers, was rapidly qualified by the experts of finitude, Chinese as well as Western, as a desparate manipulation by Mao (who had gone astray through his errors) to restore himself to power, and that he unleashed unacceptable violences in order to do so.
- One will say of May ’68 as well as its consequences in France: the biggest mass movement in Western Europe since the second World War, opening for the first time the possibility of a common political process for revolutionary students and workers on strike, was qualified, and often still is, as a tiny anarchistic tremor wrapping the “sexual liberation” in a perfectly fictitious revolutionary discourse.
One could find similar operations of the annihilation of an infinite potential through its finite covering-over in all the other truth procedures: love, art, science. Proposed exercise: look for examples in history, collective or personal.
I myself would like to undertake a variation on what the operations of covering might be in the domain of love. You see very clearly that they consist in inhabiting love from the inside out, in such a way that it is permanently haunted by an uncertainty as to its very existence. This uncertainty ends up invading love like an interior cancer. The figure of jealousy is the most complete figure of this. Proust has described it admirably. He shows quite well how jealousy institutes a sort of grid [quadrillage] that preexists the existence of the other. It slices up time in such a way that no continuity is possible any longer: its suspicion is a permanent finitization of the general movement of love, which is thus blocked up in a covering fragmentation, which is an instance of finitude. This is why one of the chapters of Proust’s book is called The Prisoner. Instead of love being the intense development of a new figure of existence à deux, it becomes a closure, an imprisonment, a prison, where what finally matters is not the other, but the other of the other. The obsession of jealousy is surveillance, but what menaces it at every moment, what puts his love in peril, is the other of the other. Is there an other of the other? This worry becomes a top priority in the end and it is this ungraspable alterity that blocks love, asphyxiates or poisons it. You see there that the covering is not exterior. It is at work in the interior of love like a kind of splitting-up that it cannot keep itself from imposing.
 Finitude and the Constructible
It is now necessary to ask: what is the logical substructure of these operations of covering? And what conditions can one oppose to them, such that the emergence of a new, true infinity be allowed, authorized?
To begin, it is first necessary to know exactly what is going to be understood by “finite,” because intuition does not serve us very well on that point. One will say that a set is finite if its elements are definable, which means that they are submitted to the dominant language in the context of this set, a language composed of well-practiced properties, known by everyone. It is these elements, already tied together by language, that the operations of covering will use to cover up precisely those “things” that risk surging up from the exterior of this barrier that I am drawing on the board, a barrier that is going to help us picture the closure of the world of order that these “things” threaten to transgress and displace. The operation of covering will let us say that these “things” in question are not, as they claim, exterior to this world and in this way they will have been completely locked out. Instead of seeing Robespierre as a revolutionary who tried to introduce figures of equality into the political system, you will see him as an “adventurist,” an “opportunist,” “bloodthirsty” and “bitter”: determinations spotted by everyone in the world such as it is.
Consequently, behind covering, there is a theory of complete submission of what exists to the documented language. In the situation, the definable parties are often what one calls “common places,” that is, the consensual stuff, shared by everyone, which can end up being “French values” or stuff like that. These are the things (statements, actions, fragments of State power) that are in reality pegged to the established language and are available for the operation of covering.
You can practice for yourselves finding examples where these procedures are constantly in use. In a dispute, for example, you are always in the process of imputing to the other that everything they say can be “covered” by what you consider to be a well-defined property, “you say that, but in reality I know very well…” That’s why so many commonplaces circulate in disputes and why the chatter of the argument is a generally meaningless, long-term chatter. Any inventiveness is broken by the fact that one taps into what is aggressively constituted in the situation one shares. These shared things can be evoked without saying much about what they are, because really the only interesting point is that they are saturated from the point of view of language. If you say, “France,” everyone knows what it means — except that it’s not true that everyone knows what it means, and today perhaps no one knows exactly what it is. But knowledge is not the true question. The true question is that, between the supposed thing, France, and the name, there is a lock-down that does not propose to go any farther. The knotting of the thing and its name will function all alone and will plaster itself upon a situation that perhaps has no relationship with it, and which it is going to try to seal off or cover up.
When one looks closer, one realizes it is a little more complicated, for the word “property” is an equivocal word. It is necessary to be suspicious of it if we want to avoid the traps of contradiction pure and simple. Even he who, wishing to oppress the people, covers over what they are, what they talk about, etc., even he tries to avoid explicit contradiction. It’s not always the case and sometimes he falls into it anyways. For example, I was very interested by the fact that Valls, the head of State, and on top of that the head of schools, claimed that, “to begin to understand means necessarily to begin to excuse.” This is a remarkable philosophical statement. What does this statement cover up, or try to cover up, if not the comprehension of what has happened? It takes a floating cliche, namely: “when something horrible happens, the urgent thing to do is to not understand it” (many people think that, perhaps we all think it in a given moment) and leads to a statement on the edge of contradiction. If you try to oppose reason to fanaticism, secularism to religion, peace to violence, etc., you cannot uphold this opposition on the fact that one must not understand what the other is. On the contrary, the imperative of reason, including political reason, would be to understand what happened. You would have to claim a fully rational construction of things. The failures of coverage: this is when one is caught red-handed wanting only to cover. If, on one side, you say that our values have been trampled by something abominable and, on the other side, you forbid people from comprehending it, you take your steps between what is definable and what is not. For how can you define what has happened, or declare it undefinable, if you don’t even know what it is about?
These operations of covering, even in their propagandist vacuity, are thus taken to deploy a certain coherence. In every case, in order to comprehend them, we must try to see how to render the general concept of covering perfectly comprehensible. For that it is necessary that we give a rigorous definition to the notion of ‘property’. It is for this reason, and not by some obsession, that the complete theory of covering is a mathematical theory. We admit that it is extraordinarily tedious. No one wants to deal with it. But these are the dull things of thinking. In any case, we cannot do without knowing that we must do them; that would be another semi-covering of real activity… We will suppose then that we have done this work, that we have a formally rigorous language at our disposal, and that effectively we know what a property is and that we know what is definable, namely, a set constituted by elements endowed with well-defined properties. Starting from there, we will treat four points that I will now enumerate, for they form a strategy:
- The definition of a “set marked by finitude” is a particular concept of the finite. In reality, the finite is only intelligible in the type of procedure of finitude that is at stake in it. Finitude is not a objective given independent of a process. Finite means: that which one can use in a covering. It is finite in the sense that it serves to cover over, disidentify, and finally render incomprehensible the emergence of a novelty on the side of the transgression of the order, of something one could have imagined infinite.
- The encounter of an alternative. It is quite striking that one cannot avoid the fact that perhaps everything is finite, meaning that the upholders of the order are right, and that whatever is not of the order assigned to finitude is in reality impossible, inexistent, even dangerous. It is not possible to demonstrate that the doctrine of the oppressors is untenable and that, consequently, their business will not work. It signifies, in a certain sense, that one must stop thinking it’s all going to collapse on its own. With Marx, we know that is certainly a hesitation on this point: sometimes, he lets it be known that History works in the right direction, towards the collapse of the system of domination; and at other moments, particularly when he is concerned with building the International, there is another music: for it seems it would be very difficult, that it precisely does not go without saying, but goes through very complicated twists and turns, etc. But neither could you demonstrate that, if you supposed something that cannot be covered, you are wrong. Which means that at some time there is a choice. Every rational thought is thus inhabited by a fundamental choice and it cannot be shirked. We cannot say that we are convinced through and through, and up to the end, by a rational demonstration that the position you will choose is true, appropriate, and victorious at the conclusion. It cannot be done, not at the level of extreme abstraction which is the theory of covering. And one cannot demonstrate the contrary either, that the position of the adversary is necessarily victorious.
- In what condition can the infinitizing position be sustained? Because it does not sustain itself by a rigorous demonstration, one can choose it. But what does “choice” mean here?
- What I call fundamental ethics sums up all of this. It is the determination of what must be assumed in order to be on the side, let us say, that I believe to be the good: the thesis according to which it is not true that everything can be covered.
I will take up these points one by one.
1. To begin, we must first know precisely what is going to be understood by a “finite set.” There, “finite” means: what can be used in a covering. A “set marked by finitude,” in the sense of covering, is not a quantitative notion: it is not especially small, and moreover we shall see that things that appear infinite can, in reality, be finite from the point of view of covering. What counts is its composition. The point of departure is the following. Any set whatsoever will be called finite from the moment it has for elements only multiplicities that, in another preexisting set, figure as definable parts. A definable part of a set, as we have seen, is a part submitted to the dominant language in the context of this set.
To put it very simply: let there be set A. Let there be a property P that is clearly defined, in the sense that we know what it means for an element of A to possess property P. Then the set of elements of A that have property P constitute a definable part of A (this part is defined by property P). A definable part of a set is thus a part submitted to the dominant language in the context of this set, a language composed of well-practiced properties that are known by everyone.
Let’s see how a finite set (also called a constructible set) is constructed. This construction is going to be made in an ordered, hierarchical way, designing a sort of range in which the sets situated at the furthest point of departure are only going to be composed by definable parts of the preceding set. Put otherwise: at every stage, the constructible set only retains the definable of the previous stage.
In the most radical doctrine, the point of departure is the void. As there is nothing definable in the void (because nothing is there), you mark the set void. This is the only element of the set that follows, namely, the one. Afterwards, you pass to the next level by “drawing” all the definable parts from the preceding set: at each stage, you will have constructible sets composed entirely of things definable in a formal language, beginning from the previous definable multiplicities. You can arrive by levels up to considerable complexities that do not exclude your having an infinite constructible set. The finite is therefore not defined by the small or by the large, but by its internal structure: its submission to the current language. It is in this sense that one can say it is closed.
[Figure 1 illustrates the operation of covering. On the left side is the regime of properties (x) well known to the situation, where set A can be described and circumscribed in the dominant language. The “barrier” in the middle represents the closure of the world that the possible infinite set, represented by the circle with a dotted line on the right, threatens to transgress. The arrows that cross the barrier designate the aggressive move to define the emergent infinity through properties (x) from the dominant language of the world.]
The constructible is a category that in earlier days would have been called “ideological,” because admits as existing only the things that are already submitted to the dominant language. In this affair, you do not accept that there is something undefinable. The finitude here is the finitude of submission. It is a limit where the undefinable is unacceptable. If you only admit what is definable, this means, from a certain point of view, that you only admit what the world already knows, what it has already named, structured, practiced, etc. That is the structure of a dominant ideology as general conservation of the system. It only admits operations upon its own definable, i.e., in the language it utilizes to name things and hierarchise them in the order of the definable. Constructible sets are the general form of all the materials utilized in oppressive procedures, and singularly in the oppressive procedures of covering. This is more sophisticated than the notion of dominant ideology, because it constitutes itself in networks capable of covering everything at the interior of the order. This does not mean that new things won’t appear. You can always add a stage, but in the new stage there will only be something definable coming from the previous stage. This will be “new” because it combines the definable in different way, but it will not be new in the sense that it would not be of the definable. There will be a type of auto-morphy of the dominant order that, from the point of view of the relation between multiplicities and the names given to them, will automatically maintain itself under the aegis of the dominant language, without anything ever showing through that would not be reducible to this language. Put otherwise: there will not be any unnameable (which is, as you know, the title of a novel by Samuel Beckett).
In the end, the thesis supported here is that the world, in this dominant register that contains only constructible sets, which only knows the definable and hierarchized, is closed in this sense. It is closed according to the internal composition of what composes it.
 Non-Constructible or Generic Sets
2. Is it possible to accept that only constructible sets exist? The greatest logician of the 20th century, Kurt Godel, who invented the concept of the constructible, demonstrated with virtuosity that it was not contradictory to admit that all existing sets are constructible. This means that if you add to general set theory the axiom, “everything is constructible,” well, it does not collapse. When the masters of a situation say, “everything is construcible,” it holds to the road. They are not going to ruin the general system of possible thought. Let us underline, however, that the fact that this is not contradictory is not the same as it being true…
What happened was something quite interesting: the mathematics in which everything is constructible, the “easiest” from a certain point of view, practically no mathematician wanted it, it did not fascinate them. Practically no one rushed into the paradise of the constructible, where everything is classified, named, and registered. Mathematicians instead posed the following question: since Godel demonstrated that it was not contradictory to accept that all existing sets are constructible, could one demonstrate that it is also not contradictory to accept that there is some inconstructible? This was a huge challenge. Because if you want to introduce some non-constructible, you are going to have to construct something that is not definable, something that escapes the dominant system of language. Mathematics, for decades, was haunted by this problem: how is it possible to demonstrate that something could exist that, from the dominant point of view, is not constructible?
It would seem impossible: the imperative to construct the inconstrucible. In my view, this is the problem confronting every creation, in a universal way: how to construct something that from the dominant point of view is not constructible? You can say this about a revolutionary party as much as an early cubist painting, the first dodecaphonic works of Schonberg, or Galois’ theory. In all these examples, and in many others, one produces something that, precisely from the point of view of the established order, is not constructible, something that ultimately cannot be covered, that cannot be buried underneath the constructible because it is confirmed as non-constructible. These are the mysteries of creation. Creation always lurks in the vacinity of that which is not already there in the form of the constructible and definable. And at the same time, one works with what is already there. You can surpass the world, but you surpass it from the interior of this world. The procedures you invent necessarily borrow, whether they want to or not, from the ambient definable. This ambient definable will have to be twisted, maneuvered, to lead to something that it itself refuses. Every invention, from this point of view, is as it were refused by the world in which it is produced. It is not just difficult; it is refused, because the immanent law of the world is the imperium, the commandment of the constructible.
Finally Paul Cohen found the means to demonstrate that, yes, one can accept sets that will not be reached through a constructible hierarchy, that are intrinsically non-constructible. And it is absolutely remarkable that he would name these sets generic. This word, generic, has a long history. In the Manuscripts of 1844, Marx uses it to designate the proletariat. He says that the proletariat is the representation of generic humanity, of humanity as such: the representation of that which, in humanity, falling exclusively under the heading of humanity, is not of the definable order imposed by determined society. The point that touches humanity as generic humanity, humanity as a genre of existence that is not coded or precoded in the figure society always imposes on it. This question of the generic in Marx indicates that what he understood by the proletariat was the non-constructible point of bourgeois society, the existing non-constructible point. It exists, indeed, the people are there, but as a subjective capacity, it was a point that the order not only could not construct but could not even imagine being constructed. Now, I don’t know if there was a direct filiation — I don’t think so anyhow — but spontaneously, one could say, Paul Cohen rediscovered this old word generic to designate, not the humanity immanent to the proletariat as that stripped of properties come from outside, but non-constructible sets.
[Figure 2 shows the two fundamental choices. On the left side, accepting the axiom of constructibility, the new set is constructed from properties of previous sets. On the right side, across the barrier of the closure of the world, the non-constructible or infinite set is again represented by a circle with a dotted line, but sets from the constructible side have endeavored to “cover” it. The choice which says there is something non-definable, that not everything is subject to covering, is represented by the point of relaunch at the center of the infinite set.]
So we found ourselves in the following situation: it is possible to declare that everything is constructible; it is also possible to declare that, no, there is some inconstructible. What to do in this situation? One must choose. There is nothing else to do. You cannot say both at the same time. If the mathematician does not assume the axiom of constructibility, it cannot be for reasons of coherence. To assume it is simpler and just as coherent. When he decides to not be situated in the field of the constructible, it’s simply that he finds it more interesting to settle down in the field of the non-constructible. More interesting why? Because if you accept the non-constructible, you are going to accept that something that cannot be covered exists, something radically exterior to the field of the constructible. It is not constructible, and thus is it not composed of the definable. In one place, there is the undefinable. We can speak here of a relaunch, for it will necessarily implicate a surpassing of the limit. It is stabilized because there is a point that in any case was discovered, manifested, that is in excess. It is a relaunch inasmuch as you can rely on this point to build other things, and to modify the very definition of definability. Because you could say things are definable either in the old sense of the term, or in a new sense: the old sense of the term plus this point that cannot be covered. Thus you are also in a state to construct a new universe of the definable, and not simply to clash with the definable. It is enough to add new generic entities to it, which will work from inside on the new definable through a type of permanent instability.
This is exactly what Marx thought. The proletariat was the support of the revolution as generic, in that it deployed, from the interior of the society where everything is defined by proprieties, the social hierarchy, etc., something impossible to grasp from the point of view of the covering. This “something” becomes the principle of a reorganization of the whole of sociality, in a second time, around this point that will itself diffuse and disappear in such a way that what ultimately exists is generic humanity. The proletariat will render the whole of humanity generic, leaving behind the previous system that defined the system of social positions.
We can retain this: there is a fundamental choice, though naturally it appears in concrete circumstances. It is a choice that you encounter each time you are confronted with the possibility, the upsurge, of something other, and consequently with the logic of covering, which confonts you intensely, for X number of reasons. A part of what I call events is summed up in this point of view. One function of the event — an uprising, a creation, etc. — is to bring this choice to the light of day. An event can be defined by the necessity, with regard to what happens, to decide to stay in the constructible or to leave it, which is to expose oneself to the generic, even though it is something that, for quite a while, is undefined, poorly defined, impossible to grasp, for it is generic and cannot be classified, defined, etc.
This determination as coefficient of incertitude was a fundamental quality of the proletariat, though it lost it later on, to be sure. The proletariat in fact was simultaneously the promise of the future but also the phantom of society, unlike that which was constructible or definable by society or through it. It is necessary that politics guard this, that it remain a politics of the generic. If it redefines everything, reclasses everything, it substitutes one constructible order for another; we call this a relative constructibility. There is a general constructibility that starts with the empty set, and you can very well take the “proletariat” this way, as closed off in a unique and closed genericity, and then rebuild the definable universe starting with this closure. This is what happens if the State is the only new reality. The “proletarian State” is largely the reconstitution of a new type of definability, of course, but it is also loses the generic’s character of being in movement and its capacity to dissolve, its capacity to spread throughout the entirety of humanity, where it dissolves the constructions of and subordinations to the dominant language.
This proves that an event can be correlated to something very simple but, in reality, very complex, though formally very simple: that ultimately every fundamental choice is always a choice to accept a genericity, in one point. I believe this absolutely. It is to accept that something will escape the system of authority of the dominant language. But if you do this, it will also escape you in part, because you are also in the dominant language. There is thus an effort for the acceptance of the generic to be a process, for the consequences to be drawn from it, and for it to not just be undermined or anesthestized in relation to previous definitions.
I think that the antinomy Godel-Cohen — which was not really an antinomy, since they were both in perfect agreement; neither of them really liked the constructible, and Godel was very happy to see that another choice could be made — this antinomy is still an admirable formalization of what freedom of thought is. Because there we must come to the fact that the choice is not prescribed, nor prescribable, because you cannot claim that it is coherent. You can say, “the constructible is still better, because it is clear and stable. It is language in its element.” You can say, “the generic is formidable, for it means adventure and trouble; it is what bursts the banks of definitions.” This discussion is in fact permanent; it is everywhere, at every level of human existence. The twists and turns of existence make it such that one is often in one register on one side and wholly in another register on the other; it’s not a global or systematic distribution. Mathematicians saw that in its profundity and it is a major existential point, because at the end of the day there is a fundamental choice: Am I going to take my place in the order of constructibility, of the definable? Will I seek to be placed? Because the constraint of the definable is that you will be placed somewhere; you have your attributes, your name, and likewise with everything surrounding you. Or am I going to assume something that cannot be placed? Because that’s what the generic is: something that is unstable as to its name, as to its disposition, and even as to its phantom-like existence. Because, for example, two generic sets are very difficult to distinguish from each other, obviously, since they don’t have a stabilized definition. They are alike. We have to assume simultaneously the completely different and the completely identical. This is well known in fraternal political undertakings, amorous ventures, and similar initiatives. Every intellectual history of the interpretation of love has always oscillated between the fact that what is formidable in love is that there were two [on était deux] and the fact that what is formidable in love is that there was one [on était un]. One could say: love à la Godel, love à la Cohen.
 Fundamental Ethics of the Idea
3. Every thought contains a fundamental choice. Thinking is thus free in a profound sense, and not because it can say whatever it likes, which is the freedom of indifference and is of no interest, the freedom of whatever stupidity. Suppose now that one has chosen to be on the side of the non-constructible, for one reason or another. What does that mean, what are the consequences? It is not inevitable, I insist, that one has a non-constructible set in hand, for a non-constructible set is not to be found just anywhere, unlike the constructible, which is easy to find. Your fundamental choice can be presented under the form: there is some non-constructible. But what is going to materialize this? Because in fact the choice for the constructible is a clear choice; in the end, what does not conform to the dominant language doesn’t exist. Whereas for the generic, one affirms it exists, but what does that mean? Because you are not going to just gossip about the subject, find some names, etc. It is simply the idea that there is some novelty that is not definable by the established order.
In reality, there one truly touches infinity. Ultimately, it must be affirmed that there is some infinity, in the strict sense, that is, a non-constructible infinity. It must be affirmed and, afterwards, you will see if — by working out the idea in the world — it is verified, constructed, etc. Consequently, non-constructible subjectivity, generic subjectivity, always supposes that you suppose the existence of a non-constructible infinity, a supposition that you will have to work out in the real. It is not an inert supposition. If you suppose it, it means you will watch over it attentively, defend against attempts to cover it up, denounce the easily definable, track down the declarations of constructibility that are manifestly and specifically designed to maintain the order, and so forth. The whole thing is hard work, in every order of thought. But you will not do this work if you’ve not made the fundamental choice to do it, that is, if you have not in one way or another opted for the supposition that there really is some non-constructible infinity.
And that is what I call an Idea. An Idea, whatever it may be, is always an infinite ancitipation of the existence of a possibly generic universe. This type of infinity will help you testify to the fact that, in effect, something that transgresses the dominant order can exist. On this point, mathematicians have done terrific work. They have demonstrated that certain types of determined infinities exist that, if one accepts that they exist, attest by their very existence that the universe is not constructible. They have, in a way, demonstrated the power of the Idea. If you believe in this type of infinity (because you cannot demonstrate that a non-constructible infinity exists), it will testify that there is some non-constructible. It can be shown that the universe in its entirety cannot be reduced to the constructible by the sole fact that such an infinity exists somewhere. That has been demonstrated. It is enough to affirm the existence of a certain type of determined infinity to make the universe tip over completely to the side of the possibility of the non-constructible.
I think this is an absolutely remarkable existential indication. It signifies that if you have an Idea and you are in a state to really support it — which comes down to saying that you affirm its existence, that you happen to put this idea in place in a small fragment of the real somewhere — well, then you have a good chance that the world will tip over out of the constructible. But if you have no Idea at all, it will not be easy to leave the constructible. The first form of this mathematical demonstration was discovered by the mathematician Scott in a theorem that says: if one “measurable set” exists (very poorly named, by the way), then the universe is not constructible, there is some non-constructible. This was earth-shattering, because we can see how the constructible and the non-constructible could appear to be a question about the entire universe; the question of whether everything is constructible or non-constructible seems to be about a characteristic of the entire universe. Whereas here, it enough that there be one witness, if I may say so, one sole configuration, very particular, one set having certain properties, for the theory of the constructible to be rejected right away.
I think it is always like that that an invention, a novelty, a creation takes place in the real: it’s because someone, somewhere, had an Idea. They had an idea in the strong sense, meaning: they affirm this idea existentially. They support it with their life, with their creations, with what they do, and they organize their existence around the fact that this thing, whose existence is affirmed by the Idea, can exist. In that moment, they are in the situation of Scott’s theorem, meaning that if it exists enough for one to say that it exists, for others to mock the fact that it exists, that it has consequences, etc., well, it will mean that the universe was not as constructible as they said. And that therefore something of the order of covering, of domination, etc., was chipped into, reduced.
It is utterly surprising, the symbolic connection between the formal theory of the constructible and everything we have just said about the challenge to covering. Because if you hold firm to the Idea, to the type of infinity it contains, it means that you have the means to oppose yourself to covering, because covering only survives by assuming that, in the end, everything is covered by the constructible. To extract yourself from the covering, you must have an Idea, in the precise sense I have said: the possible recognition of a type of existence whose consequence would be that the universe is not constructible. It’s something totally different than encountering by chance something that would not be constructible! It is a hard labor that reworks our perception of the world in such a way that you find paths that in fact establish little by little the coherence of your Idea. Because we know it is coherent, Cohen has shown it. You will not be contradicted in this affirmation. You assume it exists, it exists. Perhaps you will find nothing. But the theorem says that you should normally find something, because if the correlate of your Idea exists, then the universe is not constructible and there are limits to the covering.
4. From all that, we can draw a fundamental ethics, which will serve as a conclusion: you must always take responsibility for [assumer] an Idea; participate in the discovery; free yourself in this way from finitude; and open thought to the real infinite.
‘You must assume an Idea,” that is, you must oppose yourself to the fundamental thesis of our contemporary world, the imperative, “Live without an Idea!”, which has a whole doctrine of covering behind it. This is what is uniquely hidden behind the apparently anodine, even progressive motif of the death of ideologies. The death of ideologies means: “Enjoy (if you can), live without an idea. Enjoyment [jouir] is a sufficient norm. Stand before the great planetary market, buy something that will be good if you can manage, otherwise don’t embrace the spirit with your ideas.” So the first point is to hold on to an Idea. To hold on to an idea is a political Idea, obviously, but it is bigger than that. It means: put your existence under the sign of what will not yield on an Idea [placer son existence sous le signe de ce qu’on ne cédera pas sur une Idée], that is, a type of infinity. You will act in such a way that, in the end, the encounter with the generic will have taken place. The fact that the universe will no longer, for you and for those around you, be constructible, will happen. This is what I mean by: always assume an Idea.
“Participate in the discovery.” Obviously, armed with the Idea, you can intervene and undo coverings. Coverings are precarious from the moment someone has an idea, that much is sure. There are many very concrete examples of this, even in ordinary life. If you have an Idea of what life can be, it will not let itself be easily covered over by mortifying debris, by the miserable bits.
Between “free yourself from finitude” and the Idea, there is a path, obviously, which is the path of the first fundamental choice (“I am Cohen”).
“Open thought to the real infinite”: that is the synthesis of it all. The synthesis will retrospectively demonstrate that infinity is always relative to a given constructivism, and infinite is always to have the strength to not let oneself be covered; it is always to hold on to the Idea; it is always to free oneself in this way from finitude (partially, never totally); and consequently, it is to make a creation out of one part of one’s existence. If it were absolute, it would be a chimera. But of one part of one’s existence, surely a creation can be made. A creation that will not be covered, when you safeguard it so it will not be covered.