Alain Badiou. Toward A Positive Definition of The Infinite.

Alain Badiou. Toward A Positive Definition of The Infinite. in: EGS. 2011. (English).

So I recapitulate the most important points of the lesson of yesterday. First, our goal is to constitute the dialectical relationship between the finite and the infinite as a fundamental question for philosophy today. We can say also that our goal here is to find the new form of the question because sometimes the question of the infinite is seen as an old question, as a question of classical metaphysics, something like that. So our goal is also to find the form of the question which is appropriate to our world and our lives. And I think we can say today, not a great development concerning the form of the question, but we have some idea concerning the general form of the question, the general form of the question is divided in two parts. First, is there a positive definition of the infinite and not only a negative one? And a positive definition of the infinite is the possibility to define the infinite not by its opposition to the finite, not as something which is beyond the finite, after the finite, in another world than the finite and so on. So is it possible to propose a new concept of the infinite which is not in a negative relationship to the finite, and so to reverse the classical order, the finite first and after that the infinite as a form of negation of the finite? [This is] the first part of the general form of the question. And the second part is, are we human beings, are we able to have a true relationship to the infinite? So are we able to have a true relationship to the positivity of the infinite because this second part depends on the first. If we find a positive definition of the infinite, we have the new question, are we able to have a true and positive relationship to this positivity? This is my first point, the question as such.

The second point, the beginning of a historical examination of the old forms of the question, to find the new form of the question we have also to know the old forms of the question. And I propose in this direction three periods, three sequences, antiquity, Christian age and modernity. I want to say something more concerning these words, “antiquity,” “Christian age” and “modernity.” All these words are pure approximations. They are not really precise. “Antiquity” is largely an academic name, a sort of historical sequence with no precise definition, in fact, so Greece, Roman Empire, but also Egypt and China and so on. “Antiquity” is a very suspect word, but the philosophical content is, as we have seen, classical age. Classical age of the Western world and the relationship between finite and infinite can be named classicism, a classical relationship. So we can say “antiquity,” which is something like an objective definition, but maybe the most important point is that all that is in the framework of what we can name classical age.

And after that, “Christian age” is the name of the origin of the second sequences. Maybe it’s not the name of the sequence as such, the name of the beginning of the sequence because it’s reality is inside the Roman Empire, which is inside the first sequence. Inside the Roman Empire we have that sort of rupture of subjective and religious, the name of which is “Christianity.” But it’s the beginning of the sequence is the beginning of a new relationship between the infinite and the finite. Finally we have proposed to say “romanticism” after classicism. “Romanticism,” which is the name appropriate to the end of the sequence and not to the beginning, naturally. At the beginning we have the contradiction between all the world, old gods and so on and the new Gospel. But at the end we have a subjective determination of all that that we can name “romanticism,” which is much more appropriate, finally, to our problem.

And for the third sequence, I propose “modernity,” which is also a very obscure name, but it’s a polemic name because it’s against something. It’s against, first, the difference between modernity and contemporary world. I think that we are now today in the sequence of modernity. There is no fundamental difference between the two last centuries and today. And so it’s also against the definition of post-modernity, naturally. If we are in the same world there is no post-modernity at all. We are in a declination, a new form of modernity itself and not after modernity. All that is to say that the sequence is really one sequence, a sequence of modernity, and we have not a fundamental rupture, for example, at the beginning of the last century or today or something like that. I cannot explain all that in details, but it’s the same world for many reasons. First, it’s the same political and economical world. That is, we are in the world which has been created at the end of the eighteenth century, the name of which is capitalism, capitalism as a global form of organization of economy, societies and so on. And not only are we in this world, but we are in the complete development of this world. It’s much more true today that we are in this world than it was in the time of Marx. The world is much more Marxist today than it was because global market, extension of capitalism in new very important countries, China, Russia and so on and more and more of the development of the capitalist law against all what is outside this law, national states and so on.

And so it’s today that we really know what is modernity. It’s not because in pots-modernity. It’s because we are in the completely developed form of this world itself. And so maybe the most appropriate word would be “intense modernity” after a long sequence of weak modernity when capitalism was not in all the world, when there had been some contrary hypotheses, some socialist states and so on and so on. All that was a context of weak capitalism, and today we are in a strong capitalism in fact. That is really the intense form of modernity. It’s the same thing for all the developments concerning science, technology, new forms of art and so on. On all these point we can demonstrate that we are in the ultimate consequences of modernity and not after modernity. So it is why I name the sequence modernity.

There is also something more to say concerning the temporal disposition. I think we have something like that, antiquity, maybe six b.c., five b.c., so it’s the first sequence, but we know something, that at zero we have the Christ. So there is something like a complex beginning of the second sequence inside the first, naturally, during maybe some century. So from something between this five centuries after the birth of Christ and for the second sequence maybe something here and around sixteen after Christ. But in fact we can propose a different, we can say something much more precise by eighteenth century because eighteenth century is really the beginning of modernity at the level of development of science, economic creation of the capitalist form in England and so on, the beginning of imperialism, of western imperialism and so on. But in fact the third sequence also begins sometime before because the third sequence also depends on scientific creation before the eighteenth century at the beginning of seventeen in any case, and so we have much more something like that for the third sequence, so classicism, the birth of romanticism and modernity. All that is not exactly in the world as a complete totality, but is the spiritual history of the western world. So in some sense it’s an imperialist vision. It’s not a representation of the global history. It’s something much more different.

And my third point is concerning the two first sequences. I will propose to you new forms, more articulate, more precise than yesterday. For the first sequence, being, but being which is the determination of finite possibilities. It’s clear in the conception of the world itself, of being as such during antiquity, being is a complex of finite possibilities, being is finite by itself, and so the disposition of possibilities are closed by the finitude of being as such. We can name all that cosmos, which is the Greek word for world, but inside the idea of cosmos there is the idea of finitude of the world. That is the essential point. And on the other side we have existence under the condition of the cosmos, if you want, in that sort of cosmos, in the mental representation of the world as cosmos. And we have said that the relationship between being as finite possibilities and existence is the realization of as much as we can of possibilities. So the complete realization of finite possibilities is perfection, and the name of this perfection is the One. That is something like the complete realization of finite possibilities by concrete existence, and the paradigm of this realization are gods, which are not at all at the level of infinity, but are precisely something like possible examples of a harmony between finite possibilities and existence because the possibilities of god are also finite possibilities and not at all infinite possibilities in the Greek world. This is why very often gods are not at all happy. They have sad gods very often. They are jealous and so on, but they are better than we are, finally, only because they are immortal. And, you know, there is a very interesting sentence of Aristotle. Aristotle writes that the goal of the life must be to live as an immortal. It is the perfect life. The perfect life is if we can live as an immortal. So it’s really a paradigm. It’s really an image, finally. The Greek gods are possible images, because they are immortal, of the true life as such, the good life. The good life is when we are near gods concerning the relationship between finite possibilities and concrete existence.

And finally we have the abstract idea of infinite possibilities, and this point is for concrete existence a bad goal, an illusion. And we know that the vision of existence under the idea of infinite possibilities is precisely evil as such, is precisely a bad choice, hubris in Greek and, in fact, tragedy. So a bog part of the Greek vision can be found in tragedy because tragedy is a representation, the only possible representation of the effect of the idea of infinite possibilities. In tragedy we have exactly this point, infinite possibilities and the effects of infinite possibilities as, precisely, tragic consequences, tragic effects. And all that is opposed, finally, to the destiny of gods, which are, certainly, not infinite at all but which represent the possible harmony between finite possibilities and existence. And so there is really a tension between being as such and infinite possibilities, and so infinite possibilities is really something purely imaginary it’s an illusion, a representation, nothing else, and it’s a bad and dangerous representation, which creates, finally, a form of existence which as a tragic form.

That is the recapitulations for the first sequence, and now for the second sequence, in the same manner, I begin always by being. It’s very difficult to begin in another manner than from being! It’s the first word of the logic of Hegel, to be, to be or not to be, to be first, and it is why in all sequences the beginning is being, but in the second sequence, naturally, being is an immediate relation with the infinite. So we have being, the infinite, existence, and we have a complete harmony between being, infinite, and existence in the form of the One but not in the sense of the one as only the possible unification between being and existence across finite possibility, but inside a separate realm, which is the realm of god. So we have really the creation of another world. That is the most important point during all the second sequence, the affirmation that there exists another world, another world which is precisely a new distribution between existence and infinity. And so the One has not at all the same meaning as in the first sequence. The One is precisely the realization of a complete unity between existence and infinity, and so the real creation of infinite possibilities, not as a bad dream as it was in the first sequence, but as the realization of being as such. And inside this infinite possibility we have the creation of the second world, our world, which is precisely the realization of the infinite possibilities inside the first world, which is the world of god. And so we have another world, and in this other world we have being, being of the world, we have existence and notably existence of human beings because human beings are fundamentally interested in human beings, you know that, certainly animals, plants and so on, but human beings first. And so there is something finite, naturally, in existence. The human existence is finite, which is why death is so important in this orientation. You know that death is, for the religious form of this sequence, the moment where we have a relation between the finitude of human existence and the other world, which is why the resurrection, the new world, paradise and so on is only the possibility of a new opening of the finite existence to the infinite being in the mediation, the negative mediation of death.

But, in fact, all the question in this vision is the relationship between finite existence and something as a real being, which is, finally, infinite. And there is no direct relationship. That is the point. There is no possibility of direct relationship. There is the necessity of a mediation. So the point is that across mediation the being in the second world, the world of creatures, is in relationship with the being real, the being as such, which is the divine being. So there is no direct relation, but there can be an indirect relation, a dialectical relation with a third term, which is the mediation, and the mediation, naturally, is, and I don’t insist on this point, the mediation is not inside directly the laws of the world. It is something which is between the second world and the first. And so it opens a new access to the relationship between the infinite and the finite. And, naturally, the beginning of all that, of this sequence, is the figure of the Christ because the figure of the Christ is precisely on this point, by a pure decision of god. The infinite possibilities is also the possibility of the mediation, but the mediation is created by god as all what exists in the religious vision.

There is the possibility, the bad possibility is to affirm that there exists no mediation at all. It is the form of negativity in the second sequence. It’s the reverse of the position in antiquity. In antiquity the bad choice is to affirm that we can do something infinite, that there exists infinite possibilities. It’s hubris and tragedy. In the second sequence, the bad choice is not at all to say there exists no mediation. The bad choice is to affirm that there exists no mediation and so we cannot open the human existence to the infinite as such. And we can name this choice, the finite is our destiny forever without any exception, we can name this vision nihilism. So you must see a symmetry between the nihilism of the Christian sequence and the tragedy inside the first sequence. And we can say that nihilism is the personal tragedy of the second sequence, no mediation, we are enclosed in our finite destiny, and there is nothing more than death. We are for the death, and after the death nothing at all. and so we must do what we want in the form of a return to the finite possibility, naturally, without any access to the infinite, without mediation. And no future, you know this determination, the true meaning of no future is no infinity. It’s the true meaning of no future because if we have the possibility to access the infinite, naturally, something is open, which is the future for our destiny. If you have a mediation you have a new future. In the religious framework the future is another life, a life in another world, a new life. But outside the scope of the religious vision we can have the idea that if we break the finite limits of our world we can open something like a new possibility, but if we can have a new possibility we cannot say no future, naturally. We have a future. And so there is a direct relationship between nihilism and finitude. It is the same thing in some sense. Finitude without any vision of the creation of a new possibility is in fact nihilism itself, and nihilism itself is no future. So no future is no infinite vision at all, no possibility of creation of a new possibility. So that is the general existence of the second sequence.

The third sequence now, the third sequence, that is the sequence of modernity, which is our sequence. The third sequence begins by a trouble, a trouble in all that, which is the possibility for the world itself to be infinite. Maybe infinity is not a pure determination of the being of god, something like that. Maybe the infinite is not the pure determination of the other world, but the world as it is probably infinite. Science, the birth of modern science is naturally the beginning of this trouble, and it’s possible to say that the third sequence is opened by science exactly as the second sequence is opened by religion. After the Christ, Galileo, and it is why a part of the beginning of the third sequence is a very hard conflict between science and religion as we know. The eighteenth century, in France especially, we have a very terrible fight against Christianity, and a more important argument of this fight is the existence of positive science. So during maybe two centuries, eighteen and nineteen, we have, as a principle contradiction, the contradiction between new science and all religion. But it’s the beginning. The beginning of the sequence is clearly the birth of new physics, not new mathematics first, but new physics, physics inside which we find the idea of first an infinite world and, second, that in this infinite world human beings don’t live in the center, don’t have the center of the world. Finally we are in a small planet in a corner of the world without any interest. So it’s a great lesson of modesty for human beings. They are not in the place of salvation. They are not extraordinary beings and so on. They are special animals in a corner of the world. And so it was really a subjective revolution to understand all that. The sun, in some sense, is much more important than our living planet and so on. You know perfectly all that, but a sign of all that is a title of the book of Alexandre Koyré, a very good book, very important book, the title of which is From The Closed World to The Infinite Universe, and in this book Koyré describes precisely the beginning of all that, that is, for us, the beginning of the third sequence. You now that directly the title of Koyré concerns the relationship between the closed world, so the finite world, and the new infinite universe, which is opened by the new physics. And so the scientific revolution, the beginning of all that with Galileo, Newton and so on, is to affirm that there is no reason for the finitude of the world. There is good reason to affirm that the concrete world, the material world is infinite the infinite universe.

And so we have the creation of a new separation between the One and infinity. In the second sequence the One is the unity between being and existence in the infinity of god, but what begins with the scientific revolution is the idea that there is no immediate relationship between infinity and the One because the world as such, which is clearly also a multiplicity, which is clearly not One in the sense of god, the universe itself, the world itself is probably infinite. So, you know, there is a complete trouble concerning all the names, all the dispositions of the problem. First, maybe there exists different meanings for the word “infinite.” When we affirm that the world is infinite, and when we affirm that god is infinite, is “infinite” the same word? It is a very complex problem. If it is the same word it will be difficult to separate god from the world, and it was, in fact, the idea of Spinoza. At the beginning of the sequence, the idea of Spinoza, Spinoza affirmed that finally inside the concept of infinity we have a unity between god and the world, or in the words of Spinoza, god is nature, nature as such. All what exists is god. It’s a first possibility, but we have other possibilities to distinguish different meanings of the infinite. And if the world is infinite and if god is infinite is another sense, what is the relationship between not only finite and the infinite, but between different meanings of “infinite” itself? So we have a new set of questions really, first, possibilities of existence of many meanings for the word “infinite,” second, the One is not in all the relationship with the infinite and, third, the relationship between all that becomes very complex.

And at the end, the fundamental question, which is how human beings can have an access to the infinite, the disposition is completely different. I propose a first account of this disposition, the disposition of the problem. We have, first, in some sense, this infinite, and there is a distribution of infinite on the side of the world and maybe on the side of god. You know, the battle field of the eighteenth century, the new thinking, is to affirm that the infinite is a dimension of the world and not at all of god, and the religious disposition, the religious reaction is to say, “No, the true infinite is the infinite in the direction of god,” and on this side we have something like a false infinite, which is a name that we find in Hegel, for example, and the relationship between a false infinite and a true infinite becomes a completely new question of great interest. If we have in the world human beings, the question becomes is the relationship between human beings and the world finally a mediation in the direction of the infinite? So is it possible that we can find in the world itself, because the world is infinite, a possibility to extract from the human existence something which really is in the direction of infinity. And so there is the possibility of a mediation which is not a mediation outside the world, but a mediation inside the world itself because the relationship between human beings and the world itself is also a relationship between human beings and something which is infinite in some sense because, after all, we don’t know exactly what all that signifies.

And you see the first problem, second problem and third problem. First, what is, if we maintain something like a god, what is the meaning of infinite concerning god? If we affirm that the world is infinite, what is the signification of infinite in the direction of the existence of the world? What is the relationship between the meaning of the two infinites? And, finally, what is the relationship between something which is finite in human beings, death and so on, and the fact that the world is infinite, and so maybe we can have a mediation between human existence and the infinite and, in the religious vision, finally a relationship between human beings and god too. But this new relationship will be across two different meanings of the infinite, you know? The first one, which is infinite as in the world and the second, which is infinite as in the direction of god. And it’s today too a real problem in the religious framework. It’s the question, can we accept all the dimensions of the world as a possible mediation to god himself? It’s something like a new theological possibility because in the second sequence there is really two different worlds, and this difference as the difference between the infinite and the finite. And so we must have a mediation. It’s impossible to go directly form the finite to the infinite and it is why all the second sequence is romantic in the sense to find a mediation. If there is no mediation it’s nihilism which is true. So the great disposition in the second sequence is between religious disposition, messianic disposition, on one side and nihilism on the other side. This is the real fight of the second sequence.

For the third sequence, it’s not the same thing as the second sequence. Maybe there is the possibility to accept something of the laws of the world, there is only one world, finally, god exists but god doesn’t create a world completely separate from our world, and so maybe we can find something in our world which is really by itself and not by a miracle or something like that, something which is by itself a mediation to god. And it is why the question of the world as it is is much more important today concerning the religious determination that it was. Because in the second sequence the question was really the relationship between two different world, but now maybe we can find something new, something like a possible mediation in the world itself. But for that we must dispose of the possibility of two different significations of the infinite because if we have not two different significations of the infinite we cannot have the certainty that god is real outside the world. We can have the solution of Spinoza, god and the world is the same thing, and so there is only one dimension of the infinite, there is no transendency at all.

So to resume this very complex situation we can say that we have today a lot of problems concerning this point. It is why we must use eight days to have the solution at the end. Some of these problem are the least of problems, problems which are today too a sort of program of modern philosophy. First, which are also a succession of possibilities in some sense, first, to find a new definition of god. If god is dead there is no new definition of god except that god is dead. To find a new definition of god we can name modern theology. And why we must find a new definition of god? It’s because we cannot have a direct separation of god by the concept of the infinite as it was in the first sequence at the beginning of the second sequence. God was infinite and so god was defined by his proper infinity, but if something else is infinite, for example, the world, we cannot do it like that. So we must find a new definition of god, which is not reducible to infinity, potency and so on. There is even the possibility if the world is infinite that god would be finite in a new sense. It’s the idea of a weak god, a god which is not like a terrible king, a god which is not a power, which is not…a god which is really like the Christ in some sense, which is really a poor god, a god which is completely good and not strong, a god which explains the possibility of the existence of the good, and so a god which is only a paradigm for existence, but a god who decides nothing. It’s a sympathetic god in some sense, a good god, a good god because the god of the second sequence was in the paradigm of the father, of the king. And so the possibility to find a new definition of god outside the direct affirmation of another world which is infinite and with power and so on, is to define god as the principle of the weakness and the glory of the good, the glory of the good, but the weakness too, the humility of the good. It’s one of the radical possibilities to find a new definition of god, and it’s a big possibility of determination faced today.

Second possibility [is] to find a new concept of infinity. And why it’s a necessity? It’s a necessity first because we have two meanings here of the infinite, the infinite of the world and the possible infinity of god. So there is something in the third sequence which opens the possibility of different types of the infinite, different forms of the infinite and maybe different concepts of the infinite. It’s a part of the task of modern mathematics. We return to this point, modern theology, to find a new definition of god, modern mathematics to find a new concept of infinity, or many different concepts of infinity. And after that, the relationship between the two. There is a relationship or not between modern mathematics and modern theology.

There is a story, you know probably, the great mathematician in this field is Cantor. In some sense Cantor is the great make of our week too, and Cantor, we shall say in detail, Cantor proposed a vision of different types of the infinite. So with Cantor we have a complete separation between the infinite and the One. This is the point. The old religious conception where the infinite is also the big One, if you want, is destroyed in some sense by Cantor, which proposed in the field of mathematics the possibility of different types of infinity without the big infinite, without the One as such, without the final infinite. And Cantor was a Christian, so he was in the second sequence as a terrible destiny to become the fundamental man of the third sequence, but personally he was completely in the second sequence. He was convinced that only god is really infinite. So we have a drama, we have a tragedy of Cantor between mathematic work and the religious conviction. That is the point for Cantor. And Cantor has returned a letter to the pope. It’s a very extraordinary story. He wrote a letter to the pope to say, for this question, “I have the proof that there exist completely different real infinites and how all that is compatible, all that comes with my religious conviction that only god is properly infinite.” So in the letter Cantor proposes also a solution to the pope, to the new problem for the pope. The solution was there is numerical infinities on one side and qualitative infinity on the other side, so quantitative and qualitative infinity, “and my creation, my mathematic creation in the field of mathematics is only to create new infinities, but the real qualitative infinity is, finally, only god.”

But Cantor was not completely satisfied by his solution because what is exactly the qualitative infinity, and what is the relationship, finally, between qualitative infinity and numerical infinity? Is there a relationship? Is there no relationship? And so he was really at the end of the letter, all that was very important for him to have the opinion of the pope, all these questions. There is no answer during a long time. All is very, there is no speed in the universe of the pope. We can do something across centuries. No, it’s not true. Tomorrow is nothing for the pope. And so finally there is an answer of a cardinal, and not of a pope, but of something very important for the pope, saying that he was very interested by the problem, but finally the problem was not so important because, in fact, all what counts today are only numbers and, naturally, god is beyond numbers. It was true in some sense. It was only a typical answer of the second sequence, to say that, yes, when we speak of the infinite we speak of something concerning the other world, and there is nothing in our world which is really a similar or in contradiction with the other world. And so all that is something like a game for mathematicians, the game of numbers, and there is no ontological existence of all that. That is the true content of the answer of the pope, that we must affirm that only god is infinite and that all forms of infinity which are not the infinity of god are not really infinite, but are forms of finitude disguised or hidden behind something which is, in fact, absolutely finite.

So, to take an example of the question of the second problem, the second direction, to find a new concept of infinity. A third possible task is to suppress god in the death of god, and it was a very important idea during all the nineteenth century to replace god with humanity, to say that the only god today is humanity as such. It’s what I can name the modern scientific humanism. And if we replace god with humanity you affirm, in fact, the infinity of humanity as such, and it is why it’s impossible to replace god with human being as such, but with humanity, with all the history of human beings, but not personal, individual human beings. So it’s something like a religion of humanity. The most important representative of all that is Auguste Comte, the French thinker, which is really the creation of a religion of humanity, and, naturally, the religion of humanity is also a religion of all human beings dead or alive with no fundamental differences finally. Auguste Comte wrote that in humanity there exists more dead than alive. It’s true. And so it’s like the task to have a religion which is in relationship not only with human beings as alive creations but with humanity as a big set of living people with dead people too. Dead people is also an existence, and every creature must take inside the infinity of humanity.

Fourth possibility, to suppress infinity, to return to a pure thinking of finitude and to affirm that, finally, infinity is always an abstraction, maybe a religious abstraction, maybe a mathematical abstraction, maybe a physical abstraction, but that there is no concrete existence of something infinite. And so it’s something like a return to classicism, this vision. It’s a large part of modern phenomenology, in fact, the analytic of finitude. And it’s also a part of e new scientific positivism, which says that the idea of infinity is a purely abstract vision and that we can do in the scientific field itself with only finite operations. We know that today it’s a possibility that the world will be finally finite. It’s a possibility in the new framework of relativity and so on, and with the big bang we can have something like the history of a finite world. And so we are not, at the scientific level, at the absolute continuity with the sequence itself. So inside the sequence where the infinity of the world is suppose we can have the possibility to return to a complete analytic of finitude as the goal of the thinking as such. So the goal of modern phenomenology in some sense is an analytic of finitude, and there is the possibility of a new scientific positivism, which is that finally science itself can do with only finite procedures and that the world, finally, is finite also.

We can find here the point I spoke yesterday, that is the possibility today of a return to classicism. So we return to something which is before the second sequence itself. We must do with our finitude. Okay, that is the point, and so we have to return to the idea of the complete realization of our finite possibilities without any abstract question of access to new possibilities. So inside the third sequence we have the possibility of a return to the first. Maybe it’s a circle, after the third sequence a return to the first. And it’s very interesting to see something like that. And it is the reason for which the enemy of the contemporary world is romanticism, paradoxically, romanticism as a form of illusion concerning the infinite, finally. So if we are in this form of the third sequence we are in a fight against romanticism, so against the second sequence, which prepares a return to the first. Against romanticism we must accept finitude. The problem is to do that without nihilism because maybe the modern return tot eh first sequence is much more nihilism than classicism because it’s a negative reaction against the possibility which has been opened by the second and the third sequence. It’s a negative reaction and as a negative reaction it’s always a possibility to say there is no mediation, there is no access to the infinite, and so we must stay in finitude in a nihilistic manner.

Another possibility, five, is to return to the One in some sense, that the One as infinite, but by saying that the One as infinite is only the name of the virtual potency of life, that the true name of the One separate from the infinite is not a god separate from a world, but the immanent potency of life, the immanent possibility for life as such to create something new. The idea is that all what happens is a result, an effect, of this infinite potency of life. It’s another idea of Spinoza, finally, the new forms of the idea of Spinoza and, as you know, is certainly the pot of view of Nietzsche and Deleuze. So, you know, we return to the possibility of a fusion between the One and the infinite not in the separate form of a god, but as the virtual possibilities of life, which are in this vision infinite, infinite creative possibilities of life. And so we return to the One as infinite without a separate god, but as an immanent animation of the world as such, and so we can find in the becoming of the world, in the different forms of life, a relationship to the infinite, which is inside the life itself and not outside. And the fundamental idea, which is of ethical nature, is that there exists virtually an infinity of new forms of life and that we can realize these possibilities so it’s the classical idea of realization but with the infinite and not with finite possibilities. It is a new context. In the new context of infinity we have the classical idea of realization, realization of the virtuality, of the potentiality, which are infinite, of life. So it’s also a solution to the paradoxical problems of the third sequence.

Another possibility is to begin by the separation between the One and the infinite. It’s the reverse of the attempt of Spinoza and to affirm the pure infinity of the multiple as such. So to use inside philosophy not only the simple opposition between the infinite and the finite, so to use inside philosophy to create something new inside philosophy, not only with the simple opposition, the binary opposition between the infinite and the finite, but the infinite differences between different types of infinity and to introduce in philosophy not the binary opposition between finite and infinite, but what was in fact opened by Cantor and some others, that is the difference, opposition, contradiction between different forms of infinity itself. So as a metaphor, as an image, to create a world where we have also many gods, but all infinite and not finite like in the Greek world. But the point, the difficulty, is to organize a thinking of infinity with that sort of possibility, what is finally the relationship between two different infinities? It may be, for example, the infinite possibilities of life are not the same as the infinite possibilities of thinking, for example, that we cannot reduce the infinite possibilities of thinking to the infinite possibilities of life, and that is possible if, precisely, there exist real differences inside the realm of infinite, if exist different infinite, really. Or maybe, if you want, that the infinity of the world as it is different from the infinity of the truth concerning the world, maybe.

So we, in this vision, we sacrifice completely the One. We create a vision purely inside the multiplicity, not only of the finite multiplicity, but also the infinite multiplicity, and the infinite multiplicity of different forms of infinity itself. And so it will be a death of the One. It’s my problem. Not only the death of god, but more fundamentally the death of the One, and we must assume completely that all is multiple, that there is no One properly, but inside a vision where we do not sacrifice the infinite, absolutely not. We separate completely the destiny of the infinite and the destiny of the One, and we assume that there exists not the potency of the One even under the form of the potency of the life like in Deleuze, be have really only multiplicities, but inside all multiplicities we have different forms, in fact, different infinite possibilities of the infinite itself. And after that we can think the world, think out life, think the experience in general inside this vision. But we understand immediately that the difficulty is always to give substance to all that and to first understand what is really two different infinities, the beginning of that sort of thinking, and it will be a part of our program. For the moment, our program is to stop a moment.

Alain Badiou. Different Philosophical Orientations Toward The Infinite. 2011

So, as you understand, my program is probably much more the position of the sixth possibility, which is to separate the destiny of the One from the destiny from the infinite, to propose a philosophy which is appropriate to Cantor and to propose, too, the possibility of a creative access to the infinite and not only a purely immanent access. I explain this point. I think that in Spinoza, Nietzsche or Deleuze we have an access to the infinite under the condition of the One, the name of the One is life. But I think that, finally, this access is a realization like in the classic vision. It’s the realization of something virtual. Deleuze named all that actualization. So creation is actualization because the place where the infinite and the One are the same is virtual, is the virtuality of life. So it’s an ontology of the virtual as the point where we find the identity between the infinite and the One. So it’s something like a purely immanent god without the name of god. So it really depends on Spinoza certainly. And infinity is not separated, and infinity is not without the One. Infinity is without the One, but without separate from the world and from our existence. So it’s an immanent position of the identity between the One and the infinite.

It’s a very interesting position, but I think that, for me, that it’s a choice. I return to this question of choice. For me it is too much classic, but with my definition of classicism, too much in the sense of realization, actualization of something which in some sense exists before as virtual, exists as in a latent form, is an indistinct form in the potency of life. But for me life is purely neutral. It’s not properly a creative position. So I must maintain that there is a distinction between creation and actualization, that we cannot think completely a creation as an actualization and that actualization is too much near realization, that is, too much classic. And it is why my program is different but in relationship to the other program as always. [It] is to really separate the One from the infinite. There is no common name for the infinity of the One and the infinite. There is not something like the name life, which is, from Spinoza, the name of that sort of new immanent unity between the One and the infinite. The complete separation, so in some sense the One does not exist. There is no fundamental name, if you want, neither god nor life, something like that. There is only pure and neutral multiplicities. Nothing works for us, neither life nor history nor god nor destiny. Nothing works for us. So we cannot realize something because realization is always of the supposition that there is something before the action, something which works for us naturally. So, maybe something exists like a mediation but not like a condition.

But before we go into the difficulties of all that, which are very numerous difficulties, in fact, the question is really a difficult one. And I want to ask, precisely, the question of the choice here. What are the possibilities in the sense of philosophical orientations? What are really the different philosophical orientation? In the point where we are in the third sequence but in a difficult moment of the third sequence where there is something like a strange fight between romanticism and classicism inside the third sequence, if you want, like today in the third sequence, the third period, we have the fight between the first and the second sequence, romanticism but with a very dangerous nihilism on one side and classicism, but with a terrible, something which is also something very dangerous, which is the desperation of creation and the victory of pure, individual realization as a unique norm. so a classicism of individual destiny, to have a good life in the sense of the realization of finite number of possibilities, that is, for me to become something like an animal. But I love animals. But it’s really to have a very short vision of life, of human life, a vision of human life without any greatness. But on the other side we have the possible return to romanticism, but without any spirituality, without any god and any religious framework and so on. Today romanticism practically must be a form of nihilism, a form of destruction of the self in experience without any guarantee, without any norm, without any vision. And it’s a strange situation, which is our situation today, that sort of definition of the third sequence by a struggle between the first sequence and the second sequence. And so, in some sense we must open the third sequence. We are inside but we must re-open once more the third sequence.

Third sequence was the struggle between science and religion, the beginning of the struggle between science and religion, but I think today the struggle between science and religion is without any interest. So we have the struggle between classicism and romanticism in fact, but romanticism is practically no future and classicism is practically to have a good place in the market. It’s not a very interesting choice between no future and the market. So maybe if philosophy is something, philosophy must help to find another way, another choice, and it is why I want to finish this lesson by clarifying exactly the possible choice. And it’s a real choice that we must do in our live, and we are in this choice, certainly.

First great possibility, to maintain a close relationship between the One and the infinite, it’s a very fundamental option. You can say that’s very abstract and so on, but not at all. Everybody decides something concerning this point, without knowing, naturally. It’s difficult to find somebody who said, “Last night I maintained the relationship between the One and the infinite.” If we find somebody like that immediately you write me that you have found something like that. But it’s the abstract form of the choice. But the choice is here. The choice has been made in some sense. So you maintain the close relationship between the One and the infinite, and either you have faith in the existence of a god, you maintain, inside the third sequence, faith in the existence of a god, and so you maintain the transendency of the Christian age, and probably you have, as a duty, to transform the idea of god, in some sense, outside the pure vision of power. I think it’s a more interesting way in this direction, which is not mine, which is really a possible choice, the most interesting orientation is the orientation in the direction of the weak god, the god of weakness and the pure god of good without any power.

So it’s the first possibility if you maintain the close relationship between the One and the infinite. But you can also not maintain this faith. You can have no faith in the existence of god. For you god is dead so the Christian age is really finished, and so you maintain the relationship between the One and the infinite but not in the form of a god, but in the form of a purely immanent form, and it is what I was speaking just before, Nietzsche, Deleuze and Spinoza too. And the name of the relationship between the one and the potency of the infinite can be the potency of life, infinity of forms of life, creativity of nature and so on. So in the first two possibilities…and you understand in the first possibility, the question is to propose a new vision of god, in fact, not by necessity a new religion because in religion you can transform the concept of god and in that case many, many times. God is not something absolutely, purely immobile, absolutely not. And in the second vision, the immanent vision of the relationship between the One and the infinite, you must transform, probably, the concept of nature, something like that, the concept of life. This second tendency is very active today, to have nature as the fundamental variance because nature is the point where lies creativity and with fear of destruction of nature and so on, ecology in some radical sense.

The other big choice is to suppress the relationship between the One and the infinite. Inside this choice, either you maintain faith in the existence of something divine. I don’t say exactly a god, but something divine, which is not the realization of a unity between the One and the infinite, naturally, because we are inside the second, great choice. You suppress this great relationship between the One and the infinite, but you have faith in the existence of something divine, and you must return either to a multiplicity of gods inside nature itself, a new paganism, or, once more, to a god without real power, in some sense to a finite god. And you must create what I can name a new spirituality, which is in close relationship to nature too. So we must find in this option, the work is to find something divine in nature itself, in existence itself, not in the form of a separate One, but something which is different forms in side the real world, inside nature, maybe some gods because it’s a possibility to us today to create a new paganism. Because if we have a sort of return to classicism, we have also a return to the possibility of differences between gods or differences between some divine forms of existence inside the world and not outside. We can find some paradigm of all that in Oriental culture much more than in the western world, this idea there is something divine in some aspects of the sensible world. It’s near Buddhism much more than the western, occidental tradition.

Or you have, that is, god is dead, really. We cannot find something divine in the world, which is neutral. There is no particular appropriation between us and the world. And you affirm that we human beings are wandering in the infinity of what exists. We are not at the place which is a sacred or divine place. We are the great wanderers of the infinity of what exists, without any last resort, without any guarantee. And in this last possibility of choice we have a clear philosophical duty, first, to develop a concept of the infinite appropriate to its objective nature, to make precise the possibility of differences inside the realm of infinity, so to introduce the multiple inside the question of the infinite, to achieve the separation between the One and the infinite. If we must separate the One and the infinite, we must appropriate the infinite itself to multiplicity.

Second, to examine the question of truth because it’s very difficult to have a real notion of truth without any transcendent guarantee, without any One. The classical concept of truth is always in relationship to something transcendent, and it’s another question, if there exists no truths, there cannot exist something like philosophy. You can have morality, you can have a religious vision, but certainly not philosophy. The beginning of philosophy is to separate truth and opinion. If we have only opinions, philosophy is of no use at all. But it’s not simple to have an idea of truth in the context of the complete separation between the One and the infinite, in pure multiplicities, in fact, in a world without any guarantee, any transcendence, any god, without something divine in the world itself. What is a truth? A very obscure question. And if we can solve this question the third point is to examine the question of action and the question of creation as something else than realization. And for all that we find many difficulties, and the first difficulty is to make precise the concept of the infinite, the infinite without the One.

So you know my choice on this orientation. Finally you see you have four possibilities. It’s finite! You have four possibilities. If the One and the infinite are in relationship we have faith in an existence of a god and so we must propose something like a new definition of god itself, first choice. Second, you have not faith in a god, but you maintain a relationship between the One and the infinite. So we have a purely immanent action of the infinite, and so we must propose a new concept of creativity of life or creativity of nature or a new conception of becoming, more generally, if you want. Third choice, you destroy, you suppress the relationship between the One and the infinite, but you have faith in the existence of something divine, something which is a possible reference, something which is an image of perfection. And so we propose, in some sense, a new religion, but not a new religion of transcendency, not a new religion of god as a transcendent power, but the religion of maybe a pure multiplicity of gods by a return to classicism, maybe a new god which is inside the world as fragmentary image of possible perfection. Or, finally, we are reduced to the choice inside the pure multiple without any immanent or transcendent references to the One as such.

So all these choices are real possibilities, and they exist, naturally, as philosophical tendencies. What are my objections against three of the choices? You know, it’s always more interesting to have the exposition of the choice, to have an exposition of the negative reason to have a choice much more than another. I agree with Deleuze on this point. Positivity is always more interesting than negativity. It’s really a very important political problem. We return to this point because it’s precisely the question of the place of the infinite in political determination. But I must say some words concerning the difficulties with my three other choices. Concerning the first possibility in my conviction, I see this position like a reactive position. I am developing a concept of what is the reactive subject in my Logic of Worlds. A reactive subject is not something which is in a completely reactionary vision, not at all. a reactive subject is not a subject which repeats something which is old, which is past , which is finished because a reactive subject must create something new, for example, a new vision of god in the case of the first possibility. So I say a reactive subject is in some sense a reactive one but does not, as a subject, create anything, which is more complex. So I think that the reactive position is always to maintain with something new the old sequence inside the new sequence. It’s a problem you can find examples of, when you are in a new situation, but your desire is to maintain something of the old situation. To maintain really something of the old situation in the new situation, you must create something new. That is the newness of the old sequence, the new forms of the old sequence because what is finished is finished. So if you want to maintain what is finished you must create something new beyond this end. And it’s always a very interesting position, for example, a new vision of what is a god, to maintain god, finally, but to maintain the god of the second sequence inside the third sequence, we must modify the concept of god and to create a god appropriate to the third sequence. But that is a reactive position, a reactive subjectivity. The most important point is to maintain the old form of the problem.

Concerning the second choice is my discussion with Deleuze or Spinoza, and I think that life is not a possible name for a new form of a relationship between the one and the infinite. I think that life is a purely blind process, a chemical blind process. And so there is no creative possibility in the sense of true thinking in life as such. It’s a very complex discussion naturally. Very often in thinking we must work against the blind process of life and not with it. And so we must find the origin of novelty, not in continuity of life, but in some ruptures, life as such in it’s creative process, which is a blind process, completely blind, completely neutral, completely indifferent to our destiny. Human beings can disappear like old monsters. There is nothing in life for us, naturally. We must live. Without life there is nothing at all certainly, but it’s not because without life there is no thinking. Thinking is with life.

Concerning the third position, I think that a new paganism is, for me, naturally also a reactive subjectivity, a reactive position, but most important for me, it’s a purely aesthetic position, very beautiful in some sense. Mythology, many gods and so on is really an aesthetic world, and to create a new mythology is a temptation, is something interesting, but for aesthetic reasons, finally, much more than existential reasons. And the weak god, the poor god, I think it’s only a projection of our experience, and today more than ever our experience that a new truth, a new norm, a real creation is always weak at the beginning. But there is always a real weakness of a new creative disposition, especially today because, for objective reasons, power is not on the side of creation. Power is on the side of pure continuation of what exists, and power is on the side of abstraction because money is abstraction, and money is the most important symbol of power today. And so It’s true, it’s a reality that a new truth is like a weak god, that a weak god, a poor god is on the side of creativity of truth today. We cannot have today simultaneously truth and glory, truth and power, truth and strengths. There is something weak, something poor in all what is really important today from the point of view of human beings, which are not purely animals. It’s true that we can have a good life without any relationship with truths, new gods, universality and so on today because a norm of a good life is a norm of the market. And so if we want the way of a new truth and in the condition where we have no guarantee on the side of the relationship between the one and the infinite, certainly the beginning of all that is perfectly weak, perfectly without any real importance for the world as it is.

And I think that the idea of a new weak god, a poor god is only a projection of that sort of situation, a sort of generalization of a sort of image, if you want, of our situation today, which is that novelty is without glory, without immediate potency. That is absolutely the situation. And it is why I think that we must do the choice of the multiplicity as such without any form of transendency, without any immanence, fusion between the One and the infinite, and without a good, even a poor, immanent god. But, once more, difficulties are numerous, and I don’t begin with difficulties today but only tomorrow. Thank you.