Towards a New Concept of Existence by Alain Badiou

Tonight I am not going to engage in any kind of criticism. Instead, I intend to propose a new concept of existence. And I shall be as abstract as this intention forces me to be. You can find a less arid but not complete exposition in a chapter of my “Briefings on Existence,” and a complete one in my last book, Logiques des mondes, which is out in French and will be published in English at the end of next year, I hope.

As all of you know perfectly well, the fundamental problem is to distinguish on the one hand, being as such, being qua being, and, on the other hand, existence, as a category which precisely is not reducible to that of being. It is the heart of the matter. This difference between being and existence is often the result of the consideration of a special type of being. It is the case for Heidegger, with the distinction between Sein and Dasein. If we take into account the etymological framework, we can see that “existence,” which depends on Dasein, is a topological concept.  It means to be here, to be in the world.  And in fact, I also shall propose to determine the very general concept of “existence” by the necessity of thinking the place, or the world, of everything which is.  And this place is not deducible from being as such.

But clearly for Heidegger, Da-sein, and finally, existence, is a name for human being, for historical destiny of thinking, for crucial and creative experience of the becoming of being itself. I shall propose a concept of being-here and of existence without any reference to something like consciousness, experience, or human being.  I shall construct before you a pure relational concept of the slight distance between a multiplicity and the same multiplicity here, in its place, in a world.

If we now examine the work of Sartre, we can see that the distance between being and existence is a dialectical consequence of the difference between being and nothingness.  In fact, existence is the effect of nothingness within the full and stupid massiveness of being qua being.  This effect is the absolutely free subject in whom existence precedes essence.

I shall also propose to determine the concept of existence under the condition of something like negation.  Ontologically, it is for me the question of the void, the question of the empty set.  Logically, it is the question of negation, in its intuitionist sense.  But all that will have no relationship with something like a subject, and even less with freedom.

You will certainly notice that I am taking something from Kant: precisely, that existence is something like a degree or an intensity, of being-there or of being–in–the-world.  This idea we can find in the famous passage of the first Critique, concerning the anticipations of perception.  And I am taking something from Hegel, namely, that existence has to be thought as the movement from pure being to being-there, or from essence to phenomenon, or appearing, or seeming—as Hegel explains in two obscure and profound chapters of his Logics.  But I am attempting to do the same thing without a transcendental subject, and without the becoming of the absolute idea.  My proposal will be in three parts.  First, a very short ontological part.  What is our concept of being qua being?  The answer will be: multiple, a multiplicity.  Second, what is our concept of the localization of something which is?  What is being-there? The answer will be: a transcendental field, without subject.  Third, what is existence? The answer will be: the degree of something’s identity to itself in a world is its existence in this world.

“What is a thing?”  It is the title of a famous Heidegger essay.  What is a thing as some thing which is without any determination of its being, except precisely being as such?  We can speak of an object of the world.  We can distinguish it in the world by its properties or predicates.  In fact, we can experience the complex network of identities and differences by which this object is clearly not identical to another object of the same world.  But a thing is not an object.  A thing is not yet an object.  Like the hero of the great novel by Robert Musil, a thing is something without qualities.  We must think of the thing before its objectivation in a precise world.

The Thing is: das Ding, maybe das Ur-Ding.  That is this form of being which certainly is after the indifference of nothingness, but also before the qualitative difference of object.  We must formalize the concept of “thing” between, on the one hand, the absolute priority of nothingness and, on the other hand, the complexity of objects.  A thing is always the pre-objective basis of objectivity.  And that is the reason for which a thing is nothing other than a multiplicity.  Not a multiplicity of objects, not a system of qualities, a network of differences, but a multiplicity of multiplicities, and a multiplicity of multiplicities of multiplicities.  And so on.  Is there an end to that sort of “dissemination,” to speak like Jacques Derrida?  Yes, there is an end point.  But this end point is not a primitive object, or an atomic component, it is not a form of the One.  The end point is of necessity also a multiplicity.  The multiplicity which is the multiplicity of no multiplicity at all, the thing which is also no-thing: the void, the empty multiplicity, the empty set.  If a thing is between indifference and difference, nothingness and objectivity, it is because a pure multiplicity is composed of the void.  The multiple as such has to do with difference and pre-objectivity.  The void has to do with indifference and complete lack of object.

From the work of Cantor at the end of the 19th century, we know that it is perfectly rational to propose that sort of construction of pure multiplicities from the void, as a framework for mathematics.  That’s why I have written that if ontology is the science of the thing, of the pure “something,” we must conclude that ontology is mathematics.  The thing is formalized as a set; the elements of this set are sets; and the point of departure of the whole construction is the empty set.

Our question now is to understand the birth of objectivity.  How can a pure multiplicity, a set, appear in a world, in a very complex network of differences, identities, qualities, intensities and so on?

It is impossible to deduce something like that from the purely mathematical thinking of the multiplicities as sets of sets, ultimately composed of the purity of the void.  If ontology as a theory of things without qualities is mathematics, phenomenology as the theory of appearing and objectivity concerns the relationship between qualitative differences, problems of identities and of existence.  And all that is on the basis of a place for appearance, or for being-there, a place we name: a world.

After the mathematics of being qua being we have to develop the logic of the worlds.  Unlike the logic of things, which are composed of sets of sets, the logic of worlds cannot be purely extensional.  This logic must be that of the distribution of intensities in the field where multiplicities not only are, but also appear here, in a world.  The law of things is to be as pure multiplicities (as things), but also to be-there as appearing (as objects).  The rational science of the first point is mathematical ontology.  The rational science of the second point is logical phenomenology, in a much more Hegelian than Husserlian sense.  Against Kant, we have to maintain that we know being qua being and that we also know the way by which the thing as such appears in a world.  Mathematics of multiplicities, logics of the worlds, that is—if we adopt the Kantian distinctions—our first two “critics”.  The third one is the theory of event, truth and subject.  But I am not going to talk about that today.  Existence is a general category of the logic of appearance, and we can talk about existence completely apart from any consideration about subjectivity.  In the framework of the present paper, “existence” is an a-subjective concept.

Let us suppose now that we have a pure multiplicity, a thing, which can be formalized as a set.  We want to understand what is exactly the appearing, or being-there, of this thing, in a determinate world.  The idea is that when the thing, or the set, is localized in a world, it is because the elements of the set are inscribed in a completely new evaluation of their identities.  It becomes possible to say that this element, for instance x, is more or less identical to another element, for instance y.  In classical ontology, there are only two possibilities: either x is the same as y, or x is not at all identical to y.  You have either strict identity, or difference.  By contrast, in a concrete world as a place for being-there of multiplicities, we have a great variety of possibilities.  A thing can be very similar to another, or similar in some ways and different in others, or a little identical to, or very identical but not really the same, and so on.  So every element of a thing can be related to others by what we shall name: a degree of identity.  The fundamental characteristic of a world is the distribution of that sort of degrees to all multiplicities which appear in this world.

So, in the very concept of appearing, or of being-there, or of a world, we have two things.  We have first a system of degrees, with an elementary structure which authorizes the comparison of degrees.  We must be able to observe that this thing is more identical to this other thing than to that third thing.  So the degrees certainly have the formal structure of an order.  They admit, maybe within certain limits, the “more” and the “less.”  This structure is the rational disposition of the infinite shades of a concrete world.  I name the ordinal organization of the degrees of identities: the transcendental of the world.  Second of all, we have a relationship between the things, (the multiplicities) and the degrees of identities.  That is precisely the meaning of being-in-a-world for a thing.  With these two determinations we have the meaning of the becoming object of the thing.

Let us suppose that we have a couple of elements of a multiplicity which appears in a world.  A degree of identity corresponds to this couple.  It expresses the “more” or “less” of identity between the two elements in this world.  So, to every couple of elements there corresponds a degree of the transcendental of the world.  This relationship we call: an identity function.  An identity function which is active between some multiplicities and the transcendental of the world is the fundamental concept of the logic of being-there or of appearing.  If a pure multiplicity is a thing, a multiplicity with its identity-function is an object in a world.

So the complete logic of objectivity is the study of the form of the transcendental, as a structural order, and the study of the identity function between multiplicities and the transcendental.

Formally, the study of the transcendental is the study of some types of structural order; it is a technical matter.  There is here an interplay between formal fragments of mathematics and logics and fundamental philosophical intuition.  And the study of the identity function is in fact the study of an important philosophical problem : the problem of the relationship between things and objects, between indifferent multiplicities and their concrete being-there.  Here we can restrict ourselves to three points.

First, it is very important to remember that there are many types of orders, and therefore many possibilities for the logical organization of a world.  We have to assume the existence of an infinite multiplicity of different worlds, not only at the ontological level (some multiplicity, some thing, is in a world and not in another world), but at the logical level, the level of appearing and existence.  Two worlds with the same things can be absolutely different from each other, because their transcendentals are different.  That is to say: the identities between elements of the same multiplicity can radically differ at the level of their being-there, from one world to another world.

Second of all, there always are some limits of intensity of appearing in a world.  That is to say: a degree of identity between two elements varies between two limit cases : the two elements can in fact be “absolutely” identical, practically indiscernible in the logical framework of a world ; they can also be absolutely non-identical, absolutely different from each other, without any point in common.  And between these two limits, the identity function can express the fact that the two elements are neither absolutely identical, nor absolutely different.  You can easily formalize this idea.  You have, in the transcendental order, a minimal degree of identity, and a maximal degree of identity.  And most of the time you have a whole lot of intermediate degrees.  So, if, in a world, for a couple of elements, the identity function takes the maximal value, we say that the two elements are, in this world, absolutely identical, or have the same appearing, or the same Being-there.  If the identity function takes the minimal value, we say that the two elements are absolutely different from each other, and if the identity function takes an intermediate value, we say that the two elements are identical to some extent, an extent which is measured by the intermediate transcendental degree.

Third of all, there are structural laws of the transcendental which let us speak of more global determinations of an object.  We can examine for example the intensity of the being-there of a part of the world, and not only of some elements of it, or we can develop a theory of the smallest parts of an object, what I call the atoms of appearing.

We have here a profound and difficult understanding of what happens to a multiplicity when it really appears in a world, or when it is not merely reducible to its pure immanent composition.  The appearing multiplicity must be understood as a very complex network of degrees of identity between its elements, parts and atoms.  We have to take care of the logic of its qualities, and not only the mathematics of its extension.  We must think, beyond its pure being, of something like an existential intensity.

There I have said it: existence, existential.  I am finally under the title of my lecture.  What is the process of definition of existence, in the transcendental framework of appearing, or being-there? I give you immediately my conclusion: Existence is the name for the value of the identity function when it is applied to one and the same element.  It is, so to speak, the measure of the identity of a thing to itself.

Given a world and an identity function having its values in the transcendental of this world, we will call “existence” of a being that appears in this world, the transcendental degree assigned to the identity of this being to itself.  Thus defined, existence is not a category of being (in mathematics), it is a category of appearing (in logic).  In particular, “to exist” has no sense in itself.  According to an intuition of Sartre’s, “to exist” can only be said relatively to a world.  In effect, existence is a transcendental degree which indicates the intensity of appearance of a multiplicity in a determined world, and this intensity is in no way prescribed by the pure multiple composition of the being in consideration.

We can apply to existence the formal remarks of the previous part of my lecture.  If, for instance, the degree of identity of a thing to itself is the maximal degree, we can say that the thing exists in the world without any limitation.  The multiplicity, in this world, completely affirms its own identity.  Symmetrically, if the degree of identity of a thing to itself is the minimal degree, we can say that this thing does not exist in this world.  The thing is in the world, but with an intensity which is equal to zero.  So we can say that its existence is a non-existence.  We have here a striking example of the distinction between being and existence.  The thing is in the world, but its appearance in the world is the destruction of its identity.  So the being-there of this being is to be the inexistent of the world.  The theory of the inexistent of a world is very important.  I have shown that the situation of the inexistent is fundamental in Jacques Derrida’s work.

Often, the existence of a multiplicity in a world is neither maximal nor minimal.  The multiplicity exists to some extent.

To conclude I would summarize this abstract theory with a question linked to the concept of existence: the question of death.

To understand the question of death, it is essential to remember that it is only by its being-there that a being exists, and that this existence is that of a degree of existence, situated between inexistence and absolute existence.  Existence is both a logical concept and an intensive concept.  It is this duel status that permits us to rethink death.

We are first tempted to say that a thing is dead when, in the world of reference, its degree of existence is minimal, or when it inexists in this world.  Asserting that a thing is dead would be tantamount to concluding that identity of the thing to itself is equal to the minimal degree.  This would also means that death is the absolute non-identity to self.  But absolute non-identity to self defines inexistence, and not death.  Death must be something other as inexistence, because death happens, and this « happening » necessarily concerns an existent, and not the inexistent of the world.  We  define death as the coming of a minimal value of existence for a thing endowed with a positive evaluation of its identity, and not the minimal value as such.  All that can be asserted of “dying” is that it is a change in appearing, the effect of which is that a thing passes from an existence with a positive intensity—even if it is not maximal—to an existence that is minimal, that is to say null relatively to the world.  The whole problem is what does such a passage consist of? We limit ourselves to two remarks.

1) The passage from one identity or existence value to another cannot be an immanent effect of the multiplicity concerned.  For this being has precisely no other immanence to the situation, and consequently to its own identity, as its degree of existence.  The passage is necessarily the result of an exterior cause, which affects, locally or globally, the logical evaluations, or the laws of the Being-there-in-the-world.  In other words, what occurs in death is a change in the identity function of a given multiple.  This change is always imposed on the dying thing, and this imposition comes from outside the thing.  The precise proposition is Spinoza’s: “No thing whatever can be destroyed, except by an exterior cause.”  So it is impossible to say of a multiple that it is “mortal”.

2) It follows that the meditation of death is in itself vain, as Spinoza also declares: “The free man thinks of nothing less than of his death, and his wisdom is a meditation on life, and not a meditation on death.”  It is because death is only a consequence.  What thought must turn towards is the event which locally transforms the identity function.

All of this indicates why we cannot agree with a philosophy of mortality and finitude.  There is no ontological status of death.  Of no existent we can say that it is a “being-for-death”.  Because existence is a transcendental degree and nothing else, we must ask with Saint Paul: “Death, where is thy victory?”  Dying, exactly like existing, is a mode of being-there, and therefore a purely logical correlation.  The philosophy of death is included in one sentence: Do not be afraid by the logic of a world, or by the games of existence.  We are living and dying in many different worlds.

Alain Badiou’s Biography

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