Badiou’s ‘Existence and Death’ (translation with Alberto Toscano)

Alain Badiou, Nina Power and Alberto Toscano
Vol. 24, No. 1, Mortals to Death (Winter 2002), pp. 63-73
A translation of a short text by Alain Badiou on questions of existence and death that discusses Descartes, Sartre, Kant, Cantor, Spinoza.
[Complete text follows below]

Existence and Death

Alain Badiou

Translated by Nina Power and Alberto Toscano

1. Being and Existence, Life and Death

“Thus speaks the Lord God: I exist!” Is it not indeed a privilege of the divinity to be able, in all creative certainty, to utter his own existence? That Descartes links the “I think” to an “I am,” indiscernible in Latin from an “I exist,” probably has the sole effect, as has been noted for some time, of transferring the attributes of transcendence to Man. The ontological kinship is striking between the God who proffers “ego sum qui sum,” which Gilson interpreted as the identity, in God, of pure existence and essence, and the “cogito, existo” by which a point-subject comes to support, by the evidence of his act alone, the entire reconstruction of certainties. This is because Descartes endows the subject, prior to any substantiality, with this interior transcendence that is called freedom. This is why the existentialist Sartre, for whom, as one knows, existing is originary, ante-predicative, and preliminary to any identity that one may ascribe to it, recognized in Descartes one of his most determinate predecessors. He found proof of this in the Cartesian assertion according to which freedom, as pure power of affirmation or negation, is just as infinite in man as it is in God. Freedom, this subjective name of existence.

But if existence as freedom is the infinite power of negation, then one must indeed come to declare that its “essence” is nothingness, a statement that in effect is the cornerstone of the Sartrean edifice. For [End Page 63] in being “nothing” but the power of nihilation (néantisation) of every given of being, freedom, or existence—ek-sistence, that which holds itself outside all of the identities that a consciousness confers upon itself—cannot be anything but the being of this nothing, or, nothingness as the generic name of every particular “nothing.” It is this “Cartesian” motif of the subject as infinite-existence in and by freedom that supports the famous Sartrean definition of consciousness, that is to say of existence: “a being that is in its being the question of its being, insofar as this being implies a being other than itself.” A definition about which a humorist once remarked that it used the word “being” five times only to designate nothingness. The immediate consequence of this definition is indeed that consciousness is not what it is, and is what it is not. If existence is infinite freedom, it is the constant putting back into question of its being, never identifying itself with the forms of being that it takes on, and holding itself beyond these forms which are nothing but its singular outside, or its transitory objectifications. Another of Sartre’s formulas: existence transcends its own being. As if to say that it is pure negativity, and that, were one to attempt to inscribe it within an ontological set-up, one would need to admit that existence is what objects to any being which one would presume to be “its own,” that it is its “surpassing,” and that therefore it is not this being; and of any being which one presumes is not “its own,” one would need to recognise that existence can be its conscious aim, in the free spoliation of its own being, and that therefore existence is this being. Now, the only appropriate name of that which is not being, and is what no being can be, is assuredly nothingness.

Existence, in a Sartrean or Cartesian sense, and moreover in a Lacanian, as well as in a Hegelian sense, distinguishes itself from being to the exact degree that it is nothingness. To exist is to be free, and therefore indeterminate with regard to being, prey to the work of nothingness. Existence gnaws at being or makes a hole in the real. The only being of existence is the lack-of-being (manque-à-être).

But isn’t then death to life exactly what existence is to being? For death is no more exterior to life than nothing-consciousness (la conscience-néant) is to being. Just as it is only by transcending any presupposed being that consciousness affirms itself as freedom, and therefore as nothingness, so it is only because it is haunted by the originary dissolution of its own vital composition that an organism affirms itself as living, or as participating in life. Death transcends any particular life, like freedom transcends any form of being. For death is that whereby all successive forms of the living are deposed and terminated to the advantage of the single formless power of life, élan vital for Bergson, inorganic life for Deleuze, blind folds of DNA molecules for contemporary biology. The infinite value of life [End Page 64] affirms itself only through death. Only the constant disappearance of billions of singular individuals, of millions of specific forms, attests that vital affirmation and its particular chemistry are generic forces of being, indifferent to what manifests them. Death is, for any particular living thing, the transcendence of life in it. Death is that whereby, beyond the derisory being-multiple of living individuals, the existence of life affirms itself. Every time that a living thing dies, what is silently spoken is: “I, life, exist.”

The freedom of life is precisely that every living thing be mortal, just as the freedom of consciousness is that none of its states define it, and that it transcends them all. The evolution of species and the conversions of consciousness say the same thing. The detail of beings is nothing in the eyes of what makes them be and which, itself, is not: nothingness as consciousness (of) self, the existence of life as death.

We can thus shed light upon the secret philosophical complicity between the theories that ground sense in the intentionalities of consciousness (let us say, to be brief, phenomenological orientations) and the, at first glance, completely opposing theories which make life into the active name of being (let us call these the vitalisms: Nietzsche, Bergson, Deleuze). This complicity rests upon the axiomatic admission of a term that has the power to transcend the states that deploy, or unfold it, so that any singularity of being is only thought with precision in the finest possible description of the single act which both constitutes it and relates it to the One, of which it is a transitory mode. Of course, the One-term is in the first case intentional consciousness, whose real figures are the constitutive acts, and in the second case inorganic life, its power or élan, of which organisms, and ultimately all actual singularities, are evanescent modalities. But the movement of thought is the same, posing at the edges of the in-existent (the free nothingness of consciousness, the chaotic formlessness of life as such) a kind of over-existence whose creative activity is unfolded in the infinite multiplicity of what is (states of consciousness, or figures of the subject, and living individuals). Thus to exist means: to be in the constitutive movement of the originary over-existence. Or: to exist is to be constituted (by consciousness, by life).

But to be constituted also means to be nihilated (néantisé). For the constitutive act only proves its over-existence in the deposition (the precariousness, the mortality) of what it constitutes. A state of consciousness is ultimately nothing but its dissolution in time, which is why Husserl directed his enterprise towards an infinite description of the temporal flux as such. “Intimate time-consciousness,” which is the passage of death within constituted consciousness, affirms, in [End Page 65] an exemplary way, the over-existence (the intemporality) of constitutive consciousness. And, as we have already remarked, the death of a singular life is the necessary proof of the infinite power of life.

We can therefore say that the term common to both phenomenology and vitalism is death; death attests for finite existence, which is the simple modality of an infinite over-existence, or of a power of the One that we would only come to experience ‘in reverse’: in the passive limitation of everything that it has deigned to constitute, or, as Leibniz would say, to fulgurate.

Let us say that in both cases the guarantee of the One as constitutive power (natura naturans, as Spinoza put it) is the mortality, or finitude, of the multiple as constituted configuration (natura naturae: states of consciousness, actual individuals). Death is the only proof of life. Finitude is the only proof of the transcendental constitution of experience. And, in both cases, there operates in the background a secularized, or sublimated, God, over-existing puppeteer of being. One can call it life, Consciousness, or—like Spinoza—Substance. It is always with Him that we are dealing, this underlying infinite of which death is the terrestrial writing.

To tear earthly existence away from its mortal correlation requires that one also axiomatically tear oneself away from the phenomenological constitution of experience, as well as from the Nietzschean nomination of being as life.

To think existence without finitude. This is the liberating imperative, which saves existing from being pinned to the ultimate signifier of its submission, death.

It is true, as Hegel said, that the life of spirit (that is, free life) is that which “does not retreat before death and maintains itself within it.” This means: the life indifferent to death. The life that does not measure its actuality in terms of either the transcendental constitution of experience or the chaotic sovereignty of life.

Under what conditions is existence, our own, the only that we can attest to and think, the existence of an Immortal? It is, and Plato and Aristotle were at least in agreement on this point, the only question of which it can be said that it pertains to philosophy, and to it alone.

2. Being, Appearance, Truth

Let us pose, in the style of ancient atomism, that being is pure multiplicity, without ground or sense. Let us take the mourning of the One to its ultimate consequences: there is no constitution of experience, there is no generic life. There is only the flat surface of[End Page 66] multiplicities. Ever since the Greeks, the thought of this surface bears the name of mathematics: that which is only concerned, in a multiplicity, with its being-multiple, to the exclusion of any quality as well as of any intensity.

Under these conditions, for a multiple to be is to belong to another multiple, whose being is already presupposed. We will call this referential multiple a “situation,” such that it dispenses its slight being to everything that inscribes itself within it as an element. One will then say that to be is to belong to a situation. If we retain the formalism of set-theory, as it is taught in schools, and whose appropriation to an ontology of neutral multiplicity is not in doubt, if e is the multiple of which existence is affirmed, and if S is the referential situation, the statement that assures the being of e is written:

Nevertheless, this assertion of being does not yet tell us in what sense the element e exists. For existence is nothing if not a quality of being.

On this point, one must reverse the Kantian reversal of Descartes. Descartes intended to prove the existence of God on the basis of the fact that perfection of the divine, or his infinity, as it can be ideally formulated, would be contradicted by his inexistence, considered as an imperfection. In other words: our idea of the infinite is coherent. Now, that the infinite does not exist de-infinitizes it (or subtracts a thinkable perfection from it), thus introducing a contradiction. Therefore, the infinite exists.

This is certainly exact: Cantor has shown that the infinite exists. However, it is by no means required that this infinite be a God. Rather, it is “like a Number.”

Kant believes that he is refuting the Cartesian argument by arguing that existence is not a predicate or a quality of the thing. To be blue, one must exist, but to exist . . . Thus, you cannot move from the concept to its existence. But Kant makes short shrift, in this matter, of the innumerable demonstrations of existence attested to by mathematics. Descartes is right in saying that given a concept, the existence it subsumes can be the object of a demonstration, generally an apagogic one (reductio ad absurdum): if the thing subsumed did not exist, there would be a contradiction in the concept, which is presumed to be coherent. And this is indeed what Descartes says. If God does not exist, our ideal universe is incoherent, which cannot be the case. Why can’t this be the case? Because we see that it is coherent (clear and distinct idea). To tell the truth, [End Page 67] Kant also presupposes that our conceptual universe is coherent. It is an axiom of thought in general.

The weakness of Descartes’ argument does not in any way lie in the idea that existence can be a predicate, or a property. Being, the pure multiple, is not a property. But existence is. For something can be without existing, as mathematics shows us all the time. This is the case, for example, with irrational length for the mathematicians of Ancient Greece. Its being is not in doubt. But what are we to say of its existence? Take the infinitesimal in Leibniz. Its being is coextensive with its thought, therefore it is. But for Leibniz it does not exist, being nothing but a useful fiction. This is because existence is a singular quality of being, an intensity of being, and not simply the being that every concept presupposes. Anyone who remains unmoved by the sirens of empiricism (they awoke Kant, but perhaps he would have done better to remain asleep) must hold firmly to the distinction between being and existing, which implies that existence is a singular quality of being that can be the object of a proof. One will nevertheless maintain that only what is has the power to exist, allowing for the fact that being could inexist (and be the object of a proof of inexistence).

What must be objected to Descartes is by no means that it is impossible to prove the existence of the infinite, or that existence is not a property. For it is with regard to the being of the infinite that Descartes goes astray, not with regard to its existence. Descartes imagines that the infinite, the One, or God, are the same being. Nothing of the sort. The infinite is itself pure multiplicity, a multiplicity of multiplicities. The infinite is the number of beings in general. This is stated as follows: every situation is infinite. Consequently, since existing presupposes to begin with that one is, and since to be is to belong to a situation, we can also say: it is in the being of existence to inscribe itself within the infinite.

If we now add that existence is a quality of the being-existent, an intensity of what makes a being-multiple be, the formula becomes: existence is the proper intensity with which a multiple inscribes itself into the infinity of a situation.

To exist is to participate, to a measurable degree, in the infinite.

Therefore one always exists more or less. Let us say that given a multiple e, its existence, which is its degree of being, expressed in the exact value of the formula , will be set between “absolute” existence (the belonging of e to the infinite S is certain and complete, the formula is true) and inexistence (the belonging of e to the infinite S is proven to be null, the formula is entirely false: the being e inexists in S). These two extreme polarities of existence by no means exclude that there be others, more or less numerous [End Page 68] and nuanced, which amount to saying that the multiple e exists in S “to a certain degree.” All of this depends on the existential resources of the situation S.

But what exactly is the “existential resource” of the situation S? To comprehend it, we must again think of the obligation, for any multiple, to only be “present”—and thus to be, period—insofar as it belongs to a situation. This obligation results from the fact that there is no Whole (Tout). That there is no referential Totality, no single, stable Universe (or for that matter any universal History) is a point which, in the mathematical theory of the pure multiple, is demonstrable: it is inconsistent to posit a set of all sets, which means: the total Multiplicity (which would actually be a One-All [Un-Tout]) cannot come to be.

But if there is no Whole, the being of a multiplicity, having no “cosmic” place in which to affirm itself, presupposes a particular, or local, referent. Being is necessarily tied to its presencing localization, whose space is the (infinite) situation to which it belongs. Being is essentially being-there (Da-sein). And that which fixes localization is never anything but a multiple that is “already-there” (whose being is proven), and which is the S of every e, its situation.

Now, how does the situation confer upon the multiples belonging to it their localization? What is the “there” of being-there? In a given situation, the localization of a pure multiple can only be fixed by a network of relations which determines its difference from the other elements of the situation.

We shall call appearance that which, of being as such (a mathematical multiple), is caught in a situated relational network, such that one can say that this being is more or less different from that other being.

Ontologically, a multiple could not differ “more or less” from another. A multiple is only identical to itself, and it is a law of being qua being that the least local difference, bearing for example on a single element amidst an infinity of others, entails an absolute global difference. According to appearance this is not the case. It is clear that in a situation, multiples can differ more or less, resemble or neighbor each other, etc. One must therefore recognise that what governs appearance is not the ontological composition of a particular being (a multiple), but the relational evaluations fixed by the situation and localized within it. Unlike in the legislation of the pure multiple, these evaluations do not always identify local difference with global difference. They are not ontological. This is why one will call logical the laws of the relational network which fix the appearance in a situation of being-multiple. Every situation possesses a logic, which legislates upon appearance, or upon the “there” of being-there. [End Page 69]

The minimal requirement for any localization is the possibility of fixing a degree of identity (or of non-identity) between an element a and an element b, supposing that both belong to the situation. One therefore has grounds to think that there exists in every situation what we will call a function of appearance, which, given two elements of the situation S, measures their degree of identity. We will write the function of appearance as i(a,b). It denotes the degree to which, based on the logic of the situation, we can say that the multiples a and b appear identical.

But what are the values of the function of appearance? What measures the degree of identity between the apparitions of two multiplicities? Here again, there is no general or totalizing answer. The standard of evaluation of appearance, and therefore the logic of a situation, depends on the situation. What can be said is that, in every situation, such a standard exists.

We will call what, in any given situation, works as the domain of evaluation of the identities and difference of appearance, the transcendental of the situation. Like everything that is, the transcendental is a multiple, which, of course, belongs to the situation of which it is the transcendental. But this multiple is endowed with a structure authorizing that on its basis the values (the degrees) of identity between two multiples that appear in the situation are set out.

This structure has properties that vary according to the situation. But it also has invariable general properties, without which it could not operate. There is a general mathematics of the transcendental, which we of course will not here venture into. 1

Simply, let us say that every transcendental possesses a minimum value, µ, and a maximum value, M. Given two elements of the situation, a and b, if the function of appearance i(a, b) has a value µ, it is because the identity in situation of a and b is minimal, which, for whomever “inhabits” this situation, means that it is null: in effect, from the interior of a situation, the minimum necessarily functions as an expression of nullity or of the zero. In this case, one will therefore say that a and b are absolutely distinct. Now, if the function i(a, b) has the maximum value M, this means, for any inhabitant of the situation S, that a and b are absolutely identical. If the value of the function of appearance is neither µ nor M, a and b appear as neither identical nor absolutely different. They have a certain degree of relatedness, expressed by the value, in the transcendental, of the function i(a, b).

We can now give a rigorous definition of existence. We call existence of any multiple whatsoever, relative to a situation, the degree according to which, in this situation, the multiple appears as identical to itself. [End Page 70]

Formally, the existence of the being a, relative to a situation S, is the value of the function of appearance i(a, b) in the transcendental of the situation.

If, for example, i(a, a) = M, which means that the self-identity of the appearance of a is maximal, one will say that, in the situation S, a exists absolutely, or that the existence of a is coextensive with its being. If instead i(a, a) = µ, one will say that the existence ofa in the situation S is null, or that a inexists in S. This means that its existence is totally unhinged from its being. There will also be the intermediary cases, in which the element a exists “to a certain degree.”

It is essential to see that existence as such is not a category of being, but a category of appearance. Or, put more rigorously, that existence pertains to the logic of being, and not to its ontological status. It is only according to its being-there, and not according to its multiple composition alone, that a being can be said to exist. And this saying is at the same time that of a degree of existence, placed between inexistence and absolute existence. Existence is at once a logical concept and an intensive concept.

3. Death Revisited

One is tempted to say that a being is dead when, in its referential situation, its degree of existence is minimal, or when it inexists in the situation. Affirming of a being e that it is dead would amount to acknowledging that one possesses the equation: i(e,e) = µ.

This also means that death is the absolute non-identity to self, the loss of this logical minimum of existence that is a non-null value of identity.

However, this would be to ignore that death is something other than existence. Death happens (survient). And necessarily it happens to the “living,” or in any case to the existing. Here lies all the profundity of the canonical platitude: “a quarter of an hour before his death, he was still alive,” which resists mockery, as one experiences its truth with pain and stupefaction when beside a seriously ill person.

One will thus say that death is the coming of a minimal value of existence for a being endowed with a positive evaluation of its identity.

Formally, we have the death of a being e when we “pass” from the existential equation i(e,e) = r (where r is a non-minimal value, let us say, r>µ) to the equation i(e,e) = µ.

Note that death is not of the order of being. It is a category of appearance, or, more precisely, of the becoming of appearance. Or: death is a logical, and not an ontological, concept. All that can be [End Page 71] said about “dying” is that it is an affection of appearance, which makes one “pass” from an existence in a situation that can be positively evaluated (even if it is not maximal) to a minimal existence, that is to say, an existence that is null relatively to the situation. No “in itself,” moreover, can have any sense for a given multiple. One can only call ontologically “null” the empty set, which, presented or unpresented, is never exposed to dying, nor even to “passing” from one degree of existence to another.

The entire problem lies in knowing of what such a “passage” consists. In order to have complete understanding of this point, nothing less is required than a theory of natural multiples, accompanied by a theory of the event. 2 We will restrict ourselves to two remarks.

1. The passage from a value of identity, or of existence, to another, could not be an immanent effect of the being in question. For this being has precisely no other immanence to the situation, and consequently to its own identity, than its degree of existence. The passage results necessarily from an external cause that affects, locally or globally, the logical evaluations, or the legislation of appearance. In other words, what comes to pass in death is a change in exteriority of the function of appearance of a given multiple. This change is always imposed on the being that dies, and this imposition is contingent.

The right formula being that of Spinoza (Ethics III P4: “No thing can be destroyed except by an external cause”), it is impossible to say of a being that it is “mortal,” if by this one understands that it is internally necessary for it to die. At most one can admit that for it death is possible, in the sense in which it can be overcome by a drastic change in its function of appearance, this change being a minimalization of its identity, and thus of its degree of existence.

2. It follows that the “meditation on death” is vain, as Spinoza himself declares (Ethics IV P67). For death is but a consequence, and what thought must turn towards is the event upon which depends the local alteration of the functions of appearance.

Finally, existence and death, logical parameters of what in a situation, comes to appear, are only thinkable insofar as one passes through the ontological theory of the pure multiple (mathematics of sets) and through the logical theory of the relations of identity (mathematics of categories). Existence and death name the interval of these two superimposed mathematics. Pertaining at once to being, the immutable entanglement of thinkable multiplicities, and to appearance, the power of localization of intensities, to exist and to die are modes of being-there. [End Page 72]

Alain Badiou was born in Morocco in 1937. He has taught at Université Paris-VIII and is currently the head of the department of philosophy at l’Ecole Normale Supérieure. His books include L’Etre et l’événement (Seuil, 1988; English translation by Oliver Feltham forthcoming from Athlone Press, 2002), Manifesto for Philosophy (SUNY Press, 1999), Ethics: An Essay on the Understanding of Evil (Verso, 2001), Beckett: L’increvable désir (Hachette, 1995), Saint Paul et la fondation de l’universalisme (PUF, 1997), Deleuze: The Clamor of Being (U of Minnesota P, 2000), and the novel Calme bloc ici-bas (P.O.L., 1997).

Nina Power is a Masters student at the University of Warwick. She is currently translating Alain Badiou’s writings on Samuel Beckett and has recently published articles on Nietzsche and atomism.

Alberto Toscano is currently completing doctoral research on Gilles Deleuze and the philosophy of individuation at the University of Warwick. He is an editor of Pli: The Warwick Journal of Philosophy and, with Ray Brassier, of Alain Badiou’s Theoretical Writings (Continuum, 2003).


1. Presented and commented upon in a seminar, the mathematics of the transcendental is contained in a booklet, a new edition of which will be available in January 2000.

2. One will find these developments (natural multiples and the event) in L’être et 1’événement (Paris: Seuil, 1988).