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Alain Badiou “Logics of Worlds” (V-VII raamat ja kokkuvõte)

Badiou, Alain 2009 [2006]. Logics of Worlds. Being and Event, 2. London, New York: Continuum.

Book V. The Four Forms of Change

Truth be told, we cannot find the means to identify change either in the order of mathematics, the thinking of being qua being, or in that of logic, the thinking of being-there or appearing. To put it bluntly: the thinking of change or of singularity is neither ontological nor transcendental. (357)

We will call  ‘modification’ the rule-governed appearing of intensive variations which a transcendental authorizes in the world of which it is the transcendental.Modification is not change. Or better, it is only the transcendental absorption of change, that part of becoming which is constitutive of every being-there. (359)

So what is the source of the real change that certain worlds undergo? An exception is required. An exception both to the axioms of the multiple and to the transcendental constitution of objects and relations. An exception to the laws of ontology as well as to the regulation of logical consequences. (360)

It is necessary to think dis-continuity as such, a discontinuity that cannot be reduced to any creative univocity, as indistinct or chaotic as the concept of such a univocity may be. (362)

Take any world whatever. A multiple which is an object of this world—whose elements are indexed on the transcendental of the world—is a ‘site’ if it happens to count itself in the referential  field of its own indexing. Or: a site is a multiple which happens to behave in the world in the same way with regard to itself as it does with regard to its elements, so that it is the ontological support of its own appearance. Even if the idea is still obscure, its content is plain: a site supports the possibility of a singularity, because it summons its being in the appearing of its own multiple composition. It makes itself, in the world, the being-there of its own being. Among other consequences, the site endows itself with an intensity of existence. A site is a being to which it happens that it exists by itself. (363)

The ontology of the site is entirely that of what cannot be maintained, since it is, by a reflexive violence, an exception to the laws of being, in particular of the law that forbids a multiple from being an element of itself (this is formally expressed in the axiom of foundation). (368)

The ontology of a site can thus be described in terms of three properties:

1. A site is a reflexive multiplicity, which belongs to itself and thereby transgresses the laws of being.

2. Because it carries out a transitory cancellation of the gap between being and being-there, a site is the instantaneous revelation of the void that haunts multiplicities.

3. A site is an ontological  figure of the instant: it appears only to disappear. (369)

Only a com-plete power of existing differentiates a site from the simple network of modifications in which the law of the world persists. A site that does not exist maximally is a mere fact. Though ontologically identifiable, it is not, within appearing, logically singular. (372)

We have called modification the simple becoming a world, seen from the standpoint of an object of that world. Since it is internal to the established transcendental correlations, modification does not call for a site. We will call fact a site whose intensity of existence is not maximal. We will call singularity a site whose intensity of existence is maximal. We now have at our disposal three distinct degrees of change: modifica-tion, which is ontologically neutral and transcendentally regular; the fact, which is ontologically supernumerary but existentially (and thus logically) weak; singularity, which is ontologically supernumerary and whose value of appearance (or of existence) is maximal. (372)

We reserve the name ’event’ for a strong singularity [singularité forte]. (374)

The strong singularity can thus be recognized by the fact that its con-sequence in the world is to make exist within it the proper inexistent of the object-site. (377)

In a more abstract fashion, we will propose the following definition: Take a site (an object marked by self-belonging) which is a singularity (its intensity of existence, as instantaneous and evanescent as it may be, is nonetheless maximal). We will say that this site is a ‘strong singularity’ or an ‘event’ if the value of the entailment of the (nil) value of its proper inexistent by the (maximal) value of the site is itself maximal. (377)


Axiom 1. An event is never the concentration of vital continuity or the immanent intensification of a becoming. It is never coextensive with becoming. On the contrary, it is a pure cut in becoming made by an object of the world, through that object’s auto-appearance; but it is also the sup-plementing of appearing through the upsurge of a trace: the old inexistent which has become an intense existence. With regard to the continuum in the becomings of the world, there is both a lack (impossibility of auto-appearance without interrupting the authority of the mathematical laws of being and the logical laws of appearing) and an excess (impossibility of the upsurge of a maximal intensity of existence). ‘Event’ names the conjunction of this lack and this excess. (384)

Axiom 2. The event cannot be the undivided encroachment of the past on the future or the eternally past being of the future. On the contrary, it is a separating evanescence, an atemporal instant which disjoins the previous state of an object (the site) from its subsequent state. We could also say that the event extracts from one time the possibility of another time. This other time, whose materiality envelops the consequences of the event, deserves the name of new present. The event is neither past nor future. It presents us with the present. (384)

Axiom 3. The event cannot result from the actions and passion of a body, nor can it differ in kind from these actions and passions. On the contrary, an active body adequate to the new present is an effect of the event, as we shall see in detail in Book VII. We must here reverse Deleuze—in the sense that he himself, following Nietzsche, wants to reverse Plato. It is not the actions and passions of multiples which are synthesized in the event as an immanent result. It is the blow of the evental One which magnetizes multiplicities and constitutes them into subjectivizable bodies. And the trace of the event, itself incorporated into the new present, is obviously of the same nature as the actions of this body. […] For Deleuze, the event is the immanent consequence of becomings or of Life. For me, the event is the immanent principle of exceptions to becoming, or Truths. (385)

Axiom 4. There can be no composition of that which is by a single event. On the contrary, there is a de-composition of worlds by multiple event-sites. Just as it is the separation of time, so the event is a separation from other events. Truths are multiple and multiform. They are also in exception of worlds, not the One that makes worlds chime with one another. (385)

As a localized dysfunction of the transcendental of a world, the event does not possess the least sense, nor is it sense. The fact that it only abides as a trace does not entail that it must be tipped over onto the side of language. It simply opens up a space of consequences in which the body of a truth is composed. As Lacan saw, this real point is strictly speaking senseless, and its only relationship to language is to make a hole in it. This hole cannot be filled by that which, according to the transcendental laws of saying, is sayable. (386)

To break with empiricism is to think the event as the advent of what subtracts itself from all experience: the ontologically un-founded and the transcendentally discontinuous. To break with dogmatism is to remove the event from the ascendancy of the One. It is to subtract it from Life in order to deliver it to the stars. (387)

Why do we need to say  ‘it happens’? Because this is not something that could  be. In what concerns its exposition to the thinkable, the pure multiple obeys the axioms of set-theory. Now, the axiom of foundation forbids self-belonging. It is thus a law of being that no multiple may enter into its own composition. The notation  A  ∈  A is that of an ontological (mathematical) impossibility. A site is therefore the sudden lifting of an axiomatic prohibition, through which the possibility of the impossible comes to be. This effectuation of the impossible can be put in the following way: a being appears under the rule of the object whose being it is. In effect, the ‘it happens’ makes A appear in the referential field of the object (A, Id). Needless to say, it is impossible to conceive any stabilization of this sudden occurrence of A in its own transcendental field or under the retro-active jurisdiction of its own objectivation. The laws of being immediately close up again on what tries to except itself from them. Self-belonging annuls itself as soon as it is forced, as soon as it happens. A site is a vanishing term: it appears only in order to disappear. The problem is to register its consequences in appearing. (391)

That which inappeared now shines like the sun. ‘We have been nought, we shall be all’—that is the generic form of the evental trace, named ε in Book I, the trace whose position with regard to the body tells us on which subjective type that which comes to be under the name of truth relies. (394)


Book VI. Theory of Points

The point is ultimately a topological operator—a corporeal localization with regard to the transcendental—which simultaneously spaces out and conjoins the subjective (a truth-procedure) and the objective (the multiplicities that appear in a world). (399)

Even more simply, there is a ‘point’ when, through an operation that involves a subject and a body, the totality of the world is at stake in a game of heads or tails. Each multiple of the world is then correlated either to a ‘yes’ or to a ‘no’. (400)

‘Decision’ is here a metaphor for a characteristic of the transcendental: the existence (or relative weakness thereof) of these kinds of appearances of the degrees of intensity of appearing before the tribunal of the alternative. We could also say, just as metaphorically, that a point in a world is that which allows an exposition to be distilled into a choice. (400)

But, in a more subtle way, we could say that it is the point that localizes the body-of-truth with regard to the transcendental. […] A point, which dualizes the infinite, concentrates the appearing of a truth in a place of the world. Points deploy the topology of the appearing of the True. (409)

The points of a world constitute a veritable power of localization (technically speaking, a topological space). […] When we say  ‘form of being-there’, we privilege instead the localization of a multiple, that which wrests it away from its simple mathematical absoluteness, inscribing it in the singularity of a worldly place. (410)

What is worthy of note is that every world may be considered as a topological space once it is thought in terms of the points that its transcendental imposes as a test on the appearing of a truth of that world. The expression ‘being-there’ here takes on its full value. Exposed to points, a truth which finds its support in a body veritably appears in a world as though the latter had always been its place. (414)

The transit from being to being-there is validated in a world by the reduction of all the degrees of intensity to the elementary  figure of the  ‘yes’ or  ‘no’, of the  ‘either this or that’, in its exclusive sense. (415)

A point concentrates the degrees of existence, the intensities measured by the transcendental, into only two possibilities. Of these two possibilities, only one is the  ‘good one’ for a truth-procedure that must pass through this point. Only one authorizes the continuation, and therefore the reinforcement of the actions of the subject-body in the world. All of a sudden, the trans-cendental degrees are in fact distributed into two classes by a given point that treats the becoming of a truth: the degrees associated with the ‘good’ value and those associated with the bad one. (416)

In that which puts the power of truth of appearing to the test it is possible to decipher that this appearing is, in its essence, a topos: appearing, considered as the support of a truth tested by the world, is the taking-place of being. (419)

A world is said to be atonic when its transcendental is devoid of points. The existence of atonic worlds is both formally demonstrable and empirically corroborated. We have said enough to make it clear that in such worlds no faithful subjective formalism can serve as the agent of a truth, in the absence of the points that would make it possible for the efficacy of a body to confront such a truth. This explains why democratic materialism is particularly wellsuited to atonic worlds. Without a point there’s no truth, nothing but objects, nothing but bodies and languages. That’s the kind of happiness that the advocates of democratic materialism dream of: nothing happens, but for the death that we do our best to put out of sight. Every-thing is organized and everything is guaranteed. One’s life is managed like a business that would rationally distribute the meagre enjoyments that it’s capable of. (420)

Let us call ‘isolate’ a non-minimal degree of positive intensity such that nothing is subordinated to it, except for the minimum. In other words, there is nothing between it and the nothing. Where everything communicates infinitely, there exists no point. Empirically, an isolate is an object whose intensity of appearance is non-decomposable. To evaluate its pertinence in a construction of truth we do not need to analyse it, to decompose it and to reduce it. It is a halting point in the world. Such a halting point attests that at least in one place the atony of the world is undermined and that one is required to decide to say ‘yes’ or ‘no’ to a truth-procedure. (421)

To the violent promise of atony made by an armed demo-cratic materialism, we can therefore oppose the search, in the nooks and crannies of the world, for some isolate on the basis of which it is possible to maintain that a ‘yes’ authorizes us to become the anonymous heroes of at least one point. To incorporate oneself into the True, it is always necessary to interrupt the banality of exchanges. Like René Char invoking the silence of Saint-Just on the 9 Thermidor, it is necessary to ‘forever close the crystal shutters over communication’. (422)

Though often isolates are rare, we should also keep in mind that it is equally possible for a transcendental to have as many of them as it has degrees. Such is the disposition of tensed worlds, which are thereby opposed to atonic worlds. So many degrees of intensity of appearance, so many possible points; decision, which is nowhere in an atonic world, is everywhere in a tensed world. (422)

A point is a kind of analytic mediation between the transcendental complexity of a world (its often non-classical logic) and the (always classical) imperative of binarity or decision. (439)


Book VII. What is a Body?

Broadly speaking, an event is a site which is capable of making exist in a world the proper inexistent of the object that underlies the site. This tipping-over of the inapparent into appearing singularizes—in the retro-action of its logical implications—the event-site. (452)

Simplifying considerably (we now recapitulate Book I): the static system of consequences of an event is a (generic) truth. The immanent agent of the production of the consequences (of a truth), or the possible agents of their denial, or that which renders their occultation possible (that which aims to erase a truth)—all of these will be called subjects. The singular object that makes up the appearing of a subject is a body. Whatever subject we may be dealing with, a body is what can bear the subjective formalism […] (453)

A multiple-being which bears this subjective formalism and thereby makes it appear in a world receives the name of ‘body’—without ascribing to this body any organic status. (453)

We can therefore define the body: the set of elements of a site—in this case the sea—which entertain with the resurrection of the inexistent (consciousness and life) a relationship of maximal proximity. The function of appearing identifies as far as possible these elements (huge air, wind’s reviving, exploding wave. . .) to what has become—as the measure of the event’s force—the site’s central referent: the inexistent suddenly raised to the maximal degree of existence, the metamorphosis of he who is ‘all open to these shining spaces’ into he who says ‘No, no! Arise! The future years unfold’. (466)

Since the inexistent which is made incandescent is the trace of the event, we have a limpid abstract formula: a post-evental body is constituted by all the elements of the site which invest the totality of their existence in their identity to the trace of the event. Or, to employ a militant metaphor; the body is the set of everything that the trace of the event mobilizes. (467)

In our vocabulary, we can say that these elements incorporate themselves into the evental present. A body is nothing other than the set of elements that have this property. […] Subjective movement is the point of existence that names all the others. (467)

[…] a body is the totality of the elements of the site incorporated into the evental present. We can also call these the  ‘contemporary’ elements of the event, meaning those elements which are as identical as possible, within appearing, to the trace of the event: the inexistent projected into existence, the inapparent that shines within appearing. Let me propose another formulation: a body is composed of all the elements of the site (here, all the maritime motifs) that subordinate themselves, with maximal intensity, to that which was nothing and becomes all. (468)

Conceptually, this means that the structure of a transcendental, which might be infinite, is made to appear before the tribunal of the decision (or the pure choice, or the alternative), which comes down to saying ‘yes’ (1) or ‘no’ (0). The subjective metaphor of the point can be expressed as follows: To decide is always to filter the infinite through the Two. (468)

Of course, that which in Book I we marked with the letter ε, the first declaration, is expressed in the logic of a subject of truth as follows: the event has taken place, I say ‘yes’ to it, I meld with the suddenly sublimated inexistent. And it is true that it is ‘my book’ (the poem itself) that the ‘huge air opens and shuts’. Nonetheless, without the efficacious regions of the body, without the organs that locally synthesize these regions, we would be merely left with principles. (470)

A body, in its totality, is what gathers together those terms of the site which are maximally engaged in a kind of ontological alliance with the new appearance of an inexistent, which acts as the trace of the event. A body is what is beckoned and mobilized by the post-evental sublimation of the inexistent. Its coherence is that of the internal compatibility of elements, as guaranteed by their shared ideal subordination to the primordial trace. But the efficacy of a body, which is oriented towards consequences (and therefore towards the subjective formalism, which is the art of consequences as the constitution of a new present), is played out locally, point by point. A body’s test is always that of an alternative. A point is what directs the components of a body to the summons of the Two. In order for this to happen, there must be efficacious regions of bodies, which validate the  ‘yes’ to the new consequences against the inertia of the old world; there must also be, besides the brilliance of the trace, appropriate organs for such a validation. These organs are the immanent synthesis of the regional efficacy of a body. It is only by working out an organization for the subjectivizable body that one can hope to ‘live’, and not merely try to. (470)

These five conditions for the existence of a subjectivizable body can be summed up as follows: the world must not be atonic; there is a site-object and its trace, namely the maximal becoming-existent of an inexistent; elements of the object are maximally correlated to the trace and group themselves in a compatible manner; in the body constituted by all of its elements there are subsets which are its organs with respect to points. (474)

Be that as it may, let’s hold on to the notion, which we have seen at work in both mathematics and poetry, that the sequence world–points–site–body–efficacious part–organ is indeed the generic form of what makes it possible for there to be such things as truths. This authorizes the materialist dialectic to contend that beyond bodies and languages, there is the real life of some subjects. (475)

One will also appreciate the fact that this effect of marking is described as the  ‘shearing effect’ [effet de cisaille], a powerful image which I interpret in the following way: the becoming of a subjec-tivated body establishes the present in the perpetual danger that its ineluctable division—its ‘shearing’, one could not put it better—becomes that of its reactive negation, or even of its obscure occultation. This is the precarious equilibrium of the body under erasure as it resists the obliterated body and the vanished body. The consequence is that, when it comes to the subject-body to which we incorporate our fleeting animality, we are always tempted to say either that it exists (dogmatism, the tempta-tion of the faithful subject) or that it does not exist (scepticism, the temptation of the reactive subject). (479)

But the crucial teaching bequeathed by Lacan remains the following: it is in vain that some, under the impulse of democratic materialism, wish to convince us, after the comedy of the soul, that our body is the proven place of the One. Against this animalistic reduction, let us repeat the Master’s verdict: ‘the presupposition that there is somewhere a place of unity is well suited to suspend our assent’. (482)



It is not a world, as given in the logic of its appearing (the infinite of its objects and relations), which induces the possibility of living—at least not if life is something other than existence. The induction of such a possibility depends on that which acts in the world as the trace of the fulgurating disposition that has befallen that world. That is, the trace of a vanished event. Within worldly appearing, such a trace is always a maximally intense existence. (507)

It is not enough to identify a trace. One must incorporate oneself into what the trace authorizes in terms of consequences. This point is crucial. Life is the creation of a present […] It is necessary to enter into its composition, to become an active element of this body. The only real relation to the present is that of incorporation: the incorporation into this immanent cohesion of the world which springs from the becoming-existent of the evental trace, as a new birth beyond all the facts and markers of time. (508)

The unfolding of the consequences linked to the evental trace—consequences that create a present—proceeds through the treatment of the points of the world. It does not take place through the continuous trajectory of a body’s efficacy, but in sequences, point by point. (508)

Life is a subjective category. A body is the materiality that life requires, but the becoming of the present depends on the disposition of this body in a subjective formalism, whether it be produced (the formalism is faithful, the body is directly placed ‘under’ the evental trace), erased (the formalism is reactive, the body is held at a double distance by the negation of the trace), or occulted (the body is denied). […] To live is thus an incorporation into the present under the faithful form of a subject. If the incorporation is dominated by the reactive form, one will not speak of life, but of mere conservation. (508)

If incorporation is dominated by the obscure formalism, one will instead speak of mortification. Ultimately life is the wager, made on a body that has entered into appearing, that one will faithfully entrust this body with a new tem-porality, keeping at a distance the conservative drive (the ill-named ‘life’ instinct) as well as the mortifying drive (the death instinct). Life is what gets the better of the drives. (509)

For democratic materialism, the present is never created. Democratic materialism affirms, in an entirely explicit manner, that it is important to maintain the present within the confines of an atonic reality. That is because it regards any other view of things as submitting the body to

the despotism of an ideology, instead of letting it roam freely among the diversity of languages. Democratic materialism proposes to call ‘thought’ the pure algebra of appearing. This atonic conception of the present results in the fetishization of the past as a separable ’culture’. Democratic material-ism has a passion for history; it is truly the only authentic historical materialism. […] In democratic materialism, the life of language-bodies is the conservative succession of the instants of the atonic world. It follows that the past is charged with the task of endowing these instants with a  fictive horizon, with a cultural density. This also explains why the fetishism of history is accompanied by an unrelenting discourse on novelty, perpetual change and the imperative of modernization. The past of cultural depths is matched by a dispersive present, an agitation which is itself devoid of any depth whatsoever. There are monuments to visit and devastated instants to inhabit. Everything changes at every instant, which is why one is left to contemplate the majestic historical horizon of what does not change. (509-510)

For the materialist dialectic, it is almost the opposite. What strikes one first is the stagnant immobility of the present, its sterile agitation, the vio-lently imposed atonicity of the world. There have been few, very few, cru-cial changes in the nature of the problems of thought since Plato, for instance. But, on the basis of some truth-procedures that unfold subjectivizable bodies, point by point, one reconstitutes a different past, a history of achievements, discoveries, breakthroughs, which is by no means a cultural monumentality but a legible succession of fragments of eternity. That is because a faithful subject creates the present as the being-there of eternity. Accordingly, to incorporate oneself into this present amounts to perceiving the past of eternity itself. To live is therefore also, always, to experience in the past the eternal amplitude of a present. (510)

It is true that, if there is nothing but bodies and languages, to live for an Idea necessarily implies the arbitrary absolutization of one language, which bodies must comply with. Only the material recognition of the ‘except that’ of truths allows us to declare, not that bodies are submitted to the authority of a language, far from it, but that a new body is the organization in the present of an unprecedented subjective life. (510)

Democratic materialism presents as an objective given, as a result of historical experience, what it calls ‘the end of ideologies’. What actually lies behind this is a violent subjective injunction whose real content is: ‘Live without Idea’. But this injunction is incoherent. (511)

I believe in eternal truths and in their fragmented creation in the present of worlds. My position on this point is entirely isomorphic with that of Descartes: truths are eternal because they have been created and not because they have been there forever. […] That it belongs to

the essence of a truth to be eternal does not dispense it in the least from having to appear in a world and to be inexistent prior to this appearance. (512)

Eternal necessity pertains to a truth in itself […] But its process of creation does not – since it depends on the contingency of worlds, the aleatory character of a site, the efficacy of the organs of a body and the constancy of a subject. (512-513)

I too affirm that all truths without exception are ‘established’ through a subject, the form of a body whose efficacy creates point by point. But, like Descartes, I argue that their creation is but the appearing of their eternity. (513)

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