1. THOUGHT IS THE PROPER MEDIUM OF THE UNIVERSAL

By "thought", I mean the subject in so far as it is constituted through a process that is transversal relative to the totality of available forms of knowledge. Or, as Lacan puts it, the subject in so far as it constitutes a hole in knowledge.

Remarks:

a. That thought is the proper medium of the universal means that nothing exists as universal if it takes the form of the object or of objective legality. The universal is essentially 'anobjective'. It can be experienced only through the production (or reproduction) of a trajectory of thought, and this trajectory constitutes (or reconstitutes) a subjective disposition.

Here are two typical examples: the universality of a mathematical proposition can only be experienced by inventing or effectively reproducing its proof, the situated universality of a political statement can only be experienced through the militant practice that effectuates it.

b. That thought, as subject-thought, is constituted through a process means that the universal is in no way the result of a transcendental constitution, which would presuppose a constituting subject. On the contrary, the opening up of the possibility of a universal is the precondition for there being a subject-thought at the local level. The subject is invariably summoned as thought at a specific point of that procedure through which the universal is constituted. The universal is at once what determines its own points as subject-thoughts and the virtual recollection of those points. Thus the central dialectic at work in the universal is that of the local, as subject, and the global, as infinite procedure. This dialectic is constitutive of thought as such.

Consequently, the universality of the proposition "the series of prime numbers goes on forever" resides both in the way it summons us to repeat (or rediscover) in thought a unique proof for it, but also in the global procedure that, from the Greeks to the present day, mobilizes number theory along with its underlying axiomatic. To put it another way, the universality of the practical statement "a country's illegal immigrant workers must have their rights recognized by that country" resides in all sorts of militant effectuations through which political subjectivity is actively constituted, but also in the global process of a politics, in terms of what it prescribes concerning the State and its decisions, rules and laws.

c. That the process of the universal or truth - they are one and the same - is transversal relative to all available instances of knowledge means that the universal is always an incalculable emergence, rather than a describable structure. By the same token, I will say that a truth is intransitive to knowledge, and even that it is essentially unknown. This is another way of explaining what I mean when I characterize truth as unconscious.

I will call particular whatever can be discerned in knowledge by means of descriptive predicates. But I will call singular that which, although identifiable as a procedure at work in a situation, is nevertheless subtracted from every predicative description. Thus the cultural traits of this or that population are particular. But that which, traversing these traits and deactivating every registered description, universally summons a thought-subject, is singular. Whence thesis 2:

2. EVERY UNIVERSAL IS SINGULAR, OR IS A SINGULARITY

Remarks:

There is no possible universal sublation of particularity as such. It is commonly claimed nowadays that the only genuinely universal prescription consists in respecting particularities. In my opinion, this thesis is inconsistent. This is demonstrated by the fact that any attempt to put it into practice invariably runs up against particularities which the advocates of formal universality find intolerable. The truth is that in order to maintain that respect for particularity is a universal value, it is necessary to have first distinguished between good particularities and bad ones. In other words, it is necessary to have established a hierarchy in the list of descriptive predicates. It will be claimed, for example, that a cultural or religious particularity is bad if it does not include within itself respect for other particularities. But this is obviously to stipulate that the formal universal already be included in the particularity. Ultimately, the universality of respect for particularities is only the universality of universality. This definition is fatally tautological. It is the necessary counterpart of a protocol - usually a violent one - that wants to eradicate genuinely particular particularities (i.e. immanent particularities) because it freezes the predicates of the latter into self-sufficient identitarian combinations.

Thus it is necessary to maintain that every universal presents itself not as a regularization of the particular or of differences, but as a singularity that is subtracted from identitarian predicates; although obviously it proceeds via those predicates. The subtraction of particularities must be opposed to their supposition. But if a singularity can lay claim to the universal by subtraction, it is because the play of identitarian predicates, or the logic of those forms of knowledge that describe particularity, precludes any possibility of foreseeing or conceiving it.

Consequently, a universal singularity is not of the order of being, but of the order of a sudden emergence. Whence thesis 3:

3. EVERY UNIVERSAL ORIGINATES IN AN EVENT, AND THE EVENT IS INTRANSITIVE TO THE PARTICULARITY OF THE SITUATION

The correlation between universal and event is fundamental. Basically, it is clear that the question of political universalism depends entirely on the regime of fidelity or infidelity maintained, not to this or that doctrine, but to the French Revolution, or the Paris commune, or October 1917, or the struggles for national liberation, or May 1968. A contrario, the negation of political universalism, the negation of the very theme of emancipation, requires more than mere reactionary propaganda. It requires what could be called an "evental revisionism". Thus, for example, Furet's attempt to show that the French Revolution was entirely futile; or the innumerable attempts to reduce May 1968 to a student stampede toward sexual liberation. Evental revisionism targets the connection between universality and singularity. Nothing took place but the place, predicative descriptions are sufficient, and whatever is universally valuable is strictly objective. In fine, this amounts to the claim that whatever is universally valuable resides in the mechanisms and power of capital, along with its statist guarantees.

In that case, the fate of the human animal is sealed by the relation between predicative particularities and legislative generalities.

For an event to initiate a singular procedure of universalization, and to constitute its subject through that procedure, is contrary to the positivist coupling of particularity and generality.

In this regard, the case of sexual difference is significant. The predicative particularities identifying the positions "man" and "woman" within a given society can be conceived in an abstract fashion. A general principle can be posited whereby the rights, status, characteristics and hierarchies associated with these positions should be subject to egalitarian regulation by the law. This is all well and good, but it does not provide a ground for any sort of universality as far as the predicative distribution of gender roles is concerned. For this to be the case, there has to be the suddenly emerging singularity of an encounter or declaration; one that crystallizes a subject whose manifestation is precisely its subtractive experience of sexual difference. Such a subject comes about through an amorous encounter in which there occurs a disjunctive synthesis of sexuated positions. Thus the amorous scene is the only genuine scene in which a universal singularity pertaining to the Two of the sexes - and ultimately pertaining to difference as such - is proclaimed. This is where an undivided subjective experience of absolute difference takes place. We all know that, where the interplay between the sexes is concerned, people are invariably fascinated by love stories; and this fascination is directly proportional to the various specific obstacles through which social formations try to thwart love. In this instance, it is perfectly clear that the attraction exerted by the universal lies precisely in the fact that it subtracts itself (or tries to subtract itself) as an asocial singularity from the predicates of knowledge.

Thus it is necessary to maintain that the universal emerges as a singularity and that all we have to begin with is a precarious supplement whose sole strength resides in there being no available predicate capable of subjecting it to knowledge.

The question then is: what material instance, what unclassifiable effect of presence, provides the basis for the subjectivating procedure whose global motif is a universal?

4. A UNIVERSAL INITIALLY PRESENTS ITSELF AS A DECISION ABOUT AN UNDECIDABLE This point requires careful elucidation.

I call "encyclopedia" the general system of predicative knowledge internal to a situation: i.e. what everyone knows about politics, sexual difference, culture, art, technology, etc. There are certain things, statements, configurations or discursive fragments whose valence is not decidable in terms of the encyclopedia. Their valence is uncertain, floating, anonymous: they exist at the margins of the encyclopedia. They comprise everything whose status remains constitutively uncertain; everything that elicits a 'maybe, maybe not'; everything whose status can be endlessly debated according to the rule of non-decision, which is itself encyclopedic; everything about which knowledge enjoins us not to decide. Nowadays, for instance, knowledge enjoins us not to decide about God: it is quite acceptable to maintain that perhaps 'something' exists, or perhaps it does not. We live in a society in which no valence can be ascribed to God's existence; a society that lays claim to a vague spirituality. Similarly, knowledge enjoins us not to decide about the possible existence of "another polities": it is talked about, but nothing comes of it. Another example: are those workers who do not have proper papers but who are working here, in France (or the United Kingdom, or the United States ...) part of this country? Do they belong here? Yes, probably, since they live and work here. No, since they don't have the necessary papers to show that they are French (or British, or American ...), or living here legally. The expression "illegal immigrant" designates the uncertainty of valence, or the non-valence of valence: it designates people who are living here, but don't really belong here, and hence people who can be thrown out of the country, people who can be exposed to the non-valence of the valence of their presence here as workers.

Basically, an event is what decides about a zone of encyclopedic indiscern-ibility. More precisely, there is an implicative form of the type: E --> d(), which reads as: every real subjectivation brought about by an event, which disappears in its appearance, implies that , which is undecidable within the situation, has been decided. This was the case, for example, when illegal immigrant workers occupied the church of St. Bernard in Paris: they publicly declared the existence and valence of what had been without valence, thereby deciding that those who are here belong here and enjoining people to drop the expression "illegal immigrant".

I will call the evental statement. By virtue of the logical rule of detachment, we see that the abolition of the event, whose entire being consists in disappearing, leaves behind the evental statement , which is implied by the event, as something that is at once:

- a real of the situation (since it was already there);

- but something whose valence undergoes radical change, since it was undecidable but has been decided. It is something that had no valence but now does.

Consequently, I will say that the inaugural materiality for any universal singularity is the evental statement. It fixes the present for the subject-thought out of which the universal is woven.

Such is the case in an amorous encounter, whose subjective present is fixed in one form or another by the statement "I love you", even as the circumstance of the encounter is erased. Thus an undecidable disjunctive synthesis is decided and the inauguration of its subject is tied to the consequences of the evental statement.

Note that every evental statement has a declarative structure, regardless of whether the statement takes the form of a proposition, a work, a configuration or an axiom. The evental statement is implied by the event's appearing-disappearing and declares that an undecidable has been decided or that what was without valence now has a valence. The constituted subject follows in the wake of this declaration, which opens up a possible space for the universal.

Accordingly, all that is required in order for the universal to unfold is to draw all the consequences, within the situation, of the evental statement.

5. THE UNIVERSAL HAS AN IMPLICATIVE STRUCTURE

One common objection to the idea of universality is that everything that exists or is represented relates back to particular conditions and interpretations governed by disparate forces or interests. Thus, for instance, some maintain it is impossible to attain a universal grasp of difference because of the abyss between the way the latter is grasped, depending on whether one occupies the position of "man" or the position of 'woman'. Still others insist that there is no common denominator underlying what various cultural groups choose to call "artistic activity"; or that not even a mathematical proposition is intrinsically universal, since its validity is entirely dependent upon the axioms that support it.

What this hermeneutic perspectivalism overlooks is that every universal singularity is presented as the network of consequences entailed by an evental decision. What is universal always takes the form --> , where e is the evental statement and is a consequence, or a fidelity. It goes without saying that if someone refuses the decision about , or insists, in reactive fashion, on reducing e to its undecidable status, or maintains that what has taken on a valence should remain without valence, then the implicative form in no way enjoins them to accept the validity of the consequence, titi. Nevertheless, even they will have to admit the universality of the form of implication as such. In other words, even they will have to admit that if the event is subjectivated on the basis of its statement, whatever consequences come to be invented as a result will be necessary.

On this point, Plato's apologia in the Meno remains irrefutable. If a slave knows nothing about the evental foundation of geometry, he remains incapable of validating the construction of the square of the surface that doubles a given square. But if one provides him with the basic data and he agrees to subjectivate it he will also subjectivate the construction under consideration. Thus the implication that inscribes this construction in the present inaugurated by geometry's Greek emergence is universally valid.

Someone might object: "You're making things too easy for yourself by invoking the authority of mathematical inference." But they would be wrong. Every universalizing procedure is implicative. It verifies the consequences that follow from the evental statement to which the vanished event is indexed. If the protocol of subjectivation is initiated under the aegis of this statement, it becomes capable of inventing and establishing a set of universally recognizable consequences.

The reactive denial that the event took place, as expressed in the maxim "nothing took place but the place", is probably the only way of undermining a universal singularity. It refuses to recognize its consequences and cancels whatever present is proper to the evental procedure.

Yet even this refusal cannot cancel the universality of implication as such. Take the French Revolution: if, from 1792 on, this constitutes a radical event, as indicated by the immanent declaration which states that revolution as such is now a political category, then it is true that the citizen can only be constituted in accordance with the dialectic of Virtue and Terror. This implication is both undeniable and universally transmissible - in the writings of Saint-Just, for instance. But obviously, if one thinks there was no Revolution, then Virtue as a subjective disposition does not exist either and all that remains is the Terror as an outburst of insanity inviting moral condemnation. Yet even if politics disappears, the universality of the implication that puts it into effect remains.

There is no need to invoke a conflict of interpretations here. This is the nub of my sixth thesis:

6. THE UNIVERSAL IS UNIVOCAL

In so far as subjectivation occurs through the consequences of the event, there is a univocal logic proper to the fidelity that constitutes a universal singularity.

Here we have to go back to the evental statement. Recall that the statement circulates within a situation as something undecidable. There is agreement both about its existence and its undecidability. From an ontological point of view, it is one of the multiplicities of which the situation is composed. From a logical point of view, its valence is intermediary or undecided. What occurs through the event does not have to do with the being that is at stake in the event, nor with the meaning of the evental statement. It pertains exclusively to the fact that, whereas previously the evental statement had been undecid-able, henceforth it will have been decided, or decided as true. Whereas previously the evental statement had been devoid of significance, it now possesses an exceptional valence. This is what happened with the illegal immigrant workers, who demonstrated their existence at the St. Bernard church.

In other words, what affects the statement, in so far as the latter is bound up in an implicative manner with the evental disappearance, is of the order of the act, rather than of being or meaning. It is precisely the register of the act that is univocal. It just so happened that the statement was decided, and this decision remains subtracted from all interpretation. It relates to the yes or the no, not to the equivocal plurality of meaning.

What we are talking about here is a logical act, or even, as one might say echoing Rimbaud, a logical revolt. The event decides in favour of the truth or eminent valence of that which the previous logic had confined to the realm of the undecidable or of non-valence. But for this to be possible, the univocal act that modifies the valence of one of the components of the situation must gradually begin to transform the logic of the situation in its entirety. Although the being-multiple of the situation remains unaltered, the logic of its appearance - the system that evaluates and connects all the multiplicities belonging to the situation - can undergo a profound transformation. It is the trajectory of this mutation that composes the encyclopedia's universalizing diagonal.

The thesis of the equivocity of the universal refers the universal singularity back to those generalities whose law holds sway over particularities. It fails to grasp the logical act that universally and univocally inaugurates a transformation in the entire structure of appearance.

For every universal singularity can be defined as follows: it is the act to which a subject-thought becomes bound in such a way as to render that act capable of initiating a procedure which effects a radical modification of the logic of the situation, and hence of what appears in so far as it appears. Obviously, this modification can never be fully accomplished. For the initial univocal act, which is always localized, inaugurates a fidelity, i.e. an invention of consequences, that will prove to be as infinite as the situation itself. Whence thesis 7:

7. EVERY UNIVERSAL SINGULARITY REMAINS INCOMPLETABLE OR OPEN

All this thesis requires by way of commentary concerns the manner in which the subject, the localization of a universal singularity, is bound up with the infinite, the ontological law of being-multiple. On this particular issue, it is possible to show that there is an essential complicity between the philosophies of finitude, on the one hand, and relativism, or the negation of the universal and the discrediting of the notion of truth, on the other. Let me put it in terms of a single maxim: The latent violence, the presumptuous arrogance inherent in the currently prevalent conception of human rights derives from the fact that these are actually the rights of finitude and ultimately - as the insistent theme of democratic euthanasia indicates - the rights of death. By way of contrast, the evental conception of universal singularities, as Jean-Francois Lyotard remarked in The Differend, requires that human rights be thought of as the rights of the infinite.

8. UNIVERSALITY IS NOTHING OTHER THAN THE FAITHFUL CONSTRUCTION OF AN INFINITE GENERIC MULTIPLE

What do I mean by generic multiplicity? Quite simply, a subset of the situation that is not determined by any of the predicates of encyclopedic knowledge; that is to say, a multiple such that to belong to it, to be one of its elements, cannot be the result of having an identity, of possessing any particular property. If the universal is for everyone, this is in the precise sense that to be inscribed within it is not a matter of possessing any particular determination. This is the case with political gatherings, whose universality follows from their indifference to social, national, sexual or generational origin; with the amorous couple, which is universal because it produces an undivided truth about the difference between sexuated positions; with scientific theory, which is universal to the extent that it removes every trace of its provenance in its elaboration; or with artistic configurations whose subjects are works, and in which, as Mallarme remarked, the particularity of the author has been abolished, so much so that in exemplary inaugural configurations, such as The Iliad and The Odyssey, the proper name that underlies them - Homer - ultimately refers back to nothing but the void of any and every subject.

Thus the universal arises according to the chance of an aleatory supplement. It leaves behind it a simple detached statement as a trace of the dis-appearance of the event that founds it. It initiates its procedure in the univocal act through which the valence of what was devoid of valence comes to be decided. It binds to this act a subject-thought that will invent consequences for it. It faithfully constructs an infinite generic multiplicity, which, by its very opening, is what Thucydides declared his written history of the Peloponnesian war - unlike the latter's historical particularity - would be: , "something for all time".