In a lecture published in the Cardozo Law Review in 2008, Alain Badiou articulates his understanding of Being, Event, and Simulacrum in relationship to Logic and Law. With an incredible power of precision, Badiou reminds his audience of Aristotle’s three main pillars of the process of thought (Identity, non-contradiction, and the excluded middle), which he then uses to delineate the three kinds of negation he understands to be at work: classical, intuitionistic, and paraconsistent. With these “three kinds of negation,” Badiou aims to underscore how Events transpire in a world; and what the impact of an Event, according to each kind of negation, actually means.
In Classical logic, negation obeys Aristotle’s principles of non-contradition and the excluded middle. That is to say, the relationship between P and non-P is that either the former is true, or the latter is true, but not both simultaneously. Additionally, there is no third term available in this truth relation. All throughout Badiou’s lecture, he provides us with examples of such a logic. For Badiou, the most common understanding of how classical logic defines a certain kind of negation is seen in the concept of God: “Certainly, God as such pertains to classical logic: between his existence and his non-existence, there is no third possibility” (Badiou, 2008). Badiou makes it explicit that classical logic pertains to God, only because the concept of God itself is an ontological concept. Thus we arrive at the first of Badiou’s main themes: Being (which operates according to classical logic and it’s specific kind of negation).
In intuitionistic logic, negation obeys the law of non-contradiction but does not obey the law of the excluded middle. So according to intuitionistic logic, the relation between P and non-P does not excluded any number of intermediary possibilities between those two extremes. Now, intuitionistic logic, as one might be able to already see, cannot pertain to be Being qua being (either God exists or does not exist, and it cannot be said that God exists between those two claims). However, Badiou finds intuitionistic logic useful (“valid”) when it comes to making claims about concrete worlds. Thus, keeping in mind his audience is a room full of law students and professors, he gives an example through the institution of law as to how intuitionistic logic allows us to comprehend the world:
So, if the great field of the law is always a concrete world, or a concrete construction, its logic is not classic. If we take “law” in its strict legal sense, we know that perfectly well. If the sentence P is “guilty,” and non-P “innocent,” we have always a great number of intermediate values, like “guilty with attenuating circumstances,” or “innocent because certainly guilty, but with insufficient proof,” and so on (Badiou, 2008).
Thirdly, in paraconsistent logic, negation obeys the law of the excluded middle but not the law of non-contradiction. This is defined by Badiou as “non-perceptible change at the level of the inexistent.” However, in order to get a better understanding of how paraconsistent logic fits into the ‘three kinds of negation’ Badiou is articulating, it’s helpful to turn to his own example which he believes spells this out more clearly. Regarding Events occurring in a world, Badiou claims that we have the twofold task of defining the event ontologically (abiding by the rules of classical logic) and existentially (abiding by the rules of intuitionistic logic):
To be complete, we must define first an event at the ontological level: what sort of multiplicity is an event? And after that, we must define an event at the phenomenological or existential level: how does an event appear in a determinate world? Today, and for you, I simplify the matter. I suppose that an event is a sudden change of the rules of appearing; a change of the degrees of existence of a lot of multiplicities which appear in a world…For example, the political existence of poor workers in a revolutionary event…The question for an event is: what is the destiny, after the event, of an inexistent of the world? What becomes of the poor worker after the revolution? (Badiou, 2008)
In order to account for the nature of an Event in a world, Badiou redeploys the three kinds of logic in order to trace an Event in its most effective form (classical) to an Event in its least effective form, that is to say as a non-Event (paraconsistent). If the most effective Events are those which operate under classical logic it is because the Event, as that which institutes a disruption of the reason or conventions of a world, brings about the strongest contrasts between existents and inexistents in a world. As Badiou writes,
The test is that among the consequences of this change, we have the maximal value, the maximal intensity of existence, for an object which was an inexistent, which appeared with the minimal degree of intensity. The poor worker, who before the revolution appears as nothing in the political field, becomes the new hero of this field. The abstract painting, which was purely decorative before an artistic revolution, becomes an essential trend of the history of the arts, and so on. (Badiou, 2008).
Thus, for Badiou, the Event which is most effective in disrupting the conventions and rationale of a world is that which can reduce the world into a duality between minimal intensity, or inexistence, and maximal intensity. “And that sort of world, with only two degrees of intensity, is always classical. We shall say in this case that the change is a true event, simply, if the context is clear, an Event” (Badiou, 2008). Now, the Event which accords to intuitionistic logic is the second possibility of an Event’s occurrence in the world. This type of Event institutes neither maximal nor minimal change, but rather intermediate changes in the world. “The poor worker appears in the political field, but it is not at all a new hero of the field. The abstract figures can be used in painting, but they are not really important. In this case, the logical framework of the event, and of its consequences, is clearly intuitionistic. There is no obligation for the event to be of maximal intensity” (Badiou, 2008). This type of Event, which institutes changes in a world that do not cause fundamental breaks, shifts, or novel ways of doing art, politics, or science, abide by the principle of non-contradiction but not by the law of the excluded middle – hence, it’s intuitionistic logical nature.
Finally, we arrive at the Event which corresponds to paraconsistent logic. This kind of event is characterized as the indecidability between event and non-event. “Yes, something happens, but, from the point of view of the world, everything is identical. So we have event and non-event simultaneously. And there are no new values between affirmation and negation, because the world is exactly the same. The principle of excluded middle is true, the principle of contradiction is false; so we have a paraconsistent logic. We say then that we have a false event, or a simulacrum“ (Badiou, 2008, my emphasis). Thus, for Badiou, true change only occurs in a world when the Event alters or interferes with the rules which govern a world – hence why he still claims that change occurs when Events abide by classical and intuitionistic logic (the former being a radical change, the latter being reformist). It is because of this that Badiou ends his lecture with this statement: “The lesson is that, when the world is intuitionistic, a true change must be classical, and a false change paraconsistent” (Badiou, 2008).
Perhaps one of Alain Badiou’s strongest allies in his articulation of the Event is an anachronistic one. Jacques Vergès, a French-Vietnamese lawyer, was made famous by his defense of Djamila Bouhired, Algerian nationalist and fighter in the National Liberation Army in Algeria in the late 50′s. Using what he termed the ‘rupture defense,’ Vergès claimed that the French State had no grounds to try Bouhired due to its history of colonial violence against the Alergian people. Thus, instead of defending Bouhired in terms of the French legal system, Vergès approached the trial from the ‘outside.’ As he stated in an interview with Der Spiegel,
The other French attorneys who had taken over the defense in Algiers tried to begin a dialogue with the military judges there. The judges saw the FLN as a criminal group. But the Algerian defendants saw their attacks as a necessary act of resistance. In other words, there was no consensus over the principles that were to be applied in reaching a verdict. For me, it meant that I had to shift the events to outside the courtroom and win over public opinion for the defendants.1
This lack of consensus marks the paraconsistent nature of the trial: it is both the case that Bouhired was guilty and innocent; guilty from the point of view of the State and innocent from the point of view of the FLN. It is this confrontation of viewpoints that Vergès brought to the forefront of the trial. As Emilios Christodoulidis writes, “the defense of ‘rupture’ aims at a confrontation with the system that is represented by the prosecution’s case. In its confrontation with the law of the State, its main aim is to derail the process all the time both using and contesting it…” (Christodoulidis, 2008). Or as Vergès himself writes “rupture traverses the whole structure of the trial. Facts as well as circumstances of the action pass onto a secondary plane; in the forefront suddenly appears the brutal contestation with the order of the state” (Christodoulidis, 2008). Ultimately, the strategy of rupture aims at a confrontation between defense and prosecution that, “excludes all compromise” (Christodoulidis, 2008).
It is here that we arrive at the classical logic that underpins Vergès approach: in defending Bouhired through the contestation of the legitimacy of the French legal system, by putting their judgment of Bouhired into contrast with France’s history of colonialism, and their use of torture on Algerian’s despite the State’s acknowledgment of the rights of the subjects of French colonies, Vergès disrupts the State’s legitimacy by positing its actual illegitimacy. That is to say, either France is guilty of ongoing colonial violence and thus revokes its legitimacy as a supposed, neutral, judicial third party; or France is not guilty of ongoing colonial violence and retains its authority, with no third possibility. The rupture defense, then, is an Event in the classical sense.
This defense which constitutes a rupture, is only a rupture (or an Event), since it achieves a critique which contests and posits “new rules of appearing”; since for Badiou, “an event is a sudden change of the rules of appearing; a change of the degrees of existence of a lot of multiplicities which appear in a world” (Badiou, 2008). As seen above, Vergès led a defense of Bouhired not on the terms articulated by the court, but on the grounds of the principles which defined the legitimacy of the court itself. That is to say, what Vergès sought was a new set of ‘rules of appearing.’ Instead of terrorists, Bouhired was part of the resistance against colonialism; instead of a criminal, Bouhired was a revolutionary; instead of a murderer, she executed a traitor. And here we can see Vergès, and Badiou after him as an articulation of Fanon’s decolonial principle that “challenging the colonial world is not a rational confrontation of viewpoints. It is not a discourse on the universal” (Fanon, 2005).
By establishing the incommensurability between the lives of colonized peoples and the legal structure of the French state, Vergès showed how the tactics of the FLN “could no longer be rationally contained within the context of the operations of the French municipal system of justice,” once France was seen for what it was: “a facilitator of the colonial brutality against an emergent people no longer subsumable to ‘le peuple’ (Christodoulidis, 2008). Thus, Fanon’s argument about race and class relations in colonized Algeria takes on a new meaning: not only is one rich because one is white, and white because one is rich; within the French system of justice, one is just because one is white, and white because one is just. Within this logic of colonialism, there is no category by which the Algerian resistor can be recognized by except by the notions of an irrational ‘animal,’ a ‘terrorist,’ and a ‘criminal.’