Being and Event
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Being and Event (1988) is a book by French philosopher Alain Badiou on being and event.
The major propositions of Badiou's philosophy all find their basis in Being and Event, in which he continues his attempt (which he began in Théorie du sujet) to reconcile a notion of the subject with ontology, and in particular post-structuralist and constructivist ontologies. A frequent criticism of post-structuralist work is that it prohibits, through its fixation on semiotics and language, any notion of a subject. Badiou's work is, by his own admission, an attempt to break out of contemporary philosophy's fixation upon language, which he sees almost as a straitjacket. This effort leads him, in Being and Event, to combine rigorous mathematical formulae with his readings of poets such as Mallarmé and Hölderlin and religious thinkers such as Pascal. His philosophy draws upon both 'analytical' and 'continental' traditions. In Badiou's own opinion, this combination places him awkwardly relative to his contemporaries, meaning that his work had been only slowly taken up. Being and Event offers an example of this slow uptake, in fact: it was translated into English only in 2005, a full seventeen years after its French publication.
As is implied in the title of the book, two elements mark the thesis of Being and Event: the place of ontology, or 'the science of being qua being' (being in itself), and the place of the event – which is seen as a rupture in being – through which the subject finds realization and reconciliation with truth. This situation of being and the rupture which characterizes the event are thought in terms of set theory, and specifically Zermelo–Fraenkel set theory (with the axiom of choice), to which Badiou accords a fundamental role in a manner quite distinct from the majority of either mathematicians or philosophers.
Mathematics as ontology
For Badiou the problem which the Greek tradition of philosophy has faced and never satisfactorily dealt with is that while beings themselves are plural, and thought in terms of multiplicity, being itself is thought to be singular; that is, it is thought in terms of the one. He proposes as the solution to this impasse the following declaration: that the one is not. This is why Badiou accords set theory (the axioms of which he refers to as the Ideas of the multiple) such stature, and refers to mathematics as the very place of ontology: Only set theory allows one to conceive a 'pure doctrine of the multiple'. Set theory does not operate in terms of definite individual elements in groupings but only functions insofar as what belongs to a set is of the same relation as that set (that is, another set too). What individuates a set, therefore, is not an existential positive proposition, but other multiples whose properties (i.e., structural relations) validate its presentation. The structure of being thus secures the regime of the count-as-one. So if one is to think of a set – for instance, the set of people, or humanity – as counting as one, the multiple elements which belong to that set are secured as one consistent concept (humanity), but only in terms of what does not belong to that set. What is crucial for Badiou is that the structural form of the count-as-one, which makes multiplicities thinkable, implies (somehow or other) that the proper name of being does not belong to an element as such (an original 'one'), but rather the void set (written Ø), the set to which nothing (not even the void set itself) belongs. It may help to understand the concept 'count-as-one' if it is associated with the concept of 'terming': a multiple is not one, but it is referred to with 'multiple': one word. To count a set as one is to mention that set. How the being of terms such as 'multiple' does not contradict the non-being of the one can be understood by considering the multiple nature of terminology: for there to be a term without there also being a system of terminology, within which the difference between terms gives context and meaning to any one term, is impossible. 'Terminology' implies precisely difference between terms (thus multiplicity) as the condition for meaning. The idea of a term without meaning is incoherent, the count-as-one is a structural effect or a situational operation; it is not an event of 'truth'. Multiples which are 'composed' or 'consistent' are count-effects. 'Inconsistent multiplicity' [meaning?] is [somehow or other] 'the presentation of presentation.'
Badiou's use of set theory in this manner is not just illustrative or heuristic. Badiou uses the axioms of Zermelo–Fraenkel set theory to identify the relationship of being to history, Nature, the State, and God. Most significantly this use means that (as with set theory) there is a strict prohibition on self-belonging; a set cannot contain or belong to itself. This results from the axiom of foundation – or the axiom of regularity – which enacts such a prohibition (cf. p. 190 in Being and Event). (This axiom states that every non-empty set A contains an element y that is disjoint from A.) Badiou's philosophy draws two major implications from this prohibition. Firstly, it secures the inexistence of the 'one': there cannot be a grand overarching set, and thus it is fallacious to conceive of a grand cosmos, a whole Nature, or a Being of God. Badiou is therefore – against Georg Cantor, from whom he draws heavily – staunchly atheist. However, secondly, this prohibition prompts him to introduce the event. Because, according to Badiou, the axiom of foundation 'founds' all sets in the void, it ties all being to the historico-social situation of the multiplicities of de-centred sets – thereby effacing the positivity of subjective action, or an entirely 'new' occurrence. And whilst this is acceptable ontologically, it is unacceptable, Badiou holds, philosophically. Set theory mathematics has consequently 'pragmatically abandoned' an area which philosophy cannot. And so, Badiou argues, there is therefore only one possibility remaining: that ontology can say nothing about the event.
Several critics have questioned Badiou's use of mathematics. Mathematician Alan Sokal and physicist Jean Bricmont write that Badiou proposes, with seemingly "utter seriousness," a blending of psychoanalysis, politics and set theory that they contend is preposterous. Similarly, philosopher Roger Scruton has questioned Badiou's grasp of the foundation of mathematics, writing in 2012:
- There is no evidence that I can find in Being and Event that the author really understands what he is talking about when he invokes (as he constantly does) Georg Cantor's theory of transfinite cardinals, the axioms of set theory, Gödel's incompleteness proof or Paul Cohen's proof of the independence of the continuum hypothesis. When these things appear in Badiou's texts it is always allusively, with fragments of symbolism detached from the context that endows them with sense, and often with free variables and bound variables colliding randomly. No proof is clearly stated or examined, and the jargon of set theory is waved like a magician's wand, to give authority to bursts of all but unintelligible metaphysics.
An example of a critique from a mathematician's point of view is the essay 'Badiou's Number: A Critique of Mathematics as Ontology' by Ricardo L. Nirenberg and David Nirenberg, which takes issue in particular with Badiou's matheme of the Event in Being and Event, which has already been alluded to in respect of the 'axiom of foundation' above. Nirenberg and Nirenberg write:
- Rather than being defined in terms of objects previously defined, ex is here defined in terms of itself; you must already have it in order to define it. Set theorists call this a not-well-founded set. This kind of set never appears in mathematics—not least because it produces an unmathematical mise-en-abîme: if we replace ex inside the bracket by its expression as a bracket, we can go on doing this forever—and so can hardly be called “a matheme.”' (http://criticalinquiry.uchicago.edu/uploads/pdf/nirenbergs_badiousnumber_complete.pdf, pp. 598–9)
The event and the subject
The principle of the event is where Badiou diverges from the majority of late twentieth century philosophy and social thought, and in particular the likes of Foucault, Butler, Lacan and Deleuze, among others. In short, it represents that which is outside ontology. Badiou's problem here is, unsurprisingly, the question of how to 'make use' of that which cannot be discerned. But it is a problem he views as vital, because if one constructs the world only from that which can be discerned and therefore given a name, it results in either the destitution of subjectivity and the removal of the subject from ontology (the criticism continually leveled at Foucault's discursive universe), or the Panglossian solution of Leibniz: that God is language in its supposed completion.
Badiou again turns here to mathematics and set theory – Badiou's language of ontology – to study the possibility of an indiscernible element existing extrinsically to the situation of ontology. He employs the strategy of the mathematician Paul J. Cohen, using what are called the conditions of sets. These conditions are thought of in terms of domination, a domination being that which defines a set. (If one takes, in binary language, the set with the condition 'items marked only with ones', any item marked with zero negates the property of the set. The condition which has only ones is thus dominated by any condition which has zeros in it [cf. p. 367-71 in Being and Event].) Badiou reasons using these conditions that every discernible (nameable or constructible) set is dominated by the conditions which don't possess the property that makes it discernible as a set. (The property 'one' is always dominated by 'not one'.) These sets are, in line with constructible ontology, relative to one's being-in-the-world and one's being in language (where sets and concepts, such as the concept 'humanity', get their names). However, he continues, the dominations themselves are, whilst being relative concepts, not necessarily intrinsic to language and constructible thought; rather one can axiomatically define a domination – in the terms of mathematical ontology – as a set of conditions such that any condition outside the domination is dominated by at least one term inside the domination. One does not necessarily need to refer to constructible language to conceive of a 'set of dominations', which he refers to as the indiscernible set, or the generic set. It is therefore, he continues, possible to think beyond the strictures of the relativistic constructible universe of language, by a process Cohen calls forcing. And he concludes in following that while ontology can mark out a space for an inhabitant of the constructible situation to decide upon the indiscernible, it falls to the subject – about which the ontological situation cannot comment – to nominate this indiscernible, this generic point; and thus nominate, and give name to, the undecidable event. Badiou thereby marks out a philosophy by which to refute the apparent relativism or apoliticism in post-structuralist thought.
Badiou's ultimate ethical maxim is therefore one of: 'decide upon the undecidable'. It is to name the indiscernible, the generic set, and thus name the event that re-casts ontology in a new light. He identifies four domains in which a subject (who, it is important to note, becomes a subject through this process) can potentially witness an event: love, science, politics and art. By enacting fidelity to the event within these four domains one performs a 'generic procedure', which in its undecidability is necessarily experimental, and one potentially recasts the situation in which being takes place. Through this maintenance of fidelity, truth has the potentiality to emerge.
In line with his concept of the event, Badiou maintains, politics is not about politicians, but activism based on the present situation and the 'evental' (his translators' neologism) rupture. So too does love have this characteristic of becoming anew. Even in science the guesswork that marks the event is prominent. He vigorously rejects the tag of 'decisionist' (the idea that once something is decided it 'becomes true'), but rather argues that the recasting of a truth comes prior to its veracity or verifiability. As he says of Galileo (p. 401):
- When Galileo announced the principle of inertia, he was still separated from the truth of the new physics by all the chance encounters that are named in subjects such as Descartes or Newton. How could he, with the names he fabricated and displaced (because they were at hand – 'movement', 'equal proportion', etc.), have supposed the veracity of his principle for the situation to-come that was the establishment of modern science; that is, the supplementation of his situation with the indiscernible and unfinishable part that one has to name 'rational physics'?
While Badiou is keen to reject an equivalence between politics and philosophy, he correlates nonetheless his political activism and skepticism toward the parliamentary-democratic process with his philosophy, based around singular, situated truths, and potential revolutions.
