Being And Event

1. Being is Pure Multiplicity: Ontology as Mathematics

In mathematics, being, thought, and consistency are one and the same thing.

Mathematics as Ontology. Badiou posits that mathematics, specifically set theory, is ontology, the science of being qua being. This means that the fundamental structures of reality are best understood through mathematical concepts, particularly the concept of the pure multiple. This challenges traditional philosophical approaches to ontology, which often rely on intuition, language, or experience.

Set Theory as the Foundation. Cantor's set theory, with its focus on the infinite and the structure of multiplicities, provides the framework for Badiou's ontology. The axioms of set theory, such as the axiom of separation and the axiom of choice, become the tools for understanding the nature of being.

Rejection of Foundationalism. By identifying mathematics as ontology, Badiou rejects the need for a separate philosophical foundation for mathematics. The apodeictic nature of mathematics is directly warranted by being itself. This move circumvents traditional philosophical debates about the nature of mathematical objects and their relationship to reality.

2. The One is Not: Subtractive Ontology

The one, being an operation, is never a presentation.

Rejection of the One. Badiou's ontology is characterized by a rejection of the One as a fundamental principle. He argues that the One is not a pre-existing entity but rather an operation, a result of counting or structuring a multiplicity. This challenges traditional philosophical systems that posit the One as the ultimate source or ground of being.

The Count-as-One. Instead of a being of the One, Badiou emphasizes the "count-as-one" as the structuring force that organizes multiplicities. The count-as-one is an operation that imposes a structure on a situation, allowing us to identify and enumerate its elements.

Inconsistent Multiplicity. Badiou posits that being, in its pure state, is an inconsistent multiplicity, a collection of elements without any inherent unity or structure. It is only through the operation of the count-as-one that this multiplicity is organized into a consistent and comprehensible situation.

3. The Event: Rupture and Supplementation

A truth is solely constituted by rupturing with the order which supports it, never as an effect of that order.

The Event as Rupture. Badiou introduces the concept of the event as a radical rupture in the order of being. An event is an occurrence that cannot be predicted or explained by the existing structure of a situation. It is a point of absolute contingency that disrupts the established order.

Supplementation. The event is not simply a destructive force but also a source of new possibilities. It supplements the existing situation, opening up new avenues for thought and action. This supplementation is not a natural or inevitable process but requires an active intervention.

Examples of Events. Badiou identifies events in various domains, including politics (e.g., the French Revolution), art (e.g., the invention of serialism in music), science (e.g., Cantor's set theory), and love (e.g., the encounter that initiates a love affair).

4. Intervention: Naming the Unnameable

A subject is nothing other than an active fidelity to the event of truth.

The Role of Intervention. The event, in itself, is a chaotic and unformed occurrence. It requires an intervention to name it, to give it a meaning and significance. This intervention is not a neutral act of observation but a deliberate and transformative act of naming.

Illegal Nomination. The intervention is often an "illegal" act, a transgression of the established norms and conventions of the situation. It involves choosing a name for the event that is not authorized by the existing order.

The Logic of the Two. The intervention creates a division, a "logic of the two," between those who recognize the event and those who remain bound to the old order. This division is the foundation for the emergence of a subject.

5. Fidelity: The Subject's Response to the Event

A subject is nothing other than an active fidelity to the event of truth.

Active Fidelity. The subject is not a passive observer of the event but an active participant in its unfolding. Fidelity involves a commitment to exploring the consequences of the event, to working out its implications for the transformation of the situation.

Generic Procedures. Fidelity is not a blind adherence to a fixed set of beliefs but a dynamic and creative process of inquiry. It involves developing "generic procedures" that are applicable to all aspects of the situation, regardless of their specific content.

Militant of Truth. The subject is a "militant of truth," someone who is willing to challenge the established order and to fight for the recognition of the event's transformative power. This militancy is not necessarily violent or aggressive but involves a persistent and unwavering commitment to the truth.

6. The State: Managing the Unmanageable

The structure of situations does not, in itself, deliver any truths.

The State as Metastructure. Badiou introduces the concept of the State as a metastructure that attempts to manage and control the multiplicities of being. The State is not simply a political institution but a general principle of organization that operates in all domains of existence.

The State's Limitations. The State, by its nature, is incapable of grasping the event or the truth. It is limited to the realm of knowledge, to the established order of things. The event, as a rupture in that order, necessarily escapes the State's grasp.

Normalcy, Singularity, and Excrescence. Badiou identifies three types of being in relation to the State: normalcy (what is both presented and represented), singularity (what is presented but not represented), and excrescence (what is represented but not presented). These categories provide a framework for understanding the dynamics of power and resistance in any situation.

7. Truth: Generic Procedures and Indiscernibility

The being of a truth, proving itself an exception to any pre-constituted predicate of the situation in which that truth is deployed, is to be called ‘generic’.

Truth as Generic. Badiou argues that truth is not a property of statements or beliefs but a generic procedure, a process that unfolds independently of any pre-existing categories or predicates. A truth is "generic" in the sense that it is indifferent to the particularities of the situation in which it emerges.

Indiscernibility. Truth is also characterized by indiscernibility. A truth is a multiplicity that cannot be circumscribed by any particular predicate. It concerns everyone inasmuch as it is a multiplicity that no particular predicate can circumscribe.

The Thought of the Generic. The thought of the generic supposes the complete traversal of the categories of being and of the event. It crystallizes concepts to such a point that it is almost impossible to give an image of it.

8. Forcing: Bridging the Gap Between Being and Truth

Subjective production: decision of an undecidable, disqualification, principle of inexistents.

Cohen's Forcing. Badiou draws on Paul Cohen's mathematical technique of forcing to develop a theory of the subject. Forcing is a method for constructing new mathematical universes by adding "generic" elements to existing ones.

From Indiscernible to Undecidable. Badiou uses forcing to show how the indiscernible can give rise to the undecidable. By adding a generic element to a situation, we create new possibilities for truth that were previously inaccessible.

The Technique of Forcing. The technique of forcing involves starting with a "quasi-complete" situation and adding a generic element to it. This generic element is indiscernible in the original situation, but it has specific properties that allow us to prove new theorems.

9. The Limits of Knowledge: Constructivism and the Void

To know how to make thought pass through demonstrations as through plainsong, and thus to steep an unprecedented thinking in disparate springs.

Constructivist Thought. Badiou critiques constructivist thought, which seeks to build up knowledge from a set of basic principles. He argues that constructivism is limited by its reliance on pre-existing categories and its inability to grasp the event.

The Folding of Being. Badiou introduces the concept of the "folding of being" to describe the way in which being is both revealed and concealed by knowledge. Knowledge, in its attempt to grasp being, inevitably distorts and simplifies it.

The Sovereignty of Language. Badiou critiques the idea that language is the ultimate foundation of knowledge. He argues that language is always limited and that it cannot fully capture the richness and complexity of being.

10. Beyond Lacan: A New Theory of the Subject

Chance, from which any truth is woven, is the matter of the subject.

Theory of the Subject. Badiou develops a new theory of the subject that goes beyond both Cartesian and Lacanian conceptions. The subject is not a substance or a consciousness but a local active dimension of a generic procedure.

Subjectivization. Subjectivization is the process by which an individual becomes a subject, by actively engaging in a truth procedure. This process involves intervention, fidelity, and the production of new knowledge.

Subject and Truth. The subject is not the origin or foundation of truth but rather a local active dimension of a generic procedure. To be a Subject (and not a simple individual animal) is to be a local active dimension of such a procedure.

Last updated: April 2, 2025