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Parmenides was among the first to propose an ontological characterization of the fundamental nature of reality.

Ontology (from onto-, from the Greek ὤν, ὄντος "being; that which is", present participle of the verb εἰμί "be", and -λογία, -logia: science, study, theory) is the philosophical study of the nature of being, existence, or reality, as well as the basic categories of being and their relations. Traditionally listed as a part of the major branch of philosophy known as metaphysics, ontology deals with questions concerning what entities exist or can be said to exist, and how such entities can be grouped, related within a hierarchy, and subdivided according to similarities and differences.^{[citation needed]}

Overview[link]

Ontology, in analytic philosophy, concerns the determination whether some categories of being are fundamental and asks in what sense the items in those categories can be said to "be." It is the inquiry into being in so much as it is being, or into beings insofar as they exist—and not insofar as, for instance, particular facts can be obtained about them or particular properties belong to them.^{[citation needed]}

Some philosophers, notably of the Platonic school, contend that all nouns (including abstract nouns) refer to existent entities. Other philosophers contend that nouns do not always name entities, but that some provide a kind of shorthand for reference to a collection of either objects or events. In this latter view, mind, instead of referring to an entity, refers to a collection of mental events experienced by a person; society refers to a collection of persons with some shared characteristics, and geometry refers to a collection of a specific kind of intellectual activity.^[1] Between these poles of realism and nominalism, there are also a variety of other positions; but any ontology must give an account of which words refer to entities, which do not, why, and what categories result. When one applies this process to nouns such as electrons, energy, contract, happiness, space, time, truth, causality, and God, ontology becomes fundamental to many branches of philosophy.^{[citation needed]}

Some fundamental questions[link]

Principal questions of ontology are "What can be said to exist?", "Into what categories, if any, can we sort existing things?", "What are the meanings of being?", "What are the various modes of being of entities?". Various philosophers^[who?] have provided different answers to these questions.^{[citation needed]}

One common approach is to divide the extant subjects and predicates into groups called categories. Of course, such lists of categories differ widely from one another, and it is through the co-ordination of different categorical schemes that ontology relates to such fields as library science and artificial intelligence. Such an understanding of ontological categories, however, is merely taxonomic, classificatory. The categories are, properly speaking,^[2] the ways in which a being can be addressed simply as a being, such as what it is (its 'whatness', quidditas or essence), how it is (its 'howness' or qualitativeness), how much it is (quantitativeness), where it is, its relatedness to other beings, etc.^{[citation needed]}

Further examples of ontological questions include:^{[citation needed]}

• What is existence, i.e. what does it mean for a being to be?
• Is existence a property?
• Is existence a genus or general class that is simply divided up by specific differences?
• Which entities, if any, are fundamental? Are all entities objects?
• How do the properties of an object relate to the object itself?
• What features are the essential, as opposed to merely accidental attributes of a given object?
• How many levels of existence or ontological levels are there? And what constitutes a 'level'?
• What is a physical object?
• Can one give an account of what it means to say that a physical object exists?
• Can one give an account of what it means to say that a non-physical entity exists?
• What constitutes the identity of an object?
• When does an object go out of existence, as opposed to merely changing?
• Do beings exist other than in the modes of objectivity and subjectivity, i.e. is the subject/object split of modern philosophy inevitable?

Concepts[link]

Essential ontological dichotomies include:

• Universals and particulars
• Substance and accident
• Abstract and concrete objects
• Essence and existence
• Determinism and indeterminism

History of ontology[link]

Etymology[link]

While the etymology is Greek, the oldest extant record of the word itself is the New Latin form ontologia, which appeared in 1606, in the work Ogdoas Scholastica by Jacob Lorhard (Lorhardus) and in 1613 in the Lexicon philosophicum by Rudolf Göckel (Goclenius); see classical compounds for this type of word formation.^{[citation needed]}

The first occurrence in English of "ontology" as recorded by the OED (Oxford English Dictionary, second edition, 1989) appears in Nathaniel Bailey's dictionary of 1721, which defines ontology as ‘an Account of being in the Abstract’ - though, of course, such an entry indicates the term was already in use at the time. It is likely the word was first used in its Latin form by philosophers based on the Latin roots, which themselves are based on the Greek.^{[citation needed]}

The current on-line edition of the OED (Draft Revision September 2008) gives as first occurrence in English a work by Gideon Harvey (1636/7-1702): Archelogia philosophica nova; or, New principles of Philosophy. Containing Philosophy in general, Metaphysicks or Ontology, Dynamilogy or a Discourse of Power, Religio Philosophi or Natural Theology, Physicks or Natural philosophy - London, Thomson, 1663.^{[citation needed]}

Origins[link]

Parmenides and monism[link]

Parmenides was among the first to propose an ontological characterization of the fundamental nature of existence. In his prologue or proem he describes two views of existence; initially that nothing comes from nothing, and therefore existence is eternal. Consequently our opinions about truth must often be false and deceitful. Most of western philosophy, and science - including the fundamental concepts of falsifiability and the conservation of energy - have emerged from this view. This posits that existence is what can be conceived of by thought, created, or possessed. Hence, there can be neither void nor vacuum; and true reality can neither come into being nor vanish from existence. Rather, the entirety of creation is eternal, uniform, and immutable, though not infinite (he characterized its shape as that of a perfect sphere). Parmenides thus posits that change, as perceived in everyday experience, is illusory. Everything that can be apprehended is but one part of a single entity. This idea somewhat anticipates the modern concept of an ultimate grand unification theory that finally explains all of existence in terms of one inter-related sub-atomic reality which applies to everything.^{[citation needed]}

Ontological pluralism[link]

The opposite of eleatic monism is the pluralistic conception of Being. In the 5th century BC, Anaxagoras and Leucippus replaced ^[3] the reality of Being (unique and unchanging) with that of Becoming and therefore by a more fundamental and elementary ontic plurality. This thesis originated in the Greek-ion world, stated in two different ways by Anaxagoras and by Leucippus. The first theory dealt with "seeds" (which Aristotle referred to as "homeomeries") of the various substances. The second was the atomistic theory,^[4] which dealt with reality as based on the vacuum, the atoms and their intrinsic movement in it.^{[citation needed]}

The materialist Atomism proposed by Leucippus was indeterminist, but then developed by Democritus in a deterministic way. It was later (4th century BC) that the original atomism was taken again as indeterministic by Epicurus. He confirmed the reality as composed of an infinity of indivisible, unchangeable corpuscles or atoms (atomon, lit. ‘uncuttable’), but he gives weight to characterize atoms while for Leucippus they are characterized by a "figure", an "order" and a "position" in the cosmos.^[5] They are, besides, creating the whole with the intrinsic movement in the vacuum, producing the diverse flux of being. Their movement is influenced by the Parenklisis (Lucretius names it Clinamen) and that is determined by the chance. These ideas foreshadowed our understanding of traditional physics until the nature of atoms was discovered in the 20th century.^{[citation needed]}

Plato[link]

Plato developed this distinction between true reality and illusion, in arguing that what is real are eternal and unchanging Forms or Ideas (a precursor to universals), of which things experienced in sensation are at best merely copies, and real only in so far as they copy (‘partake of’) such Forms. In general, Plato presumes that all nouns (e.g., ‘Beauty’) refer to real entities, whether sensible bodies or insensible Forms. Hence, in The Sophist Plato argues that Being is a Form in which all existent things participate and which they have in common (though it is unclear whether ‘Being’ is intended in the sense of existence, copula, or identity); and argues, against Parmenides, that Forms must exist not only of Being, but also of Negation and of non-Being (or Difference). Universals do not have an existence over and above the particular things which instantiate them.^{[clarification needed]}

In his Categories, Aristotle identifies ten possible kinds of thing that can be the subject or the predicate of a proposition. For Aristotle there are four different ontological dimensions:^{[citation needed]}

i) according to the various categories or ways of addressing a being as such

ii) according to its truth or falsity (e.g. fake gold, counterfeit money)

iii) whether it exists in and of itself or simply 'comes along' by accident

iv) according to its potency, movement (energy) or finished presence (Metaphysics Book Theta).

According to Avicenna, and in an interpretation of Greek Aristotelian and Platonist ontological doctrines in mediaeval metaphysics, being is either necessary, contingent qua possible, or impossible. Necessary being is that which cannot but be, since its non-being entails a contradiction. Contingent qua possible being is neither necessary nor impossible for it to be or not to be. It is ontologically neutral, and is brought from potential existing into actual existence by way of a cause that is external to its essence. Its being is borrowed unlike the necessary existent, which is self-subsisting and is impossible for it not to be. As for the impossible, it necessarily does not exist, and the affirmation of its being is a contradiction.^[6]

Other ontological topics[link]

Ontological and epistemological certainty[link]

René Descartes, with "je pense donc je suis" or "cogito ergo sum" or "I think, therefore I am", argued that "the self" is something that we can know exists with epistemological certainty. Descartes argued further that this knowledge could lead to a proof of the certainty of the existence of God, using the ontological argument that had been formulated first by Anselm of Canterbury.^{[citation needed]}

Certainty about the existence of "the self" and "the other", however, came under increasing criticism in the 20th century. Sociological theorists, most notably George Herbert Mead and Erving Goffman, saw the Cartesian Other as a "Generalized Other", the imaginary audience that individuals use when thinking about the self. According to Mead, "we do not assume there is a self to begin with. Self is not presupposed as a stuff out of which the world arises. Rather the self arises in the world" ^[7][8] The Cartesian Other was also used by Sigmund Freud, who saw the superego as an abstract regulatory force, and Émile Durkheim who viewed this as a psychologically manifested entity which represented God in society at large.^{[citation needed]}

Body and environment, questioning the meaning of being[link]

Schools of subjectivism, objectivism and relativism existed at various times in the 20th century, and the postmodernists and body philosophers tried to reframe all these questions in terms of bodies taking some specific action in an environment. This relied to a great degree on insights derived from scientific research into animals taking instinctive action in natural and artificial settings—as studied by biology, ecology^[9], and cognitive science.^{[citation needed]}

The processes by which bodies related to environments became of great concern, and the idea of being itself became difficult to really define. What did people mean when they said "A is B", "A must be B", "A was B"...? Some linguists advocated dropping the verb "to be" from the English language, leaving "E Prime", supposedly less prone to bad abstractions. Others, mostly philosophers, tried to dig into the word and its usage. Heidegger distinguished human being as existence from the being of things in the world. Heidegger proposes that our way of being human and the way the world is for us are cast historically through a fundamental ontological questioning. These fundamental ontological categories provide the basis for communication in an age: a horizon of unspoken and seemingly unquestionable background meanings, such as human beings understood unquestioningly as subjects and other entities understood unquestioningly as objects. Because these basic ontological meanings both generate and are regenerated in everyday interactions, the locus of our way of being in a historical epoch is the communicative event of language in use.^[7] For Heidegger, however, communication in the first place is not among human beings, but language itself shapes up in response to questioning (the inexhaustible meaning of) being.^[10] Even the focus of traditional ontology on the 'whatness' or 'quidditas' of beings in their substantial, standing presence can be shifted to pose the question of the 'whoness' of human being itself.^[11]

Prominent ontologists[link]

See also[link]

References[link]

External links[link]

Look up ontology in Wiktionary, the free dictionary.

Wikimedia Commons has media related to: Ontology

• Ontology. Its Theory and History from a Philosophical Perspective
• Logic and Ontology entry by Thomas Hofwebwer in the Stanford Encyclopedia of Philosophy
• Free Open access book: Paolo Valore (ed), Topics on General and Formal Ontology.
• International Ontology Congress

This article relies on references to primary sources or sources affiliated with the subject, rather than references from independent authors and third-party publications. Please add citations from reliable sources. (September 2011)

Manuel De Landa, (born 1952 in Mexico City), is a writer, artist and philosopher who has lived in New York since 1975. He is presently the Gilles Deleuze Chair of Contemporary Philosophy and Science at the European Graduate School in Saas-Fee, Switzerland; a visiting professor at the University of Southern California School of Architecture in Los Angeles^{[citation needed]}; a lecturer at the University of Pennsylvania School of Design in Philadelphia, Pennsylvania; and an adjunct professor at the Pratt Institute School of Architecture in Brooklyn, New York.^[1] He was previously an adjunct professor in the Graduate School of Architecture, Planning and Preservation at Columbia University and a lecturer at Canisius College in Buffalo, New York. De Landa has a BFA from New York's School of Visual Arts.

He is the author of War in the Age of Intelligent Machines (1991), A Thousand Years of Nonlinear History (1997), Intensive Science and Virtual Philosophy (2002) and A New Philosophy of Society: Assemblage Theory and Social Complexity (2006). He has published many articles and essays and lectured extensively in Europe and in the United States. His work focuses on the theories of the French philosopher Gilles Deleuze on one hand, and modern science, self-organizing matter, artificial life and intelligence, economics, architecture, chaos theory, history of science, nonlinear dynamics, cellular automata on the other.

Alongside his intellectual work, De Landa made several short Super 8 and 16mm films in the 1970s and early 1980s. He pulled them from circulation after the original negatives were lost. In 2011, Anthology Film Archives restored and reissued them. Cited by filmmaker Nick Zedd in his Cinema of Transgression Manifesto, De Landa associated with many of the experimental and art filmmakers of this New York based movement. Much of De Landa's film work is inspired by his interest in philosophy and critical theory; one of his best known films, Raw Nerves, has been described as a 'Lacanian thriller' by at least one critic.

His latest book (as of March 2011) is Philosophy and Simulation: The Emergence of Synthetic Reason, which explores simulations of emergence in systems of different scales, from the atomic to the social.

Books[link]

• War in the Age of Intelligent Machines (1991)
• A Thousand Years of Nonlinear History (1997)
• Intensive Science and Virtual Philosophy (2002)
• A New Philosophy of Society: Assemblage Theory and Social Complexity (2006)
• Deleuze: History and Science (2010)
• Philosophy & Simulation: The Emergence of Synthetic Reason (2011)

See also[link]

• Gilles Deleuze
• Noosphere
• Realism
• Wargaming

External links[link]

• Manuel de Landa Faculty profile at European Graduate School EGS. Biography, bibliography, photos, quotes and video lectures.
• Manuel DeLanda Annotated Bibliography with links to articles
• Various texts
• http://www.canisius.edu/topos/delanda.asp
• Interview
• Interview on Ctheory
• Other interview by Paul Miller
• "Markets and antimarkets in the world economy" by DeLanda

Notes[link]

1. ^ See: Manuel de Landa Faculty profile at European Graduate School

Alain Badiou

Alain Badiou. Fnac Montparnasse (Paris). February 5th, 2010
Born	(1937-01-17) 17 January 1937 (age 75) Rabat, French Morocco
Era	Contemporary philosophy
Region	French philosophy
School	Marxism Continental philosophy
Main interests	Set Theory, Mathematics, Metapolitics, Ontology, Marxism
Notable ideas	Événement (Event), ontologie du multiple (ontology of the multiple & ontology is mathematics), Un n'est pas ("The One is Not")
Influenced by Plato, Marx, Cantor, Albert Lautman, Mao Zedong, Lacan, Althusser, Paul Cohen, Sartre, Deleuze, Lyotard, Hegel, Mallarmé, Beckett, Fernando Pessoa, Sylvain Lazarus
Influenced Slavoj Žižek, Peter Hallward, Simon Critchley, Ray Brassier, Sylvain Lazarus, Jason Barker, Quentin Meillassoux, Bruno Bosteels, Alberto Toscano, Oliver Feltham, Justin Clemens, Nina Power

Alain Badiou (French pronunciation: [alɛ̃ badju]  (listen) (help·info); born 17 January 1937 in Rabat, Morocco) is a French philosopher, professor at European Graduate School, formerly chair of Philosophy at the École Normale Supérieure (ENS).^[1]

Badiou has written about the concepts of being, truth and the subject in a way that, he claims, is neither postmodern nor simply a repetition of modernity. Politically, Badiou is committed to the far left, and to the communist tradition.

Slavoj Žižek has written of Badiou that he is "a figure like Plato or Hegel walk[ing] here among us".^[2]

Biography[link]

Badiou was a student at the Lycée Louis-Le-Grand and then the Ecole Normale Supérieure (1957–1961). He taught at the lycée in Reims from 1963 where he became a close friend of fellow playwright (and philosopher) François Regnault,^[3] and published a couple of novels before moving to the University of Paris VIII (Vincennes-Saint Denis) in 1969.^[4] Badiou was politically active very early on, and was one of the founding members of the Unified Socialist Party (PSU). The PSU was particularly active in the struggle for the decolonization of Algeria. He wrote his first novel, Almagestes, in 1964. In 1967 he joined a study group organized by Louis Althusser, became increasingly influenced by Jacques Lacan and became a member of the editorial board of Cahiers pour l’Analyse.^[4] By then he "already had a solid grounding in mathematics and logic (along with Lacanian theory)",^[4] and his own two contributions to the pages of Cahiers "anticipate many of the distinctive concerns of his later philosophy".^[4]

The student uprisings of May 1968 reinforced Badiou's commitment to the far Left, and he participated in increasingly militant groups, such as the Union des communistes de France marxiste-léniniste (UCFml). To quote Badiou himself, the UCFml is "the Maoist organization established in late 1969 by Natacha Michel, Sylvain Lazarus, myself and a fair number of young people".^[5] During this time, Badiou joined the faculty of the newly founded University of Paris VIII/Vincennes-Saint Denis which was a bastion of counter-cultural thought. There he engaged in fierce intellectual debates with fellow professors Gilles Deleuze and Jean-François Lyotard, whose philosophical works he considered unhealthy deviations from the Althusserian program of a scientific Marxism.

In the 1980s, as both Althusserian Marxism and Lacanian psychoanalysis went into decline (with Lacan dead and Althusser in an asylum), Badiou published more technical and abstract philosophical works, such as Théorie du sujet (1982), and his magnum opus, Being and Event (1988). Nonetheless, Badiou has never renounced Althusser or Lacan, and sympathetic references to Marxism and psychoanalysis are not uncommon in his more recent works (most notably Petit panthéon portatif/Pocket Pantheon).^[6][7]

He took up his current position at the ENS in 1999. He is also associated with a number of other institutions, such as the Collège International de Philosophie. He was a member of "L'Organisation Politique" which, as mentioned above, he founded in 1985 with some comrades from the Maoist UCFml. This organization disbanded in 2007, according to the French Wikipedia article (linked to in the previous sentence). Badiou has also enjoyed success as a dramatist with plays such as Ahmed le Subtil.

In the last decade, an increasing number of Badiou's works have been translated into English, such as Ethics, Deleuze, Manifesto for Philosophy, Metapolitics, and Being and Event. Short pieces by Badiou have likewise appeared in American and English periodicals, such as Lacanian Ink, New Left Review, Radical Philosophy, Cosmos and History [1] and Parrhesia. Unusually for a contemporary European philosopher his work is increasingly being taken up by militants in movements of the poor in countries like India, the Democratic Republic of Congo and South Africa where he is often read together with Frantz Fanon.^{[citation needed]}

Lately Badiou got into a fierce controversy within the confines of Parisian intellectual life. It started in 2005 with the publication of his "Circonstances 3: Portées du mot 'juif'" – The Uses of the Word "Jew".^[8] This book generated a strong response with calls of Badiou being labelled Anti-Semitic. The wrangling became a cause célèbre with articles going back and forth in the French newspaper Le Monde and in the cultural journal "Les temps modernes." Another philosopher, Jean-Claude Milner, has accused Badiou of Anti-Semitism.^[9]

Key concepts[link]

Badiou makes repeated use of several concepts throughout his philosophy. One of the aims of his thought is to show that his categories of truth are useful for any type of philosophical critique. Therefore, he uses them to interrogate art and history as well as ontology and scientific discovery. Johannes Thumfart argues that Badiou's philosophy can be regarded as a contemporary reinterpretation of Platonism.^[10]

Conditions[link]

According to Badiou, philosophy is suspended from four conditions (art, love, politics, and science), each of them fully independent "truth procedures." (For Badiou's notion of truth procedures, see below.) Badiou consistently maintains throughout his work (but most systematically in Manifesto for Philosophy) that philosophy must avoid the temptation to suture itself (that is, to hand over its entire intellectual effort) to any of these independent truth procedures. When philosophy does suture itself to one of its conditions (and Badiou argues that the history of philosophy during the nineteenth and twentieth centuries is primarily a history of sutures), what results is a philosophical "disaster." Consequently, philosophy is, according to Badiou, a thinking of the compossibility of the several truth procedures, whether this is undertaken through the investigation of the intersections between distinct truth procedures (the intersection of art and love in the novel, for instance), or whether this is undertaken through the more traditionally philosophical work of addressing categories like truth or the subject (concepts that are, as concepts, external to the individual truth procedures, though they are functionally operative in the truth procedures themselves). For Badiou, when philosophy addresses the four truth procedures in a genuinely philosophical manner, rather than through a suturing abandonment of philosophy as such, it speaks of them with a theoretical terminology that marks its philosophical character: inaesthetics rather than art; metapolitics rather than politics; ontology rather than science; etc.

Truth, for Badiou, is a specifically philosophical category. While philosophy's several conditions are, on their own terms, "truth procedures" (i.e., they produce truths as they are pursued), it is only philosophy that can speak of the several truth procedures as truth procedures. (The lover, for instance, does not think of her love as a question of truth, but simply and rightly as a question of love. Only the philosopher sees in the true lover's love the unfolding of a truth.) Badiou has a very rigorous notion of truth, one that is strongly against the grain of much of contemporary European thought. Badiou at once embraces the traditional modernist notion that truths are genuinely invariant (always and everywhere the case, eternal and unchanging) and the incisively postmodernist notion that truths are constructed through processes. Badiou's theory of truth, exposited throughout his work, accomplishes this strange mixture by uncoupling invariance and self-evidence (such that invariance does not imply self-evidence), as well as by uncoupling constructedness from relativity (such that constructedness does not lead to relativism).

The idea, here, is that a truth's invariance makes it genuinely indiscernible: because a truth is everywhere and always the case, it passes unnoticed unless there is a rupture in the laws of being and appearance, during which the truth in question becomes, but only for a passing moment, discernible. Such a rupture is what Badiou calls an event, according to a theory originally worked out in Being and Event and fleshed out in important ways in Logics of Worlds. The individual who chances to witness such an event, if he is faithful to what he has glimpsed, can then introduce the truth by naming it into worldly situations. For Badiou, it is by positioning oneself to the truth of an event that a human animal becomes a subject; subjectivity is not an inherent human trait. According to a process or procedure that subsequently unfolds only if those who subject themselves to the glimpsed truth continue faithful in the work of announcing the truth in question, genuine knowledge is produced (knowledge often appears in Badiou's work under the title of the "veridical"). While such knowledge is produced in the process of being faithful to a truth event, it should be noted that, for Badiou, knowledge, in the figure of the encyclopedia, always remains fragile, subject to what may yet be produced as faithful subjects of the event produce further knowledge. According to Badiou, truth procedures proceed to infinity, such that faith (fidelity) outstrips knowledge. (Badiou, following both Lacan and Heidegger, distances truth from knowledge.) The dominating ideology of the day, which Badiou terms "democratic materialism," denies the existence of truth and only recognize "bodies" and "languages." Badiou proposes a turn towards "dialectical materialism," which recognizes that there are only bodies and languages, except there are also truths.

Inaesthetic[link]

In Handbook of Inaesthetics Badiou coins the phrase "inaesthetic" to refer to a concept of artistic creation that denies "the reflection/object relation". Reacting against the idea of mimesis, or poetic reflection of "nature", Badiou claims that art is "immanent" and "singular". It is immanent in the sense that its truth is given in its immediacy in a given work of art, and singular in that its truth is found in art and art alone. His view of the link between philosophy and art is tied into the motif of pedagogy, which he claims functions so as to "arrange the forms of knowledge in a way that some truth may come to pierce a hole in them". He develops these ideas with examples from the prose of Samuel Beckett and the poetry of Stéphane Mallarmé and Fernando Pessoa (who he argues has developed a body of work that philosophy is currently incapable of incorporating), among others.

[edit] Introduction to 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.^[11] 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,^[12] 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.^[13] 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[link]

	Set theory portal
	Mathematics portal

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 separates sets out therefore is not an existential positive proposition, but other multiples whose properties validate its presentation; which is to say their structural relation. 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 elements which belong to that set, it can then secure the multiple (the multiplicities of humans) as one consistent concept (humanity), but only in terms of what does not belong to that set. What is, in following, crucial for Badiou is that the structural form of the count-as-one, which makes multiplicities thinkable, implies 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, does not coincide with what is understood by 'terminology', which is precisely difference (thus multiplicity) conditioning meaning. Since the idea of conceiving of a term without meaning does not compute, the count-as-one is a structural effect or a situational operation and not an event of truth. Multiples which are 'composed' or 'consistent' are count-effects; inconsistent multiplicity is 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. Russell's paradox famously ruled that possibility out of formal logic. (This paradox can be thought through in terms of a 'list of lists that do not contain themselves': if such a list does not write itself on the list the property is incomplete, as there will be one missing; if it does, it is no longer a list that does not contain itself.) So too does the axiom of foundation – or to give an alternative name the axiom of regularity – enact such a prohibition (cf. p. 190 in Being and Event). (This axiom states that all sets contain an element for which only the void [empty] set names what is common to both the set and its element.) 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 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.

The event and the subject[link]

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 of 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 [sic] (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’?

Badiou, whilst keen to stress the non-equivalence between politics and philosophy, thus finds his political approach – one of activism, militancy, and scepticism of parliamentary-democratic process – backed up by his philosophy based around singular, situated truths, and potential revolutions.

L'Organisation Politique[link]

Alain Badiou is a founding member (along with Natacha Michel and Sylvain Lazarus) of the militant French political organisation L'Organisation Politique, which was active from 1985 until it disbanded in 2007.^[14] It called itself a post-party organization concerned with direct popular intervention in a wide range of issues (including immigration, labor, and housing). In addition to numerous writings and interventions, L'Organisation Politique stressed the importance of developing political prescriptions concerning undocumented migrants (les sans papiers), stressing that they must be conceived primarily as workers and not immigrants.^[15]

Works[link]

English translations[link]

Journals[link]

• The International Journal of Badiou Studies
• "The Cultural Revolution: The Last Revolution?", transl. by Bruno Bosteels; positions: asia critique, Volume 13, Issue 3, Winter 2005; (Durham: Duke University Press, 2005): ISSN 1067-9847
• "Selections from Théorie du sujet on the Cultural Revolution", transl. by Alberto Toscano with the assistance of Lorenzo Chiesa and Nina Power; positions: asia critique, Volume 13, Issue 3, Winter 2005; (Durham: Duke University Press, 2005): ISSN 1067-9847
• "Further Selections from Théorie du sujet on the Cultural Revolution", transl. by Lorenzo Chiesa; positions: asia critique, Volume 13, Issue 3, Winter 2005; (Durham: Duke University Press, 2005): ISSN 1067-9847
• “The Triumphant Restoration", transl. by Alberto Toscano; positions: asia critique, Volume 13, Issue 3, Winter 2005; (Durham: Duke University Press, 2005): ISSN 1067-9847
• "An Essential Philosophical Thesis: 'It Is Right to Rebel against the Reactionaries'", transl. by Alberto Toscano; positions: asia critique, Volume 13, Issue 3, Winter 2005; (Durham: Duke University Press, 2005): ISSN 1067-9847

DVD[link]

Lectures[link]

Further reading[link]

Notes[link]