Justin Clemens & Oliver Feltham “An Introduction to Alain Badiou’s Philosophy”

Clemens, Justin; Oliver Feltham 2004. An Introduction to Alain Badiou’s Philosophy. – Badiou, A. Infinite Thought: Truth and the Return of Philosophy. London; New York: Continuum: 1-38.

Badiou’s guiding question: How can a modern doctrine of the subject be reconciled with an ontology? (3)

The problem with poststructuralism is that exactly the same of negative definitions serves to delimit its implicit ontology (whether of desire or difference): there are no self-identical substances, there are no stable products of reflection, and since there are no stable objects there can be no correlates of such objects. Thus in poststructuralism there is no distinction between the general field of ontology and a theory of the subject; there is no tension between the being of the subject and being in general. Where Badiou sees an essential question for modern philosophy, then, poststructuralism sees nothing. (3-4)

[…] Badiou recognizes a distinction between the general domain of ontology and the theory of the subject. […] he defers the problem of identity […] while he concentrates on the problem of agency. (6)

For Badiou, the question of agency is not so much a question of how a subject can initiate an action in an autonomous manner but rather how a subject emerges through an autonomous chain of actions within a changing situation. That is, it is not everyday actions or decisions that provide evidence of agency for Badiou. It is rather those extraordinary decisions and actions which isolate an actor from their context […] For this reason, not every human being is always a subject, yet some human beings become subjects; those who act in fidelity to a chance encounter with an event which disrupts the situation they find themselves in. (6)

A subject is born of a human being’s decision that something they have encountered, which has happened in their situation – however foreign and abnormal – does in fact belong to the situation and thus cannot be overlooked. (6)

There is nothing other than chance encounters between particular humans and particular events; and subjects may be born out of such encounters. […] Thus, Badiou displaces the problem of agency from the level of the human to the level of being. (8)

Thus the relation between the being of the subject and the general domain of Badiou’s ontology is a contingent relationship, which hinges on the occurrence of an event and the decision of a subject to act in fidelity to that event. (9)

Situations include all those flows, properties, aspects, concatenations of events, disparate collective phenomena, bodies, monstrous and virtual, that one migth want to examine within and ontology. The concept of ’situation’ is also designed to accomodate anything which is, regardless of its modality […] (10)

[…] unity is the result of an operation termed the count-for-one. This count is what Badiou terms the situation’s structure. A structure determines what belongs and does not belong to the situation by counting various multiplicities as elements of the situation. An element is a basic unit of a situation. A structure thereby generates unity at the level of each element of the situation. It also generates unity at the level of the whole situation by unifying the multiplicity of elements. This is a ’static’ definition of a situation: a situation is a presented multiplicity. (11)

[…] for Badiou unity is the effect of structuration – and not a ground, origin, or end. The consequence of the unity of situations being the effect of an operation is that a multiple that belongs to one situation may also belong to another situation: situations do not have mutually exclusive identities. (11)

The distinction between a situation and its structuring count-for-one only holds, strictly speaking, within ontology; the situation is nothing other than this operation of ’counting-for-one’. If a situation is a counting-for-one, then Badiou also has a dynamic definition of a situation. Once he has both a dynamic as well as a static definition of a situation – the operation of counting-for-one, and unified presented multiplicity – he is able to join his doctrine of multiplicity to a reworking of Heidegger’s ontological difference. (11)

Unlike Heidegger, however, the being of a situation is not something that only a poetic saying can approach; it is, quite simply and banally, the situation ’before’ or rather, without the effect of the count-for-one; it is the situation as a non-unified or inconsistent multiplicity. (12)

Badiou’s ’inconsistent multiplicity’ is therefore not to be equated with Aristotelian ’prime matter’; its ’actual’ status is, moreover, ’undecidable’. Precisely because a situation provokes the question ’What was there before all situations?’ but provides no possible access to this ’before’ that is not irremediably compromised by post-situational terminology and operations, it is impossible to speak of in any direct way. With the thought of ’inconsistent multiplicity’, thought therefore touches on its own limits; what Badiou calls, following Lacan, its ’real’. (13)

The void of a situation is simply what is not there, but what is necessary for anything to be there. […] This is the null-set, a multiple of nothing or of the void. On the sole basis of this set, using operations regulated by formal axioms, set theory unfoldas an infinity of further sets. Set theory thus weaves its sets out of a ’void’, out of what, in any other situation, is the substractive suture to being of that situation. […] In each and every non-ontological situation, its inconsistent multiplicity is a void. The only possible presentation of a ’void’ in set theory is the null-set. (16)

If one compares set theory to classical ontologies, indeed even to that of Deleuze, its modernity is immediate. It makes no claims concerning the nature of being, nor concerning the adequation of its categories to being. (18)

Consequently, in set theory ontology, the regime of identity and difference is founded upon extension, not quality. That is, every difference is localized in a point: for two sets to be different, at least one element of one of the sets must not belong to the other. (19)

The conclusion Badiou thus draws from set theory for the traditional philosophical problem of the relationship between language and being is that, although language bestows identity on being, being is in excess of language. […] In meta-ontological terms, the axiom of separation states that an undefined existence must always be assumed in any definition of a type of multiple. (22)

[…] it [set theory] has nothing to say about beings themselves – this is the province of other discourses such as physics, anthropology and literature. This is one reason why Badiou terms set theory a subtractive ontology: it speaks of beings without reference to their attribute or their identity; it is as if the beings ontology speaks of have had all their qualities subtracted from them. (23)

In meta-ontological terms, the power-set is the state of a situation. This means that every multiple already counted as one, is counted again at the level of its sub-multiples: the state is thus a second count-for-one. (24)

There are three types of multiple: normal multiples, which are both presented in the situation and represented by its state (they are counted-for-one twice); excrescent multiples, which are only represented by the state; and singular multiples, which only occur at the level of presentation, and which escape the effect of the second count-for-one. (24)

Natural situations are defined as having no singular multiples – all of their multiples are either normal or excrescent, and each normal element in turn has normal elements. Neutral situations are defined as having a mix of singular, normal and excrescent multiples. Historical situations are defined by their having at least one ’evental-site’; a sub-type of singular multiple. In set theory terms, a singular multiple is an element of a set, but not one of its subsets. Since each of a set’s subsets is made entirely of elements that already belong to the initial set, the definition of a singular multiple is that, first, it is an element of an initial set, and, second, some of its own elements in turn do not belong to the initial set. It is these foreign elements which are responsible for the singularity of a singular multiple. An evental-site is an extreme variety of a singular multiple: none of an evental-site’s elements also belong to the initial set. (24-25)

Howver, the existence of an evental-site in a situation does not guarantee that change will occur. For that something extra is required, a ’supplement’ as Badiou says, which is an event. […] The occurrence of an event is completely unpredictable. There is no meta-situation – ’History’ – which would programme the occurrence of evetns in various selected situations. (27)

[…] every multiple found in the model can be discerned using the tools of language. A generic set, on the other hand, is a subset that is ’new’ insofar as it cannot be discerned by that language. For every property that one formulates, even the most general such as ’this apple and this apple and this apple …’, the generic set has at least one element which does not share that property. […] The generic subset is only presented at the level of inclusion, and, unlike all the other subsets, it cannot be known via its properties. (29-30)

For Badiou, the actual work which carries out the wholesale change of a historical situation – in his terms, the fidelity practised by subjects to an event – consists of such experiments; infinite enquiries into the nature of the event, using an invented idiom to approximate what is discovered throug such enquiries. […] What results from such subtractions is a praxis made up of a hazardous series of bets, bets on the nature of the situation to come. Many of these bets will fall wide of the mark, but those that hit the target will help construct the new situation. (31)

Ontology only speaks of the structure of multiplicity: it has nothing to say about the qualities or identity of any concrete situation. (32)