Badiou and Saint Paul
Well it's been a while, but this is the rather rough paper I gave the other day at the University of Bristol's 10th Postgraduate Conference on Theology and Religous Studies (12th March 2005). It is essentially yet another introduction to Badiou, but I managed to get to grips with certain important themes in his work whilst writing this. But let me know what you think.
Badiou and Saint Paul
[1] As my abstract suggests, this paper is predominantly about Alain Badiou, rather than Saint Paul, and as such is essentially a philosophical paper that I hope will be of interest to a wider, theologically minded audience. What I aim to achieve is an introduction to Badiou’s philosophy, which will attempt to make some of his more abstract and mathematical concepts more accessible through an engagement with Badiou’s own work on Saint Paul.
[2]Although Badiou’s work is becoming increasingly well known, it is still prudent to assume that most people, outside of a certain specialist area of research in continental philosophy, will have had a limited encounter with his philosophy. Badiou is a somewhat controversial figure in contemporary continental philosophy, much maligned by philosophers from both analytical and continental backgrounds. The cause for such rancour is Badiou’s use of contemporary mathematics married to a radical political stance, which is recognisably continental. His use of mathematics is seen as yet another ‘bad’ appropriation of Science by continental philosophers, whereas his attempt to resurrect such unfashionable concepts as universal truths, rationalism, and systematic thought, along with the claim that ontology is nothing more than mathematics has alienated him from certain strands of continental philosophy. He is still alive, and working today, and is in my opinion one of the most exciting and challenging of contemporary philosophers.
[3] Before continuing, I would like to highlight the two points that I will examine in relation to Badiou and his work on Saint Paul, these are: first, the initially strange sounding concept of the possibility of a material faith, and the consequences of such a faith, which is a truth procedure which founds a universal truth. Second, a truth procedure, which founds such a universal truth, is governed by a fidelity, or faith, to some event that has ‘happened’. The inexplicable nature of this event means that the procedure operates without reference to any rule, or law. These are two common themes within the letters of Saint Paul; the superiority of faith over works and that faith operates free from the law. In a sense, one of Badiou’s aims is to wrest religion’s final defence from it; the invocation of faith, and make it operate in a wholly material fashion, devoid of all theological reference. In order to be able to understand Badiou’s interpretation of the works of Saint Paul it will be necessary to elaborate in some detail the workings, and concerns that drive Badiou’s systematic thought.
[4] Badiou’s philosophical concerns clearly belong to a contemporary strand of continental thought, perhaps best called philosophies of difference, or the event, which are most familiarly associated with the works of the later Heidegger, Derrida and Deleuze and Guattari, to name but a few. These philosophies tend to be preoccupied with the generation, or creation of novelty, in all its forms, be it scientific, natural, artistic etc. The fundamental problem stems from what Badiou succinctly calls his ‘wager’: that the One is not. Anything that counts for a One, or a unity is not, the correlate of this is that what is is pure multiplicity, or pure difference. This is the root of Badiou’s anti-theological stance, which he equates with any system of thought that has as its fundamental ground of existence in some unity, be it a transcendent omnipotent entity, or the unity of some impersonal vital force that somehow permeates all reality. It is important to note that Badiou’s rejection of theology acknowledges that it is not something that can be disproved or debunked, the very language of a wager on multiplicity, as opposed to unity, recalls the language of Pascal wager on the existence of God.
[5] Introducing some important terminology, this pure multiplicity is completely unordered and un-orderable, it cannot be taken as a unity or totality; it is therefore inconsistent multiplicity. That which can be unified, or counted as one, is consistent multiplicity. What will be of interest is the relation or, as it will turn out, non-relation between consistent and inconsistent multiplicity. It is at this juncture that Badiou’s indebtedness to mathematical set-theory begins to assert itself. At the beginning of his seminal work L’être et l’événtment Badiou states: ‘what must be said is that the one, which is not, exists solely as operation. Or; there is no one, there is only the count-for-one.’ This count for one presents what has been counted to consist as a unity, what has been gathered together to form a one, but this pure operation has, as yet nothing to operate on. It is the foundational step of applying this pure process of naming to inconsistent multiplicity that grounds all possible systems of related and consistent unities. This operation when applied to what is, inconsistent multiplicity, can present, as consistent, precisely nothing. All that appears, or is presented, is the pure operation of gathering.
[6] Set theory is concerned with the manipulation and relation of consistent multiplicities, or aggregates. In this theory there is only one founding axiom that existentially asserts the existence of a set. This is the empty set axiom. All the other axioms state how to manipulate sets which have already been given. The empty set has its own special symbol Æ, but is in essence simply a pair of empty braces {}, nothing but the presentation of the operation of gathering, or drawing together as a one. It is also possible, within this theory, to show that all other sets can be generated from this one set through the application of the remaining axioms.
[7] Inconsistent multiplicity, or the Void as Badiou sometimes calls it, cannot be presented, but it founds all possible presentation. The empty set is therefore what Badiou calls a pure, or empty name, it is not the presentation of the Void but its name. Therefore inconsistent and consistent multiplicity are linked through this axiomatic naming through the application of the count for one, the empty set sutures the presentation of consistent multiplicities, which are not, to inconsistent multiplicity, which is: Æ, the empty set, is the proper name of being. It also has a strange universal property; it is included in every set but never belongs. Therefore every set represents the void, but it is never presented and its universal property does not amount to much, it is simply the representation of nothing.
[8] What this recognises is that there is no ultimate, or absolute, first element with regards to a consistent set-theoretical construction. This foundational naming is a decision taken in the face of the void, an empty naming which makes consistent construction possible. All such foundational elements will always be essentially empty; therefore any regressive philosophy that attempts to understand itself through an ever more thorough examination of its foundations will fail. Badiou acknowledges a point already made clear in Heidegger’s Being and Time, that one always already has a primordial understanding of one’s situation, and finds oneself in the midst of things. In being capable of examining anything, one must have already understood the situation in order to orientate oneself towards what is being examined. The horizon of a situation cannot itself, as horizon, be bought into the foreground and examined: it is the condition of possibility for making things present. The same is true of the foundational nature of the empty set, and the axiomatic approach in general, they constitute the conditions of possibility for a situation, such that anything can appear at all.
[9] What does appear, in this mathematical model of a situation, are consistent multiples, or sets. Now with regards to sets Badiou places a lot of emphasis on the difference between belonging , the fundamental non-logical operation of set theory, and inclusion, being a subset. The importance of these two different operations is that they are not equal, although every element that belongs to a set is also included as a subset in it; it is not true that every subset is itself an element of the original set. To make this distinction clear let me take the example of the people in this room. Taken together we form a set, precisely of all the people in this room. But this set can be divided into a number of parts, for example we could divide it between men and women, speaker, chair and audience, and so on. With a finite number of people n, there are only a set number of ways of dividing us up, in fact 2n ways, but it should be noted that there are always more parts to a set than elements.
[10] What Badiou claims is that this difference between being an element of (belonging to) a set and being a subset, or part, of a set has huge ontological significance. For Badiou, a situation is simply the material elements that compose it; a situation is a set. The actuality of a situation is its presented material elements. The possibility inherent in any situation is simply the totality of possible arrangements of its elements, that is to say, the totality of its parts/subsets. What a subset does, in relation to a situation, is to re-present a part of it, therefore the totality of such subsets is a re-presentation of the situation taking into account all the possible ways that it might appear. This re-presentation, or the set of all subsets, is called the power set of a given set and is one of the most powerful concepts in set theory. At a finite level the power set of a set is strictly calculable, 2n, but one of the fundamental aspects of set theory is that it allows for completed infinite sets, such as the set of all natural/whole numbers. At an infinite level the concept of all possible arrangements does not seem to have an intuitively obvious meaning, and in fact turns out to be un-decidable. It is this aspect of in-determination that appears in the heart of mathematics that Badiou is interested in, and means that his philosophical appropriation of mathematics is not a simple return to determinism.
[11] It will be useful to recap some of the points made above. What I have been trying to highlight with the above rapid overview of Badiou’s philosophy is the following. All there is is inconsistent multiplicity; an empty founding decision forecloses a consistent realm against the inconsistency of the void. The realm of consistent multiplicity that has been founded through this subtraction from the void is a consistent self-contained world, or universe, governed by two limits: first the material of the situation which is presented as a set, this can be thought of as the actuality of the situation. And the possibility inherent in this situation, which is limited by the re-presentation of the situation in terms of its parts; these are the categories and divisions which can be brought to bear on it. What is problematic is that this second limit of possibility is un-decidable with reference to an infinite situation (all situations are, for Badiou, infinite). For the world to remain consistent and foreclosed against the void an extra condition will have to be brought in to give a measure to the un-decidable excess of the power set of a situation. The fact that the power set of an infinite set is un-decidable does not mean that a consistent measure cannot be given to it. The situation constitutes what can appear, and the horizon (power set) limits how it appears. And as long as there is a strict relation between the two, i.e. a measure has been given to the excess of re-presentation over presentation, then this world operates in a consistent manner, totally subtracted from and un-related to the void.
[12] We are now in a position to approach the central concern of Badiou: the event. The event constitutes a basic question that concerns many philosophies of difference: how can novelty be created, or generated? It is clear from the above model of how a consistent world operates that everything possible has already been accounted for. Badiou does not want to seek novelty in changing the situation, the content is to some extent irrelevant to his highly formal philosophy. Any such operation from ‘outside’ the current consistent world would be an unwarranted appeal to some transcendent factor. It would put the possible comprehension of novelty beyond every situation, if it is always intruded on from ‘outside’ or ‘beyond’. What Badiou wants is an event that triggers the possibility of novelty from fully within a given situation, using nothing more than what is already available to the situation: its material elements. An event is immanent to a situation and always disrupts the status quo of that situation. It is a revolutionary moment and demands militant action. What an event will provoke is the transformation of a situation, not into something which completely destroys or erases the previous consistent world, but one which transforms and extends it.
[13] The way that this may occur will rest on the relation between presentation and re-presentation, and the measure given to this representation. The state of a situation is what Badiou calls the re-presentation of a situation that is controlled by some measure, hence there is no gap between a situation and its state; the state accounts for all legitimate possible expressions of the situation. In some sense the state of a situation can be thought of as the language that expresses it. What is clear is that if a certain number and type of illegitimate expressions can somehow be made to consist within this consistent system they will disrupt and undermine the authority of the situations state. If it is insisted that these expressions truly belong to this system then the language of this system will have to be extended in order to accommodate them. The system will then have been transformed and extended, by using initially illegal expressions. It is important that these expressions are formed only from the material of the situation, and do not import anything from outside, as they would lose all chance of claiming legitimacy. By holding to the belief that these supposedly illegal expressions really are expressions of the situation it will be possible to modify the language to act ‘as if’ they were legitimate. The most complicated part of Badiou’s appropriation of set theory rests on how these illegitimate expressions can be held to in such a way as to modify and extend the language of expression/representation. Also, not just any expression can be used, they have to be ones that if acted on ‘as if’ they were expressions of the situation do not lead to fundamental paradoxes and inconsistency within the new extended system.
[14] The most important thing to understand in this attempt is the difference between an intentional and extensional conception of sets. Set theory only requires sets to be extensional, that is they are identified solely by their elements. An intentional definition would recognise the elements of a set as fulfilling some condition. For example, the set of all even numbers has an intentional definition; all its members fulfil the condition of being even. The intentional definition for a set, if it exists, can be substituted for its laborious extensional definition: the set with elements x, y, z,… One of the key ways of limiting the state of a situation is to only allow sets which have an intentional definition; they are sets which can be constructed according to some rule or law. The simple rules of construction which at a finite level can easily calculate all the possible permutations a finite set can be consistently modified to work on infinite sets, but it is no longer clear that this process of calculating permutations will actually exhaust all possible compositions of infinite sets. This difference is recognised by the two categories of constructible and non-constructible sets.
[15] It is these non-constructible sets that will form the heart, or site, of an event. It is clear that such a set cannot have a condition of membership by definition, such sets are completely unstructured. If a situation is governed by a state which only allows constructible sets, then a non-constructible set, although composed of the same material elements of the situation, will not be represented as a possibility of the situation, it will be invisible. The existence of such sets can only be asserted to exist; one must have a belief in them, and a faithful fidelity to the consequences that such a belief will deploy. This is what occurs in a truth procedure, stemming from the declaration of an event, which is simply the assertion that a number of non-constructible sets exist as possibilities of the situation. This fidelity to an event will force the language, or representation, of the situation to operate in a new way which will extend its usual functioning, such that it will begin to incorporate and make visible the consequences of holding such an event as true. The only way for this to happen is to investigate the situation element by element, and ask whether each element belongs to the non-constructible sets we are asserting exist. Every element must be investigated as the non-constructible set has no rule or condition that might include, or exclude any element in advance of an actual immanent investigation. The full sequence of these investigations constitutes an extension of the original representational range of the state of a situation; to such an extent that it can now consistently operate ‘as if’ the non-constructible set belonged to the representation of the situation.
[16] The last stage in this somewhat laborious overview will be the more philosophical distinction between a subject and an individual in Badiou’s philosophy, before finally turning to Badiou’s work on Saint Paul. A subject for Badiou is simply a finite portion of an infinite truth procedure. By investigating an infinite set, element by element, it is clear that a truth procedure is an infinite affair; any finite portion of this procedure can constitute a subject. An individual will simply be the notion of someone defined entirely by the legalistic definitions deployed in the state of a situation, be it their physical materiality, their belonging to a certain community or country etc. In other words, an identity centred on some definable trait, what such an individual is capable of is to be traversed by a truth procedure; that is to be taken up by it, such that his identity is shifted away from a comfortable constructible identity and moves toward a faith in a non-constructible, unstructured event.
[17] Due to a lack of time, my engagement with Badiou’s work on Saint Paul may well appear as a somewhat clumsy mapping of the terms introduced above onto the figure of Saint Paul. To some extent this is Badiou’s approach. He wants to conceive Saint Paul, and his activity in a purely formal light, in such a light Paul’s activity and response to the event of Jesus Christ’s death and subsequent resurrection appears as a Badiouian truth procedure. Paul becomes a subject in his fidelity and faith to the event of Christ’s death and resurrection, and this is manifested in his wondering militant preaching of the Gospel, not only to fellow Jews but also to the Gentiles. The message must be truly universal, as the event held to introduces a number of non-constructible elements, which if adhered to as true requires that this ‘message’ must be taken to all elements of the situation. In this case the situation is that of social world of the Roman Empire, and the preaching of the Gospel must be carried out as a systematic militant investigation of every element of that situation. No group can be assumed to belong to this truth in advance, according to some condition such as the laws governing Judaism, nor can any group be excluded in advance due to any condition. I think realistically I can only concentrate on perhaps one element of Badiou’s relation to Saint Paul in the time remaining, and that will be Saint Paul’s consideration of the law.
[18] Badiou’s strongest engagement, can perhaps predictably, be seen in his investigation of Paul’s relation to the law, and the message that Christ’s death and resurrection brings to the law. The discussion on law is taken up in Paul’s letter to the Romans, where the law is seen as death, and that which introduces the possibility of sin. This is the life of the flesh, and for Badiou is the simple animal life that we lead as mere individuals, living only according to specified rules and laws equates with the controlled representation, or state of a situation. Such laws can either be fulfilled or negated, and their very invention leads to a desire to violate and transgress them. Such transgressions do not challenge the law, but merely affirm their status and justify the need for their existence. Law and transgression form a neat binary relation. Both of which can be easily formulated in the language of the situation in terms of a condition, and the negation of that condition. The event for Badiou, in this case the death and resurrection of Christ, is not illegal in this sense, the event’s non-constructible elements are invisible to the legal constraints of a situation, the law lacks the ability to be able to properly talk about an event; it can neither affirm nor condemn it. But also Christ’s resurrection is a resurrection into life. The death to sin and the life of the flesh does not mean an eradication of law and sin, but only that through a faith and fidelity to an event one operates according to faith and not according to law. One can only investigate a situation’s elements according to a non-constructible set if one holds that this set exists, as no proof as to its non-constructible nature can ever be given. What this new life according to faith does is to transform and extend the situation, to add something truly new, to create something new from the given material. There is no intervention, or addition of new material from outside, this novel transformation happens immanently through the faith in an event which disrupts the relation between the horizon of a situation and what can appear within that horizon. The resurrection and life according to faith is a true life, a life that is truly creative as it deploys the consequences of an event and transforms its situation. This life of faith proceeds in a lawless fashion, distributing its message in a universal way to the furthest reaches of a situation.
Badiou and Saint Paul
[1] As my abstract suggests, this paper is predominantly about Alain Badiou, rather than Saint Paul, and as such is essentially a philosophical paper that I hope will be of interest to a wider, theologically minded audience. What I aim to achieve is an introduction to Badiou’s philosophy, which will attempt to make some of his more abstract and mathematical concepts more accessible through an engagement with Badiou’s own work on Saint Paul.
[2]Although Badiou’s work is becoming increasingly well known, it is still prudent to assume that most people, outside of a certain specialist area of research in continental philosophy, will have had a limited encounter with his philosophy. Badiou is a somewhat controversial figure in contemporary continental philosophy, much maligned by philosophers from both analytical and continental backgrounds. The cause for such rancour is Badiou’s use of contemporary mathematics married to a radical political stance, which is recognisably continental. His use of mathematics is seen as yet another ‘bad’ appropriation of Science by continental philosophers, whereas his attempt to resurrect such unfashionable concepts as universal truths, rationalism, and systematic thought, along with the claim that ontology is nothing more than mathematics has alienated him from certain strands of continental philosophy. He is still alive, and working today, and is in my opinion one of the most exciting and challenging of contemporary philosophers.
[3] Before continuing, I would like to highlight the two points that I will examine in relation to Badiou and his work on Saint Paul, these are: first, the initially strange sounding concept of the possibility of a material faith, and the consequences of such a faith, which is a truth procedure which founds a universal truth. Second, a truth procedure, which founds such a universal truth, is governed by a fidelity, or faith, to some event that has ‘happened’. The inexplicable nature of this event means that the procedure operates without reference to any rule, or law. These are two common themes within the letters of Saint Paul; the superiority of faith over works and that faith operates free from the law. In a sense, one of Badiou’s aims is to wrest religion’s final defence from it; the invocation of faith, and make it operate in a wholly material fashion, devoid of all theological reference. In order to be able to understand Badiou’s interpretation of the works of Saint Paul it will be necessary to elaborate in some detail the workings, and concerns that drive Badiou’s systematic thought.
[4] Badiou’s philosophical concerns clearly belong to a contemporary strand of continental thought, perhaps best called philosophies of difference, or the event, which are most familiarly associated with the works of the later Heidegger, Derrida and Deleuze and Guattari, to name but a few. These philosophies tend to be preoccupied with the generation, or creation of novelty, in all its forms, be it scientific, natural, artistic etc. The fundamental problem stems from what Badiou succinctly calls his ‘wager’: that the One is not. Anything that counts for a One, or a unity is not, the correlate of this is that what is is pure multiplicity, or pure difference. This is the root of Badiou’s anti-theological stance, which he equates with any system of thought that has as its fundamental ground of existence in some unity, be it a transcendent omnipotent entity, or the unity of some impersonal vital force that somehow permeates all reality. It is important to note that Badiou’s rejection of theology acknowledges that it is not something that can be disproved or debunked, the very language of a wager on multiplicity, as opposed to unity, recalls the language of Pascal wager on the existence of God.
[5] Introducing some important terminology, this pure multiplicity is completely unordered and un-orderable, it cannot be taken as a unity or totality; it is therefore inconsistent multiplicity. That which can be unified, or counted as one, is consistent multiplicity. What will be of interest is the relation or, as it will turn out, non-relation between consistent and inconsistent multiplicity. It is at this juncture that Badiou’s indebtedness to mathematical set-theory begins to assert itself. At the beginning of his seminal work L’être et l’événtment Badiou states: ‘what must be said is that the one, which is not, exists solely as operation. Or; there is no one, there is only the count-for-one.’ This count for one presents what has been counted to consist as a unity, what has been gathered together to form a one, but this pure operation has, as yet nothing to operate on. It is the foundational step of applying this pure process of naming to inconsistent multiplicity that grounds all possible systems of related and consistent unities. This operation when applied to what is, inconsistent multiplicity, can present, as consistent, precisely nothing. All that appears, or is presented, is the pure operation of gathering.
[6] Set theory is concerned with the manipulation and relation of consistent multiplicities, or aggregates. In this theory there is only one founding axiom that existentially asserts the existence of a set. This is the empty set axiom. All the other axioms state how to manipulate sets which have already been given. The empty set has its own special symbol Æ, but is in essence simply a pair of empty braces {}, nothing but the presentation of the operation of gathering, or drawing together as a one. It is also possible, within this theory, to show that all other sets can be generated from this one set through the application of the remaining axioms.
[7] Inconsistent multiplicity, or the Void as Badiou sometimes calls it, cannot be presented, but it founds all possible presentation. The empty set is therefore what Badiou calls a pure, or empty name, it is not the presentation of the Void but its name. Therefore inconsistent and consistent multiplicity are linked through this axiomatic naming through the application of the count for one, the empty set sutures the presentation of consistent multiplicities, which are not, to inconsistent multiplicity, which is: Æ, the empty set, is the proper name of being. It also has a strange universal property; it is included in every set but never belongs. Therefore every set represents the void, but it is never presented and its universal property does not amount to much, it is simply the representation of nothing.
[8] What this recognises is that there is no ultimate, or absolute, first element with regards to a consistent set-theoretical construction. This foundational naming is a decision taken in the face of the void, an empty naming which makes consistent construction possible. All such foundational elements will always be essentially empty; therefore any regressive philosophy that attempts to understand itself through an ever more thorough examination of its foundations will fail. Badiou acknowledges a point already made clear in Heidegger’s Being and Time, that one always already has a primordial understanding of one’s situation, and finds oneself in the midst of things. In being capable of examining anything, one must have already understood the situation in order to orientate oneself towards what is being examined. The horizon of a situation cannot itself, as horizon, be bought into the foreground and examined: it is the condition of possibility for making things present. The same is true of the foundational nature of the empty set, and the axiomatic approach in general, they constitute the conditions of possibility for a situation, such that anything can appear at all.
[9] What does appear, in this mathematical model of a situation, are consistent multiples, or sets. Now with regards to sets Badiou places a lot of emphasis on the difference between belonging , the fundamental non-logical operation of set theory, and inclusion, being a subset. The importance of these two different operations is that they are not equal, although every element that belongs to a set is also included as a subset in it; it is not true that every subset is itself an element of the original set. To make this distinction clear let me take the example of the people in this room. Taken together we form a set, precisely of all the people in this room. But this set can be divided into a number of parts, for example we could divide it between men and women, speaker, chair and audience, and so on. With a finite number of people n, there are only a set number of ways of dividing us up, in fact 2n ways, but it should be noted that there are always more parts to a set than elements.
[10] What Badiou claims is that this difference between being an element of (belonging to) a set and being a subset, or part, of a set has huge ontological significance. For Badiou, a situation is simply the material elements that compose it; a situation is a set. The actuality of a situation is its presented material elements. The possibility inherent in any situation is simply the totality of possible arrangements of its elements, that is to say, the totality of its parts/subsets. What a subset does, in relation to a situation, is to re-present a part of it, therefore the totality of such subsets is a re-presentation of the situation taking into account all the possible ways that it might appear. This re-presentation, or the set of all subsets, is called the power set of a given set and is one of the most powerful concepts in set theory. At a finite level the power set of a set is strictly calculable, 2n, but one of the fundamental aspects of set theory is that it allows for completed infinite sets, such as the set of all natural/whole numbers. At an infinite level the concept of all possible arrangements does not seem to have an intuitively obvious meaning, and in fact turns out to be un-decidable. It is this aspect of in-determination that appears in the heart of mathematics that Badiou is interested in, and means that his philosophical appropriation of mathematics is not a simple return to determinism.
[11] It will be useful to recap some of the points made above. What I have been trying to highlight with the above rapid overview of Badiou’s philosophy is the following. All there is is inconsistent multiplicity; an empty founding decision forecloses a consistent realm against the inconsistency of the void. The realm of consistent multiplicity that has been founded through this subtraction from the void is a consistent self-contained world, or universe, governed by two limits: first the material of the situation which is presented as a set, this can be thought of as the actuality of the situation. And the possibility inherent in this situation, which is limited by the re-presentation of the situation in terms of its parts; these are the categories and divisions which can be brought to bear on it. What is problematic is that this second limit of possibility is un-decidable with reference to an infinite situation (all situations are, for Badiou, infinite). For the world to remain consistent and foreclosed against the void an extra condition will have to be brought in to give a measure to the un-decidable excess of the power set of a situation. The fact that the power set of an infinite set is un-decidable does not mean that a consistent measure cannot be given to it. The situation constitutes what can appear, and the horizon (power set) limits how it appears. And as long as there is a strict relation between the two, i.e. a measure has been given to the excess of re-presentation over presentation, then this world operates in a consistent manner, totally subtracted from and un-related to the void.
[12] We are now in a position to approach the central concern of Badiou: the event. The event constitutes a basic question that concerns many philosophies of difference: how can novelty be created, or generated? It is clear from the above model of how a consistent world operates that everything possible has already been accounted for. Badiou does not want to seek novelty in changing the situation, the content is to some extent irrelevant to his highly formal philosophy. Any such operation from ‘outside’ the current consistent world would be an unwarranted appeal to some transcendent factor. It would put the possible comprehension of novelty beyond every situation, if it is always intruded on from ‘outside’ or ‘beyond’. What Badiou wants is an event that triggers the possibility of novelty from fully within a given situation, using nothing more than what is already available to the situation: its material elements. An event is immanent to a situation and always disrupts the status quo of that situation. It is a revolutionary moment and demands militant action. What an event will provoke is the transformation of a situation, not into something which completely destroys or erases the previous consistent world, but one which transforms and extends it.
[13] The way that this may occur will rest on the relation between presentation and re-presentation, and the measure given to this representation. The state of a situation is what Badiou calls the re-presentation of a situation that is controlled by some measure, hence there is no gap between a situation and its state; the state accounts for all legitimate possible expressions of the situation. In some sense the state of a situation can be thought of as the language that expresses it. What is clear is that if a certain number and type of illegitimate expressions can somehow be made to consist within this consistent system they will disrupt and undermine the authority of the situations state. If it is insisted that these expressions truly belong to this system then the language of this system will have to be extended in order to accommodate them. The system will then have been transformed and extended, by using initially illegal expressions. It is important that these expressions are formed only from the material of the situation, and do not import anything from outside, as they would lose all chance of claiming legitimacy. By holding to the belief that these supposedly illegal expressions really are expressions of the situation it will be possible to modify the language to act ‘as if’ they were legitimate. The most complicated part of Badiou’s appropriation of set theory rests on how these illegitimate expressions can be held to in such a way as to modify and extend the language of expression/representation. Also, not just any expression can be used, they have to be ones that if acted on ‘as if’ they were expressions of the situation do not lead to fundamental paradoxes and inconsistency within the new extended system.
[14] The most important thing to understand in this attempt is the difference between an intentional and extensional conception of sets. Set theory only requires sets to be extensional, that is they are identified solely by their elements. An intentional definition would recognise the elements of a set as fulfilling some condition. For example, the set of all even numbers has an intentional definition; all its members fulfil the condition of being even. The intentional definition for a set, if it exists, can be substituted for its laborious extensional definition: the set with elements x, y, z,… One of the key ways of limiting the state of a situation is to only allow sets which have an intentional definition; they are sets which can be constructed according to some rule or law. The simple rules of construction which at a finite level can easily calculate all the possible permutations a finite set can be consistently modified to work on infinite sets, but it is no longer clear that this process of calculating permutations will actually exhaust all possible compositions of infinite sets. This difference is recognised by the two categories of constructible and non-constructible sets.
[15] It is these non-constructible sets that will form the heart, or site, of an event. It is clear that such a set cannot have a condition of membership by definition, such sets are completely unstructured. If a situation is governed by a state which only allows constructible sets, then a non-constructible set, although composed of the same material elements of the situation, will not be represented as a possibility of the situation, it will be invisible. The existence of such sets can only be asserted to exist; one must have a belief in them, and a faithful fidelity to the consequences that such a belief will deploy. This is what occurs in a truth procedure, stemming from the declaration of an event, which is simply the assertion that a number of non-constructible sets exist as possibilities of the situation. This fidelity to an event will force the language, or representation, of the situation to operate in a new way which will extend its usual functioning, such that it will begin to incorporate and make visible the consequences of holding such an event as true. The only way for this to happen is to investigate the situation element by element, and ask whether each element belongs to the non-constructible sets we are asserting exist. Every element must be investigated as the non-constructible set has no rule or condition that might include, or exclude any element in advance of an actual immanent investigation. The full sequence of these investigations constitutes an extension of the original representational range of the state of a situation; to such an extent that it can now consistently operate ‘as if’ the non-constructible set belonged to the representation of the situation.
[16] The last stage in this somewhat laborious overview will be the more philosophical distinction between a subject and an individual in Badiou’s philosophy, before finally turning to Badiou’s work on Saint Paul. A subject for Badiou is simply a finite portion of an infinite truth procedure. By investigating an infinite set, element by element, it is clear that a truth procedure is an infinite affair; any finite portion of this procedure can constitute a subject. An individual will simply be the notion of someone defined entirely by the legalistic definitions deployed in the state of a situation, be it their physical materiality, their belonging to a certain community or country etc. In other words, an identity centred on some definable trait, what such an individual is capable of is to be traversed by a truth procedure; that is to be taken up by it, such that his identity is shifted away from a comfortable constructible identity and moves toward a faith in a non-constructible, unstructured event.
[17] Due to a lack of time, my engagement with Badiou’s work on Saint Paul may well appear as a somewhat clumsy mapping of the terms introduced above onto the figure of Saint Paul. To some extent this is Badiou’s approach. He wants to conceive Saint Paul, and his activity in a purely formal light, in such a light Paul’s activity and response to the event of Jesus Christ’s death and subsequent resurrection appears as a Badiouian truth procedure. Paul becomes a subject in his fidelity and faith to the event of Christ’s death and resurrection, and this is manifested in his wondering militant preaching of the Gospel, not only to fellow Jews but also to the Gentiles. The message must be truly universal, as the event held to introduces a number of non-constructible elements, which if adhered to as true requires that this ‘message’ must be taken to all elements of the situation. In this case the situation is that of social world of the Roman Empire, and the preaching of the Gospel must be carried out as a systematic militant investigation of every element of that situation. No group can be assumed to belong to this truth in advance, according to some condition such as the laws governing Judaism, nor can any group be excluded in advance due to any condition. I think realistically I can only concentrate on perhaps one element of Badiou’s relation to Saint Paul in the time remaining, and that will be Saint Paul’s consideration of the law.
[18] Badiou’s strongest engagement, can perhaps predictably, be seen in his investigation of Paul’s relation to the law, and the message that Christ’s death and resurrection brings to the law. The discussion on law is taken up in Paul’s letter to the Romans, where the law is seen as death, and that which introduces the possibility of sin. This is the life of the flesh, and for Badiou is the simple animal life that we lead as mere individuals, living only according to specified rules and laws equates with the controlled representation, or state of a situation. Such laws can either be fulfilled or negated, and their very invention leads to a desire to violate and transgress them. Such transgressions do not challenge the law, but merely affirm their status and justify the need for their existence. Law and transgression form a neat binary relation. Both of which can be easily formulated in the language of the situation in terms of a condition, and the negation of that condition. The event for Badiou, in this case the death and resurrection of Christ, is not illegal in this sense, the event’s non-constructible elements are invisible to the legal constraints of a situation, the law lacks the ability to be able to properly talk about an event; it can neither affirm nor condemn it. But also Christ’s resurrection is a resurrection into life. The death to sin and the life of the flesh does not mean an eradication of law and sin, but only that through a faith and fidelity to an event one operates according to faith and not according to law. One can only investigate a situation’s elements according to a non-constructible set if one holds that this set exists, as no proof as to its non-constructible nature can ever be given. What this new life according to faith does is to transform and extend the situation, to add something truly new, to create something new from the given material. There is no intervention, or addition of new material from outside, this novel transformation happens immanently through the faith in an event which disrupts the relation between the horizon of a situation and what can appear within that horizon. The resurrection and life according to faith is a true life, a life that is truly creative as it deploys the consequences of an event and transforms its situation. This life of faith proceeds in a lawless fashion, distributing its message in a universal way to the furthest reaches of a situation.
posted by Brian at 12:52 pm
1 Comments:
A very powerful piece of writing indeed. By this I mean that it is brilliantly succinct and focussed on what is such a difficult system to grasp. It has a similar quality to Deleuze’s ‘Kant’s Critical Philosophy’ in that both are able to summarise great and complex systems without destroying their motive power and genetic whole.
I am reminded by Badiou’s ‘empty set’ of Deleuze’s ‘Logic of Sense’ and the concern with nonsense as a mobile element of a decentred circle. It circulates around different series and thus assures the univocity of a Nature that cannot be totalised. Deleuze wants to avoid a notion of the whole/one/unity that is supported by Ideas of god, the self and the world (these being upholders of good sense that deny the mobile and genetic element of difference/non-sense). Would it be true to say that Badiou holds true to a ‘counting-as-one’ but not through any of these three Ideas or conditions? If affirming all of chance in one single throw is unable to account for novelty, there must be fidelity to the event in order to attain that which is universal. The universal, being that which is included but never belongs, alone attains the genetic power that Deleuze attributes to difference or nonsense as the mobile circulation. Then of course there is Rancière’s ‘part without a part.’ Deleuze’s Stoicism in the ‘Logic of Sense’ leads him to attribute to immaterial sense-events, which are caused by the depth of bodies, a quasi-causality in which the new may arise through the mobile operator (nonsense). This latter causes two different series to resonate. Badiou’s formal axiomatic and contention that pure difference is what is seem to rule out any appeal to such vitalism. Does he leave Nature to science and deny any genetic role to it? Perhaps these are not good questions but I suppose that axiomatic thinking is so challenging, especially when we have philosophies like Deleuze’s making use of evolutionary theory and biological differentiation (germinal life). Does the consistent multiplicity have to be purely mathematical in order that the inconsistent multiplicity can introduce novelty without being drowned in the clamour of differences? Could science grasp an event? Is there any sense to being at one with nature – one thinks of Robinson’s Crusoe in Deleuze’s essay entitled ‘Michel Tournier and the World Without Others’ – given an ontology of mathematics? Would this perhaps have to follow from fidelity to an event? Does make nature the tool of a truth procedure? One thinks of Kant making nature an analogy or symbol.
The subject being a ‘finite portion’ of a truth procedure certainly differs from Deleuze's fracturing of the self through the transcendental form of time (Aion). Creativity is the activity of the eternal return for Deleuze since the past can be re-inscribed by futural dice throws. This tortuous circle is that in which only the different returns. What do you think Badiou makes of time in his account? I haven’t figured this out yet in my reading of him. Does it have a creative function in the stretching of the subject along a finite portion of the infinite truth procedure? Is the time of the event freed from the organisation that space imposes in a situation? Is the time of the event one wholly open and unencumbered by a past or is there to be repetition or re-inscription? You mention the ‘transformation and extension’ of the situation and I wonder how this relates to Deleuze’s eternal return. Can novelty allow for a continuous development between consistent and inconsistent? Does the notion of the folding of virtual into actual, of their circuit. I suppose that I am trying to locate the point of connection in the absence of differential relations, of infinitesimals creating a continuum. Let me know if these are bad questions.
Certainly seems good – if not inevitable - to continue this discussion in the long term on this blog. I was thinking that continental philosophy is very preoccupied with resistance and the political subject at the moment. We seem to be heading that way on the blog to some extent. Perhaps it is just in the air at the moment but it seems to be infecting my reading of Deleuze, a problem that won’t go away and is productive (but that of course makes it sounds Deleuzian). It is also a recurring theme of conferences and journals at present. St Paul seems to have opened up this intense problematic further and has certainly got me thinking.
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