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Alain Badiou “Being and Event”

Badiou, Alain 2005. Being and Event. London, New York: Continuum

 Badiou-an_original_drawing

The One and the Multiple

What has to be declared is that the one, which is not, solely exists as operation. In other words: there is no one, only the count-as-one. […] In sum: the multiple is the regime of presentation; the one, in respect to presentation, is an operation result; being is what presents (itself). (24)

I term situation every presented multiplicity. […] Every situation admits its own particular operator of the count-as-one. This is the most general definition of a structure; it is what prescribes, for a presented multiple, the regime of its count-as-one. […] One must not forget that every situation is structured. (24)

It is therefore in the after-effect of the count that presentation is uniquely thinkable as multiple, and the numerical inertia of the situation is set out. Yet there is no situation without the effect of the count, and therefore it is correct to state that presentation as such, in regard to number, is multiple. (24-25)

I will maintain, and it is the wager of this book, that ontology is a situation. (27)

 

The Void: Proper Name of Being

Any situation, seized in its immanence, thus reverses the inaugural axiom of our entire procedure. It states that the on is and that the pure multiple – inconsistency – is not. (52)

To be sure, there is no antecedence of the multiple which would give rise to presentation because the latter is always already-structured such that there is only oneness oneness or consistent multiples. But this ’there is’ leaves a remainder: the law in which it is deployed is discernible as operation. And although there is never enythong other – in a situation – than the result (everything, in the situation, is counted), what thereby results, marks out, before the operation, a must-be-counted. It is the latter which causes the structured presentation to waver towards the phantom of incosistency. (53)

A situation never proposes anything other than multiples woven from ones, and the law of laws is that nothing limits the effect of the count. (54)

The nothing names that undecidable of presentation which is its unpresentable, distributed between the pure inertia of the domain of the multiple, and the pure transparency of the operation thanks to which there is oneness. The nothing is as much that of structure, thus of consistency, as that of the pure multiple, thus inconsistency. It is said with good reason that nothing is subtracted from presentation, because it is on the basis of the latter’s double jurisdiction, the law and the multiple, that the nothing is the nothing. (55)

I term void of a situation this suture to its being. Moreover, I state that every structured presentation unpresents ’its’ void, in the mode of thus non-one which is merely the subtractive face of the count. (55)

I will establish later on (Meditation 17) that for the void to become localizable at the level of presentation, and thus for a certain type of intra-situational assumption of being qua being to occur, a dysfunction of the count is required, which results from an excess-of-one. The event will be this ultra-one of a hazard, on the basis of which the void of a situation is retroactively discernible. (56)

Naturally, because the void is indiscernible as a term (because it is not-one), its inaugural appearance is a pure act of nomination. This name cannot be specific; it cannot place the void under anything that would subsume it – this would be to reestablish the one. The name cannot indicate that the void is this or that. The act of nomination, being a-specific, consumes itself, indicationg nothin other than the unpresentable as such. In ontology, however, the unpresentable occurs within a presentative forcing which disposes it as the nothing from which everything proceeds. The consequence is that the name of the void is a pure proper name, which indicates itself, which does not bestoq any index of difference within what it refers to, and which auto-declares itself in the form of the multiple, despite there being nothing which is numbered by it. (59)

 

The  Mark Ø

The  solution to the problem is quite striking: maintain the position that nothing  is delivered  by  the  law  of  the  Ideas,  but  make  this  nothing be through  the assumption of a  proper name. In other words: verify,  via  the excedentary choice  of a  proper  name,  the  unpresentable  alone  as existent;  on  its basis the Ideas will subsequently cause all admissible forms of presentation to proceed. (66-67)

The unpresentable is that to which nothing,  no multiple, belongs; consequently,  it cannot present itself in its difference. To  negate belonging  is  to  negate presentation  and therefore  existence because existence is being-in-presentation. The  structure of  the  statement that  inscribes  the  ‘first’  existence  is  thus,  in truth,  the  negation  of  any

existence according to belonging. This statement will say something like: ‘there  exists  that  to  which  no  existence  can  be  said  to  belong’;  or,  ‘a ‘multiple’  exists  which  is  subtracted  from  the  primitive  Idea  of  the multiple.’ (67)

In  its metaontological formulation the axiom says:  the unpresentable is presented, as a subtractive term of the presentation of presentation. Or: a multiple is, which is not under the Idea of the multiple. Or: being lets itself be named, within the ontological situation, as that from which existence does not exist. (67-68)

We  thus arrive  at  the  following remarkable conclusion:  it is  because  the one is  not that the void is  unique. Saying that the null-set is unique is equivalent to saying that its mark is a proper name. Being thus invests the Ideas of the presentation of the pure multiple in the form of unicity signalled by a proper name. (69)

 

The Point of Excess

[…] even  if for commodity’s sake  we  sometimes  use  the  word  ‘part’  to designate a  subset, there is no more  a concept of a  whole,  and thus of a part,  than  there  is  a  concept  of  the one.  There  is  solely  the  relation  of belonging. (83)

The  non -coincidence  of inclusion and belonging signifies that there is an excess of inclusion over belonging; that it is impossible that every part of a  multiple belongs to it. On the other hand, it is in no way ruled out that everything which belongs to a multiple is also included in it. (89)

[…] in set theory,  what  I  count  as  one  under  the  name  of  a  set  a,  is  multiple­of-multiples. It is thus necessary to distinguish the count-as-one, or structure, which produces the  one  as  a nominal seal  of the multiple,  and  the one as effect, whose fictive being is maintained solely by the structural retroaction in  which  it  is  considered. (90)

I  can thus consider that the set  {0},  which counts-as-one the result of the  originary count-the one-multiple which  is  the  name of the  void is the  forming-into-one of this  name. Therein  the  one  acquires  no further being than that conferred upon it operationally by being the structural seal of the multiple.  Furthermore,  {0}  is a multiple,  a  set. It so happens that what belongs to it,  0,  is unique, that’s all. But  unicity is not the one. (91)

 

The State, or Metastructure, and the Typology of Being

All multiple-presentation is exposed to the danger of the void: the void is its being. The consistency of the multiple amounts to the following: the void, which is the name of inconsistency in the situation (under the law of the count-as-one), cannot, in itself, be presented or fixed. (93)

The  apparent solidity  of the  world  of presentation  is merely a result of the action of structure, even if nothing is outside such a result. It is necessary to prohibit that catastrophe of presentation which would be its encounter  with  its  own  void,  the  presentational  occurrence  of  inconsistency as such,  or the ruin of the One. (93)

[…] something, within presentation, escapes the count: this something is nothing other than the count itself. The ‘there is Oneness’ is a pure operational result, which transparently reveals the very operation from which the result results. It is thus possible that, subtracted from the count, and by consequence a-structured,  the structure  itself be the point where  the  void  is  given.  In  order  for  the  void  to  be  prohibited  from presentation,  it  is  necessary  that  structure  be  structured,  that  the  ‘there  is Oneness’  be  valid for the  count-as-one.  The  consistency  of presentation thus requires that all structure be doubled by a metastructure which secures the former against any fixation of the void. (93-94)

[…] all situations are structured twice. This also means: there is always both presentation and representation. (94) – structure and metastructure

Any ordinary  situation  thus contains  a  structure,  both  secondary  and supreme, by means of which the count-as-one that structures the situation is in turn counted-as-one, The guarantee that the one is is thus completed by the following:  that  from which its being proceeds-the count-is,  ‘Is’ means ‘is-one’, given that the law of a  structured presentation dictates the reciprocity of ‘being’ and ‘one’ therein, by means of the consistency of the multiple. (95)

[…] I will hereinafter term state of the situation that by means of which the structure of a situation – of any structured presentation whatsoever – is counted as one, which is to say the one of the one-effect itself […] (95)

A structure  is  precisely not a Term  of  the  situation,  and  as  such  it  cannot  be  counted,  A  structure exhausts itself in  its effect. which is  that there is  oneness, Metastructure therefore cannot simply re-count the terms of the situation  and  recompose  consistent  multiplicities,  nor  can  it  have  pure operation as its operational domain; that is, it cannot have forming a one out of the  one-effect  as  its direct role. (95)

[…] the theorem of the point of excess. This theorem establishes that within the framework of the pure theory of the multiple, or set theory, it is formally impossible, whatever the situation be, for everything which is included (every subset) to belong to the situation. (97)

The definition of the state of a situation is then clarified immediately. The domain of meta structure is parts: metastructure guarantees that the one holds for inclusion, just as the  initial  structure  holds for belonging.  Put  more precisely,  given  a  situation  whose  structure  delivers  consistent  one­multiples,  there  is  always  a  meta structure-the  state  of  the  situation -which counts as one any composition of these consistent multiplicities. What is included in a situation belongs to its state. The breach is thereby repaired via which the errancy of the void could  have fixed itself to the multiple,  in  the  inconsistent  mode  of  a  non-counted  part.  Every  part receives the seal of the  one  from  the  state. (97)

We should note that the state is a  structure which is intrinsically separate from  the  original structure of the  situation. (98)

On  the  other  hand,  the  state  is  always that  of  a  situation:  what  it presents, under the sign  of the one, as consistent multiplicities, is in turn solely composed of what  the situation presents; since what is included is composed of one-multiples which belong. As  such,  the  state  of a  situation  can  either be  said to be  separate  (or transcendent) or to be attached (or immanent) with regard to the situation and its native  structure. (98)

Once  counted  as  one  in  a  situation,  a  multiple  finds  itself  presented therein.  If it is also counted as  one  by  the  metastructure,  or state of the situation, then it is appropriate to say that it is represented. This means that it belongs to the situation (presentation), and that it is equally included in the situation (representation). It is a term-part. Inversely,  the theorem of the point of excess indicates that there are included  (represented)  multiples which  are not presented  (which do not belong). These multiples are parts  and  not  terms.  Finally,  there  are  presented  terms  which  are  not represented,  because  they  do  not  constitute  a  part  of the  situation,  but solely one of its immediate terms. I will call normal a term which is both presented and represented. I will call excrescence a term which is represented but not presented. Finally, I will term Singular a term  which is presented but not represented. (99)

Singular terms are subject to the one-effect. but they cannot be grasped as parts because they are  composed, as multiples,  of elements  which are not  accepted by  the  count. (99)

Thus it must be understood that:

– presentation,  count-as-one,  structure,  belonging and element are on the side of the situation;

– representation,  count  of  the  count  metastructure,  inclusion,  subset and part are on the side of the state of the situation. (103)

 

The state of the historical-social situation

[…] the essence of the State is that of not being obliged to recognize individuals-when it is obliged to recognize them in concrete cases, it is always according to a  principle of counting which does not concern the individuals as such. (105)

The State is simply the necessary metastructure of every historico-sociol situation, which is to say the law that guarantees that there is Oneness, not in the immediacy of society – that is always provided for by a non-state structure – but amongst the set of its subsets. (105)

[…] the State is not founded upon the social bond, which it would express, but rather upon un-binding, which it prohibits. Or, to be more precise, the separation of the State is less a result of the consistency of presentation than of the danger of inconsistency. (109)

[…] politics can be defined therein as an assault against the State, whatever the mode of that assault might be, peaceful or violent. It ‚suffices’ for such an assault to mobilize the singular multiples against the normal multiples by arguing that excrescence is intolerable. However, if the government and even the material substance of the State apparatus can be overturned or destroyed; even if, in certain circumstances it is politically useful to do so, one must not lose sight of the fact that the State as such – which is to say the re-securing of the one over the multiple of parts (or parties) – cannot be so easily attacked or destroyed. (110)

[…] politics  stakes  its  existence  on  its capacity  to  establish  a  relation  to  both  the  void  and  excess  which  is essentially different from  that of the State;  it is this difference alone that subtracts politics from the one of statist re-insurance. (110)

 

Evental Sites and Historical Situations

It is rational to think the ab-normal or the anti-natural, that is, history, as an omnipresence of singularity – just as we have thought nature as an omnipresence of normality. The form-multiple of historicity is what lies entirely within the instability of the singulat; it is that upon which the state’s metastructure has no hold. It is a point of subtraction from the state’s re-securing of the count. (174)

I will term evental site an entirely abnormal multiple; that is, a multiple such that none of its elements are presented in the situation. The site, itself, is presented, but ‚beneath’ it nothing from which it is composed is presented. As such, the site is not a part of the situation. I will also say of such a multiple that it is on the edge of the void, or foundational […] (175)

The border effect in which this  multiple touches upon the void originates in its consistency (its one-multiple) being composed  solely  from  what,  with  respect  to  the  situation,  in-consists. Within  the situation,  this multiple  is,  but  that  of which  it  is multiple  is not. (175)

One of the profound characteristics of singularities is that they can always be normalized: as is shown, moreover, by socio-political History; any evental site can, in the end, undergo a state normalization. However, it is impossible to singularize natural normality. […] history can be naturalized, but nature cannot be historicized. (176)

[…] the negative aspect of the definition of evental sites – to not be represented – prohibits us from speaking of a site ‚in-itself’. A multiple is a site relative to the situation in which it is presented (counted as one). A multiple is a site solely in situ. In contrast, a natural situation, normalizing all of its terms, is definable intrinsically, and even if it becomes a sub-situation (a sub-multiple) within a larger presentation, it conserves its character. (176)

[…] there are in situation evental sites, but there is no evental situation. (176)

I will term situations in which at least one evental site occurs historical. I have chosen the term ‘historical’ in opposition to the intrinsic stability of natural situations. I  would insist  upon  the  fact  that  historicity is a  local criterion:  one  (at  least)  of the  mUltiples  that  the  situation  counts  and presents is a site, which is to say it is such that none of its proper elements (the multiples from which  it forms a one-multiple)  are presented in the

situation. A historical situation is therefore, in at least one of its points, on the edge of the void. (177)

 

The Matheme of the Event

Ordinarily, conceptual construction is reserved for structures whilst the event is rejected into the pure empiricity of what-happens. My method is the inverse. The count-as-one is in my eyes the evidence of presentation. It is the event which belongs to conceptual construction,  in the double sense that it can only be thought by anticipating its abstract form, and it can only be revealed in the retroaction of an interventional practice which  is itself entirely thought through. (178)

In natural or neutral situations, there are solely facts. (178)

[…] the existence of a multiple on the edge of the void merely opens up the possibility of an event. It is always possible that no event actually occur. Strictly speaking, a site is only ‚evental’ insofar as it is retroactively qualified as such by the occurrence of an event. (179)

I term event of the site X a multiple such that it is composed of, on the one hand, elements of the site, and on the other hand, itself. (179)

If there exists an event, its belonging to the situation of its site is undecidable from the standpoint of the situation itself. (181)

In our hypothesis, the event blocks its total singularization by the belonging of its signifier to the multiple that it is. In other words, an event is not (does not coincide with) an evental-site. It ‘mobilizes’ the elements of its site, but it adds its own presentation to the mix. (182)

To  declare that an event belongs to  the situation comes down  to saying  that it is conceptually distinguished from its site by the interposition of itself between the void and itself This interposition, tied to self-belonging, is the ultra-one, because it counts the same thing as one twice:  once as a presented multiple, and once as a multiple presented in its own presentation. (182)

The undecidability of the event’s belonging to the situation can be interpreted as a double function. On the one hand, the event would evoke the void, on the other hand, it would interpose itself between the void and itself. It would be both a name of the void, and the ultra-one of the presentative structure. And it is this ultra-one-naming-the-void which would deploy, in the interior-exterior of a historical situation, in a torsion of its order, the being of non-being, namely, existing. (182-183)

 

Being’s Prohibition of the Event

[…] the ontological situation originally names the void as an existent multiple, whilst every other situation consists only insofar as it  ensures  the  non-belonging  of  the  void,  a  non-belonging  controlled, moreover, by the state of the situation. The result is that the ontological matrix  of  a  natural  situation,  which  is to say an  ordinal,  is  definitely founded, but it is done so uniquely by the void. In an ordinal, the Other is the name of the void, and it alone. We will thus allow that a stable natural situation  is  ontologically  reflected  as  a  multiple  whose  historical  or foundational term is the name of the void, and that a historical situation is reflected by a multiple which possesses in any case other founding terms, non-void terms. (188)

In non-ontological situations, foundation via the void is impossible. Only mathematical ontology admits the thought of the suture to being under the mark Ø. (188)

[…] an event is ontologically formalized by an extraordinary set. We could. But the axiom of foundation forecloses extraordinary sets from any existence,  and ruins any possibility of naming  a  multiple-being  of the event. Here  we  have  an  essential  gesture:  that  by  means  oj’  which  ontology declares that the event is not. (190)

 

The Intervention: Illegal choice of a name of the event

I term intervention any procedure by which a multiple is recognized as an event. (202)

An intervention consists, it seems, in identifying that there has been some undecidability, and in deciding its belonging to the situation. However, the second sense of intervention cancels out the first. For if the essence of the event is to be undecidable, the decision annuls it as event. (202)

[…] if the essence of the event is to be undecidable, the decision annuls it as event. (202)

The essence of the intervention consists – within the field opened up by interpretative hypothesis, whose presented object is the site (a multiple on the edge of the void), and which concerns the ‚there is’ of an event – in naming this ‚there is’ and in unfolding the consequences of this nomination in the space of the situation to which the site belongs. (203)

The Revolution of 1789 is certainly ‘French’, yet France is not what engendered and named its eventness. It is much rather the case that it is the revolution which  has  since  retroactively  given  meaning-by  being  inscribed,  via decision, therein-to that historical situation that we call France. (203)

The initial operation of an intervention is to make a name out of an unpresented element of the site to qualify the event whose site is the site. […] The name of the event is drawn from the void at the edge of which stands the intrasituational presentation of its site. (204)

The intervention touches the void, and is thereby subtracted from the law of the count-as-one which rules the situation, precisely because its inaugural axiom is not tied to the one, but to the two. As one, the element of the site which indexes the event does not exist, being unpresented. What induces its existene is the decision by which it occurs as two, as itself absent and as supernumerary name. (205)

‚The’ term which serves as name for the event is, in itself, anonymous. The event has the nameless as its name: it is with regard to everything that happens that one can only say what it is by referring it to its unknown Soldier.(205)

This nomination is essentially illegal in that it cannot conform to any law of representation. […] Given a multiple of presented multiples, its name, correlate of its one, is an affair of the state. But since the intervention extracts the supernumerary signifier from the void bordered on by the site, the state law is interrupted. (205)

Intervention generates a discipline: it does not deliver any originality. There is no hero of the event. If we now turn to the state of the situation, we see that it can only resecure  the belonging of this supernumerary name, which  circulates at random, at the price of painting out the very void whose foreclosure is its function. (207)

Every time that a site is the theatre of a real event, the state – in the political sense, for example – recognizes that a designation must be found for the couple of the site (the factory, the street, the university) and the singleton of the event (strike, riot, disorder), but it cannot succeed in fixing the rationality of the link. This is why it is a law of the state to detect in the anomality of this Two – and this is an avowal of the dysfunction of the coutn – the hand of a stranger (the foreign agitator, the terrorist, the perverse professor). (208)

[…] the possibility of the intervention must be assigned to the consequences of another event. It is evental recurrence which founds intervention. In other words, there is no interventional capacity, consitutive for the belonging of an evental multiple to a situation, save within the network of consequences of a previously decided belonging. An intervention is what presents an event for the occurrence of another. It is an evental between-two. (209)

Time – if not coextensive with structure, if not the sensible form of the Law – is the intervention itself, thought as the gap between two events. (210)

One  important  consequence  of  evental  recurrence  is that no  intervention whatsoever can legitimately operate according to  the idea of a primal event,  or a  radical beginning. […] This thought is unaware  that the event itself only exists insofar as it is submitted,  by an intervention whose possibility  requires  recurrence-and  thus  non-commencement-to  the ruled  structure  of the  situation;  as such,  any  novelty  is  relative, being legible solely after the fact as the hazard of an order. What the doctrine of the event teaches us is rather that the entire effort lies in following the event’s consequences, not in glorifying its occurrence. There is no more an angelic  herald  of  the  event  than  there  is  a  hero.  Being  does  not commence. (210-211)

[…] its [event’s] sole foundation lies in a discipline of time, which controls from beginning to end the consequences of the introduction into circulation of the paradoxical multiple, and which at any moment knows how to discern its connection to chance. I will call this organised control of time fidelity. (211)

 

Fidelity, Connection

First, a  fidelity is always particular,  insofar as it depends on an event. There is no general faithful disposition. Fidelity must not be understood in any way as a capacity, a subjective quality, or a virtue. Fidelity is a situated operation which depends on the examination of situations.  Fidelity is a functional relation to  the event.

Second, a  fidelity is not a  term-multiple of the situation, but, like the count-as-one,  an operation,  a  structure.  What  allows  us  to  evaluate  a fidelity is  its  result: the count-as-one of the regulated effects of an event. Strictly  speaking,  fidelity  is  not.  What  exists  are  the  groupings  that  it constitutes of one-multiples which are marked,  in one way or another, by the evental happening.

Third, since a fidelity discerns and groups together presented multiples, it counts the parts of a situation. The result of faithful procedures is included in the situation. Consequently, fidelity operates in a  certain sense on the terrain of the state of the situation. A fidelity can appear, according to the nature of its operations, like a counter-state, or a sub-state. There is always something institutional in a fidelity, if institution is understood here, in a

very general manner,  as what is  found in  the  space of representation, of the  state,  of the  count-of-the-count;  as  what  has  to  do  with  inclusions rather than belongings. (233)

What must  be  retained  and  conceptually  fixed  is  that  a  fidelity  is conjointly defined by a situation-that in which the intervention’s effects are  linked  together according  to  the  law  of the  count-by  a  particular multiple-the event as named and introduced into circulation-and by a rule  of connection  which  allows  one  to  evaluate  the  dependency  of any particular existing multiple with respect to the event. given that the latter’s belonging to the situation has been decided by the intervention. (234)

A fidelity, on the other hand, discerns the connection of  presented  multiples  to  a  particular  multiple,  the  event,  which  is circulated  within  the  situation  via  its  illegal  name. (236)

For my part,  I will call subject  the process itself of liaison between the event  (thus  the  intervention)  and  the  procedure  of  fidelity  (thus  its operator of  connection). (239)

 

The Folding of Being and the Sovereignty of Language

[…] if one assumes that every multiple is constructible, the event is not, the intervention is non-interventional  (or legal), and the un-measure of the state is exactly measurable. (304)

With  the  hypothesis  of  constructibility,  everything  changes. This  time one can actually demonstrate that no (constructible)  multiple is evental. In other  words,  the  hypothesis  of  constructibility  reduces  the  axiom  of foundation to the rank of a theorem, a  faithful consequence of the other Ideas of the multiple. (304)

At base,  the  sovereignty  of language-if one  adopts the constructivist vision-produces the following statement (in which I short-circuit quantitative explanation,  and  whose  charm  is  evident):  the  state  succeeds  the situation. (309)

Everybody can see that the constructible universe is-in its refined procedure even more than in  its result-the  ontological symbol of knowledge. (309)

The  ethic  of  knowledge  has  as  its  maxim:  act  and  speak such  that everything be clearly decidable. (314)

 

The Thougth of the Generic and Being in Truth

‘Generic’ and ‘indiscernible’  are  concepts which are almost equivalent. Why play on a  synonymy?  Because  ‘indiscernible’  conserves a  negative connotation, which indicates uniquely,  via non-discernibility, that what is at stake is subtracted from knowledge or from exact nomination. The term ‘generic’  positively  designates  that  what  does  not  allow  itself  to  be discerned is in reality the general truth of a situation, the truth of its being, as considered as the foundation of all knowledge to come.  ‘Indiscernible’ implies a negation, which nevertheless retains this essential point: a truth is always that which makes a hole in a  knowledge. (327)

Knowledge is the capacity to discern multiples within the situation which  possess  this  or that property;  properties  that  can be  indicated by explicit phrases of the language, or sets of phrases. The rule of knowledge is  always  a  criterion  of  exact  nomination.  In  the  last  analysis,  the constitutive  operations  of  every  domain  of  knowledge  are  discernment (such  a  presented  or  thinkable  multiple  possesses  such  and  such  a property)  and classification  (I  can  group  together,  and designate  by  their common  property,  those  mUltiples  that  I  discern  as  having  a  nameable characteristic in common). Discernment concerns the connection between language and presented or presentable realities.  It is  orientated towards presentation. Classification concerns the connection between the language and  the  parts  of  a  situation,  the  multiples  of multiples.  It is  orientated towards representation. (328)

We shall posit that discernment is founded upon the capacity to judge (to speak of properties), and classification is founded upon the capacity to link judgements  together  (to  speak  of  parts).  Knowledge  is  realized  as  an encyclopaedia. An encyclopaedia must be understood here as a summation of judgements under a common determinant. Knowledge-in its innumerable  compartmentalized  and  entangled  domains-can  therefore  be thought. with regard to its being.  as assigning to this or that multiple an encyclopaedic  determinant  by means  of  which  the  mUltiple  finds  itself belonging  to  a  set  of  multiples,  that  is,  to  a  part.  As  a  general  rule,  a multiple (and its  sub-multiples) fall under numerous determinants. These determinants  are  often  analytically  contradictory,  but  this  is  of  little importance. (328)

Remember that  knowledge  does  not  know  of the  event  because  the name  of  the  event  is supernumerary,  and  so  it does  not  belong  to  the language of the situation. When I say that it does not belong to the latter, this  is  not  necessarily  in  a  material  sense  whereby  the  name  would be barbarous,  incomprehensible,  or non-listed.  What  qualifies the name of the event is that it is drawn from the void.  It is a matter of an evental  (or historical) quality, and not of a signifying quality. But even if the name of the event is very simple, and it is definitely listed in the language of the situation,  it is supernumerary as name of the event,  signature of the ultra­one, and therefore it is foreclosed from knowledge. It will also be said that the event does not fall under any encyclopaedic determinant. (329)

[…] every finite part of the situation is classified by at least one  knowledge:  the  results  of  an  enquiry  coincide  with  an  encyclopaedic determinant. This is entailed by every presented multiple being nameable in the language of the situation. (331)

It is as though  knowledge  has  the  power  to  efface  the  event  in  its  supposed effects,  counted  as  one  by  a  fidelity;  it  trumps  the  fidelity  with  a peremptory  ‘already-counted!’ This is the case,  however,  when these effects are finite.  Hence a  law,  of considerable weight: the true only has a chance of being distinguishable from the veridical when it is infinite. A truth (if it exists) must be an infinite part of the situation,  because  for  every  finite  part  one  can  always  say  that  it  has already been discerned and classified by knowledge. (333)

The general idea is to consider that a  truth groups together all the terms of the situation  which  are positively  connected  to  the event. (335)

Our problem is finally the following: on what condition can one be sure that the set  of terms of the situation which are positively connected to the event is in no manner already classified within the encyclopaedia of the situation?  We cannot  directly  formulate  this  potential  condition  via  an ‘examination’ of the infinite set of these terms, because this set is always to-come  (being infinite)  and moreover,  it  is  randomly composed  by the

trajectory of the enquiries: a term is encountered by the procedure, and the finite enquiry in which it figures attests that it is positively connected, that it is an x(+). Our condition must necessarily concern the enquiries which make up the very fabric of the procedure of fidelity. (336)

Thus: if an infinite faithful procedure contains at least one finite enquiry  which  avoids  an  encyclopaedic  determinant,  then  the  infinite positive result of that procedure (the class of x(+)’s) will not coincide with that part of the situation whose knowledge is designated by this determinant.  In  other  words,  the  property,  expressed  in  the language  of  the situation which founds this determinant,  cannot be  used,  in any case,  to discern the infinite positive result of the faithful procedure. (337)

The  fact  that  the  procedure  is  generic  entails  the  non­coincidence  of  this  part  with  anything  classified  by  an  encyclopaedic determinant.  Consequently,  this part is  unnameable by the resources  of the language of the situation alone. It is subtracted from any knowledge; it has not been already-counted by  any of the domains of knowledge, nor will be, if the language remains in the same state-or remains that of the State.  This part, in which a truth inscribes its procedure as infinite result, is an indiscernible of the situation. (338)

For what the faithful procedure  thus rejoins is none other  than  the  truth  of  the  entire  situation.  insofar  as  the  sense  of  the indiscernible is that of exhibiting as one-multiple the very being of what belongs insofar as it belongs. Every nameable part. discerned and classified by  knowledge,  refers  not  to  being-in-situation  as  such.  but  to  what language  carves  out therein  as  recognizable  particularities.  The  faithful procedure. precisely because it originates in an event in which the void is summoned. and not in the established relation between the language and the state. disposes, in its infinite states. of the being of the situation. It is a one-truth  of  the  situation.  whilst  a  determinant  of  knowledge  solely specifies veracities. (339)

1 have to say that philosophy does not generate any truths either,  however painful this admission may be. At best, philosophy is conditioned by the faithful procedures of its times. Philosophy can aid the procedure which conditions it. precisely because it depends on it: it attaches itself via such intermediaries to the foundational events  of  the  times,  yet  philosophy itself does  not  make  up  a  generic procedure.  Its  particular  function  is  to  arrange  mUltiples  for  a  random encounter with such a  procedure. However,  whether such an encounter takes  place,  and  whether  the  multiples  thus  arranged  turn  out  to be connected to the supernumerary name of the event, does not depend upon philosophy.  A  philosophy worthy  of the  name-the name  which  began with  Parmenides-is  in  any  case  antinomical  to  the  service  of  goods, inasmuch  as it endeavours to be at the service of truths;  one can always endeavour to be at the service of something that one does not constitute. Philosophy is thus at the service of art, of science and of politics. That it is capable of being at the service of love is more doubtful (on the other hand, art, a  mixed procedure,  supports truths of love). In  any case, there is  no commercial philosophy. (340-341)

The ultimate effect of an evental caesura, and of an intervention from  which  the  introduction  into  circulation of  a  supernumerary  name proceeds, would thus be that the truth of a situation, with this caesura as its principle, forces the situation to accommodate it: to extend itself to the point at  which  this  truth-primitively  no  more  than  a  part,  a  representation-attains belonging, thereby becoming a presentation. (342)

However,  it would remain subtracted from knowledge if the language of the situation was not radically transformed. Not only is a truth indiscernible, but its procedure requires that this indiscernibility be. A truth would  force  the  situation  to  dispose  itself  such  that  this  truth-at  the outset  anonymously counted  as  one  by  the  state  alone,  pure indistinct excess over the presented multiples-be finally recognized as a term, and as  internal.  A  faithful  generic  procedure  renders  the  indiscernible immanent. (342)

As such, art science and politics do change the world, not by what they discern, but by what they indiscern therein. And the all-powerfulness of a truth is merely that of changing what is, such that this unnameable being may be, which is  the  very being of what-is. (343)

 

The Existence of the Indiscernible: the Power of Names

[…]the  indiscernible  is  without being.  In reality,  an inhabitant of S can only believe in the existence of an indiscernible-insofar as if it exists, it is outside the world. (373)

Certainly,  an indiscernible  for S exists outside S-but where is the paradox? What we want is an indiscernible internal to  a situation.  Or,  to be precise, a set  which:  a.  is  indiscernible in a  situation;  b. belongs to that situation. We want the set to exist in the very place in which it is indiscernible. The entire question resides in  knowing to which  situation  SJ  belongs.  Its floating exteriority to S cannot satisfy us, because it is quite possible that it belongs  to  an as yet unknown  extension  of  the situation,  in  which,  for example,  it would be constructible with  statements of the  situation,  and thus completely discernible. (375)

The  ‘nominalist’  singularity of  the  generic extension  lies  in  its elements being  solely  accessible  via  their  names. (381)

 

Theory of the Subject

I  term subjectivization  the  emergence  of an  operator,  consecutive  to  an interventional  nomination .  Subj ectivization  takes place  in  the  form of  a Two.  It is  directed towards  the  intervention on  the  borders of the  evental site .  But  it  is  also directed towards  the situation  through  its  coincidence with  the  rule  of  evaluation  and  proximity  which  founds  the  generic procedure.  Subj ectivization  is  interventional  nomination from  the  standpoint of the situation,  that  is,  the  rule  of the intra -situational effects  of the supernumerary  name’s  entrance  into  circulation .  It  could  be  said  that subjectivization  is  a  special  count,  distinct  from  the  count-as-one  which orders  presentation,  just  as  it  is  from  the  state’s  reduplication.  What subjectivization  counts  is whatever is faithfully connected to the name of the event. (393)

What the proper name designates here is that the subject, as local situated configuration, is neither the intervention nor the operator of fidelity, but the advent of their Two, that is, the incorporation of the event into the situation in the mode of a generic procedure. The absolute singularity, subtracted from sense, of this Two is shown by the in-significance of the proper name. But it is obvious that this in-significance is also a reminder that what was summoned by the interventional nomination was the void, which is itself the proper name of being. Subjectivation is the proper name in the situation of this general proper name. It is an occurrence of the void. (393)

[…] subjectivization is that through which truth is possible. (393)

Subjectivization, aporetic knot of a name in excess and an un-known operation, is what traces, in the situation, the becoming multiple of the true, starting from the non-existent point in which the event convokes the void and interposes itself between the void and itself. (394)

A  truth  alone  is  infinite,  yet  the  subject  is  not coextensive with it. The truth of Christianity-or of contemporary music. or  ‘modern  mathematics’-surpasses  the  finite  support  of  those  subjectivizations  named  Saint  Paul.  Schoenberg  or  Cantor;  and  it  does  so everywhere, despite the fact that a truth proceeds solely via the assemblage of those enquiries,  sermons, works and statements in which these names are realized. (395)

[…] the subject is consituted by encountering its matter (the terms of the enquiry) without anything of its form (the name of the event and the operator of fidelity) prescribing such matter. If the subject does not have any other being-in-situation than the term-multiples it encounters and evaluates, its essence, since it has to include the chance of these encounters, is rather the trajectory which links them. However, this trajectory, being incalculable, does not fall under any determinant encyclopedia. (395-396)

The subject is literally separated from knowledge by chance. The subject is chance, vanquished term by term, but this victory, subtracted from language, is accomplished solely as truth. (396)

Because the subject is a local configuration of the procedure, it is clear that the truth is equally indiscernible ‚for him’ – the truth is global. ‚For him’ means the following precisely: a subject, which realizes the truth, is nevertheless incommensurable with the latter, because the subject is finite, and the truth is infinite. Moreover, the subject, being internal to the situation, can only know, or rather encounter, terms or multiples presented (counted as one) in that situation. Yet a truth is an un-presented part of the situation. (396)

[…] the  subject  cannot  make  a  language  out  of anything except  combinations  of  the  supernumerary  name  of the  event and  the  language  of the  situation.  It  is  in  no  way  guaranteed  that  this language will suffice for the discernment of a truth,  which, in any case,  is indiscernible for the resources of the language of the  situation alone.  It is absolutely  necessary  to  abandon  any  definition  of  the  subject  which supposes that it knows the truth,  or that it is adjusted to the truth. (396)

The singular relation of a subject to the truth whose procedure it supports is the following: the subject believes that there is truth, and this belief occurs in the form of a knowledge. I term this knowing belief confidence. (397)

[…] the names used by a subject – who supports the local configuration of a generic truth – do not, in general, have a referent in the situation. Therefore, they do not double the established language. But what use are they? These are words which designate terms, but terms which ‚will have been’ presented in a new situation: the one which results from the addition to the situation of a truth (an indiscernible) of that truth. (398)

With the resources of the situation, with its multiples, its language, the subject generates names whose referent is in the future anterior: this is what supports belief. Such names ‚will have been’ assigned a referent, or a signification, when the situation will have appeared in which the indiscernible – which is only represented (or included) – is finally presented as a truth of the first situation. (398)

Every subject can thus be recognized by the emergence of a language which is internal to the situation, but whose referent-multiples are subject to the condition of an as yet incomplete generic part. (398)

[…] the reference of the names, from the standpoint of the subject, remains for ever suspended from the unfinishable condition of a truth. (399)

Here, language (la langue) is the fixed order within which a finitude, subject to the condition of the infinity that it is realizing, practices the supposition of reference to-come. Language is the very being of truth via the combination of current finite enquiries and the future anterior of a generic infinity. (399)

They [names] displace established significations and leave the referent void: this void will have been filled if truth comes to pass as a new situation […] (399)

A subject is thus, by the grace of names, both the real of the procedure […] and the hypothesis that its unfinishable result will introduce some newness into presentation. A subject emptily names the universe to-com which is obtained by the supplementation of the situation with an indiscernible truth. At the same time, the subject is the finite real, the local stage, of this supplementaion. Nomination is solely empty inasmuch as it is full of what is sketched out by its own possibility. A subject is the self-mentioning of an empty language. (399-400)

Sliding  without  quilting  point.  In  fact,  the  meaning  of  a  subject­language is under condition. Constrained to refer solely to what the situation presents,  and  yet  bound  to  the  future  anterior  of  the  existence  of  an indiscernible, a statement made up of the names of a subject- language has merely a  hypothetical Signification. […] I say ‘will have been’ because the veracity in question is relative to that other situation, the situation to-come in which a  truth  of  the  first  situation  (an  indiscernible  part)  will  have  been presented. (400)

A subject always declares meaning in the future anterior. What is present are  terms  of  the  situation  on  the  one  hand,  and  names  of  the  subject­language on the other. Yet this distinction  is artificiaL beca use the names, being  themselves  presented  (despite  being  empty),  are  terms  of  the situation. What exceeds the situation is the referential meaning of the names; such meaning exists solely within the retroaction of the existence (thus of the representation) of an indiscernible part of the situation. […] such a statement of the subject-language will have been veridical if the truth is such or such. (400)

[…] a fundamental law of the subject (it is also the law of the future anterior). […] if a statement of the subject-language is such that it will have been veridical for a situation in which a truth has occurred, this is because a term of the situation exists which both belongs to truth (belongs to the generic part which is that truth) and maintains a particular relation with the names at stake in the statement. (401)

I will term forcing the relation implied in the fundamental law of the subject. That a term of the situation forces a statement of the subject-language means that the veracity of this statement in the situation to come is equivalent to the belonging of this term to the indiscernible part which results from the generic procedure. It thus means that this term, bound to the statement by the relation of forcing, belongs to the truth. […] A term forces a statement if its positive connection to the event forces the statement to be veridical in the new situation (the situation supplemented by an indiscernible truth). (403)

A subject is a local evaluator of self-mentioning statements: he or she knows – with regard to the situation to-come, thus from the standpoint of the indiscernible – that these statements are either certainly wrong, or possibly veridical but suspended from the will-have-taken-place of one positive enquiry. (404)

[…] a subject is at the intersection, via its language, of knowledge and truth. Local configuration of a generic procedure, it is suspended from the indiscernible. Capable of conditionally forcing the veracity of a statement of its language for a situation to-come (the one in which the truth exists) it is the savant of itself. A subject is a knowledge suspended by a truth whose finite movement it is. (406)

Grasped in its being, the subject is solely te finitude of the generic procedure, the local effects of an evental fidelity. What it ‚produces’ is the truth itself, and indiscernible part of the situation, but the infinity of this truth transcends it. It is abusive to say that truth is a subjective production. A subject is much rather taken up in fidelity to the event, and suspended from truth; from which it is forever separated by chance. (406)

[…] it is not possible to modify the established veracity of a statement by adding to a situation a truth of that situation; for what would mean that in truth the statement was not veridical in the situation. Truth is subtracted from knowledge, but it does not contradict it. […] it is impossible by means of the existing resources of knowledge alone to decide whether it is veridical or erroneous. (406)

This capacity [to decide] is so important that it is possible to gve the following definition of a subject: that which decides an undecidable from the standpoint of an indiscernible. Or, that which forces a veracity, according to the suspense of a truth. (407)

[…] empirically, novelty (for example, political novelty) is accompanied by destruction. But it must be clear that this accompaniment is not linked to intrinsic novelty; on the contrary, the latter is always a supplementation by a truth. Destruction is the ancient effect of the new supplementation amidst the ancient. (407) A destruction is not true: it is knowledgeable. (408)

The autonomy of the generic procedure excludes ant thinking in terms of a ‚balance of power’ or ‚power struggles’. A ‚balance of power’ is a judgement of the encyclopaedia. What authorizes the subject is the indiscernible, the generic, whose supplementary arrival signs the global effect of an event. There is no link between deciding the undecidable and suppressing a presentation. (408)

A subject is thus also that which measures the possible disqualification of a presented multiple. And this is very reasonable, because the generic or one-truth, being an indiscernible part, is subtracted from the determinants of knowledge, and it is especially rebellious with regard to the most artificial qualifications. The generic is egalitarian, and every subject, ultimately, is ordained to equality. (408-409)

[…] if a presentation’s qualification in the new situation is linked to an inexistence, then this presentation was already qualified thus in the ancient situation. This is what I term the principle of inexistents. […] inexistence is retroactive. […] The positive version of the principle of inexistents runs as follows: a subject can bring to beat a disqualification, but never a de-singularization. What is singular in truth was such in the situation. (409)

A subject is that which, finite instance of a truth, discerned realization of an indiscernible, forces decision, disqualifies the unequal, and saves the singular. By these three operations, whose rarity alone obsesses us, the event comes into being, whose insistence it had supplemented. (409)

 

Forcing: from the indiscernible to the undecidable

[…]the  names are all that the inhabitants of the situation know of the  generic  extension,  since  the  latter  does not  exist in  their universe. (410)

[…] although  an  inhabitant  of  the  situation  does  not  know anything  of the  indiscernible,  and  so  of the  extension,  she  is capable  of thinking that the belonging of such  a  condition to a  generic description is equivalent to the veracity of such a  statement within that extension. It is evident  that  this  inhabitant  is  in  the  position  of  a  subject  of  truth:  she forces  veracity  at  the  point  of  the  indiscernible.  She  does  so  with  the nominal resources of the situation alone,  without having to represent that truth  (without  having  to  know  of  the  existence  of  the  generic extension). (411)

a.  Given a quasi-complete denumerable situation, in which the Ideas of the multiple are for the most part veridical-thus, a  multiple which realizes the schema of a  situation in which the entirety of historical ontology is reflected-one can find therein a set of conditions whose principles,  in  the  last  analysis,  are  that  of  a  partial  order  (certain conditions are ‘more precise’ than others), a coherency  (criterion of compatibility), and a  ‘liberty’  (incompatible dominants).

b. Rules intelligible to an ‘inhabitant’  of the situation allow particular sets of conditions to be designated as correct parts.

c.  Certain  of these  correct  parts,  because  they  avoid any coincidence with parts which are definable or constructible or discernible within the situation,  will be said to be generic parts.

d.  Generally,  a  generic part  does  not  exist  in  the  situation,  because  it cannot  belong  to  this  situation  despite  being  included  therein.  An inhabitant of the situation possesses the concept of generic part, but in no way possesses an existent mUltiple which corresponds to this concept. She can only ‘believe’ in such an existence. However, for the ontologist  (thus, from the outside), if the situation is denumerable, there exists a generic part.

e.  What  do  exist  in  the  situation  are  names,  multiples  which  bind together conditions  and  other  names,  such  that  the  concept  of  a referential  value  of these  names  can  be  calculated  on  the  basis  of hypotheses concerning the  unknown generic part  (these hypotheses are  of  the  type:  ‘Such  a  condition  is  supposed  as belonging  to  the generic part.’).

f  One terms generic extension of the situation the multiple obtained by the fixation of a  referential value for all the names which belong to the  situation.  Despite  being unknown, the  elements  of the  generic extension are thus named.

g.  What is at stake is definitely an extension, because one can show that every  element  of  the  situation  has  its  own  name.  These  are  the canonical names,  and they are independent of the particularity of the supposed  generic  part.  Being  nameable,  all  the  elements  of  the situation are also elements of the generic extension, which contains all the referential values of the names.

h.  The  generic  part,  which  is  unknown  in  the  situation,  is  on  the contrary an element of the generic extension.  Inexistent and indiscernible  in  the  situation,  it  thus  exists  in  the  generic  extension. However, it remains indiscernible therein. It is possible to say that the generic extension results from the adjunction to the situation of an indiscernible of that situation.

i.  One can define,  in the situation, a  relation between conditions,  on the one hand, and the formulas applied to names, on the other. This relation is called forcing. […]

j.  In using forcing, one notices that the generic extension has all sorts of properties which were  already those of the situation. It is in this manner that  the  axioms,  or  Ideas  of the  multiple,  veridical  in the situation, are also veridical in the generic extension. If the situation is quasi-complete, so is the generic extension: it reflects, in itself, the entirety of historical ontology within the denumerable. In the same manner the part of nature contained in the situation is the same as that contained by the generic extension, insofar as the ordinals of the second are exactly those of the first.

k.  But certain statements which  cannot be demonstrated in ontology,

and  whose  veracity  in  the  situation  cannot  be  established,  are veridical in the generic extension. It is in such a manner that sets of conditions exist which force, in a generic extension, the set of parts of Wo  to  surpass any given cardinal of that extension.

I.  One can thus force an indiscernible to the point that the extension in which it appears is such that an undecidable statement of ontology is veridical therein,  thus decided. (427-428)

Veracity  thus  has  two  sources:  being,  which  multiplies  the  infinite knowledge of the pure multiple; and the event, in which a truth originates, itself  mUltiplying  incalculable  veracities.  Situated  in  being,  subjective emergence forces the event to decide the true of the situation. There  are  not  only  significations,  or interpretations.  There  are  truths, also. But the trajectory of the true is practicaL and the thought in which it is delivered is in part  subtracted from language  (indiscernibility),  and in part subtracted from the jurisdiction of the Ideas (undecidability) . (430)

 

Descartes/Lacan

What still  attaches Lacan  (but this still  is the modern perpetuation of sense)  to the  Cartesian  epoch  of science  is the thought that the subject must be maintained in the pure void of its subtraction if one wishes to save truth.  Only  such  a  subject allows itself to be  sutured  within the  logical, wholly transmissible, form of science. (432)

A truth,  if it is thought as being solely a generic part of the situation, is a  source  of  veracity once a  subject  forces  an  undecidable  in  the  future anterior. But if veracity touches on language  (in the most general sense of the term), truth only exists insofar as it is indifferent to the latter,  since its procedure is generic inasmuch as it avoids the entire encyclopaedic grasp of judgements. (433)

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