Being and Event A Users Guide to 7, 8, 10

Point of Excess I For centuries, philosophy has employed two dialectical

couples in its thought of presented-being, and their conjunction produced all sorts of abysses, the couples being the one and the multiple and the part and the whole. It would not be an exaggeration to say that the entirety of speculative ontology is taken up with examinations of the connections and disconnections between Unity and Totality. It has been so from the very beginnings of metaphysics, since it is possible to show that Plato essentially has the One prevail over the All whilst Aristotle made the opposite choice. (81)

The Intervention of Set Theory The multiplewhose concept it thinks without defining its

significationfor a post-Cantorian is neither supported by the existence of the one nor unfolded as an organic totality. The multiple consists from being without-one, or multiple of multiples, and the categories of Aristotle (or Kant), Unity and Totality, cannot help us grasp it.

Belonging vs. Inclusion the originary relation, belonging, written , which indicates

that a multiple is counted as element in the presentation of another multiple. (81)

But there is also the relation of inclusion, written , which indicates that a multiple is a sub-multiple of another multiple (81)

Belonging is primitive even if for commoditys 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)

Two Counts belonging and inclusion, with regard to the multiple a, concern two distinct

operators of counting, and not two different ways to think the being of the multiple. The structure of a is a itself, which forms a one out of all the multiples which belong to it. The set of all the subsets of a, p(a), forms a one out of all the multiples included in a, but this second count, despite being related to a, is absolutely distinct from a itself. It is therefore a metastructure, another count, which completes the first in that it gathers together all the sub-compositions of internal multiples, all the inclusions. The power-set axiom posits that this second count, this metastructure, always exists if the first count, or presentative structure, exists. (84)

However, there is an immediate consequence of this decision: the gap between structure and metastructure, between element and subset, between belonging and inclusion, is a permanent question for thought, an intellectual provocation of being. I said that a and p(a) were distinct. In what measure? With what effects? This point, apparently technical, will lead us all the way to the Subject and to truth. What is sure, in any case, is that no multiple a can coincide with the set of its subsets. Belonging and inclusion, in the order of being-existent, are irreducibly disjunct. (84)

N.B. Metastructure = State

Excess The question here is that of establishing that given a

presented multiple the one-multiple composed from its subsets, whose existence is guaranteed by the power-set axiom, is essentially larger than the initial multiple. This is a crucial ontological theorem, which leads to a real impasse: it is literally impossible to assign a measure to this superiority in size. In other words, the passage to the set of subsets is an operation in absolute excess of the situation itself. (84)

C.f. ToS

Point of Excess II the multiplicities which possess the property of not belonging

to themselves (~(b b)) [we call] ordinary multiplicities (84) those which belong to themselves (b b) [we call] evental

multiplicities. (85) The void is thus clearly in a position of universal inclusion. (87)

Ex falso quadlibet

there must exist, since exists, the set of its subsets, p(). (88)

Void and One Four meanings of the One

count-as-one, or structure, which produces the one as a nominal seal of the multiple (90)

the one as effect, whose fictive being is maintained solely by the structural retroaction in which it is considered. (90)

Unicity: A multiple is unique inasmuch as it is other than any other. The theologians, besides, already knew that the thesis God is One is quite different from the thesis God is unique. In Christian theology, for example, the triplicity of the person of God is internal to the dialectic of the One, but it never affects his unicity (mono-theism) (90)

Forming-into-one is not really distinct from the count-as-one; it is rather a modality of the latter which one can use to describe the count-as-one applying itself to a result-one. (91)

The set {} is thus simply the first singleton. (91) N.B. {{}} {}

State I What Heidegger names the care of being, which is the ecstasy of

beings, could also be termed the situational anxiety of the void, or the necessity of warding off the void. 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) C.f. ToS re: anxiety, Jacques Alain-Miller re: action of structure

Cannot guarantee solidity with just the count: The fundamental reason behind this insufficiency is that something, within presentation, escapes the count: this something is nothing other than the count itself.

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. (93-4)

The Being So Nice They Counted it Twice

The thesis that all presentation is structured twice may appear to be completely a priori. But what it amounts to, in the end, is something that each and everybody observes, and which is philosophically astonishing: the being of presentation is inconsistent multiplicity, but despite this, it is never chaotic. All I am saying is this: it is on the basis of Chaos not being the form of the donation of being that one is obliged to think that there is a reduplication of the count-as-one. The prohibition of any presentation of the void can only be immediate and constant if this vanishing point of consistent multiplicitywhich is precisely its consistency as operational resultis, in turn, stopped up, or closed, by a count-as-one of the operation itself, a count of the count, a metastructure. (94)

C.f. Remark in interview about how LoW is motivated by the fact that worlds appear with a logic and consistency

State II there is always both presentation and representation. To think this

point is to think the requisites of the errancy of the void, of the non-presentation of inconsistency, and of the danger that being-qua-being represents; haunting presentation. (94)

C.f. Marx, Derrida Any operation of the count-as-one (of terms) is in some manner

doubled by a count of the count, which guarantees, at every moment, that the gap between the consistent multiple (such that it results, composed of ones) and the inconsistent multiple (which is solely the presupposition of the void, and does not present anything) is veritably null. It thus ensures that there is no possibility of that disaster of presentation ever occurring which would be the presentational occurrence, in torsion, of the structures own void. (94)

C.f. ToS, Cahiers

Note on the Imaginary The structure of structure is responsible for establishing, in

danger of the void, that it is universally attested that, in the situation, the one is. Its necessity resides entirely in the point that, given that the one is not, it is only on the basis of its operational character, exhibited by its double, that the one-effect can deploy the guarantee of its own veracity. This veracity is literally the fictionalizing of the count via the imaginary being conferred upon it by it undergoing, in turn, the operation of a count. (94-5)

State III I will hereinafter term state of the situation that by means of which

the structure of a situationof any structured presentation whatsoeveris counted as one, which is to say the one of the one-effect itself, or what Hegel calls the One-One (95)

Metastructure therefore cannot simply re-count the terms of the situation and re-compose 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)

Theorem of the point of excess: including>belonging there are always sub-multiples which, despite being included in a

situation as compositions of multiplicities, cannot be counted in that situation as terms, and which therefore do not exist. (97)

An inexistent part is the possible support of the followingwhich would ruin structurethe one, somewhere, is not, inconsistency is the law of being, the essence of structure is the void. (97)

What is included in a situation belongs to its state. (97)

Typologies I will call normal a term which is both presented and

represented. (99) I will call excrescence a term which is represented but not

presented. (99) Finally, I will term singular a term which is presented but not

represented. (99)

Typologies II Normality consists in the re-securing of the originary one by

the state of the situation in which that one is presented. (99) a singular term is definitely a one-multiple of the situation,

but it is indecomposable inasmuch as what it is composed of, or at least part of the latter, is not presented anywhere in the situation in a separate manner. This term, unifying ingredients which are not necessarily themselves terms, cannot be considered a part. (99)

an excrescence is a one of the state that is not a one of the native structure, an existent of the state which in-exists in the situation (100)

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Being and EventPoint of Excess IThe Intervention of Set TheoryBelonging vs. InclusionTwo CountsExcessPoint of Excess IIVoid and OneState IThe Being So Nice They Counted it TwiceState IINote on the ImaginaryState IIITypologiesTypologies IISlide Number 16