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Philosophies of Disenchantment: Brassier & Badiou – Nihil Unbound, Chapter IV
We will now proceed to survey Brassier’s treatment of Alain Badiou’s meta-ontological enterprise, in relation to the question of negation. Badiou subscribes to the ideal of disenchantment; post-Kantian philosophy denigrates scientific rationality because it remains entrenched in a reactive Romanticism, balking thought from drawing on the full force of Nihilism unleashed by the ‘death of God’. Indeed, it is post-Kantian philosophy’s obsession with the human subject, and the thematic of finitude. As we saw in the previous chapter, this thematic often shelters on the question of access and therefore within the (metaphysical) specter of experience. But Badiou sees the lesson of the scientific mathematization of Nature and the desacralizing circuit of capital as precisely undermining this figure of the ‘bonding’ of being; the idea that being can give itself in its specificity as presence or through presencing to thought. Badiou in fact assigns philosophy to the militant purging of these residual specters, delivering thought from the pathos of finitude and its circumscription to experience to the immanent mathematical infinite sustained by nothing but void as background:
“We're far from having exhausted the consequences of the question of the death of God. The philosophical destiny of atheism, in a radical sense, lies in the interplay between the question of being and the question of infinity. The real romantic heritage--which is still with us today--is the theme of finitude. The idea that an apprehension of the human condition occurs primordially in the understanding of its finitude maintains infinity at a distance that's both evanescent and sacred, and holds it in the vicinity of a vision of being that's still theological. That's why I think the only really contemporary requirement for philosophy since Nietzsche is the secularization of infinity.” [Interview by Lauren Sedofsky, 1994]
This will lead Badiou into asserting a regime of universality not bonded by the idea of being’s ‘withdrawal’ from our presencing, like Heidegger contemplated, but by the un-binding of being from the spectral figure of the One which delivers it to the pure multiple, i.e. the multiple without the One, with no qualitative determinations. This in turn reveals the power of Nihilism – the rupture of the bond exposes the bottomless void which subtracts being from all stable presentation; the One is revealed in turn as an operational result with no being of its own. So Badiou can claim ‘The One is not’:
As far as nihilism is concerned, we shall grant that our era bears witness to it precisely insofar as nihilism is understood as the rupturing of the traditional figure of the bond; unbinding as the form of being of everything which acts as a semblance of the bond. […] That everything that is bound testifies that it is unbound in its being; that the reign of the multiple is, without exception, the groundless ground of what is presented; that the One is merely the result of transitory operations; these are the ineluctable consequences of the universal placement of the terms of our situation within the circulatory movement of the general monetary equivalent. […] This is obviously the only thing that can and must be saluted in capital: it exposes the pure multiple as the ground of presentation; it denounces every effect of oneness as a merely precarious configuration; it deposes those symbolic representations in which the bond found a semblance of being. That this deposition operates according to the most complete barbarism should not distract us from its genuinely ontological virtue. To what do we owe our deliverance from the myths of presence, from the guarantee it provided for the substantiality of bonds and the perenniality of essential relations, if not to the errant automation of capital? […] I propose the following paradox: only since very recently has philosophy become capable of a thinking worthy of capital, because even in its own domain, it had abandoned the terrain to the vain nostalgias for the sacred, to the specter of presence, to the obscure domination of the poem, and to doubts as to its own legitimacy. (Badiou 1989: 35–9, 1999: 55–8 translation modified − ‘tm’)
But of course this shouldn’t lead us to believe that the renunciation of the bond relegates the thought of being to irrationality. As we will see, it is the rupture of this bond by the force of mathematical thought which enables being to be thought in its pure multiplicity alone. “Thus it is not enough to denounce the hypostatization of being in the myth of presence; it is the phenomenological myth of presencing itself which must be deposed.” [Pg: 98]
Brassier means to say that it is not sufficient to denounce that being could ever become present in the form of the One; which was already prescribed by Heidegger’s trenchant opposition to ‘ontotheology’ and his critique of all ‘metaphysics of presence’. We must also relinquish the myth of a non-substantive and subtractive presencing which bonds Dasein to the figure of being qua being in the figure of the gift in the open (the whole theme of being’s unconcealment to presencing - ‘aletheia’). Only this way we can avoid the nostalgic gaze backwards which diagnose in scientific thought the derail of being’s withdrawal, ‘the forgetting of the forgetting’, and the silent expectation of a second beginning of thought which would somehow retrieve the lost wisdom and co-appropriate being and Dasein beyond metaphysics or scientific rationality. Interestingly enough, we should note this (Heideggerean) trajectory is also shared by Adorno who, in spite of all the reservations to the ‘jargon of authenticity’, assigns our epoch the same fate and prescribes the need for a reflexively historical stance in crossing to ‘second nature’.
Badiou proposes to complete his undoing of the bond by assigning ontology to mathematics. Being is simply mathematics; neither meaningful nor infused with the depth of truth, so that the age-old question ‘of being’ is thereby only the formal thought of the multiple as such, the naked multiplicity lacking all aspiration of meaning, purpose or sacrosanct profundity. Against all phenomenological ontologies, Badiou thereby advances the presentation of ontology separated from all presence “For presence is the exact contrary of presentation’ [Badiou 1988: 35, 2006: 27]. Next we will consider more closely how Badiou’s meta-ontological enterprise attempts this equation of ontology to mathematics, and the concrete philosophical import of the thesis that being is what subtracts itself from all presentation as such.
4.2 The a priority of ontological discourse.
The first thing we must understand is that ontology is a claim about discourse and not the world: ontology clarifies what it means for discursive intelligibility what is being qua being irrespective of all qualitative determinations. For this, ontology (mathematics) presents being as multiple (since it is thought here without a concept) and yet unitary (given consistently, ‘counted-as-one’ and presented in consistent form). But in order to preserve this distinction, the multiple qua being can never coincide with its consistent presentation, ontological or otherwise. For this would be to reestablish the bonding between being and the One. Instead, Badiou proposes to distinguish between consistent, which is the operational result of counting, and inconsistent multiplicity. Since the general form of presentation is consistent, all (multiple) situations are thereby structure and have their own regime of the count, including the ontological situation. Inconsistent multiplicity, on the other hand, is that upon which the counting operates as a retroactive positing of being after the count. This is crucial since the inconsistent multiplicity must therefore remain perpetually subtracted from structured presentation, what appears in a situation is always consistent multiplicities, and it is only retroactively that one identifies the being of inconsistency as the inertia of the domain upon which the count operates. Anything that is must be counted-as-one, but this unity is not identified with being, but merely stipulated as the result of the count and therefore of structure. So being can never be equated with the multiple qua one (in non-ontological situations) or with the consistent unity confered upon them in ontology (in the consistent form of their mathematical presentation); it is what eternally subtracts itself from every count, i.e. inconsistent multiplicity. Ontology is therefore the theory of inconsistent multiplicity as such, the presentation of the multiple qua multiple outside any determination besides the fact that it must never coincide with what it is counted as. Ontology is therefore on the one hand just another situation, clearly presenting consistent multiplicities like any other, and never quite presenting being as such. Ontology is no ‘all encompassing situation’; there isn’t such a thing. On the other hand, since all being is accessible through presentation, as that which subtracts itself from every structured series, ontology deploys the discursive intelligibility of presentation’s general subtractive form in which multiplicities are operationally knit to each other. It is therefore the presentation of presentation as such.
It is therefore forbidden for ontology to provide a concept of being, since the latter must be thought as inconsistent multiplicity, and therefore subtractive from any structured presentation and every consistent multiple. This means that ontology operates without an explicit concept of what it is, i.e. one cannot ‘count’ inconsistent multiplicity to render it presentable in the ontological situation since it is, by definition, that which is eternally subtracted from the effect of the count: “When anything is counted as one in a situation, all this means is that it belongs to the situation in a mode particular to the effects of the situation’s structure.” [Ibid: Pg 24] This means that in the ontological situation, being must be counted as nothing, a name for non presentation. To render inconsistency palpable would be to subordinate it to consistency, to its appearance under the rubric of the concept, to the One and therefore to render it structurally accessible rather than retroactively posited. This would reintroduce a distinction between being and its concept, allowing for the qualitative differentiation of individual terms. But being is rather that which inconsists in every situation, not the hard kernel to be retrieved in its corners to solicit a topology of beings: ‘it is necessary that the operational structure of ontology be able to discern the multiple without having to make it one, and hence without relying on a definition of the multiple’ (Badiou 1988: 37, 2006a: 29 tm).
The discourse of set-theory is up to the task, since it deploys its relations in a purely axiomatic manner, prescribing the rule for compositions of terms rather than providing a conceptual (semantic) clarification of its terms. Adherence to the rules is guaranteed, and the rules prescribe all possible formation from the axiomatic of the system, without recourse to a specification of the domain objects it composes. To be is to be a set, and to be a set is to be a set of sets, related by the singular operation of ‘belonging’ alone. To be is to belong to a set, everything that belongs is itself a set, and all sets are defined insofar as they belong. This axiomatic form is necessary, Brassier underlines, to avoid the reification of being in the form of the object or the ruin of the One. So the meta-ontological presentation must describe the operations of set-theory without re-presenting them by providing a concept of what being is, or what a set (a multiple) is.: ‘For by putting being in the general position of an object, its re-presentation would immediately undermine the necessarily de-objectifying condition of ontological deployment’ (Badiou 1988: 17–18, 2006a: 11 tm). Next Brassier proposes to analyze more closely Badiou’s concept of presentation.
4.3. The Law of Presentation
The unity presented by ontology is explicitly operational since set-theory only composes its terms through the axiomatic organization of sets/multiplicities: the One is an operation, not a presentation- the One has no being as such, it presupposes the effect of structure. This means that structure, although it articulates all presentation (since anything that presents itself is counted), has no being. Rather, structure is a nomological effect of discursivity, not an ontological characteristic of being: being has no inherent structure, but structure presupposes being. Isn’t Badiou merely reproducing the age-old distinction between phenomenal reality (subject to structural distinctions and causal relations) relative to thought and the permanently inaccessible noumenal realm of being-in-itself? But this is not the case, since Badiou is really proposing a tacit isomorphy between the inexistent structure (the count has no being), and the inexistence of inconsistency (being as such does not present itself). The necessity of the count by subtracting being from presentation is the same thing as the foreclosure of ontological inconsistency. It is not that being is consistent but inaccessible; ontology cannot afford the form of a presentation of inconsistency. The non-being (non-être) of the One qua the merely nomological dignity of structure is correlative to the being-nothing (être-rien) of inconsistent multiplicity. It is not the job of ontology to demarcate two spheres of being, but to forever separate being as that which subtracts itself from every presentation.
In this sense Badiou can accept Parmenides’ equation of thinking and being, since in their being, they are the same without relation, i.e. they are nothing. So structured consistency is merely the presupposition required in order to stipulate de-structured inconsistency, one cannot construct the difference between thought and being according to a conceptual/categorical differentiation of how being distinguishes itself in some presentations, since being is by definition unpresentable. Brassier stipulates the price to be paid for this is a brand of idealism whereby the continuous inconsistency of the real is only interrupted through the decision of thought in light of the event; but it is unclear at this point why he would privilege decision at the side of thought in Badiou’s materialist dialectical account. Let us defer this issue for the time being, until Brassier advances his exposition thoroughly later on and proceed to the next section, on the crucial delineation Badiou makes between a structure and metastructure, presentation and representation.
4.4 Structure, metastructure, representation
All situations are structured twice; there must be a count-of-the-count to avoid the void from fixing itself in the situation and ruin the alleged consistency of presentation. The meta-count must therefore ward off the void intrinsic to every situation. How is this metastructure guaranteed?
All presentation is structured; its consistency results from the operation of the count. But the count doesn’t count itself in what it counts, which means that the operation it transparently reveals remains without count:
“The prohibition of any presentation of the void can only be immediate and constant if this vanishing point of consistent multiplicity, which is precisely its consistency as operational result- is, in turn, stopped up, or closed, by a count-as-one of the operation itself, a count of the count, a metastructure.” [BE: Pg 55]
Brassier distinguishes between ontological metastructure and non-ontological representation: the former is distinguished by describing the latter, since only in the ontological situation is the void operates in the guise of a proper name designating the empty set. All other situations, then, ward off the void precisely by the effects described in the ontological metastructure of the count-of-the-count. The necessity for this meta-count is generated via two axioms for Badiou, centered in the distinction between belonging and inclusion. We should indicate, to clarify, that for Badiou to presentation refers to belonging while re-presentation to parts; to be presented in a situation means to belong to the situation. To be included, on the other hand, refers to parts: x is included in y just in case everything that belongs to x belongs to y. With this in place we can present the two axioms:
1) Power-set axiom: For every set T there exists the set P which counts all the subsets (parts) of T. [This axiom is in turn guaranteed by the axiom of separation, which stipulates that for any existing set one can separate in it the parts which have a determinate property]
2) Theorem of the point of excess: The set of subsets of any set T is larger than T. [This is supplemented by the Cohen-Easton theorem, which stipulates that the excess of the power-set over the set is immeasurable, i.e. its cardinality is non-quantifiable.]
Since the set of parts is always bigger than the set in question, counting its elements always results in uncounted parts. But this means that something was included in the situation without being counted; this void in the situation is thereby re-appropriated by the count-of-the-count which indexes it to metastructure. It thereby salvages the disastrous encounter of a situation with its own inconsistency. In order to ward off this excess of parts over elements, the metastructural count of the count stabilizes the situation turning this inconsistency into the consistency of a part which is included but doesn’t belong (which Badiou will fittingly call an excrescence). It thereby closes the gap between the situation’s structure and the presupposition of its underlying inconsistent void. This veracity is granted to the situation, Badiou says, as the ´fictionalizing of the count via the imaginary being conferred upon it by undergoing, in turn, the operation of a count.” [Ibid] The void can thereby never appears, locally (a term, since it is subtracted from the count) or the whole (it is the nothing of the whole). To avoid that the void fix itself in the uncounted parts, therefore, metastructure provides the seal of the one by recounting the structure and imposing the constraint of structure upon the excess inherent to the count. So the meta-structure deals with parts. Badiou will call this metastructural count of the situation the state-of-the-situation; the state totalizes the situation’s initial count by reducing its enigmatic excess to the structure. There is thus always presentation and representation, situation and its state. This is required by the nothingness of the count which reveals itself in the count of its parts by the theorem of the point of excess:
“It comes to exactly the same thing whether one says that the operation of the count is nothing insofar as it is the source of the one, but is not itself counted, or whether one says that what is nothing is the pure multiple which is operated upon by the count, since it is distinct ‘in itself’, which is to say as un-counted, from itself as manifested by the count. (Badiou 1988: 68, 2006a: 55 tm)
The nothingness of presentation is thus finally warded off as the nothingness of being itself, and thus of inconsistency, the subtractive suture to being. But we need to clarify this suture to the unpresentable more thoroughly.
4.5 The suture to the unpresentable
Since the multiple deployment of set theory to separate parts in sets depends on the prior giveness of a set (axiom of separation), Badiou must determine which set can be determined from which all others can be said to follow. This is the empty set, or as we will call it heretofore: the void set. Ontology, presentation of presentation, presentation of the count-as-one, cannot affirm the existence of any set or any relation of belonging before affirming the existence of that to which nothing belongs. This existential point affirms the non-existence of the belonging, the non-existence of the count, as the starting point for the axiomatic deployment of the multiple: it is the inconsistent void of that to which nothing belongs which is the starting point, not the giveness of structure. The affirmation of the void set does not exactly pose the existence of something which does not exist, it affirms the being of the unpresentable as the negation of presentation, affirmation of what inexists as founding every situation. We can tentatively suggest that this axiom in fact stipulates the non-being of existence tout court. Brassier clarifies that the affirmation of the existence of the void set is just the ascription of a mark of belonging, required for the compositional deployment of the set-theoretical axiomatic. It is by negating this mark of belonging that the axiom of the void operates thus affirming the existence of a mark of non-belonging as the foundational point for any presentation. This is how Badiou finally subtracts being from every presentation, since the first existential is the negation of presentation and thus of the non-being of the One as indiscernible from the being-nothing of inconsistency:
“Thus the inexistence of the void, the assertion of the negation of belonging, is both the precondition for the operation of the One qua belonging, since all belonging presupposes the existence of (the name of) non-belonging; and that which ensures that the existence of belonging per se is never affirmed. Set-theory begins by declaring that non-belonging exists, a non-belonging which authorizes all subsequent belonging, but the theory neither asserts nor presupposes the existence of belonging.”
Presentation appears unified, but this unification is really split between consistency (its counted terms) and inconsistency (the non-being of the count indiscernible as being-nothing of the void). To ward off this indiscernibility, which reveals the latent inconsistency of the void as the truth of any structured situation, demands the meta-count of parts by the state, and its measure of the gap separating belonging and inclusion. Since the latter measures an irremediable excess over belonging, it thus registers that something remains uncounted by the structure itself. So it avoids the fixation of the void as the immeasurable latency of a residue from the count in presentation itself, the inconsistency of what is consistently presented.
“Consequently, since everything is counted, but since the one of the count, being merely a result, implies as its ghostly remainder the fact that multiplicity does not originally have the form of the one, it is necessary to acknowledge that, from within a situation, pure or inconsistent multiplicity is at once excluded from the whole, and hence excluded from presentation as such, but also included as what presentation itself or in itself ‘would be’, were that which the law forbids as inconceivable to be conceivable: that the one is not, and that the being of consistency is inconsistency.
(Badiou 1988: 66, 2006a: 53 tm)
At the same time, this inconsistency is only retroactively asserted; it remains a shadow of the impossibility of appearance, or the emptiness of the void of being. It is thereby subtracted from every possible experience. This means that presentation cannot ever be a phenomenon (which is defined in terms of presence for a representational subject, of the presencing of Dasein’s pre-theoretical exposition to being in the open, etc). But this does not locate being outside the regime of presentation, as an un-representable reality or infinitely dense Virtual realm, or the mystical avowal of the ‘absolutely Other’ (God, the Other…). This ‘Great Temptation’ is avoided by saying that being’s inconsistency entails the denial of any immediate or non-discursive access to being, and that all one can provide in the ontological situation is this unpresentability of the inconsistency. The axiomatic guarantees that the inconsistent multiplicity can only result in its subtraction from every presentation as measured in the excess of parts to what appears, countered by the state of the ontological situation’s metastructural closing of the gap between belonging and inclusion. This allows us to thereby describe the representational covering of the void which made invisible by the count of parts, and which remains blind to the situation’s internal inconsistency, which supports it. It is in ontology’s retroactive designation of the metastructure appropriation which locates the non-being of the count as the origin for all structured presentation. This violates any possibility for the intellection of being as such; the anti-phenomenal quality of the mathematical ontology, inscribed formally in the mark of the non-presentable. Structure unleashes the force it forbids, and ontology marks it as the proper name of the void:
“Thus the structure of presentation envelops a strictly ‘non-phenomenologizable’ scission which can only be inscribed in the formal ideography of set-theory. Ultimately, only an insignificant letter, Ø, indexes the originary fissure whereby presentation deposes presence and binds itself to the mark of the unpresentable. Ø is the initial incision that marks the hinge between consistency and inconsistency, non-being and being-nothing.” [Brassier, Pg: 107]
Notice that because of this, ontology as such cannot ever encounter inconsistency, since the State counters this excess in its measure: ontology cannot have its own excrescences. Since ontology presents presentation, all sets are constructed on the basis of the operation of belonging, and so inclusion must arise from belonging and belonging alone, what it counts is only one more multiple term that belongs. Because of this, the ontological situation does not have a state properly, which means it cannot expulse its own void. In fact, the void is its singular presupposition, from which the uniform regime of structured presentation is allowed to proceed. Badiou’s formulation is staggering:
“The integral realization, on the part of ontology, of the non-being of the one leads to the inexistence of a state of the situation that it is; thereby infecting inclusion with the void, after already having subjected belonging to having to weave with the void alone. The unrepresentable void herein sutures the situation to the non-separation of its state.” [BE: Pg. 101]
4.7 The metaontological exception
Brassier asks whether presentation can obtain in non-ontological situations, given ontology’s discursive subtraction of the former from all experience. This question is relevant insofar as non-ontological situations effectively pose a ban on the void, by submitting everything to the law of the count in the assertion of the being of the One. So, it is relevant to ask whether the mathematico-ontological blueprint which includes the void as its point of departure for the deployment of belonging, and which Badiou’s metaontological register indexes as the ‘presentation of presentation’, can in fact obtain outside ontology in which it is affirmed on the contrary that the One is not. Brassier will suggest that Badiou cannot accomplish this connection without excepting metaontology to describe how in the condition of an event in a decision for thought, ordinary situations can indeed sublate the stability of their structural order, thereby crossing the strictly non-conceptual resources of set-theory. This ultimately leads Brassier into claiming Badiou falters by endorsing a discursive brand of idealism. But let us follow this piece by piece:
In non-ontological (i.e. non-mathematical) situations, multiplicity is only possible insofar as the law explicitly subordinates it to the law of the count […] Ordinary situations, if one grasps them from their own immanent standpoint, invert the axiom which inaugurates our entire procedure. They state that the one is, and that pure multiplicity – i.e. inconsistency – is not. This is entirely natural, since not being the presentation of presentation, ordinary situations necessarily identify being with what is presentable, and hence with the possibility of the one […] Thus it is veridical […] from a standpoint internal to what a situation establishes as the form of knowledge, that to be is to be unifiable. Leibniz’s thesis (‘What is not a being, is not a being’) governs the immanence of situations as their horizon of veridicality. It is a thesis of the law.” (Badiou 1988: 65–6, 2006a: 52–3 tm)
Yet metaontology is not mathematics itself, since it moves in a conceptual register where concepts extraneous to the strictly mathematical make way, such as ‘presentation’ or ‘being’. Mathematics operates blindly, and its axiomatic is engendered without appeal to anything like a (meta) ontological conceptuality. The status of metaontology is thereby ambiguous. Metaontology is not:
1) Ontology / The presentation of presentation - Since it is written conceptually, not sutured to being (the void set) directly.
2) Subject to conditions of verification in ordinary situations – Since it has suspended the isomorphy between being and the One by claiming the being of inconsistency and the non-being of the count.
So where is metaontology to be situated, if not in ontology or in ordinary situations? Perhaps Badiou could retort metaontological claims should not be taken to be conceptual insofar as they are transparently isomorphic to ontology’s non-conceptual register. This would amount to saying that metaontology does not quite represent ontology, but merely codifies it. Even if Brassier correctly claims that ontology’s putative non-conceptual axiomatic is what sutures it to the void as the science of being, one can say that the reflexive determination made by metaontological claims is not conceptual insofar as it remains indifferent to the contents of presentation: a pure multiplicity is analogous to a set since it is not underwritten by any qualitative determinations. If so, then ‘presentation’ need not be ‘transcendent’ to the recourses of set axiomatic theory, as Brassier stipulates they must be, even if the jargon it mobilizes is not-coextensive with that of ontology; the latter can be reinscribed in metaontological theses without invoking any appeal to conceptuality extraneous to it.
This would mean, contra Brassier, that the defining characteristic of the set-theoretical axiomatic is not its non-reflexivity, since the mathematical deployment surely necessitates at least the positing of its terms, but the non-reification of its terms by appeal to concepts not immanent to the resources of the axiomatic. In this sense, the metaontological register through which Badiou explains the ontological presentation of presentation does not reify conceptually the intrinsic ontological theses; it simply transcribes it into the meta-ontological jargon rendering palpable its intrinsic relational structure around the denial of belonging. But of course, Brassier thinks that the strictly extra-ontological import which is unwarranted is the concept of presentation; since the latter is used by Badiou by distinguish between ontological/non-ontological situations: and the latter are not founded on the void transparently, so the relation between the stipulated being of the void and the ordinary world must remain transcendentally guaranteed by the metaontological register which was only supposed to be one more situation. Without the gloss of ‘presentation’, the exclusive suture of being to the void in ontology becomes palpable. What then, guarantees the putative necessity of ordinary situation’s structure; why isn’t there only ontological presentation?
In other words, Brassier would probably insist on the metaontological externality to ontology implicit in the concept of presentation as such, since only in the ontological situation the suture to the void, which ‘infects’ inclusion, is allowed. If metaontology is not ontology proper, then it is an ordinary situation. But it cannot be an ordinary situation insofar as ordinary situations, as Badiou states above, begin by affirming the being of the One, while metaontology expressly claims being is that which subtracts itself from all presentation. Metaontology is as such not an ordinary situation, since it is not subordinated to the immanence of either the ontological situation or ordinary situations under the Law of the One.
Perhaps Badiou could insist here that metaontology in fact does suture itself to the void qua the inconsistency of being, and that therefore the metaontological situation is immanent to the ontological situation by isomorphy. And the metaontological discursivity may indeed be subject to the suture of the void and in the inclusion of the void insofar as it is not sufficient for the event. But herein lies the problem, since metaontology does not only remain in the inert irreflexivity which ensures the consistency of ontology next to its included void as the presupposition of inconsistency. It also stipulates the radical breaking of the ontological stability through the subjective decision which founds the event. Let us trace the route to this problematic in Brassier’s account to see how this is so.
First, we must notice that for Badiou philosophy is conditioned by external truth-procedures, which it tries to compose together. These truth procedures are conditioned insofar as in their status as truth-procedures, they are not reducible to norms of knowledge, which they subvert in their evental becoming. But philosophy itself is not a truth-procedure, there is no philosophical subject, and so its conceptual recourse to explain the theory of the event does not only exceed the strictly ontological discursivity (whose internal stability excludes the event) but it would presumably not even belong to those ordinary situations in which truth-procedures happen unexpectedly. So the meta-ontological therefore seems to enjoy a particular privileged status among all other situations and ‘presentations’, including the ontological one. Brassier says Badiou is at pains to explain how metaontology can be exempted from the conditions of knowledge in ordinary situations; or phrased differently: the non-specification of the status of metaontology oscillates between a representation of ontology’s presentation of being and ‘the presentation of the imaginary re-presentations’ of ordinary knowledge, since it can describe them without being subjected to its laws. Because metaontology splits situations between ontology and ordinary situations, it cannot coincide with either pole: it offers a theory of the event and presentation extraneous to mathematics, and non-subjection to the count of ordinary situations. So between the three registers: metaontological, ontological and ordinary, one finds it difficult to articulate the anti-phenomenological separation between presentation and presence.
Badiou’s argument proceeds by the decision to affirm mathematics as ontology, thereby being unverifiable to the stricture of knowledge. The evental self-grounding of thought’s decision is what marks the event’s subtractive split with structure. It is in terms of a split within the set-theoretical axiomatic which describes the stability of structured situations that Badiou locates the capacity for thought to locate a breakdown of being in thought’s embrace of inconsistency. It is within metaontology that thought can be true to the being of inconsistency and not the ordinary scripture of the being of the One. Brassier claims Badiou’s metaontological register where presentation pertains differently with respect to ontology’s suture to the void, and ordinary suture to the One. So the real question underlying the question of presentation is different in both cases, given the thesis that being never presents itself and is therefore subtracted from presentation.
”For despite the putative ‘a priority’ of ontological discourse as ‘condition for the apprehension of every possible access to being’, it is far from clear whether the argument of Being and Event proceeds a priori from the void of being to the multiplicity of presentation, or on the contrary, and a posteriori, from the multiplicity of presentation to the void of being. In other words, how is it that the unpresentable can give rise to anything but subtractive – ontological – presentation?” [Pg: 110]
Here I am not sure I follow Brassier, for the question of the argumentative order is not clearly posed. Clearly, the ontology presupposes presentation, and presentation presupposes the warding off of the void in the stability of the multiple presentation under the one. Ontology explains how the unpresentable inconsistency gives rise to ordinary situations (described in subtractive ontology) in the ontological determination of the necessity of the State of the situation which cloaks the inherent inconsistency via the count of parts. So inconsistency gives rise to this ordinary situation in that it refuses the void by totalizing the situation, while ontology achieves the thought of the multiple qua multiple insofar as it is sutured to void. Presentation thus concerns univocally pure multiplicities, but they are distinguished by their ontological non-representability and their ordinary (ontic) representational necessity. Only when the void is formally posited in the form of a proper name that it can be positioned in universal inclusion and thereby provide the framework for ordinary situations, which must remain oblivious to being’s inconsistency. It is only in the ontological retroactive identification of the excess of inclusion over belonging that it subtracts inconsistent being from presentation. What is missing here? Why is Brassier dissatisfied with this?
Here comes the most subtle point: only ontology begins with the stipulation of the non-existence of belonging in the affirmation of the void set – but this relies on the axiomatic deployment of the multiple qua the operational effect of the count. Where such a supposition is missing, outside ontology, what does it mean to say that ‘presentation is never chaotic’? It cannot rely to empirical confirmation; since this is vitiated from the get go. But what then, guarantees the existence of non-ontological consistency? Why must presentation never be chaotic in the non-ontological statist count which, non-founded by the void, is subject to the event? Although ontology grounds the immanent excess occasioned by inclusion, it less than clear how this translates into the necessity of non-ontological situations. If Badiou wants to say more than the tautological affirmation that what’s consistent is not inconsistent’ then he needs to say more.
We can stipulate that Badiou might answer as follows: to say presentation is never chaotic is just to say that in ordinary situations the void can never fix itself as a term, nor does it define a global status, (since it is the nothing is this totality) since the state counts every-thing as a term and does not permit anything to escape its count. This separation between the situation and its state, signals the gap between the necessarily inconsistent presentation (haunted by the excess of parts of over elements) and its reduplication by the state where this errant excess is counted. But it remains only for the ontologist to see that the state’s reduplication in fact veils the errancy of the excess of being’s inconsistency to presentation. But perhaps Brassier is concerned about whether the retroactive presupposition of the void, such as articulated in set-theory to account for its consistency, has any warrant in ordinary situations where on the contrary the being of the one is asserted: how is their structure necessitated by the inconsistency prescribed by the ontological axiomatic? Clearly, the suggestion is that Badiou only does this via recourse to the quasi-transcendental status of the metaontological appeal to presentation, which delivers the multiple to the void as its sole ground.
It here seems Badiou can answer the question “If unity is only ever the result of an inexistent operation, then what non-tautological instance accounts for the necessary ubiquity of consistency?” by simply saying that the necessity of consistency must remain blind to ordinary situations, since it cannot observe its own retroactive appropriation of excess by the state. However, this puts us in a position where the anti-phenomenological ban on the import of experience begins to tilt, since this apparent necessity of reduplication can at the most remain guaranteed in the ontological axiomatic, but it is less clear how ordinary situations exhibit this same necessity for structural balance. I am not persuaded that the speculative status of ontology qua presentation of presentation is insufficient to close this gap; however, i.e. Badiou can say that the necessity of reduplication is guaranteed by the State’s excess as explained by ontology. That in ordinary situations the void is not a term does not mean that, with respect to its being, the excess does not occur, it is simply not registered retroactively.
If ontological situations are distinguished as being the only situations founded by the void alone, as Badiou contests, then it is only the presentation of presentation which renders palpable the inconsistency annulled by re-presentation in ordinary situations. However, since the distinction between ontological and non-ontological presentation is not immanent to ontology, then Brassier must at least be right in that metaontology has an undecided status that conveniently abstracts from the requirements of two and which serves as the necessary mediator for being to bear on the world, as well as for the theory of the event. As for what grants the necessity of a non-ontological situation, the ontic-specificity to ordinary situations, Badiou supplements his formal ontology with a theory of appearance in Logics of Worlds which designate the necessity of a transcendental structure which gives the form of the object in every situation or ‘world’. This should be sufficient to relieve the tension Brassier detects in establishing a link between the inconsistency of being in non-ontological situations. But let’s move on.
4.8. The two regimes of presentation.
Ontology and metastructure, non-ontology and re-presentation. Ontology cannot be represented, insofar as it grounds the possibility of access to being: it is entirely coded in the operation of belonging, inclusion is only ever a variant of the primitive operation, so there is no state of the ontological situation – it presents presentation as such, and as such the metastructure expressly closes the gap between belonging and inclusion. This is why ontology precludes the possibility of interruption with structure, since by localizing the void in inclusion, closing the gap; it cannot ever encounter its own singularities (non-represented terms) and thus the possibility of the event. Ontology is closed. Ontology effectively presents nothing, it deploys the multiple its axiomatic on the basis of the manipulation of the inscription of the name of the void set alone, and so carried by the non-being of the One from the start, and so it’s the one situation where its consistency is derived from inconsistency. It thus never count the inclusion of nothing but the void.
On the other hand, non-ontological situations begin by the being of the one, and the triumph of consistency, it presents everything in unity. It is here that singularities proper can emerge, a gap in re-presentation, in the latent inconsistency of their unity, and which provides the blueprint for the evental break with the closed parameters of ontological presentation. This is of course requiring the intervention of the subjective decision, in the undecideable split it inflicts upon the situation. From the side of the situation, the being of the event occurs as an excrescence, an empty name circulating whose specificity in the situation it cannot recognize. From the event’s side it is a singularity, the designation of an internal gap in the consistent structure, designating a non-counted term which escapes the state’s immanent count. It is this undecideability which calls for subjective act, and which allows for a split in the ontological architecture itself. The subject thus makes consistent the latent inconsistency which lurks in a situation, unrecognizable by the state in the form of singularities (terms which are presented but not re-presented):
"The transcendence of the subject can be given a precise definition in contradistinction to the objective immanence of ontological discourse: whereas the latter is the consistent presentation of the inconsistency latent in the void, the subject is the consistent presentation of the inconsistency latent in unity (it effectuates the generic)…
The axiomatic consistency of ontological discourse encounters its own ‘impossibility’, that is, its own extra-discursive ‘real’, at the point at which the immanent disjunction between structure and metastructure turns into the transcendent excess of re-presentation over presentation. In other words, the ontological a priori (mathematical discourse) intersects with the a posteriori (the ‘world’) at the point where its effectuation of the inconsistency of consistency (the being nothing of non-being) flips over into an effectuation of the consistency of inconsistency (the non-being of being-nothing, or subjective ‘truth’) through the mediation of the event.” ” [Pg; 113]
This is why it is in the event’s nature to disappear: it effectuates forces into the situation the nomination of an illegal nomination which, if successfully accomplished by the subjective act, will thereby be inscribed in the situation, where the event’s forced rupture by subjective intervention vanishes. Brassier condoned this surplus of ‘transcendent’ activity which guarantees the link between the fixity of ontology and the consistency of its bedrock in their void, and the world wherein the enigmatic excess can be positivized by subjective intervention.
”Badiou bridges the gap between ontological discourse and mundane reality by surreptitiously converting an immanent hiatus in ontological presentation into a transcendent interruption of ontological consistency. As a result, his philosophy simply stipulates an isomorphy between discourse and reality, logical consequences and material causes, thinking and being. Thinking is sufficient to change the world: such is the ultimate import of Badiou’s idealism.” [Ibid]
Brassier condones this assignment to event’s to thought, insofar as they remain strictly rooted in subjective decision (albeit subtractive), which renders all occurrences in the universe as rather irrelevant glimmers for the metaontological discourse. The Big Bang is not an event, but the October Revolution is. This is what Brassier deems Badiou’s ‘noocentrism’ rather than anthropocentrism.
But in order to guarantee the possibility of change in his theory of the event, Badiou must mediate the ontological presentation (stable) and non-ontological situations (with the potential for the event, where truth-procedures occur) through metaontology. It converts the discursive immanent disjunction between belonging and inclusion in the former, into the source for the evental transcendence in the latter: the excess of re-presentation over presentation in the undecideable gap located between the state's excess demarcation on parts which do not belong (excrescences) and the evental singularity in which the decision of a new existence is forced in the world. Since within ontology nothing happens (the event is forbidden), the only thing tying being to the world is Badiou’s own metaontological register. And this is achieved by a non-warranted assumption: that presentation must occur in non-ontological situations, while ontology only indicates the existence of the ontological situation as such, founded in the void. It knows nothing of the excrescence which confuses it revealing the inconsistency of presentation, and the identification of a singularity wherein the force of the event can pass through. Either he chooses to deny that ontology is one more situation, which requires hypostasizing it into the status of metaphysics, or else one uncompromisingly embraces the subtractive nature of presentation defies all non-ontological consequences and so undermines the theory of the event.
4.9 Consequences of Subtraction
If ontology is no mere situation, but is transcendent with respect to the world, Badiou resurrects the empiricist distinction between form and content, which he abjured in The Concept of Model. To avoid this he must show how presentation must occur in non-ontological contexts. But because ontology begins with the assumption that the one is not, whereas all other situations begin with its opposite, it is impossible to effectuate this link with the resources immanent to ontology. So the purported presentation of presentation, accessed by ontology, is compromised. More importantly, the interplay between consistency and inconsistency makes it undeterminable how non-discursive presentation (non-ontological) occurs. The empiricist alternative can only lead to pragmatist embrace of empirical content underlying choice of conceptual scheme (as Quine shows), whereas the alternative is an idealism where ontological discursive consistency provides a theory of worldly inconsistency, which places thought’s subtractive capacity to affirm the event’s happening as the only way to engender further consistency. Of course, this whole problematic underlies Badiou’s own careful separation of materialism and idealism, but it remains the case, Brassier would say, that the subtractive subjective operation which founds the event’s disturbance with all discursive stability is an act of thought, and which re-establishes the discursive coherence as soon as it happens in effacing the event’s being.
Here Brassier diagnoses two alternatives: Badiou supplements subtractive ontology with a doctrine of appearance in concrete worlds, or the logic of subtraction deposes presentation of all potential disturbances against the event. But Brassier thinks Badiou’s opting for the former alternative (in his Logics of Worlds) is disappointing, since the speculative import of his theory is not the theory of the event, but the subtractive ontology which disenchants being from all conceptual registers, metaphysical or phenomenological. The meaning of being is abandoned as an antiquated leftover for nostalgic Heideggereans to fantasize over. Brassier deems this subtractive portion of his theory is in good accord with naturalized epistemological accounts, such as that of Churchland’s celebration of the PVA paradigm against anthropocentric, folk-psychological variants. So, Brassier suggests, instead of attempting to supplement the subtractive ontology with a phenomenological theory, it needs to further separate itself from all phenomenological registers and the dyadic structures of temporalization / spatialization, continuity/discontinuity, quantity/quality. This means abandoning the discursive idealism Brassier attributes to Badiou, as well as the latter’s unwarranted belief in the necessity of existing consistent situations. Here Brassier wants to move towards Laruelle to posit that it is possible to accomplish an affirmation of the void without recourse to mathematics and without recourse in phenomenological or empirical supplements.
”The discursive structure of presentation seems to stipulate an isomorphy between nomological and ontological structure which conflicts with the realist postulates of the physical sciences, which assume that objects exhibit causal properties rooted in real physical structures that obtain quite independently of the ideal laws of presentation. At the same time, the dualism of ontological form and ontic content generates a dichotomy which also seems to contradict the requirements of scientific realism: either discursively structured presentation or unstructured chaos.” [Pg: 117]
Next we will see how this is possible in the work of Francois Laruelle.
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