Badiou's Mathematical Platonism

The Meta-Ontological Exception:
Notes on Badiou's Mathematical Platonism
_____________________________________________

“The concept of model is strictly dependent, in all its successive stages, on the (mathematical) theory of sets. From this point of view, it is already inexact to say that the concept connects formal thought to its outside. In truth, the marks ‘outside the system’ can only deploy a domain of interpretation for those of the system within a mathematical envelopment, which preordains the former to the latter. […] Semantics here is an intramathematical relation between certain refined experimental apparatuses (formal systems) and certain ‘cruder’ mathematical products, which is to say, products accepted, taken to be demonstrated, without having been submitted to all the exigencies of inscription ruled by the verifying constraints of the apparatus." (AB, The Concept of Model)

Zachary-Luke Fraser advances a nice rejoinder to Ray Brassier’s outstanding analysis from Nihil Unbound. There Brassier asks what precise role metaontology comes to play vis the distinction between ontological and non-ontological situations. On the one hand, metaontology is clearly not ontology itself, since the latter only speaks of sets while the former speaks of presentations in general. As such metaontology cannot be said to be ‘founded on the void’ in the same way as ontology, since it operates with resources strictly external to the latter. On the other hand, metaontology suspends Leibniz’s thesis, which asserts the identity of being and the One (or being and unity), declaring the latter to be a mere operation (the count-as-one which structures every presentation). So it seems that metaontology stands somewhere inbetween the two ‘fields’ of presentation, enacting the transitivity of the very concept of presentation across the two domains, affirming the identity of ontology and mathematics. Luke Fraser thus seeks to dissolve the pertinence of the polarity between discourse and world in Badiou's mathematical Platonism by arguing that non-ontological presentations, thought in their being, must be already mathematized, i.e. must be thought of as models for set theory.

This way, it is not that set-theory qua singular discourse is ‘connected’ to its outside in non-ontological presentations via metaontology. Rather, all presentations are thinkable ontologically only as mathematically treated as a domain for the testing of the set-theoretical axioms: thus stipulating that insofar as ontology thinks of the form of presentations as sets, it thinks them in their being. This is part of the ‘mathematical Platonism’ that dissolves the transcendent bond between a formal language and its outside, and thereby dissolves the tension between a true materialism and what would appear to be a discursive brand of idealism anchored in set theoretical mathematics. So ontology and non-ontological situations are at once indiscernible as immanent (every presentation is immanently presupposed as having being mathematically intelligible in its being) and as transcendent (ontology is just one situation among others in itself;no situation contains all others; the concept of general presentation formally described by ontology is bridged through the meta-ontological decision):

“The point to which this brings us is this: To the extent that a mathematical ontology of concrete situations is possible, it must be possible to treat these as ‘models’ of set theory. Accordingly, these situations must be apprehended as being already mathematical in some sense, however crudely or vaguely understood. To the extent that ontology avoids the ‘empiricist’ mandate of being an ‘imitative craft’ (a characterisation against which Badiou rails in The Concept of Model), the correspondence between the ontological situation and its outside can be classified as neither a relation of transcendence nor immanence, but must be thought as a point of indiscernibility between the two. This is the source of all the obscurity attributable to the ‘Platonist’ position of metaontology, which forces us to ask, as Brassier does”,

“Where is Badiou speaking from in these decisive opening editations of Being and Event? Clearly, it is neither from the identity of thinking and being as effectuated in ontological discourse, nor from within a situation governed by knowledge and hence subject to the law of the One. […M]etaontological discourse seems to enjoy a condition of transcendent exception vis-àvis the immanence of ontological and non-ontological situations”(NU: Chapter IV)”

The relation between ontology/non-ontology is not strictly transcendent because non-ontological situations can only be thought in their being as already mathematized, i.e. for ordinary situations to be treated as models requires their mathematization into domains for set theory. It is not strictly immanent either because the ontological situation does not present all others, but only their general form as ‘sutured to their being’, inside the characteristic mode of thought that is ontology, i.e. there is no presentation encompassing all others, but only presentations of presentations, and void/nothingness.

However, the equation of mathematics with ontology, and thus the affirmation that set theory alone renders the form of presentation in all non-ontological situations, can only be performed by metaontology as declaring the equation of being qua presentation and inconsistent multiplicity qua the inertia of the domain of set theory. This in turn requires the primitive inconsistency of presentation to be foundational for the axiomatic, which Badiou perceives in the existential inscription of the pure name of the void as the primitive and radically non-phenomenological sign from which the entire stock of operations are woven in continuity with the axioms of set theory and on the basis of the primitive relation of ‘belonging’ alone. Metaontology is thus prerequisite to establish the indiscernibility of set theory as a unique situation and the wealth of possible non-ontological situations insofar as they are thought in their being.

Why must we assume that inconsistent multiplicity underlies the consistency of the pure multiple, which amounts to thinking being as fundamentally ‘without unity’ or as being-nothing? It is because the primitive subtraction of being from the count-as-one is thought in accordance with the Parmenidean statement that whatever is not One must be by necessity multiple. Since multiplicity resists unity, and given that being is essentially multiple, any discourse on being qua being will begin from the assumption of the non-being of the One, or the lack of any foundational figure of oneness.

Badiou assigns the multiplicity of presentation to its properly discursive (ontological) domain through the unique consistency of ZF set theory, which proceeds in the assumption of existence of a set with an empty extension. Once the operation of belonging to x can be said to be tantamount to ‘being presented to x’ via the speculative move, set theoretical strictures appear fittingly to depart from the sole assumption of the lack of a phenomenological given. Badiou explains the presupposition of lack required to render multiple being discursively through the sterility of the presentational domain set theory inscribes with the mark of the void. This identifies presentation with inconsistent multiplicity, and as such tethers being to set theory as ontology, enacting the thinking of that which primitively proceeds from the absence of unity, i.e. from accepting Parmenides’ embrace of the form of presentation as essentially multiple. The ‘suture to being’, again, thus remains strictly meta-ontological.

Of course, the additional assumption, also spotted by Brassier, is that non-ontological presentation is distinguished insofar as it presents the One, which necessarily makes the ontological situation qua theory of the multiple as the unique situation in which presentation is thought of in ‘its being’. The fictive being of the one is expressed as set theory operates consistently on the basis of the primordial lack of the void itself. It is thus that all unity is given in ontology solely against the impenetrable background of the void’s empty inertia. Each set is constructed on the basis of the primitive lack indexed by the void’s proper name, and is determined purely extensionally in terms of what it presents (which is always nothing but a function of replacement operating over the proliferation of subsets woven from the void alone -this is guaranteed via the axioms of void, powerset and replacement). Oneness remains thus the result of the operation of belonging, which presents sets whose being is nevertheless indexed to the void in the last instance.

“This splitting of unity into operation and effect is integral to the thinking of presentation and the metaontological delivery of the formal thinking of presentation to mathematics, and specifically, to set theory. It is set theory itself that formalizes this split, and provides us with a figure of multiplicity adequate to the thinking of presentation, and, more dramatically, to the univocal determination of the existent as presentation (and so of presentation as the presentation of presentations). To speak of a presentation is to speak of presentation affected by an operation of the count-as-one, and not of a presentation solidified according to the intrinsic unity characteristic of entity. The unity of a presentation is always extrinsic.” [ZLF Pg. 68]

It is this split between the one as an operation and as effect which becomes occluded in non-ontological presentations, where being attains fictive unity in closing this gap. It thus assumes itself identical to what it presents, or to its own singleton: x = {x}, thus violating the constraint set to it in well founded set theory by the axiom of foundation and extensionality (the couple of which require a set’s extensional determination or identity, and its incapacity to belong to itself). This indistinction between the one as operation and the one as result is thus the violation of what Zachary Luke Fraser designates as the two principles of multiplicity for Badiou:

a) Material component - Every set is extensionally determined.[1]

b) Formal unity – Every set is different from itself by a pure differentiation ( grounded in the axiom of foundation).

Consistency is thus the formal unity in which a presentation is given, its being-counted-as-one (yet different from itself) in the situation (one as result). On the other hand, presentation itself remains necessarily inconsistent as the retroactive presupposition of the multiple gathered is but merely counted-as-one, and thus presupposes its prior existence, not exhausted by what it unifies or presents in its formal unity (one as operation). In ordinary situations where this gap is closed, we do not think according to the being of what is presented, which necessarily differs from itself formally but on the basis of the fictional consistency of unity in which it appears.

The evaluation of such situations in the ‘moment of the One’, as we know, becomes properly the subject of Badiou’s Greater Logic in Logics of World and the phenomenology of objects.

- Annotations on Meditation 26 (The Concept of Quantity) in Alain Badiou’s Being and Event

In Alain Badiou’s theoretical framework set-theory as ontology comes to explicate the notion of quantity through some technical concepts worth elucidating in close detail, even if, as Badiou admits that the formal exposition of the ontological operations can exceed philosophical (and therefore meta-ontological) interest. In particular, it is easy to overlook Badiou’s explication of the concept of a ‘function’, since it is delegated to a short (but doubtlessly crucial) Annex at the end of the book. There, a function is described straightforwardly as a particular kind of multiple, in unproblematic continuity with the strictures of set-theory and the pure multiple. In what follows we’ll try to elucidate the surrounding notions, since the prose in the book lends itself to easy confusion.

A function f of a given set α to a set β, which can be written f(α) = β, establishes a one-to-one correspondence between the two sets, where it is understood that:

- For every element of α there corresponds via f an element of β.

- For every two different elements of α there corresponds two different elements of β

- For every element of β there corresponds via f, an element of α.

At this point, the set-theoretical grounding becomes quite necessary to follow Badiou’s argumentation, since the concept of ‘function’ outlined above is defined, after all, as simply a particular kind of multiple. What kind of a multiple is at stake here? Here we must move to Appendix 2 of the book, which provides the sought for clarification.

Badiou begins by describing multiples which constitute relations between other multiples. These are structured as series of ordered pairs, and are written as follows:

Let’s assume the existence of a relation R between two given multiples α and β: R(α, β). Badiou describes relation as getting behind two ideas: that of the pairing of the two elements, and that of their sequence or order. This second condition guarantees that even if R (α, β) obtains in a given situation, it is possible that R(β, α) does not. The first condition entails that all relations can be expressed as consisting of two element multiples, written in the form <α, β>, so that to say that there exists a relation R between two existing elements α and β finally amounts to no more than saying: <α, β> ε R. Given that for any two existing elements α and β there exists necessarily the set which has α and β as its sole elements {α, β}[2], although se will see right away that this set is not identical to <α, β> . The only problematic aspect pending is finally that of order, and thus of the stipulated asymmetry between R (α, β) and R(β, α):

Interestingly enough, the ‘ordered pair’ solicited by Badiou is not simply the pairing of α and β, but actually the pairing of the singleton of α, and the pairing of α and β. So we get:

<α, β> ↔ { {α}, {α, β} }

This set must exist, given that the existence of α and β guarantees the existence of their respective singletons, as well as their pair. Therefore the union of either of the first terms with their conjunction must also exist. In other words, for any given two multiples α and β there exist two different possible ordered pairings, which are not identical:

<α, β> ≠ < β, α> .↔. { {α}, {α, β} } ≠ { {β}, {β, α} }

Notice, however, that both ordered pairings are completely indifferent with respect to order in the terms of the set {β, α} / {α, β}; which are transparently identical sets. The impossibility of substitution and thus the asymmetry of the two orderings laid above occurs in the difference occasioned by the choice between {α} or {β}. This must mean that an ordered pair always consists, for any two elements supposed existent, of the two-element set consisting of the singleton of one of the two elements and the two-element set consisting of the two already given elements. Additionally, it is implied that:

<α, β> = <г, у> .->. (α = г) & (β = y)

Finally, to say a relation R obtains between two given sets α and β entails:

<α, β> ε R or <β, α> ε R

Having established that a relation is a multiple composed of ordered pairs, Badiou proceeds to explain how a function may be described a particular kind of relation. The trick here consists in grasping adequately the abovementioned idea of ‘correspondence’. Let us assume a function f that makes a multiple β correspond to α: f(α) = β. Having established functions are relations, and relations are sets of ordered pairs, it plainly follows that functions are sets of ordered pairs. If we then allow R_f to stand for the function of α to β, we can write as follows:

<α, β> ε R_f

But the peculiarity of the function resides on the uniqueness of β, so that no other element can correspond to it by it. This means that for any two multiples β and y that correspond to α via a function R, it must be the case that β and y are identical. Formally we write:

[f(α) = β .&. f(α) = y] -> β = y

Or, alternatively:

(<α, β> ε R _f .&. <α, y > ε R_f) -> β = y

If we want to unpack this formula, we write:

({{α}, {α, β}} ε R_f .&. {{α}, {α,y}} ε R_f) -> β = y

With this Badiou completes his reduction of the concept of relation to pure set-theoretical constructed multiplicities. The next step is to ground the comparison between sets in the series of ordinals (natural multiples[3]). With respect to a multiple’s ‘size’ or ‘magnitude’, there always exists an ordinal which is equal to it (which is not to say only natural multiples exist; we know this isn’t true given the existence of historical multiples). Badiou claims that thus ‘nature includes all thinkable orders of size” [BE: Pg. 270]. Here things turn a confusing, since Badiou doesn’t really provide an example until later. We can, however, give a very simple case to illustrate how exactly this happens.

First, recall that the series of ordinals are woven from the void alone, as the structured sequence or passage from the void into its singleton, and thus consecutively in serial manner. If we repeat the basic example laid above where R_f stands for the function of α to β. We got:

[R(α, β)] ↔ [f(α) = β] ↔ [< α, β> ε R_f]

Or, more explicitly:

{ {α}, {α, β} } ε R _f

However, we can easily see that the multiple thus produced has the same power as the ordinal which composes the Von Neumann ordinal Two, and which is guaranteed given the sequence of ordinals:

Π: {{Ø}, {Ø, {Ø}}

Notice, however, that although this ordinal certainly has the same power as the given set, there’s an infinity of ordinals with the same power as the laid set: we can easily imagine the ordinal: {{{Ø}}, {{Ø}, {{Ø}}} and successive variants, all with the same power. The requirement is merely that there will be at least one ordinal with the same power. Identity as such is guaranteed through the comparison of a set's extensions, where the axiom of foundation guarantees the void lingers within each form of presentation (forbidding non-wellfounded sets from proliferation indefinately; self-belonging becomes forbidden). I will continue with these notes later.

---

[1] See the annotations below to explain the procedure of the determination of the identity of a set on the basis of the extensional determination of each set; which delivers us to the concept of quantity.

[2] See Being and Event, Meditation 12.

[3] Meditations 11-12.

Alien Theory - Chapter IV: Laruelle's Pantheism and Badiou's Noological Idealism

- ALIEN THEORY: CHAPTER IV -

LARUELLE'S PANTHEISM AND BADIOU'S NOOLOGICAL IDEALISM
____________________________________________________________

How can we guarantee that the transcendental realist appeal to a ‘matter itself’ won’t end up reinscribing matter within the concept by simply evoking it in discourse? How can we move towards making matter independent of all idealization and co-determination if we cannot help but evoke it in and through discourse? How do we avoid the materiological trap? Here we see how Laruelle lays the conditions for non-materialism, and a non-philosophical 'realism'. We should keep in mind however, that Brassier has later sought to qualify Laruelle’s ‘non philosophical’ step outside Decision and will instead call it a ‘non-correlationist’ philosophy. Instead of circumscribing matter inside Decision as objectifying transcendence, non-philosophy is a ‘performative’ set of operations which enact a characterization of matter itself as immanently foreclosed to Decision (Pg: 96). This immanence does not presuppose transcendent Decision distinguishing between materialism and idealism, i.e. to the distinction between material immanence and ideal transcendence. Immanence is foreclosed to all Decisional dyads, even if it ultimately determines them through their occasion.

Materialism / Idealism

The distinction between ‘materialism’ and ‘idealism’ is not pre-given or obvious. We should enquire transcendentally into the conditions in which these categories are produced, i.e. deducing the ‘genetic a priori’ which conditions all their productions independently of the particular contents given to them. The idea is to make materialism and idealism autonomous to particular politico-scientific investments by making of them immanent transcendental criteria which condition philosophy tout court. In other words, instead of investing them with specific contents through philosophical explication, which invariably ends up in ideological investments, materialism and idealism should be immediately determining a split between materialism or matter and the concept; distinguishing the former’s autonomy from the philosophical reinscription into the latter. As we will see, this will entail turning philosophical Decision / objectifying transcendence into an empirical instance which occasions its Real determination in-the-last-instance.

Laruelle points out that the specificity of materialism comes in how it not only gives metatheoretical conditions for its own production, but also its a priori conditions for distinction from idealism; whereas the latter does not necessarily distinguish itself from the former. A genetic difference a priori separates the materialist from the idealist utterance: “Against the empiricist mistake, which consists in injecting into these categories an ‘immediate’ content which is in reality already mediated, it is a question of thinking them at once in themselves and in terms of what is more important than them, their relation, and more important than their relation: their absolute difference” (Laruelle, 1981, p.104.). The absolute difference between idealism and materialism must be, however, pertaining to neither, and so it must remain a-signifying or non-conceptual. This baffled me a bit, since it was first said that the difference between the two is proper to materialism and then that their absolute difference is non-conceptual and proper to neither. However, the idea that is explained behind this seems to rest on a distinction between the materialist distinction between itself and idealism, and the absolute difference which pertains to neither; the non-conceptual condition which enact their transcendental distinction. So there’s at once a theoretical distinction or relation which materialism theoretically lays out (relation of relation and non-relation), and is also transcendentally determined as already given, where the non-theoretical indifference already gives itself on the basis of the Real (enacting the non-relation of relation and non-relation). We will see this later in more substantive detail, but the idea is to separate thought’s theoretical determination or relational differentiation from the performative separation which transcendentally generates the condition for a non-theoretical separation of real and ideal which gives itself without the need for conceptual mediation or as we will say ‘without givenness’ – i.e. independent of all signification and discourse. We will see how Laruelle effects this separation gradually, since it is very subtle and unfortunately convoluted, even in Brassier’s exposition.

A PRELIMINARY CONFRONTATION: NON-PHILOSOPHY AS PANTHEISM

Yet we should provisionally ask why exactly must materialism distinguish itself from idealism as part of its ‘generic a priori’- why can’t it simply construct itself independently of all idealism, that is to say, for Laruelle, philosophy? This will prove to be a particularly striking feature of Laruelle and Brassier’s endorsement of non-philosophy here. This necessity to distinguish itself from idealism, we will see, rests on materialism’s non-philosophical presupposition of the necessity for Decision to be given as occasional cause to enact its Real determination. Thinking presupposes a minimum of objectifying transcendence, which serves as occasional cause to effect the radical and unilateral separation of the immanent Real foreclosed to thought and the object as given through objectifying transcendence given the latter’s non synthetic identity-in-the-last instance the being-foreclosed of the Real which has always already determined it. The real needs objectifying transcendence in order distinguish itself absolutely from it, identifying the transcendental foreclosure of the object in thought to the foreclosure of the immanent real.

But the question is of course why should we presuppose that materialism needs a minimum of objectifying transcendence? This seems to rest on the presupposition not only that all philosophy is idealist, but that realism must necessarily establish itself by distinguishing itself from idealism gratuitously. It is not clear whatsoever why this is inherently a condition for materialism; and why idealism is on the other hand allowed to operate independently. Perhaps we can stipulate that there is a necessity in any materialism to distinguish the reality of the utterance from the real which determines it; but this seems a reproduction of the all-too obvious theoretical representationalist dyadic split between real-concept.

It is precisely this distinction which appears as necessary and possibly rigorous enough to avoid bilateral co-determination. It is necessary since, as we saw, the incapacity to distinguish between Concept and Matter, or the Parmenidean fate, ends up enacting such an idealist co-constitution. We saw this in particular through the purported transvaluation of the transcendental in the machinic constructivism proper to Deleuze and Guattari, and in Henry’s ultimate negative co-determination of enstatic immanence through ekstatic transcendence. Therefore, the indistinction of matter and idea cannot but become idealist, according to Laruelle, since it must render the Real as co-determined by its philosophical positing or Concept; as in Deleuze’s dynamic heterogenetic production of intensivity as the machinic phylum, which was also the transcendence of immanence-to-itself through the circuitous self-sublation of the virtual/actual through ‘And’ as tensor of inclusive disjunction. In turn, materialism must guarantee matter’s transcendental separation from the Idea/Concept without being co-determined by the latter. This is what non-philosophy promises for thinking in its performative determination-in-the-last-instance by the Real through the occasion of objectifying transcendence / Decision. So Laruelle surely needs philosophy to remain the empirical instance from which the Real is freed: something which seems especially urgent if one thinks all philosophy is victim of transcendence, or more strongly still, that thought presupposes a minimum of objectifying transcendence (as Brassier notes in NU). This should lead is into questioning where exactly the empirical sciences stand in this conundrum: are they also occasions of objectifying transcendence which are used by non-philosophy? Or is transcendental realism finally a non-philosophical thesis, which does not exclude a potential non-scientific realism of some sort?

It is already unclear, as Brassier notes in Nihil Unbound, that all philosophy can be amalgamated uniformly through the filter of Decision. It is even less clear, however, that Laruelle can also corner scientific discourse as occasions of objectifying transcendence which can be therefore used as occasions for their non-philosophical determination. And if not, then it is also radically unclear how the purported liberation of a transcendental realism by non-philosophy can somehow vindicate those disastrous results for the ‘empirical domain’ which we saw earlier. Clearly, Laruelle must think that the empirical domain targeted by the natural scientist is somehow coextensive to the presupposition of the empirical as given in the correlation to the operation of givenness in Decisional thought. But this seems atrociously speculative. Instead, we get a Real simultaneously identical-in-the-last-instance to the transcendentally given object insofar as it is foreclosed to Decision as unilateralized identity, and the Real’s radical indifference from the objective being of the given as absolutely differentiated from unobjectifiable immanence as unilateralized difference. But this sheds no light as to how scientifically objectivated claims could somehow not be merely Ideal configurations on the same level as all other philosophical variants. If the occasional cause envelops both Decisional philosophy and science, then scientific discursivity remains idealizing in-itself; and the only thing that is capable of making it autonomous is non-philosophical determination-in-the-last instance of the occasion.

However, as we saw, it remains entirely unclear how science indeed falls within the ambit of objectifying transcendence, or that indeed thought requires to presuppose its givenness for its determination as an empirical given through the Real. This ultimately renders the non-philosophical Real to be something of an ineffable first mover-without-movement (to risk ridiculity); an immanent radical pantheism where the 'Son’s' occasional manifestation as given is supported by its ultimate transcendent identity to an immanent sphere of indivisible Oneness, lading to the point of unilaterality (for it is the occasion of the Son as Man or empirical occasion which is given for its determination-in-the-last-instance as God, while the latter is radically indifferent to Man’s empirical givenness and thus foreclosed to all objectivation it allows itself to be unilateral and not determined by Man (or any kind of ideality) in return- i.e. as radical immanence given-without-givenness). This makes the entire non-philosophical attempt a little too close to a pantheistic theodicy. On the other hand, if scientific discourse remains indeed independent from Decision or objectifying transcendence, then it remains totally unclear how scientific realism can be supported by the performative non-philosophical non-materialistic determination of Decision. Either way, things don’t look all better for the empirical than they did with the machinic constructivism, as in the case of Deleuze and Guattari.

Materialism/Idealism – Continued

In any case let’s continue with Brassier’s exposition so we can flesh out the specifics in more substantive detail. Laruelle distinguishes between three categorical ascriptions of materialism and idealism which fail to give an account of the a priori generic difference sought for. Matter and Idea are not to be taken as [AT Pg: 100]:

1) Given objectivities – Say, in techno-economic production or ideology.

2) Supposedly given significations – “[W]hereby, on the one hand, the concept of ‘Matter’ combines general features of ‘materiality’ abstracted from nature with empirical characteristics drawn from sense-perception; while, on the other, that of the ‘Idea’ combines general features of ‘ideality’ abstracted” from culture with empirical characteristics drawn from ‘inner sense’ or self consciousness.

3) Produced discursive categories (rather than given) – This is what Laruelle calls ‘structural Marxism’ where materialism and idealism have no specific conceptual signification but are given contingent configurations through the various politico-scientific discourses which constantly transform the differentiations. So the statement relates to differential elements which are given from particular politico-scientific configurations, they have no meaning in themselves and become a-signifying. Here we find the name of Althusser, according to Laruelle, and it seems as if Laclau’s position would be most appropriate here as well.

However, this third account, although seductively persuasive. Laruelle objects to it that it finds it impossible to make it a-signifying and non-conceptual while being differential and relational at the same time: that is to say, dependent on an empirically presupposed structure of irreducible given elements in signifying coordination. And since these objectivities are subject to socio-economic articulation or conditions they are already mediated in forms of conceptual presupposition (hegemonic struggle must be ultimately based on popular demands to the Master…). The distinction between materialism remains produced rather than determining or giving.

“The real, a priori, transcendental separation between ‘materialism’ and ‘idealism’ as intrinsically distinct modalities of theoretical utterance cannot be confused with the ideal, a posteriori and ultimately empirical differentiation between ‘materialism’ and ‘idealism’ as distinct discursive modalities produced through relations of reciprocal determination.” [Pg. 100]

Here we have once again foresee Laruelle’s split between the bilateral reciprocity inherent to all intra-theoretical Decisional-dyads where materialism/idealism are invested in peculiar configurations, and the metatheoretical non-Decisional determination of the Decisional giving of the object as the empirical occasional cause for non-philosophy to determine as already given unilateral duality which comprises:

a) The unilateralized identity (without unity) between the Real as being-nothing as identical-in-the-last-instance with the object’s being-foreclosed to knowledge. (instantiated by determination-in-the-last instance).

b) The unilateralized difference (without distinction) between objective being and the object’s unobjectifiable as being-nothing. (instantiated by objectifying transcendence as occasional cause)

Thought thereby distinguishes the already given a priori split between a radically immanent real (materialism) which determines its own objective foreclosure as being-nothing, and its transcendental objectification (idealism) where specific investments of the empirical materialist/idealist dyad are distinguished unilaterally from the Real. This is accomplished through the use of Decision as an empirical occasion for thought to enact its determination-in-the-last-instance with the Real; so that former distinguishes itself from the latter while the latter remains utterly indifferent to the former. Determination-in-the-last-instance finally allows thought to enact the generic a priori which is the unobjectifiable duality of matter and concept, real and ideal, by using the objectifying transcendence as an empirical occasion for its determination. In this way the bilateral reciprocity is severed through unilateralization; the object becomes subjective agency and patient of its own determination. Since the Real cannot distinguish itself from being, it can only be performatively thought as already-given-without givenness, foreclosed to reflection and thereby to bilateral appropriation.

Unlike the produced difference of particular versions of the materialist/idealist dyad in their empirical differentiations (which structural Marxism presumes as produced rather than producing), non-materialist theory is truly performative insofar as it transcendentally separates both. The unilateral duality enacted by non philosophy must therefore be sharply distinguished from the structural differentiation of Decision. The latter constructs the difference between the two terms from the reflective position which overseas the two and reciprocally constitutes them; whereas the former enacts performatively the unilateral duality where the Real is strictly foreclosed as already given, and absolutely separated, or utterly indifferently, to Ideal objectivation. We substitute the circularity proper to the reflexive Ideal differentiation of relation and non-relation, with the unilateral, immanently transcendent non-relation of relation and non-relation. In structural Marxism, relation remains the hypostasized Idea, as in machinic constructivism’s relational continuum: “In the primacy of ‘relations’ (of production, of force, of texts, of power) which we took for materialism, and which is one in effect, that is to say, an offshoot of idealism, there is only a transfer of difference in and as the Idea,[...] an ultimate primacy of ideality over the real, of Being over the entity” (Ibid., p.106). Materialism-idealism, like the actual-virtual doublet enters into a reversible circuit between continuum-cut, as the Ideal transcendence of materiality, as in the hyletic continuum’s ceaseless heterogenetic co-production of plane and Concept. Laruelle attacks at once all systems of differential structuring as circularly auto-positional, self-producing Ideality:

“Generally, in the systems of Difference, materialism is merely idealism in the nth degree, in the ‘andth ’ degree, infinitely intensified. In raising ideality to the level of auto-production in this circular fashion, which is to say, to the status of causa sui (‘will to power’), they [the systems of Difference-RB] confirm ideality through itself, rendering the genesis of ideality and of its forms impossible” (Ibid., p.106-107).

This genesis must be impossible, since it is indistinguishable, and co-determining. The difference in structural Marxism and machinic constructivism suspends the empirical dogmatic split of materialism/idealism at the cost of making them contingent products of the auto-producing Idea of Repetition- as ‘matter’s’ shuffling differential continuum of socio-economic relations, in perpetual circuitous transcendent determination as immanence to self. This is what ultimately compromises structural systems of difference into the same fate as Deleuzean hyletic idealism, rendering materialism ultimately formally indistinguishable from absolute idealism.

The Materiological Amphiboly of Utterance and Statement

Idealisms embody the noological syntax which establishes the primacy of Relation, the infinite self-positing relation of the All (the plane, the continuum, the Idea, matter, Being…). It is a thinking that “proceeds through the absolute” (AT: Pg 101). Because of this it cannot explain the origin of Relation as self-reproducing Ideality, it is causa sui. Theory and the matter presupposed for and in the theory is co-dependent on the theory: immanent material utterance and ontological saying are reversible. The utterance gives material immanence while the saying the transcendence necessary for its determination and inseparable repetition, both becoming entangled in a circuitous and reversible exchange.

“More precisely, just as it posits its own presupposition, materiology deliberately reinscribes its own conditions of enunciation within the enunciated theory162. Like a serpent swallowing its own tail, it absorbs the real conditions of utterance for materialism within the ideal realm of materialist theory.” (AT: Pg: 102)

So while material constructivism servers the duality between signifier-signified, and the endless post-phenomenological hermeneutical/deconstructive aporias by making ideality the very circuitous and reversible exchange between its positing and presupposition. It thereby establishes the equivalence between utterance and statement in the Ideal sublation (of Repetition of the plane, of the material flux in perpetual socio-economic differentiation, etc…). How then, to avoid the transcendental separation of thought/thing, subject/substance, in which the real becomes ontologized and phenomenalized, and where idealism is indistinguishable from idealism? The non-philosophical alternative will thus not be strictly materialistic, insofar as it doesn’t insert itself in its Decisional forms. Non-decisional immanence must be foreclosed to the transcendent division of materialism and idealism, while establishing matter as first name or non-conceptual symbol for unobjectifiable immanence (Pg; 104).

The Decline of Materialism / One or Multiple? Laruelle and Badiou

Matter must remain foreclosed to materialism; the utterance must be separated from its Decisional hybrid envelopment by the Ideal saying. Matter must be shorn of all semantic intelligibility, of all ‘consistency’ and Ideal sufficiency, to become radically indifferent to this ideal self-positioning, rather than correlative to it. Transcendental determination must absolutely separate the Real from the Ideal, without thereby allowing this separation to be semantically explicit as a relation of difference between two reified terms: matter and idea, difference/indifference. Rather, immanent matter must enact its foreclosure to self-positing transcendence by making the latter the occasion for its ultimate determination-in-the-last instance as separating objective being from its being-nothing, while the nothing remains utterly foreclosed to any differentiation, even the one between difference and indifference. The latter, the pure zero-level void, is by virtue of unilateralizing identity effected as radically indifferent to any kind of ontological investment; a radically insufficient, yet necessary positing of matter itself as first symbol, using objectifying transcendence as the already given empirical instance to enact a rigorous condition for its absolute separation from it, but only in the last instance.

“The ‘Decline’ of materialism is thus the sacrifice of materialism in order to rescue matter from all Ideal envelopment, the better to uncover: a more secret knowing of matter, one which would no longer tread the luminous paths of the logos..., nor the amphiboly, the limitless fusion of ideality and the real in the hyle” (Laruelle., p.107)

“Whereas in materiological theorizing the ideality of statement invariably became co-constitutive of the reality of the utterance through which it was produced, the statements of non-materiological theory now allow themselves to be axiomatically determined by the unobjectifiable reality of utterance -via the intervention of ‘matter itself’ as non- conceptual symbol- without presuming to co-constitute the reality of utterance in return… a thinking that is no longer ‘of’ matter in the sense of attempting its Decisional objectivation, but ‘of’ matter in the sense of being adequate to matter’s foreclosure to materiological determination.” (AT: Pg. 106)

This last instance’ should provisionally start to appeal to us as somewhat mysterious, as it points to a sort of “proper-name of the void”, with the difference that here it is not the subtractive instance of ontological presentation which then is problematically discursive form for all the infinite multiplicity of non-discursive presentational situations (as we’ve seen in Brassier’s trenchant critique of Badiou in Nihil Unbound, Chapter IV). Rather, matter as first name or non conceptual symbol indexes a Real Nothingness exempt from all ontological form, even that of attained in the consistent theory of the inconsistent pure multiple. The Real is foreclosed and indifferent to discourse, as the latter distinguishes itself unilaterally from it. The Real as the figure of the One, as proper name, then is the presupposed Name-of-God as the ineffable, the first-mover enacting its insurmountable gap and the determination of the objective instance it thinks as its immanent Real cause: "The non-materialist axiomatic engenders modalities of theorematic description for 'matter itself' qua radical hyle which are each incommesurable at the phenomenological level but phenomenally equivalent insofar as all are determined as adequate-in-the-last-instance to the radical hyle as phenomenon-without-logos... Remember that matter itself is no longer some ineffable, transcendent philosophical thing for us, and that the radical hyle is no longer an attempt to conceptualize the ineffable but merely a non-conceptual symbol for matter's foreclosure to Decision, a foreclosure now effectuated in non-materialist thinking through the Alien-subject's positing of the non-conceptual symbol enacting that foreclosure...the radical Hyle is the non-Determinable as the already-determined which determines the onto-logical amphiboly of description" (AT: Pg. 138)


But because it requires Decision as occasion for its determination, it is also a Real that is entirely impervious to processes which not for being non-philosophical or non-Decisional presuppose an empirical occasion of objectifying transcendence. For once again we must ask Laruelle whether all science is also victim of Decision, in which case the effectuation of the Real’s autonomous immanence can never become sensitive to intra-theoretical changes in scientific discursive domain(since change must then be, at most, a mere ‘reshuffling’ of the empirico-transcendental doublet proper to every Decision- phenomenally equivalent insofar as they ar are adequate to the real in the last instance). In such a case, the function of this ‘last instance of the Real’ would be to simply render all discursivity as materiality indifferent; and all difference between philosophical theories (or even scientific ones) formally equivalent. But the simplified generalization with which ‘Decision’ purports to swallow the entire history of speculative thought, coupled with its ultimate resilient insistence to identify the Real as the integral undifferentiated oneness; is simply to favor the severing of the bond between transcendent thought and the Real in non-speculative unity instead of the possible discursive contact with it in the transcendental forcing of the indiscernible generic Real as pure multiplicity, for which speculative thought is formally articulated in set theory and in which subjectivity intersects with this intervention. In this latter case, we can say that the discursive materialism which opens the way for transcendent intervention once again requires transcendence (which exists in every world imposing a Logic of appearing) to determine the Real multiple; but thereby also effecting a communicational bond between discursivity in general and truth; albeit its production must remain functionally a subjective operation (of fidelity).

In any case, if Laruelle seeks to make matter autonomous and thereby save the veritable field of the empirical (which machinic constructivism threatened to undermine), then is seems once again painfully difficult to see how this radical Real resembles matter in the natural-scientific sense in any distinctive way. For if all thought is presupposes its occasion of objectifying transcendence which sufficiently serves for its Real determination-in-the-last instance, then it seems the last-instance is perfectly insensitive to whether the objective occasion is constructed around schizophrenics or victims of demonic possession. Each and every time the Real is capable of determining the occasion as identical to it in the last instance; it ceases to be a transcendent positive being with a particular instantiation in order to become a void of nothingness uniformly disseminating itself in every empirical occassion. Determination-in-the-last instance seems to make every empirical occassion an instance of the Real, a Christo-generator which substitutes the ineffability of the transcendent substance in favor of the all-disseminating occasion indexing the ineffability of nothingness' foreclosure to Decisional hybridization (this is in fact how Zizek encourages us to read Christ's crucifiction: Christ dies not as man, but as God himself; which is to say he is the occasion which indexes the foreclosure of the One as substantial transcendence).

"The expression ‘One-in-One’ or ‘vision-in-One’ indicates the absence of any operation that would define the latter; the fact that it is not inscribed within an operational space or more powerful structure; its immanence in itself rather than to anything else; its naked simplicity as never either exceeding or lacking, because it is the only measure required, but one that is never a self-measurement, one that measures nothing so long as there is nothing to measure. (Laruelle 2003: 175–6)

If, on the other hand, Badiou’s generic subjective truth seems impervious to the actual unfolding of the truth-procedures it formally describes, it is because philosophy does not produce truths of its own. Yet in that case, philosophy’s putatively meta-ontological status generates the transferability of the concept of presentation to non-ontological situations under the presupposition of an 'ordinary consistency' (or of their transcendental organization regulating the laws of the multiple's appearing in a world). The Real qua pure multiple contains its condition for differential objectivation, and not just the foreclosure to all objectivation in the last instance.

It thus seems as if Laruelle’s purported rescuing of the empirical domain is only alleviating if we take the ultimate Real causality to 'validate' every single empirical instance as determinable by the ultimate Real cause, since they are all indifferently cases of objectifying transcendence qua occasional causes for DLI. But if so, then the axiomatic ultimation carried forth by the Stranger-subject through 'matter' as first non-conceptual symbol is little more than a hyperbolized substitute for God as first name for a ineffable immanence; a paradoxical transcendent pantheism which is nothing but which ultimately determines univocally all Decision in being already given-without-givenness. And yet if this determination is uniformly determining for all occassions of thought, then it remains utterly unclear how any difference can be of the order of the Real. It appears all distinctions, except the non-philosophical unilateralized difference, are merely occasions for an indifferent Real in which the primacy of non-relation stubbornly lingers. If not transcendence’s ultimate immanence to itself which is self-positing, the non-philosophical subtlety lies in the utter sterility of its ‘Real’ and the contingency of the occasion through which objectifying thought becomes determined by it.

“Radical immanence is non-problematic: it does not call for thinking, it does not petition Decision, it simply has no need for thought. But since there is thinking, or since philosophical Decision is the immediate, empirically given form within which thinking is already operating164, non-materialist theory will use the Decisional hybridization of thought and matter the materiological amphiboly of unobjectifiable reality and objectivating ideality, as its occasional but non-determining cause… That is to say, non-Decisional materialism will use thought’s transcendence, its pretension to absolute, self-positing sufficiency (exemplified by the hyletic continuum’s absolute auto-position) as the contingently given empirical occasion for thought’s determination by the necessary but non-sufficient immanence of material utterance. The unobjectifiable immanence of utterance as necessary condition for theory does not need discursive objectivation, but since the form of philosophical thinking has, in a sense, ‘always already’ articulated itself within that amphibological mixture of utterance and statement, the latter can be used as the occasional cause, the empirical support, for a thinking-in accordance- with the unobjectifiability of utterance taking that objectivating amphiboly, that Decisional hybridisation itself, as its object.

The key difference is this: whereas materiological thought mistakes its own hybridization of unobjectifiable immanence and objectivating transcendence for the Real (i.e. matter as Idea) because it believes that Decision is sufficient unto the Real, non-materiological thinking unilaterally determines the Decisional mixture of objectivating transcendence and unobjectifiable immanence on the basis of unobjectifiable immanence alone. It uses materiological Decision as the occasion for a non-materiological theory which lets the unobjectifiable immanence of material utterance determine or dualyse the materiological confusion of ‘matter itself’ and ‘matter as such’ via the non- Decisional positing of ‘matter itself’ as first name for the unobjectifiable immanence which determines all Decision in-the-last-instance.” (Pg. 106-107)

As we have seen, it’s far from clear how the empirical is salvaged this way, save in the disappointingly empty sense in which thought is always occasion for its real determination as identical-in-the-last-instance. However, seeing how radically this notion of the Real opposes ontologization, all we have in return is the lock of that first name which indexes an indivisible nothingness, the pure presupposition of a non-substantial, ultimately subtractive ineffable unity. This seems a dangerously crossbreeding of theological pantheism with transcendent realism through the disseminating effect of determination-in-the-last-instance enacting the non-synthetic unilateralized identity of the Real and the being foreclosed of the object. Matter as ‘non-conceptual symbol’ becomes therefore something of a sacred court for speculative thought to attain its honorary claim to realism, one which must obtain already outside the logical space of reasons and its contingently given occasions, and which transcendentally posits itself in non-philosophy as already posited-without-position, allotting thought to the objectifying transcendence / Decision determined by the Stranger-subject.

If, however, as Brassier has suggested, the extrapolation of Decision to philosophy tout court is untenable, then it seems extremely hard to see how the contingent determination of the objective by the Real can be carried outside strictly correlationist philosophical contexts. In that case, it seems 'matter' as radical hyle is ultimately only adequate as thinking unilateralizes philosophical correlation though the object’s determination-in-the-last-instance, rendering it identical to the nothingness of the Real as being-foreclosed. But then scientific discursivity and the exact theoretical status of non-correlationist thought is left entirely in the dark; for example, mathematics can no longer enjoy any putatively privileged status to be ‘ontology’ since philosophy must enter to make change in the real a subjective function, and never autonomously the form of generic forcing which it names. By the same token, for non-philosophy the relation between ‘Real change’ must remain incommensurable to any philosophical theory of discursive dynamism (as in Deleuze's machinic heterogenesis) in order to ‘avoid’ idealization. But this non-ontological Real as given-without-givenness rests, again, on an all too pious surrender to the unity of the Real as indivisible, in rendering it not only autonomous and determining in the last instance, but utterly indifferent and insensitive to relationality of any sort.

If Deleuze's machinic constructivism falls into a re-ontologising idealisation in immanence-to-itself as transcendent Repetition within the circuit of plane/fold - virtual/actual, then Laruelle's Real can be said to function as something like undeterminable determinant which, in the bare a-signifying utterance of the name, it allows itself to stand for the name of the void; one which preserves only in it the mark of its radical foreclosure and separation from all discursive objectification, its absolute difference from all positing and conditioning conceptuality or objectivating transcendence. The apparent infinite plasticity Brassier applauds in Laruelle cannot then but strike us in its glaring monotony: the operation of non-philosophical thinking on the basis of Decision as the structural filter to process the entire philosophical tradition seems 'infinately flexible' precisely because it's so radically indifferent to the peculiarities of the system upon which it operates. For now the problem is not that the empirical can never be adequate to the Real, but that it cannot help but be adequate to it in the foreclosure of a last instance brought about only through non-philosophical thought. Notably, Brassier will accept this monotony constitutive of Laruelle's 'Decisional' mould and will attempt to restrict its scope to correlationism (Nihil Unbound: Chapter 5). But as we've seen this makes the relation (or lack thereof) between the Real and scientific discursivity (as well as all non-correlational discursive spheres) utterly mysterious, and seems to rather confine realism to the vision-in-One which obtains when determination-in-the-last-instance enacts the Real's utter foreclosure as identical to the essence of the object X. This is the ultimate reach and scope of Laruelle's purported non-materialism; rather than to rehabilitate the logical space of reasons for a realist relation between scientific discourse and the Real, a purported metatheoretical enacting of a Real as foreclosed to all discursivity through the empiricity of correlational thinking/philosophy: "Materialism subjectivates matter philosophically by repressing subjectivity; non-philosophy materializes subjectivity by rendering philosophical subjectivation empirical." (AT: Pg 149)

One should be quick to point out that Laruelle enacts the non-materialist determination of 'matter itself' on the basis of phenomenological Decision by making the latter the occassion for unilateralizing their duality, through thought's determination-in-the-last-instance of radical hyle as foreclosed to the Decisional envelopment of the hyletic continuum. However, since it is ultimately thought that contingently effectuates this axiomatic ultimation, it requires of a radically subjective agency which, just like Badiou's, intervenes as radically foreclosed to Decision. So although the Stranger-subject determines Decision as already-given empirical occasion, this is an empiricity void of givenness. By enacting its own foreclosure to its Decisional occasion, the Stranger enacts the non synthetic identity-in-the-last instance between the Real and the radical hyle, and the unilateral duality separating this identity from its Decisional investment. But if this is the case, then it is thought which finally determines transcendentally the foreclosure of the Real to objectification, not the object itself. The latter remains as necessary and ultimately last-cause-in-the-last distance only against the background of the radical subjective agency of the Stranger determining the occasion's determination-in-the-last-instance as adequate to the real.

But then what guarantees that this 'transcendental effectuation' or axiomatic ultimation of the Real is actually based on the Real's foreclosure? That is to say, what can guarantee that thought's determination is adequate to the Real and not simply to non-Decisional (that is to say, non-correlational) ideality. For if radical hyle's foreclosure to Decision can only operate on the background of the determination of the Alien-subject, nothing guarantees that outside all instances of occasion the Real is actually a causality of any sort; not even that of the last-instance effectuated by non-philosophical thinking. If so, then the determination of non-synthetic identity as adequate to the Real remains undecideably split between a non-correlational idealizing instance, and a realist determination by the Real as real cause. For Laruelle cannot claim that the Real is only Real cause for thought or in thought's enacting of determination-in-the-last-instance on the basis of Decisional occasion, without vitiating the identity between this Real as nothingness and the object as foreclosed (for what would guarantee this non-synthetic foreclosure of the object?). Doing so immediatly reinscribes the reciprocal co-dependence of thought-real proper to materiology. At the same time, the Real understood as necessary but non-sufficient cause implies thought's non-philosophical determination of the object as adequate/identical to the Real must be independent of all subjectivity, even the radical agency of the Alien-subject which enacts the identity-in-the-last-instance between matter itself as the radical hyle of the Real. But if this is so then the contingent determination given through Decisional occasions is supervenient on the necessarily subjective effectuation of an identity between the Real as being-foreclosed and the object's foreclosure. Because of it, Laruelle seems caught inbetween a correlational and thus materiological reinscription of the Real into the Ideal on one end, and a non-correlationist / non-philosophical transcendental mediation of the Real through the subjective agency of the Stranger-subject enacting in every case the identity-in-the-last instance between the Real foreclosure on the basis of a contingent occasion for thought determined in turn as foreclosed. The 'first non-conceptual symbol' of matter-itself or radical hyle thus serves for non-philosophy to mediate over and above all discursive occasions, effecting the identity of the presupposed Real and the posited foreclosed essence of every object. Since this Real is only foreclosed for thought through an empirical instance, Laruelle's non-philosophical performative enacting of matter's radical autonomy comes at the price of making the nothing-ness of the Real a function for the uniform foreclosure of matter from any empirical determination, save in the-last-instance as identical to radical hyle as first name for matter or the Real:

"[T]he For in fact, rather than simply separating ‘matter itself’ from ‘matter as such’, the structure of the Alien-subject enacts the non-Decisional separation between the radical hyle as non-conceptual Identity of ‘matter itself’, and the materiological mixture or hybridisation of ‘matter itself’ and ‘matter as such’ –which is to say,the hyletic continuum... ; a hybridisation now reconfigured as a strictly unilateral Duality between the hyletic continuum asempirically determinable occasion, and the Alien-subject as transcendental determinant for that occasion." (AT: Pg 148)

Given this operation merely guarantees the monotonous repetition of determination-in-the-last-instance to render every objectivation relative to the void of the Real, the self-explaining performativity carried by that Stranger-subject required for realism ends up assuming all philosophical variants (from mysticism to Churchland) are finally adequate in the last instance to the Real insofar as they are identical to as being foreclosed enacted through non-philosophical theory. This makes the Real bereft even of the minimal transivity between the Real and Discourse found in Badiou through the generic nomination proper to a truth process ultimately dependent on the inconsistent presentation of the multiple forced into a given world. The name-of-the-void serves in Badiou's meta-ontology to support the ontological mark for the presentation of the inconsistent multiple as identified with the Real as philosophy transcendentally guarantees its pertinence for all other (non-ontological) situations, determined by the transcendental of the world. In Laruelle's case, radical hyle as first non-conceptual symbol serves for non-philosophical vision-in-One, enacting the identity-in-the-last-instance between the Real as foreclosed nothingness and that of the Alien-subject's foreclosure through the from phenomenally invested Decision. But this already given transcendental-realist determination only works through the non-philosophical positing of the a-signifying symbol of the Real as the One-of-nothingness which separates itself from Decisional (objectivating) thinking through the agency of the Stranger-subject. Just like non-chaotic presentation is guaranteed as adequate to the form of the multiple as ontologically expressed by mathematical set theory via philosophical discourse's determining transcendental objetivation / appearing of worlds, the Decisional in Laruelle's view is guaranteed as adequate to the Real in-the-last-instance, as non-philosophy mediates by determination-in-the-last-instance's enacting of unilateral duality. Just as Badiou needs of transcendental objectivation to render the ontological discourse of set-theory proper to the Real qua pure multiple, Laruelle needs Decisional correlation as the occasion for thought to enact the non-philosophical autonomy of the radical hyle as vision-in-One and of the empirical's adequation in the last instance to it:

"With the suspension of the Principle of Sufficient Determination - the belief that Decision is sufficient to determine the Real- the bi-lateral correspondence between thought and the Real is replaced by an Identity-of-the-last-instance only, and transcendental truth becomes adequation-without-correspondence." (AT: Pg. 151; Laruelle, 2000a, Pg.239-241; 2000b, Pgs. 89-92)

The radical difference is that in Laruelle's case the radical subjectivity of the Stranger-subject is located in the indifferent and monotonous enacting of empirical Decision through determination-in-the-last-instance; Badiou places subjectivity, on the other hand, on the evental subjective intervention which disrupts the ontological order and effectuates the generic through the operation of forcing. The former's non-philosophical schema determines all its empirical occasions as adequate to the Real, while latter places subjectivity in the transformative intervention in sight of singular exceptions to the empirical order of objectivity. Perhaps this is ultimately the split between nihilistic voiding and heroic subtraction.