Badiou and Deleuze- brothers in relational arms?

Though I remain admittedly rather confused on the tricky issue of relation versus being, it appears to lie at the crux of what my project is attempting to get hold of. Again this is where Badiou's usage of Category Theory in Logics of Worlds is crucial. Badiou seeks to deny relation (for him deployed to describe the logic of appearance, or, as he puts it, of being there) an ontological primacy: relation comes after its terms, and has no bearing upon them. As Hallward describes it in Subject to Truth:

"Categorial elements are nothing but relations of self-identity, expressed by a function of appearing or measure of existential intensity. If relation does not create difference, we might say, it is because it creates identity itself" (Subject to Truth pp.314-5).

In summary then, Badiou employs two different regimes: being/the ontological/set theory and appearing/logic/category theory. Within the latter domain, whilst at first it might appear as if relationality is key, in fact this is constrained to self-relationality, with relations between elements being strictly a secondary derived property of this. Perhaps I am confusing things here, but it certainly seems that in this regard Badiou comes very close to Deleuze, in that relations between elements are always secondary to the relations of those elements to themselves (cf: difference-in-itself) This comes close to Deleuze's position (as Schoolboyerrors puts it):

"... the differential relation between bodies/forces/etc, in which the two terms in the relation are brought together, their degree of power measured against one another, and given specific qualities on the basis of this. (like, in the determination of forces two forces come into contact and the one that is of a greater quantity of force is designated active, the other reactive...)."

Instead of “quantity of force” we might read “existential intensity” or in CT terms, degree of self identity. Hallward's final word on this matter however is positively intriguing, critiquing both an ontological viewpoint determined solely by elements, with no regard to relations (ie- set theory) and an onto-logy/logic of appearing determined entirely by (self) relations and ignoring all elements. vis:

"...the alternative to either of these singular positions [is] that both elements and relations can be accounted for only together, as co-implied in a single process that maintains the elementary integrity of what is related precisely insofar as it is related." (Subject to Truth p.315).

In a sense this posits a genuinely relational theory and hints in the direction of Hallward's own project on relationality. A thorough going investigation of this question is essential in order to fully grasp an intersubjective theory of groups. Further, an interesting parallel presents itself. It is almost as if Badiou, in writing Logics of Worlds, is following the path of Sartre once more. Sartre's philosphical arc between his early work such as Transcendence of the Ego and Being and Nothingness and the later Critique of Dialectical Reason is one of attempting to build into his earlier, ultimately non-relational theory some degree of relationality, in this case admitting the social into a previously highly individualistic system. This attempt was not entirely succesful, given that he denies any positive role for sociality outside of the group-in-fusion, and even within it the relation is always between individuals, who remain entirely primary. Badiou begins from a different position of course, with his daring wager that the discourse of being-qua-being is set theory. His latest work attempts to introduce relationality into the system, but does so only on the basis of a primacy being given to self-identity or existential intensity within the domain of the logic of appearances. Further the relation between his two domains, between relation and being, remains somewhat obscure. In a similar fashion to his forebare, it appears that though Badiou gestures towards the direction in which he wishes to travel, he appears unable to complete the journey.

Why groups? Why then and now...?

One question which has to be addressed is as to the relevance of group theory as such at all. Why was it that in seeking to update his basic existential-phenomenological theory of the subject did Sartre necessarily need to invoke some kind of group dynamic for what was at least initially an absolute individual freedom of consciousness? One can only presume that this was in the face of his more doctrinaire Marxist critics, who pointed to the very real exigencies which face his conception when applied to the social world. In acknowledging these criticisms, and in light of his discovery and near obsession with the dialectic, Sartre phrased his new project as a return to a pure Marxism, free from the dogmas which had befallen it by the time of the early 1960s. Whilst it is true that an overly determinist-mechanistic view of history combined with a dangerously obsequious pro-Soviet Union line were damaging the intellectual and moral credibility of continental Marxist parties, what Sartre did was quite distinct from a mere corrective. In actuality his project (in Critique of Dialectical Reason and Search for a Method) emerges as a way of integrating the Marxist dialectic with his previous work, and as such there remained an irreducible tension. This tension, between the grand sweep of the dialectic and the ultimate freedom of the individual reaches its highest point in his understanding of the group, for it is here that individual freedom, dialectical motion, and the exis of the practico-inert situation meet and are negotiated. For Sartre at least the theory of the Group evolved as the solution to the tensions of combining an individualistic existential phenomenology with a dialectical view of history. In this sense the group is the point where he cedes some ground (in terms of the originary freedom of the individual) in the face of the viscous gluey stability of the already socially formed world.

Why now? Because the problem still hangs partially unresolved. Whilst Badiou prima facie (in Being and Event) at least seems to dodge the question entirely, both he and Guattari have recourse to strikingly crypto-Sartrean accounts. In terms of empirical history, the very issue which was both the spur and ultimate limit for the CDR remains highly problematical to anyone thinking post-Marxist political theory: the collapse of the Soviet project into a tyrannical bureaucratic Stalinism. Any account of revolutionary strategy must deal with this, and it will be interesting to disentangle this historical challenge in the works of Badiou and Guattari. For Guattari the resistance to micro-fascisms is a central part of his answer. For Badiou his ethics of the truth process would seem to preclude such collapses into neo-Stalinism. But still, whilst these answers go some of the way towards satisfying the need for an answer to this question, in operational terms they remain somewhat unsatisfactory, mere moralising injunctions against such a collapse - for me at least there is a need to answer at the very level of the intersubjective structure of the revolutionary group itself.

Badiou and the mathematical group-subject.

A fascinating footnote in Hallward's Badiou: A Subject to Truth relating the advantages of category theory for his project:

Among other things, category theory allows Badiou to reformulate his theory of the subject, conceived as a group in the mathematical sense (Court traité d'ontologie transitorie, p.165-77). In categorial terms "a group is a category that has one single object, and whose arrows are all isomorphisms" (p.172). This sole object provides the name of the group, its "instantiating letter". Call it "G". Its arrows all go from G and end in G, and these provide its "operative substance." they emphasise the fact that what makes a group a group, what makes G, G, is "the set of different ways in which the object-letter G is identical to itself." Any such "group-subject is infinite" that is, the number of ways it has of being identical to itself is inexhaustible" (Court traité d'ontologie transitorie, p.176).

Badiou: A Subject to Truth (p.418, n.32)

What we can see here are definite vestigial traces, albeit in highly mathematised forms, of Badiou's Sartrean legacy at work. If, as I understand it, a subject is here defined as a group through its manner of self-identity, expressed via the "sole object", then there are parallels with Sartre's non-mathematical group's identity being forged via the relations with the third party, seen by each member as "the common individual". Obviously, I think this may well be somewhat of a simplification, but it would be an intriguing argument to trace elements of Badiou's underlying mathematical ontology back towards a CDR-era Sartrean schema. Adding to these complications however is the fact that here we are clearly dealing with topos/category theory, rather than the earlier and slightly more transparent set theory (used as the basis of Badiou's discussion of being-qua-being in Being and Event) and hence why this begins to stray into the territories explored by Badiou in Logics of Worlds. Referring again to Hallward on the distinctions between these methodologies:

Category theory and set theory offer opposing approaches to "all the decisive questions of the thought of being (acts of thought, forms of immanence, identity and difference, logical framework, admissible rationality etc...)" (Topos, ou logiques de'lonto-logique: Une Introduction pour philosophes, tome 1 p.5) They are, in short, different ways of conditioning philosophy. If the first volume of l'Etre et l'envenement was written under the sole mathematical condition of set theory, the second volume will be written under the double condition of both theories... Where set theory directly articulates being-as-being, category theory is "the science of appearing, the science of what signifies that every truth of being is irredemably a local truth" (Court traité d'ontologie transitorie, p.199)... in categorial logic "relation precedes being" (Court traité d'ontologie transitorie, p.168)... The theory offers "a highly formalized language especially suited for stating the abstract property of structures." ... the theory is designed to allow for the most general possible description of logical relations or operations between such structures and entities... Methodologically, the way these structures are represented is essentially geometric: isolated manageable parts of a category are expressed in diagrams... These diagrams are made up of objects, on the one hand, and of arrows or "morphisms" on the other. Arrows are "oriented correlations between objects; an arrow 'goes' from object a (its source) to object b (its target)." ... The single most important principle of category theory is that all individuating power or action belongs to these dynamic arrows alone...

Badiou: A Subject to Truth (pp. 303-306)

All this certainly goes someway to explaining how a category theory "group" can be constructed. The type of category known as a group is specifically designated by a structure consisting of only one object, but an infinite number of isomorphic arrows (each beginning and ending with the object). Diagrammatically perhaps (!):

What remains to be seen however is the manner in which Badiou applies this: is he getting at a kind of internal structure to the group-subject? Certainly it seems his deployment of category theory (specifically the world-building device of the sub-species of category theory known as topos) is designed to enable him to think through the local logical implications of decisions set in motion by truth process sequences. Further this brings us dangerously near towards the vexed question of relationality, (for that is what the logic of appearance in Badiou's system ultimately enables him to do, to think relations rather than merely bare being-qua-being as in the ontological discourse of set theory). This idea of relationality in many ways can be seen as operating at the core of dialectical reason and transversality also, and hence will have to be a central theme of this work.

A few brief thoughts on individuality and subjectivity.

If we are to think of the chief difference between Sartre and Guattari as being rooted in the distinction between an ultimately individualistic and group/social conceptions of subjectivity, (with Sartre essentially holding that even a group is ultimately still predicated upon the ternary relations existing between individuals, and Guattari holding that even prior to the formation of any explicit subject group subjectivity is social and pre-personal) the interesting point which is raised is where precisely that leaves Badiou. For him at least the subject does not exist prior to the group, prior indeed to the truth process. Outside of such sequences there is no subject in any meaningful sense, or at least, in any sense which Badiou himself is interested in. If we are to consider this line of thinkers as a gradual withdrawal from an existential-individual conception of the subject, we might place Badiou as lying at the furthest remove from Sartre, arguing in Being and Event that a subject is "any local configuration of a generic procedure from which a truth is supported" (BE p.391) and further "the subject is rare... the generic procedure of a situation being singular every subject is rigorously singular" (BE p.392). The latter point demonstrates how far Badiou's subject is from Guattari's also: There is no need for a process of transversalisation to restore singularity- the subject, if it is to exist at all, is radically singular, situated and effectuated only in response to a specific truth process, at a particular site. One point of investigation for this project might be on how close these notions of singularity are between Guattari and Badiou.

Another problem is clearly how Badiou structures his subject(s). We know they are finite portions of a (potentially at least) infinite truth process, but what of the relation between subjects? A number of related questions: Is there a single subject to each truth, of which individual human beings are merely (and only from the standpoint of the situation) segments of? Does Badiou have anything to tell us about the internal relations within (for example) groups of revolutionaries, or scientists, artists etc? In his transformation of subjectivity into an incredibly rare and specific thing, has he abandoned any interest in the complexities of the social, in a trade off with an elegant hyper-structuralist formalism?

Decisions, or the eternal war against the practico-inert.

Progress upon the project proper has become bogged down somewhat in the effort to change course. However it is necessary to focus on the new, as ever, and this focus now rests precisely upon the idea of the relation between political revolution, the group, and subjectivity. This is an idea which seems to be most strongly born out of my readings earlier this year of Jean Paul Sartre's Critique of Dialectical Reason and Search for a Method, and which has bled across and significantly coloured my understandings of Felix Guattari's later solo works and Alain Badiou's more recent project. The question which arises is that of how significantly the blasted defeated wreckage of the CDR hangs over its successors. What was most appealing about the earlier work, rather than its arrogantly naive teleology of dialectical progress, was Sartre's interest in the relation between the individual and group, and the extremely subtle (if perhaps not entirely convincing) manner in which he sketched the structure, necessarily contingent and fragile, which holds such groups together.

Guattari's work certainly evades many of the problems which beset Sartre: his privileging of the social over the individual, the removal of the dialectic as engine of history, and his use of transversality as conceptual stratagem to continually liquidate the sticky morass of the forces of the practico inert. However whilst his work evolves against a backdrop of French intellectual life in the early 60s dominated by Sartre, and he (and Deleuze) continue to refer broadly to a similar schema of subject group versus subjugated group (which parallels group in fusion versus inert collective gathering in Sartre's own schema) I am still not entirely clear on how he is able to think the interrelation between constituent elements within a group. Sartre's own analysis rests upon his notion of reciprocity. For him any gathering of individuals (and for Sartre the individual remains primary- which is perhaps his greatest failing) the relations between members is mediated via reciprocity, itself via "the third party". In a collective gathering structured in seriality this third party is deemed to be "other", which maintains the serial nature of the collective (1+1+1+1...etc). As structurated by alterity or otherness this collective's freedom, and the freedom of each individual within it, is severely curtailed by the forces of the practico-inert. This inertia may be broken down most effectively only through group action, such groups being formed in response to an event (usually for Sartre an external threat or crisis) which engenders a praxis, this praxis redeeming the third party from alterity, suddenly shifting to being seen by each member of the collective as "mine" or "the common individual." For any analysis of the relation between the Sartrean view of the group and Guattari's, this notion of alterity is key. Beyond merely maintaining a post-Sartrean delineation of group types, Guattari holds onto the need for alterity in relation to autopoesis, as detailed in Chaosmosis. I need to make sure here that the idea of alterity is the same as Sartre's-- certainly Gary Genosko's reading of this is that this form of alterity does not imply a dialectical openness to the genuinely "alter". A closer reading of Chaosmosis will be necessary to clarify this point I believe.
Further in Guattari's earlier work on institutional psychotherapy at La Borde clinic, in his development of the idea of transversality we find further eerie echos of Sartre's work: in positioning transversality as a device to critique the operations of the institution itself, the way the object (here the mental institution itself) comes to be known is via the group's subjectivity, itself created in the space opened up via applications of transversality. There appears here to be similarities between this idea of group activity leading to the object of the activity becoming known and Sartre's own idea of the progressive regressive method within Search for a Method (and undeniable shades of the dialectic of course). What Guattari appears to add is crucial however: that subjectivity is always already a group phenomena. One question which arises from this is of the relation between dialectical reason and transversality. And of the nature of group subjectivity implied. For Sartre there is no real group subjectivity as such, no gestalt or hyperorganism is formed in the group-in-fusion. The change occurs at the level of the commonality of the third party.