30 October 2006

Of Operations: Badiou and Structured Situations

Regardless of what one thinks about the specific claims of Badiou's ontology, his use of set theory, his account of the event and the subject, his programmatic tone, and so on, it is my view that Badiou is nonetheless of tremendous value insofar as he clearly formulates the central ontological thesis that so much thought in our age is grappling with in an unconscious or non-explicit fashion. This thesis is formulated in non-set theoretical terms in the first meditation of Being and Event. There Badiou observes that,
Since its Parmenidean organization, ontology has built the portico of its ruined temple out of the following experience: what presents itself is essentially multiple; what presents itself is essentially one. The reciprocity of the one and being is certainly the inaugural axiom of philosophy-- Leibniz's formulation is excellent; 'What is not a being is not a being'-- yet it is also its impasse; an impasse in which the revoling doors of Plato's Paremenides introduce us to the singular joy of never seeing the moment of conclusion arrive. For if being is one, then one must posit that what is not one, the multiple, is not. But this is unacceptable for thought, because what is present is multiple and one cannot see how there could be an access to being outside all presentation. If presentation is not, does it still make sense to designate what presents (itself) as being? On the other hand, if presentation is, then the multiple necessarily is. It follows that being is no longer reciprocal with the one and thus it is no longer necessary to consider as one what presents itself, inasmuch as it is. This conclusion is equally unacceptable to thought because presentation is only this multiple inasmuch as what it presents can be counted as one; and so on. (23)
This deadlock can be discerned everywhere in the history of philosophy, if only one has eyes to see it. It appears first in Parmenides, where the world of entities or beings disappears insofar as being is and non-being is not, leading necessarily to the conclusion that other beings must not be as we would then have to say what this being is not, thereby reintroducing non-being back into being. Further, it is found in every dialectic of the whole and its parts, whether we're speaking of Plotinus, Spinoza and Whitehead, or the object as a whole composed of distinct qualitative parts, as discussed by Hegel in his account of perception and understanding in The Phenomenology of Spirit, or Husserl in his phenomenological analyses of how a being can both be composed of profiles and horizons and be one.

It would thus appear that treating being and the One as reciprocal and interdependent predicates necessarily leads to irresolvable aporia. Consequently, Badiou argues that we must make a decision to de-suture being from the One, thinking it instead as multiplicity qua multiplicity:
This decision can take no other form than the following: the one is not. It is not a question, however, of abandoning the principle Lacan assigned to the symbolic; that there is Oneness. Everything turns on mastering the gap between the presupposition (that must be rejected) of a being of the one and the thesis of its 'there is'. What could there be, which is not? (23)
The consequence that follows from this is that being is to be conceived as pure multiplicity and that the one is to be seen as a result or an effect. As Badiou puts it,
What has to be declared is that the one, which is not, solely exists as operation. In other words: there is no one, only the count-as-one. The one being an operation, is never a presentation. It should be taken quite seriously that the 'one' is a number... Does this mean that being is not multiple either? Strictly speaking, yes, because being is only multiple inasmuch as it occurs in presentation.

In sum: the multiple is the regime of presentation; the one, in respect to presentation, is an operational result; being is what presents (itself). On this basis, being is neither one (because only presentation itself is pretinant to the count-as-one), nor multiple (because the multiple is solely the regime of presentation).

Let us fix the terminology: I term situation any presented multiplicity. Granted the effectiveness of the presentation, a situation is the place of taking-place, whatever the terms of the multiplicity in question. Every situation admits its own particular operator of the count-as-one. This is the most general definition of a structure; it is what prescribes, for a presented multiple, the regime of its count-as-one.

...

A structure allows number to occur within the presented multiple. Does this mean that the multiple, as a figure of presentation, is not 'yet' a number? One must not forget that every situation is structured. The multiple is retroactively legible therein as anterior to the one, insofar as the count-as-one is always a result. The fact that the one is an operation allows us to say that the domain of the operation is not one (for the one is not), and that therefore this domain is multiple; since, within presentation, what is not one is necessarily multiple. In other words, the count-as-one (the structure) installs the universal pertinence of the one/multiple couple for any situation. (24)
I quote this passage in full because it so nicely elaborates Badiou's basic argument and the basic structure of his metaphysics. When speaking of being qua being we are invited to think pure multiplicity without any other predicates. This holds regardless of whether we are speaking about objects treated as unities or ones, systems, the universe, and so on. That is, it holds for the predicates of unity, wholeness, and identity.
...[I]f an ontology is possible, that is, a presentation of presentation, then it is the situation of the pure multiple, of the multiple 'in-itself'. To be more exact; ontology can be solely the theory of inconsistent multiplicities as such. 'As such' means that what is presented in the ontological situation is the multiple without any other predicate than its multiplicity. Ontology, insofar as it exists, must necessarily be the science of the multiple qua multiple. (28)
If these multiplicities must be conceived as inconsistent multiplicities, then this is because being, prior to the operation of the count-as-one, is without structure or any ordering operations. It is only through the operations of the count-as-one that being takes on structure and comes to consist of consistent multiplicities. Yet this pure multiplicity can only be grasped retroactively, for experience presents us with nothing but structured presentations-- objects, things, happenings, persons, animals, and so on --that are "counted-as-one". That is, multiplicity is thinkable without being presentable, and inconsistent multiplicity is not a phenomenological datum or a truth of experience, but an axiom of thought from which we begin. Just as Parmenides begins from the axiom that being is one and proceeds from there (and is followed in this by much of the philosophical tradition), Badiou asks us to begin from the premise that being is inconsistent multiplicity.

I am happy to follow Badiou in this axiom as I believe it is the central axiom of that episteme characterizing contemporary thought. Whether we are speaking of Heideggerian ontological difference, Derridean differance and dissemination, Deleuzian different/ciation, dynamic systems theory, Foucaultian archaeology and genealogy, or Lyotardian discourse analysis and differends, and so on, the thought of our time begins with the premise that being is difference or multiplicity, or that the one (whether in the form of wholes, substances, or entities) is an effect or result. The advantage of Badiou's formulation is that it 1) clearly articulates the aporia that leads to this move in the most abstract and formal terms possible (we do not get caught up in the intricacies of careful deconstructive analysis of texts or in an analysis of lived experience; not that this is without merit), and 2) it indicates the problem posed to thought by this gesture: How is it possible to produce a consistent multiplicity out of inconsistent multiplicity? Or, put differently, "how does being one?"-- here "to one" must be treated as a verb; one might even speaking of "one-ing". Again, the advantage of Badiou is the sheer abstractness-- I would call it concreteness --with which he poses this question.

My aim is not to follow Badiou in answering this question. He seems to give very little in the way of a satisfactory answer to this particular question as he is more intent on showing how being can be thought as pure inconsistent multiplicity via the resources of set theory, and clearing a space where that which is not-being-qua-being, or the event, might be articulated. While it is certainly true that his most recent work, Logiques des mondes, is designed to account for being-there or appearing (the "one-ing" of being), Badiou's discussion of Dasein here strikes me as disappointing as it is primarily descriptive of consistent multiplicities, without giving us an account of how the operations that produce Dasein operate.

It is clear that the operations operating in the production of beings pertually withdraw from view, as we are always left with the result of these operations and are never before the operations themselves. It is in this sense that the world of situations presents us with a sort of transcendental illusion, in that we take the results or effects to be being itself, rather than discerning them as products of operations from pure multiplicity. As such, we continuously fall into various versions of substance metaphysics. But what are these curious operators that preside over the count-as-one? What is the operation by which one-ing takes place? Badiou appears to follow Lacan when he claims that one-ing is the work of the symbolic. This point seems confirmed in Logiques des mondes when Badiou declares that Il n'y a que des corps et des langages, there are only bodies and languages. Yet this solution strikes me as unacceptable as there are many consistent multiplicities that are not simply cultural or symbolic. Moreover, the operators of the count-as-one cannot be minds or subjects, as there are consistent multiplicities or beings that do not depend on minds. So what then are these mysterious operators? Can we conceive of operations without operators (as I think we should, lest we fall back into humanism)? And is the gulf between inconsistent multiplicity and consistent multiplicity too great to ever explain how it is possible for pure multiplicity to produce anything like an organized situation? Is it enough to restrict the predicates of being to pure multiplicity, or must we hypothesize additional predicates to account for one-ing? These are the questions I am asking. I am indebted to Badiou for having provided a clear framework for posing them. But I am not at all sure of the solutions that he proposes, which is precisely why I frolick so easily with Deleuze and others, without being very perturbed by their various disputes with Badiou.

17 Comments:

Anonymous Anonymous said...

While it is certainly true that his most recent work, Logiques des mondes, is designed to account for being-there or appearing (the "one-ing" of being), Badiou's discussion of Dasein here strikes me as disappointing as it is primarily descriptive of consistent multiplicities, without giving us an account of how the operations that produce Dasein operate.

How could you possibly have missed the point about the "unspecified operational field made up of 'objects' on which one can define operations similar to addition and multiplication" (LdM 21) -- ?? -- Unless, of course, you've neglected to read the whole of the book itself, let alone approach something resembling what Plato calls "close thinking" in relation to an object. Supposing you've read the book, does the enveloppe not appear familiar to you, or have you forgotten everything you read in this 630 page tome--giving it the old heave ho--in favour of merely repeating this vain art of yours whereby, time and again, you recapitulate the silliest of the most widely recognizable readings of Lacan, Deleuze, Zizek, etc.; doing so whenever it seems you have gathered something to rekindle this bemusing attempt at closing the book on the only one who earnestly calls Lacan "his master."

You've also committed a foul by mingling together l'etre-la with Dasein. Sure, both translate as being-there, but that's completely arbitrary (thanks Saussure or Freud): not to rigourously distinguish between them not only forgets something every sociologist knows, but it makes you into a conceptual idealist.

November 15, 2006 4:49 AM  
Blogger Sinthome said...

Sorry to disappoint!

November 15, 2006 6:14 AM  
Anonymous Anonymous said...

It's not a disappointment, to be sure.

Perhaps you're taking on too much at once. You seem to be spreading yourself pretty thin, which appears to be standard fare for bloggists.

In any case, as Emmy Noether said of Richard Dedekind--"it's all already there in [R.D.]"--so do I find myself often wanting to affirm the same regarding Lacan. For instance, to chose an example especially relevent to the first half of your post (on Being and Event [tome 1]):

"Set theory bursts onto the scene by positing the following: let us speak of things as One that are strictly unrelated to each other. Let us put together objects of thought, as they are called, objects of the world, each of which counts as one" (Lacan SXX, p.47 [Norton 1998]).

November 15, 2006 6:50 AM  
Blogger Sinthome said...

Well perhaps it's worthwhile to reflect a bit on what the title of the blog "Larval Subjects" suggests. The blog is a site for working through ideas, concepts and themes that aren't yet fully developed. I develop an understanding of material by working through material in writing and speech, which is exactly what I'm doing here. I'm more than happy to admit that I don't have a thorough understanding of Badiou's latest work, and that I might be getting him wrong on a number of points. Logiques des mondes was just released in 2006. It's difficult enough getting down the set theory, much less the category theory. I find myself both thrilled by certain aspects of Badiou and discontent with other aspects. If I'm getting certain things wrong with his claims I'm grateful to have those pointed out and explained. Pointing out that my analyses are pedestrian or commonplaces doesn't strike me as a very productive rhetorical strategy, but to each their own. I can't say that I've come across much on Deleuze that's like anything I'm doing, and confess that my reading of Lacan is deeply indebted to the Millerian school, which characterizes my experience of Lacanian analysis in my own analysis and practice. I don't see this as a bad thing as I don't feel the goal of engagement with Lacan should be to give a unique reading. Your aim seems to be that of saying "shut up!"

November 15, 2006 7:02 AM  
Blogger Sinthome said...

I also notice that you have nothing to say with regard to the basic question of the post: what is doing the operating? Badiou seems to be in a deadlock as he wants to treat being as the domain of pure inconsistent multiplicities, but now finds that he must make reference to a domain of objects upon which operations are defined. It's precisely such a domain that Deleuze's account of individuation is designed to respond to. It was this that led me to suggest that Badiou is merely descriptivie.

November 15, 2006 7:14 AM  
Anonymous Anonymous said...

The idea of functions acting on a specified group of objects marks the limit of set-theoretical thinking on the subject of operations; in other words, so long as we remain within the realm of axiomatic set theory, operations make sense only inasmuch as they represent an operation on things. This limitation precisely where there should be none is more than enough impetus for looking outside of the set theoretical framework for a foundation even more general than set theory but one that will allow a kind of freedom in dialectical thinking one cannot get from the purely internal logic of set theory's axiomatic structure.

The turning point within set theory is precisely the category theoretic revolution of the former's way of approaching the concept of operations (in mathematics).

With category theory, the focus shifts from operations on indeterminate objects to one that takes as primary the relations between whole mathematical structures, and thus everything rests not on the objects themselves but on the particular "operatory dispositions" by which these objects are defined according to a logical network of relatons that describe possible outcomes according to the world in which they appear.

November 15, 2006 9:56 AM  
Anonymous Sinthome said...

Yes, yes, yes... You don't see how this is merely descriptive? One of the irritating things about continentalists is that they often respond to criticisms of their pet philosopher or master by resorting to hermeneutics: "you've misinterpreted, you've misunderstood, etc." The idea seems to be that if you truly understood then you would agree and see no further questions to ask. I'd ask you "what's doing the operating" which is a question that might lead one to see how Deleuze was, in certain sense, working out an onto-logy of "operatory dispisitions" despite Badiou's underhanded criticism of his work as being that of a "physicist" in The Clamor of Being, but I fear we wouldn't have a very interesting discussion on the matter and I'd get a lot of handwaving about how the text says this or that repeating the mantra that "if I just understood..."

November 15, 2006 10:12 AM  
Anonymous Anonymous said...

Thus, to answer your question: there is no "what" doing the operating. Following Badiou, our goal is not finding a "doer" or an actor that is the agent of an action both immediate and direct with respect to an object. Rather, we must instead ask ourselves what kind of subject, which of the "dispositions" works best relative to this or that world.

November 15, 2006 10:16 AM  
Anonymous Anonymous said...

reactive subject, faithful subject, etc. ...

November 15, 2006 10:17 AM  
Anonymous Anonymous said...

It wants to be descriptive, that's Badiou's point.

November 15, 2006 10:22 AM  
Anonymous Sinthome said...

That's fine, but a) presumably there are broader onto-logical issues pertaining to appearing than those of Badiou's concept of the subject, and b) appearing takes place regardless of whether there's a subject. As Badiou quite clearly points out, appearing is not appearing to a subject, but appearing to a situation, being-in-relation. Finally, Sinthome doesn't want to be descriptive, that's Sinthome's point. You're conflating issues of interpretation with issues of legitimate philosophical dispute.

You should be careful with your use of "our" plural. That's Badiou's goal, not necessarily "our" goal. Now I'm Nietzschean enough to accept the idea of "no doer behind the deed", but there are still all sorts of interesting questions to ask about operations that aren't strictly of a descriptive nature. In posing those questions I might discover that ultimately Badiou is right and that I share his point of view, but there's no a priori reason that the questions shouldn't be posed at all. In Being and Event we're told that "one-ing" is an effect of operations of the count-as-one while being told little or nothing about these operations. In Logiques des mondes these operations are described without really being accounted for or explained in a way that almost looks like Husserlian phenomenology without a transcendental subject. Now it could be that these operations are ontologically irreducible such that we need some new sort of category to talk about them and such that it makes no sense to ask what they're grounded in. Fine, but they strike me as deeply mysterious. It's of no help to behave like a graduate student citing text, and certainly isn't very philosophical.

November 15, 2006 10:38 AM  
Anonymous Sinthome said...

Or suppose we take a parallel. In meditation two Descartes argues that we are capable of recognizing the identity of substances undergoing change through an "act of understanding". Descartes has, perhaps, accounted for *what* allows us to recognize persistence through change, but he says very little in the way of *how* understanding does this. Similarly, Badiou says *that* operations one, but he says very little in the way of how these operations one. The questions I'm asking may be based on ignorance of Badiou or a failure to properly comprehend Badiou, or they may be based on something deeper. They might even be nonsensical questions. However, they aren't necessarily fatal to his project or rejections of his thought. I tend to think that Badiou, in his focus on subjects and truths, tends to ignore working out the nuts and bolts of the far more mundane dimension of situations and the encyclopedia, though he's made progress in that regard in LM. While fascinated by Badiou's truths, I'm even more fascinated by situations, encyclopedias, and their dynamics.

November 15, 2006 10:46 AM  
Anonymous Austin said...

But Sinthome, Descartes is describing change through mediation, pure and simple. That's about as basic as they come, even supposing this were--as you would have it, though understandably so--a matter of philosophy alone. But I think I've made it clear that it's not.

I wish I could have you read the thousands of pages on topos, category, and categorical logic that I've struggled through for the past six months. I know that to say such a thing is tantamount to the mantra you've mentiond above. But I would ask why you're even interested in Badiou if there is no thrill, no sense of subjective revolt, in his masterful reading (or torsion) of mathematics that makes of it the guardian of eternal truths it (by itself) cannot speak. If you got any thrill at all from BE, you must have, to a degree, allowed yourself to accept this weird knot between the two practices as your first axiom b/c it is what is meant by the initially shocking declaration that mathematics is ontology.

November 15, 2006 11:17 AM  
Anonymous Sinthome said...

Where I have anywhere suggested that there's no thrill in Badiou for me. Go through the archives, you'll find numerous diaries working to understand him, deeply indebted to him, and constantly struggling with his thought. If anything I've been a staunch defender of Badiou and an enthusiastic apostle trying to spread word of his basic concepts in accessible form. I'm the moderator of the Badiou list (where, I believe, you participate), and have presented papers on Badiou. As I recall, if you're the person I'm thinking of, you also seemed to dismiss Adrian Johnston there because he used different terminology than Badiou to explain Badiouian concepts. You seem to conflate a question about Badiou's work with a dismissal of his thought, reflecting the mind of a rigid dogmatist.

You write:

"But Sinthome, Descartes is describing change through mediation, pure and simple. That's about as basic as they come, even supposing this were--as you would have it, though understandably so--a matter of philosophy alone. But I think I've made it clear that it's not."

I have no clue as to what you're saying here about Descartes. My analogy simply pointed out that he doesn't explain how understanding comes to do this work, he merely asserts that it does. Consequently, you get thinkers later on such as Hume and Kant giving alternative explanations. For instance, Kant, in his first analogy, shows how the manifold of changing impressions are synthesized by the category of substance belonging to the understanding. Hume draws on memory and association to explain how the fiction of substance is produced. The point is thus that other philosophers subsequent to Descartes saw questions where he saw none and responded accordingly.

Anyway, echoing your sentiments that "I would ask why you're even interested in Badiou if there is no thrill, no sense of subjective revolt, in his masterful reading (or torsion) of mathematics that makes of it the guardian of eternal truths it (by itself) cannot speak", I would ask why you're interested in reading my blog if it is merely repeating "this vain art of yours whereby, time and again, you recapitulate the silliest of the most widely recognizable readings of Lacan, Deleuze, Zizek, etc.; doing so whenever it seems you have gathered something to rekindle this bemusing attempt at closing the book on the only one who earnestly calls Lacan 'his master.'"? What's your motive here? Are you trying to convince me of something? What? Are you trying to correct me on some misinterpretation? For what end? Are you offended that my desire is different than yours? That the way I relate to my "thrill" isn't through fawning dedication and unquestioning acceptance? What are your stakes in arguing with someone who's interested in Badiou and sometimes quibbles with him on this or that issue on an out of the way blog? The more this discussion proceeds, the more bizarre it gets, as you don't seem to be making any substantial claims but seem intent merely on defending Badiou against some perceived dismissal of his thought. Go publish a paper or write a dissertation or book. There's no need to swat at me without even understanding the question I'm getting at or without finding that question interesting or productive. I never asked anyone to find my questions useful or productive, though I do enjoy it when they entertain them with me and see where they might lead.

November 15, 2006 12:39 PM  
Anonymous Austin said...

My apologies for the tone of the initial post. My sole motivation was to get your attention quickly and to keep it for a while. I have no one locally with whom to discuss my work. If there's anything I would hope to convince you of, it is to commit to a study of real mathematics. I think you lost me with your comment on Descartes, or I misread what you were trying to say. Either way, sorry to have offended. I'm a lowly graduate student, not an accomplished writer and professor such as yourself.

November 15, 2006 1:20 PM  
Blogger Sinthome said...

Devlin's Joy of Sets and Goldblatt's Topoi: The Categorical Analysis of Logic are right here on my desk, along with numerous other mathematical texts scattered throughout my study. The audience of this blog is very broad and it's necessary to be capable of communiting outside of formal mathematics. This is true of continental philosophy in general. I suspect that Badiou will be dead on arrival if mastery of mathematics is insisted on.

November 15, 2006 1:30 PM  
Anonymous austin said...

The following offer tremendous insight into LdM's maths. I list them for you as a peace offering of sorts.


McLarty, Colin. "The Rising Sea: Grothendieck on simplicity and generality I." Lecture. http://www.math.jussieu.fr/
~leila/grothendieckcircle/mclarty1.pdf.

Lautman, Albert. "Symmetry and Dissymmetry in mathematics and physics." _Great currents in mathematical thought_. Ed. F. L. Lionnais. Dover, 2004. [This collection represents a translation of the complete French ed.]

Eilenberg, Samuel and Saunders MacLane. "Natural Isomorphisms in Group Theory." Proceedings of the National academy of arts and sciences 28 (1942): 537-43.

Mazur, Barry. "When is one thing equal to some other thing?" http://www.math.harvard.edu/~mazur/preprints/when_is_one.pdf

Bell, J. L. "From Absolute to Local Mathematics." Synthese 69 (1986): 409-426.

Grothendieck, Alexander. R├ęcoltes et Semailles.

Fourmann, Michael P. "The Logic of Topoi." Handbook of Mathematical Logic. Ed. J. Barwise. North-Holland, 1977.

Galois, E. "FRAGMENTS [1831]."

November 15, 2006 2:54 PM  

Post a Comment

<< Home