Abstraction


fn3ontoOne of the most attractive, problematic, and astonishing features of Badiou’s ontology is his strictly extensional understanding of sets or multiplicities. A set is not defined by its members sharing a common predicate or quality, nor by the relations among members of the set. Rather, a set is defined strictly by its extension or the members that belong to that set. From the standpoint of 20th Century French and German Continental philosophy, this thesis cannot but be a heresy, for the predominant trend in Continental thought has been a relational conception of entities. Whether we are speaking of language as a diacritical set of negative oppositions as defended by the structuralists and the post-structuralists, or Heidegger’s being-in-the-world where entities, the ready-to-hand, are defined by the relational networks to which they belong, the predominant trend has been to treat beings as bundles of relations such that the entity is nothing apart from its relations. In a spirit similar to Deleuze’s declaration that relations are always external to their terms, Badiou will have none of this. For Badiou entities are not defined by their relations and there are no intrinsic or internal relations that define the being of the entity. Rather, they are simply defined by their relations.

From the standpoint of both Heidegger’s being-in-the-world where each entity is thought as a “being-in” belonging to the worldhood of the world defined by an ensemble of relations defining meaning, or from the standpoint of structuralist and post-structuralist thought where the entity is an ensemble of internal relations from which it cannot be detached, or from the standpoint of Hegelianism where, as Hegel painstakingly shows in the Doctrine of Essence in the Science of Logic, where the entity simply is its relations or mediations, this move cannot but appear stunning. For what this extensionalist conception of sets authorizes is combinations of subsets in whatever order we might like. This, in short, is what the axiom of union tells us. What the axiom of union allows– if I understand it correctly (I’m sure Dominic will educate me if I don’t, thankfully) –is the construction of whatever sets we might like based on those elements belonging to our initial set. Thus, if I have a set composed of an umbrella, an apple, and the moon ({umbrella, apple, moon}), I certainly have a set composed of the apple and the moon ({apple, moon}), or a set composed simply of the apple ({apple}).

equalizer_category_theoryNow all of this sounds silly and unremarkable so long as we don’t contrast Badiou’s extensional notion of sets with the relational ontologies that have predominated during the 19th and the 20th century. If to be an entity is to be a bundle of internal relations, it follows that entities cannot be grouped in any way we might like. Rather, a model of the world based on internal relations dictates that each entity necessarily has a place within an Order and that the entity is nothing apart from this order. Thus the phoneme {c} is nothing apart from other phonemes such as {p}, {b}, {f}, etc., by virtue of the differentiality that allows it produce different senses at the level of the signifier: cat, pat, bat, fat. Insofar as these phonemes take on their value (in the linguistic sense of “value”) differentially in relation to one another, they are nothing independent of their relations to one another. This is what it means to say that each entity takes on a place within an Order. The Order is the totality of internal relations defining a system or structure, whereas the places are locations within that Order relative to the other terms. Because the relations are internal to the various beings in the Order, there is thus a Law that governs these beings and exhausts their being, legislating how they can and cannot act.

In proposing that sets are defined purely by their extension or their membership, Badiou undermines the thesis that to be is to be a bundle of internal relations. At the level of ontology, there is thus no intrinsic Order that defines entities. Rather, in their stark independence, the elements that make up a set not only can be decomposed into infinite subsets (through a recursive process of taking the power set of each power set), but the elements of each set can be related in a variety of different was or simply taken as singletons, thereby abolishing the notion of intrinsic or internal relations as in the case of Hegel’s logic of essence.

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fractalDominic has written a very nice post entitled “Who’s Counting?”, on how, precisely, Badiou’s operation of the count-as-one in the formation of consistent multiplicities is to be understood. I confess that for me this is a central question with respect to Badiou’s ontology that I feel has received scant treatment. I’m fine with the notion that it isn’t a mathematician that is performing this operation, I just wish to have a more robust account of just what these operations are and how they’re performed. While Badiou has certainly gone further in this direction in Logiques des mondes with his account of “the transcendental”, the whole thing still remains deeply mysterious to me. My worry is that Badiou still remains tied to a sort of human-centered idealism. While Badiou proclaims that he’s a materialist, whenever he begins to discuss structure, the transcendental, etc., it seems as if he’s only talking about social structures. Indeed, in one of his interviews (I’ll have to dig up the link), Badiou actually credits Foucault with being the thinker of the encyclopedia, which he equates with structure. There seems to be little room here for an object-oriented ontology that declares the reality of objects regardless of whether or not humans exist. Moreover, similar problems emerge with respect to his repeated insistence that being and thought are identical. I simply don’t see how one can call their thought realist or materialist if they also claim the identity of being and thinking.

Towards the end of his stellar post, Dominic references me (alongside Peter Hallward! I’m flattered, though I’m sure he’s only making a blogosphere reference in my case!),

Various people, notably Peter Hallward and Levi Bryant, have complained that Badiou’s set-theoretic ontology doesn’t do justice to the relationality of the world, a complaint that slightly baffles me as it certainly does accommodate such beings as pre-orders, equivalence relations, topological spaces, groups, lattices, sheaves…but it’s true that they are all given as second-order effects of presentation, particular kinds of unitary structure that the operation of the count can unfold. If the primacy of relationality is your thing, then this subordination of relation to composition will presumably not please you; but I’m not sure that I understand the wider stakes of the argument, which seems to lie at the heart of the differend between Badiou and Deleuze.

First, let me emphasize just how much I love Badiou. Part of my militance against Badiou in certain posts arises from the anxiety of influence. I read Badiou for the first time towards the end of my dissertation work. I had read his Manifesto for Philosophy a year or so earlier, but it hadn’t left much of an impression of me because I simply wasn’t able to hear or understand what he was claiming. However, when I came across The Clamor of Being, all of this changed. Here was a work that was engaging Deleuze as a philosopher, brilliantly and carefully. This led me to the Ethics, which in turn led me to hone my French skills enough so I could read Being and Event prior to its translation. This was a period of great excitement for me. Badiou dared to say “truth”. He dared to give arguments. Just like the title of Hallward’s famous edited collection, it felt as if it was possible, after Badiou, to think again. Indeed, this feeling was only confirmed by Hallward’s own study of Badiou along with his many articles. Where prior to Badiou we had a series of philosophical tribes, each engaged in their own dusty commentaries of master figures, Badiou’s ontology demanded argument. He was making substantial claims and suddenly, like the lifting of a cloud, it was possible once again to engage in something other than commentary, something other than “buggering philosophers to create a monstrous offspring”. Once again it had become possible to engage positions and worry over their claims. Hallward’s study of Badiou did precisely this wonderfully. I feel in certain ways as if Badiou cured me of a particular institutional form through which philosophy was being done. Those were happy days. Each page was filled with a sort of excitement that provoked you to learn entirely new things like set theory and where you didn’t feel as if the aim of philosophy was simply to comment on the texts of the tradition. Suddenly an entire way of doing philosophy seemed as if it had passed and was but a bad dream.

I think Dominic is right in what he says about Badiou and relation, however, perhaps an absence of relation isn’t the most precise way of describing the problem. I can’t speak for Peter, but for me the problem with Badiou’s ontology lies in its abstraction. It is not so much his position on relation that is at issue, but rather the manner in which the domain of the ontic seems to be diminished or to disappear in Badiou’s thought. Now to be clear, the issue here isn’t one of mathematics being “abstract”. That’s not the problem. I had already approached Deleuze via his engagement with differential calculus and found Badiou’s celebration of mathematics a welcome move in a world of Continental philosophy dominated by mathophobia and German romanticism. For me, rather, the issue is the manner in which the world of entities seems to disappear in Badiou’s ontologies, relegated to a place of unimportance. In my view, unless we roll up our sleeves and get down in the world of beings, of the ontic, and how they’re put together, how they’re assembled, there’s little hope for any sort of change. What interested me most in Badiou’s ontology, paradoxically, is what seems to interest people least in his philosophy: his discussions of situations as harboring infinite multiplicities and his discussions of how these situations are structured. I can’t help but feel that his account of the event is based on a false problem that arises from structuralist residues within his thought that lead to the question of how it is possible to escape overdetermination through structure. For me the theory of the event and the subject is the least interesting aspect of his thought, though I do find his notion of truth-procedures interesting because here, at least, we seem to have a very rudimentary engagement with the ontic. Badiou is improving with Logiques des mondes. Here, at least, we get some engagement with the ontic in his account of intensities. But still it strikes me as vastly underdetermined.

nietzscheIn Beyond Good and Evil Nietzsche famously argued that metaphysics is a product of grammar.

With regard to the superstitions of logicians, I shall never tire of emphasizing a small terse fact, which these superstitious minds hate to concede—namely, that a thought comes when “it” wishes, and not when “I” wish, so that it is a falsification of the facts of the case to say that the subject “I” is the condition of the predicate “think.” It thinks: but that this “it” is precisely the famous old “ego” is, to put it mildly, only a supposition, an assertion, and assuredly not an “immediate certainty.” After all, one has even gone too far with this “it thinks”—even the “it” contains an interpretation of the process, and does not belong to the process itself. One infers here according to the grammatical habit “thinking is an activity; every activity requires an agent; consequently—.” It was pretty much according to the same schema that the older atomism sought, besides the operating “power,” that lump of matter in which it resides and out of which it operates, the atom; more rigorous minds, however, learned at last to get along without this “earth-residuum,” and perhaps some day we shall accustom ourselves, including the logicians, to get along without the little “it” (which is all that is left of the honest little old ego). (Part 1, §17)

graph13jThe world is parsed into nouns in the form of subjects and objects, adjectives or predicates, and verbs. Subjects and objects are then treated as substances or that which endures in times and lies beneath. Verbs or events are treated as that which happens to objects and subjects, such as the movement from one position to another in space as if on a sheet of graph paper. And finally predicates are what are said of substances. The ball, a substance, is red and spherical (predicates). The ball moves this side of the table to that side of the table.

As a consequence of this parsing of the world, all sorts of metaphysical and epistemological problems emerge. Insofar as subjects and objects are conceived as substances, the epistemological question arises of how it is possible for a subject to relate to an object. The object, as a substance, forever transcends the subject, necessarily being beyond the subject in all ways. We know the object through its predicates or properties, yet we encounter the entire problem of primary and secondary qualities or the indiscernibility of properties. That is, how do we determine whether the predicates we find in the object are a product of us or whether they belong to the object itself? Is color, for example, in the object or is it in me? On the metaphysical level, is the object simply a bundle of properties or is the substance something more, in addition to its properties, beyond these predicates? If the object is nothing but a bundle of properties, doesn’t it cease to be that objects when it gains or loses properties? If the object is a substance beyond its properties, what does it mean to speak of it as this object at all insofar as the substance which the object is is always in excess of any properties that it might have (the bare substratum problem).

Yet certainly “to be”, to exist, is something more than simply being a substance characterized by identity? Generally we restrict the verb “to act” to living beings. Animals act in bringing themselves to motion. Some claim that only humans are capable of acts. Action here is conceived as necessarily containing a component of will or self-willing. A rock, it is said, does not act insofar as it cannot will itself to act but can only be made to move through external forces. Etymologically the term act comes from the Latin actus, “a doing”, and actum, “a thing done”. These are derivatives of agere, “to do, set in motion, drive, urge, chase, stir up”. These Latin terms, in turn, derive from the Greek agein, “to lead, guide, drive, carry off,” and, interestingly, agon, referring to “assembly, contest in games,” as well as agogos or “leader”.

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Take the example of Deleuze and Guattari. Anti-Oedipus is not so much a critique of psychoanalysis– though it is that as well –as it is a critique of a particular social structure and the metaphysics that accompanies it. If an engagement with psychoanalysis proves to be the privileged site for an engagement with this structure, then this is not with the aim of reforming psychoanalysis– though that as well –but because psychoanalysis provides those weapons necessary for engaging this structure and developing a praxis that would allow for an escape from this structure. Politics, we might say, was at an impasse. The Russian Revolution was a failure. It had overturned those that controlled the means of production, yet the form of social organization remained the same. The content had changed, while the form remained in place. Just as I might replace a missing piece on a chess board with quarter, the material content had changed while essentially the same function or structure was in place. “Meet your new boss, same as the old boss.” The party elite now occupied the place of exploiter, producing a machine more harrowing than the factories in its capacity and reality of alienation, and while the owners of the means of production had changed, having been socialized or democratized, the form of production– Taylorism –remained the same. The French Communist Party was not much better. Here, once again, we had the same hierarchical structure, with a party elite calling the shots, making the decisions, organized around a centralized apparatus that radiated outwards, rather than the socialization or democratization that Marx had called for.

But this, in and of itself, was not the problem. Or rather, it was a problem, but the problem also lay elsewhere. All over the place economic changes were taking place. Conditions were changing. Yet revolution did not come. Why? The vulgar and simplistic model of Marxist thought, that superstructure is a function and distorted reflection of the base, had to be mistaken. At some level, as Deleuze and Guattari, following Reich, put it, people must desire their own oppression. It is not enough to say that these structures were simply imposed on agents from without. Rather, at some level agents must desire these formations… These formations which Deleuze and Guattari refer to as “fascist”. Consequently, a critique of political economy is not enough. In addition to a critique of political economy, a critique of desire, a Critique of Pure Desire, must be written. Psychoanalysis provided these tools. Just as Marx carried out a critique of Ricardo, among others, by showing how value was not an intrinsic feature of things in themselves, but produced through labor. Freud and Lacan carried out a critique of prior psychology by formulating a desire divested of objects, a desire as such, a desire that wasn’t a function of need and instinct… A desire without an object, but as a process. Marx produced a non-representational theory of value. Freud and Lacan produced a non-representational theory of desire. Yet this critique had not gone far enough. It was still tainted by the empirical.

This desire was still tainted by certain privileged objects. Just as Kant had carried out a critique of the so-called proofs for the existence of God in the second half of the Critique of Pure Reason, it was thus necessary to carry out a Critique of Oedipal Reason. The Oedipus had been subtracted from the social sphere, treated as a private affair of the family, dehistoricized, de-sociologized, de-culturalized. But rather, the Oedipus reflected an entire metaphysics, a metaphysics extending far beyond the private. Far from being a natural and essential state-of-affairs, it already was the expression of a political metaphysics. This can be thought in fractal terms. A fractal is a pattern that iterates or repeats itself at all levels of scale.

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Far from the family being the ground upon which all other social relations are based, what we have here is a fractal structure iterating itself at the level of the family, the level of social organizations (king or leader to subjects), and at the level of God in relation to his creature. If the death of God means anything, it means the destruction of this structure… Not simply at the level of content, but at the level of form as well. Freud, as Marx to Ricardo, had glimpsed this in his earlier work where libido no longer has an object. Lacan had explicitly formulated this in his claim that “the Oedipus is Freud’s myth“, and his attempt to think beyond the name-of-the-father as a central organizing principle in his later work. The problem arises as to how a politics might be possible in a post-Oedipal or post-onto-theological world.

More to come.

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N.Pepperell of Rough Theory has been kind enough to plug my recent post “Social Assemblages and Agency“. A while back I wrote a rather whimsical post entitled “Of Cooking, Mixtures, and Milieus“. While the post might have been whimsical in tone– drawing on anecdotes from cooking and examples from Seinfeld –the point I was trying to make was a serious one about the nature of causality in relation to social formation. That is, there seems to be a tendency to adopt top-down models of causality when thinking about social phenomena, such that we are led to think one cause hegemonically dominating the social space. Whether we posit signifiers as determining social relations, the sovereign as determining social relations (a recent turn I find particularly irritating as, following Spinoza and Hegel, there is no such thing as a sovereign that doesn’t draw his power from the consent of the multitudes), language, structure, or more recently the biological, we posit a unilateral causality where one term serves as the explanation for the rest. This, of course, is the essence of metaphysics: to treat a part of the whole as explaining the whole.

Casting about for metaphors to interrupt this pattern of thought, I seized on cooking and chemistry:

If cooking is instructive for the social theorist, then this is because cooking teaches us to think in terms of mixtures, processes, intensive transformations, intensities, and irreversible processes. Tomato, garlic, cumin, and olive oil are not the same after they are mixed and heated. Rather, a qualitative transformation takes place… A transformation that is irreversible. Cooking is chemistry, rather than physics. Where, in classical physics we are enjoined to think atoms impacting one another in relations of force such that the atoms nonetheless retains its identity, changing only in velocity, chemistry leads us to think mixtures, temperatures, pressures, etc., that lead to qualitative transformations of the elements involved. The garlic is not the same after it is cooked and mixed. Nor can I return the garlic to its previous uncooked state. Rather, it has undergoing a qualitative transformation that now has different potentialities. For instance, if I roast garlic in tinfoil and olive oil in the oven, I can now spread it on a nice loaf of sour dough bread like butter, whereas before this would not have been possible. Under these conditions, the flavor becomes sweet, where before it was pungent.

Cooking, chemistry, requires us to think a milieu of individuation where a milieu of individuation is to be understood as the relation something entertains to other things in the world such that it would not be that thing without these other things. If you enjoy wine then you know that where the wine comes from and the year the wine was made make a tremendous difference as to what the wine is. Wine, wine grapes, always emerge in a milieu of individuation defined by the weather, the soil conditions, other plants, animals, and insects in the region and so on. Wine from one and the same vinyard can be radically different from one year to the next. The same is the case with cheese. Each individual entity is itself attached to a world, a local morphogenetic field, through which it produces itself as an ongoing process by interacting with that world.

In cooking or chemistry there is no one thing that causes the rest. Rather, we instead have to think relations of feedback and interaction where all the elements or ingredients interact. This entails that there will not be a “one size fits all” sort of explanation for social phenomena. Rather, following Freud, we might instead talk of “overdetermination”. Of course, this approach to thinking the social and political will cause some to recoil as the complexity of our object is vastly complicated. Social and political philosophers strike me as liking simple answers and schematizations of their objects (I think actual social scientists often fare much better and are much less reductive). On the other hand, an approach that emphasizes interaction at multiple levels, multiple levels of non-linear causation, and complexity might also undermine some of the pessimism (that sometimes seems almost celebratory in tone) that sometimes seems to haunt social and political philosophy (the all or nothing attitude that asks empty questions like “how do we overcome capitalism” and then finds itself impotent when it comes to doing anything at all). That is, such a view might allow us to diagnose false problems that result from overly schematic and simplified conceptions of the social. At any rate, N.Pepperell has recently written a couple of very nice posts on Diane Elson’s work, who appears to be thinking in a similar groove (here and here). Well worth the read!

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Even in its best moments, philosophy perpetually abstracts the philosopher from the world the philosopher describes. The philosopher surveys the whole as a view from nowhere, as an impassive and independent look, without itself being implicated in that upon which it gazes. When discussing contradiction or antagonisms, for instance, these antagonisms are set side by side and investigated by the philosophical subject, as if the philosophical subject were a neutral onlooker that is itself outside or independent of these antagonisms. Yet if, as Deleuze argues in the 16th chapter of The Logic of Sense, “…the individual is inseparable from a world” (109), determined by a distribution of pre-individual singularities, how could such a gaze fail to be a point of view. However, here I must take care in how I express myself, for as Deleuze remarks in The Fold, “To the degree that it [a site or point of inflection] represents variation or inflection, it can be called point of view. Such is the basis of perspectivism, which does not mean a dependence in respect to a pregiven or defined subject; to the contrary, a subject will be what comes to the point of view or rather what remains in the point of view” (19). Just as Einstein observed with the constancy of light, it is not subjects that individuate points of view, but rather points of view that individuate subjects.

There are brief moments where philosophy approaches a form, a writing, that would be equal to this content. Perhaps Nietzsche’s use of the aphorism as a method expresses such a form. As Deleuze argues in Nietzsche & Philosophy,

Understood formally, an aphorism is present as a fragment; it is the form of a pluralist thought; in its content it claims to articulate and formulate a sense. The sense of a being, an action, a thing– these are the objects of the aphorism… Only the aphorism is capable of articulating sense, the aphorism is interpretation and the art of interpreting. In the way the poem is evaluation and the art of evaluating, it articulates values. But because values and sense are such complex notions, the poem itself must be evaluated, and the aphorism interpreted. (31)

We look in vain for a unifying philosophy behind the aphorisms; but if this is the case then it is because the aphorisms are mandibles that grasp, articulate, or render a fragment of a world. The aphorisms are heterogeneous universes of value or interpretations. Or better yet, they are ways of being in a world that no longer exists as an irreducible unity within which a plurality of agents exist. It is in this sense that the aphorisms form a properly pluralistic thought, where we no longer have a world as such, but rather fragments or competing points of view in which agents are individuated and where a clamor of voices, filled with antagonisms, fill our ears… Our ears which are also among and within these fragments. Perhaps we also find a similar writing in Blanchot’s Writing of Disaster, or Adorno’s Minima Moralia and Prisms. These are moments in the history of philosophy where form strives to be adequate to the content, and the form of the sovereign subject is itself shattered, such that it can only enter into the work as one voice among others.

Describing the literature of Roger Vailland, Lefebvre writes,

In this book [325,000 francs], as in Vailland’s earlier novels, the author appears as such. He says: “I”. He intervenes as a witness, designating the characters and situating them, entering into dialogue with them, inviting the reader to decide what attitude to adopt towards them: what judgment to make. Here judgment is inseparable from event; it is rigorously included in the story. This authorial presence has various meanings, and not simply on the level of technique. It is Roger Vailland’s way– and a very simple way it is –of resolving a difficult literary problem, that of novelistic consciousness or of consciousness in the novel. Who is speaking? Who is seeing, who saw the actions in the story? Who bridges the gap between the lived in the true. How has the speaker seen or heard about the things he narrates? How has he been able to foretell or sense what will happen next? Who has detected the character’ motives (hidden even to themselves)? And as he is drawn on by the great movement called ‘reading’, with whom does the reader identify, in whose consciousness does he participate? (Critique of Everyday Life, Volume I, 26)

In Vailland’s literature the author is no longer a sovereign onlooker outside the events narrated, but is there amongst the events as a point of view. Nor are we confronted simply with a first person point of view or a stream of consciousness, but rather a heterogeneity of points of view. In this way, the reader is implicated or participates in the novel as yet another point of view in a manner similar to how Brecht strives to implicate the audience in the spectacle. Antagonisms are thereby able to reveal themselves as antagonisms, blind spots as blind spots as blind spots, points of hesitation and indecision as points of indecision. The author is no longer transcendent to the novel, but immanent to the novel, and the reader is no longer a voyeur… Or rather, perhaps the reader becomes aware precisely of his voyeurism by being implicated in the events.

Would it be possible to write philosophically in a way adequate to this form? Would it be possible to write philosophically in a way that no longer posits a meta-theory in this way? Plato sometimes seems to be a joker of this sort.

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Throughout its history, philosophy seems particularly prone to three interrelated errors– or perhaps they would be better referred to as “transcendental illusions”? –that it shares with doxa or common sense and that plague thought.

First, in approaching the explanation of phenomena in the world, philosophy perpetually has recourse to the primacy of the Concept, the Form, or Essence, to the detriment of the individual or actually existing entity. Perhaps the most famous example of this primacy is to found in the opening sections of Hegel’s Phenomenology, entitled “Sense-Certainty”. There Hegel begins with the epistemological thesis that all knowledge originates in the immediacy of sense-certainty or the sensible given. Taking this thesis at its word, Hegel goes on to show how our attempt to say the sensible immediate or given always fails insofar as language is only composed of general terms that are unable to grasp the individual given presented within the sensible field. I say that the individual given is this given, here, at this time, yet these same terms can apply indifferently to any number of other objects, such that I am only apply to express the universal, never the individual. The outcome of this contradiction or deadlock within sense-certainty is that Spirit comes to recognize that the individual given was never the object of knowledge, that it is always-already mediated by the universal, and that these universals are the true object of knowledge.

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