I couldn’t have said it better myself:
The supposed neutrality of Badiou “not saying what does the counting” does not get him off the hook. He does not deserve the benefit of the doubt here. We all know that humans can assemble things in sets, and we all know that Badiou’s examples of events that go beyond the state of the situation are all things experienced by humans. (And it seems pretty clear to me that they are also generated by humans. What’s the point of a militant philosophy like Badiou’s if you’re going to claim that “Being” is responsible for the Chinese Cultural Revolution? That’s Heidegger, not Badiou.)
Read the rest here.
One of the things I’ve found very difficult as I’ve worked through Badiou on this blog and elsewhere is that often there seem to be a set of normative commitments that cloud discussions of just these sorts of very basic issues. On the one hand, there seems to be so much excitement and fascination surrounding Badiou’s account of events, the subject, and truth (which I think are largely solutions to a poorly posed problem, stemming from an underdetermined, yet fascinating, ontology), that scant attention gets devoted to how Badiou proposes to account for the structuration of what, in Being and Event he called “situations” and in Logiques des mondes he now calls “worlds”. Certainly we deserve a robust account of the transition from inconsistent multiplicities to consistent multiplicities.
Badiou’s discussion of the count-as-one seems designed precisely to give such an account (pardon the pun), yet this solution, regardless of whether Badiou describes it as “materialism”, seems doomed to lead us into idealism. Badiou’s discussions of materialism appear to be based on a sort of equivocation or sophism where a position is described as “materialist” if it mathematizes the world, yet is there not a difference between the material and the mathematical? More worrying, it seems impossible to treat the count-as-one as doing the work of structuring situations without presupposing a counter. Now Badiou can, following Husserl and Frege in their critique of Mill and psychologism, make noises about how this counter is not human; but ultimately he must still be talking about some version of a transcendental subject. All worlds then get shackled to the activity of this transcendental subject as what structures situations through the count-as-one, undermining the possibility of entities that are as they are regardless of the presence of any subject. What we thus seem to get in Badiou– amply confirmed by his turn to “the transcendental” in his most recent work –is a new variant of Kantianism or correlationism sans the categories of the understanding and the role played by intuition and finitude.
February 14, 2009 at 12:50 pm
Does the statement “Being presents (itself)” (from chapter 1 of B&E) already strike you as invoking or requiring a transcendental agent of presentation, or is it just the fact that this presentation is characterised as determination of unity (counting as one) that makes it seem as if it must necessarily be the work of an absolutised transcendental subjectivity?
I’m becoming increasingly sympathetic to the way Ray Brassier uses Laruelle against Badiou (and Deleuze, and Churchland, and just about everybody else…no-one’s immune!), but that’s really another story…
February 15, 2009 at 6:07 am
Dominic, if we change that statement to a Heideggerian “being reveals itself”, and then the problem becomes clear. The fact that Heidegger starts ascribing responsibility to being itself rather than to Dasein for many things does not get him off the correlationist hook. Impersonalizing reality changes nothing as long as a human must always be there as one of the two ingredients of any situation.
I’m still waiting for an answer as to how you think Badiouians would react if I gave rocks and earthworms the ability to engage in the count-as-one and to experience truth-events. (Well actually you already answered that about events, which you said on your blog are merely human, but it wasn’t clear to me why you think that being and event are different in this respect).
February 15, 2009 at 7:20 pm
The short answer, which I don’t think moves things on very much, is that because the count-as-one is impersonal it makes no more sense to ascribe it to rocks and earthworms than to ascribe it to human beings. Because a truth-procedure involves evental nomination, and the constitution of a faithful subject, it requires something capable of “supporting” a truth – rocks and earthworms don’t seem to qualify here, as neither can very readily be organised into a militant collective subject.
February 15, 2009 at 9:27 pm
“Count” and “event” are ontological terms; “truth”, “truth procedure” etc. are ontic. A truth is a multiple, as is a subject. An evental site is a multiple, but an event is not (or not for long).
I don’t think it’s a problem that “truths” (in Badiou’s particular sense, rather than just the referents of veridical statements about the world) depend on the existence of thinking beings, any more than it’s a problem that milk depends on the existence of lactating beings – so long as one isn’t also saying that the Milky Way depends on the existence of lactating beings…
February 16, 2009 at 12:04 am
As I’ve mentioned before, I don’t see it making much difference that the operator of the count-as-one is impersonal. This is the standard thesis about the functioning of structure among structuralists and post-structuralists, and is directed at a certain version of humanism. Nonetheless, these structures only exist in and through humans, thereby remaining in the correlationist circle. The same holds likewise for being presenting itself. The presentation of being, if I’ve understood Badiou correctly, is the presentation of consistent multiplicities. But consistent multiplicities are only through the operations of the count-as-one. Badiou’s ontology could only attain realism through a presentation of being that was in no way dependent on humans, whether impersonally or otherwise. Given Badiou’s constant emphasis on the identity of thought and being, this seems unlikely to be found in his philosophy, thereby insuring that his thought remains in the orbit of idealisms. And indeed, in the latest work we find all the usual suspects where idealism is concerned: the transcendental, etc.
February 16, 2009 at 10:04 am
If I understand correctly, it is indeed Badiou’s linking of presentation to counting – to structuration – that makes you certain that such presentation is accomplished only in and through humans. Is this because you think that the world is primally unstructured, and that structure is always a by-product of human ideation, or is it specifically mathematical structures that only exist in and through humans, as a kind of second-order systematisation of already-given structure?
I still find it difficult to understand why counting can’t just be a first-order ontological operation – to me it seems no more intrinsically human-centred than, say, differentiation.
I hope you’ll forgive me for banging on about this – what I’m interested in is locating the precise point where some people jump one way, and some people jump another – why Peter Hallward, for instance, tends to depict the count-as-one as a kind of individuation in the socio-political domain whereby categories such as “French Student” come into effect, while Ray Brassier seemingly has no trouble just accepting it as an ontological primitive (but rather more trouble with the philosophical meta-ontology developed alongside it).
February 16, 2009 at 1:48 pm
Dominic,
I’m not entirely sure I understand your question, but I’ll take a shot at it anyway. As I understand him, the world is primarily unstructured and takes on structure through an operation of counting. I find it difficult to understand how counting could be a first-order ontological operation because Badiou explicitly claims, in a number of places, that being and thought are identical to one another. In order for counting to be a first order operation we would require operations of counting that weren’t identical to thought. This, I think, would be one of the watershed differences between Badiou and Deleuze. Where, for Badiou, the operation of the count is always related to a thinker in some way, for Deleuze processes of individuation are entirely immanent and independent of the human as playing any special role. As I’ve remarked in previous posts, it seems to me that appeals to impersonal and anonymous nature of these operations of counting is a dodge. Here I take it that Badiou is following thinkers like Frege and Husserl in their rejection of the psychologism advocated by Mill in his account of mathematics. However, when Frege and Husserl reject psychologism, they do so in the name of a transcendental form of subjectivity similar to Kant’s as a universal condition underlying these processes. Transcendental subjectivity is purely impersonal and anonymous, but nonetheless intrinsically tied to the human (especially if Meillassoux’s arguments are to be conceded). Hence we still find our ontology still linked to the human as a special condition among all the other conditions. That said, I very much like your particular version of the impersonal and first-order operations; I just think that’s your particular ontological intuition, not Badiou’s.
Additionally, I don’t think these issues are mere technicalities in Badiou, but have very real consequences for how he thinks about issues. Because Badiou elides the operations of counting into social structure, and because he treats entities as “pure vehicles” of the count (https://larvalsubjects.wordpress.com/2009/02/10/the-thermodynamics-of-being/), he’s led to a whole problematic where the question arises of how it is possible for anything to change. That is, this violation of Latour’s Principle leads him into an ontological vision where the only possible form of change is an event from elsewhere. By contrast, if we begin from the premise that there’s no entity that doesn’t contribute a difference, that no entity never serves as a pure, frictionless vehicle of another entity, then this problematic collapses and looks rather different. I’ve never gotten the sense that you’re much interested in Badiou’s account of the event. You seem far more focused on his account of mathematics as an ontology.
February 16, 2009 at 3:01 pm
If I might pose a supplementary question: must an impersonal transcendental necessarily be a form of subjectivity? What gets called the transcendental of a world in LoW fairly clearly isn’t, for example.
You’ll have seen this before, but just to recall it in this context:
“Deleuze always paid tribute to Sartre as the figure who, during the thirties and forties, woke French philosophy from its academic slumbers. He considered the 1937 article, ‘The Transcendence of the Ego’, the origin of everything: why? It is because, in this text, Sartre proposes the idea – I am citing Deleuze – of ‘an impersonal transcendental field, having the form neither of a personal synthetic consciousness nor subjective identity-the subject, to the contrary, always being constituted.’ I want to emphasize this remark of Deleuze’s all the more insofar as the motif of an impersonal transcendental field is dominant throughout my Greater Logic, where it is effectuated, in the finest technical detail, as a logic of appearance or worlds.”
February 16, 2009 at 3:11 pm
“Where, for Badiou, the operation of the count is always related to a thinker in some way”
I wonder also if you could indulge me by citing chapter and verse on this, as nothing that I’ve read of Badiou has left me with that impression.
February 16, 2009 at 6:24 pm
Dominic,
I am making the inference to the assumption of a thinker based on Badiou’s claims about the structure of situations and his habit of equating the structure of situations to knowledge or the encyclopedia. You’ll find the relevant passages in my article “Symptomal Knots and Evental Ruptures” (specifically section 2 and 3):
http://www.zizekstudies.org/index.php/ijzs/article/view/30/89
As Badiou remarks in his article “Truth: Forcing and the Unnameable”:
In addition to this, my understanding of Badiou’s account of the count-as-one comes from what he has to say about the role played by metastructure and constructivist orientations of thought in Being and Event. For example, he writes:
You’ll find a fuller discussion of my interpretation of these aspects of Badiou’s thought in sections 2 and 3 of my article, but these passages are a good start.
Now, here’s my point. The issue, for me, isn’t whether the count-as-one is tied to a transcendental subject, but rather whether the count-as-one is tied to the human. Badiou explicitly restricts the count-as-one to the human in equating it to knowledge and structure. Knowledge, as Badiou explicitly states in his interview “Being by Numbers” is to be equated with what Foucault calls knowledge or the encyclopedia (http://findarticles.com/p/articles/mi_m0268/is_n2_v33/ai_16315394). It is the encyclopedia that presides over the count-as-one for situations or what Badiou now calls world.
Granting this interpretation, evoking a transcendental field independent of transcendental subjectivity does not get Badiou out of the circle of correlationism. As Ricoeur had already argued, structuralism is “Kantianism without the transcendental subject” (The Conflict of Interpretations). That is, the structuralist innovation is not so much to shift away from correlationism, but rather to conceive a form of correlationism without a transcendental subject in which it is language that does the structuring. In short, beings are still sutured to the social or language under this model. As I read him, Badiou very much endorses this position.
The question then not whether or not a transcendental field is tied to a form of transcendental subjectivity, but whether the transcendental field is tied to the human. Deleuze’s version of the transcendental field differs radically from Badiou’s in that Deleuze’s transcendental field is not in any way restricted to the human: It is not premised on a transcendental subject, language, power, or the social, but exists regardless of whether any language, power, or social (i.e., human) things exist. By contrast, when Badiou ties the count-as-one structuring situations to language and knowledge, he is restricting it to the human after the manner of Foucault or other thinkers. This is why I simply can’t derive your thesis that operations of the count-as-one belong to being as such (i.e., existence) rather than the human in some way.
February 16, 2009 at 8:30 pm
Here I think is a clear point of disagreement, one where I can say quite clearly where my understanding differs from yours.
The language of the situation provides the means for predicatively discerning different subsets of the situation (or different elements of the state of the situation, which counts subsets), establishing a variety of epistemic mappings of the presented multiple. The encyclopedia of the situation is the set of such mappings that are operative (whether actively or latently) within it. Badiou identifies Foucault as the pre-eminent philosopher of the encyclopedia, of “structure” as the structure of knowledge. Nomination, indexing and predication are the operations of this structure, which is that of the known world of human societies.
The structuration performed within presentation, by the operation of the count, is not of this order. It is the primary structuration of the situation within which both the language of the situation, and the collections of presented multiples it indexes, are presented. This primary structuration is developed on the minimal basis of a single relation, that of belonging, from which further mathematical relations – of inclusion, of order, of mapping, modelling, measuring, placement and all the rest – can be derived. The order that it unfolds is not that of knowledge, but of the situation itself qua presented multiple.
The language of the situation does not present, but indexes the represented (note that it is elements of the powerset of the presented multiple that it quantifies over). It is not the means through which the consistency of the count-as-one is secured, but the means through which an already-consistent situation is given to knowledge in representation.
It is not the encyclopedia which presides over the count-as-one of situations! This is precisely where Badiou’s ontology breaks with the structuralist regime of truth as effected by language, and insists on the possibility of a novel configuration of being (the generic subset) that would not be merely a combinatorial reshuffling of the elements of the encyclopedia.
Things get more complicated around the question of the constructivist orientation, which I won’t go into right now, but the fundamental point is this: the count-as-one is not an operation of nomination, indexing or predication; it presents the very intrasituational material – the language of the situation – that is deployed in these operations, the field of which is not presentation but representation, or the state of the situation. The operations of knowledge are certainly tied to the human; the operation of the count is not.
February 16, 2009 at 9:10 pm
I’ve been saying over and over again that the count-as-one does not present a multiple as the extension of a predicate. Now here we have Badiou saying that “The function of the language of the situation consists in gathering together the elements of the situation according to one or other predicative traits, thereby constituting the extensional correlate for a concept”.
It seems as if one of two two things must true: either a) the count-as-one presents a multiple as the extension of a predicate, and the operation of the count is effected by the language of the situation (which leads to an odd circularity, whereby the a part of the situation – the language it affords – effects the count of the situation itself), or b) the count-as-one does not present a multiple as the extension of a predicate, and the operation effected by the language of the situation is not that of the count-as-one.
My reading is definitely b)!
February 16, 2009 at 9:30 pm
Yes, we would differ quite significantly on this point. I am not sure, how under your analysis, we are to understand passages like the following:
“The count-as-one is no more than the system of conditions through which the multiple can be recognized as a multiple” (BE, 29 my italics).
Why the emphasis on recognition in relation to the count-as-one?
Second, if your thesis is true, I have a difficult time understanding Badiou’s thesis about what philosophy does in comparison to sophistry in Manifesto for Philosophy. As you will recall, there he argues that philosophy gives the argument of the sophist a slight twist showing how truth is possible. Plato takes up the tools of the sophist (dialectic) so as to produce a truth. In our current historical context, this would move would consist in conceding the argument of the modern-day sophist (Derrida, Lyotard, Wittgenstein) and showing how truth is possible on these grounds. The position of the modern-day sophist is that of linguistic constructivism. As I read him, Badiou concedes this argument at the level of structured situations while one upping the sophist by arguing that being qua being is not structured multiplicities (multiplicities counted as one), but rather multiplicity qua multiplicity. As such, under my reading anyway, the elements belonging to a situation would still fall under the correlationist circle.
Third, what would it mean for something to be uncounted if your interpretation is true? Badiou’s whole account of the event hinges on something being uncounted or not belong to the structuration of a situation. We can understand how this would be possible very clearly from the standpoint of a social situation, e.g., what it would mean for science at an existing time to have ignored some dimension of being or another, or what it would mean for a social organization or encyclopedia to have no place for the illegal immigrant, etc. However, it strikes me as bizarre to suggest that the illegal immigrant or causal mechanisms governing relativity or atoms, etc., to not exist in its own right. In other words, this whole argument only makes sense if the count-as-one pertains to knowledge not to existence.
I think a lot of the confusion here is that Badiou simply doesn’t tell us a whole lot as to what he has in mind by operations, the count-as-one, and the structure of situations. However, I have a great deal of difficulty understanding the logic of his theory of event if their structuration as an effect of the count-as-one is a characteristic of the being itself rather than how we categorize beings in a regime of knowledge.
February 16, 2009 at 9:35 pm
Dominic, wouldn’t option a be the reason that Badiou distinguishes between the metastructure and structure or the count-of-the-count and the count-as-one? I think you’ll find, however, if you go through his discussion of structure and the count-as-one that he constantly speaks of predicates. I don’t see this as being a contradiction. Ontology, as Badiou understand it, is not concerned with consistent multiplicities (results of the count-as-one) but of what can be said of being qua being independent of any predicate of one-ness, i.e., the inconsistent multiple subtracted from all operators of identity, the one, totality, etc.
February 16, 2009 at 10:05 pm
Going point by point…
i) “Recognised” I think here means something equivalent to “legally recognised”, e.g. legitimated by the axioms of set theory. But I agree that it’s a slightly confusing use of language – I don’t think Badiou really means to introduce questions of cognition here.
ii) I think you’re missing a level in between the state of the situation (representation, encyclopedic knowledge, extensions of concepts etc.) and pure inconsistent multiplicity, and that level is the situation itself. Badiou concedes that knowledge is as the sophist says it is, but is not immediately driven back into poetic evocation of the inconceivable flux of being itself, precisely because he has a subtractive ontology which is not based on predication.
iii) Why does no-one ever talk about the matheme of the event, the ultra-one, etc.? The event is an axiomatically forbidden (non)-multiple, a structural absurdity. It’s an immanent exception, not just the reappearance of an “excluded” element. (I find Peter Hallward’s treatment of this theme especially suspect).
Again, if one’s talking about predicates quantifying over subsets of the situation, it makes sense to talk about included and not-included elements – every subset has a complement. But the event is not simply the breakdown of a conceptual scheme, a kind of auto-deconstruction of some binary opposition. It’s a nomological infraction, “illegal” at the level of the axiom system governing presentation itself.
This creates problems of its own, as I’ve said in conversation with Graham, and I’m not hugely satisfied with the way Being and Event conceptualises the event; but it’s really about the subtraction from presentation of an evental site, not the addition of an incongruous element to a conceptual order.
(An evental site, incidentally, is any presented multiple whose sub-multiples are not directly presented in the situation that presents it – so its contents are “invisible” to the language of the situation, which has no terms with which to nominate or index them. This may be where the idea comes from that the event is the reappearance of the “uncounted”. But actually, every sub-multiple of the evental site is counted, by the evental site itself which just is the count-as-one of those sub-multiples. The event is the malfunction of precisely this count!)
February 16, 2009 at 10:25 pm
In S={a, b, x}, where x={a, b}, the language of the situation S is able to discern the elements of x (they are those in the part of S, or element of P(S), {a, b}), but in {a, b, x} where x={c, d} it is not, and x is therefore an evental site of S.
The event of x would be the illegal (non-)multiple ex={c, d, ex}, illegal because a set that contains itself violates the axiom of foundation and creates all kinds of problems for other set-theoretic operations.
February 16, 2009 at 10:58 pm
and
I think you’re missing my point in both of these remarks. I understand what the event is. The point is not that there is no matheme of the event, but rather that the very idea of an event makes no sense if the consistent multiples are a matter of beings as such rather than discourses about beings. Take Badiou’s example of Galileo as an example of a truth and event. This is only an event relative to a discourse about what is stemming from Aristotle and the Scholastics. If what Galileo said about beings is true, then it held for beings regardless of whether or not anyone spoke about it. That is, these properties of objects were properties of objects independent of any discourse. It makes no sense to talk about an event in relation to beings themselves– at least in science –as these beings have this property. The event only makes sense relative to the consistent multiples of a social discourse about beings. Legality here is not a property of beings themselves, but discourse legislating over beings. Your point about submultiples makes this very point. The submultiples are measured relative to a dominant discourse that presides over the counting of elements. A nuanced point, but one that is necessary to make, I think, if Badiou is to be understood.
February 17, 2009 at 7:45 am
ZF set theory specifically excludes the treatment of multiples as extensions of a predicate, because this approach leads to paradox; it restricts predicative separation to existing – that is, already counted, already presented – multiples.
What first determines an evental site as abnormal is nothing other than the relations of inclusion – and these are primitive – between itself and the situation of which it is a site, the other multiples that are presented in this situation, and the multiples that the site itself presents. It is true that an evental site is not intrinsically foundational, but only foundational with respect to a situation in which it is situated in this way. But it is no more the case that this is a matter of discourse than it is a matter of discourse that a natural multiple as transitive with respect to inclusion. These are absolutely elementary structural types, defined according to the typology of being.
February 17, 2009 at 9:56 am
Relations of belonging, damn it, not inclusion. Inclusion isn’t primitive…
February 17, 2009 at 3:05 pm
Right, but isn’t this in many respects already the structuralist thesis? That is, it is not a predicate that defines belonging under a signifier, but rather a simple extension. Or, put alternatively, there is not a predicative meaning that defines the signifier.
February 17, 2009 at 5:12 pm
A multiple isn’t really a signifier, is it? (Although a signifier is presumably a multiple). Signifiers are laid out as a system of differences, a single internally-differentiated field without positive terms. Multiples are presented according to an axiomatic scheme; the difference between {{}} and {{}, {{}}} isn’t merely nominal.
If there’s an equivalent to “the symbolic” in Badiou, I think it’s the encyclopedia of the situation, not the multiple-composition of the situation itself.
February 17, 2009 at 5:36 pm
Dominic,
If I follow your position correctly, you’re carefully distinguishing the structure of the situation and the metastructure of a situation, relegating knowledge or the encyclopedia to the metastructure of the situation and excluding it from the structure of the situation. If true, this would open the possibility of a realist version of Badiou wherein the elements belonging to the structure of the situation are presented independently of the encyclopedia of the situation. Your charge against me would be that I am conflating the count-as-one with metastructure or the encyclopedia. When I have some time I’ll have to go back to Badiou to determine whether or not I think this reading holds up. Here the questions would shift markedly. The issue would no longer be one of whether or not Badiou falls into idealism– the his equation of being and thought strongly supports this conclusion –but rather whether the count-as-one is sufficient for giving a robust account of the individuated presented multiples. Here the extensionalism of set theory would also seem to be problematic insofar as entities maintain all sorts of other relations with other entities in their ongoing genesis. While I certainly know that set theory has the resources to describe relations, Badiou places his emphasis on extensionalism which seems to distort the manner in which entities maintain relations to their world. Of course, some of these problems are overturned in his most recent work and his turn towards category theory.
February 17, 2009 at 6:15 pm
I think those are more like what I think are the real problems!
The language of the situation is given as part of its structure, but is used to nominate parts of the situation, or elements of its meta-structure. The encyclopedia of the situation is the collection of different ways in which parts of the situation can be discriminated by predicates formed using the linguistic elements presented within the situation itself (note that the situation is not composed of linguistic elements, it just happens to present some alongside other things).
For example, given the situation of France, the set of French students is a subset of everything presented as France, an element of the metastructure of that situation; the language of the situation allows predicates to be composed that can discriminate students from non-students, French citizens from non-French citizens and so on. Here the language of one situation is involved in the predicative separation of another, and in this sense the count-as-one of French students does involve predication – but only with respect to an already-counted multiple. That is a core restriction of ZF set theory: the formation of sets is not initially tied to predication, although the elaboration of further sets on the basis of a given set may involve predicative “moves”. One might note that France itself is in the position of being a sub-multiple separated from a larger situation – that of the global human situation – by predication. But this does not mean that the count-as-one is primordially correlated to human / linguistic conceptual mappings, but rather that such mappings are themselves enabled by the axioms governing the count – in particular the powerset axiom and the axiom schema of separation.
February 21, 2009 at 1:43 am
[…] recent posts have been written jumping in on the critiques of Badiou’s ontology by Graham and me. Over at Complete Lies, Michael develops a critique of Badiou on the grounds of onto-ontology. […]
February 5, 2010 at 4:18 am
Hello, I just stumbled across this blog. I haven’t read all the comments, and of Badiou’s work I’ve only read B&E.
Nonetheless, isn’t asking for an account of the count-as-one akin to asking for a definition of ‘set?’ But the concept of set is considered self-evident by mathematicians (and ontologists, for Badiou), so I don’t see why he would ever provide such an account. As I read it, the count-as-one is inherent to what is self-evidently called a set.
March 1, 2010 at 4:04 pm
It seems to me that the count-as-one is not a set but rather the function of choice, but I could be wrong. Can anyone explain the difference between the count-as-one and the function of choice?