Tag Archives: badiou

If Only You Had Been Right

I’m thinking – what else would I be doing? – about the valuation (in left-accelerationism and elsewhere) of the cognitive, its overvaluation or undervaluation. Here, for example, is what the internet already knows to be Dominic Fox’s Favourite Andrea Dworkin Quote:

There is also, possibly, sexual intelligence, a human capacity for discerning, manifesting, and constructing sexual integrity. Sexual intelligence could not be measured in numbers of orgasms, erections, or partners; nor could it show itself by posing painted clitoral lips in front of a camera; nor could one measure it by the number of children born; nor would it manifest as addiction. Sexual intelligence, like any other kind of intelligence, would be active and dynamic; it would need the real world, the direct experience of it; it would pose not buttocks but questions, answers, theories, ideas – in the form of desire or act or art or articulation.

I imagine an allergic reaction to this being triggered almost immediately by the word “intelligence”, and the reader breaking out in hives at the valuation of the “active and dynamic”, the masterful and virile intellect posing its “questions, answers, theories, ideas” to “the real world”. A pose of aggressive sufficiency, in which “desire or act or art or articulation” is always caught up in a movement of intelligence from itself to itself, “discerning, manifesting, and constructing”, making things smart. This vision of what intelligence is, and does, is indeed what I love in Dworkin: I think it is more characteristic of her than almost anything else; even her macabre involvement with extremes of violence, horror and humiliation is subservient to it, driven relentlessly forward by it. Pessimism of the intellect, but never pessimism towards the intellect. (Firestone was much the same).

We see also here Dworkin’s devaluation, in which I share wholeheartedly, of the world of appearances – “painted clitoral lips”, the imaginary realm scoped out by scopophilia, turned into manifest reality by pornographic staging. For her there is a dreadful fall from the qualitative – the deep interior of things, that which intellect must delve into and reason out – into the quantitative, that which can be measured, posed, addictively consumed. Intelligence has nothing to do with this “unreal” world, the world of commerce and communication (and this is where my Dworkin meets my Badiou, in their shared disdain for the democratic-materialist unworld of circulating signifiers). There is nothing to be learned from the “posed”, the “painted”. An entire dimension of performativity – everything that can happen on a stage, in front of a camera, for the amusement of an audience – is condemned here as essentially unworthy of thought. (Dworkin is in this sense perhaps the least “queer” lesbian ever).

My imagined allergic reader feels the lash of this condemnation and recoils. A part of humanity, perhaps a preponderant part, is to be carved away and cast into the fire. You can try to offer reassurance, but it’s too late. Most people don’t experience their intellect as in any way sufficient to their lived reality; the demand that everything be filtered through “intelligence” feels tyrannising and small-minded. They say that Dworkin hated sex; she didn’t, she found it endlessly rich and fascinating and complex. A challenge for thought, a genuinely worthy problem – “not the fun kind”, as she said of herself. What she hated was the kind of inane cruelty that comes out when things slip the reins of intellect and people’s childish wishes are brought garishly into fruition (the porn fairy waves her plastic wand…); the way this cruelty demands subordinated bodies to play its games with, to fashion into the material of its enjoyment. I’m with her there, 100%: obscenity and transgression are always fun for someone, and damn that someone to hell (even if, or especially when, it’s me). But you cannot separate humanity from obscenity: there is no possible “integrity” that does not involve some kind of compact with the unavowable.

Notes on “the digital”

It is mathematically demonstrable that the ontology of set theory and the ontology of the digital are not equivalent.

The realm of the digital is that of the denumerable: to every finite stream of digits corresponds a single natural number, a finite ordinal. If we set an upper bound on the length of a stream of digits – let’s say, it has to fit into the available physical universe, using the most physically compact encoding available – then we can imagine a “library of Boole”, finite but Vast, that would encompass the entirety of what can be digitally inscribed and processed. Even larger than the library of Boole is the “digital universe” of sequences of digits, D, which is what we get if we don’t impose this upper bound. Although infinite, D is a single set, and is isomorphic to the set of natural numbers, N. It contains all possible digital encodings of data and all possible digital encodings of programs which can operate on this data (although a digital sequence is not intrinsically either program or data).

The von Neumann universe of sets, V, is generated out of a fundamental operation – taking the powerset – applied recursively to the empty set. It has its genesis in the operation which takes 0, or the empty set {}, to 1, or the singleton set containing the empty set, {{}}, but what flourishes out of this genesis cannot in general be reduced to the universe of sequences of 0s and 1s. The von Neumann universe of sets is not coextensive with D but immeasurably exceeds it, containing sets that cannot be named or generated by any digital procedure whatsoever. V is in fact too large to be a set, being rather a proper class of sets.

Suppose we restrict ourselves to the “constructible universe” of sets, L, in which each level of the hierarchy is restricted so that it contains only those sets which are specifiable using the resources of the hierarchy below it. The axiom of constructibility proposes that V=L – that no set exists which is not nameable. This makes for a less extravagantly huge universe; but L is still a proper class. D appears within L as a single set among an immeasurable (if comparatively well-behaved) proliferation of sets.

A set-theoretic ontology such as Badiou’s, which effectively takes the von Neumann universe as its playground, is thus not a digital ontology. Badiou is a “maximalist” when it comes to mathematical ontology: he’s comfortable with the existence of non-constructible sets (hence, he does not accept the “axiom of constructibility”, which proposes that V=L), and the limitations of physical or theoretical computability are without interest for him. Indeed, it has been Badiou’s argument (in Number and Numbers) that the digital or numerical enframing of society and culture can only be thought from the perspective of a mathematical ontology capacious enough to think “Number” over and above the domain of “numbers”. This is precisely the opposite approach to that which seeks refuge from the swarming immensity of mathematical figures in the impenetrable, indivisible density of the analog.

Rationalism in the present

The label “rationalism” has already a somewhat anachronistic aura about it, as if it named something that had no proper place in the present. We have been (or, plausibly, “have never been“) rationalists; but who could be such a thing now? Both the rationalism of the past and the rationalism of the future have a phantasmal quality; it doesn’t seem unreasonable to many people to treat them purely as objects of fantasy, and to focus their critique, such as it is, at the level of libidinal investment. What do these strange people want from rationality? How do these wants relate to the usual generators of desire – anxiety about social position, for example? Why the embattled posture, the rhetoric of transcendence?

Answers to these questions are not difficult to produce – in a sense they’re encoded into the questions themselves – and so the desire-named-rationalism can without much effort be rendered transparent and intelligible. What the would-be rationalist really wants – we are immediately sure of it – is to recover a (fantasised-as-) lost position of mastery, no doubt imbricated with the self-image of the colonial slaveowner; they feel threatened by women and queers and people of colour, whose political demands they wish to subordinate to their own privileged sense of what would be “reasonable”; and so on. Inasmuch as all of this registers only at the level of unconscious fantasy, they are (for now) at least one step away from the out-and-out racists and sexists and reactionaries. If only they could be brought to acknowledge the unsavory unconscious content of all their high-minded talk, they might yet be saved.

Now, this hermeneutic has its own self-sufficient logic: it supplies to itself guarantees of its own correctness. It does not have to reckon with rationalism as a concrete position, taken in the here-and-now, because its founding gesture is one of incredulity that such a position could be held in earnest, that it might have any ramifications beyond the fugitive gratification it offers to a handful of hapless nerds. You cannot be serious. It will not, for example, distinguish between the doing of mathematics, an activity which has real ramifications inasmuch as one thing really does lead to another, and the performance of mathiness, the brandishing of the matheme as a totem of sophistication (or abstract fedora). In short, the source of its power (as a derailer of argument) lies in its capacity for inattention: since I already “know” that the object of your attention is a fantasy with no real purchase on the present, I am authorised to focus my attention on your attention, rather than upon the thing attended-to.

It’s in the specific polemical context in which proponents of rationalism encounter this hermeneutic – and while that is often a very narrow and specialised context indeed, it is nevertheless legitimately of concern to us – that we find ourselves both at bay, and empowered by concrete demonstrations of the viability of rationalism in the present. The terrain under dispute is not, or not immediately, that of the concrete conditions of everyday life. What we’re trying to do, ultimately, is strengthen the hand of a certain kind of argument, in the hope of bringing closer some of the goods that this kind of argument is – we believe – uniquely able to envisage. It’s all pretty meta. But we do think it’s important – or we wouldn’t bother – and I for one do find it galling when people whose reaction to the accelerationist manifesto was to describe its program as inextricably colonialist, then describe the accelerationists’ sense of being put somewhat on the back foot as histrionic.

A few words are in order about the use made of mathematics. I don’t believe, and don’t believe that anyone else believes, that a sound knowledge of category theory is necessary for salvation. We’re not trying to become Pythagorean sages here. What I think has become apparent during the course of the HKW summer school is that the current rationalist use of “higher” mathematics is partly revisionary and partly metaphorical: it’s about taking apart some old and creaky logico-mathematico-ideological constructions, which had trapped us in a false image of thought, and provoking new images of thought by giving a motivated and metaphorically suggestive account of the technical machinery used to do so. Some of the work involved in doing this is very technical, and requires those performing it to learn and practice some real and quite difficult mathematics. But the ultimate purpose is not to become surpassingly good at maths, but to get away from an inadequate sense of what “rationality” can mean, so that we are not presented with a bogus choice between (for example) first-order predicate logic on the one hand, and everything that isn’t first-order predicate logic on the other. Rationalism in the present moment means using whatever tools are available to reflect on rationality and extend our sense of what it is capable of. It turns out that fancy mathematics is quite indispensable to this endeavour, but we do not hold it to be synonymous with thinking itself. In fact, those of us who are good Badiousians will be well-accustomed to the vertiginous transit between mathematics and poetry:

Someone saw that very clearly, my colleague, the French analytic philosopher Jacques Bouveresse, from the Coll├Ęge de France. In a recent book in which he paid me the honor of speaking of me, he compared me to a five-footed rabbit and says in substance: “This five-footed rabbit that Alain Badiou is runs at top speed in the direction of mathematic formalism, and then, all of a sudden, taking an incomprehensible turn, he goes back on his steps and runs at the same speed to throw himself into literature.” Well, yes, that’s how with a father and a mother so well distributed, one turns into a rabbit.

The good rationalist, I submit, will be a five-footed rabbit, composing a living present out of the energetic, irreconcilable distribution of antecedents.