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Females, or, the set of all sets


Luara Karlson-Carp
27 July 2021

Even writing feels like complicity these days. Whacking a bit of something congealed on a plate for friends, hypothetical friends and critics isn’t so bad, but there is no escaping the knowledge that our creative secretions are the nectar of our godless god. I keep finding munching negation machines everywhere. The university gorging on my labour (whether I’m sincere or not), Lacan’s bitter Hegel, billionaires masticating Byron Bay, the forever-chemicals raining on the great lakes, human cattle yard units gnawing on the internal corners of Brunswick, cybernetics constitutively, Irigaray on the Plato-to-Freud pipeline, in Sam’s opinion my mother, the banal finality of the form/content distinction we’re all routed into suckling the smartphone twitter teat blah blah blah. The outside is prefigured and we know it; that anyone still writes is a tragic miracle.

The logic of the negation machine is as follows: it is a machine that eats the outside, it assumes that what exceeds the systematicity of its informational structure will be eventually negated in its particularity and apprehended by that structure as information. You know, like Gucci window dressings awash with scenes of passionately cool protestors in impeccably agonistic plaid, how resistance to capital is prefigured as a desirable, commodifiable aesthetic. What does this machine feed on though, exactly? I don’t think I’m a negation machine, though I do feel I’m being munched. I think it’s a sex thing.

Consider Russell’s paradox: if I have a set, essentially just a nominated aggregate, say the set of all women who write about their mothers, then the set of all women who write about their mothers is not one of these women, so isn’t included in the set. But consider a different set, the set of all things which aren’t women writing about their mothers. This set includes itself; it is not writing about its mother. Things all seem fine, and Frege (the author of “set theory”, now called “naïve set theory” thanks to Russell) was quite excited about it. But then Russell wrote Frege that infamous letter, a paean to the problem of the mother, I reckon, in which he asked: what about the set of all sets that do not include themselves, does it include itself?

You see, Frege was a mathematician and logician trying to logicise maths, as numbers were still kind of magical, and it behoved a man of science to see this amended. The set of all sets: we have the set of all women who write about their mothers, which doesn’t include itself, as we have already encountered, and we have the set of all things which are not their mothers, which does include itself. Frege dreamed a wily dream that using this kind of logic could make everything work: all that exists could be ensconced in a water-tight matrix of syllogisms, this thing in this set, that thing in that, all the way down, forever more. A dream of a good night’s sleep1 that never ends. But Russell knew he was still awake, and so asked: does the set of all sets that do not include themselves include itself in its own set? Does the envelope of the world contain itself? Does the envelope of the daughter contain herself, daughters all the way down… Can we write the new. I’m asking, does the munching negation machine contain itself?

Now, set theory is to be distinguished from the predicate logic of class. By this I mean the logic of those who might call a woman an adult human female. They know, they go so hard, they have found two beautiful predicates, adult and female, to attach to the attribute woman, which then finds its home in the warmly god-gaze of the universal, “human”. All shines down brilliant and bright from this singular sun, the horror of the munching negation machine is shielded by the infinite light of that brightest nothing over a nothing, the signifier human over the void of what-the-fuck. This is predicate logic, the logic of what in set theory are called classes, which are distinguished from sets. The attribute apple has the predicates redness and roundness, which distinguish them from other fruits as apples. And likewise, women are definitely shiny, round and red adult females, always better if the juices stream down the chin. It is good to be clean. “Sets”, unlike classes, aren’t defined by predicates, but are aggregates that follow the logic of membership. The set of all fruits contains apples, maybe women, but it doesn’t aim at Being. There is no question of the copula, what a thing is, but rather the concern is merely with whether it is included in the set or not. Being, or the universal, is therefore not the referent; the ultimate referent is irrelevant as membership is not concerned with the fundamental taxonomy that underlines the notion of class, but merely arbitrary groupings. Set theory leaves hermeneutic suspicion at the door.

This focus is on the question of membership alone, and not what qualifies membership, in some ways this mirrors (contra the predicate-fascism of the TERFs) the (post-)performativity notion of gender in which a woman is no more than what woman does, and she does what we say she is.2 But this is still a little too sceptical, and therefore philosophical, for Lacan, who considers the issue thusly: there are apparently these things called women, and it’s impossible to know what they want. Women are like sets that include themselves, they can’t be universalised because there’s no exception that could enclose their outside. The set of all things which are not men includes itself. We know what men want, they want money, fame, power and hole. Their desire is sustained by imagining someone who has all these things in infinite supply.3 Perhaps, then, they are like the set which doesn’t include its object-cause of desire, the set which doesn’t include itself. The logic of the signifier, the word, the position of the universal, requires the set-that-doesn’t-include-itself logic, as there is an exclusion in the form of the set itself, which stands against those things included in the set and encloses them as a “whole”, as an “all”. Woman isn’t orchestrated by any such exclusions, for Lacan. For woman, the object-cause of desire isn’t over there, excluded, closing off a totality. It remains internal. She is included in her own set. She is not-whole, there is an intimate exteriority which defines her, prevents her from closing up, maybe, and this logical oddity can therefore not, strictly speaking, be said to exist.4

TERFs are part of the lineage who think to define woman as lacking this structural coherence, access to psychic universality etc., is sexist. Queer theory was in part born from the ashes of debates between those who took this non-coherent, nonuniversalisable, predicateless notion of women seriously, namely Lacan and his detractors. If you don’t believe me, consider the premise of Gender Trouble: that no notion of “women” can ground feminist theory and politics without excluding someone it means to capture. Whilst responding to many more concrete contexts and struggles than Lacan probably ever dared to dream to schematise, Butler’s thesis is surely, in part, an Anglo extension of the woman does not exist. Butler universalises this position of nonexistence, melting the problem of the pure difference of sex, at least in the formal sense of her psychoanalytic interlocutors, down into the flat multiple of gender. The idea of gender nullifies an operative difference here that can’t be understood via the logic of predicates (as Butler knew but the TERFs forgot), but just because predicates are dumb when it comes to defining sex, this doesn’t mean there isn’t difference at play, that there isn’t a systematicity to be reckoned with. In universalising woman does not exist, queer theory leaves the corollary question in relation to men and the universal unattended. Men (white…) have kind of grounded history, assumed the universal, the historical form of politics. Surely the notion that we can flatten this position into one identity among many speaks to a kind of moment of historical abstract mediation that is more symptomatic than liberatory. I can’t really claim Lacan has teeth on this problem either, but he seems alight to the fact that even if the content of the pure difference of sex cannot be pinned down with some kind of wishful-thinking metaphysic, neither can the paradoxical heart of the universal be wished away.

At this juncture, Lacan turns to the logic of the set, and to this question of the paradox of the set of all sets, and the impossibility of answering the question of whether this set does or does not include itself, to think sex. If we try to think the set of all sets that don’t include themselves, the set of all of man, we see that this set excludes itself from membership. If I include the set of all sets that don’t include themselves, it becomes a set which includes itself. It disappears. Desiring, now, from the other side.

Andrea Long Chu in Females is, as such, indubitably set theoretical. When she tries to think the set of all sets that don’t include themselves, or the totality of man, she comes up with a beautifully Russellian answer: everyone is Female. The totality of man, everyone, moves from the masc universal (which doesn’t include itself) to the place of woman, a set that does include itself, ending in disaster and paradox. Everyone is female. This is to say, for Chu, that everyone desires someone to do their desiring for them, that being female is to sacrifice something of the self to make a space in which to host the desires of another. With this ratbag soothsaying, like Lacan, instead of chickening out, (e.g., capitulating to predicate logic like white feminists scared of losing their identitarian claim to capital because the cat girls are fucking with the definition of woman), Chu resists the cult of poststructuralist dissolution and formalises the paradox. Everyone is Female, but not all females are women. I think we need this weird washed-up structuralism to meet the munching negation machine head on.

I’ve finally written an abstract for my thesis, I’m realising it as we speak:

“I’m walking along a headland just after my mum nearly died. The sunset is beautiful but I’m too aware of the performance involved in taking beauty seriously to go there, so I awkwardly meditate on the mediating alienation instead.”

This is exciting. It’s not. Its cathartic but you can probably already tell that from where I’m standing, catharsis always peters out into the swill of layered abstractions too quickly for anything to actually move. I’m writing an MA on Luce Irigaray and all I see in her work is mediation, the mediation between something which has the potential to be different, a new that is beyond novelty, a difference that could *make a difference*, and the negation munching machines that stillbirth it all as the same old shit before we can even be moved. Particularly, essentially, moved at the level of speaking. So that we might speak a language other than mimesis, parroting. Being aware of the performance involved in witnessing a difference that could make a difference, getting caught in the alienation of a sunset’s beauty after near-bereavement, for example, leaves one with the option to either fall into nihilism or try to mobilise that performance imperfectly, maybe even disgustingly, to push the performative form to its parodic, bombastic extreme. This is the route taken by performativity, patron lifestyle-methodology of queer theory, contra nihilism. The nihilism of refusing to not be alienated, to resist catharsis, even parodic catharsis. Both these strategies confront the perfect beauty and absent alienness of the mother, of that heaving artifice called nature, of one’s sex, of all these things that speak to each other, negatively of course, between the lines of cybernetic negation of the excess, though their capture as figural outsideness is always prefigured in the circuit and they know it.

I know it’s convoluted, but this is the move I am trying to stick, or that simply won’t wash off: try and make a set of all sets, and you get a woman, though it’s impossible to say what that is. The resources for the logical coherence of the set are undermined by aiming for the ultimate abstraction, asking the question of sexual difference. Try to think the universality of man and out pops a universal Female. A universal problem of desire. Chu states, then, that we ought understand sexual difference as a difference at the level of phantasmatic defense. She writes,

“Everyone is female, but how one copes with being female—the specific defense mechanisms that one consciously or unconsciously develops as a reaction formation against one’s femaleness, within the terms of what is historically and socioculturally available—this is what we ordinarily call gender. Men and women must therefore be understood not as unreconcilable opposites, or even as two poles of a spectrum, but more simply as the two most common phyla of the species Females.”5

If we consider this defense against being “Female” as a defense against castration, then Ladies and Gentlemen, Chu is the Lacanian of our time. Especially if we replace “phyla” with “set”, and understand Females as animals who reproduce in the hollow of lack that is filled with the misrecognised desire of the other, in other words, Lacan’s universally castrated subject.

But does Chu also just reify a (post/anti/something) humanist universal at the end of the day in this figure of the Female? A predicative one, even? I don’t think so, because it serves the function of a formalisation of a paradox. Everyone is female, and everyone hates it. This is what generates the desire, the desire to be other than female, though the lack constitutive of the female is the condition of the possibility of desire as such. To take this one step further, to really fuck with you, perhaps we have never even been female, perhaps the female is also simultaneously the horizon of our desire, this sissy desire to go all the way, as well as the diabolical marker of that which we wish to transcend, whilst also being the condition of our desire. With such hysterical demands, the species Female can then be best captured, in logical terms, by naïve set theory and Russell’s paradox. Only the paradox here isn’t the evidence of a bung theory, but a manifestation of the real, the real of desire as contradiction.

Only Bertrand Russell knows why I can’t write my thesis. It is a set of all sets that don’t include themselves, and when I try to gather my desire, that is, gather all these sets which don’t include themselves together into this document, these 30,000 words, I hit the paradox. The thing I desire comes to include itself and therefore ceases to be. Someone once said, I think it was Russell, that there is a red-thread connection between finishing a thesis and killing your mother. A mother is also a Russellian paradox. Try to make a set of her sets and she’s finished. She cannot include herself, even at the level of the set of sets, the word “mother”, for she is defined by including another. Her logic is constitutively inconsistent, but this inconsistency is the mother of all desire: the desire to correct inconsistency, or the desire to express it. The desire for the impossible axiomatisation of set theory, the creation of a metaphysics, or if you’re really lucky, some art. Or fucking, if sublimation is just too gauche. The desire for failure. The desire to be something other than a daughter.

I suppose there’s a kind of bad nihilism involved in becoming so obsessed with trying to pin down this contradiction, to put forward this very laboured metaphor, maybe the metaphor of labour, the status of the labourer as the one who produces offspring, or the proletariat. In Latin, proles is “offspring”, and proletarius is “the man whose only wealth is his offspring, or whose sole service to the state is as father”. We are, indeed, all females when our ancestral fathers are the midwives to the state. But it’s a bit stultifying to dedicate one’s time to reifying this fact in the discourse of the university, and in such polite company too. If I can’t write my thesis because my essence is contradictory desire, the university knows this and draws my passion from my throat to teach its doomed little zoomers. The dream of the utopic university, a temple for the thrill of the intergenerational exchange of seminal ideas, the birth of the new and not merely the novel, the sanctity of equality before a well-endowed HECS scheme—my lust for all this has kept me in un(der)paid work as a casual tutor for years. A dream perhaps not to correct inconsistency, nor express it, but share in it. The university’s recognition of the passion of this dream is its business model. We are all females to Duncan Maskell.

But maybe this is the problem. How historical is Chu’s shit-posty structuralist anthropology? Have we always been Female, or is this loathsome status the product of a feminised labour market and the decline of capital accumulation’s need for a reserve army of proles, and therefore the requisite strict sexual divisions of labour? Has desire always occupied the hollow of the sacrificial self?6 Maybe we are all females, but let us also consider that maybe we still haven’t quite made it. I think I began by discussing the prefiguration of the outside and I think of this in accordance with the economisation of femaleness, of the capacity for production in that vacant self (sometimes body), of femaleness culturally realised as the lever of a possible circulation of value, even surplus value. Is it possible to imagine the new, creativity, in terms other than value? Can we imagine an opposite for value, beyond its binary of valuable/valueless? Can we denature its status as master signifier?

I can’t write my thesis and someone important says to me it’s like this: if our mothers are deeply implicated in the formation of our desires and so too the form of our selfdestruction, the Eros and Thanatos, Apollo and Dionysus, the jouissance that keeps us eating ourselves, then the desire to write a thesis is the same desire which prevents its being written: the desire for desire, that suspension in infinite potential sustaining all desires, keeping them alive at the cost of any final consummation. It is both carrying on the family tradition of hysteria, dutifully, and carrying on the family tradition of hysteria, in horror. The horror of being a dutiful daughter is the horror of being woman. The horror of being a woman is to wear universal femaleness on one’s sleeve, to shitpost the wounds of the negation machine on the body. But I want to not know what a body can do, again. Speaking should be left for a voice ready to articulate contradiction. I don’t want my body to speak for the family, for anyone, not even me.

  1. “Anyone can just take a look at any sleeping animal to realise that sleep is designed to suspend the ambiguousness that there is in the body’s relation to itself, namely the deriving of jouissance therefrom.” Jacques Lacan, …or Worse: The Seminar of Jacques Lacan, Book XIX (Cambridge: Polity Press, 2018), 193. 

  2. Susan Stryker and Stephen Whittle, The Transgender Studies Reader (London: Routledge, 2006), 10. 

  3. To be a bit belabourious, in Lacan’s infamously tedious Seminar XX “sexuation graphs”, he defines man as he whose existence has an exception, a fantasised exception to the rule of castration, and he relates this through Freud’s story of the Primal Father/Primal Horde, in which a primeval band of brothers come together to kill their father for monopolising all the women. Integral to Lacan’s man is the latent presence of this myth of there being one whose cock is always good for it, and everyone knows it. So, he perhaps (this is kind of in Seminar XIX but I’m really stretching it) is like a set which doesn’t include itself—the set itself stands apart from its aggregate, much like that primal father. The set of all men who have killed their father because he was too chad. 

  4. Jacques Lacan, Le séminaire de Jacques Lacan. Livre XX, Encore: 1972-1973. Ed. Jacques-Alain Miller (Paris: Seuil, 1975), 68. 

  5. Andrea Long Chu, Females (London: Verso Books, 2019), 12-13. 

  6. I’m thinking of you, Eva Birch! 

Cover image: Sacrifice (halter neck), Aodhan Madden.