Essay: Rebecca Hillon kinship

From the Exchange of Women to Sexual Difference

The etymology of the word ‘patriarchy’ defines an order in which the father is the sole ruler. This is inexact from the perspective of feminist theory; the societies that feminist theorists designate as patriarchal are fundamentally sustained by alliances between groups of men. That is, they are societies in which bonds between men are the privileged social bonds, and these alliances allow men to dominate women. In This Sex Which Is Not One, Luce Irigaray suggests that women are not only marginalised by homosocial bonds between men; they are excluded from participating in these relationships as subjects. While women do not function as subjects in patriarchal systems, Irigaray argues that they are fundamental to men’s homosocial bonds, they are like objects that men exchange with one another to sustain their inter-subjective relationships.

The conceptualisation of patriarchy as a system in which women are exchanged by men is indebted to Claude Lévi-Strauss’ transcultural theory of alliance in his monumental work The Elementary Structures of Kinship, first published in French in 1949. In a structuralist argument that synthesizes a vast amount of Western anthropological research, Lévi-Strauss argues that all human cultures are founded on the exogamous exchange of women between men through marriage. His theory rests on two linked principles: (1) the prohibition of incest and (2) gift giving. For Lévi-Strauss, the incest taboo is not motivated by the fear of moral transgression, or a potential biological danger associated with consanguineous marriage. The taboo is fundamentally about facilitating exogamous relationships between men. In other words, the prohibition on incest compels previously unrelated men to form alliances with one another. Their alliances are established by exchanging gifts, and the most precious gifts are women, who are ‘valuables par excellence from both the biological and social point of view’. For Lévi-Strauss, the basis of marriage is much less a union between a man and a woman, than the formation of an alliance between previously unrelated groups of men. It makes a society of men. The importance of exogamous exchange cannot be overstated. It is the ‘archetype for all other exchange relations based on reciprocity’ and ‘… it provides the fundamental and immutable rule ensuring the existence of a group as a group’.

Lévi-Strauss is insistent that exchange is at the origin of all marriage, and that the incest prohibition is ‘a universal and fundamental rule’. In considering the kinship system of his own society in France in the late 1940s, he says that the incest taboo divides women between the categories of prohibited spouse and permitted spouse. A man chooses his wife from the permitted group of women.

Where Lévi-Strauss claims universality for his theory, Irigaray’s 1977 engagement with Lévi-Strauss is more circumscribed. She focuses on his theory’s implications for the systems of thought and societies that are called western. Irigaray is silent about the tremendous distortions and violence of western anthropological studies of so-called ‘primitive’ societies and the imbrication of this knowledge production in the world-wide disordering of the colonial project. To this 2022 reader of This Sex Which Is Not One, the silence of her text is jarring. To be clear, what jars is not that Irigaray makes claims about the worlds of non-western peoples, because her text does not do this; what is troubling is the failure of her text to acknowledge that the production of western research is deeply implicated in the extractive and genocidal destructions of the colonial project.

While Irigaray’s engagement with Lévi-Strauss does not acknowledge the intimate entwinement of western thought in the colonial project, her reading offers a brilliant analysis of Lévi-Strauss’ theory of kinship. She suggests that it can be read as a theory of patriarchy that describes the objectification and appropriation of women, signs, and what is called nature in western thought and culture. This ordering of the world is alienated from the earth and from what it means to be living. Irigaray does much more than analyse this alienation and diagnose its continuity in the ongoing devastation of what is called nature; she elaborates suggestions for people raised in the patriarchal norms of western culture about ways to think and live differently. For her, this demands a thinking of sexual difference.

Thinking sexual difference is an immense task and the primary concern of all Irigaray’s works since her pathbreaking monograph of 1974, Speculum of the Other Woman. In An Ethics of Sexual Difference, Irigaray argues that this undertaking requires nothing less than ‘a revolution’ in western thought and life. Sexual difference is a critical project of diagnosing sexed hierarchy. The thinking of sexual difference is also and fundamentally a generative task that strives to transform western thinking and relations to life through the elaboration of a non-hierarchical sexuate philosophy. Many of Irigaray’s elaborations of sexual difference are posited through the close reading and transvaluation of texts from the western philosophical canon. Her reading of Lévi-Strauss in This Sex Which Is Not One is one instance of this life-long project.

This essay focuses on Irigaray’s appropriation of Lévi-Strauss to describe western patriarchy and the implications of her philosophy of sexual difference for rethinking western kinship. Irigaray’s postulation of non-hierarchical sexual difference does not abolish the dominant western model of kinship. It does, however, profoundly modify its structuration so that the exchange of women would no longer be possible. In short, Irigaray argues for an irreducible interval between masculine and feminine subjects, which would allow each sex to enter alliances with another sex and to remain as a specific sexuate subject for himself or for herself. I argue that an attentive reading of Irigaray also reveals the interval as a foundational threshold for queer and trans subjects in relation to themselves and in relationships with others. The interval must be respected in the alliances between feminine subjects, between masculine subjects, in the relations that queer and nonbinary subjects make with other sexed subjects and between woman and man.

Irigaray’s engagement with Lévi-Strauss is both a critique and an appropriation of his theory for the feminist purpose of articulating the key features of western patriarchy. Her complex argument blends Lévi-Strauss with Marx’s famous analysis of the status of the commodity in capitalism. Irigaray’s reading of Marx with Lévi-Strauss suggests that woman is a ‘like’ a commodity. The claim that woman is like a commodity is analogical. To say that her argument is based on analogy between woman and commodity is to acknowledge that while there are commonalities between the status of a commodity and the status of woman, there is also a divergence between them.

Situations in which people are rendered as commodities in the strict sense are not addressed by Irigaray. In the monumental crime of slavery people are commodified. Saidiya Hartman describes slavery as ‘the ghost in the machine of kinship’ in her genre-defying monograph, Lose Your Mother: A Journey Along the Atlantic Slave Route. For Hartman, ‘the most universal definition of the slave is the stranger.’ The slave is ripped‘… from kin and community, exiled from one’s own country, dishonored and violated, the slave defines the position of the outsider. She is the perpetual outcast, the coerced migrant, the foreigner, the shamefaced child in the lineage.’ This ‘ghost in the machine’ haunts all thinking on kinship.

The concept of ‘woman’ in This Sex Which Is Not One should be read to describe signs of woman and the feminine in western discourse. Irigaray’s ‘woman’ can also be taken up to think about cis women, trans women and men, queers, nonbinary people, and cis men located in the feminine position of object of exchange between men. The concept of ‘man’, the ‘subject’ and ‘men’ in Irigaray’s This Sex Which Is Not One, should be read as signs in western discourse that can be deployed to consider cis men, cis women, trans men, trans women and nonbinary people who take up the masculine position in the patriarchal system. At this point in my essay, the sex of ‘the subject’ and of ‘woman’ in Irigaray’s account of the traffic in women would appear to be determined by positions emanating from the system of patriarchy rather than biological sex. And Irigaray’s figurations of woman and man appear to be congruent with Judith Butler’s signature theory of gender as performance, in which, famously, gender is ‘what you do’, rather than the anatomical sex of your body. Irigaray’s This Sex Which Is Not One does have implications for trans, queer, and feminist thinking about all sorts of bodies functioning like subjects and objects in the system of patriarchal exchange. But her argument diverges from the performative theory of gender elaborated by Butler and her many followers, because of Irigaray’s insistence on the hidden but fundamental importance of the maternal function of bodies with wombs in the hierarchical distributions enacted by patriarchy. For Irigaray, the secret motivation for the traffic in women, the very motivation of patriarchy, is driven by the patriarchal desire to control the maternal. This means that while woman and the feminine are signs that can be attributed to all sorts of bodies, woman and the feminine overwhelmingly tend to be attributed to bodies that are thought to have the potential to birth children.

What is the maternal? Irigaray describes the maternal as a reproductive and functional aspect of women’s bodies. The maternal should be understood in terms of pregnancy, giving birth, and breast feeding; it also extends to other forms of childcare. There are essential functions of mothering that can only be carried out by people with wombs that gestate a foetus and birth a little human, and there are some maternal functions that can be carried out by partners, fathers, and other kin. How to designate the raising of children in institutions where stolen children, adoptees, and orphans were and are still raised by nuns, priests, employees of the state, and private institutions? What about carers working in childcare centres and people who work as au pairs? And what about the unpaid labour of nannies in colonial subjection and slavery? (Ryan Gustafsson’s parsing of the ways in which transnational adoptees make kin with one-another through being-curious, further complicates the manifold senses of maternal care and child raising). The distinctions between these workers, the maternal care of mothers and people raising themselves among peers are very complex, and I do not claim resolve them. In contrast to mothers and family members raising their own children, most care workers are paid wages and the children are not their kin. As is well known, childcare workers and nannies are among the lowest paid workers in Australia and in many patriarchal societies. This is presumably because of the proximity of this work to the maternal functions that emanate directly from the reproductive aspects of the bodies of people with wombs. In Sexes and Genealogies Irigaray says the fact that mothers are unpaid is telling. The maternal is the unacknowledged substratum of western patriarchy and capitalism. Without the labour of the maternal, society could not exist.

The awesome power of maternity is downplayed and hidden in western patriarchy. To return to Lévi-Strauss, women are described as ‘valuables par excellence from the biological and social point of view.’ This framing reduces women’s reproductive functions to the status of resources for men. Exogamous marriage is the way that groups of men control and contain the maternal.

Irigaray argues that in this system, woman is the instrument for the reproduction of society: she reproduces children, she cares for them, and she gives care to men. She cannot exist for herself, and her children carry the name of her husband. They are his.

As mother, woman remains on the side of (re)productive nature and, because of this, man can never fully transcend his relation to the ‘natural.’ His social existence, his economic structures and his sexuality are always tied to the work of nature: these structures thus always remain at the level of the earliest appropriation, that of the constitution of nature as landed property, and of the earliest labor, which is agricultural. But this relationship to productive nature, an insurmountable one, has to be denied so that relations among men may prevail. This means that mothers, reproductive instruments marked with the name of the father and enclosed in his house, must be private property, excluded from exchange. The incest taboo represents this refusal to allow productive nature to enter into exchanges among men. As both natural value and use value, mothers cannot circulate in the form of commodities without threatening the very existence of the social order. Mothers are essential its (re)production (particularly inasmuch as they are [re]productive of children and of the labor force: through maternity, child-rearing, and domestic maintenance in general). Their responsibility is to maintain the social order without intervening so as to change it.

In some respects, this Irigarayan account of the position of the mother is dated. In the wake of second wave feminism, many mothers now live independently of men and have autonomy in their relations with men – though these changes are both partial and contingent. It is only in very recent history in the west that a woman’s legal rights to custody of her children in divorce has been asserted and women’s autonomy and their rights to their children remain controversial. In the United States, the recent overturning of Roe vs Wade is a terrifying demonstration of the endurance of patriarchy and the masculine desire to control and dictate the maternal conditions of life.

In addition to making explicit the fundamental violence of patriarchal efforts to contain and appropriate the maternal and its flow on effects for the feminine and people with wombs, Irigaray’s reading of Lévi-Strauss elaborates the following features of patriarchy:

  • Women do not exist independently for themselves, they are defined exclusively in relation to men. In this system, woman is either a wife, a sex worker, a mother, or a virgin.
  • Women do not exist as a community among themselves because they are defined by their relationships to men.
  • Women have no intergenerational existence in the kinship system, which is patrilineal.
  • The interests and values of society emanate from the patriarchal system of exchange.
  • Only masculine desire counts, and women are allowed no desire on their own terms.
  • The most valued social ties are homosocial bonds between men.
  • Men’s desire for women is played out in the context of their relationships with other men (Irigaray’s argument partly anticipates Eve Sedgwick’s queer analysis of the foundational status of male homoeroticism to western modernity).
  • The ‘commodity’ and ‘woman’ have senses that exceed the human to designate the commodification of what is called is called nature.

Irigaray’s appropriation of Lévi-Strauss for the purpose of describing patriarchy is also a feminist revaluation of his terms, as Gail Schwab has pointed out. She draws attention to suffering of women and girls: ‘What Lévi-Strauss calls exogamy, … [Irigaray] calls ‘the theft and violation of the daughter’s virginity and the use of her virginity for commerce between men, including religious commerce …’ Another way that Irigaray reconfigures the exogamous society theorized by Lévi-Strauss is by calling it the order of ‘one sex.’ The expression ‘one sex’ makes explicit, not only that patriarchal society is made up of subjects of one sex, the sex of man, but also that man’s sex is rigid and monological. To be a subject is to strive to conform to this phallic and active figure of man.

Irigaray’s critical description should not be read as totalising. If patriarchy were totalising, she could not speak against it – indeed no feminist could analyse patriarchy if she were entirely consumed by the system. Nonetheless, Irigaray is sometimes misread in this way. This is presumably because some readers mistake her quotations of Lévi-Strauss and other male philosophers for positions that she endorses as her own. Her texts are polyphonic, and readers need to pay close attention to the different voices at work in her writing and to her use of irony. This is especially pertinent in a work such as This Sex Which is Not One. She mimics the language of patriarchy, which is precisely a discourse of totalisation. This is the opening paragraph of ‘Women on the Market’:

The society we know, our own culture, is based upon the exchange of women. Without the exchange of women, we are told, we would fall back into the anarchy (?) of the natural world, the randomness (?) of the animal kingdom. The passage into the social order, the symbolic order, into order as such, is assured by the fact that men, or groups of men, circulate women among themselves, according to a rule known as the incest taboo.

The question marks are Irigaray’s, otherwise is she is blending quotation and close citation of Lévi Strauss with minimal modification to his language. When she rewrites his universalist theory to draw out its hierarchical and violent implications, she deploys universalizing frames in her theory. But she also teaches that there are elsewheres, excesses to the system. For Irigaray, the excesses of the system are fundamental to her rewriting of the traffic in women into a teaching of sexual difference. (It is hardly news in Indigenous civilizations that there are other worlds. Gladys and Jill Milroy of the Palyku teach that trees are their family, and that caring for life on this continent means living in respect of Indigenous relational worlds and Country. This teaching addresses all peoples and all living beings, Indigenous and non-Indigenous.)

I argued that woman is a sign in patriarchal thought and that woman can be applied to the bodies of women and other humans, as well as what is called nature. Woman is ‘… never anything but the locus of a more or less competitive exchange between two men, including the competition for the possession of mother earth’. I also claimed that woman is intimately related the reproductive functions of engendering children. In patriarchy, this means that while woman and the feminine are signs that can be attributed to all sorts of bodies, woman and the feminine are overwhelmingly attributed to bodies that have the potential to birth children. In patriarchal thought woman and the feminine are defined in terms of their subordinate relationship to the masculine subject – the feminine and woman have no autonomous existence. The binding of the concepts of woman and the feminine into a subservient relationship with the masculine subject needs to be qualified; woman and the feminine are not consumed in their patriarchal functions. Woman and the feminine also remain elsewhere. When Irigaray makes this claim, she is not contradicting herself; she is deploying a different voice, a revolutionary voice that affirms woman and the feminine. The excesses and elsewhere of the feminine are fundamental because they are beyond patriarchy, and they are the very places in which thinking and living differently is elaborated.

For sexual difference to take place, what needs to be done? The western patriarchal system needs to be dismantled and this means that there needs to be an opening to other ways of thinking and living.

  • Woman’s subjectivity must be elaborated autonomously from the masculine. She can longer serve as man’s opposite, complement, or be reduced to sameness.
  • Patriarchal thought valorises the position of the mother, but she is only conceived as the ground of the masculine subject. The mother must be thought beyond serving as the ground of her sons.
  •  While the mother already figures in patriarchal representation, the creativity of her bringing of life into the world is occluded. Her gift demands respect and acknowledgment, a gift for which there can be no reciprocity.
  • Woman’s subjectivity is not reducible to the maternal, she must exist as a sexed subject for herself, and in relation to sexed human others in carnal and non-carnal contexts.
  • Relationships to the maternal must be articulated as foundational features in the emergence of both masculine and feminine subjectivity. The maternal does not function in the same way for masculine and feminine subjects. For trans and nonbinary folk, the maternal is different again, both for trans and nonbinary offspring, and for trans and nonbinary people who birth and raise children.
  • There must be a thinking of women’s community and of mother-daughter relations in which women are not reduced to diabolical rivals competing for masculine attention. In an ethics of sexual difference women among themselves will not relate to each other in the same way as they do in patriarchy.
  • There must be a radical transformation of the relation to Nature. Where Nature is commodified for man’s consumption in western capitalist patriarchy, Irigaray suggests that Nature must be affirmed as the non-totalisable source of all life.

Sexual difference is not an inversion where the feminine is on top and the masculine is on the bottom; sexual difference is a sustained effort to think a non-hierarchical relationship between the sexes. This requires marking the difference between the sexes. The generative sense of sexual difference as the affirmation of a non-hierarchal relationship between the masculine and the feminine is sometimes misread as nothing but a proscription for a happy heterosexuality. This is wrong, Irigaray argues for two kinds of subjects who are irreducible to one another. Her argument has profound implications for heterosexuality, homosexuality, and queerness. For Irigaray, human nature is made up two sexes. In later work, Irigaray responds to criticism and to questions from her students influenced by queer theory and trans studies. She clarifies that what is needed is a society in which there are ‘at least two sexes.’ Jules Gill-Peterson, a trans feminist of difference, describes a conversation with Irigaray while Gill-Peterson was attending Irigaray’s Bristol seminar. Gill-Peterson and another student asked Irigaray her position on trans subjectivities. According to Gill-Peterson’s recollection:

“I never meant that there can only be two sexes,” she offered, turning to look at us with what I had to interpret as feeling. “I would be unhappy if those who have read my work use it for such ends. We can say that there may be ‘at least two’ sexes. My point is that we have only a single sex at this time.”

In the ‘at least two’ of sexual difference, the masculine would no longer be ‘one sex.’ There would a multiplicity of the masculine, a multiplicity of the feminine, and a multiplicity of genderqueer and trans subjectivities. These multiplicities do not collapse into a big multitude of what Gilles Deleuze and Felix Guattari call ‘a thousand tiny sexes.’ Multiplicity must be thought from the irreducible difference of sexual difference that engenders at least two sexes.

The different sexes (multiplicities) must be affirmed in non-hierarchical relationships with one another, and the concept of non-hierarchical relation is central to the affirmative sense of sexual difference. This threshold has many names in Irigaray’s writing, including the interval, difference, the in-between, the remainder and the space of silence. What is this threshold of many names? The interval is both material and immaterial, spatial, and temporal, and beyond any effort at rigid definition. This living concept can be gestured at with language but remains beyond language. Irigaray’s thinking of the interval of sexual difference is a thinking of the myriad becomings of life. These becomings are both corporeal and incorporeal, both extensive and intensive, as I’ve explored elsewhere in The Interval and ‘Between Her and Her.’

In a culture of sexual difference in the affirmative sense, the interval marks a founding ethical interdiction for respectful relations between people of different sexes. The irreducibility of the interval means that one sex is never entirely consumable by another sex. This means that there is no consummation in coitus or in any other form of intersubjective intimacy. There is always a remainder between subjects. The remainders that are most irreducible are those between subjects of different sexes. In some works, Irigaray describes specifically feminine intervals; for instance, the lips and the mucous relate to woman’s body in relation to herself. Irigaray does not elaborate specifically masculine intervals, though I think that she would regard this as a task best left to men.

The interval cannot be overcome, and this remains the case in the most terrible of situations. When the vitality of the other is violated or destroyed by the one or by a murderous gang striving for mastery, the interval in remains in play. In a material sense a person or a people may be mutilated or dead but there remains the alterity of the others in time, and this difference can never be colonized or killed.

The interval is central to Irigaray’s thinking of Nature as non-totalisable. She elaborates on this in Through Vegetal Being, a 2016 epistolary collaboration with Michael Marder. Irigaray suggests that in meditation and in close reading of Patanjali’s Yoga Sutras she has learned to cultivate her senses in relation to different kinds of living beings. She says that in the cultivation of her senses she learns to share energy with other life forms, and she suggests that contemplation of and with living beings through all the senses can lead to a state of ecstasy. According to Irigaray, Patanjali teaches a process of mental internalization that can lead to state in which the subject and object distinction is abolished, such that, for instance, a tree and a woman merge. In contrast to Patanjali, for her, the beings do not merge, there is instead an ecstasy in which a tree and a woman remain in a state of duality. There is sharing and participation by remaining different. This mode of relation – interval – goes beyond the senses of touch, taste, smell, sound, and sight, though it arises from a silent letting be through these senses. This is a sensing that is invisible.

Irigaray’s vision of a world of sexual difference does not speak directly to the fate of the incest taboo that is central to Lévi-Strauss’s framework of kinship. Perhaps this limit will remain in place after patriarchy. If it does remain, the prohibition on incest will no longer function as part of an infrastructure that renders woman as an object of exchange.

In the coming of the ‘at least two’ of sexual difference, Lévi-Strauss’s conceptualisation of the gift is radically transformed. Where his system of kinship occludes the mother’s gift of life and appropriates her offspring for the homosocial economy, Irigaray’s world of sexual difference acknowledges the maternal gift. In sexual difference the mother’s offspring are not appropriated into a system of exchange as subjects and objects, nor are they possessions of the maternal. The mother’s offspring become independent of her as they grow up into sexed beings.

In sexual difference no one is commodified into an object of exchange between subjects. Instead, the gift designates the becoming of a sexed subject in her relation to another sexed subject, who is irreducible to her. Each subject is characterized by their rhythm of sexed becoming, their rhythm of giving. Between the subjects there is the interval, the condition of the integrity of sexed selfhood and of subjects becoming together in an encounter. Encounters between sexed subjects generate alliances without consummation and without mastery.

The interval of sexual difference has fundamental implications for rethinking human beings in relation to Nature and thinking relationality beyond the human. This open threshold situates human beings as participants in Nature, in a cosmos of living becomings which are never totalised.

Works Cited

Judith Butler, Gender Trouble: Feminist and the Subversion of Identity. Routledge: 1990.

Gilles Deleuze and Felix Guattari, A Thousand Plateaus translated by Brian Massumi. Minnesota University Press: 1987.

Jules Gill-Peterson, ‘The Miseducation of a French Feminist’. e-flux journal: 2021.

Ryan Gustafsson, ‘Curious Entanglements’. Sydney Review of Books: 2022.

Saidiya Hartman, Lose Your Mother: A Journey Along the Atlantic Slave Route. Serpent’s Tail: 2006.

Rebecca Hill, The Interval: Relation and Becoming in Irigaray, Aristotle and Bergson. Fordham University Press: 2012.

Rebecca Hill, ‘Between Her and Her: Place and Relations between Women in Irigaray and Wright’ Thinking Life with Luce Irigaray, edited by Gail Schwab. SUNY Press: 2020.

Luce Irigaray, Speculum of the Other Woman, translated by Gillian C. Gill. Cornell University Press: 1985.

–––, This Sex Which is Not One, translated by Catherine Porter. Cornell University Press: 1985.

–––, An Ethics of Sexual Difference, translated by Carolyn C. Burke and Gillian C. Gill. Cornell University Press: 1993.

–––, Sexes and Genealogies, translated by Gillian C. Gill. Columbia University Press: 1993.

Luce Irigaray and Michael Marder, Through Vegetal Being: Two Philosophical

Perspectives. Columbia University Press: 2016.

Luce Irigaray and Stephen D. Seely, ‘What Does it Mean to Be Living’ Philosophia vol.8, no. 2, pp. 1-12, 2018.

Claude Lévi-Strauss, The Elementary Structures of Kinship, translated by James Harle Bell and John Richard Von Sturmer. Beacon Press: 1969.

Gladys Idjirrimoonya Milroy and Jill Milroy, ‘Different Ways of Knowing: Trees are Our Family Too’ in Heartsick for Country: Stories of Love, Spirit and Creation edited by Sally Morgan, Tjalaminu Mia and Blaze Kwaymullina. Freemantle Press: 2008.

Gail Schwab, ‘Mothers, sisters, and Daughters: Luce Irigaray and the Female Genealogical Line in the Stories of the Greeks’ in Luce Irigaray and ‘the Greeks’, edited by Elena Tzelepis and Athena Athanasiou. SUNY: 2010.

Eve Sedgwick, Epistemology of the Closet. Harmondsworth, Penguin: 1991.

Published September 19, 2022
Part of Rewriting Kinship: The SRB and non/FictionLab have joined forces to commission new essays that reimagine kinship beyond its traditional framing. All Rewriting Kinship essays →
Rebecca Hill

Rebecca Hill lives in Narrm. She is Senior Lecturer in the School of Media...

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