Levi-Strauss' approach arose, fundamentally, from the philosophy of Hegel who explains that in every situation there can be found two opposing things and their resolution; he called these "thesis, antithesis, and synthesis." Levi-Strauss argued that, in fact, cultures have this structure. He showed, for example, how opposing ideas would fight and also be resolved in the rules of marriage, in mythology, and in ritual. This approach, he felt, made for fresh new ideas. He stated:
His work in South America is his best known. Early on he showed there are "dual organizations" throughout Amazon rainforest cultures, and these "dual organizations" represent opposites and their synthesis. For instance, Gê tribes of the Amazon were found to divide their villages into two halves, which were rivals; however, the members of opposite halves married each other. This illustrated two opposites in conflict and also resolved; that is, it was the classical Hegelian trio of thesis, antithesis, and synthesis. (See below for more detail.)
Such was the case in many aspects of life. Culture, he said, for example, has to take into account both life and death and needs to have a way of mediating between the two. Mythology (see his several-volume Mythologies) unites opposites in diverse ways.
Three of the most prominent structural anthropologists are Lévi-Strauss himself and the British neo-structuralists Rodney Needham and Edmund Leach, the latter being the author of such essays as "Time and False Noses" [in Rethinking Anthropology]. In this essay, Edmund Leach sought an explanation of why human societies have solemn or sacred occasions, such as the Christian celebration of Christmas, followed in a short time by their opposite: a taboo-breaking and "profane" celebration such as New Year's.
Levi-Strauss applied this distinction in his search for the mental structures that underlie all acts of human behavior: Just as we are unaware of the grammar of our language while we speak, he argues, we are unaware of the workings of social structures in our daily lives. The structures that form the "deep grammar" of society originate in the mind and operate in us unconsciously (albeit not in a Freudian sense).
Another concept was borrowed from the Prague school of linguistics, which employed so-called binary oppositions in their research. Roman Jakobson and others analysed sounds based on the presence or absence of certain features, such as voiceless vs. voiced. Lévi-Strauss included this in his conceptualization of the universal structures of the mind. For him, opposites are at the basis of social structure and culture.
In his early work he argued that tribal kinship groups were usually found in pairs, or in paired groups that both oppose one another and need one another. For example, in the Amazon basin, two different expanded families would build their houses in two facing semi-circles that together make up a big circle. He showed too that the cognitive maps, the ways early folk categorized animals, trees, and so on, were based on a series of oppositions.
Later in his most popular work, The Raw and the Cooked, he described the widely dispersed folk tales of tribal South America as all related to one another through a series of transformations—as one opposite in tales here changed into another opposite in tales there. For example, as the title implies, raw becomes its opposite cooked. These particular opposites (raw/cooked) are symbolic of human culture itself, in which by means of thought and labor, raw materials become clothes, food, weapons, art, ideas. Culture, explained Lévi-Strauss, is a dialectic process: thesis, antithesis, synthesis.
Other influences came from Émile Durkheim and Marcel Mauss. While Durkheim thought that taxonomies of the natural world are collective in origin (the "collective conscious"), meaning that social structures influence individual structures of cognition, Levi-Strauss proposed the opposite, arguing that it is the latter that give rise to the former. Social structures mirror cognitive structures, meaning that patterns in social interaction can be treated as manifestations of cognitive structures. While structural-functionalists looked for structures within social organisation, structuralism therefore seeks to identify links between structures of thought and social structures. The possibly most significant influence on structuralism came from Mauss' The Gift. In his seminal work, Mauss argued that gifts are not free but rather create an obligation to reciprocate. Through the gift, the givers give part of themselves, implying that the gift is imbued with a certain power that compels the recipient to reciprocate. Gift exchanges play therefore a crucial role in creating and maintaining social relationships by establishing bonds of obligations. The gift is therefore not merely physical but also has cultural and spiritual properties. It is a "total prestation" as Mauss called it, as it carries the power to create a system of reciprocity in which the honour of both giver and recipient are engaged. Social relationships are therefore based on exchange; Durkheimian solidarity, according to Mauss, is best achieved through structures of reciprocity and related systems of exchange. Levi-Strauss took this idea and postulated three fundamental properties of the human mind: a) people follow rules; b) reciprocity is the simplest way to create social relationships; c) a gift binds both giver and recipient in a continuing social relationship (Layton, 1997:76).
The structures are universal; the contents will be culturally specific. Based on this concept, he argued that exchange is the universal basis of kinship systems, the structures of which would depend on the type of marriage rules that are applied. Because of its strong focus on vertical social relations, Levi-Strauss' model of kinship systems came to be called alliance theory.
Levi-Strauss' model attempted to offer a single explanation for cross-cousin marriage, sister-exchange, dual organization and rules of exogamy. Marriage rules over time create social structures as marriages are primarily forged between groups and not just between the two individuals involved. When groups exchange women on a regular basis they marry together, with each marriage creating a debtor/creditor relationship which must be balanced through the "repayment" of wives, either directly or in next generation. Levi-Strauss proposed that the initial motivation for the exchange of women was the incest taboo, which he deemed to be the beginning and essence of culture as it was the first rule to check natural impulses; and secondarily the sexual division of labour. The former, by prescribing exogamy, creates a distinction between marriageable and tabooed women and thus necessitates a search for women outside one's own kin group ("marry out or die out"), which fosters exchange relationships with other groups; the latter creates a need for women to do "women's tasks". By necessitating wife-exchange arrangements, exogamy therefore promotes inter-group alliances and serves to form structures of social networks.
Levi-Strauss also discovered that a wide range of historically unrelated cultures had the rule that individuals should marry their cross-cousin, meaning children of siblings of the opposite sex - from a male perspective that is either the FZD (father's sister's daughter) or the MBD (mother's brother's daughter). Accordingly, he grouped all possible kinship systems into a scheme containing three basic kinship structures constructed out of two types of exchange. He called the three kinship structures elementary, semi-complex and complex.
Elementary structures are based on positive marriage rules that specify whom a person must marry, while complex systems specify negative marriage rules (whom one must not marry), thus leaving a certain amount of room for choice based on preference. Elementary structures can operate based on two forms of exchange: restricted (or direct) exchange, a symmetric form of exchange between two groups (also called moieties) of wife-givers and wife-takers; in an initial restricted exchange FZ marries MB, with all children then being bilateral cross-cousins (the daughter is both MBD and FZD). Continued restricted exchange means that the two lineages marry together. Restricted exchange structures are generally quite uncommon.
The second form of exchange within elementary structures is called generalised exchange, meaning that a man can only marry either his MBD (matrilateral cross-cousin marriage) or his FZD (patrilateral cross-cousin marriage). This involves an asymmetric exchange between at least three groups. Matrilateral cross-cousin marriage arrangements where the marriage of the parents is repeated by successive generations are very common in parts of Asia (e.g. amongst the Kachin). Levi-Strauss considered generalised exchange to be superior to restricted exchange because it allows the integration of indefinite numbers of groups (cf. Barnard and Good, 1984:96). Examples of restricted exchange are found in e.g. Amazonia. These tribal societies are made up of multiple moieties which often split up, thus rendering them comparatively unstable. Generalised exchange is more integrative but contains an implicit hierarchy, as e.g. amongst the Kachin where wife-givers are superior to wife-takers. Consequently, the last wife-taking group in the chain is significantly inferior to the first wife-giving group to which it is supposed to give its wives. These status inequalities can destabilise the entire system or can at least lead to an accumulation of wives (and in the case of the Kachin also of bridewealth) at one end of the chain.
From a structural perspective matrilateral cross-cousin marriage is superior to its patrilateral counterpart; the latter has less potential to produce social cohesion since its exchange cycles are shorter (the direction of wife exchange is reversed in each successive generation). Levi-Strauss' theory is supported by fact that patrilateral cross-cousin marriage is in fact the rarest of three types. However, matrilateral generalised exchange poses a risk as group A depends on being given a women from a group that it has not itself given a women to, meaning that there is a less immediate obligation to reciprocate compared to a restricted exchange system. The risk created by such a delayed return is obviously lowest in restricted exchange systems.
Levi-Strauss proposed a third structure between elementary and complex structures, called semi-complex structure or Crow-Omaha system. Semi-complex structures contain so many negative marriage rules that they effectively come close to prescribing marriage to certain parties, thus somewhat resembling elementary structures. These structures are found amongst e.g. the Crow Nation and Omaha Native Americans in the United States.
In Levi-Strauss' order of things, the basic building block of kinship is not just the nuclear family, as in structural-functionalism, but the so-called kinship atom: the nuclear family together with the wife's brother. This "mother's brother" (from the perspective of the wife-seeking son) plays a crucial role in alliance theory, as he is the one who ultimately decides whom his daughter will marry. Moreover, it is not just the nuclear family as such but alliances between families that matter in regard to the creation of social structures, reflecting the typical structuralist argument that the position of an element in the structure is more significant than the element itself. Descent theory and alliance theory therefore look at two different sides of the same coin: the former emphasising bonds of consanguinity (kinship by blood), the latter stressing bonds of affinity (kinship by law or choice).
The British brand of structuralism was mainly espoused by Rodney Needham and Edmund Leach, who were both critical towards the structural-functionalist perspective and who drew on Levi-Strauss as well as Arthur Maurice Hocart. However, they also found grounds for critiquing Levi-Strauss. Leach, who in stark contrast to Levi-Strauss was more concerned with researching people's actual lives than with the discovery of universal mental structures, found that the latter's analysis of the Kachin contained serious flaws. According to Leach, Levi-Strauss' project had been overly ambitious, meaning that his analyses were too superficial and the available data treated with too little care. While part of his analysis of the Kachin was simply based on incorrect ethnographic information, the rest reflected Kachin ideology but not actual practice.
In theory, Kachin groups were supposed to marry in a circle ideally consisting of five groups. In reality, the system was strongly imbalanced with built-in status differences between superior wife-givers and inferior wife-takers. Levi-Strauss had incorrectly assumed that wife-takers would be of higher rank than wife-givers; in reality, it was the other way round, and the former usually had to make substantial bridewealth payments to obtain wives. Overall, some lineages would accumulate more wives and material wealth than others, meaning that the system cannot be said to be driven primarily by reciprocity. In actual reality, the marriage system was quite messy and the chance of it breaking down increased with the number of groups involved. In generalised exchange systems, the more groups there are the more complex it becomes to keep track of all transactions and to ensure that all wife-givers will eventually be on the receiving end, an issue that Levi-Strauss had already foreseen. He thought that in practice there will be competition for women, leading to accumulation and therefore asymmetries in the system. According to Leach, in Kachin reality instabilities arose primarily from competition for bridewealth. Men sought to get the maximum profit in forms of either bridewealth or political advantage out of the marriage of their daughters. Levi-Strauss had only accorded a symbolic role to marriage prestations, effectively overlooking their significance within the system. Leach argued that they are also (or even primarily) economic and political transactions, and are frequently connected to transfers of rights over land, too.
Kinship is therefore not an isolated domain but linked to economic and political structures. Marriage exchanges need to be analysed within their wider economic and political context rather than in isolation, as Levi-Strauss tended to do. Leach charged the latter with neglecting the effects of material conditions on social relations. He also challenged the claims to universality made by Levi-Strauss about the model, doubting whether structures generated by marriage rules would be the same in different social contexts.
By the late 1970s/early 1980s the heyday of alliance theory were over. With the advent of postmodern, interpretive-hermeneutic thought, structuralist and functionalist theories went out of fashion. However, there were also a number of internal incoherences and a range of intrinsic limitations that reduced its appeal.
By overstressing the structural significance of affinal ties, alliance theory effectively neglected the importance of descent and genealogical ties. Some societies (e.g. African tribal societies) employ descent as the primary organizational principle. In others, alliances are of primary significance, as in e.g. many Southeast-Asian societies and amongst Amazonian tribes; and still others place emphasis on both. The Yanomamö fit very well into the alliance theory mold while the Tallensi or Azande do not. Holy (1996) pointed out that some Middle-Eastern societies cannot be conclusively explained by either descent or alliance theory. Critics also saw weaknesses in Levi-Strauss' methods, in the fact that he looked for ideal structures, thereby neglecting the reality and complexity of actual practices. On the other hand, though, his model was ironically too powerful. As Kuper (1988:223) pointed out, if the structures of the mind really are universal and Levi-Strauss' model is correct, then why is it that not all human societies act accordingly and structure their kinship systems around alliances and exchanges? A central assumption of his was that exchange is the universal form of marriage, but there could be other significant factors. And even if reciprocity was the primary principle that underlies marriages, the return does not have to be in kind but could take other forms (such as money, livestock, services or favours of various kinds). Also, social cohesion through reciprocity does not have to rest primarily on the exchange of women. Mauss' definition of the gift showed that different cultures use all kinds of gifts to create and maintain alliances. Feminists in particular took offense at Levi-Strauss' claim that the underlying principle according to which all societies work is the exchange of women by men, who dispose of them as if they were objects. Others, for example Godelier, critiqued structuralism's synchronic approach that led it to be essentially ahistorical.
Marxists shifted the attention within anthropology from an almost exclusive preoccupation with kinship to an emphasis on the economic dimension. For them, social structures were primarily shaped by material conditions, property relations and class struggles.
Finally, a great weakness of structuralism is that its main propositions were not formulated in a way so that they could be subject to verification or falsification (cf. D'Andrade, 1995:249; Barnes, 1971:165-171). Levi-Strauss did not develop a framework that could prove the existence of his concept of the fundamental structures of human thought but simply assumed them to be there, an unfortunate mistake considering that this concept underpinned all of his work. Consequently, it was comparatively easy for post-structuralists such as Derrida to simply reject this notion.
Other weakness of structurlism are; 1.) Static, ahistorical nature of theory (Seymour-Smith 1986) 2.) Theory does not account for human individuality 3.) Theory does not account for independent human acts 4.) Theory does not address dynamic aspects of culture