1 This text has been taken from an article entitled, “Le symbolique et le religieux: analyse comparée de la formule canonique de Lévi-Strauss et du schéma L de Lacan” (The Symbolic and the Religious: A Comparative Analysis of Lévi-Strauss’ Canonical Formula and Lacan’s L Schema), published in Diacritica (Scubla 2009). We are grateful to Cristina Alvarez for allowing us to use a lightly edited version of the article here.
2 The original version had a double objective. The first objective was to supplement the work that we had devoted to the canonical formula of the myth in 1998. The purpose of this was to take into account, on the one hand, a new mathematical model of this formula, which had been subsequently proposed by Jack Morava and, on the other, the regular intellectual exchanges that had taken place between Lévi-Strauss and Lacan when the former was developing his formula, the full impact of which we had not previously gauged. The second objective was to present new arguments in favor of the idea that, in the work of Lévi-Strauss, the canonical formula represents an involuntary and implicit recognition of the principal theory of the École de sociologie française (French school of sociology). This was a theory of the primacy of the religious—a theory that structural anthropology has always refuted, although its formula can be seen to represent a resurfacing of the repressed.
3 The Elementary Structures of Kinship is, in fact, a war machine directed against The Elementary Forms of the Religious Life. By maintaining that the taboo of incest is merely the reverse side of a positive rule of exchange, and that the principle of reciprocity underlying exchanges is sufficient to form stable societies, Lévi-Strauss aims to show that the religious, which Durkheim places at the foundation of the social, is in reality superfluous. It has no greater reality than the phlogistics of old chemistry. The sacred, so dear to Durkheim has to be eliminated therefore, as does the hau, its Maori avatar. Mauss also needlessly turns to the hau, because he separates exchange—the principle behind the immediate synthesis of myself and the Other—into three obligations, which then appear falsely independent. The Savage Mind and Mythologiques pursue the same goal by, on the one hand, separating myth from rite and, on the other, by presenting ritual and sacrificial operations as a desperate attempt to unravel the classifications and careful distinctions of totemic and mythical thought that make societies coherent and the world intelligible. Far from being a generating principle of social and symbolic order, the religious constitutes a secondary, regressive element that is, fortunately, destined to fail.
4 Against this background, the significance of the canonical formula becomes clear: the veiled, but very real, recognition that structuralism is unable, in the end, to deny the intractability and transcendence of the religious. Indeed, paradoxically, Lévi-Strauss first applied his canonical formula, not to myths, but to headhunting and sacred royalty rites in his classes at the Collège de France. Furthermore, the very structure of the formula demonstrates the need to resort to a point of reference, which, far from being integrated into the structures of exchange and reciprocity, extends beyond them and encompasses them.
5 The text below is a small excerpt from the file. It shows that Lacan is more lucid in his reasoning than Lévi-Strauss in their quest to replace the religious with the symbolic. He suspects that this substitution will be to no avail. This is perhaps because the psychoanalyst, despite his atheism, never reneged on his Christian culture, while the anthropologist never overcame his aversion to the Jewish religious culture.
6 * * *
7 Lévi-Strauss . . . fears that, under the form of the autonomy of the symbolic register, a masked transcendence might reappear, for which, with all his affinities and personal sensitivities, he feels only fear and aversion . . . He does not want the symbol, even under the extraordinarily purified form in which he himself presents it, to simply be the reappearance of God in disguise. (Lacan 1978, 48)
8 For around two decades, Lévi-Strauss and Lacan appear to have sustained an amicable, intellectual relationship.  Their exchanges appear to have been one-sided, however, with the psychoanalyst clearly borrowing much from the anthropologist without exerting much influence in return.
9 Indeed, there are several concepts or theories that subsequently came to be associated with Lacan, which he owes to Lévi-Strauss. The notion of the “neurotic’s individual myth” and the idea that the subconscious is “structured like a language,” for example, both come directly from Lévi-Strauss’s 1949 article on “the effectiveness of the symbolic,”  which predates the principle of the signifier on the signified presented in his introduction to Mauss’s work.  Lacan’s taste for formalization may also have been encouraged, even stimulated, by The Elementary Structures of Kinship. The quadripartite structure of his L Schema, too, which set out to restructure the Oedipal triangle,  may have been inspired by the quaternary forms that abound in Lévi-Strauss’s work. Lacan’s debt to Lévi-Strauss is undeniable and he expressly acknowledges the fact, but he is never a servile imitator. Drawing from multiple sources, he takes in other people’s ideas and reformulates them in original ways.  It is therefore possible that this inventive spirit has, in turn, contributed to the development of Lévi-Strauss’s ideas or, in any case, that Lacan’s own speculations may have enlightened those of Lévi-Strauss, given that their work shared largely the same roots.
10 While this conjecture is plausible, it is not, however, firm evidence. While Lacan appears quite open to an anthropological perspective, Lévi-Strauss appears just as closed to a psychoanalytical one. Even though he presents it as one of his “three mistresses” (Lévi-Strauss 1955a, 49) in a famous page from Tristes Tropiques, the simple fact that he associates it with geology and Marxism demonstrates the purely academic nature of the recognition he affords it. His fundamental intellectualism is radically opposed to an approach that tends to subordinate the intellect to the affective. It is, therefore, highly significant that Lévi-Strauss, whether writing on kinship, totemism, or myth, directly challenges the author of Totem et tabou (Totem and Taboo) three times during his career [1967, 562–4; 1962a, 100–1; 1985, 243–59). For him, psychoanalysis is not a form of knowledge, but rather of mythology. At best, it might be an object of science. Anthropology has to take Freud’s thoughts on the Oedipus myth into account, but these thoughts are an “integral part” of the myth, and are simply a new transformational variant, obeying the same structural laws as the others (Lévi-Strauss 1958, 242). It is useful to compare analytical treatment to shamanic treatment but even then, the relationship is unequal. Shamanism helps to better understand psychoanalysis, but psychoanalysis does not really help to explain shamanism (Lévi-Strauss 1958, 201–2 and 217–26). As far as Lacan is concerned, Lévi-Strauss only refers to him once (1950, xx). This is at the start of their relationship and the reference is made “above all out of friendship” (Lévi-Strauss and Éribon 1988, 108), as he stated nearly forty years later.
11 Given these conditions, it is somewhat surprising to see that Lévi-Strauss ultimately relies on a technical aspect of Freudian theory—the theory of double traumatism —to substantiate his canonical formula of myth or to give us access, in other words, to the holy grail of the structural theory of mythology. We will review how this situation came about. The anthropologist was seeking a formula that would provide a law to determine all the variables of any myth. Through a process where the final stages are very difficult (or even impossible) to follow or reconstruct, he arrived at a formula that appears, to any attentive reader, to have just dropped out of the sky or been pulled out of a hat.  He deigned no more to explain how it came into being than he did how to use it. He does not give one example. Noting that the formula establishes a relationship of equivalence between two situations, he merely adds the following comment: “This formula becomes highly significant when we recall that Freud considered that two traumas (and not just one as is so commonly said) are necessary in order to produce the individual myth in which a neurosis consists” (1958, 253 ). Make of that what you will. 
12 Independent of its oracular tone, it is not just the scholarly reference to a little-understood aspect of Freud’s work that is striking about this passage. It is also the fact that it is coupled with a probable reference to Lacan’s lecture on the neurotic’s individual myth, which outlines a quadripartite model of mental illnesses and of the human subject, more generally, from which Lacan later developed the L Schema. This hypothesis of a subtle reference to Lacan, whose lecture was already renowned in Parisian intellectual circles, could also explain, at least in part, the elliptical nature of Lévi-Strauss’s statement.  With the anthropologist calmly confirming that a detour through psychoanalysis would doubtlessly “provide a more precise and rigorous formulation of the genetic law of myth”  (1958, 253), we can understand how, having drawn from the same source, the L Schema and the canonical formula appeared almost simultaneously in 1955.  The two models can be seen to represent the mental and cultural aspects of the same structure—the individual and collective faces of a single reality. The fact that the two were published simultaneously is not a coincidence but is, rather, the result of work carried out in parallel, and perhaps also an unspoken rivalry between the two models.
13 It is, nonetheless, impossible to know for certain whether this is the case just from studying the writings of Lévi-Strauss and Lacan. Fortunately, the minutes of a Société française de philosophie (French society of philosophy) meeting on May 26, 1956 substantiates our hypothesis and perhaps even dispels any remaining doubts. On that day, Lévi-Strauss made a presentation on “the relationships between mythology and ritual” before a select gathering of philosophers and anthropologists, including Dr. Lacan. He presented the bulk of the ideas that he went on to publish not long afterwards, in tribute to Jakobson, and which he returned to two years later in Anthropologie Structurale (1958, 257–66). During the meeting, Lacan made a long speech.  He felt that Lévi-Strauss had “retreated” from his 1955 article and expressed his astonishment that he had not used the very elaborate transformation formulae found within it. Lacan argued at his conference on the neurotic’s individual myth that he, himself, had almost immediately applied the formulae with great success in the case of the Rat Man.  Even if the description of the formula that he says he used does not entirely correspond to the standard formula, there is no doubt that it has the main features of it. “I went” he says, “so far as to be able to strictly formalize the case based on a formula provided by Claude Lévi-Strauss. According to this formula, a is initially associated with b, while c is associated with d and the two exchange partners in the second generation, but not without there being an irreducible residue remaining in the form of the negativation of one of the four terms, which correlates with the transformation of the group.”  With the exception of a few notations, we clearly find here the exchange of variables and the double torsion that characterize the canonical formula.
14 This declaration is surprising because it implies that Lacan was the first to use the canonical formula or, at least, its initial version. This is paradoxical as his conference dating from 1953 or even 1952, according to some sources, took place two or three years before the official presentation of the formula itself. Levi-Strauss, however, does not contest it any more than he contests the possibility of the formal explicit treatment of the ethnographic material that he had just presented. He says only that he had to abandon it as he was unable to do it justice in the time allotted to him.  This being the case, everything points to the probability that Lévi-Strauss had begun to trace the basic outline of his canonical formula in 1951/2 in his lectures on mythology at the École pratique des hautes études, and that Lacan had been following his progress. This is all the more likely given that, according to a psychoanalysis historian, our two structuralists plus Émile Benveniste had begun to meet regularly from 1951 with the mathematician Georges Guilbaud, founder of the Social Mathematics Center at the École pratique des hautes études, to work together on problems of formalization (Roudinesco 1993, 469). Although both Lévi-Strauss and Lacan kept very quiet about their collaboration with Guilbaud, it nevertheless lasted until the mid-1960s for the former and seemingly until the end of his life for the latter. There can, therefore, no longer be any doubt remaining that the canonical formula and the L Schema both come from the same intellectual place and from a network of mutual influences and interactions, which it would be very difficult, and perhaps also futile, to unravel. Beside their common characteristics, however, both models have original aspects, which call for a comparison that is both easy and productive to make.
15 The issue here is the status of what Lévi-Strauss termed symbolism and Lacan termed the symbolic (a term the anthropologist avoided putting to any substantive use).  We would like to demonstrate that this small difference in vocabulary corresponds, in fact, to a significant difference in meaning, and that this should be clearly identified in order to avoid any misunderstanding.
16 Lévi-Strauss begins with a daring intellectual feat. The term “symbolic function” generally refers to the ability to use signs or symbols or, in other words, to use things that allow us to refer to other things in their absence. This definition, which is particularly suited to language, is already far richer than it appears but Lévi-Strauss does not stop there. On the grounds that language is never a neutral medium but that it contributes to forging the image of the things that it enables us to describe, the anthropologist defines symbolic function as the ability that the human mind has to impose structural laws, usually unconsciously, to a formless material and particularly to the affective and impulsive aspects of the mind. Since language is common to all men, it immediately follows that there is a new definition of the unconscious, adopted by Lacan, as “a mediating term between myself and others” (1950, xxxi). All of that is well known, but extremely vague (most commentators pretend not to know this) because Lévi-Strauss, who never provides many examples in his great theoretical texts, does not present a single “structural law” in his 1949 article on “symbolic efficiency.” At best, he mentions laws that would be analogous to those of phonology. It is not until the mid-1960s that he provides the only precise example that we are aware of—that of the “culinary triangle,” developed through analogy with the vocalic triangle (1965).
17 That is not all. When Lévi-Strauss tried, during this fermenting of ideas period, to define his conception of symbolism (particularly in his introduction to Mauss’s work), he began by focusing symbolic function on language, then narrowed language down to communication,  and finally reduced communication to exchange and reciprocity, as though structural laws all led back to the laws of the kinship and alliance systems. In short, “symbolic function” and the “principle of reciprocity” are considered, in the end, to be two different names for one and the same thing. Admittedly, when he analyses dualistic organizations, he seems to first recognize the existence of a religious vertical axis, well attested in ethnography, which is quite distinct from the horizontal axis of exchanges. All his efforts, however, then tend to be focused on interpreting the vertical axis as a sort of secondary consequence of the horizontal one (1958, chapter VIII).
18 With Lacan, despite his Gongoric style, things are far clearer.  We have reproduced the L Schema below in its developed form as well as in its simplified version in the form of a Z. As the schema shows, the symbolic, far from being encompassed by reciprocity, actually opposes it. Indeed, we can see in the schema the two orthogonal axes discussed above. The o?o’ axis represents the relationship that Lacan termed “imaginary” because each of its terms is the mirror image of the other. This relationship is a relationship of double symmetry: that of communication, exchange, and reciprocity. The O–S axis is that of the symbolic. It crosses the former axis, governs it, and frames it. On the detailed diagram of the L Schema below, this transcendence of the symbolic is marked by the fact that O, representing the “capitalized Other,” is the only one of the four terms to have two arrows leading from it and, consequently, no arrows leading toward it. In the simplified diagram, we can see that because the o?o' axis is situated on the oblique line of the Z, the imaginary is immediately encompassed by the symbolic. Furthermore, it is interesting to note that the symbols o and o’ have been switched around here, as though to better show that the terms they designate are interchangeable.
Normal form (left) and simplified form (right) of Lacan’s L schema
Normal form (left) and simplified form (right) of Lacan’s L schema
19 All in all, the principle of reciprocity for Lacan, far from being the alpha and omega of human relationships, is subordinate to something more powerful.  His L Schema reveals and assumes the need to reintroduce the vertical axis of transcendence, which, when it is not simply refuted in Lévi-Strauss’s work, is sometimes implicit but never acknowledged. Everything takes place as though the psychoanalyst, while leaning heavily on structural anthropology, were revealing its insufficiencies and beginning a sort of insertion or reinsertion of the “elementary structures of kinship” into the “elementary forms of religious life” without leaving his own domain. This is a reintegration of one of Durkheim and Mauss’s cardinal arguments, which is one that Lévi-Strauss had thought that he could break free from. Lacan addresses things, in fact, from the perspective of the individual, but his structural analysis of the individual psyche sketches out a richer, and also no doubt more complete and accurate, description of the social than that of Lévi-Strauss.
20 It is true that there are many obscurities in the details of Lacan’s schema, and these are often aggravated, rather than clarified, by comments from its author and his followers. In the absence of any clear examples, we have long taken it, as with the canonical formula itself, for a sort of Baroque monument, like a characteristic representation of a type of preciosity that was highly popular in the middle of the last century in certain Parisian intellectual circles. It was only on studying Rousseau that we discovered the first convincing example of the L Schema, demonstrating that it is not an inconsequential construction, but a plausible representation of a structure that is actually at work in the life of man. The case of Rousseau is all the more interesting, for our present purposes, because he was a social theorist and political thinker as well as an analyst of the most intimate areas of human life. He is therefore able to contribute to bringing to life the preceding abstract considerations and to supporting, and even validating, them.
21 We know that, having had to abandon public readings of his Confessions, Rousseau then began to write another work aimed at exonerating him from the accusations leveled at him, whether these were real or imagined. Abandoning the notion of an account in the first person—a self-description of Jean-Jacques—he went on to compose three dialogues, entitled Rousseau, Judge of Jean-Jacques. In the dialogues, two characters, Rousseau and the Frenchman, compare the respective images they have of Jean-Jacques. A mad undertaking or an undertaking written by a madman? Certainly neither. Even if he sometimes mixes the real and the imaginary in his account of the persecution of the enemies of Jean-Jacques, the Dialogues is far from being a delusional work and is essential for understanding the fundamental principles of Rousseau’s political thought, as well as the nature of the social connection itself (Scubla 1992, 117 and 124).
22 We should limit ourselves here to the general architecture of the work. An autobiography is never a simple relationship of the self with the self, for it presupposes a mediation between the writing and the audience to which it is addressed. Dialogues is, however, based on a more complex form of mediation than that of Confessions. In Rousseau, Judge of Jean-Jacques, it is clearly not Jean-Jacques acting as judge of Jean-Jacques, nor Rousseau acting as judge of Rousseau, nor is it the writer acting as judge of man, for Rousseau does not appear here as the author but as one of the characters in the book. In the text, Jean-Jacques plays “the author of the books” opposing “the author of the crimes,” who his critics thought they saw in him. Dialogues is also different from Confessions in another way. Confessions was, in a sense, beneath publication, since Rousseau thought it preferable to read it himself in the hope of thus reaching out—in every sense of the word—to his audience more directly. Having learnt from this unsuccessful attempt, Dialogues was beyond publication, so to speak, in the sense that it did not address man, but God. We all know the anecdote recounted by Rousseau himself: despairing of never being able to present his contemporaries with the true portrait of Jean-Jacques, Rousseau called on divine judgment. He decided to place the manuscript of his text at the high altar of Notre-Dame in Paris in the hope that it might at least be seen by his earthly lieutenant, the King. Unfortunately, on the day that he had planned to carry out this solemn act, he caught sight of a barrier preventing access to the choir, which he had never noticed before. It was as though God himself were telling him of his refusal to hear him or of his invincible transcendence.
23 We have, here, four terms in all, and the relations between them correspond perfectly to the configuration of Lacan’s L Schema. Indeed, it is very easy to set out the basic structure of Dialogues on the schema in the form of a Z. Rousseau and the Frenchman, whose dialogues form the content of the book, communicate along the imaginary o?o’ axis and occupy opposite poles. Jean-Jacques, the subject of the book, is S, and God, the book’s target audience, is O. We can see even more clearly the religious character of the symbolic S?O axis on the diagram proposed by Michel Foucault in his excellent introduction to Rousseau, Judge of Jean-Jacques. The framework of his schema can be obtained by rotating Lacan’s schema  to the left, thus putting the imaginary relation in a horizontal position and, as a consequence, the symbolic relation in a vertical position. This arrangement then reveals a double symmetry. On the one hand, there is the symmetry of the two terms of the imaginary relationship represented by the characters in Dialogues and, on the other, the symmetry of the two structuring terms in the symbolic relationship, represented by God, situated at the top of the grid, and Jean-Jacques, such as he would be after death had finished with him. We cannot think of a better way to emphasize the religious character of the symbolic relationship.
Rousseau’s according to Lacan’s L schema (left) and according to Foucault’s analysis (right)
Rousseau’s according to Lacan’s L schema (left) and according to Foucault’s analysis (right)
24 The significance of these exercises of formal comparison should not, of course, be exaggerated. While they help to better grasp the ideas of the two paragons of structuralism, their properties clearly do not determine the nature of things. It is nonetheless noteworthy to see structuralism come up against significant difficulties in replacing the religious by the symbolic. If two such powerful minds were not able to achieve such an undertaking, it is perhaps because it is futile.
25 One thing is certain. Lacan realized that Lévi-Strauss’s symbolism was incapable of replacing the religious. What he calls the “symbolic” is not a variant of Lévi-Strauss’s symbolism, but is, strictly speaking, orthogonal to it. In that case, it is, without doubt, more capable of fulfilling the function sought by Lévi-Strauss. However, this undeniable superiority of the psychoanalyst over the anthropologist does not resolve the issue. One might ask oneself whether the symbolic, rather than rendering religion just as obsolete in the social sciences as phlogistics is in the natural sciences, does not simply constitute a new avatar of the sacred, or whether it does not reduce itself to a scientifically correct manner of reintroducing the sacred through the back door, without actually reworking the concept. It therefore seems most appropriate to conclude with an invitation to reflect upon the conclusion of an old article by Vincent Descombes:
It is very true to say that the symbol is the origin of man. But what is the origin of the symbolic? By exchanging the “sacred,” a notion that is certainly disconcerting, for the “symbolic,” a concept apparently purified of all mystery, French sociology has thought to progress in the intelligence of its aim. But it asks services of this notion of the symbolic that it is incapable of carrying out. It would have to be both algebraic (i.e. the manipulation of symbols) and symbolically efficient, as Lévi-Strauss says (i.e. the sacraments). Sacrifices and sacraments have the effect of producing the social body from which arise algebraists: we begin to dream of an autoproduction, an algebra that would allow the social body to be manipulated. Thus, the theory of the symbolic still lies between two domains: semi-algebraic and semi-religious algebras.
27 It is therefore essential to abandon this prestigious notion of the “symbolic” in order to be able to envisage once again, beyond structuralism, the enigmatic reality of the sacred. (Descombes 1980, 94)
28 This appeal to re-examine the question of the sacred dates back nearly thirty years. It would seem that it has scarcely been heard. As we have shown in our book on the canonical formula and, to some extent, in this article, it is nonetheless possible to reply to it and to take some promising steps in this direction.
Lévi-Strauss was introduced to Lacan by Alexandre Koyré a short while after his return from the United States (Lévi-Strauss and Éribon 1988, 80; see also 107–8). For many years, they sustained a private, and sometimes even public, intellectual relationship. In late 1954, Lacan devoted a whole seminar session to discussing the presentation that Lévi-Strauss had given the previous day (Lacan 1978, 39–53). Their relationship seems to have come to an end as a result of the death, at the beginning of 1965, of one of Lacan’s patients, Lucien Sebag, a young, highly gifted follower of Lévi-Strauss.
Lévi-Strauss 1949 (taken up again in Lévi-Strauss 1958, ch. X). In this article (Lévi-Strauss 1958, 220–5), Lévi-Strauss opposes the individual myth, constructed by the psychoanalyst’s patient, and the social myth, used by the shaman to heal his own patients. Furthermore, he assimilates the subconscious to the symbolic function, which, he says “is practiced according to the same rules for all men” (Lévi-Strauss 1958) and which “comes down, in fact, to the collection of these laws” (Lévi-Strauss 1958). In this sense, the subconscious, which is purely formal, is “always empty” (Lévi-Strauss 1958). “It is an organ with a specific function, which is confined to imposing structural laws, exhausting its reality, to unarticulated elements that come from elsewhere: impulses, emotions, representations, memories” (Lévi-Strauss 1958, 224). Lévi-Strauss does not, however, give any examples of such structural laws. He only mentions the laws of phonology (Lévi-Strauss 1958, 225) and, elsewhere, those of communication (Lévi-Strauss 1950, passim).
“[T]he symbols are more real than the things they symbolize; the signifier precedes and determines the signified” (1950, xxxii).
On the need to substitute the Oedipal system with a quaternary system, see Lacan (2007, 43–8). This text is the written version of a lecture given by Lacan in 1952 (or in March 1953, according to some sources), provided by J.-A. Miller in 1978. Another version, which had not been corrected by Lacan, began circulating in 1953. Neither version explicitly contains the L Schema, but it is clearly present in embryonic form.
This way Lacan had of freely using other people’s work as simple construction blocks for his own original thoughts has led to misunderstandings. He has been accused, for example, of not having understood, or of having distorted, the ideas of Saussure (cf. Mounin 1968, 13).
Freud presents his theory of double traumatism with a prime example in La Naissance de la psychoanalyse (1956, 364–5).
The canonical formula is written as follows: Fx(a) : Fy(b) :: Fx(b) : Fa-1(y). In order to become familiar with it and to understand its significance, it should first be noted that it takes the form of a classic analogy of the type A : B : C : D, which is the same as the proportional form: A/B = C/D. The formula establishes, therefore, an equivalence between two relations, or an equality between two ratios. We can see that it is made up of two basic functions, Fx and Fy, and of two possible arguments for each of them, a and b. We, therefore, have four possible values for these functions: Fx(a), Fx(b), Fy(a) and Fy(b). Having established this, it is possible to reconstruct the formula in two stages. Its basic structure is as follows: Fx(a) : Fy(b) :: Fx(b) : Fy(a) or Fx(a)/ Fy(b) = Fx(b)/Fy(a). It is as simple as that. By passing from the left-hand side to the right-hand side of the formula, the two basic functions have exchanged their arguments, and the formula expresses the fact that this exchange leaves their relationship itself unchanged. This is what would happen, for example, if two husbands (x and y) from exogamous marriages were to swap wives (a and b). We can recognize Lévi-Strauss’s “restricted exchange” here, the form par excellence of the principle of reciprocity. It is necessary to carry out a second operation, however, to arrive at the canonical formula itself. This is double torsion, which consists in replacing, first, Fy(a) with Fa-1(y) by exchanging the value of argument (a) and, second, the value of function (y) by substituting (a) with its inverse (a-1). We can see that this operation draws us away from pure reciprocity or at least integrates a more complex structure within it.
The English translation is taken from Jerry D. Moore, Visions of Culture: An Introduction to Anthropological Theories and Theorists (Rwoman Altamira, 2000), 296.
Questioned about this enigmatic phrase by a student at the École polytechnique, who was working under our guidance at the start of the 1990s, Lévi-Strauss had brushed aside their request for clarification as though it were of no interest. We concluded that it was futile to pursue it. It is thanks to Juan Pablo Lucchelli, who attempted to re-read Lacan’s lecture in light of the canonical formula (cf. Scubla 2001), that we resumed our inquiry.
The fact that Lévi-Strauss does not quote Lacan and that his text is destined for an American journal does not disprove this hypothesis. In the same article, he defines myth as an “absolute object” (Lévi-Strauss 1958, 231), without either defining it or mentioning the fact that he was borrowing the notion from a work published by Pierre Auger in 1952 (see Scubla 1996, 475 and 490, note 416). His refusal, however, to comment on his reference to psychoanalysis during the discussion mentioned in the previous footnote would rather appear to support our conjecture since it only serves to confirm his desire to minimize his past collaboration with Lacan, once significant but long since over, as in his discussions with Didier Éribon.
11 The English translation of this quote is taken from Claude Lévi-Strauss, “The Structural Study of Myth,” in Structural Anthropology (New York: Basic Books, 1963), 228.
The L Schema appeared for the first time in Lacan’s seminar class of May 25, 1955 (Lacan 1978, 284) and the canonical formula, in the publication of the final quarter of 1955 of an American journal (Lévi-Strauss, 1955b).
Minutes of the meeting of 26 May 1955, 113–8 (Lacan 2007, 101–11).
In his seminar on December 1, 1954, Lacan had already lamented the fact that Lévi-Strauss “through frequent movement among people who introduce new ideas” (Lacan 1978, 43) had demonstrated “a sort of hesitation to maintain the full strength of the argument” (Lacan 1978, 43) during his presentation on systems of kinship that he had given the day before.
Minutes of the meeting of May 26, 1955, p. 115 (Lacan 2007, 105).
This sensible response is skilful and plausible but nonetheless suspect. In what seems very likely to be the written version of his conference, Lévi-Strauss, as though he wanted to honor his response to Lacan, adds the outline of an application of his canonical formula to the principle myth that he had spoken about—that of the pregnant boy (Lévi-Strauss 1958, 265), but in a very clumsy and obscure manner (Scubla 1998, 44–45). The text was published in honor of Jakobson and makes no mention of Lacan.
It was only in later texts (i.e. those after his split with Lacan) that Lévi-Strauss substantively used the word “symbolic,” most notably in a passage in the third volume of Mythologiques in which, strangely, he too associates the term with that of the “real” and the “imaginary.” He maintains that the myths that he had been studying could be reduced to one single message, but were transformed differently by projection onto two axes—one stylistic, the other lexicological. “Some are associated with the literal and others, with the figurative. Further, the vocabulary that they use corresponds to three distinctive orders: the real, the symbolic, and the imaginary.” The examples, which he goes on to give, show, however, that these three terms, which are definitely reminiscent of Lacan’s RSI triad, are in some way “secularized” and returned to their ordinary usage here: “For it is a fact of life that there are clingy women and philandering men, symbolized by hooked involucres and serpentile penises, and that the marriage of a man to a frog or a worm comes only from the imagination (Lévi-Strauss 1968, 68).
“The ethnological problem is therefore, in the final analysis, a problem of communication” (Lévi-Strauss 1950, xxxii). Together with many of his contemporaries, Lévi-Strauss shared the naïve hope of seeing the development of “a vast science of communication,” encompassing linguistics and ethnology, based most notably on Shannon’s theorems (id., xxxvi–xxxvii). Lévi-Strauss misjudged and overestimated the significance of these theorems, as did the majority of social scientists with no mathematical background (and even some commentators today who still follow him). In 1952, he even wrote an article entitled “Toward a General Theory of Communication” (L’Arc 26: 82.
The L Schema is supposed to describe the structure of the subject as it appears in the analytical relationship, which is not a dual relationship but a quaternary relationship comparable to a game of bridge (Lacan 1966, 589). This is how the author, himself, presents the simplified version of his L Schema, which we have reproduced below. “[T]he condition (neurosis or psychosis) of subject, S, is dependent on what is unfolding in the Other, O. What is unfolding is articulated like a discourse (the unconscious is the discourse of the Other) . . . Why would the subject be interested in this discourse if he were not taking part in it? Indeed, he is taking part in it insofar as he is stretched out to the four corners of the schema: S—his ineffable, stupid existence, o—his objects, o’—his ego, namely that which is reflected of his form in his objects, and finally O—the locus from which the question of his existence can be presented to him” (Lacan 1966, 549). English translation of quotes taken from Douglas Robinson, The Devi Gita: The Song of the Goddess: A Translation, Annotation, and Commentary (Suny Press, 2001), 149 and Jacques-Alain Miller, ed., Book I: Freud’s Papers on Technique (New York: Norton, 1988) http://lacan.com/seminars1.htm.
Jacques-Alain Miller commented on the L Schema as follows: “Symmetry or reciprocity belongs to the imaginary register and the position of the Third Party implies that of the fourth, who is given, depending on the levels of analysis, the name of barred subject or dummy (mort)” (annotated table of the diagrams, in Lacan 1966, 904). This short summary of the quaternary structure does not limit itself to explicitly reintroducing the sacred under the appearance of the transcendent Third Party and the dummy. It also brings together all the elements implied by Girard’s theory of the sacred: the mimetic rivals of o and o’, generators of the sacrificial crisis, and the complementary figures of death (S) and god (O), resulting from its violent resolution. The only thing that is missing to connect it all, from a dynamic point of view, is the victim mechanism. English translation of quote taken from Aron Dunlap, Counting to Four: Assessing the Quaternity of C.G Jung in the Light of Lacan and Sophiology (Proquest, 2008), 151.
We do not know whether Foucault, whose text dates to 1962, took inspiration from Lacan’s schema or not, or whether, as is likely, he spontaneously found the same configuration in Rousseau’s work.