Sexuation 1– The Logic of the Signifier

The Real, Repetition, Incompleteness, and Inconsistency

As I remarked in a previous post, Lacan’s graphs of sexuation can be understood as two ways in which the totalization of language fails and the jouissance that emerges as a result of this failure of totalization.

According to Lacan, there is a masculine and feminine way in which this failure occurs. The masculine failure of totalization and the jouissance this failure produces can be found on the left side of the graph, while the feminine failure of totalization and the failure it produces can be found on the right side of the graph of sexuation. We can refer to the upper portion of the graph of sexuation where the equations are located as “the logic of the signifier”, while we can refer to the lower portion of the graph with the arrows as “the logic of jouissance. The left or masculine side of the graph of sexuation can be referred to as failure as incompleteness. That is, the masculine way of attempting to totalize the symbolic or the big Other leads to a constitutive incompleteness calling for a supplementary element or term. Likewise, the feminine way of attempting to totalize or complete the symbolic leads to a constitutive inconsistency.

It is important to note that biologically gendered subjects can occupy either side of the graph of sexuation or neither side of the graph of sexuation. Thus, for example, you can have a male body that is structured according to the feminine side of the graph of sexuation. Likewise, psychotic subjects occupy neither side of the graph of sexuation. In this respect, it comes as no surprise that postmodernity, where the name-of-the-father is largely foreclosed in the social field (the structural failure in the borromean knot that generates psychosis), is also accompanied by a plurality of sexes and sexual identities. This is exactly what we would expect in the absence of Oedipal structure. In this connection, I believe that the debates between Copjec and Žižek directed at Deleuze and Guattari, Foucault, and Butler premised on the real of sexual difference are poorly formed because the two sides of the debate are dealing with very differently structured systems at the level of the logic of the signifier.

Read on

In a marvelous passage from Seminar 17, The Other Side of Psychoanalysis, Lacan remarks that

The inside does not explain the outside. We are dealing with a relationship of weaving, of text– of fabric, if you like. It remains no less true that this material has a texture, that it captures someting– not everything, to be sure, since language shows the limit of this word which only exists through language. It shows that even in the world of discourse nothing is everything, as I say– or better, that “everything” as such is self-refuting, founds itself, even, on having to be reduced in its employment. (54)

Lacan’s point here is that nothing can totalize the field of the signifier (“nothing is everything”) and that the field of the signifier is therefore constitutively incomplete or inconsistent. It is this incompleteness and inconsistency that Lacan will refer to as “truth” and the “real”. Truth is therefore not to be understood as an adequation between a proposition and a state-of-affairs in the world, but rather as that which falls outside of, is excluded from, the symbolic. Truth is the failure of totalization. Consequently, Lacan will assert that “…’truth’ is not a word to be handled outside of propositional logic…” (The Other Side of Psychoanalsysis, 55).

If truth is not to be handled outside of propositional logic, then this is not because propositional logic delivers us to the truth– after all, the real is impossible to represent –but because it allows us to circumscribe the real or locate that site where the real emerges as that which always returns to its place within any attempted symbolic totality. In the graph above, we do not see the real or impossible which always returns to its place, but rather encounter the trace of this real that emerges out of an attempt to totalize the symbolic. These deadlocks or failures of totalization, in their turn, become the site of repetitive jouissance or the symptom insofar as the subject perpetually strives to mend this formal deadlock, while the failure perpetually returns. As Lacan will put it a few years later in Seminar 22, RSI, “…the symptom… never ceas[es] to be written” (Feminine Sexuality, 166).

Unlike psychotherapies that dream of a cure or disappearance of the symptom, Lacan’s position is that there is no subject without a symptom. This is a direct consequence of the fact that the real, as an “impasse of formalization” (Seminar 20), is that which produces the symptom. However, while the symptom cannot be eradicated, this does not entail that the form the symptom takes is fixed. As Lacan also observes in Seminar 22, “…the symptom… [as a]… function [is] to be understood as the f of the mathematical formula f(x)” (166). Just as a mathematical function can produce many values depending of the value placed in the “x”– the letter, according to Lacan –of the function, the symptom can undergo a number of different permutations. What is crucial is that it is this impasse of formalization that accounts for why the subject repeats in opposition to the laws governing the pleasure principle.

It is ultimately repetition that distinguishes jouissance from pleasure. Where pleasure is a decrease in tension within the psychic system, jouissance is an increase in tension. Where activity ceases when pleasure is achieved (we don’t continue eating when we’re full), activity repeats in the case of jouissance. The translation of jouissance as “enjoyment” is thus extremely misleading. Jouissance can often be experienced as exceptionally painful as in the case of the person that obsessively continues to eat after full, or masturbating twenty times in a day, or washing one’s hands repetitively until they are raw, cracked, and bleeding.

The Logic of The Signifier

The Masculine Formal Impasse of Totalization

Consequently, another way of reading the graphs of sexuation is as an account of how repetition, the symptom, the death drive, comes into being. In the upper portion of graphs representing the logic of the signifier, both the upper and lower propositions are to be read together as encircling an impasse of formalization or a deadlock. The masculine side embodies the logic of incompleteness and can be understood understood as a formalization of the logic of sovereignity and hierarchical models of social relations. Unfortunately this blog won’t allow me to use the formal notation, so for the existential quantifier I shall use “E” and for the universal quantifier, I shall use “V”.

Before discussing the structure of masculine sexuation, it is worthwhile to make a brief comment as to just why the symbolic, as a totality, is consistutively incomplete or inconsistent. In Seminar 14, The Logic of Fantasy, Lacan remarks that “the signifier cannot signify itself” and that there is no universe of discourse. If the signifier cannot signify itself, then this is because every signifier must refer to another signifier to produce effects of signification (“the signifier represents the subject for another signifier”). The consequence of this is that language cannot form a totality as language, following Russell’s paradox, is a set composed of sets that are not members of themselves. Thus, language leads to an impasse of formalization. If we were to form a set of all sets belonging to language, we would be violating the principle that the signifier cannot signify itself as this prohibits the belonging of the signifier to itself thereby generating an inconsistent set. Likewise, if something must always be missing from the totality of language it follows that we have not formed the set of all signifiers, thereby generating an incomplete set. I have dealt in detail with these paradoxes here, here, here, and here. It is for this reason that “there is no universe of discourse” (no totality), or that the big Other does not exist. This formal impasse at the heart of language is precisely what generates the subject. Because the subject only comes into being through alienation in language, and because this alienation constitutes a loss of being, the subject searches for a signifier that would name its being, fixing it in place and giving it substance. However, because the signifier cannot signify itself, this proves to be an impossible task, as one signifier perpetually slips to another signifier. As I’ll show a bit later, this is what lies at the foundation of jouissance as the cause of the subject. It should be kept in mind– and this is of crucial importance –that, as Jacques Alain-Miller puts it, while “‘The Other does not exist,’ [this] does not prevent the Other from functioning, for many things function with without existing.” The subject produces a semblance of the Other, a sham, through fantasy that makes up for the hole or incompleteness of the Other allowing it to function.

The masculine way in which totalization fails is as follows:

Ex~Φx
VxΦx

The lower proposition reads “all speaking-beings are subject to the phallic function”. Another way of saying would be that “all speaking-being are subject to the law of castration”. Castration, of course, is to be understood as the loss we bear as a result of being subordinated to the signifier in language. The signifier introduces an a priori lack into our being, insofar as it 1) institutes the distinction between word and object allowing for absence to be introduced into the world, and 2) allows us to envision absent beings such as El Dorado. Castration can thus be understood as the sacrifice that every subject makes in order to enter the symbolic order or the social field. In Civilization and its Discontents, Freud, for example, shows how our introduction into the social is accompanied by a significant sacrifice of enjoyment.

The masculine side of the graph of sexuation thus posits a universal feature shared in common by all speaking beings. However, in order to formulate a universal it is necessary to posit an exception so that the rule might be discernible.

Thus, in the upper equation of the graph reads “there exists a speaking being that is not subject to the phallic function or the law of castration”. This being is a being that does not make a sacrifice of jouissance in order to enter the social field. This being can be the Primal Father of Totem and Taboo, God, the sovereign in the work of Carl Schmitt, the father of the Oedipal triangle, the nation, and so on. The key point not to be missed is that this being is a phantasmatic entity produced as an effect of the universalization of the law. It now becomes possible to see why the masculine side of the graph of sexuation is a logic of incompleteness. Insofar as the universalization of the law generates the necessity of an exception so that the law might be discernible, there is always at least one entity that escapes or stands above the law. It is insofar as the universalization of the law of the signifier requires the supplement of an exception that it is constitutively incomplete. This exception is, of course, a fantasy, sham, or fiction that creates the illusion that the Other exists, but it functions no less for all that.

The Feminine Formal Impasse of Totalization

Universal propositions are also propositions pertaining to the logical function of necessity. When we say that something is universally the case we are making the claim that it is a necessary truth or that it is impossible to be otherwise without implying a logical contradiction. By contrast, when we say that something is contingent, we are saying that the opposite is possible. Thus, for example, the claim that the square of the hypotenuse of a right triangle is equal to the sum of the squares of its other two sides, is a necessary and universal truth insofar as its opposite is impossible, while the claim that “Levi is wearing a brown dress shirt” (Dejan would be aghast at my color choice) is a particular and contingent truth because the opposite (wearing a shirt of some different color or style or no shirt at all) implies no logical contradiction.

Drawing on the traditional square of opposition, we can thus see how differently universality (the upper portion of the square) and contingency (the lower portion of the square) function. In the upper portion of the square “A” and “E” (affirmo and nego universal propositions) cannot both be true. While in the bottom portion of the square, “I” and “O” propositions can both be true, i.e., the opposite being true does not involve a logical contradiction. Masculine sexuation is a logic of universality and necessity, whereas feminine sexuation is a logic of contingency and particularity.

Consequently, in the case of masculine sexuation the claim is being made that all subjects are necessarily subject to the law of castration. Again and again, wherever this structure is present, we see the positing of an exception that marks the rule. This is clearest in the case of theology, where God is often thought as the exception that grounds and creates the world. Thus God is conceptualized as omnipotent, infinite, and absolutely free; or rather not subject to the law of limitation. This comes out most clearly in the case of Descartes’ volunterist conception of God and truth, and Leibniz’s conception of God as the sufficient reason for all other beings or creatures. There was a reason that Lacan encouraged his students to study theology as theology can be thought as a fetishized version of the structures of the unconscious and the subject.

With feminine sexuation the attempt to totalize the signifier generates a very different formal impasse. Here we shift from the universal quantifier (V) to the existential quantifier (E), indicating that we’ve shifted from the order of necessity (universality) to contingency (particularity or singularity). Lacan writes the feminine structure of sexuation as follows:

~Ex~Φx
~VxΦx

As is the case with masculine sexuation, the two formulas or propositions are to be read together as encircling the real of attempts to totalize the signifier. The upper formula should be read as stating that “there does not exist a speaking being that is not subject to the law of castration or language”. Initially one might take this proposition to be equivalent to the claim that all subjects are subject to the law of castration or the lower formula in the masculine side of the graph of situation. Yet here we have moved from the universal quantifier (V) to the existential quantifier (E). Where masculine sexuation presents a universal law under which all subjects fall (the logic of the same), feminine sexuation is premised on the existential or particular (E), where each subject is taken on a case by case basis. In other words, in feminine sexuation the subject is certainly subject to the law of castration but this differs for each particular individual.

The lower formula for the feminine graph of sexuation reads “not all of speaking-being is subject to the law of castration.” In short, there is something of being that escapes the loss imposed by language or that cannot be articulated in language. It is between these two propositions that we encounter the inconsistency of feminine sexuation. On the one hand, not all of speaking-being is subject to the law of the signifier, yet on the other hand there does not exist a speaking being that is not subject to this law. The shift from the universal quantifier in masculine sexuation (V) to the existential quantifier in feminine sexuation, has important consequences for how the speaking-being in question experiences herself. Insofar as we are no longer talking about a universal and a necessity, but a contingency and a particularity, it follows that there is no signifier in the symbolic order capable of providing a fixed and stable identity for the subject in question. That is, we are dealing with singularities rather than universally shared features. As a result, this subject experiences their relation to the symbolic order as fraught and where they have no secure or stable place.

An Aside on Biological Sex and Sexuation

In a previous post I had remarked that I see no reason as to why Lacan refers to the two sides of the graph of sexuation with the signifiers “masculine” and “feminine” insofar as subjects that are biologically male and female can occupy either side. It seems to make more sense to simply refer to the two sides of the graph as incompleteness and inconsistency. However, in working through the graphs more carefully, I do believe we can come up with historical and cultural reasons as to why this might be the case. While having a penis or a vagina does not assign a speaking-being to one side of the graph or another, there are certain social relations between biological men and women that provide a plausible reason as to just why those that are biologically female tend to fall on the feminine side of the graph of sexuation.

Freud’s practice began with the treatment of hysterics or women suffering from hysteria. Although hysteria was a common and well known neurosis prior to Freud, what made Freud’s practice unique is that rather than classifying hysteria as a sham illness or a form of feigning illness, or occupying the position of the master that knows how to solve the hysteric’s problem, Freud instead listened to what his patients had to say. In other words, Freud’s practice was premised on the presence of the subject, of the patient’s own subjectivity, rather than its exclusion from the clinical setting. If you read Freud and Breuer’s Studies on Hysteria, the common thread in all of these cases is the presence of a failing father. The father might be sick such that the daughter is forced to care for him (often symptoms of hysteria came into view following the death of the father), the father might have been impotent, the father might have been having an extra-marital affair (Dora) indicating another desire or incompleteness, etc. However, in all cases we get this theme where it is revealed that the father does not have the phallus.

Here, then, we get the beginnings of an account as to just why there might be a high statical correlation between those that are biologically female and the feminine side of the graph of sexuation. In his earlier work, “The Signification of the Phallus”, Lacan had distinguished the sexes based on being-the-phallus and having-the-phallus. Here the phallus is to be understood not as the penis, but as the signifier of the Other’s desire. To be-the-phallus (the feminine position) was to be the object of the Other’s desire, while to have-the-phallus is to possess signifiers of mastery with respect to identity (money, power, knowledge, strength, intelligence, wisdom, prestige, etc). If, as we shall see later, one of the ways in which the feminine sexuated subject deals with the impasse of formalization or the inability to totalize language is to pursue the phallus, then this is because such subjects are searching for a signifier that would be capable of providing a fixed an stable identity for her within the symbolic order. In other words, these speaking-beings search for someone capable of naming what they are.

Yet what is it that leads a speaking-being to experience the symbolic in terms of the existential quantifier or particularity and contingency, rather than the universal quantifier or necessity? The latter believes in a universal law and objectivity, while the former does not. Why? Is it possible that those that are biologically sexed female often encounter those who claim to have the phallus as being a sham, masquerade, or charade? In other words, the masculine subject claims to have the phallus, but in her intimate dealings with this man, the woman discovers that this is a sort of illusion that we find in the case of the man who puffs himself up and brags, always displaying his phallus, while in truth being divided from the phallus. Thus, in the example of Monica Lewinsky, Clinton had the phallus in the sense of political power, but in her intimate dealings with him she discovered that he was a castrated subject, requesting, as my friend Tim jokingly put it, the ultimate rejoinder to Freud’s claim that “sometimes a cigar is just a cigar”. Despite having complete power, Clinton still had a desire for something else and was still haunted by a structural incompleteness. What Lewinsky discovered is that Clinton, while having the phallus, also did not possess it. And likewise with the many daughters that Freud examined early in his career.

We can imagine that based on this experience of men, women shift from the universal to the particular, the universal to the existential, taking subjects on a case by case basis and developing a certain skepticism towards universal identities. What they discover in their dealings with others is both that the phallus is a sort of illusion or charade not unlike that of the puffer fish that makes itself look much larger than it is, and that there is always something that the symbolic fails to deliver. The conversion symptoms that so often accompany hysteria are a sort of mute testament to this incompleteness of the symbolic and the sham of the phallus. It could thus be said that the masculine side of the graph of sexuation is the side of the sham, of semblance, of illusion, while the feminine side is the side of truth or the real. All subjects, under this model, are sexed feminine insofar as all subjects emerge as subjects due to a fundamental failure of the big Other or the in-existence of the Other, yet masculine sexuation is almost a sort of disavowal of this impasse, producing instead the fantasy of an operative or functional totality (hence the tendency of masculine sexuation towards perversion, i.e., the disavowal of castration).

Two Political Observations

On the basis of the foregoing, it can be argued that masculine and feminine sexuation also correspond to two different types of social and political organization. On the masculine side we get centralized and hierarchical forms of social organization often associated with nationalism, totalitarianisms, authoritarian leaders, etc. In my next post I will outline the jouissance that corresponds to these structures. Corresponding to the feminine side of the graphs of sexuation, we get networked, non-linear, decentralized forms of socialization. It can indeed be said that today we are moving from masculine based structures of the social to feminine based structures. However, it should not be presumed that these structures do not possess their own deadlocks and antagonisms. Indeed, it could be said that network based social relations are far more resistant to critique and engagement than are masculine based structures.