We return to our discussion of anxiety and the object of psychoanalysis.

Anecdotally, we typically assert that anxiety is something like an ungrounded fear. If we are anxious, or if we have an ‘anxiety-disorder’, or if somebody we know claims to have anxiety, then this is something which has its source in something obscure. At best, those who publicly proclaim their anxiety – by asking for some pills, for example – are signalling to us that the source is in their intense work load, their children’s demands, and so on. Lacan wants to point out that this sort of anxiety is not the object of psychoanalysis. Anxiety is not fear without an object, but rather anxiety is a signal, and, as such, it is not without an object. To be not without an object is to have as the source of one’s anxiety something which is quite obscure, something which can not be grasped easily, something which, for all of these reasons, remains somewhat inaccessible to us.

Lacan begins to develop his critique of the object of science. Scientific objects are symbolized, and they are symbolized precisely to avoid anxiety. This is strange and even paradoxical: scientists symbolize their objects so as to avoid anxiety and yet anxiety is the signal by which they can be sure they are close to their object. Anxiety sustains the relationship of not being without an object, and science, by symbolizing their objects, attempt to avoid not being without an object, precisely by making their object something they have or do not have. For psychoanalysis it is therefore not a question of being with an object, and neither is it a question of being without an object, but, as we have said, things are much more obscure: psychoanalysis is not without its object.

Today we are approaching a discussion of the concept lack. To begin with, Lacan states that anxiety introduces us to the function of lack. Lack, in this dimension, is a concept which seems to consolidate or condense the formula not without an object into a single word: lack. To lack is thus to not be without an object. And we are introduced to this lack precisely through anxiety. But there is much more at stake here than simply psychoanalysis. In the field of logic there has been, according to Lacan, a history of successes in masking Lack. What could this mean? It means, for example, of filling in the lack. Logicians have been unable to account for the lack and so they attempt to cover over it by way of intricate formulas and topologies.

The question to which Lacan now turns concerns the place of lack. What he states up front is the following: there is no lack in the real, lack is only graspable through the intermediary of the symbolic. While the latter point makes a lot of sense to me, for reasons which shall become apparent, the former point seems more difficult. Lacan seems to be suggesting that there is no lack of lack inasmuch as the real is what is lacking within the space of the symbolic. In this case, however, what is the precise place of the real? This can not be the proper reading because it would conflate the real and lack into the same conceptual point and thus rule out any necessity for distinguishing between the two concepts. So Lacan’s point must be something else. Perhaps Lacan is pointing out that the real, which perhaps occurs outside of the symbolic, is different from lack which occurs as the real inherent to the symbolic. This makes more sense to me and it gives further credibility to a point rarely brought up by Lacanians about the different orders of the real itself: there is a real-real, a real within which nothing is lacking, and a real-symbolic, a real which occurs as the impasse of the symbolic order.

Lacan seems to also be making a point about ‘the negation of the negation’. He wants to point out that the negation of the negation does not give one an affirmation. For example, he was in search of four prints within a volume in his library. However, the volume is missing. So here there are two things missing: the four prints as well as the volume itself. So, one could argue that (1) the volume is missing and (2) the four prints are missing – (1) negation, and (2) negation. What results is clearly not that the four prints appear, as some affirmative reading of the negation of negation would have it. So – what could happen here? I’m taking great liberties in my reading and I hope that somebody will correct any faults they see in my interpretation. If the volume itself is missing, inside of which one was searching for four prints, then, of course, one might replace the missing four prints by way of another volume. This is a substitution of the original missing prints. The book itself, which is missing, had everything. It was not missing anything. But what one misses is the content of the book, a small part of it – and this small part remains missing. So one discovers it elsewhere. Something intervenes. More to the point, somebody intervenes – perhaps a librarian who says “No!” We don’t have it.

The Case of the Missing “Volume”

The symbolic intervenes into the real. This is my own interpretation, I’m not sure that it was what Lacan meant. I need to work this out more. However, this does not help to explain how something like the symbolic can come into being out of the (first order) real, out of the real which has nothing lacking within it. In any case, the lack is a concept to explain that which is missing, that which is absent. If we were to attempt to use a Eulerian diagram – a Venn diagram – to understand lack, we’d run into a problem. This requires us to study briefly how a Euler diagram works. Minimally, there are two overlapping circles. This is the basic relationship between “sets”. The circles can intersect (overlap with one another with some part of each outside of the other), subset (one circle inside of the other), or disjoint (each circle is completely untouched by the other). The logic for each one is simple: to overlap means that there are elements of each set that are shared and elements of each set that are not shared, to subset means that the elements of one set are entirely a part of the elements of a larger set, and to disjoint means that no elements are shared between any of the two sets. Here we run into a problem. The problem that Lacan seems to be defining is the following: we are dealing with “elements” of each set as if they were concrete things, concrete values, pure affirmations. A set, in the Eulerian universe, always implies that there are things which are shared or not shared. The Euler diagram, it seems, can not portray a sense in which what is shared is precisely lack itself.

Euler Diagrams

There was a missing volume in Lacan’s library, perhaps what was really missing was volume itself: Lacan moves back to more multi-dimensional topologies using the concept of the plane and the surface. Lacan does not define these concepts so I returned to Euclid’s first book of Elements to get a definition: a surface is defined with two dimensions [being] length and breadth only, and a plane is a surface which lies evenly with the straight lines on itself. So what we know is that a surface is a type of plane. As far as I can tell, Euclid maintains that a plane, as opposed to a surface, is what gives support to the surface precisely by way of the lines (which are, it should be said, connections between “points”), that delineate the surface. This is probably why Lacan wrote that there must be a plane that supports the surface. The relationship between the plane and the surface can be made complex quite fast.

Euclid’s Elements

Take, for example, the ring of the torus: “this surface has the appearance of being one of the most readily imaginable […] [but] one can see [that] the function of the hole [lack] is varying rather oddly.” So – where are the holes in the torus? It seems to me that there are a few. First, there is the hole that exists most obviously in the very middle of the major ring. Second, there is the hole that exists within the minor ring, that is, within the tube itself. Third, and less obvious, there is the hole that exists outside of the ring itself – the one that is not captured by the stage of the drawing. I’m not sure that Lacan pointed out all of these holes. In any case, the torus provides an example of the way that a hole can be closed up. You can see that in both of the first two examples the rings are “contained” by the plane surface. Yet, at the same time, the hole is not filled in within the torus. This is an important point. If, within the Euler diagram, the “elements” fill in the holes as sets, then, within the torus, there are holes which are very clearly left as holes.


But we need to go back to Euclid’s Elements again. He began his first book with a point. The first definition in the book is the following: “A point is that which has no part.” Lacan never explains this definition but it is absolutely essential for our understanding. You see – a point is a bit like the flick of the tongue, the spark of the flint, the first cut which is without voice and which sets off everything. Indeed, this was the function of the point for Euclid. [I can not go without mentioning the importance of the concept “point” for Badiou’s work – here, a point has a similar function and yet it is on the side of the subject inasmuch as, we could say, Euclid provided the world with something absolutely new by making his first point into a new count. This will have to be the topic of a future discussion.]

Euclid’s point / line

We should now return to the cross-cap. Lacan’s argument is interesting: when you cut the cross-cap you will never find a circle that can be reduced to a point. In other words, the cross-cap, when cut, does not give you a point even if it gives you a surface. Isn’t this interesting? This shows that there was a revolution at some point in the basic point of Euclid’s geometry – the ground was lifted from Euclid’s philosophical apparatus. So the cross-cap allows us to approach an understanding of a surface with an irreducible lack, a grounding even, which is without a coherent point.

“Elements” of a “Cross-Cap”

So lack is this radical irreducible hole in any surface which constitutes subjectivity as such. We meet this irreducible lack at every “twist and turn” of clinical experience – there is always a structural fault of sorts and this is the place where something like a signifier is made possible. If, then, something like a signifier is made possible at this location then it is because there is a potential relation to the Other, the place of the signifier. And yet Lacan states that it is irreducible and this means that it is also a site that can not be signified. So, what it is is a signifier without a signified, a signifier that can not be made into a sign.

Now we have entered into the domain of signifiers, signifieds, and signals. Lacan claims once again that the lack is always a part of the symbolic order: nothing lacks that is not part of the symbolic order. Privation, on the other hand, is something real. Privation is something that occurs from the real – what is lacking are the essential functions of the symbolic order. Lack is something that occurs from the symbolic – what is lacking is a signifier, a lack-of-signifier. This distinction is important for understanding developments in some of the other clinical structures. So privation is not castration. Castration is another way of stating the phenomenon of lack. Indeed, one might claim that it is a more up-to-date way of discussing the logic of castration. What we are really up against when we discuss the phenomenon of lack is the relation that one has to the big Other.

The subject must constitute himself as a subject in relation to the big Other, and this occurs always at the level of symbolization. There is an imaginary support for this relation, as we’ve noted in previous classes as minus-phi. Minus-phi can now be understood as the imaginary support of castration. Or, if I may take some liberties, minus-phi is the imaginary support for lack. This, claims Lacan, will allow us to get beyond the stopping-point of the castration complex as outlined by Freud. Now we may be able to go a little further.

Simplified Mirror Schema
Simplified Mirror Schema

Lets return to the cut in the cross-cap, which gives us our mobius strip. Here we have another surface. The hole, as it were, in the middle, is not at all like the torus. The whole is often called an “infinite eight” because it goes around to the inside and around to the outside – it doesn’t stop connecting inside to outside. Yet the hole of the torus is different – it is only outside, there is really no connection to the inside. Or else, if you take a different point of view, it is only inside without a connection to the outside. We return to that image on the cover of the book: an ant walks along the mobius strip. This brings to mind the “ants” in Deleuze’s philosophy. I recall that in A Thousand Plateaus, Deleuze and Guatarri remarked upon the fact that they imagined each character in the book to be a bit like an ant. They would have visions each morning that the ants on one page would walk around to the other pages and off the book, and even back onto the book. What surface did Deleuze and Guatarri describe here? It is a plane, certainly, but it is not the plane that holes the infinite eight. It is a plane of immanence, where everything is connected.

“infinite eight” (Mobius Strip)

In contradistinction, the ants on the mobius strip walk along the surface and at any point they believe themselves to have more to explore, an outside they can still move toward, and yet in the big picture they’ve already covered it all. This amounts to the following: without knowing it, the insect is exploring the only face that exists and yet from moment to moment there is indeed a back face. So, the interior eight is irreducible, it is the “shortest route” that the ant can take to get to the other side. And yet, nothing can compensate for this hole. It is the object a. This is how the symbol of the “8” introduces absence into the real. If there is nothing lacking in the real then, with the construction of the mobius strip, there is, finally, an absence in the form of the object a as “infinite eight”.

One Possible Image of “the plane of immanence”

The question we ask as analysts is: what should our relationship, as the Other, be to the object a of our analysands? This is a variation on the question of how it is that we “handle” or “organize” the transferential relationship. We must first come to understand the transference. If the transference happens on the stage then it is, for neurotics, the a which asks to be on the stage but is in all cases refused.

We are approaching the question of mourning. But this is a question that Lacan poses in more broad terms. It is not necessarily the specific aspect of mourning but rather the logic of mourning which concerns Lacan. Freud’s definition of mourning implied the identification of the patient with the lost object. Lacan claims that this is not good enough. The more correct formulation is that we mourn for “he whom we can say ‘I was his lack’.” This is a step too far, although this has already been covered this in previous classes. We know that one in some cases wants to be the object of the Other’s desire. So, this object of the Other’s desire is that which remains unfulfilled, hollowed out, absent, lacking. To leave the Other’s desire lacking is really just another way of stating to be the Other’s desire. So we mourn when we are no longer the object of the Other’s desire, when we no longer sustain the lack of the Other. This is why Lacan has been stating that to love is to give what we haven’t got.

Shifting gears.

Lacan turns to the question of responsibility. Here, I note, that responsibility, as a word, seems to carry the ethical connotations and not the more literal tone: it is not that one responds but rather that one takes something upon him or herself. The analyst always assumes too much responsibility on behalf of her analysand. For example, many times analysts have to go to court on behalf of their analysands. Lacan notes that one analyst argues that there are different responsibilities on the part of the analyst for each clinical structure. For example, when dealing with psychosis, the analyst is almost completely responsible (for hospitalizations, care, etc), when dealing with neurosis, the analyst must transfer responsibility to the analysand. But then an additional remark is made: somewhere between psychosis and neurosis is neurotic personality disorder. In this case, the analyst must take more responsibility for the analysand. But Lacan notes that what some people refer to as neurotic personality disorder is really just another way of stating what he has been naming acting-out. This changes things. Acting-out, as we know, is always on the stage of transference – the stage of the big Other. So, this implies that responsibility has already been taken, but that it was not “handled” or “organized” properly.

Kleptomania, for example, is acting-out, according to Lacan. When one is acting-out, one is essentially asking for an interpretation. We remember this from the last class: acting-out calls for interpretation. But, as we noted from last class, this does not imply that the symptom requires interpretation. Indeed, the symptom does not require interpretation. The symptom does not occur via the route of the stage, necessarily. So, according to one case (which was not Lacan’s case), the kleptomaniac was stealing but was not yet in the much required transferential relationship. We already know this to be false, but in any case, we note that the analyst fell for the performance, the spectacle, and provided many, many, interpretations. In fact the analyst provided so many interpretations that eventually she could not dream up any more and was forced to admit to the analysand that she just could not figure it out at all. But then the patient one day falls into tears over the death of a woman. This woman looked after the patient when she was young. The analyst tested various interpretations on the analysand, to no avail. Something kicks in only when the analyst admits that she can not make heads or tails out of the analysand’s mourning.

What does this teach us? It demonstrates that analysis really only kicked off here when there was someone for whom the patient could be a lack. It was when the analyst found the patient to be a mystery, a puzzle to be solved, that the analysand showed her true colours. At this moment both the analysand and the analyst were harbouring anxieties. What the analysand could not do, then, with her parents, was to occupy herself as the lack.

Lacan ends the class with a quick discussion on the goal of analysis. This forces me to ask, are the goals of analysis anything like the goals of education? At this point Lacan was exploring the possibility that the goal of analysis was to “initiate [the patient] into a scientific point of view [regarding his own being in the world].” I will admit that I fell for this possibility. Lacan did not. Lacan was no doubt quite critical of the “scientific” point of view. He problematized it. He claimed that scientists presume that lack is something that can be filled in. In art something similar happens, especially with the prevailing view that “art is sublimation.” This leaves me with a lingering question, one which Lacan does not give a lot of attention to, which is: why is it that some of the exceptional pioneers of science (for example, Isaac Newton – and is it for nothing that he was named Isaac?) – and the pioneers of psychoanalysis (for example, Freud) were active mystics in their private lives? Is it possible that mysticism provided them with the outlet they needed to keep the lack intact? In the fact of a scientific discourse which attempt to fill in the world, to provide light and enlightenment, and, moreover, knowledge, mysticism allowed for the excess to remain excess, for there to be still a place for the infinite eight? This is the question I want to answer more than any other right now.


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