NoteIt is important to point out at the beginning that these notes should not be read as independent blogs. They are to be read in order, beginning at the first set of notes for the first class of this seminar on anxiety.

Lacan is now moving toward a discussion of the importance of formalization, and, crucially toward a level of formalization which avoids the pitfalls of blind speculation. He argues that Freud was striving toward this level of formalization in his own work. He quotes Freud, from his 32nd introductory lecture, as stating: “it can truly only be a question of conceptions […] Indeed, what is involved is to find the right abstract ideas which, when applied to the raw material of observation, will bring order and clarity.” Lacan no doubt takes this method as his own. The question, of course, has to do with the raw material of observation – what is the raw material? Is it, presumably, that which exists outside of the specular relation?

We begin with the reformulation of some of the algebraic symbols we’ve been dealing with from the beginning of the seminar: i'(a), i(a), A, and a. We know that the capital A refers to the big Other and that Lacan has so far decided to place it in the middle of the relation, as the mirror itself. Lacan formulates i'(a) as the image of one’s body through the intermediary of the mirror of the Other (A). We further know that the object is situated somewhere before (whereby “before” means “on the left” and does not refer to any temporal distinction) and yet above the mirror.

There is a line drawn from to i'(a) and this demonstrates that there is communication, of sorts, between the two. If we think of the as the object libido then we can see that it reverses onto one’s own body. Imagine, for instance, that the vase with flowers is an image of one’s own body – an image that exists on the other side of the mirror. We can also see that the object libido “pours from i(a) to i'(a).” What could this mean? It means that the image of the upside down vase and flowers reflects onto the y/x concave mirror and through the mirror/Other to produce i'(a).

Mirror Schema

We’ve described the relationship, as if it were “communication”, that exists between and i'(a), but we haven’t discussed the itself . We know, from previous classes, that the object a manifests, most strikingly, as anxiety, or, more precisely, it manifests as a signal, an anxiety-signal. I name it an “anxiety-signal” because anxiety, for Lacan & Freud, always signals something. We also now know that anxiety signals a relation or an encounter with the object, object a. So, we’ve achieved some clarity, clarity which I would like to formalize:

anxiety signals an encounter with object a

I wrote “encounter” rather than “relation” because I believe that Lacan is incorrect to describe the signal as a relation. For example, the word “relation” should be reserved for that which is lacking between the sexes. So, the word “relation” has a very precise sense in Lacanian psychoanalytic theory. I want to therefore reserve the word “relation” for conceptual use. What happens when the anxiety-signal occurs, that is, what happens when anxiety signals an encounter with object a? Lacan claims that the subject fades, the subject fades because he loses his sense of autonomy. This loss of the subject (here we are using the word “subject” in a less precise sense to indicate the “individual”) is formalized by the barred-S, $.

So, Lacan wants us to recognize the fact that the object of anxiety is denoted by a letter (a): “[t]his algebraic notation has its function. […] has precisely the purpose of giving us a pure identity marker.” You can see Lacan’s fascination with formalization, and his staunch commitment to Freud’s original premise from the 32nd introductory lesson. Moreover, we can see that Lacan in fact borrowed this concept, namely, the “object”, from the traditional subject-object polarity which pervaded philosophy at the time and which no doubt began with Kant. We need to be careful here, we need to note how an object and subject are thought in Lacan’s work to properly understand the move that Lacan has made and, moreover, the difference between his object/subject and the traditional Kantian view. For example, during a seminar in 2012, Alain Badiou asked his students to distinguish between a subject, object, and thing. Badiou states that often “[our] first proposition is to say that an object is something which is opposed to the subject. It is different from the subject and in relation to the subject” (The Subject of Change, p. 103). He continues,

You know, [this] position is Kantian by necessity because if you put an object on one side and the subject on the other side then the object can not be defined like [I do] here. An object, here, is only to be in the world. There is no difference between object and subject. […] To be a multiplicity in a world is not to be in a relation to the difference between objects and subjects. If you claim that the object, and finally objectivity, is by necessity in a relationship to a subject then you are within the vision that claims that objectivity depends on subjectivity. And so it is the Kantian vision (Alain Badiou, The Subject of Changep. 103-4).

At first glance, it does seem as though Lacan is drawing a distinction between the object and the subject and then, subsequently, bringing out the precise relationship between the subject and the object. However, we should be very precise here. It is the object which constitutes the distinguishing badge of subjectivity as such and so it is very clear to me, at least at this juncture, that Lacan is following the Kantian duality but is making significant adjustments to it. Indeed, these adjustments are so significant that they lead – if one is willing to follow their implications fully – to Badiou’s position. The subject, ultimately, is always barred, but the subjectivated subject, the subject of subjectivity relies on something like the object dimension of the subject. The subject is defined by his little object a. It would be a worthwhile project at some point to trace a path from Lacan to Badiou on the question of the subject/object duality. Perhaps these positions are closer than we think.

If we read Lacan’s statement to the letter we will notice that he is not necessarily suggesting that a subject and an object are at odds with one another. Rather, he claims that the term object is borrowed from the subject-object relation. In a sense, then, the object is itself a relation. Lacan states that “the object we have to speak about under the term is precisely an object that is external to any possible definition of objectivity.” We can see the complexity here then – so we should not take for granted the status of this object which is not necessarily an object. Perhaps this is why many Lacanians choose to keep the original French, objet rather than “object”.

We next have a question about the subject. The subject is not the subject of the traditional subject-object distinction because it is a subject which is fundamentally unconscious. And to the extent that the subject is unconscious s/he is also maintained by the incidence of a signifier which reigns or stands above or prior to his or her constitution as subject. So we begin with the real of object a and then the signifier enters into the picture and organizes it. But it organizes it precisely by returning back into it, by itself being subjected to it, by “bracketing” it [I will come back to what I mean by “bracketing” momentarily, it is a concept that I use a lot in my writing]. To return to the point: we begin with the real of object and then there is a communication of sorts, or a passage, established with the specular image, the i'(a). At this point we enter the possible dimension of the uncanny.

Lacan is very cautious about the way he constructs his sentences. We notice this especially when he responds to the claim that anxiety is without an object. Afterall, it is not precise to state that anxiety has an object – because we never really have the object, do we? In a sense it is our inability to master the object that signals anxiety in us. However, it is also not true to state that anxiety does not have an object. It very clearly does have some relation to an object, and that object is the a. To put matters more correctly, since these previous two sentences are not precise enough, Lacan states that anxiety is not without an object. I will write this as a formula:

anxiety is not without an object.

To this we add the previous formula:

anxiety signals an encounter with object a

Taken together, perhaps the formula can now be read as follows:

anxiety signals an encounter which is not without an object


anxiety, which is not without an object, signals an encounter


anxiety signals an encounter not without being with an object

I’m not sure at this point which formula would be the most accurate. The first presumes that the encounter is not without an object, the second presumes that anxiety is not without an object but the encounter might be with something else or of another nature, and the third presumes that anxiety signals an encounter and that this encounter could be of any nature but is nonetheless not without an object.

In any case, what does it mean to not [be] without an object? There is a similar logic relating to the phallus – I discussed this in my commentary of the previous class. We noted that Lacan claimed that it is not true to state that there are those who do not have the phallus and those who have the phallus because, as Little Hans demonstrates, even those who do not have a phallus have a phallus. I noted that this must mean that there are different phalli in question. However, now I believe that this paradox is resolved if we note that it is not the phallus in question but one’s relation to having or not having it, and more specially one’s relation to the phallic function itself. Perhaps this this question gets resolved in the twentieth seminar on sexuation, I’m not sure. The point is that to not be without having means that things are a bit obscure. It is not that one definitely has the phallus or the object, and it is not that one definitely does not have the phallus or the object. The reality of the situation is that things are a bit more complicated. For example, if I state that my colleague Kevin is annoying or that he is not annoying, the case is closed. But if I say that Kevin is not without his annoying tendencies, things are a bit more obscure. Finally, in French, this “without” is rendered “sans” and points at something a bit more open-ended than English: sans is close to sine which means “their” and, as we know, in English “their” implies a certain ownership at the heart of being: eg., “Their Phalli.” So we are dealing with a form of not having which also carries a sense of having.

There are good reasons for this obscure rendering of not without having. Lacan notes that the truth of the exchange of women, in Freud, is that the women must not be seen to have phalli – if it gets seen then there is anxiety.

The next question we should ask concerns the object in question: if, on the left hand side of the mirror schema, there is the object, a, then, on the right side, we see the i'(a). Why is it that there is still an a, but bracketed, on the right side? Lacan provides a very easy explanation: it is because the is still present – it is just wrapped up in the specular image. There are two objects here: the main object, namely, object a, and the specular image. And then there are two types of specular images. We can understand them by noting two phases in the mirror schema. First, there is an identification with the specular image in the mirror. This constitutes the first misrecognition of the subject – the false totality. We can see the false totality from the mirror schema: the vase has the flowers inside of it and it sits on top of a floating shelf. Second, there is another relation establish via the imaginary other, which we refer to as the “semblable.” So we now know that the semblable is not the same as the specular image. There are two images here. The second, semblable, is the image or identity of the subject as retrieved from the Other’s identity.

Furthermore there are two types of objects. There are objects that can be owned, in a sense. This is an object that can either be shared or it can be an object of competition, a scarce object.  This is an object of belonging: it is either your object or it is mine. Hence, the object if belonging is always an object of rivalry. Some objects can be shared. These objects have a price on them. We come to an agreement about them, about who owns them and about the price we have to pay to have possession of them. But some objects have nothing to do with belonging, nothing to do with sharing. These objects show up when anxiety signals them. They come before the constitution of a common object. This is what is involved with object a.

This is also why psychoanalysis and communism do not share objects of study. A good amount of leftist political philosophy has either the “commune” or the “commons” as an object of study. As it goes, the commons is that which comes before government and corporate imposition. And so the commons are by necessity on the defense. On the other hand, communes come after the imposition of a new government as the prize won by who knows how many years or centuries of struggle. But psychoanalysis has as its object something much more obscure, something which is shared, no doubt, but something which also exists outside of the field of sharing, rivalry, and exchange. It is something we are not without having. The commune comes too late and the commons too soon, the object of psychoanalysis exists synchronically: it is signaled by anxiety, whether before the loss of the commons or after the victory of communism.

What are going on about here is the choice of object. The mirror schema helps us understand these objects. There are objects that are attractive to us and these are situated on the side of i'(a). But these objects can also signal anxiety – this is why the remains within brackets inside of the image. Images are not without anxiety. Perhaps this brings us back to the concept of the uncanny. In any case, the original erogenous investment is within the i'(a), it is both present and concealed (in brackets). The i’ thus frames or envelops the object.

We return to the chart from previous classes: inhibition, symptom, anxiety:

Inhibition Impediment Embarrassment ($)
Emotion Symptom Passage à l’Acte
Turmoil Acting-Out Anxiety

We further stated that things get more difficult as you move from left to right, and that things involve more movement as you move from top to bottom. In a sense, the image, the i’ is at the top left and the is at the bottom right. But we can further add now that from top to bottom involves transference. You can see the transference especially in the middle row: emotion, symptom, passage a l’acte. Perhaps this also explains why the transference is essential to getting to the anxiety, the object of our method.

Lacan then distinguishes between repetition of need and the need for repetition. This is important because the two are not similar. When we insist that transference involves repetition we necessarily risk falling back in the diachronic problem of historicization, the temporal problem, and the problem of the origin. However, when we insist on the need for repetition we are not necessarily falling into that trap. Rather, we allow ourselves to adopt the synchronic position which allows for an examination of latent determinations. However even here we risk approaching a certain limit of analysis. Something ends, it ends with, for Freud, either the castration complex or else penis envy. There is something unanalyzable here.

We turn now to the cross-cap.


The cross-cap provides us with the ability to think about the co-presence of objects: the object a and the object of the specular relation, the common object, namely, i'(a). We must ask the question: why is i'(a), the specular image, distinct from the a. Does the former represent the latter? What is the relationship between the two? We have so far only said that a line is drawn, a communication is established, between the two. What sort of transition occurs? We can say that the left becomes right and the right becomes left. We know this: when we look in the mirror, everything is inverted.I know this logic very well: as a poor kid growing up in Canada, if I lost a glove in the winter months I would simply take one from a different pair and turn it inside out.

This is how the ego works as well. It is the projection of a surface, like the glove. This explains why Freud often described the ego in topological terms (in fact I can not verify this, but Lacan certainly seems convinced by this point). The cross-cap allows us to think about the duplication of the specular image, it allows us to think about how it is that a single surface can be turned inside out. If you cut the cross-cap you end up with a mobius strip. Lacan gives us a description of this single surface: “An ant walking along one of the apparent faces will pass over to the other face without needing to go over the edge. In other words, the moebius strip is a surface that has just one face and a surface with just one face cannot be turned inside out.” (And now we know where the idea for the image on the cover of the book comes from.) It can not be turned inside out because it is already inside out, it is already both inside and outside.

On the one hand, we have the specular image – the upright case, and this is the ideal ego: i'(a). It is also constitutive of the entire world of the common object. On the other hand, we have the object a in the form of a cross-cap. This is what can be cut out of the cross-cap, what can be separated from it. Certainly, it remains attached to the specular image – it joins up with it. But it is nonetheless cut from it. When the object a is cut from it the specular image becomes uncanny, and invasive – it is the double. It is the double of the subject, but not anymore an image of him.


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