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(All parts in English)

I will today cast a few points which will rather partake of the promise.

Logic of the fantasy—such is the title I have given this year to what I intend to present to you, of what imposes itself, at the point where we now stand, from a certain path. A path which involves—I will strongly recall it today—that kind of very particular return we already saw last year as inscribed in the structure and which is properly, in all that Freud’s thought unveils, fundamental. This return is called “repetition.”

To repeat is not to retrieve the same thing, as we will articulate shortly, and contrary to what one may believe, it is not necessarily to repeat indefinitely. We will thus return to themes which, in a certain way, I have already situated long ago. This is well, too, because we are at the time of this return and of its function, that I believed I could delay no longer in delivering to you, assembled, what until now I had thought necessary as a minimal marking of this trajectory, namely that volume [Écrits, Seuil, 1966] which you now already have within your reach.

This relation to the written, which, after all, in a certain way, I had until now tried, if not to avoid, at least to delay, is because this year it will no doubt be possible for us to deepen its function, and thus again, I believed I could take this step.

These few indicative points that I will lay out before you today, I have chosen them as five.

— The first consists in reminding you of the point we have reached concerning the logical articulation of fantasy, which will be, strictly speaking, this year, my text.

— The second, in recalling the relation of this structure of fantasy, which I will have first reminded you of, to the structure, as such, of the signifier.

— The third, to something essential and truly fundamental that it is fitting to recall, concerning what we can—what we must—this year call, if we place at the forefront what I have called the logic in question, a crucial remark concerning the Universe of discourse.

— The fourth point: some indication regarding its relation to writing as such.

— Finally, I will conclude with the reminder of what FREUD articulates for us, concerning what is at stake in the relation of thought to language and to the unconscious.

Logic of the fantasy, then, we will begin with the writing I have already formed of it, namely with the formula: (S◊a)
S barred, lozenge, little (a), this in parentheses.

I remind you of what the S means: the barred S represents, stands in this formula for what is at stake concerning the division of the subject, which lies at the principle of all Freudian discovery and which consists in the fact that the subject is, in part, barred from that which properly constitutes it as a function of the unconscious.

This formula establishes something that is a link, a connection between this subject as so constituted and something else which is called little (a). Little (a) is an object whose status what I call this year “doing the logic of fantasy” will consist in determining: the status, precisely in a relation which is a logical relation in the proper sense.

A strange thing no doubt, and on which you will allow me not to dwell: I mean that what the term fantasy suggests in terms of relation to phantasia, to imagination, I will not take pleasure, not even for a moment, in marking the contrast with the term logic with which I intend to structure it.

It is no doubt because fantasy, as we claim to institute its status, is not so fundamentally, so radically antinomic as one might at first think, to that logical characterization which, properly speaking, disdains it.

Just as the imaginary trait of what is called the object (a) will appear to you even more clearly as we mark what allows it to be characterized as a logical value, it seems to me that it is, at first glance, much less related to the domain of what is, strictly speaking, the imaginary. Rather, the imaginary clings to it, surrounds it, accumulates upon it. The object (a) is of another status.

Surely it is desirable that those who are listening to me this year had the opportunity last year to form some apprehension of it, some idea. Of course, this object (a) is not something which, even so easily… for everyone and especially for those for whom it is the center of their experience: psychoanalysts …has yet, if I may say so, enough familiarity for it to be presented without fear, even without anxiety.

— “So what did you do?” one of them said to me, “what need did you have to invent this object little (a)?”

I think, in truth, that taking things from a slightly broader horizon, it was high time. Because without this object little (a)… whose effects—it seems to me—have made themselves felt rather extensively for people of our generation …it seems to me that much of what has been done as analyses, both of subjectivity and of history and its interpretation, and specifically of what we have lived through as contemporary history, and very precisely of what we have quite crudely labeled with the most inappropriate term under the name of “totalitarianism.”

Anyone who, having understood it, will apply to it the function of the category of the object little (a), will perhaps see illuminated what was at stake in that which we still surprisingly lack satisfactory interpretations for.

The barred subject, in its relation with this object little (a), is joined in this formula written on the board (S◊a) by this something, which appears as a lozenge, which I earlier called the poinçon, and which, in truth, is a sign forged specifically to conjoin within it what can be isolated from it, depending on whether you separate it by a vertical stroke or a horizontal stroke.

Separated by a vertical stroke:

it represents a double relation which can be read at first glance as greater than (>) or less than (<):
— S less than or – just as well – greater than capital A. [Lacan’s slip, actually: (a)]

— S included in or just as well excluded from capital A [slip reiterated].

What does this mean? If not that what is suggested at the forefront of this conjunction is something that is logically called the relation of inclusion or again of implication, provided that we make it reversible and which is articulated… I am going quickly no doubt, but we will have plenty of time to expand upon and revisit these things: today I merely indicate, it suffices that we lay down a few suggestive markers …this relation which is articulated from logical articulation, which is called: “if and only if.”

S barred in this sense, namely: the poinçon being divided by the vertical bar, it is the barred subject in this relation of “if and only if” with the little (a): (S◊a)

This gives us pause: there therefore exists a subject… This is what, logically, we are forced to write at the principle of such a formula. Something is proposed to us here which is the division between factual existence and logical existence.
— Factual existence of course refers us to the existence of |beings|—the word beings between two bars—beings—or not—speaking. These are generally living. I say “generally” because it is not at all necessary: we have the stone guest who does not exist only in the scene where MOZART animates him, he walks among us quite commonly!

— Logical existence is something else and as such, has its own status: there is subject from the moment we do logic, that is to say, when we have to handle signifiers.

What there is of factual existence, namely that something results from there being subject at the level of beings who speak, is something that, like all factual existence, requires that a certain articulation already be established. Yet nothing proves that this articulation is carried out in direct grip, that it is directly from the fact that there are living or other beings who speak, that they are thereby and in an immediate way determined as subjects.

The “if and only if” is there to remind us. I am repeating here articulations that we will have to go over again, but they are in themselves sufficiently unusual, sufficiently little-trodden, that I believe I must indicate to you the general line of my intention in what I have to explain before you.

Little (a) results from an operation of logical structure, one carried out not in vivo, not even on the living, not strictly speaking on the body in the confused sense the term “body” still holds for us… it is not necessarily the “pound of flesh,” although it can be, and after all, when it is, that doesn’t work out so badly …but finally, it appears that in this entity so little apprehended as the “body,” there is something which lends itself to this operation of logical structure, which remains for us to determine. You know: the breast, the scybala, the gaze, the voice, these detachable pieces and yet entirely linked to the body, these are what are at stake in the object little (a).

To make the (a), then, let us limit ourselves, since we will impose upon ourselves a certain logical rigor, to pointing out here that one needs some “ready-to-be-delivered”: that may, for the moment, suffice for us. And it solves nothing! It solves nothing regarding that into which we must venture: to make the fantasy, there must be some “ready-to-wear.”

You will allow me here to articulate a few theses in their most provocative form, since after all what is at stake is to detach this domain from the capture-fields that irresistibly bring it back to the most fundamental illusions: what is called psychological experience. What I am about to advance is precisely what will be supported, what will be founded, what will be shown to have consistency, by all that I will this year, for you, unfold.

Unfold—I have already said—it has long been done. In the fourth year of my seminar, I treated The Object Relation: already regarding the object little (a), everything has been said as to the structure of the relation of the little (a) to the Other, quite specifically and very sufficiently initiated in the indication that it is from the mother’s imaginary that the child’s subjective structure will depend. Surely, what it is for us to indicate here is how this relation is articulated in properly logical terms, that is, fundamentally depending on the function of the signifier.

But it must be noted that for someone who was then summarizing what I was able to indicate in this direction, the slightest mistake… I mean: error concerning the belonging of each of the terms of these three functions which could then be designated as subject, object—in the sense of object of love—and beyond this, our current object (a) …the slightest mistake, namely a reference to “the imagination of the subject,” could obscure the relation that was being outlined.

To not locate in the field of the Other as such, the function of the object (a) [leads someone to write?] for example, that in the status of the pervert, it is both the function, for him, of the phallus and the sadistic theory of coitus that are the determinants. Whereas it is not at all the case; it is at the level of the mother that these two effects function.

I thus advance, in what is to be stated here: to make the fantasy, one needs some “ready-to-wear.” What carries, what bears the fantasy? What carries the fantasy has two names, those that concern one and the same substance—if you will allow me that term—reduced to this function of surface as I articulated it last year… this primordial surface that we need to make our logical articulation function, you already know some of its forms: they are closed surfaces, they partake of the bubble with the distinction that they are not spherical. Let us call them “the bubble” and we will see what motivates, what attaches to, the existence of bubbles in the real …this surface that I call bubble properly has two names: desire and reality.

It is quite useless to tire oneself articulating “the reality of desire” because, primordially, desire and reality have a texture-related connection without rupture; they therefore need no stitching, they do not need to be sewn back together. There is no more a “reality of desire” than it is correct to say “the reverse of the front”: there is only one and the same fabric which has a reverse and a front.

Still, this fabric is woven in such a way that one passes from one to the other of its sides without realizing it, since it is without rupture and without seam, and that is why I emphasized so strongly before you a structure like the so-called projective plane, illustrated on the board in what is called the mitre or the cross-cap. That one passes from one side to the other without realizing it, that already says that there is only one—I mean: one face.

Nevertheless, just as in the surfaces I have just evoked, of which a partial form is the Möbius strip: there is a front and a reverse. This must be posited in an original way to recall how this distinction between front and reverse is founded as already there before any cut.

It is clear that whoever—like the animalcules mathematicians mention concerning the function of surfaces—would be entirely implicated within this surface, would see, of that nonetheless certain distinction between the front and the back, not a drop, in other words: absolutely nothing.

Everything that pertains, in the surfaces I have brought up before you, sequenced from the projective plane to the Klein bottle, to what may be called extrinsic properties, extends quite far: I mean that most of what seems most obvious to you when I illustrate these surfaces are not properties of the surface; it is in a third dimension that it takes on its function.

Even the hole in the middle of the torus—do not believe that a purely toric being would even notice its function! Nevertheless, this function is not without consequence, since it is on the basis of this that I have, my God—something like almost six years ago—already tried to articulate—for those who were listening to me then, among whom I see some now in the front row—to articulate the relations of the subject to the Other in neurosis.

Indeed, it is of this third dimension, within it, of the Other that it is a matter, as such. It is in relation to the Other and insofar as there is this other term, that one may distinguish a front from a back; this is not yet to distinguish reality and desire. What is front or back primitively at the place of the Other, in the discourse of the Other, is played heads or tails. It concerns the subject in no way, for the reason that the subject does not yet exist.

The subject begins with the cut.

If we take, among these surfaces, the most exemplary because the simplest to handle, namely the one I earlier called the cross-cap or projective plane, a cut—but not just any cut, I mean… I remind those for whom these images still retain some presence: if, I repeat, in a purely imagistic way, but one whose image is necessary, namely upon this bubble:

whose walls (let us call them anterior and posterior) come here [X], at this no less imaginary line, to intersect. It is in this way that we represent the structure of what is at stake …any incision, any cut that crosses this imaginary line will institute a total change in the structure of the surface:

— namely that this entire surface becomes what we learned last year to cut from this surface under the name of object (a),

— namely that—the surface in its entirety—becomes a flattenable disc, with a front and a back, of which one must say that one cannot pass from one to the other except by crossing a boundary.

This boundary is precisely what renders this crossing impossible—at least this is how we may articulate its function. At the start, in initio, the bubble—through this first cut, rich with an implication not immediately visible—through this first cut becomes an object (a). This object (a) retains—because it has from the outset this relation, so that anything at all may be explained from it—a fundamental relation with the Other.

Indeed, the subject has not yet appeared with this single cut whereby the bubble instituted by the signifier in the real first lets fall this foreign object which is the object (a). It is necessary and sufficient, in the structure here indicated, that one realize what is involved in this cut, in order also to realize that it has the property, by simply being doubled, of rejoining itself—in other words, that it is the same to make a single cut or to make two:

to consider the gaping of what exists here between my two twists which are but one, as the equivalent of the first cut, which indeed:
— if I spread it apart, it is this gaping that is realized,
— but if I make, in the fabric where the cut is to be made, a double cut, I extract from it, I restore from it what was lost in the first cut: namely a surface whose front continues into the back. I restore the primal non-separation of reality and desire.

How—afterwards—we will define “reality,” what I earlier called the “ready-to-wear of fantasy,” that is to say, what constitutes its “frame,” and we will then see:
— that reality, all of human reality, is nothing other than a montage of the symbolic and the imaginary,
— that desire, at the center of this apparatus, of this frame we call “reality,” is also, properly speaking, what covers, as I have always articulated, what must be distinguished from human reality and which is properly speaking the real, which is never more than glimpsed, glimpsed when the mask falters, which is the mask of fantasy—that is to say, the same thing that SPINOZA grasped when he said: “Desire is the essence of man.”

In truth, this word “man” is a term of transition impossible to retain in an atheological system, which is not the case with SPINOZA. To this Spinozist formula, we must simply substitute this formula—this formula whose misrecognition leads psychoanalysis into the crudest aberrations—namely: “Desire is the essence of reality.”

But this relation [of object (a)] to the Other—without which nothing can be perceived of the real play of this relation—is what I have tried to outline for you, resorting to the old device of Euler’s circles, as the fundamental relation. Certainly, this representation is insufficient, but if we accompany it with what it supports in logic, it can serve: what arises from the relation of the subject to object (a) is defined as a first circle, which another circle—that of the Other—comes to intersect; (a) is their intersection.

It is through this that forever…
in this relation of an originally structured place, which is the one where I tried to articulate for you, three years ago, alienation …the subject can only be instituted as a relation of lack to this (a), which is of the Other, unless it wants to situate itself within the Other, and then has it only as equally amputated of this object (a). The relation of the subject to object (a) involves what the image of Euler takes as its meaning when it is brought to the level of simple representation of the two logical operations called “union” and “intersection.”

The “union” depicts for us the linkage of the subject to the Other, and the intersection defines for us the object (a). The set of these two logical operations are the very operations I have posited as original, by saying that (a) is the result achieved by logical operations and that they must be two.

What does this mean? That it is essentially in the representation of a lack, insofar as it runs, that the fundamental structure of the bubble is instituted, which we first called the fabric of desire. Here, on the plane of the imaginary relation, is established a relation exactly inverted from that which links the ego to the image of the other. The ego is, as we shall see, doubly illusory:
— illusory in that it is subject to the avatars of the image, that is to say also delivered to the function of denial or semblance.
— It is also illusory in that it establishes a perverted logical order, whose formula we will see—in psychoanalytic theory—so far as it imprudently crosses that logical boundary, which presumes that at some given moment, presumed to be primordial in the structure, what is rejected can be called “non-ego.”

This is precisely what we contest!

The order at stake, which implies—without knowing it and in any case without stating it—the entry into play of language, admits of no such complementarity. And this is precisely what will lead us to place at the forefront, this year, in our articulation, the discussion of the function of negation.

Everyone knows, and can observe in the collection now at your disposal, that the first year of my seminar at Sainte-Anne was dominated by a discussion of Verneinung where Mr. Jean HIPPOLYTE, whose intervention is reproduced in the appendix of that volume, splendidly punctuated what Verneinung was for FREUD. The secondarity of Verneinung is articulated there powerfully enough that it can no longer in any way be admitted that it might arise straightaway at the level of that first split we call pleasure and unpleasure. That is why, in this lack instituted by the structure of the bubble, which makes the fabric of the subject, it is in no way a matter of limiting ourselves to the term—now obsolete for the confusions it implies—of “negativity.”

The signifier cannot in any way…
even if it was necessary, for a time, to drill its function pedagogically into the ears of those listening to me …the signifier…
and you may notice that I have never properly articulated it as such …is not merely that which supports what is not there.

The fort-da, insofar as it relates to the maternal presence or absence, is not the exhaustive articulation of the entry into play of the signifier. What is not there, the signifier does not designate—it engenders it. What is not there, originally, is the subject itself. In other words, originally there is no Dasein except in the object (a), that is to say, in an alienated form, which remains to mark, all the way to its endpoint, any enunciation concerning Dasein. Is it necessary to recall here my formulas: that there is a subject only by a signifier and for another signifier. This is the algorithm:

S, insofar as it stands in for the subject, functions only for another signifier. Urverdrängung, or primal repression, is this: what one signifier represents for another signifier. It doesn’t bite on anything, it absolutely constitutes nothing, it accommodates itself to an absolute absence of Dasein.

For about sixteen centuries at least, Egyptian hieroglyphs remained solitary as much as misunderstood in the sands of the desert—it is clear and has always been clear to everyone that this meant that each of the signifiers engraved in stone, at minimum, represented a subject for the other signifiers. If that were not so, no one would ever have even taken it for writing! It is in no way necessary that a writing mean something to anyone for it to be writing and for it, as such, to manifest that each sign represents a subject for the one that follows it.

If we call this Urverdrängung, that means we admit—it appears to us consistent with experience—to conceive what happens, namely: that a subject emerges in the state of the barred subject as something that comes
— from a place where it is supposed to be inscribed,
— to another place where it will be inscribed again.

Namely, in exactly the same way as when I previously structured the function of metaphor, insofar as it is the model of what happens in the return of the repressed:

Likewise, it is insofar as, with regard to that first signifier—whose nature we shall soon identify—the barred subject [S] which it abolishes comes to emerge at a place where we can now offer a formula not yet given: the barred subject, as such, is that which represents—for a signifier, the signifier from which it emerged—a meaning. I mean by “meaning” exactly what I had you hear at the beginning of a previous year under the formula: “Colourless green ideas sleep furiously.” Which may be translated into French as something that admirably depicts the ordinary order of your cogitations: “Des idées vertement fuligineuses s’assoupissent avec fureur!”

This is precisely due to the failure to recognize that they all address that signifier of the subject’s lack, which a certain first signifier becomes as soon as the subject articulates his discourse. Namely, what all psychoanalysts have nonetheless perceived well enough, though they knew not how to say anything of it that is worth the while, namely, the object (a), which at this level fulfills precisely the function that FREGE distinguished from Sinn under the name of Bedeutung [meaning], it is the first Bedeutung, the object (a), the first referent, the first reality, the Bedeutung that remains because it is, after all, all that remains of thought at the end of all discourse.

— Namely, what the poet may write without knowing what he says when he addresses his “mother Intelligence in whom gentleness flowed, what is this negligence that lets her milk run dry?”
— Namely, a gaze seized, which is that transmitted at the birth of the clinic.
— Namely, what one of my students recently took as a subject at the John HOPKINS University Congress, calling it “The voice in the literary myth.” [Guy Rosolato: The voice and the literary myth]
— Namely, also what remains of so many thoughts expended in the form of pseudo-scientific rubbish and which may as well be called by its name, as I have done for a long time regarding a part of the analytic literature, and which is called: shit. With the authors’ own admission, moreover! I mean that with a very slight failure in reasoning concerning the function of the object (a), one of them may quite well articulate that there is no other support for the castration complex than what is modestly called “the anal object.”

It is therefore not a matter of a labeling based on mere subjective judgment, but rather the necessity of an articulation whose mere formulation should stand out, since after all, it is not being offered by the least qualified pens, and since this, too, will be our method this year, in formulating the Logic of fantasy, to show where in analytic theory it comes to stumble. I have not, after all, named this author, whom many know. Let it be well understood that even a faulty reasoning is still reasoned—that is to say, open to rational capture—but that is not obligatory!

And the object (a) in question can, in a given article, appear completely naked and be unappreciated on its own. This is what we will have the opportunity to demonstrate in certain texts, which after all, I see no reason not to distribute quite broadly to you as practical work, if I have enough of them at my disposal—which is more or less the case.

This will come at the moment when we will have to tackle a certain register, and already now I want nonetheless to mark what prevents the acceptance of certain interpretations that have been given of my function of metaphor…
I mean those of which I have just given you the least ambiguous example …from confusing it with anything that would make it a kind of proportional relation.

When I wrote that substitution…
the act of grafting one signifier in place of another in the signifying chain …is the source and origin of all meaning, what I articulated is correctly interpreted in the form in which, today, through the emergence of this barred subject as such, I have given you the formula.

This demands of us the task of giving it its logical status.

But to show you right away an example of the urgency of such a task, or simply of its necessity, observe that confusion was made from this four-term relation:

the S’, the two S’s and the little s of the signified, with that proportional relation in which one of my interlocutors…
Mr. PERELMAN, the author of a theory of argumentation, reviving a rhetoric long abandoned …articulates metaphor, seeing in it the function of analogy, and claiming that it is from the relation of one signifier to another insofar as a third reproduces it by bringing forth an ideal signified, that he grounds the function of metaphor. To which I responded, at the time.
It is only from such a metaphor that the given formula may arise, namely:

S’ over the little s of signification enthroned at the top of a first register of inscription, whose underdrawn, whose Unterdrückt, whose other register substantifying the unconscious, would be constituted by this strange relation of one signifier to another signifier, from which we are additionally told that it is from there that language would take its ballast.

This so-called formula of “reduced language,” I believe you now sense, rests on an error, which is the induction of a proportional structure into this four-term relation. It is hard to see—likewise—what might come of it, since the relation S/S then becomes rather difficult to interpret. But we see, in this reference to a “reduced language,” no other aim—an aim, moreover, openly declared—than to reduce our formula that “the unconscious is structured like a language,” which, more than ever, must be taken literally.

And since today it turns out that I will not cover the five points I had announced to you, I nonetheless arrive at the point of being able—for you—to punctuate what is here the key to the entire structure, and what renders the endeavor, which has found itself thus articulated: …very precisely at the beginning of the small collection I mentioned earlier, concerning the turning point in my relation with my audience that was marked by the Bonneval Congress …it is erroneous to thus structure, on a so-called myth of “reduced language,” any deduction of the unconscious, for the following reason:
it is in the nature of every and of no signifier to never, in any case, be able to signify itself.

The hour is late enough that I will not impose upon you, in haste, the writing of that inaugural point of all set theory, which implies that this theory can only function from an axiom known as the axiom of specification. That is to say, that it is only worthwhile to operate with a set if there exists another set that can be defined by the definition of certain x within the first, as freely satisfying a certain proposition. “Freely” means independently of any quantification: “small number” or “all.”

It follows—I will begin my next lesson with these formulas—it follows that by positing an arbitrary set, and in it defining the proposition which I have indicated as specifying certain x within it, as simply being that x is not a member of itself—which, as concerns us here, namely in relation to what becomes imperative as soon as one seeks to introduce the myth of a reduced language, that there is a language which is not reduced, that is to say which constitutes, for example, “the set of signifiers.”

The peculiarity of “the set of signifiers,” I will show you in detail, necessarily includes this…
if we admit only that the signifier cannot signify itself …necessarily includes this: that there is something that does not belong to this set. It is not possible to reduce language, simply for the reason that language cannot constitute a closed set—in other words: “There is no universe of discourse.”

For those who may have had some difficulty in understanding what I have just formulated, I will simply recall something I already said at the time: that the truths I have just stated are simply those that appeared in a confused manner during the naive period of the establishment of set theory, in the form of what is falsely called “Russell’s paradox”—for it is not a paradox, it is an image—the catalog of all catalogs that do not contain themselves. What does this mean?
— Either it contains itself and it contradicts its own definition,
— or it does not contain itself and then it fails its mission.

This is in no way a paradox. One simply has to declare that in making such a catalog, one cannot carry it to completion, and for good reason.
But what I earlier stated under the formula that: in the universe of discourse there is nothing that contains everything,
this, properly speaking, invites us to be especially cautious in handling what is called “whole” and “part,” and to require from the outset that we strictly distinguish this—that will be the object of my next lecture—the One from totality…
which I have just refuted, stating at the level of discourse that there is no Universe,
which certainly leaves even more in suspense than we might suppose it would anywhere else …to distinguish this One from the countable 1, in that, by its very nature, it evades and slips away, such that it can only be the 1 by repeating itself at least once and by folding back on itself, instituting at the origin the lack in question: it is a matter of instituting the subject.