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(All parts in English)

ΜονἀςἐστιΧαθἤνἕκαστοντῶνὄντωνἓνλέγεται
Ἀριθμὁςδἑτὁἑκμονάδωνσυγκείμενονπλῆθος

(EUCLID, Elements, VII, 1-2)

[Unity: that according to which every thing that is is named one.
Number is a multitude composed of several units.
Translation Didier HENRION, 1632]

This sentence is taken from the beginning of the Seventh book of EUCLID’s Elements, and it seemed to me, all things considered,
the best that I have found to express, on the mathematical plane, this function to which I wanted to draw
your attention last time, of the ‘1’ in our problem. It is not that I had to look for it, that I had
trouble finding among mathematicians something related to it: mathematicians — at least some of them, those who in each period were at the forefront in the exploitation of their field — have concerned themselves greatly with the status of unity, but they are far from all having arrived at equally satisfactory formulas.

It even seems that for some, this went in their definitions straight in the opposite direction to what is appropriate. Be that as it may, I am not displeased to think that someone like EUCLID, who all the same in matters of mathematics cannot be regarded otherwise than as of good stock, gives this formula — all the more remarkable precisely because articulated by a geometer — that what is unity, for that is the sense of the word Μονἀς [monas], is unity in the precise sense in which I tried to designate it for us last time under the designation of what I called — I shall return again to why I called it thus — the unary trait, the trait insofar as it is the support as such of difference; that is indeed the sense that Μονἀς has here, it can have no other, as the rest of the text is going to show us.

So Μονἀς [monas], that is to say this unity in the sense of the unary trait such as here I indicate to you that it overlaps, that it points in its function to that at which we arrived last year [Cf. seminar 1960-61: Transference…, session of 07-06] in
the field of our experience to locate in FREUD’s very text as the einziger Zug, that by which each of the beings
is said to be ‘1’, with what this neuter ἕν of εἶς, which means one in Greek, brings in ambiguity, being precisely what can be used in Greek as in French to designate the function of unity insofar as it is that factor of coherence by which something is distinguished from what surrounds it, makes a whole, a One in the unitary sense of the function,
thus Μονἀς [monas], it is by the intermediary of unity that each of these beings comes to be said to be ‘1’; the advent in saying
of this unity as a characteristic of each of the beings is designated here, it comes from the use of Μονἀς
which is nothing other than the single trait.

This thing was worth being noted precisely under the pen of a geometer, that is to say of someone who is situated in
mathematics in such a way apparently that — for him at minimum must we say — intuition will preserve all its original value. It is true that it is not just any geometer, since in sum we can distinguish him in the history of geometry as the one who first introduces, as having absolutely
to dominate it, the requirement of demonstration over what one may call experience, familiarity with space.

I complete the translation of the quotation: ‘…that number, for its part, is nothing other than that sort of multiplicity which arises precisely
from the introduction of units’, of monads, in the sense in which it is understood in EUCLID’s text. If I identify this function
of the unary trait, if I make it the unveiled figure of this einziger Zug of identification, to which we were led by our path
of last year, let us point out here — before advancing further and so that you know that contact is never lost with what is the most direct field of our technical and theoretical reference to FREUD — let us point out that this is
identification of the second species, page 117, volume 13 of FREUD’s Gesammelte Werke.

It is indeed in concluding the definition of the second species of identification that he calls regressive, insofar as it is linked to some abandonment of the object that he defines as the ‘loved-object’ — which is humorously designated in TŒPFFER’s drawing with a hyphen — this loved-object ranges from the chosen woman to rare books. Fie! as someone
in my circle used to say, with some indignation at my bibliophilia, it is always to some extent linked to the abandon-
ment or loss of this object that there occurs — FREUD tells us — this sort of regressive state from which there arises this identification, he emphasizes, with something that is for us a source of admiration, as whenever the discoverer designates
a secure trait of his experience of which it would seem at first sight that nothing necessitates it, that it is a contingent character. Indeed he justifies it only by his experience.

It is quite remarkable that in this sort of identification where the ego copies in the situation now the unloved object, now the loved object, but where in both cases this identification is partial — höchstbeschränkte, highly limited, but with an accent in the sense of narrow, constricted —
that it is nur einen einzigen Zug, only a single trait of the objectalized person, which is like
the ‘ersatz’ borrowed from the German word. It may therefore seem to you that approaching this identification by the second species is for me too to beschränken, to limit myself, to narrow the scope of my approach, for there is the other one, the identification of the first species,
that singularly ambivalent one which is made against the background of the image of assimilative devouring.

And what relation does it have to the third? The one that begins immediately after this point that I indicate to you
in the Freudian paragraph: identification with the other by way of desire, the identification that we know well,
which is hysterical, but precisely which I taught you that one could well distinguish — I think you should sufficiently realize this —
only from the moment one has structured — and I do not see that anyone has done so elsewhere than here and before it was done here — desire as presupposing in its underlyingness exactly, at minimum,
the whole articulation that we have given of the relations of the subject specifically to the signifying chain, insofar
as this relation profoundly modifies the structure of every relation of the subject with each of his needs.

This partiality of the approach, this entry, if I may say so, ‘on the bias’ into the problem, I have the feeling that, while
indicating it to you, it is fitting that I legitimize it today, and I hope to be able to do so quickly enough to make myself heard
without too many detours by reminding you of a principle of method for us: that, given our place, our function,
what we have to do in our clearing-work, we must beware, let us say, of the general, and push this
as far as you like: of genus, and even of class.
It may seem singular to you that someone who for you emphasizes the pregnance in our articulation
of the phenomena we have to deal with, of the function of language, here distinguishes himself from a mode of relation
that is truly fundamental in the field of logic. How are we to indicate, to speak of a logic that must,
at the first moment of its departure, mark the mistrust, which I mean to posit as altogether original, of the notion of ‘class’?

It is precisely in this that the field we are trying to articulate here is original, is distinguished. It is no prejudice
of principle that leads me there. It is the very necessity of our object, ours, that pushes us toward what effectively develops over the years, segment by segment: a logical articulation that does more than suggest, that goes
closer and closer, specifically this year I hope, to disengaging algorithms that allow me to call ‘logic’ this chapter that we shall have to adjoin to the functions exercised by language in a certain field of the real, that in which we others, speaking beings, are the conductors. Let us therefore beware to the utmost of every Κοινονία τῶνγενῶν [Koinonia ton genon], to use a Platonic term [Plato, Sophist, 254b], of everything that is the figure of ‘community’ in any genus, and especially in those that are for us the most original.

The three identifications probably do not form a class. If they can nevertheless bear the same name
which brings to it a shadow of concept, it will also no doubt be up to us to account for that. If we operate with exactness, this does not seem to be a task above our strength. In fact, we already know that it is at the level of the particular that there always arises what for us is universal function, and we need not be too surprised at this at the level of the field where we move, since, concerning the function of identification, we already know — we have worked together enough to know it — the sense of this formula, that what happens, happens essentially at the level of structure.

And structure — Must it be recalled? And precisely I believe that today, before taking one step further, I must recall it — is what we introduced specifically as specification, register of the symbolic. If we distinguish it from the imaginary and the real, this register of the symbolic — I also believe I must point out all that there might be here of hesitation in leaving on the margin that over which I have seen no one openly worry, all the more reason to dispel all ambiguity on this point — this is not an ontological definition: these are not fields of being that I am separating here.

If from a certain moment — and precisely that of the birth of these seminars — I believed I had to bring into play this triad of the Symbolic, the Imaginary, and the Real, it is insofar as this third element, which until then was not at all
in our experience sufficiently discerned as such, is exactly in my eyes what is constituted exactly by this fact of the revelation of a field of experience. And to remove all ambiguity from this term — it is a matter of Freudian experience — I shall say, of a field of ‘experiment’: I mean that it is not a matter of Erlebnis [lived experience].

It is a matter of a field constituted in a certain way, up to a certain degree by some artifice, the one inaugurated
by psychoanalytic technique as such, the complementary face of the Freudian discovery, complementary as the obverse is to the reverse, really joined to it. What was first revealed in this field, you know well of course:
whether it be the function of the symbol and by the same token the symbolic, from the outset these terms had the fascinating, seductive, captivating effect that you know, across the whole field of culture, that shock effect of which you know that almost no thinker, and even among the most hostile, was able to escape it.

It must be said that it is also a fact of experience that we have lost, from that time of revelation and of its correlation with the function of the symbol, we have lost its freshness, if one may say so, that freshness correlative to what I called the shock effect, of surprise, as FREUD himself properly defined it as characteristic of this emergence of the relations of the unconscious.

These sorts of flashes on the imago, characteristic of that period, by which, if one may say so, there appeared to us
new modes of inclusion of imaginary beings, whereby suddenly something, which was their meaning properly speaking, was illuminated by a grasp that we could do no better, in order to qualify them, than to designate by the term
‘Begriff’. Sticky grasp, where the planes stick, function of fixation, some kind of Haftung [liability/responsibility]
so characteristic of our approach in this imaginary field, at the same time evoking a dimension of genesis where
things stretch out rather than evolve, a certain ambiguity that would make it possible to leave the schema ‘evolution’
as present, as implied, I would say naturally, in the field of our discoveries.

How in all this can we say that in the end what characterizes this dead time pointed out by all sorts of theorists and practitioners in the evolution of the doctrine under various headings and rubrics, was pro-
duced?
How did this kind of ‘fizzling out’ [long feu: misfire/slow-burning fuse] arise, which imposes on us what is properly our object here, the one where I am trying to guide you, to take up again our whole dialectic on purer principles? It is indeed that somewhere
we must designate the source of this sort of going astray which means that in sum we can say that after a certain time, these insights remained vivid for us only by referring ourselves back to the time of their emergence.

And this even more so on the plane of effectiveness in our technique, in the effect of our interpreta-
tions, in their effective part. Why have the imagos discovered by us become in some way banalized? Is it only through a sort of familiarity effect? We have learned to live with these ghosts: we brush shoulders with the vampire, the octopus, we breathe in the space of the maternal belly, at least by metaphor. Comics, they too in a certain style, humorous drawing, make these images live for us as never seen in another age, conveying the very primordial images of the analytic revelation by making them an object of ordinary amusement.
On the horizon: the soft watch and the function of the ‘great masturbator’, preserved in DALI’s images.

Is that only what makes our mastery seem to falter in the instrumental use of these images as revelatory?
Surely not only that! For projected, if I may say so, here into the creations of art, they still retain their force which I would call not only striking but critical, they retain something of their character of derision or alarm.

But that is because this is not what is at stake in our relation to the one who, for us, comes to designate them in the actuality of the cure. Here, there remains for us as the design of our action only the duty to do well, making laugh being only a very occasional path and limited in its use. And there, what we have seen happen is nothing other than an effect one may call relapse or degradation, namely that these images, we have seen them quite simply return to what has very well designated itself under the title of archetype, that is to say an old trick
from the stockroom of accessories in use.

It is a tradition that recognized itself very well under the title of ‘alchemy’ or of ‘gnosis’, but which was linked precisely to a very ancient confusion, and which was that in which the field of human thought remained entangled for centuries.
It may seem that I distinguish myself, or that I put you on guard against a mode of understanding of our reference that would be that of Gestalt. That is not exact.

I am far from underestimating what the function of Gestalt brought, at a moment in the history of thought, but to express myself quickly, and because here I am making this kind of sweeping of our horizon which I have to redo from time to time precisely to prevent the same confusions from always being reborn, I shall introduce, in order to make myself understood, this distinction:
– what makes the nerve of certain productions of this mode of exploring the field of Gestalt,
– what I shall call crystallographic Gestalt, the one that places the accent on these points of junction, of kinship between natural formations and structural organizations, insofar as they arise and are definable only from signifying combinatorics,
…it is that which makes its subjective force, the efficacy of this point — itself ontological — at which something is delivered to us
of which we do indeed have great need, namely: whether there is some relation that justifies this introduction, in the manner of a ‘ploughshare’ [soc], of the effect of the signifier into the real.

But this does not concern us, because it is not the field with which we have to deal. We are not here to judge the degree of naturalness of modern physics, although it may interest us — this is what I do from time to time before you sometimes — to show that historically it is precisely insofar as it altogether neglected the naturalness of things that physics began to enter into the real.

The Gestalt against which I am warning you is a Gestalt which — you will observe it: opposite to what the initiators of Gestalt-theory were attached to — gives a purely confusion-producing reference to the function of Gestalt, which is the one I call anthropomorphic Gestalt, the one which by whatever path confuses what our experience brings with the old analogical reference of macrocosm and microcosm, of the universal man, registers rather short in the end, and of which analysis, insofar as it believed it could find itself there again, only shows once more their relative infertility.

This does not mean that the images I humorously evoked a moment ago do not have their weight, nor that they are not there for us still to make use of them: for ourselves, the way in which for some time we have preferred to leave them crouching in the shadows must be indicative. We hardly speak of them anymore, except at a certain distance. They are there, to use a Freudian metaphor: ‘like one of those shadows that in the field of the underworld are ready to surge forth’. We have not really known how to reanimate them; we have no doubt not given them enough blood to drink. But after all, so much the better; we are not necromancers.[Cf. Traumdeutung, VII, note 1 p. 607: PUF 2004, p. 470: PUF 1967]

It is precisely here that this characteristic reminder of what I teach you is inserted, and it is there to change quite completely the face of things, namely to show that the living core of what the Freudian discovery brought did not consist in this return of old ghosts, but in another relation. Suddenly this morning I found again, from the year 1946, one of those little Remarks on psychic causality [Écrits p.151] by which I was making my return to the psychiatric circle immediately after the war.

And it appears, in this little text here — a text published in the Entretiens de Bonneval — in a sort of apostille or incidental remark at the beginning of one and the same concluding paragraph, five lines before finishing what I had to say about the imago:

‘More inaccessible to our eyes made for the signs of the money-changer…’ no matter the rest: ‘…than that of which the hunter of the desert…’ I say, which I evoke only because we found it again last time if I remember correctly: ‘…knows how to see the imperceptible trace: the gazelle’s step on the rock, one day the aspects of the imago will reveal themselves.’ The emphasis is to be placed for the moment at the beginning of the paragraph: ‘More inaccessible to our eyes…’. What are these ‘signs of the money-changer’? What signs? And what exchange? Or what money-changer?

These signs are precisely what I called upon you to articulate as signifiers, that is to say these signs insofar as they operate properly by virtue of their associativity in the chain, of their commutativity, of the function of permutation taken as such. And that is where the function of the money-changer is: the introduction into the real of a change, which is not motion, nor birth, nor corruption, nor all the categories of change outlined by a tradition we may call Aristotelian, that of knowledge as such, but of another dimension where the change in question is defined as such in the combinatorics and the topology that it allows us to define, as the emergence of this fact, of the fact of structure, as degradation on occasion, namely a fall into this field of structure and a return to the capture of the natural image.

In short, there is outlined as such what is after all only the functioning framework of thought, you will say. And why not? Let us not forget that this word ‘thought’ is present, emphasized from the outset by FREUD as no doubt not being able to be other than what it is, to designate what takes place in the unconscious.

For it was certainly not the need to preserve the privilege of thought as such, I know not what primacy of spirit, that could here guide FREUD: far from it! If he could have avoided this term, he would have done so. And what does that mean at this level? And why is it that this year I believed I had to begin: not from PLATO himself — not to speak of the others — but equally not from KANT, not from HEGEL, but from DESCARTES?

It is precisely to designate that what is at stake, where the problem of the unconscious is for us, is the autonomy of the subject insofar as it is not only preserved, but accentuated as it never was in our field, and precisely through this paradox: that these pathways that we discover there are not conceivable, if properly speaking it is not the subject who is their guide, and all the more surely so in that it is without knowing it, without being its accomplice, if I may say, conscius: because it can progress toward nothing, nor in anything, except that it marks it out only afterward, for there is nothing that is not generated by it, precisely, only insofar as it first misrecognizes it.

This is what distinguishes the field of the unconscious, as it is revealed to us by FREUD: it is itself impossible to formalize, to formulate, if we do not see that at every moment it is conceivable only by seeing there — and in the most evident and palpable way — this autonomy of the subject preserved, I mean that by which the subject can in no case be reduced to a dream of the world. Of this permanence of the subject, I show you the reference and not the presence, for this presence can be circumscribed only as a function of this reference.

I demonstrated it to you, designated it last time in this unary trait, in this function of the ‘stick’ as the figure of 1 insofar as it is only a distinctive trait, a trait precisely all the more distinctive in that almost everything distinguishing it is erased, except being a trait, by accentuating this fact that the more it is similar, the more it functions, I do not say as sign, but as support of difference. And this being only an introduction to the relief of this dimension that I am trying to punctuate before you. For in truth there is no more… there is no ideal of similarity, no ideal of the effacement of traits.

This effacement of qualitative distinctions is there only to allow us to grasp the paradox of the radical alterity designated by the trait, and after all it matters little whether each trait resembles the other. Elsewhere resides what I just now called this ‘function of alterity’.

And in ending my discourse last time, I pointed out what its function was, the one that assures repetition precisely of this: that through this ‘function’ — only through it — this repetition escapes the identity of its eternal return under the figure: of the hunter ticking off the number — of what? — of traits by which he reaches his prey, or of the divine Marquis who shows us that even at the summit of his desire, these ‘blows’, he takes great care to count them, and that this is an essential dimension insofar as it never abandons the necessity it implies, in almost none of our functions.

Counting the blows, the trait that counts: what is this? Are you still following well here? Grasp well what I intend to designate! What I intend to designate is this, which is easily forgotten in its spring, namely that what we have to do with in the automatism of repetition is this: a cycle — however amputated, deformed, abraded we define it — insofar as it is a cycle and includes a return to a terminal point, we can conceive it on the model of need, of satisfaction.

This cycle repeats itself. What does it matter whether it is exactly the same, or whether it presents slight differences; these slight differences will manifestly only be made to preserve it in its function as cycle as related to something definable as a certain type, by which precisely all the cycles that preceded it are identified in the instant as being, insofar as they reproduce it, properly speaking the same.

Let us take, to image what I am saying, the cycle of digestion. Each time we perform one, we repeat digestion. Is it to that that we refer when in analysis we speak of automatism of repetition? Is it by virtue of an automatism of repetition that we perform digestions that are sensibly always the same digestion?

I will leave you no opening to say that up to this point it is a sophism. There can of course be incidents in this digestion that are due to recalls of former digestions that were disturbed, effects of disgust, of nausea, linked to this or that contingent connection of some food with some circumstance. This will not make us cross, by one step more, the distance to be covered between this return of the cycle and the function of the automatism of repetition.

For what the automatism of repetition means insofar as we have to deal with it is this: it is that if a determined cycle that was only that one — it is here that the shadow of ‘trauma’ comes into profile, which I place here only in quotation marks, for it is not its traumatic effect that I retain, but only its uniqueness — that one then, which is designated by a certain signifier, which alone can support what we shall learn subsequently to define as a letter: Instance of the letter in the unconscious, this capital A, the initial A insofar as it is numerable, that this cycle — and not another — is equivalent to a certain signifier.

It is under this heading that behavior repeats itself: to make re-emerge this signifier that it is as such, this number that it founds. If for us symptomatic repetition has a meaning, what I indicate to you thereby to refer to is a reflection on the scope of your own thought. When you speak of repetitive incidence in symptomatic formation, it is insofar as what repeats itself is there, not even merely to fulfill the natural function of the sign, which is to represent a thing, the thing that would here be actualized, but to make present as such the absent signifier that this action has become. I say that it is insofar as what is repressed is a signifier, that this cycle of real behavior presents itself in its place.

It is here — since I have imposed on myself to give an hour-limit, precise and convenient for a certain number of you, to what I must expound before you — that I shall stop. As for what in all this imposes itself by way of confirmation and commentary, count on me to give it to you in what follows, in the most suitably articulated way, however surprising its abruptness may have seemed to you at the moment when I set it forth just now.