🦋🤖 Robo-Spun by IBF 🦋🤖

(All parts in English)

Never have I felt less like giving my seminar. I do not have the time to go into depth about the causes.
And yet, much to say… There are moments of slackening, of weariness.

Let us bring back what I said last time. I spoke to you about the proper name, insofar as we encountered it
on our path of the identification of the subject—second type of identification, regressive—to the unary trait of the Other.
With regard to this proper name, we encountered the attention it has solicited from certain linguists and mathematicians
in the function of philosophers.What is the proper name?

It seems that the thing does not yield itself at first glance but, in trying to resolve this question, we had
the surprise of rediscovering the function of the signifier, no doubt in its pure state. It was indeed in this direction that the linguist
himself was directing us when he told us: a proper name is something that counts by the distinctive function
of its sound material.

In this, of course, he was only redoubling what are the very premises of the Saussurean analysis of language, namely: that it is the distinctive trait, it is the phoneme, as coupled from a set, from a certain battery, insofar solely as it is not what the others are.

This premise, we found ourselves here having to designate what was the special trait, the use of a function of the subject in
language: that of naming by one’s proper name.It is certain that we could not be satisfied with this definition as such, but that we were nonetheless put on the track of something, and this something we were able
at least to approach, to circumscribe, by designating this: that it is—if one may say so, in a form ‘latent’ to language
itself—the function of writing, the function of the sign, insofar as it itself is read as an object.

It is a fact that letters have names. We are too inclined to confuse them with the simplified names they have in our alphabet, which seem to merge with the phonematic emission to which the letter has been reduced.
An ‘a’ seems to want to mean the emission ‘a’. A ‘b’ is not, properly speaking, a ‘bé’; it is a ‘bé’
only insofar as, for the consonant ‘b’ to be heard, it must lean on a vocalic emission.

Let us look more closely. We will see, for example, that in Greek α, β, γ, and so on, are indeed names,
and, surprisingly, names that have no meaning in the Greek language in which they are formulated. To understand them, one must realize that they reproduce the names corresponding to the letters of the Phoenician alphabet, of a Proto-Semitic alphabet, an alphabet such as we can reconstruct from a certain number of levels, of strata of inscriptions.

We recover their signifying forms: these names have a meaning in the language, whether Phoenician proper, or as we can reconstruct it, this Proto-Semitic language from which a certain number—I do not insist on the details—of the languages to whose evolution the first appearance of writing is closely linked would be derived.

Here, it is a fact that it is important at least that it come to the foreground that the very name of alef א[alf] bears a relation to the ox, whose supposedly first form of alef would reproduce, in a schematic way and in various positions, the head. Something of it still remains; we can still see in our capital A the shape
of an inverted ox skull with the horns extending it

Protosinaitic Proto-PhoenicianPhoenician archaic
Likewise everyone knows that ב[bet] is the name of the house. Of course the discussion grows complicated, even darkens,
when one attempts to make an inventory, a catalogue of what the name of the sequence of the other letters designates. When we arrive at ג[gimel] we are only too tempted to find there the Arabic name of the camel, but unfortunately there is a temporal obstacle: it is in roughly the second millennium, before our era, that these Proto-Semitic alphabets could have been in a position to connote this name of the third letter of the alphabet. The camel, unfortunately for our convenience, had not yet made its appearance in the cultural use of carrying, in these regions
of the Near East. One is therefore going to enter into a series of discussions about what this name, ג[gimel], may well represent.

Here a development on the consonantal tertiarity of the Semitic languages and on the permanence of this form at the base
of every verbal form in Hebrew.
This is one of the traces by which we can see that what is at stake, concerning one of the roots of the structure in which language is constituted, is this something first called ‘reading of signs,’ insofar as they already appear before any use of writing—I pointed this out to you in concluding last time—in a surprising way, in a way that seems to anticipate, if the thing must be admitted, by about a millennium the use of the same signs in the alphabets that are
the most common alphabets, which are the direct ancestors of ours, Latin, Etruscan, etc., alphabets which are found, by the most extraordinary mimicry[imitation] of history, in an identical form in marks on predynastic pottery of ancient Egypt. They are the same signs, even though it is beyond question that at that moment they could not in any way have been employed for alphabetic uses, alphabetic writing being at that moment far from having been born.

You know that, still further back, I alluded to those famous pebbles of Mas d’Azil, which are not for little
in the finds made in that place…
to the point that at the end of the Paleolithic a stage is designated by the term ‘Azilian,’ from the fact that it relates
to what we can define as the point of technical evolution, at the end of this Paleolithic, in the period not properly transitional, but pre-transitional from the Paleo to the Neolithic
…on these pebbles of Mas d’Azil we find analogous signs whose striking strangeness, in resembling so closely the signs of our alphabet, has been able to mislead—you know this—minds that were not especially mediocre,
into all sorts of speculations that could only lead to confusion, indeed to ridicule.It nonetheless remains
that the presence of these elements is there to let us touch with our finger something that presents itself as radical
in what we can call the attachment of language to the real.

Of course, a problem that is posed only insofar as we have first been able to see the necessity, in order to understand
language, of ordering it by what we can call ‘a reference to itself,’ to its own structure as such,
which first posed for us what we can almost call ‘its system’ as something that in no way suffices itself with a purely utilitarian, instrumental, practical genesis, with a psychological genesis, which shows us language as an order, a register, a function whose whole problematic for us is that we must see it as capable of functioning outside all consciousness on the part of the subject, and whose field we are thus led to define as characterized by structural values proper to it.

From then on we must indeed, for us, establish the junction of its functioning with this something that bears, in the real,
its mark.Where does the mark come from? Is it centrifugal or centripetal? That is where, around this problem, we are for the moment, not stopped, but at a standstill. It is therefore insofar as the subject—about something that is a mark, that is a sign—already reads before it is a matter of the signs of writing, that he notices that signs can carry
at times pieces diversely reduced, cut out from his speaking modulation and that, reversing its function,
it may be admitted that he then comes to be, as such, its ‘phonetic support,’ as they say.

And you know that this is in fact how phonetic writing is born: that there is no writing to his knowledge…
more exactly that everything that is properly of the order of writing—and not simply of a drawing—
is something that always begins with the combined use of these simplified drawings, these abbreviated drawings,
these erased drawings that are variously, improperly called ideograms in particular.

The combination of these drawings with a phonetic use of the same signs that seem to represent something,
the combination of the two appears, for example, evident in Egyptian hieroglyphs.Moreover we could,
merely by looking at a hieroglyphic inscription, believe that the Egyptians had no other objects of interest than the baggage, all in all limited:
– of a certain number of animals, of a very great number, of a number of birds truly surprising for the incidence under which birds can effectively intervene in inscriptions that need to be commemorated,
– of a no doubt abundant number of agrarian and other instrumental forms,
– of a few signs also which at all times have no doubt been useful under their simplified form the unary trait first, the bar, the multiplication cross, which moreover do not designate the operations later attached to these signs.

But in the end, taken as a whole, it is quite evident at first glance that the baggage of drawings at issue has no
proportion, no congruence with the effective diversity of objects that could validly be evoked in durable inscriptions. So too what you see, what I am trying to designate to you, and which it is important to designate
in passing to dispel confusions for those who do not have the time to go look at things more closely, is that,
for example, the figure of a horned owl, of an owl, to take a form of nocturnal bird particularly well drawn, identifiable in classical stone inscriptions, we will see it return extremely often, and why?
It is certainly not that this animal is ever in question; it is that the common name of this animal in ancient Egyptian can be the occasion of a support for the labial emission ‘m’ and that every time you see this animal figure, it is an ‘m’ and nothing else, which ‘m,’ moreover, far from being represented only under its literal value each time you encounter this figure of the said owl, is capable of something that goes roughly like this:

M

The ‘m’ will signify more than one thing, and in particular what we cannot, no more in this language than in
the Hebrew language, when we do not have the addition of the vowel points, when we are not very fixed
on the vocalic supports, we will not know how exactly this ‘m’ is completed.But we know
in any case more than enough, from what we can reconstruct of the syntax, to know that this ‘m’ can just as well represent a certain function, which is roughly: an introductory function of the type:‘see…’,
a function of attentional fixation, if one may say so, a ‘here is’.

Or again, in other cases where very probably it had to be distinguished by its vocalic support, represent
one of the forms, not of negation, but of something that must be specified, with more emphasis, of the negative verb,
of something that isolates negation under a verbal form, under a conjugable form, under a form, not simply ‘not,’ but of something like ‘it is said that no.’ In short, that it is a particular tense of a verb
that we know, which is certainly negative, or even more exactly a particular form in two negative verbs, the verb ‘imi’ on the one hand, which seems to mean ‘not to be,’ and the verb ‘tm’ on the other hand, which would indicate more specifically effective non-existence.

This is to tell you in this connection, and by introducing in an anticipatory way the function in this connection, that it is not by chance that what we find before us as we advance along this path is the relation that here is incarnated, manifests itself immediately in the most primitive coalescence of the signifier with something that immediately raises the question
of what negation is, what it is closest to.

Is negation simply a connotation, which therefore nonetheless presents itself as from the question of the moment when, with respect to existence, to the exercise, to the constitution of a signifying chain, there is introduced into it a sort of index, of added siglum, of function word as people say, which should therefore always be conceived as a sort of second invention, held by the necessities of the utilization of something situated at various levels?

Is it at the level of the response—what is called into question by the signifying interrogation ‘is it not there?’—
is it at the level of the response that this ‘is it not so?’ seems indeed to manifest itself in language as the possibility of the pure emission of negation ‘no’?

Is it, on the other hand, in the marking of relations that negation imposes itself, is suggested, by the necessity of disjunction: such a thing is not, if such another is, or could not be with such another, in short, the instrument of negation?

We know this, certainly, no less than others, but if, as regards the genesis of language, one is reduced
to making the signifier into something that must little by little be elaborated from the emotional sign, the problem of negation is something that is posed as, properly speaking, that of a leap, indeed of an impasse.

If, making of the signifier something altogether other…
something whose genesis, being problematic, carries us to the level of an interrogation on
a certain existential relation, that which as such already situates itself in a reference to negativity
…the mode under which negation appears, under which the signifier of an effective and lived negativity can arise,
is something that takes on an entirely different interest, and which is then not by chance of a nature to enlighten us, when we see that, from the very first problematics, the structuration of language identifies itself, if one may say so,
with the locating of the first conjugation of a vocal emission with the sign as such, that is to say with something that already
refers to a first manipulation of the object.

We called it simplificatory when it was a matter of defining the genesis of the trait. What is there more destroyed,
more erased than an object? If it is from the object that the trait arises, it is something of the object that the trait retains: precisely its uniqueness.The erasure, the absolute destruction: of all its other emergences, of all its other prolongations,
of all its other appendages, of everything that there may be of branched, of palpitating.

Well then, this relation of the object to the birth of something here called the sign, insofar as it interests us
in the birth of the signifier, is indeed what we are at a standstill around, and around which it is not without promise that we have, if one may say so, made a discovery, for I believe it is one: this indication that there is, let us say in a time, a locatable time, historically defined, a moment when something is there to be read,
read with language, when there is no writing yet.And it is by the reversal of this relation, and of this relation of reading the sign, that writing can then be born insofar as it can serve to connote phonematization.

But if it appears at this level that precisely the proper name, insofar as it specifies as such the rooting of the subject,
is more specially linked than another, not to phoneticization as such, to the structure of language, but to what already in language is ready, if one may say so, to receive this information of the trait. If the proper name still bears—down to us and in our usage—the trace of it under this form that from one language to another it is not translated, since it is simply transposed, it is transferred.And that indeed is its characteristic: I am called LACAN in all languages, and you too likewise, each by your name. This is not a contingent fact, a fact of limitation, of impotence, a fact of nonsense since on the contrary it is here that lies, that resides the wholly particular property of the name, of the proper name in signification.

Is this not made to make us question what is at stake at this radical, archaic point,
that we must by all necessity suppose at the origin of the unconscious.

That is to say of this something by which, insofar as the subject speaks, he can only advance always further in the chain, in the unfolding of statements, but that, moving toward statements, by that very fact,
in enunciation he elides something that is properly what he cannot know, namely: the name of what he is
insofar as subject of enunciation.In the act of enunciation there is this latent nomination that is conceivable as being the first nucleus, as signifier, of what will then organize itself as a turning chain such as I have represented it to you from the beginning, of this center, this speaking heart of the subject that we call the unconscious.

Here, before we advance further, I believe I must indicate something that is only the convergence, the point of a thematic that we have already approached several times in this seminar, several times by taking it up again at the various levels at which FREUD was led to approach it, to represent it, to represent the system, the first psychic system as he had to represent it in some way in order to make felt what is at stake, a system articulated as ‘Unconscious-Preconscious-Conscious’.

Many times I have had to describe on this board, under variously elaborated forms, the paradoxes with which FREUD’s formulations, at the level of the Entwurf for example, confront us. Today I will keep to a topologization as simple as the one he gives at the end of the Traumdeutung, namely that of layers through which crossings, thresholds, irruptions of one level into another can occur, such as what interests us most of all, the passage of the unconscious into the preconscious for example, which is indeed a problem, which is a problem… moreover, I note it with satisfaction in passing, it is certainly not the least effect that I can expect from the effort of rigor into which I draw you, which I impose on myself for you here, and which those who listen to me, who hear me, themselves carry to a degree capable even on occasion of going further, well then, in their very remarkable text published in Les Temps modernes on the subject of The Unconscious, LAPLANCHE and LECLAIRE—I do not distinguish for the moment each one’s share in this work—question what ambiguity remains in the Freudian enunciation concerning what happens when we can speak of the passage of something that was in the unconscious and that goes into the preconscious. Is this to say that it is only a change of cathexis, as they very rightly pose the question, or is there double inscription? The authors do not conceal
their preference for double inscription, they indicate it to us in their text; it is nonetheless a problem that the text leaves open, and all in all, what we have to deal with will perhaps allow us this year to bring some answer to it, or at the very least some precision.

I would like, by way of introduction, to suggest this to you, namely that if we must consider that the unconscious is
that place of the subject where it speaks, we now come to approach this point where we can say that something, unbeknownst to the subject, is profoundly reworked by the feedback effects of the signifier implicated in speech.
It is insofar—and in his very slightest word—that the subject speaks, that he can only always once more name himself without knowing it, and without knowing by what name.

Can we not see that, in order to situate in their relations the Unconscious and the Preconscious, the limit for us is not to be situated first somewhere inside, as they say, of a subject that would simply be only the equivalent of what in the broad sense is called ‘the psychic’?The subject at issue for us—and especially if we try to articulate it as the unconscious subject—entails another constitution of the boundary: what is at stake in the preconscious, insofar as what interests us in the preconscious is language, language such as effectively, not only do we see it, hear it speak, but such as it scans, articulates our thoughts.

Everyone knows that the thoughts at issue at the level of the unconscious, even if I say they are ‘structured like a language,’ of course it is insofar as they are structured in the last instance and at a certain level ‘like a language’ that they interest us, but the first thing to note, those we are speaking of, is that it is not easy to make them express themselves in common language.What is at stake is to see that the articulated language of common discourse, with regard to the subject of the unconscious insofar as it interests us, is outside.

An ‘outside’ that conjoins within it what we call our intimate thoughts, and this language that runs outside, not in an immaterial way, since we know well—because all sorts of things are there to represent it to us—we know what perhaps the cultures where everything happens in the breath of speech did not know, we who have before us kilos of language, and who know moreover how to inscribe the most fleeting speech on discs, we know well that what is spoken, effective discourse, preconscious discourse, is entirely homogenizable as something that stands outside. Language, in substance, runs in the streets, and there, there is indeed an inscription, on magnetic tape if need be.The problem of what happens when the unconscious comes to make itself heard there is the problem of the limit between this unconscious and this preconscious.This limit, how must we see it?

This is the problem that, for the moment, I am going to leave open. But what we can indicate on this occasion is that in passing from the unconscious into the preconscious, what has been constituted in the unconscious encounters an already existing discourse, if one may say so, a free play of signs, not only interfering with the things of the real, but one may say tightly, like a mycelium woven in their interval.

So too, is this not the true reason for what one may call the fascination, the idealist entanglement in philosophical experience.If man notices, or believes he notices that he has nothing but ideas of things,
that is to say that, of things, he finally knows only ideas, it is precisely because already in the world of things
this packaging in a universe of discourse is something that is absolutely not disentangleable.

The preconscious, to put it plainly, is already in the real, and the status of the unconscious, if it poses a problem,
does so insofar as it was constituted at a wholly other level, at a more radical level of the emergence of the act of enunciation.There is in principle no objection to the passage of something from the unconscious into the preconscious, which tends to manifest itself, and whose contradictory character LAPLANCHE and LECLAIRE note so well.

The unconscious, as such, has its status as something which, by position and structure, cannot penetrate to the level where it is susceptible to a preconscious verbalization. And yet, we are told, this unconscious at every moment makes an effort, pushes in the direction of making itself recognized. Assuredly, and for good reason, it is because it is at home there, so to speak, in a universe structured by discourse. Here, the passage from the unconscious toward the preconscious is, one may say, only a sort of normal irradiation effect of what turns in the constitution of the unconscious as such, of what, in the unconscious, keeps present the primary and radical functioning of the articulation of the subject as speaking subject.

What must be seen is that the order that would be that of the unconscious to the preconscious and then arriving at consciousness is not to be accepted without being revised, and one may say that in a certain way, insofar as we must admit what is preconscious as defined, as being in the circulation of the world, in real circulation, we must conceive that what happens at the level of the preconscious is something that we have to read in the same way, under the same structure, which is the one I was trying to make you sense at that root point where something comes to bring to language what one could call its final sanction: this reading of the sign.

At the present level of the life of the constituted subject, of a subject elaborated by a long history of culture, what happens is, for the subject, a reading-outside of what is surrounding, by virtue of the presence of language in the real, and at the level of consciousness, this level which, for FREUD, always seemed to pose a problem: he never ceased indicating that it was certainly the future object of a more precise specification, of a more precise articulation as to its economic function, at the level where he describes it to us at the beginning, at the moment when his thought comes free, let us recall how he describes to us this protective layer that he designates by the term ϕ: it is first of all something which, for him, is to be compared with the surface film of the sensory organs, that is to say essentially with something that filters, that closes, that sorts, that retains only that index of quality whose function we can show is homologous with that index of reality that allows us just to taste the state we are in, enough to be sure that we are not dreaming, if it is a matter of something analogous.
It is truly of the visible that we see.

Likewise consciousness, in relation to what constitutes the preconscious and makes for us this world tightly woven by our thoughts, consciousness is the surface through which the perception of this something that is at the heart of the subject receives, so to speak, from outside its own thoughts, its own discourse. Consciousness is there so that the unconscious, if one may say so, rather refuses what comes to it from the preconscious, or chooses there in the narrowest way what it needs for its offices.

And what is that?

It is indeed there that we encounter this paradox which is what I called the intercrossing of systemic functions:

At this first level, so essential to recognize, of Freudian articulation, the unconscious is represented to you by him as a flux, as a world, as a chain of thoughts. No doubt, consciousness too is made of the coherence of perceptions; the reality test is the articulation of perceptions among themselves in an organized world. Conversely, what we find in the unconscious is this significant repetition that leads us from something called thoughts, Gedanken, very well formed, says FREUD, to a concatenation of thoughts that escapes us ourselves.
 

Now, what is it that FREUD himself is going to tell us? What does the subject seek at the level of each of the two systems?

That at the level of the preconscious what we seek is properly speaking the identity of thoughts, this is what has been elaborated by the whole of this chapter of epistemology since PLATO: the effort of our organization of the world, the logical effort, is properly speaking to reduce the diverse to the identical. It is to identify thought to thought, proposition to proposition in diversely articulated relations that form the very weave of what is called formal logic.

This is what poses, for the one who considers in an extremely ideal way the edifice of science as being able or having to be, even virtually, already completed, what poses the problem of knowing whether indeed all science, all knowledge, all apprehension of the world in an ordered and articulated way, must not lead to a tautology. It is not for nothing that you have heard me on several occasions evoke the problem of tautology, and we could in no way finish our discourse this year without bringing to it a definitive judgment.

The world then, this world whose reality function is linked to the perceptive function, is still that around which we progress in our knowledge only by way of the identity of thoughts. This is not for us a paradox, but what is paradoxical is to read in FREUD’s text that what the unconscious seeks, what it wants, so to speak, that which is the root of its functioning, of its setting into play, is the identity of perceptions, that is to say that this would literally have no sense if what is at stake were not this: that the relation of the unconscious to what it seeks in its own mode of return is precisely what in the once-perceived is the identically identical, so to speak, it is the perceived of that time, it is that ring that he slipped onto his finger that time, with the hallmark of that time.

And it is precisely that which will always be missing, namely that, for any other kind of reappearance of what answers to the original signifier, at the point where there is the mark the subject received from this, whatever it may be, which is at the origin of the Urverdrängt, there will always be missing, from whatever comes to represent it, this mark which is the unique mark of the original emergence of an original signifier that presented itself once at the moment when the point, the something of the Urverdrängten in question, passed into unconscious existence, into insistence in this internal order that is the unconscious, between, on the one hand, what it receives from the external world and where it has things to bind, and from the fact that by binding them under a signifying form, it can receive them only in their difference. And that is precisely why it can in no way be satisfied by this search as such for perceptive identity, if that is the very thing that specifies it as unconscious.

This gives us the triad conscious-unconscious-preconscious in a slightly modified order, and in a certain way that justifies the formula I already once tried to give you for the unconscious by telling you that it was between perception and consciousness, as they say between skin and flesh.

This is indeed something which, once we have posited it, indicates to us that we should return to that point from which I set out in formulating things on the basis of the philosophical experience of the search for the subject as it exists in DESCARTES, insofar as he is strictly different from everything that could have been done at any other moment of philosophical reflection, insofar as it is indeed the subject itself that is questioned, that seeks to be so as such: the subject insofar as all truth is at stake concerning it, that what is questioned there is not the real and appearance, the relation of what exists and what does not exist, of what remains and what flees, but whether one can trust the Other, whether as such what the subject receives from outside is a reliable sign.

I have worked over the ‘I think, therefore I am’ enough before you for you now to be able to see roughly how the problem is posed there. This ‘I think’ of which we have said properly speaking that it was a nonsense
—and that is what makes its value—it has, of course, no more sense than the ‘I lie’ but it can do nothing, from its articulation, but notice itself that ‘…therefore I am’ is not the consequence it draws from it, but rather that it can do nothing but think, from the moment when it really begins to think.

That is to say that it is insofar as this impossible ‘I think’ passes into something that is of the order of the preconscious, that it implies as signified—and not as consequence, as ontological determination—that it implies as signified that this ‘I think’ refers to a ‘…I am’ which henceforth is no more than the ‘X’ of this subject that we are seeking, namely of what there is at the start so that the identification of this ‘I think’ may occur.

Notice that this continues, and so on: if ‘I think that I think that I am’, I am no longer in a position to ironize if I think that I can do nothing but be a think-being [pensêtre] or a being-thinking [êtrepensant], the ‘I think’ that is here in the denominator sees very easily reproduced the same duplicity, namely that I can do nothing but notice that, thinking that I think, this ‘I think,’ which is at the end of my thought on my thought, is itself an ‘I think’ that reproduces the ‘I think, therefore I am’.

Is it ad infinitum? Certainly not!

It is also one of the most common modes of philosophical exercises, once one has begun to establish such a formula, to apply that what one has been able to retain there of effective experience is in some sense indefinitely multipliable as in a game of mirrors. There is a little exercise which is the one I devoted myself to at one time, my little personal sophism, that of L’assertion de certitude anticipée concerning the game of disks, where it is from the locating of what the two others do that a subject must deduce the ‘even’ or ‘odd’ mark with which he himself is affected on his own back, that is to say something very close to what is at stake here [Cf. seminar 1954-55: The ego…, 30-03].

It is easy to see in the articulation of this game that, far from hesitation—which is indeed entirely possible to see occur, for if I see the others decide too quickly, on the same decision that I want to take, namely that I am like them marked with a disk of the same color, if I see them draw their conclusion too quickly, I will draw precisely the conclusion from it, I may on occasion see some hesitation arise for me, namely that if they saw so quickly who they were, it is because I myself am distinct enough from them to locate myself, for in all logic they must make the same reflection.

We will also see them oscillate and say to themselves: ‘Let us look at it twice.’ That is to say that the three subjects at issue will have the same hesitation together, and it is easily demonstrated that it is in fact only at the end of three hesitant oscillations that they will really be able to have, and certainly will have, and in some sense in full, figured by the scansion of their hesitations, the limitations of all contradictory possibilities.

There is something analogous here. One cannot indefinitely include all the ‘I think, therefore I am’
within an ‘I think.’ Where is the limit? This is what we cannot so easily say and know right here at once.
But the question I pose, or more exactly the one I am going to ask you to follow, because of course you may perhaps be surprised, but it is from what follows that you will see come to be adjoined here what can modify, I mean later render operative, what at first glance seemed to me only a sort of game, indeed, as they say,
a mathematical recreation:

– If we see that something in Cartesian apprehension, which surely ends in its enunciation at different levels, since indeed there is something that cannot go further than what is inscribed here, and he must indeed bring in something that comes, not from pure elaboration, on what can I base myself, what is reliable? He is indeed going to be led like everyone else to try to manage with what is lived outside, but in the identification that is the one effected by the unary trait, is there not enough there to support this unthinkable and impossible point of the ‘I think’ at least under its form of radical difference?

– If it is by ‘1’ that we figure this ‘I think’, I repeat to you: insofar as it interests us only insofar as it bears a relation to what happens at the origin of naming, insofar as this is what interests the birth of the subject: the subject is what names itself.

– If naming is first of all something that has to do with a reading of the trait ‘1’ designating absolute difference, we may ask ourselves how to cipher the sort of ‘I am’ that is here constituted, in some way retroactively, simply from the reprojection of what is constituted as the signified of the ‘I think’,
namely the same thing, the unknown [i] of what is at the origin under the form of the subject.

– If the i, which here I indicate under the definitive form that I am going to leave it, is something that is here supposed in a total problematic, namely that it is just as true that it ‘is not’, since here it ‘is’ only in ‘thinking of thinking’, is nonetheless correlative, indispensable—and this is indeed what makes the force of the Cartesian argument—to every apprehension of a thought as soon as it chains itself, this path is opened to it toward a cogitatum of something that is articulated: cogito ergo sum.

I am skipping the intermediaries for you today because you will see in what follows where they come from, and after all, at the point I am at, I had indeed to go through that. There is something of which I will say that it is at once paradoxical and why not say amusing, but I repeat to you, if it has an interest it is for what it may have of being operative. Such a formula, in mathematics, is what is called a series. I pass over what can at once arise, for anyone who has a practice of mathematics, as a question: if it is a series, is it a convergent series? What does that mean? It means that if instead of having little i you had 1’s everywhere:

An effort of formalization would allow you at once to see that this series is convergent, that is to say that,
if my memory is good, it is equal to something like:

What matters is that this means that if you carry out the operations at issue, you therefore have the values which,
if you plot them, will take roughly this form:

…until converging upon a perfectly constant value called a limit.

Finding a convergent formula in the preceding formula would interest us all the less insofar as that would mean
that the subject is a function tending toward perfect stability. But what is interesting, and this is where I make a leap, because to light my lantern I see no other way than to begin by projecting the stain and to come back afterward to the lantern: take ‘i’, trusting me, for the value it has exactly in number theory where it is called ‘imaginary’; this is not a homonymy that, by itself alone, seems to me here to justify this methodological extrapolation, this little moment of leap and trust that I am asking you to make; this imaginary value is this one: √-1.

You still know enough elementary arithmetic to know that √-1 is not any real number. There is no negative number, -1 for example, that can in any way fulfill the function of being the root of any number whatsoever of which √-1 would be the factor. Why? Because to be the square root of a negative number, that means that when raised to the square, it gives a negative number, whereas no number raised to the square can give a negative number, since every negative number raised to the square becomes positive.

That is why √-1 is nothing but an algorithm, but it is an algorithm that is useful. If you define as a complex number
every number composed of a real number ‘a’ to which is adjoined an imaginary number [a + ib], that is to say a number that can in no way be added to it, since it is not a real number made from the product of √-1 with ‘b’, if you define this as a ‘complex number’, you will be able to carry out with this complex number, and with the same success, all the operations you can carry out with real numbers.

And when you have launched yourselves on this path, you will not only have had the satisfaction of noticing
that it works, but that it will allow you to make discoveries, that is to say to notice that the numbers thus constituted have a value that allows you notably to operate in a purely numerical way with what are called ‘vectors’, that is to say with magnitudes which will themselves not only be endowed with a value diversely representable by a length, but in addition, thanks to complex numbers, you will be able to include in your connotation not only the said magnitude, but its direction, and above all the angle it makes with such other magnitude.

So that √-1, which is not a real number, proves, from the operative point of view, to have a power singularly more astonishing, if I may say so, than everything you had at your disposal up to now while limiting yourselves to the series of real numbers. This is to introduce you to what this little i is.

And then, if one supposes that what we are seeking here to connote in a numerical way is something on which we can operate by giving it this conventional value √-1. What does ‘conventional’ mean? That:
– just as we applied ourselves to elaborating the function of unity as the function of radical difference in the determination of this ideal center of the subject called the ego ideal,
– likewise in what follows—and for a good reason: namely that we will identify it with what we have up to now introduced in our own personal connotation as ϕ, that is to say the imaginary function of the phallus—we are going to set ourselves to extracting from this connotation √-1 everything in which it can serve us in an operative way.

But meanwhile, the usefulness of its introduction at this level is illustrated in this: if you seek what it does, this function, in other words, it is √-1 that is there everywhere you saw little i:

…you see appear a function which is not a convergent function, which is a periodic function,
which is easily calculable: it is a value that renews itself, so to speak, every three steps in the series.
The series is thus defined:

You will periodically recover, that is to say every third time in the series, this same value, these same three values that I am going to give you:

– The first value is i + 1, that is to say the point of enigma where we are in asking ourselves what value we may well give to ‘i’ to connote the subject insofar as the subject before any naming. A problem that interests us.

– The second value that you will find, namely: i+(1/1+i) is strictly equal to (1+i)/2 and this is quite interesting, for the first thing we shall encounter is this: namely that the essential relation of this something that we are seeking as being the subject before it names itself to the use it can make of its name simply in order to be the signifier of what there is to signify, that is to say of the question of the signified precisely of this addition of itself to its own name, is immediately to split, to divide in two, to make it so that there remains only one half of—literally (1+i)/2—what there was in presence. As you can see, my words are not prepared, but they are nonetheless well calculated, and these things are nonetheless the fruit of an elaboration that I re-did through thirty-six entryways while assuring myself by a certain number of checks, having as a sequel a certain number of switch points in the tracks that are to follow.

– The third value, that is to say when you stop the term of the series there, will be ‘1’, quite simply, which in many respects may have for us the value of a sort of loop confirmation. I mean that it is to know that if it is at the third step—curious thing, a step toward which no philosophical meditation has pushed us to stop in particular, that is to say at the step of the ‘I think’, insofar as it is itself an object of thought and takes itself as object—if it is at that moment that we seem to arrive at attaining this famous unity, whose satisfying character for defining anything whatsoever is assuredly not doubtful, but about which we may ask ourselves whether it is indeed the same unity that is at issue as the one that was at issue at the start, namely in primordial and triggering identification.

At the very least, I must leave this question open for today.