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(All parts in English)

I do not think that — however paradoxical the symbolization on which I ended my discourse last time may at first appear, making the subject be borne by the mathematical symbol √-1 — I do not think that, for you, everything in it can amount to pure surprise alone.I mean that, in recalling the Cartesian démarche itself, one cannot forget what that démarche leads its author to.

There he is, setting off at a good pace toward truth.More than that, this truth is in no way — in him as in us —
placed within the brackets of a dimension that distinguishes it from reality. This truth toward which DESCARTES advances
with his conquering stride is indeed the truth of the thing itself.

And what does this lead us to? To emptying out the world until nothing is left of it but that void called ‘extension’.
How is this possible?You know: he will choose as an example: to melt a block of wax. [Cf. Descartes:Meditation II]Is it by chance that he chooses this material, if not because he is drawn to it, because it is the ideal matter for receiving the seal, the divine signature?

Yet after this quasi-alchemical operation that he carries out before us, he will make it vanish, reduce it to being nothing more than pure extension, no longer anything in which there can be imprinted what is precisely elided in his démarche: there is no longer any relation between the signifier and any ‘natural trace,’ if I may put it that way, and quite specifically the natural trace par excellence that constitutes the imaginary of the body.This is not to say, precisely, that this imaginary can be radically repelled, but it is separated from the play of the signifier. It is what it is: an effect of the body, and as such rejected as a witness to any truth. Nothing to do with it except to live from this imaginary — theory of the passions — but above all not to think with it.

Man thinks with a discourse reduced to the self-evidences of what is called ‘the natural light,’ that is, an algebra, a logistical group that from then on could have been otherwise if God had so willed (theory of the passions).What DESCARTES still cannot perceive is that we can will it in His place[in God’s place]: that some 150 years after his death [1650] set theory is born — it would have delighted him — in which even the numbers 1 and 0
are only the object of a literal definition, of a purely formal axiomatic definition, neutral elements.
He could have dispensed with the truthful God, the deceiving God being able to be only the one who would cheat
in the solving of equations themselves.

But no one has ever seen that: there is no miracle of combinatorics, except the meaning we give to it.
That is already suspect each time we give it a meaning. That is why the Word exists, but not the God of DESCARTES. For the God of DESCARTES to exist, we would have to have a small beginning of proof of His creative will in the domain of mathematics.

Now it is not He who invented Cantor’s transfinite, it is we.That is precisely why history testifies to us that
the great mathematicians who opened this beyond of divine logic, EULER first of all, were very afraid.
They knew what they were doing: they were encountering, not the void of extension of the Cartesian step — which in the end, despite PASCAL, no longer frightens anyone, because people encourage themselves to go and inhabit it farther and farther away
— but the void of the Other, an infinitely more dreadful place, since someone is needed there.

That is why, pressing more closely the question of the meaning of the subject as it is evoked in Cartesian meditation, I do not believe I am doing anything there, even if I encroach upon a domain traversed so many times that it ends up seeming to become reserved for certain people, I do not believe I am doing something in which they themselves can take no interest, insofar as the question is current, more current than any other, and even more actualized still — I believe I can show you this — in psychoanalysis than elsewhere.

What I am therefore going to bring you back to today is a consideration, not of the origin, but of the position of the subject.Insofar as at the root of the act of speech there is something, a moment when it inserts itself into a language structure.And this language structure, insofar as it is characterized at this original point, I am trying to tighten it,
to define it around a thematic which, in an imagistic way, is embodied, is grasped, in the idea of an original contemporaneity of writing and language itself, insofar as:

– writing is signifying connotation,
– speech does not so much create it as read it,
– the genesis of the signifier at a certain level of the real, which is one of its axes or roots, is for us no doubt the principal thing for connoting the coming to light of effects, called ‘effects of meaning.’

In this primary relation of the subject, in what it projects behind itself, nachträglich by the sole fact of engaging by its speech — first stammering, then playful, even confusional — in common discourse.What it projects backward from its act is where there occurs that something toward which we have the courage to go, to question it in the name of the formula ‘Wo Es war, soll Ich werden’,which we would tend to push toward a very slightly differently accented formula, in the sense of a ‘being having been,’ of a Gewesen that subsists insofar as the subject, advancing there, cannot ignore that a labor of profound reversal of its position is required in order for it to be able to grasp itself there.

Already there, something directs us toward something which, by being inverted, suggests to us the remark that, all by itself, in its existence, negation is not, and has never been, without concealing a question.What does it presuppose?
Does it presuppose the affirmation on which it rests? No doubt.
But this affirmation, is it really, itself, only the affirmation of something real that would simply be removed?

It is not without surprise — nor is it without malice — that we can find, under BERGSON’s pen, a few lines by which he rises up against any idea of nothingness, a position fully in keeping with a thought fundamentally attached to a sort of naive realism:

‘There is more, and not less, in the idea of an object conceived as non-existing than in the idea of this same object conceived as existing, for the idea of the non-existing object is necessarily the idea of the existing object, plus the representation of an exclusion of this object, by present reality taken as a whole.’

Is that how we can be content to situate it?For a moment, let us turn our attention toward negation itself:
is that how we can be content, in a simple experience of its use, of its employment, to situate its effects?

To lead you to this point by all the paths of a linguistic inquiry is something we cannot refuse ourselves.
Besides, we have already advanced in this direction, and if you remember well, allusion was made here long ago
to the remarks, certainly very suggestive if not illuminating, of PICHON and DAMOURETTE in their collaboration
on a grammar very rich and very fruitful to consider — a grammar specifically of the French language — in which
their remarks come to point out that there is not — they say — properly speaking any negation in French.

What they mean is that this form, simplified in their view, of radical ablation as it is expressed at the end of a certain German sentence, I mean at the end, because it is indeed the term nicht which, by coming in a surprising way at the conclusion of a sentence pursued in a positive register, has allowed the listener to remain until its term in the most perfect indeterminacy, and fundamentally in a position of credence [créance/credence], and by this nicht which strikes it out, the whole signification of the sentence is excluded.

Excluded from what?From the field of the admissibility of truth.PICHON remarks, not without pertinence, that the division, the schize, the most ordinary in French of the function of negation, between a ‘ne’ on the one hand, and an auxiliary word: the ‘pas’, the ‘personne’, the ‘rien’, the ‘point’, the ‘mie’, the ‘goutte’,which occupies a position in the enunciative sentence that remains to be specified in relation to the ‘ne’ named first, that this suggests to us specifically, by looking closely at the separate use that can be made of it, attributing to one of these functions a so-called ‘discordantial’ signification, to the other an ‘exclusive’ signification.

It is precisely exclusion from the real that the ‘pas’, the ‘point’ would be charged with,
whereas the ‘ne’ would express this dissonance, sometimes so subtle that it is only a shadow, and specifically in that famous ‘ne’ of which you know that I have made much of it to try for the first time, precisely, to show in it something like the trace of the subject of the unconscious,
the so-called ‘expletive’ ‘ne’, the ‘ne’ in this: ‘Je crains qu’il ne vienne.’

You immediately put your finger on the fact that it means nothing other than ‘I was hoping he would come.’
It expresses the discordance of your own feelings regarding this coming, it conveys in some way the trace all the more suggestive for being embodied in its signifier, since in psychoanalysis we call it ‘ambivalence.’

‘Je crains qu’il ne vienne’ is not so much to express the ambiguity of our feelings as, by this surcharge, to show how much, in a certain type of relation, this distinction of the subject of the act of enunciation as such, in relation to the subject of the enunciated,
is capable of resurfacing, emerging, reproducing itself, marking itself,
in a gap,
even if it is not present at the level of the enunciated in a way that designates it!

‘Je crains qu’il ne vienne’:it is a third party.What would it be if it were said: ‘je crains que je ne fasse’ which is hardly said, although it is conceivable?Who would be at the level of the enunciated?Yet this matters little whether it is designable — you see moreover that I can make it enter there — at the level of the enunciated.And a subject, masked or not at the level of enunciation, represented or not, leads us to pose the question of the function of the subject, of its form, of what supports
it, and not to be mistaken: not to believe that it is simply the ‘I’ shifter which, in the formulation
of the enunciated, designates it as the one who, in the instant that defines the present, bears speech.

The subject of enunciation perhaps always has another support.What I have articulated is that, much more, this little ‘ne’, here graspable under the expletive form, is where we must recognize, properly speaking in an exemplary case, the support.And likewise this is not to say, of course, either, that in this exceptional phenomenon we must recognize its exclusive support.

The use of language will allow me to emphasize before you in a very banal way, not so much PICHON’s distinction…
in truth, I do not believe it sustainable through to its descriptive end. Phenomenologically it rests on the idea, for us inadmissible, that one can in some way fragment the movements of thought; nevertheless, you have this linguistic consciousness that allows you at once to appreciate the originality of the case where you only have, where you can in current usage of the language — it has not always been thus: in archaic times, the form that I am now going to formulate before you was the most common. In all languages, an evolution is marked, as by a sliding, which linguists try to characterize, in the forms of negation. The direction in which this sliding operates, I may perhaps state in a moment its general line, it is expressed under the pen of specialists but for the moment let us take the simple example of what is offered to us
…quite simply in the distinction between two equally admissible, equally accepted, equally expressive, equally common formulas: that of ‘je ne sais’ with ‘j’sais pas’.

You see, I think, at once what the difference is, a difference of accent. This ‘je ne sais’ is not without a certain mannerism: it is literary. It is still better than ‘Jeunes nations’ [pun on the sound of ‘Je ne sais’],but it is of the same order. They are both MARIVAUX, if not rivals [rivaux; pun on Marivaux/rivaux].

What it expresses — this ‘je ne sais’ — is essentially something altogether different from the other code of expression, that of ‘j’sais pas’:it expresses oscillation, hesitation, even doubt.If I invoked MARIVAUX, it is not for nothing: it is the ordinary formula on the stage, where veiled avowals can be formulated.

Beside this ‘je ne sais’, one should have fun spelling, with the ambiguity given by my play on words,
the ‘j’sais pas’:through the assimilation it undergoes owing to the proximity of the verb’s initial ‘s’, the ‘j’’ of ‘je’ which becomes
an aspirating ‘che’ and thereby a voiceless sibilant,the ‘ne’ here swallowed disappears, the whole sentence comes to rest on the ‘pas’
weighted by the stop consonant that ends it.

The expression will take its accent of somewhat derisory accentuation, even vulgar on occasion, precisely only from
its discord with what will then be expressed. The ‘ch’sais pas’ marks, one might even say, the blow of something
where, on the contrary, the subject comes to collapse, to flatten itself:
– ‘How did that happen to you?’ authority asks, after some sad mishap, of the person responsible.
– ‘Ch’sais pas.’
It is a hole, a gaping opening that opens up, at the bottom of which what disappears, what plunges in, is the subject itself.

But here it no longer appears in its oscillatory movement, in the support given to it by its original movement, but on the contrary under a form of constatation of its ignorance properly speaking expressed, assumed, rather projected, stated: something that presents itself as a ‘not-being-there’ projected onto a surface, onto a plane where it is as such recognizable. And what we approach by this path in these remarks controllable in a thousand ways, by all sorts of other examples, is something from which at minimum we must retain the idea of a double slope [double versant].

Is this double slope really one of opposition, as PICHON lets one understand?
As for the apparatus itself of negation, can a more thorough examination allow us to resolve it?
Let us first note that the ‘ne’ in these two terms seems to undergo there the attraction of what one may call the head-group of the sentence, insofar as it is grasped, borne by the pronominal form.

This leading pack [peloton de tête], in French, is remarkable in formulas that accumulate it, such as: ‘je ne le’, ‘je le lui’.
This, grouped before the verb, is certainly not without reflecting a profound structural necessity.
That the ‘ne’ should come to aggregate itself there, I would say that this is not what seems most remarkable to us.
What seems most remarkable to us is this: that by coming to aggregate itself there, it accentuates what I shall call
subjective significantization.

Note indeed that it is not by chance if it is at the level of a ‘je ne sais’, of a ‘je ne puis’, of a certain category which is that of verbs where subjective position itself as such is situated, inscribed, that I found
my example of isolated use of ne. There is indeed a whole register of verbs whose use is apt to make us notice that their function changes profoundly by being employed in the first, or the second, or the third person.

If I say ‘je crois qu’il va pleuvoir,’ this does not distinguish — from my enunciation that it is going to rain — an act of belief.
‘Je crois qu’il va pleuvoir’ simply connotes the contingent character of my forecast. Observe that things
are modified if I pass to the other persons:
– ‘tu crois qu’il va pleuvoir’ appeals much more to something: to the one I address, I appeal to his testimony,
– ‘il croit qu’il va pleuvoir’ gives more and more weight to the subject’s adherence to his credence [créance/credence].

The introduction of the ‘ne’ will always be easy when it comes to adjoin itself to these three pronominal supports of this verb which here has a varied function: from the outset, from enunciative nuance up to the enunciated of a position of the subject, the weight of the ‘ne’
will always be to bring it back toward enunciative nuance.‘Je ne crois pas qu’il va pleuvoir,’ this is even more tied to the character of dispositional suggestion that is mine. It may have absolutely nothing to do with a non-belief,
but simply with my good humor. ‘Je ne crois pas qu’il va pleuvoir’,‘je ne crois pas qu’il pleuve’ that means
that things do not seem to me to be going too badly.

Likewise, by adjoining it to the two other formulations — which moreover will distinguish two other persons — the ‘ne’ will tend to ‘I-ize’ [je-iser] what, in the other formulas, is at issue:‘tu ne crois pas qu’il va pleuvoir’,‘il ne croit pas qu’il doive pleuvoir’,it is indeed insofar as… it is indeed drawn toward the ‘I’ that they will be, by the fact that it is with the adjunction of this little negative particle that they are here introduced into the first member of the sentence.

Is this to say that opposite it we should make of ‘pas’ something that, quite brutally, connotes the pure and simple fact
of deprivation? That would certainly be the tendency of PICHON’s analysis, insofar as he indeed finds in it,
for grouping examples, every appearance of it.In fact I do not believe so, for reasons that have first to do
with the very origin of the signifiers in question.

Surely, we have the historical genesis of the form of their introduction into language. Originally, ‘je n’y vais pas’ can be accented by a comma:
– ‘je n’y vais, pas un seul pas’ if I may say so,
– ‘je n’y vois point, même pas d’un point’,
– ‘je n’y trouve goutte’,il n’en reste mie’.
It is indeed a matter of something which, far from being in its origin the connotation of a hole of absence, expresses quite the contrary
reduction, disappearance no doubt, but not completed, leaving behind it the wake of the smallest, most evanescent trait.

In fact these words, easy to restore to their positive value, to the point that they are still commonly used
with that value, do indeed receive their negative charge from the sliding that occurs toward them of the function of ‘ne’.
And even if the ‘ne’ is elided, it is indeed on them, of its charge that it is a question in the function it exercises.

Something, if one may say so, of the reciprocity, let us say, of this ‘pas’ and this ‘ne’ will be brought to us by what happens when we invert their order in the enunciating of the sentence.We say, as a logical example:‘Pas un homme qui ne mente.’
It is indeed ‘pas’ there that opens fire.What I mean here to designate, to make you grasp, is that ‘pas’, in opening
the sentence, absolutely does not play the same function that would be attributable to it — according to PICHON —
if this were the one expressed in the following formula, I arrive and I observe:‘Il n’y a ici pas un chat.’

Between ourselves, let me point out in passing the illuminating, privileged, even formidable value of the very use
of such a word: ‘pas un chat.’If we had to make the catalogue of the means of expression of negation, I would propose that we put under the heading this type of word that becomes like a support of negation. They are by no means without constituting a special category. What does ‘the cat’ have to do with the question?But let us leave that for the moment.

‘Pas un homme qui ne mente’ shows its difference from this concert of lacks: something that is at quite another level and that is sufficiently indicated by the use of the subjunctive.‘Pas un homme qui ne mente’ is at the same level
that motivates, that defines all the most discordantial forms — to use PICHON’s term — that we can attribute to ‘ne’:from the: ‘je crains qu’il ne vienne,’to the: ‘avant qu’il ne vienne,’to the: ‘plus petit que je ne le croyais,’or again: ‘il y a longtemps que le ne l’ai vu,’which pose — I tell you in passing — all sorts of questions
that for the moment I am forced to leave aside.

I point out to you in passing what a formula such as ‘il y a longtemps que je ne l’ai vu’ supports: you cannot say it about a dead person, nor about someone who has disappeared. ‘il y a longtemps que je ne l’ai vu’ presupposes that the next encounter is still possible.You see with what prudence the examination, the investigation of these terms must be handled.

And that is why, at the moment of attempting to set out, not the dichotomy, but a general table of the diverse characters
of negation in which our experience brings us matrix entries far richer than all that had been done at the level of philosophers, from ARISTOTLE to KANT, and you know what these matrix entries are called:
privation, frustration, castration. It is these that we are going to try to take up again,
to confront them with the signifying support of negation as we can try to identify it.

‘Pas un homme qui ne mente’.

What does this formula suggest to us?
‘Homo mendax’, this judgment, this proposition that I present to you under the type-form of the universal affirmative,
to which you perhaps know that in my very first seminar of this year I had already alluded,
with regard to the classical use of the syllogism: ‘all men are mortal, SOCRATES etc.’ with what I connoted in passing
of its transferential function.

I believe that something can be brought to us in approaching this function of negation, at the level of its original, radical use, by considering the formal system of propositions such as ARISTOTLE classified them
in the so-called categories:

– of the universal affirmative[A] and negative[E],
– and of the particular likewise called affirmative[I] and negative[O].

Let us say it at once: this subject called the opposition of propositions — the origin in ARISTOTLE of all his analysis,
of all his mechanics of the syllogism — is not without presenting, despite appearances, the most numerous difficulties.
To say that the developments of the most modern logistics have illuminated these difficulties would very certainly be to say something against which the whole of history registers a denial. On the contrary, the only astonishing thing it can make appear is the appearance of uniformity in adherence that these so-called Aristotelian formulas encountered up to KANT, since KANT kept the illusion that this was an unassailable edifice.

Assuredly, it is not nothing, to be able for example to point out that the accentuation of their affirmative[A]
and negative[E] function is not articulated as such in ARISTOTLE himself, and that it is much later, with AVERROES
probably, that one should mark its origin.This is to tell you that things, likewise, are not so simple,
when it comes to assessing them.For those who need a reminder of the function of these propositions,
I am going to recall them briefly.

–A–

Homo mendax — since that is what I have chosen to introduce this reminder, let us take it, then — homo and even omnis homo, omnis homo mendax: every man is a liar. The connotation of πᾶς[pan] in ARISTOTLE to designate the function of the universal.

–E–

What is the negative formula? According to a form that carries, and in many languages, omnis homo non mendax may suffice. I mean that omnis homo non mendax means that of every man it is true that he is not a liar. Nevertheless, for clarity, it is the term nullus that we use, nullus homo mendax. That is what is usually connoted by the letter, respectively A and E, of the universal affirmative and the universal negative.What is going to happen at the level of the particular affirmatives? Since we are interested in the negative, it is in a negative form that we shall be able here to introduce them.

–O–

Non omnis homo mendax: not every man is a liar.In other words I choose and I observe that there are men who are not liars.

–I–

In short, this does not mean that anyone, aliquis, cannot be a liar: aliquis homo mendax, such is the particular affirmative usually designated in classical notation by the letter I.Here, the particular negative[O] will be — the non omnis being here summarized by nullus — non nullus homo non mendax: there is not no man who is not a liar.In other words, insofar as we had chosen here to say that not every man was a liar[O], this expresses it in another way, namely that: it is not none that there is to be non-lying.

The terms thus organized are distinguished, in classical theory, by the following formulas which place them reciprocally in so-called positions of contraries or subcontraries:

That is to say that the universal propositions A and E oppose one another at their own level as not knowing and not being able to be true at the same time:

– it cannot at the same time be true that every man can be a liar, and that no man can be a liar, whereas all the other combinations are possible.

– It cannot at the same time be false that there are lying men and non-lying men.

The so-called contradictory opposition is that by which the propositions situated in each of these quadrants oppose one another diagonally [A↔O and E↔I] in that each excludes:

– being true, the truth of the one opposed to it as contradictory,

– and being false, excludes the falsity of the one opposed to it as contradictory.

If there are lying men[I], this is not compatible with the fact that no man is a liar [E].
Conversely, the relation is the same for the particular negative[O], with the affirmative[A].

What am I going to propose to you, to make you feel what, at the level of the Aristotelian text, always presents itself as what has developed in history, as embarrassment around the definition as such of the universal?
Observe first that if here I have introduced to you the non omnis homo mendax[O], the ‘not all’, the term ‘not’ bearing on
the notion of the ‘all’ as defining the particular.

This is not because this is legitimate, for precisely ARISTOTLE opposes it in a way contrary to all the development that speculation on formal logic was later able to take, namely a development, an explanation ‘in extension’ bringing into play the framework symbolizable by a circle, by a zone in which the objects constituting its support are gathered.

ARISTOTLE, very precisely before the Prior Analytics, at least in the work that precedes it in the grouping of his works — but which apparently precedes it logically if not chronologically — which is called
On Interpretation, points out that — and not without having provoked the astonishment of historians — it is not on the qualification of universality that negation should bear. So it is indeed a ‘some man’, aliquis, that is at issue, and a ‘some man’ that we must question as such. The qualification, then, of the omnis, of omnitude, of the parity
of the universal category, is here what is at stake.

Is that something at the same level, at the level of existence of what can support or not support affirmation or negation?

Is there homogeneity between these two levels? In other words, is it a matter of something that simply presupposes the collection as realized, in the difference there is from the Universal to the Particular?

Overturning the scope of what I am in the process of trying to explain to you, I am going to propose something to you,
something made in a way to answer what?To the question that links, precisely, the definition of the subject as such to that of the order of affirmation or negation into which it enters in the operation of this propositional division.

In the classical teaching of formal logic, it is said — and if one seeks to whom this goes back,I am going to tell you,
it is not without being somewhat piquant — it is said that:
– the subject is taken under the angle of quality,
– and that the attribute, which you see here embodied by the term mendax, is taken under the angle of quantity.
In other words, in the One they are all, they are several, indeed there is 1.This is what KANT still preserves,
at the level of the Critique of Pure Reason, in the ternary division. This is not without raising, on the part of linguists,
serious objections.

When one looks at things historically, one realizes that this quality-quantity distinction has an origin: it appears for the first time in a little treatise, paradoxically on the doctrines of PLATO, and this…
it is on the contrary the Aristotelian statement of formal logic that is reproduced, in an abbreviated way, but not without didactic period, and the author is none other than APULEIUS, the author of a treatise on PLATO
…turns out to have here a singular historical function, namely that of having introduced a categorization, that of quantity
and quality[…].

Here indeed is the model around which I propose for today to center your reflection.

– Here is a quadrant [1] in which we are going to place vertical strokes.the ‘stroke’ function will fulfill that of the ‘subject’, and the ‘vertical’ function, which moreover is chosen simply as support, that of ‘attribute’. I could just as well have said that I was taking as ‘attribute’ the term ‘unary’, but for the representative and imaginable side of what I have to show you, I place them vertical.
– Here [2], we have a segment of quadrant where there are vertical strokes but also oblique strokes.
– here [3] there are only oblique strokes,
– and here [4] there is no stroke.

What this is intended to illustrate is that the universal≠particular distinction, insofar as it forms a pair distinct
from the affirmative ≠ negative opposition, is to be considered as a register altogether different from the one which, with more or less skill, commentators from APULEIUS onward thought they ought to develop in these formulas so ambiguous, slippery
and confusion-producing that are called respectively quality and quantity, and to oppose it in those terms.

We shall call the universal≠particular opposition an opposition of the order of λέξις[lexis], which for us is

• λέγω[lego], I read, equally well: I choose- very exactly linked to this function of extraction, of signifying choice,
  which is what, for the moment, the ground, the footbridge on which we are advancing.

It is to distinguish it from ϕάσις[phasis], that is to say from something which here proposes itself as a speech whereby,
yes or no, I commit myself as to the existence of that something which is brought into question by the first λέξις.And indeed, you will see, of what am I going to be able to say ‘every stroke is vertical’?Of course, of the first sector of the quadrant [1], but, observe it, also of the empty sector [4]: if I say ‘every stroke is vertical’, that means: when there is no vertical,
there is no stroke. In any case this is illustrated by the empty sector of the quadrant, not only does the empty sector not contradict,
is not contrary to the affirmation ‘every stroke is vertical’, but it illustrates it: there is no stroke that is not vertical in this sector of the quadrant. Thus the universal affirmative is illustrated by the first two sectors [1 and 4].

The universal negative will be illustrated by the two sectors on the right [3 and 4], but what is at issue there will be formulated
by the following articulation: ‘no stroke is vertical’.There is, in these two sectors, no vertical stroke.

What is to be noted is the common sector [4] covered by these two propositions which, according to the formula, the classical doctrine, apparently cannot be true at the same time.What are we going to find, following our rotational movement which has thus begun very well, here [O], as formula, as well as here [1], to designate the two other possible pairings of the quadrants two by two?

Here [1], we are going to see the true of these two quadrants in an affirmative form: ‘there is…’I say it in a phasic way, I state the existence of vertical strokes:‘there are vertical strokes’, ‘there are some vertical strokes’, which I can find either here [1] always, or here [2] in the right cases.Here, if we try to define the distinction of the universal
and the particular, we see which are the two sectors [2 and 3] that correspond to the particular enunciation[O],
there ‘there are non-vertical strokes’, non nulli non verticales.

Just as a moment ago we were for an instant suspended before the ambiguity of this repetition of negation, the ‘non, non’,the alleged cancellation of the first negation by the second negation is very far from necessarily being equivalent
to the ‘yes’, and this is something to which we shall have to return later.What does that mean?
What interest is there for us in using such an apparatus? Why am I trying for you to detach this plane of λέξις from the plane of ϕάσις?I am going to go there at once, and not by roundabout ways, and I am going to illustrate it.

What can we say, we analysts? What does FREUD teach us?
Since the meaning has been completely lost of what is called ‘universal proposition’, since precisely a formulation whose heading can be placed at the Eulerian formulation which comes to represent to us all the functions of the syllogism by a series of little circles, either excluding one another, overlapping, intersecting, in other words and properly speaking in extension, to which one opposes comprehension which would be distinguished simply by I know not what inevitable manner of understanding. Understanding what? That the horse is white?What is there to understand?What we bring that renews the question is this: I say that FREUD promulgates, advances the following formula: ‘The father is God’ or ‘Every father is God’.

It follows, if we maintain this proposition at the universal level, that of ‘There is no other father than God’, which moreover, as to existence, is in Freudian reflection rather aufgehoben, rather put in suspension, even in radical doubt.What is at issue is that the order of function that we introduce with the Name-of-the-Father is that something which at once has its universal value, but which hands back to you, to the other, the burden of checking whether there is a father or not of that kind.If there is none, it is still true that the father is God.

Simply, the formula is confirmed only by the empty sector [4] of the quadrant, whereby, at the level of ϕάσις, we have: ‘there are fathers who…’ fulfill more or less the symbolic function that we have just… stated[sic]
as such, as being that of the Name-of-the-Father:‘there are some who…’, and ‘there are some who… not’.

But that there be ‘some who… not’ who are ‘not’ in all cases, which is here supported by this sector [3], is exactly the same thing that gives us support and basis for the universal function of the Name-of-the-Father, for, grouped with the sector in which there is nothing [4], it is precisely these two sectors, taken at the level of λέξις, which are found, by reason of this one, of this supporting sector that complements the other, to give its full scope to what we can state
as universal affirmation.

I am going to illustrate it otherwise, since also up to a certain point the question could be raised of its value, I am speaking
with respect to a traditional teaching, which must be what I brought last time concerning the little i.

Here, the professors discuss:‘What are we going to say?’. The professor — the one who teaches — must teach what?
What others taught before him. That is to say that he is founded on what? On what has already undergone a certain λέξις.
What results from every λέξις is precisely what matters to us in the present case, and at the level of which I am trying
to sustain you today: the letter. The professor is lettered [lettré/lettered]: in his universal character, he is the one who is founded
on the letter at the level of a particular enunciated.

We can now say that he can be so half-and-half: he may not be all letter.It will follow that
even if one cannot say that no professor is illiterate, there will always in his case be a little letter.

It remains nonetheless that if by chance there were an angle under which we could say that there are possibly, under a certain angle, some who are characterized as giving rise to a certain ignorance of the letter, this would not prevent us thereby from closing the loop and seeing that the return and the foundation, if one may say, of the universal definition of the professor is very strictly in this: it is that the identity of the formula that the professor is the one who identifies with the letter, imposes, even requires, the commentary that there can be illiterate professors.[Cf. seminar1954-55 :The ego…, 12-05].

The negative box [4], as essential correlative of the definition of universality, is something deeply hidden at the level of primitive λέξις.This means something: in the ambiguity of the particular support that we can give in the engagement of our speech to the Name-of-the-Father as such.

It remains nonetheless that we cannot make it so that anything whatsoever that, drawn into the atmosphere of the human,
if I may express myself thus, can — if one may say so — consider itself as completely detached from the Name-of-the-Father,
that even here[4 : empty] where there are only fathers for whom the function of the father is, if I may express myself thus, a pure loss, the father non-father, the ‘lost cause’ on which my seminar of last year ended, it is nevertheless as a function of this falling-away, in relation to a first λέξις which is that of the Name-of-the-Father, that this particular category is judged.

Man cannot make it so that his affirmation or his negation — with all that it engages: ‘that one is my father’ or ‘that one
is his father’ — is not entirely suspended from a primitive λέξις of which, of course, it is not a matter of common sense, of the signified of the father, but of something to which we are here provoked to give its true support, and which legitimizes, even in the eyes of professors — who, you see, would be in great danger of always being placed in some suspense as to their real function — which, even in the eyes of professors, must justify my trying to give, even at their level as professors, an algorithmic support to their existence as subject as such.