Lacan defines logic: it is the “art of producing a necessity of discourse.” And “discourse,” which is produced, by necessity, through the art of logic, has a meaning that remains veiled — or, put another way, discourse is produced precisely because its meaning is radically absent. Lacan claims that the meaning of a discourse is always positioned elsewhere: “there is no discourse that must not receive its meaning from another discourse.”
Thus, discourses interact with one another, and they do so, it would seem, because of a primary motivation: meaning, which was absent and must come to be revealed through the other discourse.
I suspect that this stuff all has something to do with sexuation. There are two discourses which are not at all in a relation with one another but who, by way of their lack of relation, come to reveal some meaning.
The logic of necessity can only occur when discourse is on the scene. This is because necessity begins with the speaking being, the speaking being who speaks through discourse. Necessity, according to Lacan, occurs only — exclusively — among speaking beings.
“The art of producing a necessity of discourse,” … the word “producing” is related to a demonstration of what was already there to begin with, namely the master’s discourse. The master’s discourse was already constituted before the speaking-being arrives on the scene, and yet, it seems to me that this produce indicates that it is “achieving through labour” that the discourse of the master arrives precisely as already constituted.
I find most of this discussion regarding necessity and “inexistent” very difficult to understand. I think it is because I am not all that familiar with Aristotle’s logic. In any case, Lacan asks himself directly: “What is necessity?”
Necessity is supposed to be “inexistent” before it is produced.
We repeat our “bricolage” (what is this? By bricolage does he mean the discourse in question?) and this is also what Lacan names a “symptom.” It is also called “automatism.”
If I am following correctly, and I doubt I am, then Lacan is suggesting that we repeat our symptom through discourse which is a supposition that the master discourse does not exist. To presume the inexistence as preliminary to necessity then it is to reject that the unconscious exists. We suggest that there is something inexistent behind the symptom. Lacan continues: “what lies behind the principle of the symptom is the inexistence of the truth that it presupposes, even though it marks out its place.”
If I am having difficulty with the terms — Aristotle’s terms — then it is probably because Lacan is engaged here in a “hypertranslation” of Aristotle. Lacan seems to be trying to force Aristotle’s insights into the psychoanalytic discourse that he is employing, while, at the same time, torturing those insights to reveal something specific to his own discourse. That is precisely what Alain Badiou calls “hypertranslation.”
Next, Lacan links “truth” in a new way — it is no longer simply the truth of the master signifier, or the truth of the symbolic unconscious — we have a new invention here that I find striking: “it is the inexistence of jouissance that the so-called automatism of repetition brings to the light of insistence, of this stamping at the door that is designated as the exit towards existence.” Thus, it is jouissance — enjoyment, if you like — that appears to be inexistent from the necessity of discourse. Lacan says: “it is rather jouissance [beyond the door of existence], such as is necessitated by discourse.” The necessity of discourse produces the jouissance that is its beyond. We still have a notion of jouissance here that is the production of a discourse rather than that which inspires discourse (as a cork).
Jouissance operates as inexistent.
But then Lacan cautions: “it still remains, however, that you cannot get down to the bone of structure when you stay at this level.” This, for me, implies that the notion of jouissance as the necessary production of of inexistence (truth) … is not the whole story on discourse.
Lacan points to the limitation: “inexistence only becomes a question on account of already having a response [discourse].” So inexistence is always the production of a discourse. Inexistence is not produced by jouissance or by truth, but by the necessity of discourse; inexistence is not nothingness.
Nothingness inspires belief – and logical discourse produces inexistence not as nothingness but as symbol (nought, zero). So, “inexistence is not nothingness, it is […] a number that is part of the series of integers.” And it goes the other way too — as we saw with Jacques-Alain Miller’s 1950s paper on “suture” and Frege — “there can be no theory of integers if you don’t take into account what is involved in nought.” Indeed, Lacan continues: “This is the path that was opened by a certain Frege […] through examining logically what is involved in the status of number.”
As it happens I wrote extensively about this in my book Lacanian Realism (Bloomsbury). Indeed, it was in Frege’s Foundations of Arithmetic that a logic of number was articulated on the basis of the non-congruence of zero and 1 within a logical operation of “succession” (what Badiou names “the count”).
Finally, my hypothesis about the retroaction of truth/inexistence is confirmed: “inexistence is only produced in the retroaction from which there first arises the necessity, namely from a discourse in which it manifests itself prior to the logician reaching it himself as a second consequence, that is, at the same time as inexistence itself.”
The necessity is the repetition itself [does this occur at the level of discourse? It seems to me that the “tuche” of jouissance, if I am correct, is not the repetition, the repetition is in the discursive response to the touch of jouissance, to the truth]. What is repeated, in this case, is the inexistence — the repression. It is what maintains the system and structure of discourse.
Life is on the side of the repeated sequencing of its discourse, whereas jouissance, the touch of death (drive), is not on this side. This is what Lacan calls the “reproduction of life.” And Lacan is not at all afraid to place it on the side of biology and bacteria. This is a crucial move, especially for sociologists to study, because for a long time sociologists rejected Freud’s “death drive” for being too “biological.” Lacan is here, perhaps without knowing it, posing a reversal: the biological drive is precisely at the level of discourse. “death drive,” jouissance, is an interruption in the life of the body/bacteria/bios.
Lacan’s next statements are fascinating. He turns to the world of animals and relates them to “one living being” who “colours all his basic needs with jouissance, needs which in other living beings are merely ways of sealing off jouissance. If the animals feed on a steady basis, it’s quite clear that this is so as to avoid knowing the jouissance of hunger. With jouissance, he who speaks […] colours all his needs […] by which he fends off death.”
This implies, to me, that the speaking-being, unlike the animal, makes use of jouissance to fend off death. But isn’t death linked with jouissance? So is jouissance here at war with itself? The animal, on the other hand, eats to fend off jouissance (of hunger/death). So is the speaking-being here equated with the same basic impulses as the animal? We speak like the animal eats: to fend off jouissance?
Lacan makes to different points of emphasis, marked by the genitive (used to express, in this case, “possession” of something).
On the one hand, there is the objective genitive: “A desire of a child” indicates that it is a child (as object) that one desires, that is the object of one’s desire.
On the other hand, there is the subjective genitive: “A desire of a child” indicates that it is the desire of a child, that it is the child who is desiring, it is a child who partakes in the act of desiring.
Lacan seems to be making the point that when one writes “A desire of a child” there is both a subjective and objective genitive implied. Well, in the phrase “the signification of the phallus” there is both objective and subjective genitive possibilities. Lacan wants us to notice, I think, is the following: “what the phallus denotes is signification.”
Frege, by examining number, was able to “found the number 1 on the concept of inexistence.” I think this is probably found in Frege’s claim that “nought [zero] is the number which which belongs to the concept of ‘not identical with itself'” (S74) — Frege continues, “Nought is the Number which belongs to a concept under which nothing falls. No object falls under a concept if nought is the Number belonging to that concept” (S75). For Frege, it is the next move in the succession that is truly interesting: “1 is the Number which belongs to the concept ‘identical with 0′” (S77). We can only have 1 if we suppose that it is identical with the concept of not being identical with itself, and being identical with not having any objects belong to that concept.”
It is this inexistence that, it seems to be, forms the basis of the real for Lacan (and, by extension, for Jacques-Alain Miller).
I am taking a detour — I paused reading Lacan for a moment — to think about the fact that “being identical with that which is not identical with itself” grounds the number 1.
0 = “not identical with itself” and “no object falls under …”
1 = “identical with 0” (which means: “identical with not being identical with itself.”)
To be identical with that which is not identical with itself — to be identical with non-existence — is precisely to form an identity out of non-existence, out of that which is inconsistent and not identical.
Lacan continues: for people to be counted as 1 they have therefore to be “divested of all qualities.” This was Marx’s position, of course: quality is eclipsed by quantity, use-value by exchange-value. For Frege, for something to be counted it must be transformed into a “unit.” Frege defines a unit as that which excludes the properties of objects. For example, Frege was fond of claiming that a “white cat” and a “black cat” each form an independent unit “cat” without any associated properties of being “white” or “black.”
Lacan goes through some work on the arithmetic triangle to show, among other things, that the addition line will always be a number not included in the preciding lines. For Frege, though, the concept of number 7 denotes 7 repetitions of no objects, 7 repetitions of that which is inexistent. The problem, as Lacan sees it, is that this does not answer how it is that something like “1” comes into existence in the first place — it only proves that we can repeat inexistence 7 times. Perhaps another way of putting this is to claim that it can prove inexistence but it can not prove existence.
Frege only accounts for the repetition of the integers and not for the actual sequence of the integers. By this, perhaps, Lacan means that Frege does not indicate or think about where the name of the concept — each new name — comes from. And so, it does not show us where 1 comes from except as a reflexive repetition of inexistence.
This class was a really difficult one for me.