Lacan is interested in logic and its ability to articulate the unconscious and its sexual “values” (I wonder, here, what the French word was for the English “values”).
Lacan immediately addresses my question: by “sexual values” he indicates the universality within language of “man” and “woman.” And he does not shy away at all from distinguishing “man” and “woman” as a foremost matter of language. This, unlike the position of Judith Butler, does not imply, it seems to me, that he is taking a “linguistic constructionist” approach, because that would reduce the field of inquiry only to language, when, for Lacan, there is always more at stake, namely the real.
Next, Lacan claims that the “he” and the “she” always exist relative to language, in all of the languages of the world, and this is the “principle behind the functioning of gender.” In other words, gender is here always relative to language, and always functions to split the genders. The “hermaphrodite” is just an attempt to playfully bring “he” and “she” into “the same sentence.” That is Lacan’s claim. I am not sure what it means – but I do not follow Lacan in this argument. He goes on to suggest that the hermaphrodite can not be an “it” but rather a bridge of the “he” and “she,” a bridging of the sexual relation, perhaps, but never in a neutral sense.
Castration can not be reduced to “anecdote” or to “mishap” or even to a “clumsy intervention.” I can only guess that the reference to “anecdote” implies that it is never temporary, or fleeting, it has staying power. It can also not be an accident – whatever that means.
The question that Lacan pursues next concerns the “object of logic.” I presume that this brings us back to the variable “x,” the birth of the signifier in the real, the birth of the subject, and the birth of the objet petit a. At this point it is worth listing all of the qualifications that Lacan has given to this little variable, this little object of logic which is often written f(x):
- the signifier
- the objet petit a
- the subject (in its notch, ditch)
Lacan adds the following: “I propose to define the object of logic as what is produced by the necessity of a discourse.”
So, my reading: if a discourse is a social bond then it always produces something like the (x), the objet petit a, the scrap of the real as a necessary consequence. Here we can see the return to the classical Lacanian version of the real as objet petit a, as that which is produced as the excrement of discourse.
Lacan confirms this but goes a step forward: “the real — a category from the triad with which my teaching got under way, the symbolic, the imaginary, and the real — is affirmed in the impasses of logic.
We also see here the word “suture,” which guaranteed Jacques-Alain Miller his statements on the “logician’s logic,” and his theory of “suture” via Frege and Lacan in the 1950s.
Within the logic of arithmetic we can find a designation of the Lacanian real: “in arithmetic something can always be stated […] which is articulated as though it stood in advance of the very thing which premises, axioms, grounding terms, whereby the said arithmetic can find a base [a foundation, a suture], enable us to presume to be provable and refutable.”
This base for Frege, I believe, was: 0 = 1. The whole net of logic — the system of numbers, in Frege’s case — is grounded, founded, upon this premise that 0 = 1 and this opens up a path to set theoretical logic wherbey the 1 always includes within itself the empty set.
Lacan then points explicitly to Godel’s incompleteness theorem. The basic argument from Godel, which he went on to prove, was that there is a limitation to every formal axiomatic system within mathematics. But Lacan phrases this in a more precise and more interesting way, which gives more credibility, no doubt, and more precision, to his concept of the real: “there will always be something that can be stated in the specific terms in comprehends which does not lie within the scope of what it posits to itself […].” So here we have a statement on the real as a piece of excess, what, in another later seminar, Lacan refers to as a “bit of the real.”
So – the real is defined as “impossible” within the limits of the logician’s logic, within the limits of a given discourse itself. This is the real that Lacan wants to “favor” within psychoanalysis. He explicitly states as much, implying, also, in the process, that this is not the only real. This I think is a very important point.
The psychoanalyst should be concerned with the real as impossible within logical discourse.
We return to discourse, but this time examining it not just as a logic but also that which establishes a social bond. Discourse is that which establishes a social bond through language – and, as such, always produces something impossible. And this impossible, this real, is related quite fundamentally to the unconscious.
So here we have a statement from Lacan that begins to examine the unconscious as real and as impossible rather than simply as a symbolic repository of signifiers. In fact, Lacan finds a problem with the symbolic version, which leads, often times, as we have seen in popular readings of Freud’s Dream book, and also in the work of Jung on architype: a certain type of “rut:” “Jung thought they would be able to revive [the sexual symbolism of the unconscious] by sliding back into the most ancient rut.”
The next few statements are very difficult for me to understand. Lacan seems to be opposes the position that there is something universal and symbolic about the sexuality of the unconscious. He is also in opposition to the position which claims that there is something “anecdotic” about the unconscious: rather, what he favours, is the approach which views the unconscious as rendering “impossible” (this is linked to the real) the “sexual bipolarity” as such.
So, the unconscious renders the impossibility of the sexual relation at the level of discourse.
Lacan confirms a suspicion of mine. He links the phallic function precisely with castration, as if, basically, they are the same thing. “All men are defined by the phallic function, the phallic function being specifically what obturates sexual relation.”
This is denoted: Ax Phi(x)
Woman, on the other hand, are “Not All woman..”
This is denoted: /Ax Phi(x) [whereby the / is used for negation]
This indicates not that woman do not have some relation to the phallic function, as some eager readers of Lacan seem to suggest (and they suggest it to respond, in haste, to charges of Lacan’s anti-feminism). Rather, it implies something more precise: “somewhere, and nothing more, woman has a relation to the phallic function.”
“Nothing can adapt this all to this not all,” Lacan says, indicating the “impossible” bar that separates man from woman via sexuation.
And why? The real — the impossible — has something to do with their different modes of jouissance: “there remains the wide gap of an indeterminancy in their common relation to jouissance.”
So the problem is already within the level of the real, of the real of the body, and its jouissance. There are different modes of enjoyment with respect to language, the signifier.
Next, we find the “one,” which appears “in spite of all”: there is “at least one” for whom truth does not concern the phallic function. This is denoted:
Ex /Phi(x) [negation of phallic function for this ‘x’]
Typically, this is the at least one of the father, of god, and so on. It was explained clearly in the work of Freud, at the level of Myth [remember, Lacan’s provide is to translate Freud’s myths into logical or topological articulations], in Totem and Taboo. If I remember correctly: there is at least one leader of the horde who has access [jouissance] to all of the women.
Lacan jumps a bit further here: this at least one enjoys precisely “what does not exist, namely all the women.”
On the side of the woman, there is:
Lacan explains, simply: “women cannot be castrated because they don’t have the phallus.” But, for woman, “it is not impossible that woman should know the phallic function.”