Formulae of sexuation

Formulae of Sexuation

In the seminar of 1970-1 Jacques Lacan tries to formalize his theory of sexual difference by means of formulae derived from symbolic logic.

The diagram is divided into two sides: on the left, the male side, and on the right, the female side.

The formulae of sexuation appear at the top of the diagram.

Thus the formulae on the male side are (= there is at least one x which is not submitted to the phallic function) and (= for all x, the phallic funciton is valid).

The last formula illustrates the relationship of woman to the logic of the not-all.

What is most striking is that the two propositions on each side of the diagram seem to contradict each other:

"Each side is defined by both an affirmation and a negation of the phallic funciton, an inclusion and exclusion of absolute (non-phallic) jouissance."^[1]

However, there is no symmetry between the two sides (no sexual relationship); eahc side represents a radically different way in which the sexual relationship can misfire.^[2]

The Seminar
Le Séminaire

Man Woman

In Le Savoir du Psychanalyste, Lacan glosses this matheme as "There exists an x determined by its saying no to the function of castration." This x corresponds to the necessary, to "that which does not cease to write itself." In this respect, it is equivalent to the symptom, or Sinthome. It is a lackless real that never ceases to repeat itself qua impossible.
Lacan equates this at-least-one (au-moins-un) who says no to castration with the mythic father-jouisseur of Totem and Taboo. He emphasizes here that from the start "the question of existence" is "tied to something of which we cannot misrecognize that it is a saying (dire)," yet reminds us that in the myth of Abraham this father is sacrificed in the form of a ram (Gilson 167). Lacan adds that, in Judaic tradition, "as in all human lines that respect themselves, its mythic ancestry (descendance) is animal" (7/1/72). In effect, for this exception to fulfil its totemic function, it must be something non-human; it must not be a speaking subject, which by definition would be constitutively divided--castrated--by the signifier by the signifier--reduced to what is represented by a signifier for another signifier. But for this exceptional existence, or ex-sistence, to "be something other than a myth," we must conceive of it terms of a structural logic in which it serves as "the inclusive function: . . . this existence plays the role . . . of the complement, or to speak more mathematically, of the edge" to the contradictory universality of the possible. In relation to the impossible, this exception is equivalent to the empty set (7/1/72).

"All are subject to the law of castration." This all corresponds to the possible, to "that which ceases to write itself."

"No x exists which is determined as subject by the saying-no (dire-non) to the phallic function" (Gilson 167). This "no x" corresponds to the impossible, to "that which does not cease to not write itself."

"Not all are subject to the law of castration." This not-all corresponds to the contingent, to "that which ceases to not write itself."

The divided subject (subject of lack).

The Phallus.

The object a. Pierre Scriabine describes the object a as both "agalma and refuse (déchet)." It is "what, in the fantasy, sutures the subject's lack in a fallacious complenitude that misrecognizes its division." It "is also what splits the subject, causing it, beyond the fantasy." But still, "as a correlate of the failure of the Other, [the object a] is the logical consistency that completes the inconsistency of the Other" (1).
In his Seminar at Barcelona, Jacques-Alain Miller states, "The object a is only the elaborated part of jouissance, it is the fantasmatic or semantic part of jouissance, the part of jouissance already drawn into the fantasy . . . Object a is a false real." In his later teachings, Lacan situates it as a point at the center of the Borromean knot, as in this diagram. This suggests that the objet a partakes of all three of the orders knotted together by the symptom (the real, the symbolic, and the imaginary) in an extimate relation to sense and to the two jouissances (phallic jouissance and the jouissance of the barred Other).

The signifier of the barred Other.

The Phallus.

"The woman does not exist."

↑ Copjec. 1994. p.24

↑ Lacan, Jacques. Le Séminaire. Livre XX. Encore, 1972-73. Ed. Jacques-Alain Miller. Paris: Seuil, 1975. p.53-4

[1] Copjec. 1994. p.24

[2] Lacan, Jacques. Le Séminaire. Livre XX. Encore, 1972-73. Ed. Jacques-Alain Miller. Paris: Seuil, 1975. p.53-4

[1]

[2]

Formulae of sexuation

Formulae of Sexuation

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	In Le Savoir du Psychanalyste, Lacan glosses this matheme as "There exists an x determined by its saying no to the function of castration." This x corresponds to the necessary, to "that which does not cease to write itself." In this respect, it is equivalent to the symptom, or Sinthome. It is a lackless real that never ceases to repeat itself qua impossible. Lacan equates this at-least-one (au-moins-un) who says no to castration with the mythic father-jouisseur of Totem and Taboo. He emphasizes here that from the start "the question of existence" is "tied to something of which we cannot misrecognize that it is a saying (dire)," yet reminds us that in the myth of Abraham this father is sacrificed in the form of a ram (Gilson 167). Lacan adds that, in Judaic tradition, "as in all human lines that respect themselves, its mythic ancestry (descendance) is animal" (7/1/72). In effect, for this exception to fulfil its totemic function, it must be something non-human; it must not be a speaking subject, which by definition would be constitutively divided--castrated--by the signifier by the signifier--reduced to what is represented by a signifier for another signifier. But for this exceptional existence, or ex-sistence, to "be something other than a myth," we must conceive of it terms of a structural logic in which it serves as "the inclusive function: . . . this existence plays the role . . . of the complement, or to speak more mathematically, of the edge" to the contradictory universality of the possible. In relation to the impossible, this exception is equivalent to the empty set (7/1/72).
	"All are subject to the law of castration." This all corresponds to the possible, to "that which ceases to write itself."
	"No x exists which is determined as subject by the saying-no (dire-non) to the phallic function" (Gilson 167). This "no x" corresponds to the impossible, to "that which does not cease to not write itself."
	"Not all are subject to the law of castration." This not-all corresponds to the contingent, to "that which ceases to not write itself."
	The divided subject (subject of lack).
	The Phallus.
	The object a. Pierre Scriabine describes the object a as both "agalma and refuse (déchet)." It is "what, in the fantasy, sutures the subject's lack in a fallacious complenitude that misrecognizes its division." It "is also what splits the subject, causing it, beyond the fantasy." But still, "as a correlate of the failure of the Other, [the object a] is the logical consistency that completes the inconsistency of the Other" (1). In his Seminar at Barcelona, Jacques-Alain Miller states, "The object a is only the elaborated part of jouissance, it is the fantasmatic or semantic part of jouissance, the part of jouissance already drawn into the fantasy . . . Object a is a false real." In his later teachings, Lacan situates it as a point at the center of the Borromean knot, as in this diagram. This suggests that the objet a partakes of all three of the orders knotted together by the symptom (the real, the symbolic, and the imaginary) in an extimate relation to sense and to the two jouissances (phallic jouissance and the jouissance of the barred Other).
	The signifier of the barred Other.
	The Phallus.
	"The woman does not exist."