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[[Image:Sexuation.jpg|right|thumb]]
According to [[Jacques Lacan]], <i>[[sexuation]]</i>, as distinct from [[biology|biological]] [[sexuality]], designates the way in which the [[subject]] is inscribed in the [[difference]] between the [[sexes]], specifically in [[terms ]] of the [[unconscious]] and [[castration]].
[[Lacan]] presented the [[complete ]] [[table of the formulas of sexuation]] on March 13, 1973, during one of the lectures of his 1972-1973 [[seminar]] <i>[[Encore]]</i>.
[[Lacan]]'s [[choice ]] of the term '[[sexuation]]', and not [[sexuality]], indicates that [[being ]] recognized as a [[man]] or [[woman]] is a matter of the [[signifier]].
The [[phallus]] is situated as a [[symbol]], the [[signifier]] of [[castration]] and thus also of [[desire]].
And this is the [[Law]] of [[castration]], which [[Lacan]] designated in his [[graph]] as the [[phallic function]], Φx.
To [[construct ]] these [[formulas]], [[Lacan]] relied on the [[Aristotle|Aristotelian]] [[logic ]] according to which propositions are categorized in four classes: # the [[universal ]] affirmative, # the universal [[negative]], #the [[particular ]] affirmative, and
# the particular negative.
But Lacan adopted modern [[symbols ]] for these [[categories]], which are based on the universal quantifier, ∀, and the existential quantifier, ∃.
On the [[left ]] side of the table, there appears the formula ∀xΦx, for all x Φ of x (all [[men]] are submitted to the [[phallic function]], that is, [[castratio]]).
But modern logic has demonstrated the [[necessity ]] of a particular negative, ∃xΦx (there [[exists]] at least one that is not submitted to the [[phallic function]]), in [[order ]] to found the universal affirmative.
This is the hypothesis that [[Sigmund Freud]] developed in his [[myth]] of the [[primal father]] in <i>[[Totem and Taboo]]</i><ref>1912-1913a</ref> and also in his argument that [[Moses]] was not a [[Jew]] in <i>[[Moses and Monotheism]]</i><ref>1939a</ref>: there always [[exists]] one who is an [[exception]].
This is how [[man]] is inscribed: by the [[phallic function]] but on the condition that this function "is limited due to the [[existence ]] of an x by which the function Φx is negated."<ref>Lacan, p. 79</ref>
This is the function of the [[father]].
The other side of the table concerns the "woman portion of [[speaking ]] beings."<ref>p. 80</ref> The upper line is read as follows: there does not [[exist ]] any x that does not fall under the [[phallic function]]. In other [[words]], [[castration]] functions for all [[women]]. But on the lower line [[Lacan]] introduced a [[negation]] marked by the barring of the universal quantifier, which is quite inconceivable from the perspective of [[formal ]] logic.
Lacan proposed that it be read as "[[not-whole]]."
The [[woman]]'s side of the table "will not allow for any [[universality]]."<ref>p. 80</ref>
[[Woman]] is not wholly within the [[phallic function]].
On this side there is no [[exception]] that could serve as the basis for a set of women.
It is from this fact that Lacan derived the [[formula]], "[[Woman does not exist]]."
This formula leaves no room for any [[idea ]] of an "[[essence]]" of [[femininity]].
Below the table of formulas, there is a "scanded indication of what is in question" (p. 80).
On the [[masculine ]] side, there is the [[barred ]] subject "and the F that props him up as signifier" (p. 80).
For the [[male]] is only able to reach his partner, the [[Other]], through [[castration]] and the mediation of the ''[[object a]]'' as its effect.
This is indicated by the arrow that crosses from the male side to the [[female ]] side, which also reproduces the [[Lacanian ]] formula of [[fantasy]]. On the [[feminine ]] side, [[woman]] is doubled: she has a relation with F, insofar as a [[man]] incarnates it for her.
But she is not wholly in that relation.
She also has a relation to the [[signifier]] of A, the [[signifier]] that the [[Other]] would [[need ]] if a set of women were going to be formed. Woman's [[jouissance]] is thus [[divided ]] between [[phallic jouissance]], linked to [[castration]] and appearing on the [[Graph]] as F, and an [[Other jouissance]] that is unique to her.
Thus there is neither symmetry between the two sides of the table, nor any complementarity between the sexes.
==References==
<references/>
# [[Lacan, Jacques]]. (1970-1971). Le séminaire-livre XVIII, d'un [[discours ]] qui ne serait pas du [[semblant]]. [On a [[discourse ]] that might not be a [[semblance]]] (unpublished seminar).
# ——. (1971-1972). Le séminaire-livre XIX, . . . ou pire [. . . or worse].(unpublished seminar).
# ——. (1998). The seminar of Jacques Lacan, book XX, on [[feminine sexuality]]: The limits of [[love ]] and [[knowledge]], encore. ([[Bruce Fink]], Trans.) New York: Norton. (Original [[work ]] published 1972-1973)
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