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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, that is, as "inhabiting language" (Lacan, 1998, p. 80)]]. [[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> (1972-1973), but as early as 1971 he began to use his own symbols for the logical quantifiers and the function Φx (figure 1). [[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]].  The [[Law ]] that is transmitted by the [[father ]] and that states the [[prohibition ]] against [[incest ]] is also the [[foundation ]] 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, castration[[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 doesn't 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 <i>a</i> ]]'' 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 [[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.