According to the psychoanalytic theory, sexuation removes the subjects from the fantasy of completeness and supposes a fundamental limit in their psychic structuring. Each subject will face this border establishing a world approach differently: psychosis, perversion and neurosis. According  this model, desire is understood from the lack: sexual difference, as well as language, are limited, which opens up to a search.  

Jaques Lacan transforms the famous myth of Oedipus into logical terms by depersonalizing the Freudian argumentation: he places the castration into language, the latter cannot respond, neither the mother can (or the maternal function). The close relationship between language  and sexuality exists because sexual demand does not obtain a response from the Other, which creates a lack in him or her. With this new approach, supposedly we could escape the old anguish of castration and the penis envy, prejudices that unfortunately are still present in our Western culture, strongly influenced by Freud. However, Lacan still conceives of the phallus (even symbolic) as the organizer and sexual division factor, once again establishing the masculine as the referential paradigm and thus making impossible the emergence of a truly other, the feminine. Luce Irigaray makes a more radical and extensive critique of philosophy and psychoanalysis starting from the affirmation that there are two different identities and subjectivities and not only one, presumed to be neuter but in fact masculine, as our tradition maintained “woman continues being this nothing of everything, this all of nothing, in which each one still comes to look for something with which to re-feed the similarity with himself (as) with the same” (Luce Irigaray, Especulo de la oltra mujer, Akal, Madrid, 2007, p. 207).

The Lacanian theorizing about sexual difference, despite appealing to logic in an attempt to systematize its reading, does not resolves the problem that Luce Irigaray raises. Lacan defines two forms of jouissance that correspond to male and female sexualities, the first one completely relating to phallic jouissance whereas the female jouissance, has a supplement. This approach still presupposes prejudice due to an assessment depending only on the phallus. For Luce Irigaray, the jouissance of the woman as such has not yet really happened, it is yet to be discovered and its happening depends on the conquest of a full identity an subjectivity, of an intimacy with herself which needs a cultivation of the relationship with her mother and her genealogy, with the other women and a more fair and ethical relationship between the two sexes.

The human being is two, not one. Irigaray warns that reason is not neutral. In fact, the logos is a masculine creation that ignores sexuate difference and prevents sexual  desire  from really happening. I launched my hypothesis, based on the proposal of Barbara Cassin (in Jaques el sofista. Lacan, logos y psicoànalisis, El Manantial, Buenos Aires, 2013) that it is a language as Organon and not as Pharmakon that Irigaray questions and denounces. Following Cassin we could affirm that Western philosophy have left sophist perspective out of game and that all the subsequent tradition has determined a worldview where a logos created by men names the objects of the world, establishing in this way a unquestionable truth and certainty in order to substantiate, count, measure the immeasurable, the fluid and the future. I proposed that the sophist logology represents a possibility for a feminine discourse. Although the sophists are in logos, they try to subvert it.

For our Western culture the advent of a feminine identity and subjectivity is urgent – i.e. the recognition of sexuate difference. What is this difference about? Instead of theorizing the sexuate difference in an anatomical or discursive way, Luce Irigaray uses an approach that transcends these debates. Indeed, it exists a previous natural difference of identities between man and woman, which asks us to assume the negative of our partiality. This difference is insurmountable, and happens prior to any logical opposition. No synthesis corresponds to this difference and the insurmountable negative that it implies gives rise to a new type of transcendence, the horizontal one. This opens up to a possible new relationships between man and woman without subjection of one to the other.

Although, for Irigaray, the logos is a masculine creation that excludes feminine subjectivity and ignores sexuate difference, another perspective seems to emerge, a theory and a politic that embraces eroticism and fantasy in human life, summoning in this way some contradictions and irrationality This would make it possible to glimpse a authentic end of domination (Luce Irigaray, En el principio, era lei, La Llave, Barcelone, 2016, p. 21) and a possibility of horizontal relationships. This is feasible through a new use of language. An example of that  is given by Irigaray that with her “I love to you”, the role of ‘to’ aiming at not reducing the other to an object – “The “to” is the guarantee of non-immediacy, mediation and reciprocity between us” (Luce Irigaray, Amo a ti, Icaria, Barcelone, 1994, p. 159). “The “to” also prevents the reduction of the other to an object, making it impossible for it to form part of my assets or properties, both immaterial and material. Making us unable to be possessive, the “to” represents a barrier or an interval that prevents the other from being alienated or losing their freedom” (Sanchez, M. C.,  Hanna Arendt y Luce Irigaray: el lenguaje de la pluralitày la intersubjectivitad en las sferas de lo politico y lo privato, Universum, vol. 3, n°2, pp. 205-228, Università Talca, 2016, p. 224).

For Irigaray, starting from the  masculine logos we could use strategies to open a place for  the feminine and make possible a new relationship between the sexes, whereas, for Lacan, it is from the non-possibility of the relationship between the sexes that the logos arises. According to Irigaray men and women inhabit language differently, which does not prevent us from being able to relate. According to Lacan, the language we inhabit pushes us towards a sexual desire but the sexual relation does not exist and the language cannot do anything about it.