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The Logical Status of Lacan's "Formulae of Sexuation"

The Letter, Issue 34, Summer 2005, Pages 114 - 143


THE LOGICAL STATUS OF LACAN'S "FORMULAE OF SEXUATION"

Geoff Boucher


In this article, I propose to investigate the logical status of Lacan's formulae of sexuation, as expounded in Seminar XX.[1] According to Lacan, 'the sexed being ... results from a logical exigency in speech''.[2] But the question of the relation between "the logical demands of language" and human sexuality is the locus for a series of objections to the psychoanalytic project. According to the contemporary doxa, the individual finds himself located within the multiple language games that constitute social reality. This involves the radically contingent construction of gender identity through dramatic performances of social roles.[3] Such critics allege that there are as many sexualities as there are language games. They oppose the "radical translation" between incompatible social worlds to sexual difference as a transhistorical reality.[4] To insist, as Lacan does, that the relation of the subject to language necessarily includes an unconscious, masculine or feminine stance, seems, to such critics to be a naturalisation of culturally constructed gender characteristics.[5] So do Lacan's formulae of sexuation represent a return to biological essentialism? What are the epistemological claims raised by Lacan's metapsychological formalisations? I depart from the assumption that a relevant indicator of the scientific status of a theory is its crossing of certain "thresholds of formalisation". I briefly explain the relevant aspects of Lacan's two distinct unconscious "grammars". Then, I consider these proposals in the light of the formalization of "transconsistent logic" in the last twenty years. Recent work in logical analysis reveals that it is possible to render so-called transconsistent systems of propositions, ones that include contradictions or undecidability, as formal logical orders. My paper will test the hypothesis that Lacan's formulae have a valid - albeit highly general - logical status and can be regarded as valid theoretical formalisations. A complete formal reconstruction in logical notation will not be essayed. Instead, the paper will turn to the discursive implications of the logical status of sexuation. Once we have described the formulae logically, we can consider their relevance to human sexuality, and therefore the appropriateness of Lacan's decision to designate these orders "masculine" and "feminine". In what sense can "masculine" or "feminine" be ascribed to logical systems, or, rather, why would masculine and feminine unconscious processes exhibit logical differences?

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