From No Subject - Encyclopedia of Psychoanalysis
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Freud uses the term 'inversion' to designate homosexuality, the idea being that homosexuality is the inverse of heterosexuality.

Lacan uses the term in this sense too in his early works.[1]

However, in Lacan's post-war works the term is used in quite a different sense.

Inversion then usually refers to a characteristic of the specular iamge.

What appears on one side of the real body appears on the other side of the image of the body reflected in the mirror.[2]

By extension, inversion becomes a quality of all imaginary phenomena, such as transitivism.

Thus in schema L, the imaginary is represented as a barrier blockign the discourse of the Other, causing this discourse to arrive at the subject in an inverted form.

Hence Lacan's definition of analytic communication in which the sender receives his own message in an inverted form.

In 1957, both senses of the term are brought together in Lacan's discussion of Leonardo da Vinci.

Taking up Freud's argument about Leonardo's homosexuality,[3] Lacan goes on to argue that Leonardo's specular identification was highly unusual in that it resulted in an inversion of the positions (on [[schema L) of the ego and the little other.[4]

  1. Lacan. 1938. p.109
  2. Lacan. 1951b. p.15
  3. Freud. 1910c.
  4. Lacan, Jacques. Le Séminaire. Livre IV. La relation d'objet, 19566-57. Ed. Jacques-Alain Miller. Paris: Seuil, 1991. p.433-4