The meaning of psychoanalysis in intension and extension takes on several forms. From the intensive work of the imaginary to the extensive work with the object in the real. From the spectacular hypnosis of the gaze to the concrete construction of letters, numbers, writing, drawing, and new signifiers of a rigorous type. From the intensive auto-analysis carried out in the consulting room to the extensive ecole, college, or school of de-monstration. From the cure to the transformation of the social link by means of a new discourse relation.

Freud’s invention was the practice of psychoanalysis and his intention was that it be carried out beyond the medical, therapeutic, and academic realm. Lacan said his invention was the object (a) – and his intention was that this object be carried out in extension – that is to extend psychoanalysis beyond the imaginary fantasy to a clinic of the real.

It is to this end that in the end Lacan took up the practice of science as mathesis and art as poesis. The work of the scientist in his laboratory and the artist in his studio is finally brought together in Lacan’s school – which models itself after the community of mathematicians who present or demonstrate their work as a form of writing – an axiomatic logic or necessary contingency – within a community of others. It is at this place where mathematics and science begins to become one with art. Conversely it is at the place where the artist brings forth his singular desire along with a metalanguage of transmission to a community of other artists who have some semblance of what is being expressed that art becomes science.

We could say that psychoanalysis is a process of bringing forth one’s symptom, delirium, or object along with a metalanguage enabling some form of transmission of the impossible to transmit. By means of this not only is a symptom refined and a savoir-faire achieved but it is shared for others to witness if not make use of. This follows Charles Peirce’s project of pragmatism. It is here where mathematic science and poetic art converge with a writing of the symptom through a speech act of de-monstration or per-formance. This is a per-formation or pere-formation in which the dead father is resurrected, the absent father is re-invented. Voltaire said: “If God did not exist it would be necessary to invent him.” Now we have no other choice than to do so. The myth of the Oedipus Complex, the myth of castration, the guilt over the killing of the king or primal father, only serves to hide the more devastating fact of his absence, a void. We a-void or avoid the void. Negative Phi equals the Empty Set.