Today in the Babelisation and disorder of the psychoanalytic movement, the Lacanian theory constitutes the open reformulation of the psychoanalytic theory invented by Freud. It is a reformulation which takes into account the transformation of scientific epistemology and progress of mathematics.
This global reference for the psychoanalytic movement has the merit of placing psychoanalysis in the field of subjective formalism and topological epistemology that allows an agreement on the conceptual notions of psychoanalysis. And, although there is dissent about the meaning (Sinn), to a certain extent, it is possible to agree on the denotation (Bedeutung) of these conceptual notions, in terms of what they mean in the structure interpreted in terms of subjective topology.
These features induce the possibility of reformulating and broadening the meaning depending on the unequal advances in mathematics and formal sciences, but especially because of the sole and divergent interests of psychoanalysts, and in particular because of the progress of each in his cure, in the theory of his practice as well as in the practice of his cures and his theoretical practice.
I therefore imagine a series of studies, as an adequate means to transmit some reformulations from the psychoanalytic science. The future of psychoanalysis, its continuation as a praxis, theory and culture, requires working at the implementation of a global network of study circles. A network where the masters of discourse will be the values of consistency and coherence: consistency of knowledge, linking unconscious and theoretical knowledge, and coherence for a completeness that confronts both the inconsistency and radical incompleteness of the psychoanalytic theory and especially its inability to be a cumulative knowledge. These conditions should allow psychoanalysis to continue and reinvent itself from one circle to another, and it should change the way its nucleus of truth can be passed on.
Indeed, the subjective topology means that, based on his or her known and unknown knowledge of the structure, every psychoanalyst may achieve an extension of psychoanalytic theory. This subjective topology is a method to expand psychoanalysis, a method open to individual differences: it allows carrying out some theoretical closeness between psychoanalysts.
Jean-Gerard Bursztein is a French psychoanalyst who has a Doctorate in philosophy. He teaches psychoanalysis and practices in Paris. He was a student of Jean-Toussaint Desanti and worked on both philosophy of mathematics and philosophy of sciences, and he continues to explore this field in studying the intrication of psychoanalysis and mathematics. He is the author of numerous books and papers, including On the Difference Between Psychoanalysis and Psychotherapy (2008). His latest book, The Topological Transformation of Freud’s Theory, is published by Karnac Books this week.
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‘The unconscious, according to Freud, has a structure. One can conjecture as to the relation between this structure and the structure found in mathematics. One of the strongest hypotheses that one can make is that the two structures are homological – they say the same thing. How to give sense to this hypothesis then becomes a problem in the field of the formalisation of psychoanalysis – a field that Jean-Gérard Bursztein opens up in his work. Philosophical and scientific problems of the structure of mathematics had already been raised in the French tradition by Jean Cavaillès and Albert Lautman, and subsequently by Jean Toussaint Desanti. Bursztein draws on these French programmes for the foundations of mathematics, as he formulates his constructions within this important and developing field.’
– Bernard Burgoyne, author of Drawing the Soul: Schemas and Models in Psychoanalysis, and co-editor of The Klein–Lacan Dialogues