Psychoanalytical praxis based on Jacques Lacan's knot topology

Raffaele De Luca Picione ¹

⁰Dynamic Psychology, Giustino Fortunato University, Via Raffaele Delcogliano, 12, 82100, Benevento, BN, Italy.

American Journal of Psychoanalysis +

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September 19, 2025

View abstract on PubMed

Summary

Jacques Lacan utilized knot topology, specifically the Borromean knot, to explore the interplay of the Imaginary, Symbolic, and Real registers in psychoanalysis. A fourth element, the sinthome, offers a unique way to manage the Real's unrepresentable nature.

Area Of Science

Psychoanalytic theory
Knot topology
Clinical psychology

Background

Jacques Lacan's work explores the unconscious through structuralist and linguistic theories.
Psychoanalysis often grapples with representing subjective experience and the limits of language.

Purpose Of The Study

To examine Jacques Lacan's theoretical framework for applying knot topology in psychoanalysis.
To elucidate the clinical implications of using the Borromean knot model.
To explore the concept of the sinthome as a unique element for subject integration.

Main Methods

Conceptual analysis of Jacques Lacan's writings on knot theory.
Application of Borromean knot topology to psychoanalytic concepts (Imaginary, Symbolic, Real).
Exploration of the sinthome as a structural element in psychoanalytic practice.

Main Results

The Borromean knot effectively models the dynamic interplay of the Imaginary, Symbolic, and Real registers.
The sinthome functions as a crucial substitute to stabilize the psychic structure when the Borromean knot unravels.
The sinthome represents a singular, non-medicalized element enabling subjects to confront the unrepresentable Real.

Conclusions

Knot topology provides a robust mathematical model for understanding complex psychoanalytic concepts.
The sinthome offers a novel perspective on symptom formation and subjective resilience.
Lacan's topological approach deepens the understanding of psychic structure and the confrontation with the Real.

Keywords:

Borromean knot Jacques Lacan psychoanalysis sinthome vs symptom topology