Mythical Permutation

Mythical permutation names the structural logic Lacan discerns in Little Hans's successive fantasies: each fantasy in the series is not a random variation but a systematic attempt to articulate, from within the symbolic, every conceivable form of resolution to a constitutively impossible deadlock. The "deadlock" in question is the collision between two incommensurable circuits — the maternal (the pre-Oedipal dyadic bond, saturated with jouissance) and the paternal (the Name-of-the-Father as the operator of symbolic castration, phallicization, and desire). Because no single fantasy can dissolve this structural impossibility, Hans's psyche generates a sequence — a permutation — cycling through all available symbolic and imaginary configurations of the impasse. The series is "mythical" in a quasi-Lévi-Straussian sense: just as myth exhausts the logical permutations of a contradictory cultural problem through narrative variants, Hans's fantasies exhaust the logical variants of an insoluble subjective problem through successive fantasmatic articulations.

The concept therefore has a precise clinical function: it allows Lacan to distinguish neurotic from perverse resolution. Where Hans's trajectory is one of successive, ultimately failing symbolic attempts — a permutational working-through in fantasy — the perverse (fetishistic) path would have short-circuited the series by installing a single fixed object (the fetish) as a permanent solution. Mythical permutation is thus the formal signature of neurosis: the compulsion to keep articulating what cannot be fully symbolized, a restless signifying labor driven by the impossibility it cannot master.

The concept appears in jacques-lacan-seminar-4, Lacan's extended clinical reading of the case of Little Hans — Freud's paradigm case for the structure of phobia. Within that seminar's argument, mythical permutation sits at the intersection of several canonical concepts. It is, first, an operation within Fantasy: each permutation is a fantasmatic formation ($ ◇ a), a new attempt to stage the relation between the barred subject and the impossible object. Because no permutation succeeds, the series as a whole enacts what fantasy theory describes as the structural incompleteness of any fantasmatic solution — the Real of the sexual non-rapport keeps returning. Second, the concept is internally calibrated against Anxiety: Hans's successive fantasies are precisely attempts to manage the anxiety produced by the proximity of the maternal Thing and the threatening absence/presence of the paternal function; the permutational series is, in effect, a sequence of anxiety-responses that each try and fail to create enough symbolic distance. Third, the concept directly articulates the differential between Neurosis and Perversion as Clinical Structures: the neurotic permutes fantasies restlessly because the Name-of-the-Father has been inscribed but is inadequately anchored (phobia as a borderline structure), whereas the pervert arrests the series by installing the Fetish as a fixed, disavowal-stabilized solution. Mythical permutation is thus an extension and specification of the general clinical-structural framework — it gives a dynamic, sequential description of what neurotic symbolization looks like when the phallic signifier fails to fully organize the subject's desire, without the perverse short-circuit of the fetish.

Seminar IV · The Object RelationJacques Lacan · 1956 (p.322)

what I have called the sequence of mythical permutations... it's a matter of how to face up to an impossible situation through the successive articulation of all the different forms of the impossibility of a solution.

The phrase "successive articulation of all the different forms of the impossibility of a solution" is theoretically dense: "successive articulation" marks this as a signifying, symbolic labor (not mere repetition), while "impossibility of a solution" insists that the series is driven not toward resolution but toward the exhaustion of every variant of an irreducible structural deadlock — aligning the concept directly with the Lacanian axiom that there is no sexual relationship and that fantasy can only circle, never fill, the void it covers.