Antinomy of the Signifier

The "Antinomy of the Signifier" names the irreducible internal contradiction that the signifier introduces into the subject's relation to itself and to its own being. In Seminar XII, Lacan formulates this by way of the proper name: when a subject says "I am so-and-so," the name objectifies them — pins them to a social, symbolic position — yet simultaneously fails to capture the "I am me" of lived self-identity. The signifier, in other words, cannot simultaneously be both a mark of identity (determining who the subject is for the Other) and a transparent vehicle of self-presence. This structural impossibility — that the signifier both constitutes and misses the subject — is what Lacan calls the antinomy. It is not a logical paradox that could be resolved by a better theory; it is constitutive of subjectivity as such. The subject is precisely what is split, or divided ($), by this very antinomy.

What prevents the antinomy from dissolving into mere inconsistency is objet petit a, which Lacan positions as that which escapes the antinomy — the remainder or surplus that falls out of the signifying operation and thereby marks both its failure and its productivity. The phonematic decomposition of proper names (as explored in Leclaire's clinical contribution referenced in the passage) enacts this antinomy at the level of the letter: the name, broken into phonemes, reveals the workings of metaphor (condensation, substitution) and metonymy (displacement, contiguity), showing how the primary processes of the unconscious are already inscribed in the very material of the signifier that is supposed to name the subject most intimately.

This concept appears once, in jacques-lacan-seminar-12-1 (p. 205), and it functions as a local intensification of several canonical Lacanian notions. It is most directly an extension of the theory of the Master Signifier: the master signifier (S1) is supposed to represent the subject for all other signifiers, yet precisely because it is tautological and lacks a stable signified, it cannot fully accomplish this representation — the antinomy names the structural reason why S1 both installs and fails the subject. The concept also redeploys Metaphor and Metonymy (the Lacanian re-readings of Freudian Condensation and Displacement) at the level of the proper name's phonematic structure: the name is not merely a label but a site where substitution and sliding — the two primary mechanisms of the unconscious — are already operative, making every act of nominal identification an act of (imperfect) signification. The relationship to Castration is equally direct: castration, understood as the structural loss imposed by the signifier on the speaking being, is another name for what produces this antinomy. The subject gives up jouissance by entering the symbolic, and the antinomy of the signifier is the formal expression of that constitutive loss — neither pole (objectification nor self-identity) can be fully occupied. Finally, Objet petit a appears explicitly as the concept's necessary complement: it is defined here as precisely that which escapes the antinomy, the leftover remainder that the signifier cannot absorb, which links the concept directly to the logic of surplus-jouissance and the cause of desire.

Seminar XII · Crucial Problems for Psychoanalysis (alt. translation)Jacques Lacan · 1964 (p.205)

I believe that it is correct to say that the signifier is pure connotation of antinomy. And to sustain at the moment of grasping what you can try to grasp of this formula, I would add that this antinomy is fundamentally in our experience the one that is constitutive of the subject.

The phrase "pure connotation of antinomy" is theoretically loaded because it refuses to assign the signifier any positive meaning (a denotation) and instead defines it purely by what it generates — a structural contradiction; "constitutive of the subject" then makes clear that this antinomy is not an accidental defect of language but the very mechanism through which a subject ($) comes into being, directly echoing the Lacanian principle that the subject is the effect of the signifier's division.