Sectioning of the Predicate

The "sectioning of the predicate" names the structural impossibility that lies at the heart of predication as such: any attempt to complete a subject by furnishing all of its predicates necessarily fails, because at least one predicate must always detach itself, standing in for the impossibility of closure rather than contributing to a totalization. The concept is developed in Seminar 20 via an intersection of ordinal number theory, Platonic myth, and Peircean semiotics. The Aristophanic "sexion" (the primordial cut that divides the originally whole being) and Diotima's figure of the intermediary/interpretant both serve as mythic-logical precedents: the cut does not find an indivisible atom at its limit, but instead reveals that every act of division generates a remainder that cannot be incorporated. In this sense, "sectioning" is not a surgical precision that isolates predicates cleanly; it is the very mark of an impossible operation—one that always leaves a predicate unaccounted for, detached, representing the impossibility of the set of all predicates.

This structural remainder is linked, in Lacan's guidance of the presentation, to the logic of nomination: 'encore' (still/again/more) names the infinite index that always exceeds any covering system—the predicate that escapes—while 'non' names the radical initial negation that infinitises every nomination from the start. Together they frame the sectioning of the predicate as the point where the symbolic order's drive to complete predication collides with the Real of its own incompleteness. The concept thus belongs to Lacan's later project of formalizing the non-all (pas-tout): the predicate that detaches itself is not a contingent omission but the structural index of the fact that no predication can close over the subject it predicates.

In jacques-lacan-seminar-20-cormac-gallagher, the sectioning of the predicate operates as a logical formalization of themes central to Seminar 20's broader argument about sexual difference, the non-all, and the limits of any symbolic totalization. It cross-references and extends at least three canonical concepts. First, it is a specification of Lack: where lack names the constitutive structural gap that prevents any subject or symbolic order from being complete, the sectioning of the predicate localizes that gap at the precise moment of predication — the grammatical-logical site where subject and attribute are supposed to be joined. The "detaching" predicate is precisely the objet-a-like remainder that marks the impossibility of closure from within the operation itself. Second, it articulates with Gap: the impossible cut of predication is not a flaw in the logical machinery but the positive structural opening that language constitutively produces — homologous to what Lacan (in Seminar VII) calls the "fashioning of the signifier" that introduces a gap or hole in the real. Third, its link to Infinite is explicit in the theoretical move: 'encore' names the infinite index that escapes any system of covering-over, directly echoing the structure of the bad infinite (endless "one more") while also gesturing toward the true infinite in which the limit is internal — the detached predicate is not simply the next item in a series but the index of the series' own incompletion.

The concept also touches on Master Signifier and Name of the Father insofar as the logic of nomination is at stake: if every predicate-system generates a remainder that represents impossibility, then the function of the master signifier or the Name-of-the-Father is precisely to suture that remainder — to give the detached predicate a name that stabilizes (without eliminating) the gap. The Interpretant connection (via Diotima's intermediary) suggests that the sectioning of the predicate is also a semiotic structure: meaning is never delivered in a final predicate but is always relayed through an interpretant that itself requires further interpretation, infinitising the chain. The concept is best understood as an extension and formalization of Lack and Gap at the level of logical grammar, made precise through the mathematical apparatus of ordinal number theory that Lacan deploys throughout Seminar 20.

Seminar XX · Encore: On Feminine Sexuality, the Limits of Love and KnowledgeJacques Lacan · 1972 (p.24)

Sectioninging of predicate is then as if that could be cut... the impossible of predication. Namely, the impossibility of providing all the predicates, of putting them together, without at least one detaching itself as representing in impossibility

The phrase "at least one detaching itself as representing in impossibility" is theoretically loaded because it converts the failure of predication from a contingent deficiency into a structural necessity: "at least one" invokes the logic of the existential quantifier that underpins Lacan's formulas of sexuation, while "representing in impossibility" means the detached predicate does not merely fall away but actively stands in for — represents — the Real of the system's incompleteness, functioning as a kind of symptom or master signifier of the non-all.