Predication-Relay Logic

Predication-Relay Logic names the structural operation by which language constitutes Being through a chain of predicates, none of which ever adequately fulfills the position of substance. In Lacan's account (Seminar 20), substance is not a positive, stable ground but is defined structurally as what is lacking — it is the "potential substance" that predication simultaneously presupposes and conceals. Each predicate steps into the place of substance, appearing momentarily to fill or name it, but in doing so only displaces the gap onto the next predicate in the chain. The relay-structure is therefore not a path toward completion but a permanently open series: predication covers over lack without ever abolishing it, and the gap is reconstituted at every step.

This logic re-frames the classical metaphysical category of substance as a function rather than a foundation. "Substance" in this sense is less a thing than a structural placeholder — the position of what-is-sought — and the relay is the mechanism by which Being gets inscribed in discourse at all. Language, on this account, "represents Being for the word": it produces the effect of ontological reference without delivering presence. The impossibility is thus not a failure of language but its constitutive condition; the infinite relay of predicates is precisely how discourse keeps open the gap that is the engine of signification.

Predication-Relay Logic appears in jacques-lacan-seminar-20-cormac-gallagher (p. 56), in the midst of Lacan's late re-working of the ontological tradition. It functions as a precise, technical specification of how several canonical concepts articulate together. It is directly an extension of Lack: just as Lack names the irreducible structural gap that is the condition of both the subject and signification, Predication-Relay Logic names the syntactic mechanism by which that gap is perpetually re-inscribed in the act of predication — "potential substance" is the symbolic slot of lack, and each relay-move re-opens it rather than closing it. The concept is equally a specification of Gap: the béance that language cannot close over itself is here given a precise grammatical form — it is the gap between substance and predicate, endlessly relayed. The cross-reference to Infinite is also illuminating: the relay-structure is precisely the "bad infinite" of endless deferral that Hegel critiques, yet Lacan reframes it not as a failure but as the very operation of Being qua discourse, suggesting an immanent or topological closure-through-opening that aligns more closely with Hegel's true infinite understood as self-limiting movement.

The links to Signifier, Language, and Being are constitutive: the relay-structure is what it means for language to "represent Being for the word" — each signifier occupies the position of substance only to pass it on, so that the chain of signifiers is nothing other than this relay. Contradiction and Singularity enter as limiting cases: the relay holds contradiction open (substance is and is not present in each predicate), and Singularity may mark the point where the relay halts or folds back — though the text itself emphasizes the openness of the operation. Together, Predication-Relay Logic gives a logical-grammatical micro-account of what the larger Lacanian corpus treats at the macro-level: the impossibility of fully symbolizing the Real, and the structural necessity of that impossibility for discourse itself.

Seminar XX · Encore: On Feminine Sexuality, the Limits of Love and KnowledgeJacques Lacan · 1972 (p.56)

The substance is a function that this will transmit to a third predicate etc.... What counts, is the operation of relays. It is the actual relation of predication which, made possible by potential substance, inscribes it and transforms it into a term, into a predicate

The phrase "potential substance" is theoretically loaded because it reformulates the classical metaphysical ground of predication — substance — as a structural potentiality (a lacking position) rather than an actuality, and the claim that predication "inscribes it and transforms it into a term, into a predicate" shows the relay completing a paradoxical loop: the very act meant to express substance converts it into just another predicate, perpetually deferring the grounding it was supposed to supply.