Bivalency

Bivalency names the classical logical law according to which every proposition must be either true or false — tertium non datur. In Lacan's usage in Seminar XIV, the law of bivalency is sharply distinguished from the principle of non-contradiction: the latter governs what cannot simultaneously be (nothing can be both true and false at once), while bivalency governs what must always be (every proposition is determinately one or the other). What is decisive in Lacan's move is that he treats this "decided-on" bivalency as problematic rather than axiomatic. He does not abolish the classical law, but he opens a gap within it — specifically the gap between two apparently equivalent but asymmetric formulations: "is it true that it is false" versus "is it false that it is true." This spacing, this nuance inscribed between the two negations, is not a logical redundancy; it is the site where a logic of truth adequate to the analytic field must be worked out.

The problematization of bivalency thus serves Lacan's larger argument that psychoanalytic discourse is governed by a logic of truth that cannot be flattened into a binary toggle. The unconscious, in violating the principle of non-contradiction (contradictory thoughts coexist without excluding each other in the primary process), does not thereby escape the domain of logical structure — it rather demonstrates that the logical field requires finer articulation than bivalency alone can provide. Free association, the rule that organizes the analytic session, functions as a strategic dissimulation of this logic: it solicits from the subject the very propositions whose truth-value is undecidable within the classical binary, thereby allowing the dimension of truth proper to the unconscious to emerge.

Bivalency appears in Seminar XIV (jacques-lacan-seminar-14 and jacques-lacan-seminar-14-1, p. 266), at a moment when Lacan is working to formally ground psychoanalytic practice within logic. It functions as a specification and complication of the cross-referenced concept of Contradiction: where Contradiction names the motor of dialectical movement and the unconscious's indifference to mutual exclusion, Bivalency names the formal logical framework — the two-valued logic of true/false — against which that dialectical movement must be measured. Lacan's point is that the unconscious's violation of non-contradiction does not license abandoning bivalency altogether; rather, it compels a more careful, nuanced deployment of it, attending to the asymmetry between the two directions of negation.

Bivalency also intersects obliquely with Language and Interpretation: if analytic interpretation operates on the material of free association, and if free association produces propositions whose truth-value cannot be decided by a simple binary, then interpretation must work in the space that classical bivalency leaves unthought. The connection to Desire and Fantasy is structural: desire's irreducibility to any fixed object, and fantasy's function as a screen that organizes reality, both depend on the fact that the subject's relationship to truth is never a clean either/or. Bivalency, as Lacan handles it, is thus not a logical curiosity but a hinge concept connecting formal logic, the structure of the unconscious, and the grounds of analytic technique within the argument of Seminar XIV.

Seminar XIV · The Logic of PhantasyJacques Lacan · 1966 (p.266)

the law of bivalency - every proposition is either true or false… this bivalency - this bivalency as decided on - is problematic. All the nuances there are and which are inscribed in, between is it true that it is false, or it is false that it is true.

The phrase "bivalency as decided on" is theoretically loaded because it reframes the classical law not as a logical necessity but as a decision — a convention that can be interrogated — which is precisely what opens the space for a psychoanalytic logic of truth. The further distinction between "is it true that it is false" and "is it false that it is true" points to the asymmetry of negation, signalling that the placement and scope of the negative operator produce non-equivalent propositions, a nuance that standard bivalency suppresses but that analytic discourse — organized around the subject's divided relation to truth — cannot afford to ignore.