Frege

In Seminar XIII, "Frege" does not name a straightforward philosophical reference but functions as a theoretical operator by which Lacan stages a critique of the limits of logico-scientific objectivity. Lacan seizes on the Fregean concept of the object — defined by its capacity to receive a proper name, i.e., to be the referent of a singular, unambiguous designation — as the exemplary modern-logical account of what science takes as its object. What is hidden in this Fregean move, Lacan argues, is that the very act of naming-as-such, of fixing a referent through a proper name, already supposes a subject: the "specifically subjective character" of Frege's object is precisely what the logician of science must repress in order to maintain the appearance of a purely objective, truth-valued discourse. The Fregean object is thus unwittingly a suture: it closes over the gap — the subject's lack-of-being — that makes logical designation possible in the first place.

This is where the objet petit a enters. What Lacan identifies as concealed within the Fregean framework is precisely the o-object, the remainder left by the subject's alienation into the signifying chain. The logician constructs a domain of referential transparency by producing the proper name as the ideal of designation, but this operation systematically occludes the fact that any name, any act of reference, is conditioned by a desiring subject who cannot themselves be named without remainder. The projective plane and the Möbius strip are then offered as the topological figures adequate to this structure, against the spherical, closed-surface model that implicitly underwrites both idealist and naively realist epistemologies. Against the Fregean ideal of bivalent, alethic logic — where every proposition is either true or false — Lacan insists that truth is not a truth-value but is entangled with the subject's desire and with the objet a as its cause.

This concept appears in jacques-lacan-seminar-13 (p. 77) and is legible only against the backdrop of several cross-referenced canonical concepts. Most directly, it extends the logic of alienation: the Fregean subject is the subject alienated into science's signifying chain, who must sacrifice being for meaning (the vel of alienation) in order to produce logically nameable objects. The proper name is the symbolic endpoint of this sacrifice — it purports to anchor reference without remainder, yet it is sustained by the very subject it erases. Similarly, the concept is a specification of the objet petit a: what the Fregean framework conceals is precisely the a, the object-cause of desire that falls out of the subject's entry into the signifier. Frege's object-defined-by-proper-name is the scientific fantasy of an object without the a — a fully specifiable, non-desiring remainder — and Lacan's intervention is to show that this fantasy is structurally impossible.

The concept also implicitly engages Das Ding: the Fregean object is in some sense the attempted domestication of das Ding — reducing the unreachable, pre-symbolic Thing to a named, logically tractable referent. Bivalent logic (alethes, true/false) is the medium through which this domestication is attempted, and it is precisely bivalent logic's inadequacy to the truth of the subject that Lacan's topological figures — Möbius strip, projective plane — are meant to expose. The ego's structure as imaginary misrecognition provides an analogical underpinning: just as the ego misrecognizes its specular image as itself, Fregean logic misrecognizes its subjectively conditioned object as purely objective. The single occurrence of "Frege" in the corpus functions as a concentrated critical pivot, where the claims of modern scientific logic are tested against the Lacanian account of the subject and found to conceal precisely what psychoanalysis brings to light.

Seminar XIII · The Object of PsychoanalysisJacques Lacan · 1965 (p.77)

the Fregian concept entirely centred on that to which one can give a proper name... there is revealed the specifically subjective character... of what, for a Frege, qua logician of science, is what characterises as such the object of science

The phrase "qua logician of science" is theoretically loaded because it marks Frege not as a general philosopher but as the representative figure of a specific epistemic project — the logicization of scientific objecthood — and by identifying the "specifically subjective character" hidden within that project's central concept (the proper name as individuating reference), Lacan turns Frege's own apparatus against itself: the very tool meant to guarantee objective designation reveals the ineliminable subject beneath it.