Frege's Anti-Psychologism

Frege's Anti-Psychologism, as reconstructed by Duroux in Seminar XII, names the philosophical-logical move by which number — and by extension, any rigorous theory of the subject — is wrested from the domain of psychological intuition and grounded instead in purely logical relations. In Frege's Grundlagen der Arithmetik, the counting subject who mentally collects, abstracts, and names quantities is explicitly disqualified as the foundation of arithmetic: number cannot be what a subject does with things, because such a grounding would make mathematics contingent on the variable activities of empirical minds. Instead, Frege insists that number must be derived from the formal relation between a concept and the objects that fall under it, with zero defined through the self-contradictory concept "non-identical to itself" — a concept under which no object can fall — and the successor operation generating the entire sequence of natural numbers from that formal void.

The theoretical stakes for Lacanian theory are immediate: if zero is grounded not in an absence that a subject notices but in a logical contradiction internal to the concept itself, then lack is a structural effect of the symbolic-logical order, not a psychological experience. This is precisely the philosophical hinge from which Miller will develop his Lacanian theory of suture, and it underwrites the broader Lacanian claim that the subject is constituted by the signifying chain rather than being its origin. Anti-psychologism thus functions as the epistemological precondition for reading arithmetic — and, by analogy, the entire symbolic order — as a domain governed by its own internal necessity, one that produces the subject as its effect rather than presupposing the subject as its ground.

In jacques-lacan-seminar-12-1, Frege's Anti-Psychologism appears as the philosophical foundation that Duroux's presentation erects before Miller's Lacanian elaboration can proceed. It is positioned as a precondition for the entire theoretical edifice of suture and the Lacanian subject: only once the psychological subject has been expelled from the grounding of number can lack, zero, and the successor operation do the work Lacan needs them to do. In relation to the cross-referenced canonical concepts, anti-psychologism is most directly the condition of possibility for the Concept-Object Distinction (Frege) and the Successor Operation — it is what forces Frege to define zero through a logically self-contradictory concept rather than through a subject's experience of "nothing," and what makes the successor operation a purely formal procedure rather than a mental act of counting on.

The concept also resonates structurally with Lack and Negation: by locating zero in the concept "non-identical to itself," Frege installs negation at the origin of number, making lack a logical rather than psychological category — precisely the move Lacan needs for his claim that "nothing in the real is missing; a lack can only be introduced when there are signs and symbols." Similarly, the anti-psychologistic expulsion of the empirical subject from the foundation of number anticipates the Splitting of the Subject and the barred Subject: if the subject is not the origin of the symbolic order but its product, then the subject is necessarily divided, constituted by lack in the Other rather than self-present. Against Foreclosure and the Signifier, anti-psychologism provides the logical-formal register within which the signifier's differential, non-substantial character can be articulated: just as number is not grounded in psychological intuition, the signifier is not grounded in the subject's meaning-giving activity but produces the subject as its own structural effect.

Seminar XII · Crucial Problems for Psychoanalysis (alt. translation)Jacques Lacan · 1964 (p.87)

If the problem is to discover what is specific in the plus sign and in the successor operation, for that it is necessary to separate out the concept of number from this psychological determination.

The phrase "separate out the concept of number from this psychological determination" is theoretically loaded because it performs the anti-psychologistic cut in one gesture: "psychological determination" designates precisely the grounding of number in a subject's mental activity that Frege rejects, while "what is specific in the plus sign and in the successor operation" names the formal-logical remainder — the purely structural operations that will become, in Lacanian translation, the mechanisms by which zero and lack generate the subject without any subjective origin.