Kierkegaard's Public as Abnormal Set

Kierkegaard's Public as Abnormal Set is a concept that performs a set-theoretic formalization of Kierkegaard's paradoxical claim that "the public" is simultaneously "all and nothing." The move draws on axiomatic set theory to argue that the public has the structure of a proper superset P⊋{{n+1},{Ø}}: it contains both a subset of "somebodies-turned-nobodies" (individuals who, upon entering the public, lose their particularity) and an empty subset whose "nothing" is not additive zero but a subtractive, self-cancelling void. What makes this formation distinctively "abnormal" in the set-theoretic sense is that the public includes itself as one of its own members — the classical Russell-paradox violation of the axiom of foundation — meaning it cannot be a well-founded or stable totality. The public's apparent excess over its membership is not plenitude but a formation-into-one-of-zero: an empty set that counts as something while adding nothing.

This reading anticipates Badiou's set-theoretic ontology insofar as the empty subset functions not as mere absence but as the constitutive interior void that prevents the public from ever cohering into a genuine whole. In this frame, the public is not a unified collective but a structure whose self-inclusive character produces a permanent ontological instability — a set that "is" only by perpetually undermining the conditions of its own being. The concept thus reframes Kierkegaard's cultural critique of the press-driven, anonymous mass as a rigorous structural claim: the public's "nothing" is the generative void that makes it appear as an entity while ensuring it remains irreducibly non-identical to itself.

Within the source (samuel-mccormick-the-chattering-mind-a-conceptual-history-of-everyday-talk-unive), this concept sits at a crossing point between Kierkegaard's nineteenth-century social critique of "the public" as a monstrous, anonymous non-entity produced by the press, and a contemporary set-theoretic ontological vocabulary. It functions as a conceptual bridge: McCormick uses the mathematical apparatus to show that what Kierkegaard diagnosed culturally is structurally formalizable, lending it ontological rather than merely rhetorical force.

Across the broader cross-referenced canonical terrain, the concept is most tightly bound to Lack and Maeontology. The empty subset {Ø} within the public's set-structure is a direct figure of what Lack designates: not a contingent absence but a constitutive void that is "not additive but subtractive," precisely paralleling the Lacanian insistence that "nothing in the real is missing; a lack can only be introduced when there are signs and symbols." The self-inclusive structure of the abnormal set equally resonates with Maeontology's core claim that non-being is ontologically generative — the public's "nothing" is not the mere privation of membership but the interior crack that makes the set appear as a formation-of-one while preventing genuine totalization. The link to the Master Signifier is implicit: the public functions like a quilting point that organizes collective identity, but unlike S1 it cannot even sustain a tautological self-grounding — it collapses into self-inclusion and paradox rather than arresting signification's slide. The connections to the Real and Negation further sharpen the concept: the public's self-inclusive structure is a figure of the impossibility that "does not cease not to be written," the structural limit that prevents any symbolic totality from closing on itself.

The Chattering Mind: A Conceptual History of Everyday TalkSamuel McCormick · 2020 (p.89)

it would amount to an abnormal set— namely, a collection of entities that includes itself as one of its members… the public includes itself.

The phrase "a collection of entities that includes itself as one of its members" is theoretically loaded because self-membership is precisely the violation of the axiom of foundation in standard set theory — the condition that generates Russell's paradox — so calling the public an "abnormal set" is not a metaphor but a claim that the public's structure is formally paradoxical, incapable of grounding itself, and therefore constitutively void rather than whole. The closing clause "the public includes itself" condenses Kierkegaard's "all and nothing" into a single structural formula: the public's attempt at self-totalization is the very operation that dissolves any stable identity it might claim.