Recursive Count

Recursive Count names the structural operation through which the "public" (Kierkegaard's abstract aggregate, formalized as P⊋{{n+1},{Ø}}) maintains itself not by adding up discrete members extensionally but by folding back on its own counting act. The matheme encodes two elements: the successor operation {n+1} (the crowd always gaining one more) and the empty set {Ø} (the nothing that is nonetheless "added"). When the nothing is added to the all, the totality is made to exceed itself — it outnumbers its own totalizing count — so the operation can never reach closure. The count that was supposed to terminate instead produces a new starting point for another count, generating the paralogistic figure Kierkegaard condenses as "tælle og tælle" (counting and counting). The structural result is a self-referential loop rather than a series, making completion formally impossible from within the operation itself.

This concept functions simultaneously as a theory of modern loquacity. Kierkegaard's Snaksomhed (chatter) and Forstandighed (common sense) are not merely sociological features of crowd life; they are the phenomenal expressions of the same recursive loop. Because the public's counting can never close, discourse within it can never conclude: every utterance generates the condition for another utterance, every opinion a counter-opinion, in an indefinitely iterated oscillation. The matheme thus formalizes what is otherwise described as the ideological "buzz" of public life — a structure of endless, self-perpetuating talk that mirrors, at the level of content, the formal incompletability of the count that defines its subject.

Within samuel-mccormick-the-chattering-mind-a-conceptual-history-of-everyday-talk-unive, the Recursive Count occupies a pivotal structural moment on p. 95 where the argument shifts from a merely sociological description of modern public discourse to a formalized, matheme-level account of it. It is positioned as an extension of the Matheme concept: just as the Lacanian matheme captures "the formalization of the impasse of formalization," the P⊋{{n+1},{Ø}} matheme captures the impasse of enumeration — the point at which counting itself becomes the obstacle to completion. The Recursive Count is also a specification of the Sorites Paradox (Fuzzy Totality) cross-reference: where the Sorites exposes the instability of vague predicates applied to heaps, the Recursive Count formalizes why the "heap" (the public) is structurally resistant to any clean boundary — not because of semantic vagueness, but because its constitutive operation is self-undermining.

In relation to Lack and the Master Signifier, the Recursive Count can be read as what happens when a quilting point (point de capiton) fails to arrest signification: instead of S1 retroactively fixing a chain, the empty set {Ø} is added to the chain, producing not a stop but a reopening. This aligns structurally with S(Ø) — the signifier of the lack in the Other — insofar as the public's matheme encodes an Other that cannot complete its own count. The Paralogos cross-reference is equally central: the "paralogos" of the abstract aggregate is not a logical error to be corrected but the very engine of the recursive operation, just as, for Lacan, the paradoxes of the subject are not defects but the productive impasses on which desire and discourse run. Ideology enters as the broader frame: the endlessness of the recursive count is the formal condition of possibility for the ideological chatter that sustains modern public life, giving Kierkegaard's social critique a structural-algebraic backbone.

The Chattering Mind: A Conceptual History of Everyday TalkSamuel McCormick · 2020 (p.95)

the mathematical structure of the public is not extensive but recursive. When 'nothing' is added to the public's 'all,' thereby causing it to outnumber its own totalizing count, the paralogos of this abstract aggregate shifts from counting alone to what Kierkegaard...can only describe as 'counting and counting [tælle og tælle]'.

The theoretical load is carried by the opposition "not extensive but recursive" and the phrase "outnumber its own totalizing count": the first term rules out a simple additive model of the public (it is not just a large number), while the second introduces the self-exceeding loop — the public's all is structurally outrun by its own operation — which is precisely what forces the shift from "counting" to "counting and counting," i.e., from a terminable act to an indefinitely iterated, self-referential one. The retention of Kierkegaard's Danish "tælle og tælle" signals that this repetition is not rhetorical but formally irreducible.