Forming-into-One

Forming-into-one names the set-theoretic and logical operation by which a collection of elements is counted as a unified whole — a "one" that encompasses its members. In the context of McCormick's analysis of Kierkegaard's "the public," the concept designates not merely the act of aggregating individuals into a totality but the reflexive recursion of that act upon itself. The public's "all" ({n+1}) and its "nothing" ({Ø}) are both subsets produced by the same forming-into-one procedure. When zero is counted — when the empty set is gathered into a one — the operation does not simply enumerate; it marks the void as a member. The critical move is that the forming-into-one is then applied a second time to the operation itself: the encompassing gesture that would include everyone and everything must itself be included, and this inclusion is the void point that prevents the total from closing on itself. The public, structurally, can never coincide with its own "all" because the counting procedure that constitutes it exceeds and haunts the resulting set.

This has a strictly Lacanian resonance: the forming-into-one is not a neutral logical step but the mechanism by which lack is installed at the heart of any apparent totality. The public is not merely incomplete; it is a structure organized around the impossibility of its own completion, because the operation that would finalize the count is simultaneously the empty subset that keeps the set from being closed. The "being-nothing" ({Ø}) is therefore not an inert residue but the structural trace of the operation's failure to master itself — the suture of a void that cannot be filled without re-opening.

The concept appears in samuel-mccormick-the-chattering-mind-a-conceptual-history-of-everyday-talk-unive (p.91) as a formalization of Kierkegaard's "public" using set-theoretic notation, and it sits at the intersection of several canonical Lacanian concepts. Most directly, forming-into-one is a specification of Suture: the operation by which the subject (or, here, a social totality) is stitched into the symbolic chain through a zero-element that is both counted and absent. Like the zero in Frege's sequence that Lacan reads through Miller's suture, the forming-into-one of {Ø} introduces an absence that functions as a positive member of the set, binding the chain while simultaneously marking its constitutive incompleteness. The concept also extends Lack: the public's void ({Ø}) is not a contingent gap but the productive, structural absence that makes the totality possible in the first place — the "it does not add up" moment that must be said for lack to appear. The forming-into-one of the operation (rather than merely of its elements) further echoes the logic of the Point de capiton and the Master Signifier: just as S1 is the signifier that organizes all other signifiers yet cannot be semantically grounded within the chain it anchors, the forming-into-one of the counting operation is the quilting move that holds the public together yet is itself the void that undoes any final closure. The concept thus acts as an extension of these canonicals into the domain of social totality and collective identity, revealing that the public's universality (Universality) is always a failed or recursive universality — one that can only include its own exclusion through the mechanism of Repetition (the operation re-applies to itself) and Metonymy (the sliding from element to operation to void that prevents the set from resting).

The Chattering Mind: A Conceptual History of Everyday TalkSamuel McCormick · 2020 (p.91)

the being-nothing that allows the public to surpass its being-all is not just the result of a forming-into-one-of-zero... It also marks a forming-into-one of the operation that allows for the encompassment of everyone and everything

The quote is theoretically loaded because it distinguishes two levels of forming-into-one: the first-order counting of zero (the empty set as member) and the second-order counting of the operation itself — the latter being precisely what prevents the totality from closing. The phrase "forming-into-one of the operation" names a reflexive recursion in which the encompassing move is itself encompassed, installing a void not at the periphery of the public but at the very heart of its counting procedure.