Regressus in Indefinitum

The regressus in indefinitum is Kant's technical resolution of the first two cosmological antinomies, redeployed in kant-immanuel-critique-of-pure-reason as a structural principle governing how reason relates to the sensory world as a series of conditions. When reason demands an unconditioned ground for the world—asking whether it is finite or infinite in space and time—it generates irresolvable contradiction (antinomy) because it treats the world of sense as if it were a complete, given totality. Kant dissolves this deadlock by converting the constitutive (dialectical) use of the cosmological idea into a regulative one: the empirical regress through the series of conditions is never a traversal of a pre-given whole. Instead, the world-series is only ever constituted through the regress itself, meaning it can always be extended further without limit — but also without ever being "complete." This is the indefinitum: not an actual infinite that is given all at once (the in infinitum that would presuppose a complete totality), but an open, unfinishable process whose horizon perpetually recedes.

The distinction between in infinitum and in indefinitum is therefore a distinction between two modes of the unlimited: one that posits a traversable, determinate infinite whole, and one that refuses totalization while also refusing to posit a determinate finite limit. The world of sense "has no absolute quantity" — it neither closes into a finite boundary nor unfolds as an already-constituted infinity. The regress is the only form of access to the series of conditions, and that regress is structurally endless without being structurally completed.

Within kant-immanuel-critique-of-pure-reason, the regressus in indefinitum is the pivot on which the antinomy chapter turns: it marks the point where Kant transforms a dialectical illusion of reason into a legitimate regulative principle. Its conceptual neighbours in the cross-referenced corpus are significant. It is structurally cognate with the canonical concept of Infinite — specifically with what the corpus calls "bad" (spurious) infinity (die schlechte Unendlichkeit): a series that goes on without reaching a terminating point, never bending back on itself into "true" self-limiting infinity. The regressus in indefinitum is, in Hegelian terms, the paradigm case of bad infinity — and Lacan's commentators treat bad infinity as the structure of desire's demand (always one more object, never satisfaction) and of capitalism's growth imperative. In this sense, the regressus in indefinitum names the very structural form that the psychoanalytic intervention is designed to interrupt.

The concept also resonates with Not-all and Lack. As noted in the Not-all synthesis, Copjec and Žižek explicitly map the mathematical antinomies onto Lacan's feminine formula: the not-all marks a series that can always be extended, whose internal limit is what Kant calls an "indefinite judgment." The regressus in indefinitum is precisely the temporal-serial analogue of this logical structure — a series without a grounding exception that could close it into a whole. From the angle of Lack, the absence of an "absolute quantity" for the world of sense is formally analogous to the Lacanian principle that "nothing in the real is missing" — it is only the symbolic demand for a totality that produces the experience of an irresolvable gap. The regressus in indefinitum could thus be read as the Kantian pre-figuration of the structural lack in the Other: the series of conditions has no final term (no Other of the Other) that would close it, just as S(Ⱥ) marks the impossibility of a completed symbolic order. Its distance from Das Ding and Real is equally telling: the Thing and the Real are precisely what the indefinite regress can never reach — they mark the non-dialectizable remainder that the regulative use of reason perpetually defers.

Critique of Pure ReasonImmanuel Kant · 1781 (page unknown)

This is equivalent to saying: 'The world of sense has no absolute quantity, but the empirical regress... proceeds in indefinitum'

The phrase "no absolute quantity" is theoretically loaded because it refuses both the finite and the actually-infinite as descriptions of the world-series, while "proceeds in indefinitum" names the specifically regulative, never-totalizing form of the series — a process that is structurally endless without presupposing a given whole, which is precisely the formal structure that Lacanian commentators identify with spurious infinity, the not-all, and the constitutive lack in the Other.