Erkennen (Cognition, Hegel)

Erkennen — Cognition — is the second shape of die Idee in the Doctrine of the Concept (GW 12 pp. 192–243), positioned between Life and the absolute Idea. Cognition is the Idea split into the theoretical (subjective Idea seeking the Object) and the practical (subjective Idea remaking the Object). Each is one-sided; their synthesis is the absolute Idea.

The theoretical Idea complements the practical's deficiency that it takes the good as merely subjective and to-be-realized. The practical Idea complements the theoretical's deficiency that it takes the world as given. The unity of theoretical and practical is the absolute Idea — Hegel's both-appropriation-and-supersession of Kant's primacy of practical reason.

Within the theoretical-Idea sub-section, Hegel develops the distinction between analytic and synthetic cognition (pp. 209–226), with detailed analyses of definition, division, theorem-and-proof in geometry, and the celebrated objection to Kant's 5+7=12 as synthetic a priori (p. 213).

Key Points

Erkennen is the Idea split. Theoretical (subjective Idea seeking Object) + Practical (subjective Idea remaking Object).
Each is one-sided. Theoretical takes the world as given; practical takes the good as merely subjective.
Their unity is the absolute Idea. The synthesis dissolves both one-sidednesses.
Hegel's Kant-engagement on practical primacy. Hegel both embraces Kant's primacy of practical reason and dialectically supersedes it: the good as "absolute postulate" remains a Sollen unless its presupposition (the world's recalcitrance) is also dissolved as already gesetzte Voraussetzung.
Analytic vs. synthetic cognition. The standard distinction is unstable and dialectically self-superseding.
Geometry as paradigm of synthetic method, reaching its limits at the irrational / incommensurable.
Arithmetic as paradigmatically analytic. Cardinal Anti-Kantian objection at p. 213: "5 und 7 und 12 sind durchaus ganz derselbe Inhalt … es ist ein blosses Fortsetzen … das es auch eine Maschine verrichten kann."
Against Wolff's universal synthetic geometric method. The famously absurd Wolffian theorems (window-width, fortification-lines) quoted in the footnote at pp. 234–235 as the reductio.
Against Jacobi's critique of demonstration. Jacobi (p. 235) showed that all Beweisen binds itself to finite necessity; Hegel endorses the critique against the synthetic method but rejects the conclusion (skepticism / Glauben).
The good as Sollen. GW 12 p. 240: "Das Gute bleibt so ein Sollen; es ist an und für sich, aber das Seyn als die letzte, abstracte Unmittelbarkeit, bleibt gegen dasselbe auch als ein Nichtseyn bestimmt."
Cognition is Trieb der Wahrheit. The theoretical Idea is drive of truth; the practical is drive of the Good; the absolute Idea is drive of self-recognition.

What the Concept Does

It articulates Cognition as the Idea split. Theoretical + Practical, each one-sided.
It supplies the synthesis through the absolute Idea. The one-sidednesses dissolve into self-knowing closure.
It refutes Kant on arithmetic as synthetic a priori. 5+7=12 is blosses Fortsetzen, mechanical, analytic.
It refutes Wolff's universal synthetic-deductive method. The window-width / fortification-lines footnote is the reductio.
It engages Jacobi's critique of demonstration — endorsed against the synthetic method, conclusion rejected.
It both embraces and supersedes Kant's primacy of practical reason. The Good as Sollen requires dissolution of its Voraussetzung — only the absolute Idea delivers this.
It anchors the Trieb-doctrine. Cognition is drive of truth; the absolute Idea is drive of self-recognition.

What It Rejects

Kant's synthetic a priori status for arithmetic — 5+7=12 is analytic, mechanical.
Wolff's universal synthetic-deductive method — the window-width reductio.
Jacobi's skeptical / Glauben conclusion from the critique of demonstration — endorsed critique, rejected conclusion.
Kant's restriction of the unconditioned to a postulate of practical reason — the absolute Idea delivers what the postulate only demands.
The independent-faculties picture of theoretical and practical — they are dialectical moments of the Idea, not independent faculties.
Mendelssohn's argument for soul-immortality (qualitative simplicity) and Kant's refutation (quantitative intensity) — both presuppose categories Hegel has shown inadequate.

Connections

is the second shape of die Idee — between Life and the absolute Idea
splits into Theoretical and Practical Idea
transitions into the absolute Idea — synthesis dissolves the one-sidedness
contains the 5+7=12 critique of Kant on arithmetic as synthetic a priori (p. 213)
contains the Wolff window-width / fortification-lines footnote as reductio of universal synthetic method (pp. 234–235)
engages and supersedes Kant's primacy of practical reason
engages Jacobi's critique of demonstration (p. 235)
is structured by U / P / I — Theoretical (U) / Practical (P) / absolute Idea (I)
is Trieb der Wahrheit* — the drive that culminates in the absolute Idea's self-recognition

Open Questions

Does Hegel's 5+7=12 is mechanical-analytic objection actually engage Kant's claim? Kant's claim is that arithmetic identities require construction in intuition, not that they are non-analytic in the strict logical sense; Hegel's objection may speak past Kant.
Does the WdL synthesis of theoretical and practical Idea genuinely supersede Kant's primacy of practical reason or does it rhetorically claim what the dialectic cannot deliver?
What is the relation between WdL Erkennen and the Encyclopedia's philosophy of subjective spirit? The Encyclopedia develops the Realphilosophie of cognition; the continuity with the WdL Erkennen-doctrine is a live scholarly question.

Sources

hegel-1816-wdl-begriff — primary locus: GW 12 pp. 192–243. Theoretical / Practical split throughout. Analytic-vs-synthetic discussion pp. 200–226. 5+7=12 objection at p. 213. Wolff window-width / fortification-lines footnote at pp. 234–235. Jacobi-engagement at p. 235. Good-as-Sollen at p. 240. Synthesis with absolute Idea at pp. 241–243.