Christian Wolff

German philosopher (1679–1754), the systematizer of post-Leibnizian rationalism into the Schulphilosophie that dominated the eighteenth-century German universities until Kant. Author of two parallel encyclopedic systems — the Vernünftige Gedanken in German (the "deutsche Logik" of 1713 and the "deutsche Metaphysik" of 1719) and a Latin counterpart (Philosophia rationalis sive logica, 1728; Psychologia rationalis, Cosmologia generalis, Theologia naturalis) — Wolff fixed the canonical schema of pre-Kantian Schulmetaphysik: a metaphysica generalis (ontology) plus three metaphysicae speciales (rational psychology, cosmology, natural theology). On this wiki Wolff enters as the negative cardinal of the WdL: Hegel's most-extended polemical foil, named in all three volumes as the figure who extended the more geometrico method to "all possible kinds of knowledge" (GW 12 raw line 2934) and so brought it into discredit. Where Spinoza and Leibniz are engaged for what they got right-but-inadequately, Wolff is engaged for the schematism that displays what is wrong with the synthetic-geometric method itself — culminating in the famous footnote at GW 12 pp. 234–235, where Hegel quotes Wolff's Anfangsgründe der Baukunst and Anfangsgründe der Fortification at full ridiculous length as reductio.

Key Points

The Schullogik and Schulmetaphysik foil. The Vorrede zur zweiten Ausgabe of GW 21 (1831) — see hegel-1832-wdl-sein — diagnoses logic as having been "verdünnt und abgemagert" through "eine lange Tradition" (raw 454). The critical apparatus identifies the post-Wolffian Lehrbücher der Logik as the specific target: "Hegels Kritik richtet sich gegen die Erweiterungen, die seit Christian Wolff in viele Lehrbücher der Logik aufgenommen worden sind" (apparatus at raw 6156).
The more geometrico method extended to philosophy (the cardinal Wolffian sin). GW 11 raw 981 names the target directly: "Spinoza, Wolf und andre haben sich verführen lassen, sie [die mathematische Methode] auch auf die Philosophie anzuwenden, und den äusserlichen Gang der begrifflosen Quantität zum Gange des Begriffes zu machen, was an und für sich widersprechend ist." Wolff is the case in which the synthetic-deductive method's pretension to philosophical adequacy "for sich selbst das Ungeschickte solcher Anwendung gezeigt und um den Credit gebracht" (GW 12 raw 2934).
The iconic reductio: window-width and fortification theorems (GW 12 pp. 234–235, raw lines 2934 + footnote). Hegel quotes verbatim:

"Wolfs Anfangsgründe der Baukunst heißt der achte Lehrsatz: Ein Fenster muß so breit seyn, daß zwey Personen gemächlich neben einander in demselben liegen können. Beweiß. Denn man pflegt sich öfters mit einer anderen Person an das Fenster zu legen, und sich umzusehen." "Desselben Anfangsgründe der Fortification: Der zweyte Lehrsatz. Wenn der Feind in der Nähe campiret, und man vermuthet, er werde durch einen Succurs die Festung zu entsetzen suchen; so muß eine Circumvallations-Linie um die ganze Festung herumgezogen werden." The architectural example is from Wolff's Anfangs-Gründe der Bau-Kunst, 1750, §440; the fortification example from Anfangs-Gründe der Fortification, 1757, §724 (apparatus at GW 12 raw 5197–5199). These are reproduced in extenso as the only place in the WdL where Hegel quotes a contemporary at full ridiculous length as reductio of universal synthetic method.
The classification of concepts as clear / distinct / adequate (klar / deutlich / adäquat). GW 12 raw 832–838 (p. 44 of the critical edition) critiques the Wolffian concept-taxonomy: "so werden die Begriffe vornemlich nach ihrer Klarheit eingetheilt, und zwar in klare und dunkle, deutliche und undeutliche, in adäquate und nichtadäquate." The classification is diagnosed as drawn "aus psychologischen, nicht aus logischen Bestimmungen" — clarity is a subjective Vorstellung-property, not a property of the concept itself; the adäquate Begriff secretly invokes the Idea (the agreement of concept with reality), but the Idea cannot appear at the level of concept-classification.
The Daseyn-side polemic: reality as positive perfection. Hegel's Daseyn-Anmerkung at GW 21 raw ~1801+ ("Die Bestimmtheit ist die Negation als affirmativ gesetzt, ist der Satz des Spinoza: Omnis determinatio est negatio") dissolves the Wolffian doctrine that reality is positive perfection and negation a mere privative lack. See dasein-hegel ("It anchors Hegel's polemic against Wolffian-positive reality-thinking") and wirklichkeit ("Anti-Wolffian. Wirklichkeit is not the existence-following-from-non-contradiction of Wolffian rational metaphysics").
The Wolffian Denkgesetze read as Reflexionsbestimmungen. The Wesen-section reads Identität, Widerspruch, ausgeschlossenes Drittes not as analytic a priori laws of thought (the Wolffian-Kantian Schullogik doctrine) but as graded dialectical moments in essence's self-articulation. See wesen-hegel ("Wolffian-Kantian formal logic (Identität, Widerspruch, ausgeschlossenes Drittes as Denkgesetze) — the Reflexionsbestimmungen are not analytic a priori truths but graded dialectical moments") and identitaet-hegel (the Wolffian "A = A" diagnosed as empty).
The calculus-Anmerkung sand-grain analogy. GW 21 raw 3135 takes a representative Wolffian populariser-move as case-in-point: "Wolf hat sie in seiner Weise, die Sachen populär zu machen, d. h. den Begriff zu verunreinigen und unrichtige sinnliche Vorstellungen an dessen Stelle zu setzen, verständlich zu machen gesucht. Er vergleicht nemlich die Vernachlässigung der unendlichen Differenzen höherer Ordnungen gegen niedrigere, mit dem Verfahren eines Geometers, der bey der Messung der Höhe eines Bergs um nicht weniger genau gewesen sey, wenn der Wind indeß ein Sandkörnchen von der Spitze weggeweht habe." The case displays the Wolffian Manier of replacing concept with sensible image as the structural error.
The metaphysica specialis as content of the objective Logic. GW 21 Einleitung (apparatus at raw 6212, body around p. 49 of the critical edition) names the three Wolffian metaphysicae speciales — Psychologia rationalis, Cosmologia generalis, Theologia naturalis — as the material that the objective Logic of the WdL takes over and resituates within speculative logic. The wiki concept modal-triad-hegel is "anti-Wolffian" precisely in dissolving the rational-cosmological treatment of modality.

Wolff in the Three Volumes of the WdL

GW 21 (1832 Doctrine of Being) — see hegel-1832-wdl-sein

Vorrede zur zweiten Ausgabe (raw 452–470): the diagnosis of logic as having been "verdünnt und abgemagert" through long tradition (raw 454) — the apparatus (raw 6156) identifies the Wolffian-Kiesewetter Schullogik additions as the specific target. The same Vorrede praises German's speculative lexical resources — words with opposite meanings (e.g., aufheben) — as a corrective to the Wolffian-philological flatness.
Einleitung (apparatus at raw 6212, body around p. 49): the three metaphysicae speciales of Wolff's Psychologia / Cosmologia / Theologia naturalis taken as the material of the objective Logic. The schema is preserved but resituated: what Wolff treats as discrete special-metaphysics is for Hegel the content the categorial logic must develop immanently.
Daseyn-Anmerkung (raw 1795–1840): "Omnis determinatio est negatio" — Wolffian positive-reality / privation-of-reality dissolves into Hegel's doctrine that every reality is itself a determinate negation. See dasein-hegel.
Quantum-Anmerkung on infinitesimal calculus (raw 3135–3145): Wolff's mountain-and-sand-grain analogy named as paradigm-case of "den Begriff zu verunreinigen und unrichtige sinnliche Vorstellungen an dessen Stelle zu setzen."
Maß / Indifferenz transition: Hegel's argument that the Sein-section aufhebt itself into Wesen depends on the Wolffian Schulmetaphysik commitment to indifferent substrate-plus-attributes proving inadequate to its own categorial requirements.

GW 11 (1813 Doctrine of Essence) — see hegel-1813-wdl-objektive-logik

Einleitung (raw 981): the cardinal Wolffian sin named directly. "Spinoza, Wolf und andre haben sich verführen lassen, sie [die mathematische Methode] auch auf die Philosophie anzuwenden." The apparatus (raw 6565) adds Wolff alongside Descartes and Spinoza as the more geometrico target.
Reflexionsbestimmungen — Identität (raw 4574–4634): the Wolffian "A = A" diagnosed as the empty form that pretends to be the Satz der Identität but cannot survive its own statement. "die Identität ist also an ihr selbst absolute Nichtidentität" (raw 4598). The classical Wolffian Denkgesetz is the form whose immanent collapse generates the further Reflexionsbestimmungen. See identitaet-hegel.
Reflexionsbestimmungen — Widerspruch (raw 4742+): Wolffian-Kantian formal logic treats Widerspruch as a mere Denkfehler (the law of non-contradiction); Hegel reads it as the productive engine of dialectic. See widerspruch-hegel and reflexionsbestimmungen.
Wesentliches Verhältnis — Seelenvermögen critique: the Wolffian Seelenvermögen (faculty psychology) tradition is engaged as treating faculties as hidden powers — diagnosed as the Kraft/Äußerung schema misapplied. See wesentliches-verhaeltnis ("Faculty psychology (Wolffian Seelenvermögen / Kantian Vermögen) treating faculties as hidden powers").
Wirklichkeit-section (raw 5851–6131): the modal triad. Wolffian rational metaphysics defines necessity from non-contradiction; Hegel's Wirklichkeit is mediated categorially, not formal-logically. See wirklichkeit and modal-triad-hegel.

GW 12 (1816 Doctrine of the Concept) — see hegel-1816-wdl-begriff

Vom Begriff im allgemeinen (p. 44, raw 832–838): the Wolffian concept-taxonomy (klar / deutlich / adäquat) dismantled. "Dieser Gesichtspunkt und die sich auf ihn beziehenden Unterschiede [sind] aus psychologischen, nicht aus logischen Bestimmungen genommen." The "deutliche Begriff" is reanalyzed as merely "der bestimmte Begriff"; the "adäquate Begriff" smuggles in the Idea. The apparatus (raw 4771) traces the taxonomy to Wolff's Vernünftige Gedanken §§8ff and Philosophia rationalis §§80–102.
Allgemein / Besonderes / Einzelnes: the Wolffian / Baumgartian quantitative-extension treatment of universal-particular-individual (the universal as wider-than-particular-wider-than-individual) is the polemical target. See allgemein-besonderes-einzelnes and the motifs cross-tradition note: "Wolff/Baumgarten's quantitative-extension treatment (universal-wider-than-particular-wider-than-individual) as the polemical target."
Erkennen — synthetic method (pp. 234–237, raw 2880–2940): the iconic reductio. Hegel reproduces Wolff's window-theorem (a window must be wide enough for two persons to lie next to one another) and fortification-theorem (Circumvallations-Linie around the besieged fortress) in extenso in a footnote whose visual effect is — uniquely in the WdL — to display the target's ridiculousness on the page. The substance of the surrounding argument: the geometric-synthetic method belongs only to geometry, where the object is "Raum, ein unsinnlich sinnliches"; its extension to philosophy "hat für sich selbst das Ungeschickte solcher Anwendung gezeigt und um den Credit gebracht."
Wahre Widerlegung (p. 16): the post-Kantian dismissal of pre-Kantian dogmatism (Spinoza, Leibniz, Wolff) is refused. Each predecessor must be entered, not attacked from outside. See wahre-widerlegung ("It organizes Hegel's predecessor-engagement. Spinoza, Kant, Leibniz, Wolff, Fichte — each is entered, not attacked from outside").
Erkennen — Wahre Widerlegung in practice: Hegel's Wolff-engagement operationalizes the wahre Widerlegung doctrine — Wolff is "entered" (the geometric method is given its strongest case in geometry, then shown why it cannot extend further) rather than dismissed.

Argumentative Role in the Wiki

Wolff functions on the wiki as:

The cardinal more geometrico-target. Where Spinoza is the philosophically serious deployment of the geometric method (worth confronting at the level of substance-monism), Wolff is the extension to all possible knowledge that displays the method's structural failure. The wiki's Hegel-on-method readings depend on this distinction: Spinoza is "ein Muster" that survived its own misuse; Wolff is the case that brought the method's misuse "um den Credit."
The Schullogik foil for Hegel's recovery of logic. The opening Vorreden of the WdL diagnose logic's Verdünnung through the Wolffian Lehrbücher-tradition — Wolff is what Hegel's Logic is reclaiming logic from. The wiki concept philosophy-of-reflection is the systematic name for what Hegel is escaping; Wolff is the chronologically-near and operationally-paradigm Schulphilosoph instance of it.
The pre-Kantian Schulmetaphysik that Schelling later positions as theological rationalism. friedrich-schelling (1809 Freedom Essay and after) traces the lineage of "the system in which Reason is all" through Descartes-voluntarism → Leibniz-intellectualism → Wolff-theological rationalism → Hegel. Wolff is the necessary middle term in Schelling's positive philosophy historical diagnostic — the Schulmetaphysik Vollendung of Leibniz that prepares the conditions for the Hegelian system Schelling later contests.
The diagnostic of Anfangsgründe-style schematism. The window-and-fortification quotations function on the wiki as a touchstone for what "applying the synthetic-deductive method outside its domain" looks like — the cultural form of the error, not just its formal description. The iconic-quotation function is what allows erkennen-hegel, freie-entlassung, and wahre-widerlegung to refer to "the Wolff reductio" as shorthand for a recognizable category of philosophical mistake.

Connections

is critiqued by Hegel's *Wissenschaft der Logik*, Doctrine of Essence regarding the more geometrico extension of mathematical method to philosophy (GW 11 raw 981) and the Wolffian-Kantian Denkgesetze read as formal-logical truths rather than Reflexionsbestimmungen
is critiqued by Hegel's *Wissenschaft der Logik*, Doctrine of the Concept regarding the klar / deutlich / adäquat concept-taxonomy (GW 12 p. 44) and the universal synthetic method whose window-and-fortification reductio appears at pp. 234–235
is critiqued by Hegel's *Wissenschaft der Logik*, Doctrine of Being regarding the post-Wolffian Schullogik-tradition that "verdünnt und abgemagert" logic (Vorrede 1831), the Wolffian positive-reality / privation-of-reality doctrine (Daseyn-Anmerkung), and the populariser-method that "den Begriff zu verunreinigen" (Quantum-Anmerkung on calculus, raw 3135)
extends Leibniz's rationalism into the Schulmetaphysik schema of metaphysica generalis + three metaphysicae speciales — which Hegel's Logic takes over as the content the speculative Logic must develop immanently rather than as discrete special-disciplines
is the Schulmetaphysik foil engaged by Kant's critical-philosophy — Kant's Verunstaltung-diagnosis of post-Wolffian logic-textbook expansions (B VIII of the Kritik der reinen Vernunft) is the immediate predecessor of Hegel's Verdünnung-diagnosis
is the third middle term in Schelling's 1809+ historical lineage (Descartes-voluntarism → Leibniz-intellectualism → Wolff-theological-rationalism → Hegelian "system in which Reason is all"); see positive-philosophy
contrasts with Spinoza (the philosophically serious more geometrico deployment) as the Schulmetaphysik extension that brought the method "um den Credit"
anchors the cultural diagnostic of Hegel's *Erkennen*-chapter's critique of universal synthetic method, via the Anfangsgründe window-and-fortification quotations
is named by freie-entlassung as the "Wolffian deductive system: Nature is deduced from logical principles" that the absolute Idea's free release into Nature is not
is named by wahre-widerlegung as one of the four predecessors Hegel "enters" (Spinoza, Leibniz, Wolff, Fichte) rather than dismisses Kantian-fashion

Open Questions

Does Hegel's Wolff-critique track the historical Wolff or only the eighteenth-century Wolffian Schule? Hegel's Logic-Vorlesungen (Werke Bd 15, pp. 478, 481, 665) treat the Wolffian Schule as roughly coextensive with Wolff's own program; later Wolff-scholarship (Ecole, Mainzer) has reopened questions about Wolff's own modal logic and his treatment of contingency that Hegel's reading flattens.
How does the Wolff window-and-fortification reductio function rhetorically vs. argumentatively? The verbatim quotation at GW 12 pp. 234–235 has an evidential weight beyond the proposition it supports — the cultural display of Wolffianism. Is this a philosophically legitimate mode of refutation, given Hegel's own wahre Widerlegung doctrine (which requires entering the opponent's strength)? Or is the Anfangsgründe-quotation a moment where Hegel violates his own principle?
Wolff's metaphysica specialis and Hegel's Realphilosophie. GW 21 raw 6212 (apparatus) flags the three metaphysicae speciales (Psychologia rationalis, Cosmologia generalis, Theologia naturalis) as content the objective Logic resituates. The detailed mapping — what survives in the Realphilosophie (the philosophies of Nature and Spirit) and what is dissolved entirely — is not worked out in the WdL itself and would require an Encyclopedia-side follow-up.
The relation between Wolff's Schulmetaphysik and Schelling's positive philosophy. Schelling's later treatment of the Cartesian-Leibnizian-Wolffian lineage as the necessary genealogy of the "system in which Reason is all" places Wolff at a structurally cardinal position not visible from the Hegelian side. See positive-philosophy.

Sources

hegel-1832-wdl-sein — GW 21: Vorrede 1831 Verdünnung-diagnosis (raw 452–470; apparatus at raw 6156 identifies the post-Wolffian Lehrbücher as target); Einleitung metaphysica specialis schema (apparatus at raw 6212); Daseyn-Anmerkung omnis determinatio est negatio (raw ~1801) as anti-Wolffian positive-reality polemic; Quantum-Anmerkung Wolff sand-grain-mountain populariser-analogy (raw 3135).
hegel-1813-wdl-objektive-logik — GW 11: Einleitung raw 981 ("Spinoza, Wolf und andre" misapplied geometric method); Reflexionsbestimmungen Identität chapter (raw 4574–4634) on the Wolffian "A = A"; Wesentliches Verhältnis on Wolffian Seelenvermögen / faculty-psychology; Wirklichkeit-section (raw 5851–6131) anti-Wolffian on necessity-from-non-contradiction.
hegel-1816-wdl-begriff — GW 12: Vom Begriff im allgemeinen concept-taxonomy critique (p. 44, raw 832–838; apparatus at raw 4771); Allgemein/Besonderes/Einzelnes engagement with Wolffian quantitative-extension treatment; Erkennen-chapter reductio of universal synthetic method via verbatim Anfangsgründe der Baukunst (1750, §440) + Anfangsgründe der Fortification (1757, §724) at pp. 234–235 (raw 2880–2940; apparatus at raw 5197–5199); Wahre Widerlegung (p. 16) on the discipline of entering Wolff rather than dismissing him.
schelling-1809-freedom-essay — Wolff at pp. 111 and 141n15 of the Love-Schmidt translation: Wolff named in Jacobi's Pantheismus-letter as the third in the Leibniz-Spinoza-Wolff school-tradition; the basis for Schelling's later positioning of Wolff as the "theological rationalism" middle term in the Descartes → Leibniz → Wolff → Hegel lineage.