Aristotle

Ancient Greek philosopher (384–322 BCE), student of Plato (no wiki page yet), founder of the Lyceum, author of the Organon (the syllogistic logic), Metaphysics, Physics, De anima, Nicomachean Ethics, Politics, Poetics, and the biological works. On the wiki, Aristotle enters as (i) the inheritor whose syllogistic Hegel both honors and supersedes in the Doctrine of the Concept ("ein unendliches Verdienst" but "eine naturhistorische Beschreibung", GW 12 pp. 35–36, 109), (ii) the categorial tradition Hegel's WdL aims to renovate (the Vorrede of GW 21 names Aristotle as the figure whose categories first received thematic treatment), (iii) the Aristoteles-im-73ten-Jahre test case (GW 12 p. 63) for the distinction between Satz and Urtheil, and (iv) Heidegger's pre-Brentano anchor: the 1862 Brentano dissertation (Von der mannigfachen Bedeutung des Seienden nach Aristoteles) is the erste Anstoß of the Seinsfrage (per *Mein Weg in die Phänomenologie* 1963).

Key Points

The syllogistic as "ein unendliches Verdienst" (GW 12 p. 35): Hegel praises Aristotle for having "diese Beschreibung zuerst unternommen" — first undertaking the systematic description of the forms of thinking. The criticism follows immediately: "es ist nöthig, daß weiter gegangen … werde" — Aristotle's syllogistic is descriptive, "eine naturhistorische Beschreibung der Erscheinungen des Denkens" (p. 109), not genetic. The Hegelian syllogism is the truth of the Aristotelian, not its replacement.
The categorial tradition. GW 21 Vorrede 1831 and the Einleitung locate Aristotle as the figure who first thematized the categories for themselves. Logic "hat sich seit Aristoteles … nicht verändert" — and this 2000-year stasis is, per Hegel, a symptom of the inherited Logic's structural inadequacy, not its perfection.
The Aristoteles-im-73ten-Jahre test case (GW 12 p. 63): "Aristoteles ist im 73ten Jahre seines Alters, im 4ten Jahre der 115. Olympiade gestorben" — a Satz, not an Urtheil. Subject and predicate are both singular; there is no original Theilung of the Concept. Hegel uses this as the cardinal example for the Satz vs. Urtheil distinction. See urtheil-hegel.
Substance / accident / cause tradition. The Wesen-section's Substanz–Causalität–Wechselwirkung progression (GW 11 raw 6181–6397) is in continuous dialogue with the Metaphysics and Physics on substance and the four causes. Hegel's Wechselwirkung is the dissolution of the Aristotelian categorial table.
Aristotle on teleology (De anima, Physics II): Hegel's Teleology-section (GW 12 pp. 154–172) renovates innere Zweckmäßigkeit against Kant's regulative restriction. Aristotle's entelechy and immanent telos anticipate Hegel's logical teleology — but only when freed from naturalist reading.
The Brentano-Anstoß (per heidegger-1963-mein-weg-in-die-phaenomenologie): Heidegger's first encounter with the Seinsfrage was via Franz Brentano's 1862 dissertation Von der mannigfachen Bedeutung des Seienden nach Aristoteles, gifted to him in 1907 by Conrad Gröber. The "mannigfache Bedeutung des Seienden" — Aristotle's recognition that being is said in many ways (pollachōs legetai to on, Metaphysics Γ 2, IV 2) — is the cardinal pre-Heideggerian anchor of the Seinsfrage. See heidegger-1963-mein-weg-in-die-phaenomenologie §"Die Brentano-Aristoteles-Begegnung."

Aristotle in the Three Volumes of the WdL

GW 21 (Doctrine of Being)

Vorrede 1831 (raw 452–520): Aristotle named as the figure whose Logic has been transmitted "verdünnt und abgemagert" through the Wolffian tradition. The categorial tradition is Aristotelian in origin; its dessication is post-Aristotelian.
Einleitung (raw 794–812): "Kant preißt sonst die Logik … darüber glücklich, daß ihr … so frühe Vollendung zu Theil geworden sey" — Kant's praise of Logic's early completion is the bound Hegel must break. The "early completion" is Aristotelian.

GW 11 (Doctrine of Essence)

Kategorie etymology (raw 4564): Hegel notes the Categoriae heritage; Kategorie etymologically traces to the courtroom-accusation register.
The Widerspruch chapter (raw 4798–4920): Hegel's most direct break with Aristotle. The Metaphysics Γ Principle of Non-Contradiction is implicitly rejected: "Alle Dinge sind an sich selbst widersprechend" (raw 4885). The Zeno-paradoxes are re-read as correct — motion is the contradictory "is here / not here," and the conclusion is not that motion is illusory but that motion is contradiction (raw 4899–4912). See widerspruch-hegel.
The Substanz-Causalität-Wechselwirkung progression (raw 6181–6397): in continuous dialogue with Aristotle on substance and cause. The progression dissolves the Metaphysics's categorial table.

GW 12 (Doctrine of the Concept)

The syllogistic Anmerkungen (pp. 35–36, 90–125): the most extended Aristotle-engagement in the WdL. Aristotle's "unendliches Verdienst" but the criticism that his account is naturhistorisch — descriptive empirical taxonomy rather than dialectical genesis.
The 73-year-old Aristotle Satz/Urtheil example (p. 63): the cardinal test case for the Satz vs. Urtheil distinction. The proposition about Aristotle's death is grammatically a judgment but argumentatively a Satz — both subject and predicate are singular, no original Theilung of the Concept.
Teleology (pp. 154–172): renovates Aristotelian entelechy / immanent telos against Kant's regulative restriction; Hegel's List der Vernunft (pp. 172–173) is the logical-categorial form of Aristotelian teleology.
The De anima scheme (implicit at GW 12 p. 192): the Life-syllogism (Sensibility / Irritability / Reproduction) echoes the De anima's nutritive / perceptive / rational soul progression — but transposed into the logical register.

Aristotle in Heidegger's Self-Narration

The 1963 *Mein Weg in die Phänomenologie* gives Aristotle a cardinal pre-Heideggerian role in the development of the Seinsfrage:

The Brentano gift (1907): Conrad Gröber gives the 18-year-old Heidegger Franz Brentano's Von der mannigfachen Bedeutung des Seienden nach Aristoteles (1862). "Die zögernden, sich ausweglos verfangenden Versuche, in die Phänomenologie einzudringen, wurden durch die fortdauernde, wenngleich kaum hilfreiche Beschäftigung mit den Schriften Brentanos genährt."
The mannigfache Bedeutung des Seienden: Aristotle's pollachōs legetai to on (being is said in many ways) is the Frage that the Seinsfrage extends. Heidegger's question becomes: if being is said in many ways, what is the unitary sense (einfache Bedeutung) that grounds the manifold?
The 1922 Aristoteles-Anzeige: Heidegger's Anzeige der hermeneutischen Situation (the Natorp-Bericht) is structurally a reading of Aristotle from the Phenomenology-of-religious-life standpoint. The published Sein und Zeit (1927) carries the Aristotle-engagement implicitly throughout (especially in the Zeit-analysis and the Logos-analysis).
See franz-brentano for the Brentano-anchor and the Aristotle-courses cluster (not yet on the wiki).

Argumentative Role in the Wiki

Aristotle functions on the wiki as:

The categorial tradition Hegel renovates. Logic's 2000-year stasis is Aristotelian in pedigree; Hegel's WdL is the first systematic break.
The descriptive-vs-genetic axis. Aristotle's syllogistic is descriptive empirical taxonomy on Hegel's reading; the Hegelian syllogism is genetic dialectical movement. The criticism organizes Hegel's relation to formal logic throughout.
The PNC counter-pole to Hegelian Widerspruch. Hegel's productive-contradiction doctrine is the break with the Metaphysics Γ Principle of Non-Contradiction. The Zeno re-reading (motion is contradiction) inverts the Aristotelian conclusion.
The pre-Heideggerian anchor of the Seinsfrage. Heidegger's first contact with the question of being is Brentano on Aristotle (1907). The mannigfache Bedeutung des Seienden is the Frage that the Seinsfrage extends.
The teleology Hegel renovates against Kant. Innere Zweckmäßigkeit / immanent telos / entelechy — Aristotle anticipates the categorial teleology Hegel restores against Kantian regulative restriction.

Connections

is renovated by Hegel's Doctrine of the Concept — the syllogistic is "ein unendliches Verdienst" but only "eine naturhistorische Beschreibung"
bequeaths the PNC that Hegel's Widerspruch inverts — Metaphysics Γ vs. "Alle Dinge sind an sich selbst widersprechend"
anticipates Hegel's logical teleology via innere Zweckmäßigkeit / immanent telos
is mediated to Heidegger by Brentano's 1862 dissertation — the mannigfache Bedeutung des Seienden as the pre-Heideggerian Frage
is the Brentano-Anstoß of the Seinsfrage — see heidegger-1963-mein-weg-in-die-phaenomenologie §"Die Brentano-Aristoteles-Begegnung"
bequeaths the categorial tradition to Kant's table of categories and to Hegel's WdL — both of which work within and then beyond the Aristotelian heritage
is the structural pole opposed to Plato in late-Heidegger's diagnostic: Plato as the beginning of metaphysics, Aristotle as the first categorial systematization of metaphysics

Open Questions

What is the precise relation between Aristotelian entelechy and Hegelian Idee / Begriff? Hegel's Life-chapter (GW 12 pp. 179–198) and the Teleology-section converge with the De anima tradition, but Hegel's claim that Leben is a logical category (not biological) marks a sharp departure.
Is the 1922 Natorp-Bericht engagement with Aristotle accurately captured by the 1963 self-narration? The mature Heidegger may rewrite his Aristotle-encounter in retrospective light. Scholarship on the Aristotle-courses cluster (1921–1924) is required to test the 1963 narration.
How does the WdL Aristotle-engagement relate to Hegel's Lectures on the History of Philosophy? The published lectures (Glockner edition) give other Aristotle-readings; the continuity with the WdL Anmerkungen is a live scholarly question.
Does Hegel's Aristotle-reception accurately track the Metaphysics Γ PNC? Contemporary Aristotle-scholarship (Łukasiewicz, Priest) has reopened the question of whether the Metaphysics Γ doctrine really excludes the Hegelian "productive contradiction" reading.

Sources

hegel-1816-wdl-begriff — GW 12 pp. 35–36, 109 (the syllogistic Anmerkungen); p. 63 (Aristoteles-im-73ten-Jahre Satz/Urtheil example); pp. 154–172 (teleology, renovating Aristotelian entelechy); p. 192 (Life-syllogism echoing De anima).
hegel-1813-wdl-objektive-logik — GW 11 raw 4564 (Kategorie etymology); raw 4798–4920 (Widerspruch chapter, the most direct break with Aristotelian PNC); raw 6181–6397 (Substanz–Causalität–Wechselwirkung in continuous dialogue with the Metaphysics).
hegel-1832-wdl-sein — GW 21 Vorrede 1831 (Aristotle as inheritor of Logic's 2000-year stasis); Einleitung on Kant's praise of Logic's "early completion."
heidegger-1927-sein-und-zeit — Aristotle-engagement implicit throughout; explicit in the Zeit-analysis and the Logos-analysis.
heidegger-1963-mein-weg-in-die-phaenomenologie — the Brentano-gift narration (1907); Aristotle's mannigfache Bedeutung des Seienden as the pre-Heideggerian anchor of the Seinsfrage.