Gottfried Wilhelm Leibniz

German philosopher and mathematician (1646–1716), author of the Monadology (1714), the Discours de métaphysique (1686), the Theodicy (1710), co-inventor (with Newton) of the differential calculus, formulator of the principium rationis sufficientis (PSR) and the principle of indiscernibles. On the wiki, Leibniz enters as a four-fold WdL-interlocutor: (i) as the Monad-doctrine engaged in the Fürsichseyn-Anmerkung (GW 21 raw ~2440–2842), (ii) as the PSR taken at deeper sense than usually granted but still inadequate (GW 11 raw 4958), (iii) as the Indiscernibles-doctrine engaged in the Verschiedenheit chapter (GW 11 raw 4708), and (iv) as the calculus-inventor whose differential is read as the qualitative moment within Quantität (GW 21 raw ~3500–4400; GW 12 p. 215).

Key Points

  • The Monad as corrective to Spinoza, but inadequate. GW 11 raw 5977–5989: the Leibnizian monad has Reflexion-in-sich that Spinozistic substance lacks — and so represents a partial corrective to substance-monism — but its limitations are prästabilirt by another being, not self-generated. GW 12 pp. 141–142: the monad is "eine mangelhafte Reflexion"; it is unfree, externally determined, has no real activity on other monads.
  • The PSR critiqued. GW 11 raw 4958–4960 (Anmerkung to Grund): "Alles hat seinen zureichenden Grund" — Hegel takes this at deeper sense than usually granted, but the Satz vom Grunde expresses only that being is not first, that what is is gesetzt. Grund is the Reflexionsbestimmung that immediately reveals itself as aufgehoben. See grund-hegel.
  • The principle of indiscernibles (GW 11 raw 4708): "Es gibt nicht zwey Dinge, die einander vollkommen gleich sind" — taken as the principle that Verschiedenheit is primitive, against Hegel's reading of Verschiedenheit as graded into Gegensatz and Widerspruch.
  • The differential calculus, in Hegel's reading, is correctly grasped by Leibniz (in some respects) as a qualitative determinacy in vanishing — but Leibniz's metaphysical justification of unendliche Differenzen is called "unzulänglich, eben so völlig begrifflos als unmathematisch" (GW 12 p. 215). The differential is not a paradoxical "very small number" but the qualitative moment within Quantität itself.
  • Natura non facit saltum — Leibniz's slogan attacked in the Knotenlinie-Anmerkung (GW 21 raw 5346): nature does leap; the water-freezing example is one of Hegel's most-cited illustrations. See knotenlinie.
  • Pre-established harmony: the framing Hegel rejects as inadequate to genuine activity; the monad is unfree precisely because its limitations and harmony are externally posited.

Leibniz in the Three Volumes of the WdL

GW 21 (Doctrine of Being)

  • Fürsichseyn / Monad-Anmerkung (raw ~2440–2842): the Leibnizian monad pluralism is engaged as a contrast to Hegel's Eins ist Viele Eins doctrine. Where Leibniz posits each monad's qualitative uniqueness, Hegel's pure Eins is qualitatively identical with every other Eins — they distinguish only by mutual exclusion (Repulsion), which because of their identity is also self-attraction (Attraktion).
  • Differential calculus Anmerkung (raw ~3500–4400): the longest single Anmerkung in the book engages the Newton-Leibniz controversy on the calculus. Leibniz's metaphysical justification of unendliche Differenzen is criticized; Hegel's positive reading is that the differential is the qualitative moment within Quantität.
  • Knotenlinie-Anmerkung (raw 5346): "Es gibt keinen Sprung in der Natur, wird gesagt" — Leibniz's natura non facit saltum attacked. Nature does leap; the categorial jump is what Maß-relations dialectically generate. See knotenlinie.

GW 11 (Doctrine of Essence)

  • Verschiedenheit chapter (raw 4708): the principle of indiscernibles. "Es gibt nicht zwey Dinge, die einander vollkommen gleich sind."
  • Grund chapter Anmerkung (raw 4958–4960): the Satz vom Grunde / PSR critiqued.
  • Modus-Anmerkung (raw 5977–5989): the monad as corrective to substance-monism but itself inadequate (limitations prästabilirt).
  • Schein-section (raw 4356): Leibniz's monad-Vorstellungen-as-bubbles named with Kant and Fichte as forms of Idealismus that fail to reach Schein properly.

GW 12 (Doctrine of the Concept)

  • Monad as mangelhafte Reflexion (pp. 141–142): explicit critique of the monad as unfree, externally determined, with no real activity on other monads.
  • The differential calculus (p. 215): "unzulänglich, eben so völlig begrifflos als unmathematisch" — Leibniz's metaphysical justification rejected, though the calculus itself is preserved as a qualitative-categorial development.

Argumentative Role in the Wiki

Leibniz functions on the wiki as:

  1. The pluralist corrective to Spinozistic monism. The monad has Reflexion-in-sich that substance lacks — and so partial credit, but ultimate inadequacy because the monad's harmony is external.
  2. The PSR-tradition Hegel dissolves. Alles hat seinen zureichenden Grund — taken at deeper sense, but Grund is the Reflexionsbestimmung that marks itself as aufgehoben. See grund-hegel.
  3. The natura non facit saltum counter-pole to Hegelian Knotenlinie. Nature does leap; the categorial jump at nodes of measure is what Hegel's Maß-doctrine articulates.
  4. The differential-calculus interlocutor. With Newton, Leibniz is the inventor whose calculus Hegel reads philosophically — preserving the qualitative-categorial reading against the metaphysical-infinitesimal one.

Connections

Open Questions

  • Does Hegel's monad-critique accurately track Leibniz's own positions? Contemporary Leibniz-scholarship has reopened many of the questions Hegel treats as settled (the freedom of the monad, the externality of pre-established harmony).
  • What is the relation between Hegel's calculus-reading and the 19th-century Weierstrass-Cantor rigorization? Hegel's qualitative-categorial reading and the modern epsilon-delta rigorization both exit the metaphysical-infinitesimal framing, but in opposed directions.

Sources

  • hegel-1813-wdl-objektive-logik — GW 11: indiscernibles (raw 4708); PSR critique (raw 4958–4960); Schein-section listing of Leibniz with Kant/Fichte (raw 4356); Modus-Anmerkung on monad as corrective-but-inadequate (raw 5977–5989).
  • hegel-1816-wdl-begriff — GW 12 pp. 141–142 (monad as mangelhafte Reflexion); p. 215 (differential calculus metaphysical justification rejected).
  • hegel-1832-wdl-sein — GW 21 Fürsichseyn-Anmerkung on monad pluralism (raw ~2440–2842); differential calculus Anmerkungen (raw ~3500–4400); Knotenlinie-Anmerkung on natura non facit saltum (raw 5346).