Arthur Schopenhauer

German post-Kantian philosopher (1788–1860) whose system — laid out in Die Welt als Wille und Vorstellung (1818, expanded 1844) — articulates a metaphysics of the Will (the thing-in-itself underlying all phenomena), an ethics of compassion (Mitleid, grounded in the collapse of the principium individuationis), and an aesthetics of art as temporary will-negation. Currently appears in the wiki as the polemical target of Simmel's love-fragment: Schopenhauer's explanation of charity and sacrifice via the metaphysical unity of being is named by Simmel as "a form of rationalism" that misses "the miracle of love" — the fact that love does not dissolve the being-for-itself of I and Thou but presupposes it as the condition under which love operates (Oakes p. 156).

Key Points

Lifespan: 1788 (Danzig) – 1860 (Frankfurt am Main). Major works late: published Welt als Wille at 30, mostly ignored until the 1850s; widespread influence only late in his life and posthumously.
Cardinal works: Über die vierfache Wurzel des Satzes vom zureichenden Grunde (1813 dissertation); Die Welt als Wille und Vorstellung (1818, expanded 1844); Über den Willen in der Natur (1836); Die beiden Grundprobleme der Ethik (1841, contains Über die Grundlage der Moral = On the Basis of Morality); Parerga und Paralipomena (1851).
Cardinal doctrines: the world as Will (thing-in-itself) and Representation (phenomenon); the principium individuationis (space-time as the principle of individuation, behind which lies the undifferentiated Will); compassion as foundation of ethics (grounded in principium-collapse); aesthetic experience as temporary will-negation; Vierfache Wurzel of the principle of sufficient reason.
Position in Simmel's love-fragment (Oakes p. 156): polemical target. Schopenhauer's metaphysical-unity-of-being grounding of compassion-and-sacrifice is rationalism — misses the miracle of love.
The 1844 supplement "Metaphysik der Geschlechtsliebe" (Metaphysics of Sexual Love) is Schopenhauer's reading of love as the species-genius operating through individuals — structurally close to what Simmel calls type-love but with metaphysical (species-Will) grounding.
Influence: Wagner (1854–60s music-philosophy); Nietzsche (initially disciple, eventually critic); Freud (indirectly, via the principium); Wittgenstein (early); Mahler, Mann, Borges; the Frankfurt School (Adorno, Horkheimer); the broader pessimist tradition (Cioran, Mainländer).
Position in the wiki: a major polemical target for Simmel's love-fragment, but otherwise not yet substantially engaged in the wiki. Future ingests of pessimist tradition, Nietzsche-corpus, Freud, and aesthetic-philosophy material would expand the engagement.

Details

Schopenhauer's Place in Simmel's Love-Fragment

The polemical anchor (Oakes p. 156):

"Nevertheless, the dynamic at stake here is different from the metaphysical unity of all being as such, from which Schopenhauer, for example, derives charity and sacrifice. This is precisely the miracle of love. It does not nullify the being-for-itself of either the I or the Thou. On the contrary, it makes this being-for-itself into a condition under which that nullification of distance and the egoistic reversion of the existential will to itself follow. This is a completely irrational phenomenon that resists the categories of logic, which in other respects hold valid. Schopenhauer's proposed explanation of this nullification of distance by means of the transcendent unity of being is a form of rationalism. His failure to comprehend the nature of love, which will be discussed below, is above all exhibited here."

The structure of Simmel's critique:

Schopenhauer derives compassion from the metaphysical unity of being. The Schopenhauerian story: in compassion, the principium individuationis (space-time differentiation) collapses for the compassionate subject; they recognize the other's suffering as one's own because, behind individuation, all is one Will. (See On the Basis of Morality, §§16–22; World as Will, I §66–68.)
Simmel calls this "rationalism". The charge is structurally precise: Schopenhauer explains the affective phenomenon (compassion / love) by deducing it from a metaphysical premise (unity of being). The phenomenon is reduced to its metaphysical ground.
The "miracle of love" is not unity-of-being: love does not nullify the being-for-itself of I and Thou; it presupposes it as the condition under which the nullification-of-distance can follow.
Love is therefore irrational in a specific sense: not "illogical" but "resistant to the categories of logic" — including the metaphysical-deductive logic Schopenhauer applies.

The Simmelian alternative: love operates between preserved I and preserved Thou, in a relation that crosses the distance without abolishing it. This is one of the cardinal anti-fusion accounts of love in the twentieth-century tradition — anticipating, in some respects, Levinas's preservation-of-alterity ethics and the later phenomenological-intersubjectivity tradition.

Metaphysics of Sexual Love (1844)

Schopenhauer's "Metaphysik der Geschlechtsliebe" is the supplement-chapter (Ch. 44 of World as Will, Volume II, 1844) treating sexual love specifically. The doctrine:

Sexual love is the most powerful manifestation of the will-to-live.
The lover's apparent attention to this individual is the species-genius operating through the individual — the species is selecting (via the lover's preferences) the best possible parents for the next generation.
The lover's individual feelings are illusions; the species is the real subject of love.
Hence the tragic structure of love: the species-aim is fundamentally indifferent to the lovers' individual happiness.

This is structurally close to what Simmel calls type-love (Faust/Gretchen as paradigm), with one crucial difference: Schopenhauer grounds all love in the species-genius / will-to-live, whereas Simmel articulates the axial revolution by which sexual attraction becomes love that transcends species-purposes. For Schopenhauer, the species is always the real subject; for Simmel, after the axial revolution, love is its own subject independent of the species.

The Simmelian critique-by-construction: Simmel's Mehr-als-Leben doctrine articulates a trans-vital level that Schopenhauer's metaphysics cannot accommodate, since Schopenhauer's Will is the unitary metaphysical substrate of all phenomena. Simmel's autonomous trans-vital strata are non-Schopenhauerian by structure.

Compassion as Foundation of Ethics

Schopenhauer's On the Basis of Morality (1841, prize essay):

The foundation of morality is Mitleid (compassion/pity).
Compassion is the affective recognition that the other's suffering is one's own — grounded in the metaphysical unity of being beneath the principium individuationis.
Compassion is the only genuine moral motivation; Kantian moral law and Christian charity are reducible to it.

Simmel's criticism applies to this doctrine in addition to the love-derivation: by deriving compassion from metaphysical unity, Schopenhauer treats compassion as a deduction from metaphysics rather than as an irreducible affective phenomenon. The same anti-rationalist criticism applies.

Other Cardinal Schopenhauerian Doctrines

The Will: the thing-in-itself underlying all phenomena. Not "will" in the ordinary psychological sense (purpose, choice) but the blind striving-force that constitutes all phenomena. Bodies are will-objectified; the human body is will-objectified-as-self-perceiving.
The principle of sufficient reason (Über die vierfache Wurzel, 1813): the four roots of the principle: becoming (causation in the physical world), knowing (logical ground), being (mathematical ground of space-time), and acting (motivation). The four-fold reading is influential in subsequent logic.
Aesthetic experience as will-negation: in aesthetic contemplation, the will is temporarily silenced; the subject becomes "pure subject of knowledge" without willing. This is one of the cardinal nineteenth-century accounts of aesthetic experience, deeply influential on Nietzsche (early), Wagner, and beyond. The cited Schopenhauerian remark in Simmel's love-fragment — "art has always attained its goal" (Oakes p. 184) — comes from this context: art does not aim at external ends; it is its own complete event.
The negation of the will: the highest ethical achievement is the negation of the will-to-live, attained through ascetic discipline, compassion, aesthetic contemplation. The pessimist tradition derives from this — the real response to the world's misery is will-negation.

Reception

Nietzsche: initially Schopenhauer-disciple (Schopenhauer as Educator, 1874); eventually Schopenhauer-critic (Twilight of the Idols, Genealogy of Morals). Nietzsche's critique: Schopenhauer's pessimism is itself a symptom of nihilism, not a response to it. The will-to-power-as-affirmation is the Nietzschean alternative.
Wagner: read Welt als Wille in 1854; the discovery reshaped his music-theoretical and dramatic compositions. Tristan und Isolde (1857–59) is the cardinal Wagnerian work under Schopenhauer's influence.
Freud: indirect — the unconscious / drive structure of psychoanalysis has Schopenhauerian Will as one of its cultural backgrounds.
Wittgenstein (early): Tractatus Logico-Philosophicus (1922) has Schopenhauerian moments; Wittgenstein's view of ethics and aesthetics in the Tractatus is partly Schopenhauerian.
Mainländer, Bahnsen, Hartmann, von Hartmann: the late nineteenth-century pessimist tradition.
Adorno, Horkheimer: critical engagement; Negative Dialectics has Schopenhauer-engagement.
Levinas (Totality and Infinity; Otherwise than Being): Levinas's preservation-of-alterity ethics can be read as anti-Schopenhauerian: alterity is preserved, not dissolved in metaphysical unity. The Simmel-Levinas-anti-Schopenhauer lineage is genealogically real, though Simmel's articulation predates Levinas's.

Connections

polemical target in simmel-1923-on-love-fragment — Schopenhauer's metaphysical-unity-grounding of compassion-and-sacrifice (Oakes p. 156).
contrasted with love-as-formative-category — Simmel's categorial-no-unity account of love opposes Schopenhauer's unity-deductive account.
contrasted with universal-philanthropy — Schopenhauer's Mitleid is structurally closer to philanthropy than to Christian love, but grounded in metaphysical fusion (which Simmel critiques).
cited (with approval) for the "art has always attained its goal" maxim in connection with more-than-life's trans-vital strata (Oakes p. 184) — even where Simmel uses Schopenhauer's insight, he detaches it from Schopenhauer's metaphysical grounding.
contemporary or near-contemporary of Hegel (1770–1831), Schelling (1775–1854); Schopenhauer was deeply hostile to Hegel especially.
cross-tradition cousin to the broader nineteenth-century pessimist tradition (Mainländer, Bahnsen, Hartmann).
direct influence on Nietzsche (early), Wagner; indirect influence on Freud, Mann, Borges, Adorno.

Open Questions

The relation between Schopenhauer's Mitleid (compassion) and Christian agape / Buddhist karuṇā. Schopenhauer himself drew on Buddhist sources (he was one of the first European philosophers to engage seriously with Buddhism); the genealogical lines are documented in Welt als Wille II.
Whether Simmel's anti-Schopenhauer critique fully applies to all of Schopenhauer's love-account or specifically to the metaphysical-unity-grounding. The compassion-account in On the Basis of Morality may be more directly subject to Simmel's "rationalism" charge than the Metaphysik der Geschlechtsliebe of sexual love (which has its own non-unity-based analytic — the species-genius operating through individuals).
The relation to Levinas's preservation-of-alterity. Possible cross-tradition cousin of Simmel's anti-Schopenhauer position.
Whether the Mehr-als-Leben structure can fully accommodate Schopenhauerian insights about will-negation in aesthetic experience. Simmel's framework treats aesthetic experience as a trans-vital stratum, but does not require will-negation as the mechanism.
Schopenhauer's relation to Hegel. Schopenhauer was openly hostile (called Hegel a charlatan); but the structural-philosophical relation between Welt als Wille and Phänomenologie des Geistes / Wissenschaft der Logik is more substantive than Schopenhauer's invective acknowledges.

Sources

simmel-1923-on-love-fragment — current wiki source; cardinal passage: the anti-Schopenhauer claim (Oakes p. 156); the approved citation of "art has always attained its goal" (p. 184).
Future ingest priorities: Die Welt als Wille und Vorstellung (especially I §§66–68 on compassion and IV; II Ch. 44 Metaphysik der Geschlechtsliebe); On the Basis of Morality (1841); Parerga und Paralipomena (1851).