G.W. Leibniz

Introduction

Gottfried Wilhelm Leibniz is the great German polymath of the late seventeenth and early eighteenth century, and the most systematically inventive of the early modern rationalists. He is also one of a very small number of figures in the history of thought who would deserve substantial articles in any of several distinct intellectual histories: as a metaphysician (the monadology, the principle of sufficient reason), as a mathematician (the co-invention of the calculus, the binary number system), as a logician (the anticipation of modern symbolic and modal logic), as a diplomat (decades of service to several courts), as a historian (extensive work on the genealogy of the House of Hanover), and as a theologian (the Theodicy, the major work on the problem of evil).

The unity of these projects is the conviction that reality is rationally intelligible through and through. Whatever happens, there is a sufficient reason why it happens rather than otherwise; whatever exists, there is a sufficient reason why it exists rather than not. The world is a rationally ordered whole, and the philosophical task is to articulate the rational structure that makes the actual world the one God selected from among the infinitely many possibilities. Leibniz's most famous (and most caricatured) doctrine — that this is the best of all possible worlds — is the working out of this commitment.

Life

Leibniz was born in 1646 in Leipzig, in the closing years of the Thirty Years War, to a family of academic and legal background. His father was a professor of moral philosophy at Leipzig; Leibniz had unrestricted access to his father's library from age six and was reading Latin and Greek philosophical and historical works as a young child. He entered the University of Leipzig at fourteen, completed the standard philosophical curriculum, took up legal studies, and qualified for the doctorate in law in 1666 at age twenty (Leipzig refused to award the degree to someone so young; Leibniz took the degree from Altdorf instead).

Rather than enter academic life, Leibniz spent his career in princely service. He served first the Elector of Mainz (1668–1672), then the Duke of Brunswick-Lüneburg and his successors at the court of Hanover (from 1676 to his death in 1716). The Hanoverian position was nominally as court historian (tasked with writing the genealogy of the House of Welf, an enormous project Leibniz never completed); in practice he served as diplomat, librarian, and intellectual factotum.

The court positions allowed Leibniz extensive travel. He spent four formative years in Paris (1672–1676), where he met Malebranche, Arnauld, and (through Christiaan Huygens) absorbed the latest French and Dutch mathematics. The Paris years were when Leibniz developed the calculus (independently of Newton; the resulting priority dispute would consume much of his later career). A brief visit to The Hague in November 1676 included a multi-day meeting with Spinoza; the substance of their discussions has been continuously debated.

Leibniz never married. He worked enormously across many domains, published relatively little in his lifetime (much of his work circulated as letters or remained in manuscript), and died in Hanover in 1716, largely neglected by the court he had served — the new king of England (the Elector of Hanover, who had become George I of Great Britain in 1714) had refused to take Leibniz with him to London, and the funeral was attended only by Leibniz's secretary.

The scale of the unpublished Leibniz corpus is extraordinary. The ongoing critical edition (the Berlin Akademie Ausgabe), begun in 1923, is projected to run to over a hundred volumes and is approximately half complete. New material continues to be published; the historical Leibniz is still being recovered from his manuscripts.

The problem he worked on

Leibniz's project was the demonstration that reality, properly analyzed, is fully rationally intelligible. The world is not a brute given; it is the optimal selection among infinite possibilities, made by an infinitely wise God for sufficient reasons that, in principle, the philosopher can grasp.

The project required addressing several specific problems. The mind-body problem (Descartes's residue): how do thinking and extended substances interact? The problem of free will and providence: if God has selected this world from among the possibilities, in what sense are creatures free? The problem of evil: if this is the best of all possible worlds, why is there so much that seems bad in it? The problem of the foundations of physics: what is matter, what is force, what is space and time? Each of these problems received Leibniz's sustained attention, and his answers shaped the early Enlightenment debate substantially.

Contributions

The monadology

Leibniz's mature metaphysics, presented in the short late work Monadology (1714) and in the Discourse on Metaphysics (1686). Reality consists of infinitely many simple substances — the monads — each of which is a unified center of perception and appetite, mirroring the entire universe from its particular point of view. Monads have no parts (they are simple), no spatial extension, no causal interaction with each other; what appears to be causal interaction is actually the pre-established harmony set up by God at creation, in which each monad's internal development corresponds with all the others.

The doctrine is among the strangest in the history of philosophy and one of the most ingenious. It is Leibniz's response to the Cartesian mind-body problem: there is no mind-body problem because there are no bodies in the strict sense; what we take for bodies are well-founded aggregates of monads. It also solves the problem of action at a distance, the unity of substances, and several other technical metaphysical puzzles — at the cost of accepting a metaphysical picture far removed from common sense.

The principle of sufficient reason

Leibniz's most characteristic single doctrine: nothing happens without a sufficient reason why it should be so rather than otherwise. The principle, sometimes called PSR, drives much of his metaphysics. The argument for the existence of God from contingent beings is one application: the existence of any contingent being requires a sufficient reason; the chain of reasons must terminate in a necessary being whose existence is its own sufficient reason; this is God. The argument from the principle of sufficient reason against absolute space (in the Leibniz-Clarke correspondence with Newton's representative Samuel Clarke) is another: if space were absolute and homogeneous, there would be no sufficient reason for God to place the cosmos at one location rather than any other, so absolute space cannot exist.

The principle has had a remarkable career. It was a primary target of Hume's empiricist critique (Hume denied that PSR has any rational foundation); Schopenhauer's doctoral dissertation On the Fourfold Root of the Principle of Sufficient Reason (1813) is one of the great nineteenth-century treatments; the contemporary literature on metaphysics still engages PSR (notably in Della Rocca's interpretation of Spinoza as the most consistent PSR theorist).

The calculus

Leibniz independently developed the calculus in the late 1670s, publishing his first papers on the subject in 1684 (the differential calculus) and 1686 (the integral calculus). Newton had developed his version (the method of fluxions) earlier but published it later. The resulting priority dispute between the British and continental scientific communities consumed both sides for decades and was unfortunate for everyone involved. The modern judgment is that the two figures discovered the calculus independently; Leibniz's notational system (the dy/dx and the integral sign) is what is universally used today, and was demonstrably more usable than Newton's notation.

Symbolic logic and the universal characteristic

Leibniz's project of a characteristica universalis — a symbolic language in which any meaningful proposition could be unambiguously expressed, and any dispute could be resolved by calculation — anticipated modern symbolic logic by two centuries. The technical work that survives (much of it unpublished in his lifetime, recovered only in the late nineteenth and early twentieth centuries) shows substantial development of formal logical notation and the analysis of inference. Bertrand Russell's A Critical Exposition of the Philosophy of Leibniz (1900) was a turning point in the modern recognition of Leibniz as a major figure in the history of logic.

The Theodicy and the problem of evil

Essais de Théodicée (1710), Leibniz's most extensive published work in his lifetime, addresses the problem of evil. Why does an infinitely wise, powerful, and good God allow evil? Leibniz's answer: among the infinitely many possible worlds, God chose the one that maximizes overall goodness, considering all the goods and ills together. Some evils are necessary conditions of greater goods; the actual world is the best possible combination. The famous (caricatured) claim that we live in the best of all possible worlds belongs to this argument; Voltaire's Candide (1759) is the most famous literary attack.

Key works

• Discourse on Metaphysics (1686). Mature statement of the metaphysics; not published in Leibniz's lifetime.
• New System of Nature (1695). Published statement of central metaphysical doctrines.
• New Essays on Human Understanding (composed by 1704; published posthumously 1765). Paragraph-by-paragraph response to Locke's Essay.
• Theodicy (1710). The major published work on the problem of evil.
• Monadology (1714). Short late summary of the metaphysics.
• Leibniz-Clarke correspondence (1715–1716). Late exchange with Samuel Clarke (representing Newton) on space, time, and theology.
• Vast unpublished corpus, still being edited.

Influences and influenced

Influenced by: Aquinas and the Scholastic tradition (Leibniz was unusually well-read in scholastic philosophy for an early modern thinker); Descartes and the rationalist tradition; Spinoza (the visit of November 1676 was substantively important, though Leibniz publicly distanced himself from Spinoza throughout his career); the contemporary natural philosophers (Huygens, Boyle, Hooke).

Influenced: the German philosophical tradition through Christian Wolff (whose systematization of Leibnizian philosophy became the standard German philosophical framework before Kant); Kant himself (the Critique of Pure Reason engages Leibniz throughout); the modern mathematical tradition through the universal use of his calculus notation; modern symbolic logic through Russell's A Critical Exposition (1900) and the subsequent recovery; contemporary metaphysics through the continuing engagement with the principle of sufficient reason.

Reception

Leibniz's reception in his lifetime was complicated by the relatively little he published. Much of his most important work circulated only in correspondence or remained in manuscript. The German philosophical tradition through Christian Wolff systematized parts of Leibniz's philosophy and made it the dominant German framework before Kant.

Voltaire's Candide (1759), with its merciless mockery of Pangloss (a caricature of Leibniz, especially the best of all possible worlds doctrine), shaped European popular reception of Leibniz for the next century. The mockery has shadowed Leibniz's reputation; the Theodicy is in fact considerably more sophisticated than the Pangloss caricature suggests.

The modern recovery of Leibniz as a major philosopher in his own right owes substantially to Bertrand Russell's A Critical Exposition of the Philosophy of Leibniz (1900), Louis Couturat's roughly contemporary French work, and the subsequent twentieth-century scholarly engagement. The ongoing Akademie Ausgabe critical edition has continued to recover and edit unpublished material, with continuing new findings.

Continuing engagement

Major recent scholarly work includes Maria Rosa Antognazza's Leibniz: An Intellectual Biography (2009; the standard biography in English), Robert Adams's Leibniz: Determinist, Theist, Idealist (1994), Donald Rutherford's Leibniz and the Rational Order of Nature (1995), and the Cambridge Companion to Leibniz. The Akademie edition is the standard scholarly reference. Active scholarly debates concern the development of the monadology, the relation between Leibniz's metaphysics and his mathematics, the place of his theology in his overall system, the historicity of the meeting with Spinoza, and the contemporary applicability of the principle of sufficient reason.

Further reading

• Rationalism — the tradition
• Descartes — the predecessor whose framework Leibniz both extends and revises
• Spinoza — the contemporary rationalist Leibniz publicly distanced himself from
• Kant — the philosopher whose Critical philosophy is in part a response to Leibnizian-Wolffian rationalism
• Substance — the category his monadology radically transforms
• Aquinas — the medieval predecessor whose work Leibniz knew unusually well

The great German polymath of the late seventeenth century. Metaphysician, mathematician, logician, diplomat, theologian.