Gottfried Leibniz

Western Philosophers 17th-century philosophy (Modern Philosophy)
Name: Gottfried Wilhelm Leibniz
Birth: July 2, 1646 (Leipzig, Germany)
Death: November 14, 1716 (Hanover, Germany)
School/tradition: Continental rationalism
Main interests
Metaphysics, Epistemology, Science, Mathematics, theodicy
Notable ideas
Calculus, innate knowledge, optimism, monad
Influences	Influenced
Plato, Aristotle, Ramon Llull, Scholastic philosophy, Descartes, Christiaan Huygens	Many later mathematicians, Christian Wolff, Immanuel Kant, Bertrand Russell, Abraham Robinson

Gottfried Wilhelm Leibniz (also Leibnitz or von Leibniz) (July 1 (June 21 Old Style) 1646, Leipzig – November 14 1716, Hanover) was a German polymath, deemed a universal genius in his day and since.

Educated in law and philosophy, and serving as factotum to two major German noble houses (one becoming the British royal family while he served it), Leibniz played a major role in the European politics and diplomacy of his day. He occupies an equally large place in both the history of philosophy and the history of mathematics. He invented calculus independently of Newton, and his notation is the one in general use since. In philosophy, he is most remembered for optimism, i.e., his conclusion that our universe is, in a restricted sense, the best possible one God could have made. He was, along with René Descartes and Baruch Spinoza, one of the three great 17th century rationalists, but his philosophy also both looks back to the Scholastic tradition and anticipates logic and analysis.

Leibniz also made major contributions to physics and technology, and anticipated notions that surfaced much later in biology, medicine, geology, psychology, knowledge engineering, and information science. Key figures in their fields submit that his writings contain anticipations of relativity, fractal geometry, and even quantum mechanics^{[citation needed]}. He also wrote on politics, law, ethics, theology, history, and philology, even occasional verse. His contributions to this vast array of subjects are scattered in journals and in tens of thousands of letters and unpublished manuscripts. To date, there is no complete edition of Leibniz's writings, and a complete account of his accomplishments is not yet possible.

Life

The only biography on Leibniz in English is Aiton (1986). A lively short account of Leibniz’s life, one also doing fair justice to the breadth of his interests and activities, is Mates (1986: 14-35), who cites the German biographies extensively. Also see MacDonald Ross (1984: chpt. 1), the chapter by Ariew in Jolley (1995), and Jolley (2005: chpt. 1). For a biographical glossary of Leibniz's intellectual contemporaries, see AG 350.

Coming of age

Leibniz was born on July 1, 1646, the child of Friedrich Leibnütz and Catherina Schmuck. He began spelling his name "Leibniz" early in adult life, but others often referred to him as "Leibnitz," a spelling which persisted until the 20th century.

When Leibniz was six years old, his father, a Professor of Moral Philosophy at the University of Leipzig, died, leaving a personal library to which Leibniz was granted free access from age seven onwards. By 12, he had taught himself Latin, a language he employed freely all his life, and had begun Greek. He entered his father's university at 14, and completed his university studies by age 20, specializing in law and mastering the standard university course of classics, logic, and scholastic philosophy. However, his education in mathematics was not up to the French and British standard of the day. In 1666, he completed his habilitation thesis (which would allow him to teach), On the Art of Combinations. When Leipzig declined to assure him a position teaching law upon graduation, Leibniz submitted to the University of Altdorf near Nuremberg the thesis he had intended to submit at Leipzig, and obtained his doctorate in law in five months. He then declined an offer of academic appointment at Altdorf, and spent the rest of his life in the service of two major German noble families.

Career

Leibniz's first position was as a salaried alchemist in Nuremberg, an area he remained interested in for the rest of his life. He soon met J. C. von Boineburg, a diplomat of the Bishop Elector of Mainz, Johann Philipp von Schönborn. Von Boineburg hired Leibniz as an assistant, and shortly thereafter introduced Leibniz to the Elector. Von Schönborn soon hired Leibniz as well as a legal and political advisor.

Von Boineburg did much to promote Leibniz's reputation, and the latter's memoranda and letters began to attract favorable notice. Leibniz's service to the Elector soon took on a diplomatic role. The main European geopolitical reality during Leibniz's adult life was the ambition of the French king, Louis XIV, backed by French military and economic might. This was especially worrisome for the German states, who had been left exhausted, fragmented, and economically backward by the Thirty Years' War. Leibniz helped von Boineburg devise a plan to protect German-speaking Europe by distracting Louis. France would be invited to take Egypt as a stepping stone towards an eventual conquest of the Dutch East Indies. Having directed it's military might at Egypt, France would have too few resources to attack Germany. This plan obtained the Elector's cautious support. In 1672, Leibniz was sent to Paris to present the idea to the French, but the plan was soon overtaken by events and became moot. Napoleon's failed invasion of Egypt in 1798 can perhaps be seen as an unwitting implementation of Leibniz's plan.

Thus Leibniz began several years in Paris, during which he greatly expanded his knowledge of mathematics and physics, and began contributing to both. He met Malebranche and Antoine Arnauld, the leading French philosophers of the day, and studied the writings of Descartes and Pascal, unpublished as well as published. He befriended a German mathematician, Ehrenfried Walther von Tschirnhaus; they corresponded for the rest of their lives. Especially fateful was Leibniz's making the acquaintance of the Dutch physicist and mathematician Christiaan Huygens, then active in Paris. Soon after arriving in Paris, Leibniz received a rude awakening; his knowledge of mathematics and physics was spotty. With Huygens as mentor, he began a program of self-study that soon resulted in his making major contributions to both subjects, including inventing his version of the differential and integral calculus.

In 1673, Leibniz made a brief trip to London. There he made the acquaintance of Henry Oldenburg. Oldenburg was then the secretary of the Royal Society, who were particularly impressed by a calculating machine Leibniz had invented - one which could perform all four arithmetical operations. That same year, Leibniz was elected a fellow of the Society.

When Leibniz returned to Paris, however, he found himself unemployed (both von Boineburg and von Schönborn had died by 1673). He had hoped for employment by the Paris Academy, but soon realized that it would not be forthcoming (he was finally accepted in 1700). He therefore somewhat reluctantly accepted a post as councilor at the court of Hanover for Duke Johann Friedrich of Brunswick-Lüneburg.

Leibniz managed to delay his arrival in Hanover until the end of 1676, after making one more short journey to London. On the journey from London to Hanover, Leibniz stopped in The Hague where he met Antony van Leeuwenhoek, the discoverer of microorganisms. He also spent several days in intense discussion with Spinoza, who had just completed his masterwork, the Ethics. Leibniz respected Spinoza's powerful intellect, but was dismayed by his conclusions that contradicted Christian orthodoxy, and found many of his proofs unsound.

In the service of the House of Brunswick (also: Braunschweig), Leibniz was engaged in a wide variety of projects. He attempted a number of complicated mechanical schemes for draining a series of mines in the Harz mountains (none of which appeared to have been successful). He was assigned the massive task of compiling a history of the Guelph lineage (of which the House of Brunswick was a part), as a means towards furthering the family's aspiriations. The Duke also enlisted Leibniz's legal and philosophical expertise in attempting to reunite the Protestant churches with the Catholic curch. Finally, Leibniz began producing the first mature expressions of his philosophy (beginning with the Meditations on Knowledge, Truth and Ideas of 1684).

The rest of Leibniz's life was occupied with various tasks associated with Hanover. He never produced the requested history of family, but nevertheless examined numerous archives and compiled much preparatory material. He traveled constantly to various courts throughout Europe, and was able to establish an Academy of Sciences in Berlin while initiating the formation of similar societies in Vienna and St. Petersburg. Despite a large number of municipal and legal projects, he maintained an extensive correspondence on nearly every topic imagineable (around 15,000 of his letters survive). It is therefore not surprising that his relations with his employers became somewhat strained, and when Duke Georg Ludwig was crowned George I of England, the family moved while leaving Leibniz in Hanover.

The last years of Leibniz's life were not happy ones. Abandoned by the House of Hanover, he made some final attempts at completing the family history and compiling an authoritative expression of his philosophy. Neither attempt was successful. He died in November of 1716.

The Calculus Dispute

Leibniz is credited, along with Isaac Newton, with inventing the infinitesimal calculus. According to Leibniz's notebooks, a critical breakthrough occurred on November 11, 1675, when he employed integral calculus for the first time to find the area under the function y = x. He introduced several notations used to this day, for instance the integral sign ∫ representing an elongated S, from the Latin word summa and the d used for differentials, from the Latin word differentia. Leibniz did not publish any of his results until 1684 (two years prior to Newton's Principia). The product rule of differential calculus is still called "Leibniz's rule."

Leibniz's approach to the calculus fell well short of later standards of rigor (the same can be said of Newton's). We now see a Leibniz "proof" as being in truth mostly a heuristic hodgepodge, mainly grounded in geometric intuition and an intuitive understanding of differentials. Leibniz also freely invoked mathematical entities he called infinitesimals, manipulating them freely in ways suggesting that they had paradoxical algebraic properties. George Berkeley, in a tract called The Analyst and elsewhere, ridiculed this and other aspects of the early calculus, pointing out that natural science grounded in the calculus required just as big of a leap of faith as theology grounded in Christian revelation.

The calculus as we now know it emerged in the 19th century, and banished infinitesimals into the wilderness of obsolete mathematics (although engineers, physicists, and economists continued to use them). But beginning in 1960, Abraham Robinson showed how to make sense of Leibniz's infinitesimals, and how to give them algebraic properties free of paradox. The resulting nonstandard analysis can be seen as a great belated triumph of Leibniz's mathematical and ontological intuition.

From 1711 until his death, Leibniz's life was envenomed by a long dispute with John Keill, Newton, and others, over whether Leibniz had invented the calculus independently of Newton, or whether he had merely invented another notation for ideas that were fundamentally Newton's. Today, the predominant view is that Newton developed his calculous first, then mentioned to Leibniz several things that his new method could accomplish (without specifying anything about the method itself). Leibniz took this cue to develop his own calculous, which he published quickly, perhaps with less-than-admirable motives.

Writings

Leibniz wrote in three languages: scholastic Latin, French, and (least often) German. During his lifetime, he published many pamphlets and scholarly articles, but relatively little philosophy. Only one substantial book appeared posthumously, his Nouveaux essais sur l'entendement humain (a response to John Locke's Essay Concerning Human Understanding. Only in 1895, when Bodemann completed his catalogs of Leibniz's manuscripts and correspondence, did the enormous extent of Leibniz's Nachlass become clear: about 15,000 letters to more than 1000 recipients plus more than 40,000 other items. Moreover, quite a few of these letters are of essay length. Much of his vast correspondence, especially the letters dated after 1685, remains unpublished, and much of what is published has been so only in recent decades. The amount, variety, and disorder of Leibniz's writings are a predictable result of a situation he described as follows:

"I cannot tell you how extraordinarily distracted and spread out I am. I am trying to find various things in the archives; I look at old papers and hunt up unpublished documents. From these I hope to shed some light on the history of the [House of] Brunswick. I receive and answer a huge number of letters. At the same time, I have so many mathematical results, philosophical thoughts, and other literary innovations that should not be allowed to vanish that I often do not know where to begin." (1695 letter to Vincent Placcius in Gerhardt, Philosophical Writings of Leibniz III: 194. Revision of translation in Mates 1986.)

The extant parts of the critical edition of Leibniz's writings are organized as follows:

• Series 1. Political, Historical, and General Correspondence. 21 vols., 1666-1701.
• Series 2. Philosophical Correspondence. 1 vol., 1663-85.
• Series 3. Mathematical, Scientific, and Technical Correspondence. 6 vols., 1672-96.
• Series 4. Political Writings. 6 vols., 1667-98.
• Series 5. Historical and Linguistic Writings. Inactive.
• Series 6. Philosophical Writings. 7 vols., 1663-90, and Nouveaux essais sur l'entendement humain.
• Series 7. Mathematical Writings. 3 vols., 1672-76.
• Series 8. Scientific, Medical, and Technical Writings. In preparation.

Some of these volumes, along with work in progress, are available online, for free. Even though work on this edition began in 1901, only 22 volumes had appeared by 1990, in part because the only additions between 1931 and 1962 were four volumes in Series 1.

Posthumous reputation

When Leibniz died, his reputation was in decline. Many thought of him primarily as the author of Théodicée, whose supposed central argument Voltaire was to lampoon in his Candide. Leibniz had an ardent disciple, Christian Wolff, who briefly generated much enthusiasm for 'Leibnizian-Wolffian' philosphy, only to become a principal target of Kant. Much of Europe came to doubt that Leibniz had invented the calculus independently of Newton, and much of his whole work in mathematics and physics was neglected. His work on law, diplomacy, and history was seen as of ephemeral interest. The vastness and richness of his correspondence went unsuspected.

Leibniz's long march to his present glory began with the 1765 publication of the Nouveaux Essais, which Kant read closely. In 1768, Dutens edited the first multi-volume edition of Leibniz's writings, followed in the 19th century by a number of editions, including those edited by Erdmann, Foucher de Careil, Gerhardt, Gerland, Klopp, and Mollat. Publication of Leibniz's correspondence with notables such as Antoine Arnauld, Sophia of Hanover, and her daughter Sophia Charlotte of Hanover, began.

In 1900, Bertrand Russell published a study of Leibniz's metaphysics. Shortly thereafter, Louis Couturat published an important study of Leibniz, and edited a volume of Leibniz's heretofore unpublished writings, mainly on logic. While their conclusions have been devated, they made Leibniz respectable among 20th century analytical and linguistic philosophers. With analytic philosophy's renewed interest in metaphysics in the 1960's and 70's, Leibniz's work has received more and more attention.

Philosopher

There are at least three challenges in developing a plausible summary of Leibniz's philosophy. First, unlike nearly every other figure in early modern philosophy, Leibniz left no substantial philosophical work which can be taken as the definitely expression of his thought. Second, Leibniz's views appear differently in different places, not only because of the development of his thought, but also because he often tailored his writings to his audience. Finally, there is the fact of the vastness of the Leibnizian corpus, which is, for all intents and purposes, simply too large for any one person to adequately survey.

Despite these challeges, certain themes are particularly noteworthy, both because they recurr in what seem to be Leibniz's main philosophical works, and because of their distinctive influence on later philosophers.

Unlike Descartes and Spinoza, Leibniz had a thorough university education in ancient and scholastic philosophy, one which he took seriously. His writings show his desire to find some element of truth in each of the various positions. Whereas the Cartesians were eager to abandon the Aristotelian notion of forms, Leibniz attempted to integrate talk of forms into a metaphysics derived from that of Descartes.

Logic

Leibniz had a remarkable faith that a great deal of human reasoning could be reduced to calculations of a sort, and that such calculations could resolve many differences of opinion:

"The only way to rectify our reasonings is to make them as tangible as those of the Mathematicians, so that we can find our error at a glance, and when there are disputes among persons, we can simply say: Let us calculate [calculemus], without further ado, to see who is right." (The Art of Discovery 1685, W 51)

Leibniz's calculus ratiocinator, which very much brings symbolic logic to mind, can be viewed as a way of making calculations of this sort feasible. Leibniz wrote memoranda (many of which are translated in Parkinson 1966) that can now be read as groping attempts to get symbolic logic—and thus his calculus—off the ground. But Gerhard and Couturat did not publish these writings until after modern formal logic had emerged in Frege's Begriffsschrift and in various writings by Charles Peirce and his students in the 1880s, and hence well after Boole and De Morgan began that logic in 1847.

Leibniz is probably the most important logician between Aristotle and 1847, when George Boole and Augustus De Morgan each published books that began modern formal logic. Leibniz enunciated the principal properties of what we now call conjunction, disjunction, negation, identity, set inclusion, and the empty set.

He proposed the creation of a characteristica universalis or "universal characteristic," built on an alphabet of human thought in which each fundamental concept would be represented by a unique "real" character.

"It is obvious that if we could find characters or signs suited for expressing all our thoughts as clearly and as exactly as arithmetic expresses numbers or geometry expresses lines, we could do in all matters insofar as they are subject to reasoning all that we can do in arithmetic and geometry. For all investigations which depend on reasoning would be carried out by transposing these characters and by a species of calculus." (Preface to the General Science, 1677. Revision of Rutherford's translation in Jolley 1995: 234. Also W I.4)

More complex thoughts would be represented by combining in some way the characters for simpler thoughts. Leibniz saw that the uniqueness of prime factorization suggests a central role for prime numbers in the universal characteristic, a striking anticipation of Gödel numbering. Granted, there is no intuitive or mnemonic way to number any set of elementary concepts using the prime numbers.

Because Leibniz was a mathematical novice at the time he first wrote about the characteristic, at first he did not conceive it as an algebra but rather as a universal language or script. Only in 1676 did he conceive of a kind of "algebra of thought," modeled on and including conventional algebra and its notation. The resulting characteristic was to include a logical calculus, some combinatorics, algebra, his analysis situs (geometry of situation) discussed in 3.2, a universal concept language, and more.

Much of Leibniz's philosophy makes use of two metaphysical principles whose names he coined. Though these principles are present in earlier philosophers, Leibniz makes the most explicit use of them of anyone up to his time.

• Identity of indiscernibles: Two things are identical if and only if they share the same properties.
• Principle of Sufficient Reason: There must be a sufficient reason, often known only to God, for anything to exist, for any event to occur, for any truth to obtain.

Both of these principles correspond closely to aspects of Leibniz's metaphysics.

The Monads

Leibniz's best known contribution to metaphysics is his theory of monads, as exposited in his Monadology. Roughly speaking, monads are to the mental realm what atoms were seen as being to the physical (Leibniz argued that matter was infinitely divisible, thus denying that atoms exist). Monads, along with God, are the ultimate elements of the universe. The monads are "substantial forms of being" with the following properties: they are eternal, indecomposable, individual, active, subject to their own laws, causally independent of one another, and each reflecting the entire universe in a pre-established harmony. Monads are centers of force; substance is force, while space, matter, and motion are merely phenomenal.

The ontological essence of a monad is its irreducible simplicity. Unlike extended substances as conceived by Descartes, monads possess no material or spatial character. They also differ from Cartesian extended substance by their complete mutual independence, so that interactions among monads are only apparent. Instead, by virtue of the principle of pre-established harmony, each monad follows a God-given, preprogrammed set of "instructions" peculiar to itself, so that a monad "knows" what to do at each moment. By virtue of these intrinsic instructions, each monad is like a little mirror of the universe.

Monads are purported to solve the problematic:

• Interaction between mind and matter arising in the system of Descartes;
• Lack of individuation inherent to the system of Spinoza, which represent individual creatures as merely accidental.

Pre-Established Harmony

Leibniz believed that each monad was metaphysically independent of everything else in the universe, save God. This independence is both ontological and causal. As long as God continues to preserve it, any particular monad could continue to exist while all others are destroyed. Further,

Theodicy and optimism

The Théodicée tries to justify the apparent imperfections of the world by claiming that it is optimal among all possible worlds. It must be the best possible and most balanced world, because it was created by a perfect God. Rutherford (1998) is a detailed scholarly study of Leibniz's theodicy.

The statement that "we live in the best of all possible worlds" drew scorn, most notably from Voltaire, who lampooned it in his comic novel Candide by having the character Dr. Pangloss (a parody of Leibniz) repeat it like a mantra. Thus the adjective "panglossian", describing one so naive as to believe that the world about us is the best possible one.

The mathematician Paul du Bois-Reymond, in his "Leibnizian Thoughts in Modern Science," wrote that Leibniz thought of God as a mathematician.

"As is well known, the theory of the maxima and minima of functions was indebted to him for the greatest progress through the discovery of the method of tangents. Well, he conceives God in the creation of the world like a mathematician who is solving a minimum problem, or rather, in our modern phraseology, a problem in the calculus of variations - the question being to determine among an infinite number of possible worlds, that for which the sum of necessary evil is a minimum."

A cautious defense of Leibnizian optimism would invoke certain scientific principles that emerged in the two centuries since his death and that are now thoroughly established: the principle of least action, the conservation of mass, and the conservation of energy. Recent scientific developments enable a bolder defense. The solar system appears to have a number of fortuitous characteristics that support Earth's long lived and melioristic biosphere: the Earth is rich in metals, is of the right size and distance from the sun, and has the right rotation period and axis tilt. The Moon and Jupiter have sizes and orbits enabling them to shield the Earth from bolide impacts; for whatever reason, such impacts have been happily rare since life emerged; and so on (Ward & Brownlee, 2000; Morris 2003: chpts. 5,6).

Bolder yet is a defense of optimism that invokes the Anthropic Principle. Contemporary physics can be seen as grounded in the numerical values of a handful of dimensionless constants, the best known of which are the fine structure constant and the ratio of the rest mass of the proton to the electron. Were the numerical values of these constants to differ by a few percent from their observed values, it is likely that the resulting universe would be incapable of harboring complexity. Our universe is "best" in the sense that it is capable of supporting complex structures such as galaxies, stars, and, ultimately, life on Earth.

Works

AG = Ariew & Garber (1989). LL = Loemker (1969). W = Wiener (1951). Woolhouse and Francks (1998) = WF.

The ongoing critical edition of all of Leibniz's writings is Sämtliche Schriften und Briefe.

The year shown is usually the year in which the work was completed, not of its eventual publication.

• 1666. De Arte Combinatoria (On the Art of Combination). Partially translated in LL §1 and Parkinson (1966).
• 1671. Hypothesis Physica Nova (New Physical Hypothesis). LL §8.I (part)
• 1684. Nova methodus pro maximis et minimis (New Method for maximums and minimums). Translation in Struik, D. J., 1969. A Source Book in Mathematics, 1200-1800. Harvard Uni. Press: 271-81.
• 1686. Discours de métaphysique. Martin and Brown (1988). Jonathan Bennett's translation. AG 35, LL §35, W III.3, WF 1.
• 1705. Explication de l'Arithmétique Binaire (Explanation of Binary Arithmetic). Gerhardt, Mathematical Writings VII.223.
• 1710. Théodicée. Farrer, A.M., and Huggard, E.M., trans., 1985 (1952). Theodicy. Open Court. W III.11 (part).
• 1714. Monadologie. Nicholas Rescher, trans., 1991. The Monadology: An Edition for Students. Uni. of Pittsburg Press. Jonathan Bennett's translation. Latta's translation. AG 213, LL §67, W III.13, WF 19.
• 1765. Nouveaux essais sur l'entendement humain. Completed 1704. Remnant, Peter, and Bennett, Jonathan, trans., 1996. New Essays on Human Understanding. Cambridge Uni. Press. W III.6 (part). Jonathan Bennett's translation.

Collections of shorter works in translation:

• Ariew, R., and Garber, D., 1989. Leibniz: Philosophical Essays. Hackett.
• Bennett, Jonathan. Various texts.
• Cook, Daniel, and Rosemont, Henry Jr., 1994. Leibniz: Writings on China. Open Court.
• Dascal, Marcelo, 1987. Leibniz: Language, Signs and Thought. John Benjamins.
• Loemker, Leroy E., 1969 (1956). Leibniz: Philosophical Papers and Letters. Reidel.
• Martin, R.N.D., and Brown, Stuart, 1988. Discourse on Metaphysics and Related Writings. St. Martin's Press.
• Parkinson, G.H.R., 1966. Leibniz: Logical Papers. Oxford Uni. Press.
• ------, and Morris, Mary, 1973. 'Leibniz: Philosophical Writings. London: J M Dent & Sons.
• Riley, Patrick, 1988 (1972). Leibniz: Political Writings. Cambridge Uni. Press.
• Rutherford, Donald. Various texts.
• Strickland, Lloyd, 2006. Shorter Leibniz Texts. Continuum Books. Online.
• Wiener, Philip, 1951. Leibniz: Selections. Scribner. Regrettably out of print and lacks index.
• Woolhouse, R.S., and Francks, R., 1998. Leibniz: Philosophical Texts. Oxford Uni. Press.

Donald Rutherford's online bibliography.

Secondary literature

Introductory:

• Jolley, Nicholas, 2005. Leibniz. Routledge.
• MacDonald Ross, George, 1984. Leibniz. Oxford Uni. Press.
• W. W. Rouse Ball, 1908. A Short Account of the History of Mathematics, 4th ed. (see Discussion)

Intermediate:

• Aiton, Eric J., 1985. Leibniz: A Biography. Hilger (UK).
• Hall, A. R., 1980. Philosophers at War: The Quarrel between Newton and Leibniz. Cambridge Uni. Press.
• Hostler, J., 1975. Leibniz's Moral Philosophy. UK: Duckworth.
• Jolley, Nicholas, ed., 1995. The Cambridge Companion to Leibniz. Cambridge Uni. Press.
• LeClerc, Ivor, ed., 1973. The Philosophy of Leibniz and the Modern World. Vanderbilt Uni. Press.
• Loemker, Leroy, 1969a, "Introduction" to his Leibniz: Philosophical Papers and Letters. Reidel: 1-62.
• Arthur O. Lovejoy, 1957 (1936). "Plenitude and Sufficient Reason in Leibniz and Spinoza" in his The Great Chain of Being. Harvard Uni. Press: 144-82. Reprinted in Frankfurt, H. G., ed., 1972. Leibniz: A Collection of Critical Essays. Anchor Books.
• MacDonald Ross, George, 1999, "Leibniz and Sophie-Charlotte" in Herz, S., Vogtherr, C.M., Windt, F., eds., Sophie Charlotte und ihr Schloß. München: Prestel: 95–105. English translation.
• Perkins, Franklin, 2004. Leibniz and China: A Commerce of Light. Cambridge Uni. Press.
• Riley, Patrick, 1996. Leibniz's Universal Jurisprudence: Justice as the Charity of the Wise. Harvard Uni. Press.

Advanced

• Adams, Robert M., 1994. Leibniz: Determinist, Theist, Idealist. Oxford Uni. Press.
• Couturat, Louis, 1901. La Logique de Leibniz. Paris: Felix Alcan. Donald Rutherford's English translation in progress.
• Ishiguro, Hide, 1990 (1972). Leibniz's Philosophy of Logic and Language. Cambridge Uni. Press.
• Lenzen, Wolfgang, 2004. "Leibniz's Logic," in Gabbay, D., and Woods, J., eds., Handbook of the History of Logic, Vol. 3. North Holland: 1-84.
• Mates, Benson, 1986. The Philosophy of Leibniz : Metaphysics and Language. Oxford Uni. Press.
• Mercer, Christia, 2001. Leibniz's metaphysics : Its Origins and Development. Cambridge Uni. Press.
• André Robinet, 2000. Architectonique disjonctive, automates systémiques et idéalité transcendantale dans l'oeuvre de G.W. Leibniz: Nombreux textes inédits . Vrin
• Rutherford, Donald, 1998. Leibniz and the Rational Order of Nature. Cambridge Uni. Press.
• Wilson, Catherine, 1989. Leibniz's Metaphysics. Princeton Uni. Press.
• Woolhouse, R. S., ed., 1993. G. W. Leibniz: Critical Assessments, 4 vols. Routledge. A remarkable and regrettably expensive one-stop collection of many valuable articles.

Online bibliography, by Gregory Brown.

External links

• Online texts in easier-to-read versions.
• Leibnitiana — Gregory Brown.
• Monadologie, in German.
• Lloyd Strickland's web page. Scroll down for many Leibniz links.
• Table of contents for the Leibniz Review, 1998-.
• European Graduate School - Gottfried Leibniz.
• John J. O'Connor and Edmund F. Robertson. Gottfried Leibniz at the MacTutor archive
• Leibniz biography and bibliography.
• Leibniz compared to Volaire and Candide
• The Internet Encyclopedia of Philosophy: Leibniz — Douglas Burnham.
• Stanford Encyclopedia of Philosophy. Leibniz on:
  • Ethics — Andrew Youpa.
  • Causation — Mark Bobro.
  • Problem of evil — Michael Murrary.
  • Philosophy of mind — Kulstad and Carlin.
• Encyclopedia Britannica, 11th ed.
• Works by Gottfried Leibniz. Project Gutenberg

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