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Gottfried Leibniz

2007 Schools Wikipedia Selection. Related subjects: Mathematicians

                              Western Philosophers
   17th-century philosophy
   (Modern Philosophy)
   Gottfried Wilhelm Leibniz
         Name:       Gottfried Wilhelm Leibniz
        Birth:       July 1, 1646 ( Leipzig, Germany)
        Death:       November 14, 1716 ( Hanover, Germany)
   School/tradition: Rationalism
    Main interests:  metaphysics, mathematics, science, epistemology,
                     theodicy
    Notable ideas:   calculus, monad, theodicy, optimism
      Influences:    Plato, Aristotle, Ramon Llull, Scholastic philosophy,
                     Descartes, Christiaan Huygens
      Influenced:    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 – November 14, 1716) was a German polymath who
   wrote mostly in French and Latin.

   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. He also invented the binary system, foundation of
   virtually all modern computer architectures. 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 modern logic and analysis.

   Leibniz also made major contributions to physics and technology, and
   anticipated notions that surfaced much later in biology, medicine,
   geology, probability theory, psychology, and information science. 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   unpublished manuscripts.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

Coming of age

   Leibniz was born on 1 July 1646 (Sunday), at 6:15 p.m in Leipzig to
   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. In later
   life, he often signed himself "von Leibniz", and many posthumous
   editions of his works gave his name on the title page as "Freiherr
   [Baron] G. W. von Leibniz." But no document has been found confirming
   that he was ever granted a patent of nobility. In the 17th and 18th
   centuries, it was not unusual for the ambitious to insert, starting in
   midlife, a "de" or "von" before their surnames, to suggest a nobility
   they in fact did not possess; cases in point include Voltaire,
   Beaumarchais, and Beethoven.

   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 courses in
   classics, logic, and scholastic philosophy. However, his education in
   mathematics was not up to the French and British standards. In 1666, he
   published his first book, also his habilitation thesis in philosophy,
   On the Art of Combinations. When Leipzig declined to assure him a
   position teaching law upon graduation, Leibniz submitted the thesis he
   had intended to submit at Leipzig to the University of Altdorf instead,
   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

   The outline of Leibniz's career is as follows:
     * 1666-74: Mainly in service to the Elector of Mainz, Johann Philipp
       von Schönborn, and his minister, Baron von Boineburg.
          + 1672-76. Resides in Paris, making two important sojourns to
            London.
     * 1676-1716. In service to the House of Hanover.
          + 1677-98. Courtier, first to John Frederick, Duke of
            Brunswick-Lüneburg, then to his brother, Duke, then Elector,
            Ernst August of Hanover.
               o 1687-90. Travels extensively in Germany, Austria, and
                 Italy, researching a book the Elector has commissioned
                 him to write on the history of the House of Brunswick.
          + 1698-1716: Courtier to Elector Georg Ludwig of Hanover.
               o 1712-14. Resides in Vienna. Appointed Imperial Court
                 Councillor in 1713 by Charles VI, Holy Roman Emperor, at
                 the Hapsburg court in Vienna.
          + 1714-16: Georg Ludwig, upon becoming George I of Great
            Britain, forbids Leibniz to follow him to London. Leibniz ends
            his days in relative neglect.

1666-74

   Leibniz's first position was as a salaried alchemist in Nuremberg, even
   though he knew nothing about the subject. He soon met J. C. von
   Boineburg, the dismissed chief minister of the Elector of Mainz, Johann
   Philipp von Schönborn. Von Boineburg hired Leibniz as an assistant, and
   shortly thereafter reconciled with the Elector and introduced Leibniz
   to him. Leibniz then dedicated an essay on law to the Elector in the
   hope of obtaining employment. The stratagem worked; the Elector asked
   Leibniz to assist with the redrafting of the legal code for his
   Electorate. In 1669, Leibniz was appointed Assessor in the Court of
   Appeal. Although von Boineburg died late in 1672, Leibniz remained
   under the employment of his widow until she dismissed him in 1674.

   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. He
   published an essay, under the pseudonym of a fictitious Polish
   nobleman, arguing (unsuccessfully) for the German candidate for the
   Polish crown. The main European geopolitical reality during Leibniz's
   adult life was the ambition of Louis XIV of France, backed by French
   military and economic might. Meanwhile, the Thirty Years' War had left
   German-speaking Europe exhausted, fragmented, and economically
   backward. Leibniz proposed to protect German-speaking Europe by
   distracting Louis as follows. France would be invited to take Egypt as
   a stepping stone towards an eventual conquest of the Dutch East Indies.
   In return, France would agree to leave Germany and the Netherlands
   undisturbed. This plan obtained the Elector's cautious support. In
   1672, the French government invited Leibniz to Paris for discussion,
   but the plan was soon overtaken by events and became moot. Napoleon's
   failed invasion of Egypt in 1798 can 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.

   When it became clear that France would not implement its part of
   Leibniz's Egyptian plan, the Elector sent his nephew, escorted by
   Leibniz, on a related mission to the British government in London,
   early in 1673. There Leibniz made the acquaintance of Henry Oldenburg
   and John Collins. After demonstrating to the Royal Society a
   calculating machine he had been designing and building since 1670, the
   first such machine that could execute all four basic arithmetical
   operations, the Society made him an external member. The mission ended
   abruptly when news reached it of the Elector's death, whereupon Leibniz
   promptly returned to Paris and not, as had been planned, to Mainz.

   The sudden deaths of Leibniz's two patrons in the same winter meant
   that Leibniz had to find a new basis for his career. In this regard, a
   1669 invitation from the Duke of Brunswick to visit Hanover proved
   fateful. Leibniz declined the invitation, but began corresponding with
   the Duke in 1671. In 1673, the Duke offered him the post of Counsellor
   which Leibniz very reluctantly accepted two years later, only after it
   became clear that no employment in Paris, whose intellectual
   stimulation he relished, or with the Hapsburg imperial court was
   forthcoming.

House of Hanover 1676-1716

   Leibniz managed to delay his arrival in Hanover until the end of 1676,
   after making one more short journey to London, where he was shown some
   of Newton's unpublished work on the calculus. This fact was deemed
   evidence supporting the accusation, made decades later, that he had
   stolen the calculus from Newton. On the journey from London to Hanover,
   Leibniz stopped in The Hague where he met 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.

   In 1677, he was promoted, at his request, to Privy Counselor of
   Justice, a post he held for the rest of his life. Leibniz served three
   consecutive rulers of the House of Brunswick as historian, political
   adviser, and most consequentially, as librarian of the ducal library.
   He thenceforth employed his pen on all the various political,
   historical, and theological matters involving the House of Brunswick;
   the resulting documents form a valuable part of the historical record
   for the period.
   Leibniz
   Enlarge
   Leibniz

   Among the few people in north Germany to warm to Leibniz were the
   Electress Sophia of Hanover (1630-1714), her daughter Sophia Charlotte
   of Hanover (1668-1705), the Queen of Prussia and her avowed disciple,
   and Caroline of Ansbach, the consort of her grandson, the future George
   II. To each of these women he was correspondent, adviser, and friend.
   In turn, they all warmed to him more than did their spouses and the
   future king George I of Great Britain.

   The population of Hanover was only about 10,000, and its provinciality
   eventually grated on Leibniz. Nevertheless, to be a major courtier to
   the House of Brunswick was quite an honour, especially in light of the
   meteoric rise in the prestige of that House during Leibniz's
   association with it. In 1692, the Duke of Brunswick became a hereditary
   Elector of the Holy Roman Empire. By virtue of being a granddaughter of
   James I, the Electress Sophia was in the line of succession to the
   British throne. Moreover she was neither Catholic nor married to one.
   Invoking these facts, the British Act of Settlement of 1701 designated
   her and her descent as the royal family of the United Kingdom, once
   both King William III and his sister-in-law and successor, Queen Anne,
   were dead. Leibniz played a role in the initiatives and negotiations
   leading up to that Act, but not always an effective one. For example,
   something he published anonymously in England, thinking to promote the
   Brunswick cause, was formally censured by the British Parliament.

   The Brunswicks tolerated the enormous effort Leibniz devoted to
   intellectual pursuits unrelated to his duties as a courtier, pursuits
   such as perfecting the calculus, writing about other mathematics,
   logic, physics, and philosophy, and keeping up a vast correspondence.
   He began working on the calculus in 1674; the earliest evidence of its
   use in his surviving notebooks is 1675. By 1677 he had a coherent
   system in hand, but did not publish it until 1684. Leibniz's most
   important mathematical papers were published between 1682 and 1692,
   usually in a journal which he and Otto Mencke founded in 1682, the Acta
   Eruditorum. That journal played a key role in advancing his
   mathematical and scientific reputation, which in turn enhanced his
   eminence in diplomacy, history, theology, and philosophy.

   The Elector Ernst August commissioned Leibniz to write a history of the
   House of Brunswick, going back to the time of Charlemagne or earlier,
   hoping that the resulting book would advance his dynastic ambitions.
   From 1687 to 1690, Leibniz traveled extensively in Germany, Austria,
   and Italy, seeking and finding archival materials bearing on this
   project. Decades went by but no history appeared; the next Elector
   became quite annoyed at Leibniz's apparent dilatoriness. Leibniz never
   finished the project, in part because of his huge output on many other
   fronts, but also because he insisted on writing a meticulously
   researched and erudite book based on archival sources, when his patrons
   would have been quite happy with a short popular book, one perhaps
   little more than a genealogy with commentary, to be completed in three
   years or less. They never knew that he had in fact carried out a fair
   part of his assigned task: when the material Leibniz had written and
   collected for his history of the House of Brunswick was finally
   published in the 19th century, it filled three volumes.

   In 1711, John Keill, writing in the journal of the Royal Society and
   with Newton's presumed blessing, accused Leibniz of having plagiarized
   Newton's calculus. Thus began the calculus priority dispute which
   darkened the remainder of Leibniz's life. A formal investigation by the
   Royal Society (in which Newton was an unacknowledged participant),
   undertaken in response to Leibniz's demand for a retraction, upheld
   Keill's charge. Historians of mathematics writing since 1900 or so have
   tended to acquit Leibniz, pointing to important differences between
   Leibniz's and Newton's versions of the calculus.

   In 1711, while traveling in northern Europe, the Russian Tsar Peter the
   Great stopped in Hanover and met Leibniz, who then took some interest
   in matters Russian over the rest of his life. In 1712, Leibniz began a
   two year residence in Vienna, where he was appointed Imperial Court
   Councillor to the Habsburgs. On the death of Queen Anne in 1714,
   Elector Georg Ludwig became King George I of Great Britain, under the
   terms of the 1701 Act of Settlement. Even though Leibniz had done much
   to bring about this happy event, it was not to be his hour of glory.
   Despite the intercession of the Princess of Wales, Caroline of Ansbach,
   George I forbade Leibniz to join him in London until he completed at
   least one volume of the history of the Brunswick family his father had
   commissioned nearly 30 years earlier. Moreover, for George I to include
   Leibniz in his London court would have been deemed insulting to Newton,
   who was seen as having won the calculus priority dispute and whose
   standing in British official circles could not have been higher.
   Finally, his dear friend and defender, the dowager Electress Sophia,
   died in 1714.

   Leibniz died in Hanover in 1716: at the time, he was so out of favor
   that neither George I (who happened to be near Hanover at the time) nor
   any fellow courtier other than his personal secretary attended the
   funeral. Even though Leibniz was a life member of the Royal Society and
   the Berlin Academy of Sciences, neither organization saw fit to honour
   his passing. His grave went unmarked for more than 50 years. Thus the
   indifference of official Germany and England to the passing of the most
   accomplished European mind since Aristotle. Leibniz was eulogized by
   Fontenelle, before the Academie des Sciences in Paris, which had
   admitted him as a foreign member in 1700. The eulogy was composed at
   the behest of the Duchess of Orleans, a niece of the Electress Sophia.

   Leibniz never married. He complained on occasion about money, but the
   fair sum he left to his sole heir, his sister's stepson, proved that
   the Brunswicks had, by and large, paid him well. In his diplomatic
   endeavors, he at times verged on the unscrupulous, as was all too often
   the case with professional diplomats of his day. On several occasions,
   Leibniz backdated and altered personal manuscripts, actions which
   cannot be excused or defended and which put him in a bad light during
   the calculus controversy. On the other hand, he was charming and
   well-mannered, with many friends and admirers all over Europe.

Writings

   Leibniz wrote in three languages: scholastic Latin, French, and (least
   often) German. During his lifetime, he published many pamphlets and
   scholarly articles, but only two "philosophical" books, the
   Combinatorial Art and the Théodicée. (He published numerous pamphlets,
   often anonymous, on behalf of the House of Brunswick-Lüneburg, most
   notably the "De jure suprematum" a major consideration of the nature of
   sovereignty. Only one substantial book appeared posthumously, his
   Nouveaux essais sur l'entendement humain. 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:


   Gottfried Leibniz

   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 in ( Mates III:
                                    194))


   Gottfried Leibniz

   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.

Posthumous reputation

   When Leibniz died, his reputation was in decline. He was remembered for
   only one book, the Théodicée, whose supposed central argument Voltaire
   lampooned in his Candide. Voltaire's depiction of Leibniz's ideas was
   so influential that many believed it to be an accurate description
   (this misapprehension may still be the case among certain lay people).
   Thus Voltaire and his Candide bear some of the blame for the lingering
   failure to appreciate and understand Leibniz's ideas. Leibniz had an
   ardent disciple, Christian Wolff, whose dogmatic and facile outlook did
   Leibniz's reputation much harm. In any event, philosophical fashion was
   moving away from the rationalism and system building of the 17th
   century, of which Leibniz had been such an ardent exponent. His work on
   law, diplomacy, and history was seen as of ephemeral interest. The
   vastness and richness of his correspondence went unsuspected.

   Much of Europe came to doubt that Leibniz had invented the calculus
   independently of Newton, and hence his whole work in mathematics and
   physics was neglected. Voltaire, an admirer of Newton, also wrote
   Candide at least in part to discredit Leibniz's claim to having
   discovered the calculus and Leibniz's charge that Newton's theory of
   universal gravitation was incorrect. The rise of relativity and
   subsequent work in the history of mathematics has put Leibniz's stance
   in a more favorable light.

   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, Samuel Clarke, 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, especially
   Russell's, were subsequently challenged, they made Leibniz somewhat
   respectable among 20th century analytical and linguistic philosophers.
   For example, Leibniz's phrase salva veritate, meaning
   interchangeability without loss of or compromising the truth, recurs in
   Willard Quine's writings. Nevertheless, the secondary literature on
   Leibniz did not really blossom until after World War II. This is
   especially true of English speaking countries; in Gregory Brown's
   bibliography fewer than 30 of the English language entries were
   published before 1946. American Leibniz studies owe much to Leroy
   Loemker (1904-85) through his translations ( Loemker) and his
   interpretive essays in ( LeClerc).

   Nicholas Jolley ( Jolley 217-19) has surmised that Leibniz's reputation
   as a philosopher is now perhaps higher than at any time since he was
   alive because:
     * Work in the history of 17th and 18th century ideas has revealed
       more clearly the 17th century "Intellectual Revolution" that
       preceded the better known Industrial and commercial revolutions of
       the 18th and 19th centuries.
     * The doctrinaire contempt for metaphysics, characteristic of
       analytic and linguistic philosophy, has faded;
     * Analytic and contemporary philosophy continue to invoke his notions
       of identity, individuation, and possible worlds;
     * The 17th and 18th century belief that natural science, especially
       physics, differs from philosophy mainly in degree and not in kind,
       is no longer dismissed out of hand. That modern science includes a
       "scholastic" as well as a "radical empiricist" element is more
       accepted now than in the early 20th century;
     * He is now seen as a major prolongation of the mighty endeavor begun
       by Plato and Aristotle: the universe and man's place in it are
       amenable to human reason.

   In 1985, the German government created the Leibniz Prize, annual awards
   of 1.55 million Euros for experimental results, and 770,000 Euros for
   theoretical ones. It is the world's largest prize for scientific
   achievement.

Philosopher

   It is very difficult to grasp Leibniz's philosophical thinking, because
   his philosophical writings consist mainly of a multitude of short
   pieces: journal articles, manuscripts published long after his death,
   and many letters to many correspondents. He only wrote two
   philosophical treatises, and the only one he published in his lifetime,
   the Théodicée of 1710, is as much theological as philosophical. Leibniz
   dated his beginning as a philosopher to his Discourse on Metaphysics,
   which he composed in 1686 as a commentary on a running dispute between
   Malebranche and Antoine Arnauld. This led to an extensive and valuable
   correspondence with Arnauld ( Ariew & Garber 69, Loemker §§36,38); it
   and the Discourse were not published until the 19th century. In 1695,
   Leibniz made his public entrée into European philosophy with a journal
   article titled "New System of the Nature and Communication of
   Substances" ( Ariew & Garber 138, Loemker §47, Wiener II.4). Over
   1695-1705, he composed his New Essays on Human Understanding, a lengthy
   commentary on John Locke's 1690 An Essay Concerning Human
   Understanding, but upon learning of Locke's 1704 death, lost the desire
   to publish it, so that the New Essays were not published until 1765.
   The Monadologie, composed in 1714 and published posthumously, consists
   of 90 aphorisms.

   Leibniz met Spinoza in 1676, read some of his unpublished writings, and
   has since been suspected of appropriating some of Spinoza's ideas.
   While Leibniz admired Spinoza's powerful intellect, he was also
   forthrightly dismayed by Spinoza's conclusions, ( Ariew & Garber
   272-84, Loemker §§14,20,21, Wiener III.8) especially when these were
   inconsistent with Christian orthodoxy.

   Unlike Descartes and Spinoza, Leibniz had a thorough university
   education in philosophy. His lifelong scholastic and Aristotelian turn
   of mind betrayed the strong influence of one of his Leipzig professors,
   Jakob Thomasius, who also supervised his BA thesis in philosophy.
   Leibniz also eagerly read Francisco Suarez, a Spanish Jesuit respected
   even in Lutheran universities. Leibniz was deeply interested in the new
   methods and conclusions of Descartes, Huygens, Newton, and Boyle, but
   viewed their work through a lens heavily tinted by scholastic notions.
   Yet it remains the case that Leibniz's methods and concerns often
   anticipate the logic, and analytic and linguistic philosophy of the
   20th century.

The Principles

   Leibniz variously invoked one or another of seven fundamental
   philosophical Principles (Mates 1986: chpts. 7.3, 9):
     * Identity / Contradiction. If a proposition is true, its negation is
       false and vice versa.
     * Identity of indiscernibles. Two things are identical if and only if
       they share the same properties. Frequently invoked in modern logic
       and philosophy.
     * 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." (LL 717).
     * Pre-established harmony. See Jolley (1995: 129-31), Woolhouse and
       Francks (1998), and Mercer (2001). "[T]he appropriate nature of
       each substance brings it about that what happens to one corresponds
       to what happens to all the others, without, however, their acting
       upon one another directly." (Discourse on Metaphysics, XIV) A
       dropped glass shatters because it "knows" it has hit the ground,
       and not because the impact with the ground "compels" the glass to
       split.
     * Continuity. Natura non saltum facit. A mathematical analog to this
       principle would go as follows. If a function describes a
       transformation of something to which continuity applies, its domain
       and range are both dense sets.
     * Optimism. "God assuredly always chooses the best." (LL 311).
     * Plenitude. "Leibniz believed that the best of all possible worlds
       would actualize every genuine possibility, and argued in Théodicée
       that this best of all possible worlds will contain all
       possibilities, with our finite experience of eternity giving no
       reason to dispute nature's perfection." (From Plenitude.)

   The converse of the second principle, known as the Indiscernibility of
   identicals, together with the Identity of Indiscernibles is often
   referred to as Leibniz's Law . However, it is the Identity of
   Indiscernibles that has attracted the most controversy and criticism,
   especially from corpuscular philosophy and quantum mechanics.

   Leibniz would on occasion give a rationale for a specific principle,
   but more often took them for granted. For a precis of what Leibniz
   meant by these and other Principles, see Mercer (2001: 473-84). For a
   classic discussion of Sufficient Reason and Plenitude, see Lovejoy
   (1957).

The Monads

   Leibniz's best known contribution to metaphysics is his theory of
   monads, as exposited in his Monadologie. Monads are to the mental realm
   what atoms are to the physical. Monads are the ultimate elements of the
   universe, and are also entities of perception. The monads are
   "substantial forms of being" with the following properties: they are
   eternal, indecomposable, individual, subject to their own laws,
   un-interacting, and each reflecting the entire universe in a
   pre-established harmony (a historically important example of
   panpsychism). 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 atoms, monads possess no material or spatial character. They
   also differ from atoms 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
   preprogrammed set of "instructions" peculiar to itself, so that a monad
   "knows" what to do at each moment. (These "instructions" may be seen as
   analogs of the scientific laws governing subatomic particles.) By
   virtue of these intrinsic instructions, each monad is like a little
   mirror of the universe. Monads need not be "small"; e.g., each human
   being constitutes a monad, in which case free will is problematic. God,
   too, is a monad, and God's existence can be inferred from the harmony
   prevailing among all other monads; God wills the pre-established
   harmony.

   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.

   The monadology was thought arbitrary, even eccentric, in Leibniz's day
   and since.

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. However,
   scientific developments in recent decades enable a more sweeping
   defense of optimism:
    1. The 3+1 dimensional structure of spacetime may be ideal. In order
       to sustain complexity such as life, a universe probably requires
       three spatial and one temporal dimensions. Most universes deviating
       from 3+1 either violate some fundamental physical laws, or are
       impossible. The mathematically richest number of spatial dimensions
       is also 3.
    2. The universe, solar system, and Earth are the "best possible" in
       that they enable intelligent life to exist. Such life has evolved
       on Earth only because the Earth, solar system, and Milky Way
       possess a number of unusual characteristics; see Ward & Brownlee
       (2000), Morris (2003: chpts. 5,6).
    3. The most sweeping form of optimism derives from the Anthropic
       Principle (Barrow and Tipler 1986). Physical reality 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 unlikely that the resulting
       universe would contain complex structures.

   Our physical laws, universe, solar system, and home planet are all
   "best" in the sense that they enable complex structures such as
   galaxies, stars, and, ultimately, intelligent life.

Symbolic thought

   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 thought symbols very important for human understanding. He
   attached so much importance to the invention of good notations that he
   attributed to this alone the whole of his discoveries in mathematics.
   His notation for the infinitesimal calculus affords a splendid example
   of his skill in this regard. Charles Peirce, a 19th century pioneer of
   semiotics, shared Leibniz's passion for symbols and notation, and his
   belief that these are essential to a well-running logic and
   mathematics.

   But Leibniz took his speculations much further. Defining a character as
   any written sign, he then defined a "real" character as one that
   represents an idea directly and not simply the word embodying the idea.
   Some real characters, such as the notation of logic, serve only to
   facilitate reasoning. Many characters well-known in his day, including
   Egyptian hieroglyphics, Chinese characters, and the symbols of
   astronomy and chemistry, he deemed not real, however Loemker, who
   translated some of Leibniz's works into English said that the symbols
   of chemistry were real characters so there is disagreement among
   Leibniz scholars on this point. Instead, 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.

   What Leibniz actually intended by his characteristica universalis and
   calculus ratiocinator, and the extent to which modern formal logic does
   justice to the calculus, may perhaps never be unambiguously
   established. A good introductory discussion of the "characteristic" is
   Jolley (1995: 226-40). An early yet still classic discussion of the
   "characteristic" and "calculus" is Couturat (1901: chpts. 3,4).

   The importance of the characteristica and calculus goes beyond their
   value for understanding Leibniz's legacy, and extends to mathematics,
   modernity, the European Enlightenment, and, more controversially, even
   to postmodern theory. The characteristica and calculus are also
   possible ways in which Leibniz's thinking can contribute to
   contemporary thinking in thermodynamics, biology, climate change, and
   resource policy, and consequently how ethics and metaphysics can
   meaningfully engage with such currently topical issues. Moreover,
   computer software employing networks of block diagrams and pictograms
   to generate the mathematics and kinetics of ecological, thermodynamic,
   and dynamic socioeconomic systems, all appear to aim at formal systems
   of the sort Leibniz dreamed about.

Formal logic

   Leibniz is 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. The principles of Leibniz's logic and,
   arguably, of his whole philosophy, reduce to two:
    1. All our ideas are compounded from a very small number of simple
       ideas, which form the alphabet of human thought.
    2. Complex ideas proceed from these simple ideas by a uniform and
       symmetrical combination, analogous to arithmetical multiplication.

   With regard to (1), the number of simple ideas is much greater than
   Leibniz thought. As for (2), logic can indeed be grounded in a
   symmetrical combining operation, but that operation is analogous to
   either of addition or multiplication. The formal logic that emerged
   early in the 20th century also requires, at minimum, unary negation and
   quantified variables ranging over some universe of discourse.

   Leibniz published nothing on formal logic in his lifetime; most of what
   he wrote on the subject consists of working drafts.

   In his book History of Western Philosophy Bertrand Russell went as far
   as claiming that Leibniz had developed logic in his unpublished
   writings to a level which was reached only two hundred years
   afterwards.

Mathematician

   Although the mathematical notion of function was implicit in
   trigonometric and logarithmic tables, which existed in his day, Leibniz
   was the first, in 1692 and 1694, to employ it explicitly, to denote any
   of several geometric concepts derived from a curve, such as abscissa,
   ordinate, tangent, chord, and the perpendicular (Struik 1969: 367). In
   the 18th century, "function" lost these geometrical associations.

   Leibniz was the first to see that the coefficients of a system of
   linear equations could be arranged into arrays, now called matrices,
   which can be manipulated to find the solution of the system, if any.
   This method was later called Cramer's Rule. Leibniz's discoveries of
   Boolean algebra and of symbolic logic, also relevant to mathematics,
   are discussed in the preceding section.

   A comprehensive scholarly treatment of Leibniz's mathematical writings
   has yet to be written, perhaps because Series 7 of the Academy edition
   is very far from complete.

Calculus

   Leibniz is credited, along with Isaac Newton, with the discovery of
   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. This
   ingenious and suggestive notation for the calculus is probably his most
   enduring mathematical legacy. Leibniz did not publish anything about
   his calculus until 1684. For an English translation of this paper, see
   Struik (1969: 271-84), who also translates parts of two other key
   papers by Leibniz on the calculus. 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. Leibniz also freely invoked mathematical
   entities he called infinitesimals, manipulating them 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.

   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.
   Hall (1980) gives a thorough scholarly discussion of the calculus
   priority dispute.

   Modern, rigorous calculus emerged in the 19th century, thanks to the
   efforts of Cauchy, Riemann, Weierstrass, and others, who based their
   work on the definition of a limit and on a precise understanding of
   real numbers. Their work discredited the use of infinitesimals to
   justify calculus. However, infinitesimals survived in science and
   engineering, and even in rigorous mathematics, via the fundamental
   computational device known as the differential. Beginning in 1960,
   Abraham Robinson worked out a rigorous foundation for Leibniz's
   infinitesimals, using model theory. The resulting nonstandard analysis
   can be seen as a belated vindication of Leibniz's mathematical
   reasoning.

Topology

   Leibniz was the first to employ the term analysis situs (LL §27), later
   employed in the 19th century to refer to what is now known as topology.
   There are two takes on this situation. On the one hand, Mates (1986:
   240), citing a 1954 paper in German by Freudenthal, argues as follows:

     "Although for [Leibniz] the situs of a sequence of points is
     completely determined by the distance between them and is altered if
     those distances are altered, his admirer Euler, in the famous 1736
     paper solving the Konigsberg Bridge Problem and its generalizations,
     used the term geometria situs in such a sense that the situs remains
     unchanged under topological deformations. He mistakenly credits
     Leibniz with originating this concept. ...it is sometimes not
     realized that Leibniz used the term in an entirely different sense
     and hence can hardly be considered the founder of that part of
     mathematics."

   Hirano (1997) argues differently, quoting Mandelbrot (1977: 419) as
   follows:

     "...To sample Leibniz' scientific works is a sobering experience.
     Next to calculus, and to other thoughts that have been carried out
     to completion, the number and variety of premonitory thrusts is
     overwhelming. We saw examples in 'packing,'... My Leibniz mania is
     further reinforced by finding that for one moment its hero attached
     importance to geometric scaling. In "Euclidis Prota"..., which is an
     attempt to tighten Euclid's axioms, he states,...: 'I have diverse
     definitions for the straight line. The straight line is a curve, any
     part of which is similar to the whole, and it alone has this
     property, not only among curves but among sets.' This claim can be
     proved today."

   Thus Mandelbrot's well-known fractal geometry drew on Leibniz's notions
   of self-similarity and the principle of continuity: natura non facit
   saltus. We also see that when Leibniz wrote, in a metaphysical vein,
   that "the straight line is a curve, any part of which is similar to the
   whole..." he was anticipating topology by more than two centuries. As
   for "packing," Leibniz told to his friend and correspondent Des Bosses
   to imagine a circle, then to inscribe within it three congruent circles
   with maximum radius; the latter smaller circles could be filled with
   three even smaller circles by the same procedure. This process can be
   continued infinitely, from which arises a good idea of self-similarity.
   Leibniz's improvement of Euclid's axiom contains the same concept.

Scientist and engineer

   Leibniz's writings are currently discussed, not only for their
   anticipations and possible discoveries not yet recognized, but as ways
   of advancing present knowledge. Much of his writing on physics is
   included in Gerhardt's Mathematical Writings. His writings on other
   scientific and technical subjects are mostly scattered and relatively
   little known, because the Academy edition has yet to publish any volume
   in its Series Scientific, Medical, and Technical Writings .

Physics

   Leibniz contributed a fair amount to the statics and dynamics emerging
   about him, often disagreeing with Descartes and Newton. He devised a
   new theory of motion ( dynamics) based on kinetic and potential energy,
   which posited space as relative, whereas Newton felt strongly space was
   absolute. While he may have been Newton's peer as co-discoverer of
   calculus, he was not in Newton's league as a physicist and may even
   deserve to be ranked below his mentor Huygens. An important example of
   Leibniz's mature physical thinking is his Specimen Dynamicum of 1695.
   (AG 117, LL §46, W II.5) On Leibniz and physics, see the chapter by
   Garber in Jolley (1995) and Wilson (1989).

   Until the discovery of subatomic particles and the quantum mechanics
   governing them, many of Leibniz's speculative ideas about aspects of
   nature not reducible to statics and dynamics made little sense. For
   instance, he anticipated Einstein by arguing, against Newton, that
   space, time and motion are relative, not absolute. Leibniz's rule in
   interacting theories plays a role in supersymmetry and in the lattices
   of quantum mechanics. His principle of sufficient reason has been
   invoked in recent cosmology, and his identity of indiscernibles in
   quantum mechanics, a field some even credit him with having anticipated
   in some sense. Those who advocate digital philosophy, a recent
   direction in cosmology, claim Leibniz as a precursor.

The vis viva

   Leibniz 's vis viva (Latin for living force) is an invariant
   mathematical characteristic of certain mechanical systems (see AG
   155-86, LL §§53-55, W II.6-7a). It can be seen as a special case of the
   conservation of energy. Here too his thinking gave rise to another
   regrettable nationalistic dispute. His "vis viva" was seen as rivaling
   the conservation of momentum championed by Newton in England and by
   Descartes in France; hence academics in those countries tended to
   neglect Leibniz's idea. Engineers eventually found "vis viva" useful
   when making certain calculations, so that the two approaches eventually
   were seen as complementary.

Other natural science

   By proposing that the earth has a molten core, he anticipated modern
   geology. In embryology, he was a preformationist, but also proposed
   that organisms are the outcome of a combination of an infinite number
   of possible microstructures and of their powers. In the life sciences
   and paleontology, he revealed an amazing transformist intuition, fueled
   by his study of comparative anatomy and fossils. He worked out a primal
   organismic theory. On Leibniz and biology, see Loemker (1969a: VIII).
   In medicine, he exhorted the physicians of his time -- with some
   results -- to ground their theories in detailed comparative
   observations and verified experiments, and to distinguish firmly
   scientific and metaphysical points of view.

Social science

   In psychology he anticipated the distinction between conscious and
   unconscious states. On Leibniz and psychology, see Loemker (1969a: IX).
   In public health, he advocated establishing a medical administrative
   authority, with powers over epidemiology and veterinary medicine. He
   worked to set up a coherent medical training programme, oriented
   towards public health and preventive measures. In economic policy, he
   proposed tax reforms and a national insurance scheme, and discussed the
   balance of trade. He even proposed something akin to what much later
   emerged as game theory. In sociology he laid the ground for
   communication theory.

Technology

   In 1906, Gerland published a volume of Leibniz's writings bearing on
   his many practical inventions and engineering work. To date, few of
   these writings have been translated into English. Nevertheless, it is
   well understood that Leibniz was a serious inventor, engineer, and
   applied scientist, with great respect for practical life. Following the
   motto theoria cum praxis, he urged that theory be combined with
   practical application, and thus has been claimed as the father of
   applied science. He designed wind-driven propellers and water pumps,
   mining machines to extract ore, hydraulic presses, lamps, submarines,
   clocks, etc. With Denis Papin, he invented a steam engine. He even
   proposed a method for desalinating water. He struggled, 1680-85, to
   overcome the chronic flooding that afflicted the ducal silver mines in
   the Harz Mountains, but his efforts were not crowned with success.
   (Aiton 1985: 107-114, 136)

Information technology

   Leibniz may have been the first computer scientist and information
   theorist. Early in life, he discovered the binary number system (base
   2), the one subsequently employed on most computers, then revisited
   that system throughout his career. On Leibniz and binary numbers, see
   Couturat (1901: 473-78). Leibniz anticipated Lagrangian interpolation
   and algorithmic information theory. His calculus ratiocinator
   anticipated aspects of the universal Turing machine. In 1934, Norbert
   Wiener claimed to have found in Leibniz's writings a mention of the
   concept of feedback, central to Wiener's later cybernetic theory.

   In 1671, Leibniz began to invent a machine that could execute all four
   arithmetical operations, gradually improving it over a number of years.
   This ' Stepped Reckoner' attracted fair attention and was the basis of
   his election to the Royal Society in 1673. A number of such machines
   were made during his years in Hanover, by a craftsman working under
   Leibniz's supervision. It was not an unambiguous success because it did
   not fully mechanize the operation of carrying. Couturat (1901: 115)
   reported finding an unpublished note by Leibniz, dated 1674, describing
   a machine capable of performing some algebraic operations.

   Leibniz was groping towards hardware and software concepts worked out
   much later by Charles Babbage and Ada Lovelace, 1830-45. In 1679, while
   mulling over his binary arithmetic, Leibniz imagined a machine in which
   binary numbers were represented by marbles, governed by a rudimentary
   sort of punched cards. Modern electronic digital computers replace
   Leibniz's marbles moving by gravity with shift registers, voltage
   gradients, and pulses of electrons, but otherwise they run roughly as
   Leibniz envisioned in 1679. Davis (2000) discusses Leibniz's prophetic
   role in the emergence of calculating machines and of formal languages.

The librarian

   In his capacity as librarian of the ducal libraries in Hanover and
   Wolfenbuettel, Leibniz effectively became one of the founders of
   library science. The latter library was enormous for its day, as it
   contained more than 100,000 volumes, and Leibniz helped design a new
   building for it, believed to be the first building explicitly designed
   to be a library. He also designed a book indexing system in ignorance
   of the only other such system then extant, that of the Bodleian Library
   at Oxford University. He also called on publishers to distribute
   abstracts of all new titles they produced each year, in a standard form
   that would facilitate indexing. He hoped that this abstracting project
   would eventually include everything printed from his day back to
   Gutenberg. Neither proposal met with success at the time, but something
   like them became standard practice among English language publishers
   during the 20th century, under the aegis of the Library of Congress and
   the British Library.

   He called for the creation of an empirical database as a means of
   furthering all the sciences. His characteristica universalis, calculus
   ratiocinator, and a "community of minds"—intended, among other things,
   to bring political and religious unity to Europe—can be seen as distant
   unwitting anticipations of artificial languages (e.g., Esperanto and
   its rivals), symbolic logic, even the World Wide Web.

Advocate of scientific societies

   Leibniz emphasized that research was a collaborative endeavor. Hence he
   warmly advocated the formation of national scientific societies along
   the lines of the British Royal Society and the French Academie Royale
   des Sciences. More specifically, in his correspondence and travels he
   urged the creation of such societies in Dresden, Saint Petersburg,
   Vienna, and Berlin. Only one such project came to fruition; in 1700,
   the Berlin Academy of Sciences was created. Leibniz drew up its first
   statutes, and served as its first President for the remainder of his
   life. That Academy evolved into the German Academy of Sciences, the
   publisher of the ongoing critical edition of his works. On Leibniz’s
   projects for scientific societies, see Couturat (1901: App. IV).

Lawyer, moralist

   No philosopher has ever had as much experience with practical affairs
   of state as Leibniz, Marcus Aurelius possibly excepted. Leibniz's
   writings on law, ethics, and politics (e.g., AG 19, 94, 111, 193; Riley
   1988; LL §§2, 7, 20, 29, 44, 59, 62, 65; W I.1, IV.1-3) were long
   overlooked by English speaking scholars but this has changed of late;
   see (in order of difficulty) Jolley (2005: chpt. 7), Gregory Brown's
   chapter in Jolley (1995), Hostler (1975), and Riley (1996).

   While Leibniz was no apologist for absolute monarchy like Hobbes, or
   for tyranny in any form, neither did he echo the political and
   constitutional views of his contemporary John Locke, views invoked in
   support of democracy, first in 18th century America and subsequently
   elsewhere. The following excerpt from a 1695 letter to Baron J. C.
   Boineburg's son Philipp is very revealing of Leibniz's political
   sentiments:

     "As for.. the great question of the power of sovereigns and the
     obedience their peoples owe them, I usually say that it would be
     good for princes to be persuaded that their people have the right to
     resist them, and for the people, on the other hand, to be persuaded
     to obey them passively. I am, however, quite of the opinion of
     Grotius, that one ought to obey as a rule, the evil of revolution
     being greater beyond comparison than the evils causing it. Yet I
     recognize that a prince can go to such excess, and place the
     well-being of the state in such danger, that the obligation to
     endure ceases. This is most rare, however, and the theologian who
     authorizes violence under this pretext should take care against
     excess; excess being infinitely more dangerous than deficiency."
     (LL: 59, fn 16. Translation revised.)

   Leibniz foresaw the European Union. In 1677, he (LL: 58, fn 9) called
   for a European confederation, governed by a council or senate, whose
   members would represent entire nations and would be free to vote their
   consciences. Europe would adopt a uniform religion. He reiterated these
   proposals in 1715.

Ecumenism

   Leibniz devoted considerable intellectual and diplomatic effort to what
   would now be called ecumenical endeavor, seeking to reconcile first the
   Roman Catholic and Lutheran churches, later the Lutheran and Reformed
   churches. In this respect, he followed the example of his early
   patrons, Baron von Boineburg and the Duke John Frederick, both cradle
   Lutherans who converted to Catholicism as adults, who did what they
   could to encourage the reunion of the two faiths, and who warmly
   welcomed such endeavors by others. (The House of Brunswick remained
   Lutheran because the Duke's children did not follow their father.)
   These efforts included corresponding with the French bishop Bossuet,
   and involved Leibniz in a fair bit of theological controversy. He
   evidently thought that the thoroughgoing application of reason would
   suffice to heal the breach caused by the Reformation.

Philologist

   Leibniz was an avid student of languages, eagerly latching on to any
   information about vocabulary and grammar that came his way. He refuted
   the belief, widely held by Christian scholars in his day, that Hebrew
   was the primeval language of the human race. He also refuted the
   argument, advanced by Swedish scholars in his day, that some sort of
   proto- Swedish was the ancestor of the Germanic languages. He puzzled
   over the origins of the Slavic languages, was aware of the existence of
   Sanskrit, and was fascinated by classical Chinese. Scholarly
   appreciation of Leibniz the philologist is hampered by the fact that no
   volume of the planned Academy edition series "Historical and Linguistic
   Writings" has appeared.

Sinophile

   Leibniz was perhaps the first major European intellect to take a close
   interest in Chinese civilization, which he knew by corresponding with,
   and reading other work by, European Christian missionaries posted in
   China. He concluded that Europeans could learn much from the Confucian
   ethical tradition. He mulled over the possibility that the Chinese
   characters were an unwitting form of his universal characteristic. He
   noted with fascination how the I Ching hexagrams correspond to the
   binary numbers from 0 to 111111, and mistakenly concluded that this
   mapping was evidence of major Chinese accomplishments in the sort of
   philosophical mathematics he admired.

   On Leibniz, the I Ching, and binary numbers, see Aiton (1985: 245-48).
   Leibniz's writings on Chinese civilization are collected and translated
   in Cook and Rosemont (1994), and discussed in Perkins (2004).

Leibniz as polymath

   The following episode from the life of Leibniz illustrates the breadth
   of his genius, and the difficulties awaiting those who try to come to
   terms with it. While making his grand tour of European archives to
   research the Brunswick family history he never completed, Leibniz
   stopped in Vienna, May 1688 – February 1689, where he did much legal
   and diplomatic work for the Brunswicks. He visited mines, talked with
   mine engineers, and tried to negotiate export contracts for lead from
   the ducal mines in the Harz mountains. His proposal that the streets of
   Vienna be lit with lamps burning rapeseed oil was implemented. During a
   formal audience with the Austrian Emperor and in subsequent memoranda,
   he advocated reorganizing the Austrian economy, reforming the coinage
   of much of central Europe, negotiating a Concordat between the
   Habsburgs and the Vatican, and creating an imperial research library,
   official archive, and public insurance fund. He wrote and published an
   important paper on mechanics. Leibniz also wrote a short paper, first
   published by Louis Couturat in 1903, later translated as LL 267 and WF
   30, summarizing his views on metaphysics. The paper is undated; that he
   wrote it while in Vienna was determined only in 1999, when the ongoing
   critical edition finally published Leibniz's philosophical writings for
   the period 1677-90. Couturat's reading of this paper was the launching
   point for much 20th century thinking about Leibniz, especially among
   analytic philosophers. But after a meticulous study of all of Leibniz's
   philosophical writings up to 1688 -- a study the 1999 additions to the
   critical edition made possible -- Mercer (2001) begged to differ with
   Couturat's reading; the jury is still out.

   Leibniz was not devoid of humor and imagination; see W IV.6 and LL §
   40. Also see a curious passage titled "Leibniz's Philosophical Dream,"
   first published by Bodemann in 1895 and translated on p. 253 of Morris,
   Mary, ed. and trans., 1934. Philosophical Writings. Dent & Sons Ltd.

Works

   Four important collections of English translations are W (Wiener 1951),
   LL (Loemker 1969), AG (Ariew and Garber 1989), and WF (Woolhouse and
   Francks, 1998).

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

   Selected works; major ones in bold. 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)
     * 1673 Confessio philosophi (A Philosopher's Creed, English
       translation)
     * 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 & Ariew, 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 (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

   The only biography in English is Aiton (1985). 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.

   For a first introduction to Leibniz's philosophy, turn to the
   Introduction of an anthology of his writings in English translation,
   e.g., Wiener (1951), Loemker (1969a), Woolhouse and Francks (1998).
   Then turn to the monographs MacDonald Ross (1984), and Jolley (2005).
   For an introduction to Leibniz's metaphysics, see the chapters by
   Mercer, Rutherford, and Sleigh in Jolley (1995); see Mercer (2001) for
   an advanced study. For an introduction to those aspects of Leibniz's
   thought of most value to the philosophy of logic and of language, see
   Jolley (1995, chpts. 7,8); Mates (1986) is more advanced. MacRae
   (Jolley 1995: chpt. 6) discusses Leibniz's theory of knowledge. For
   glossaries of the philosophical terminology recurring in Leibniz's
   writings and the secondary literature, see Woolhouse and Francks (1998:
   285-93) and Jolley (2005: 223-29).

   Introductory:
     * Jolley, Nicholas, 2005. Leibniz. Routledge.
     * MacDonald Ross, George, 1984. Leibniz. Oxford Univ. 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).
     * Brown, Gregory, 2004, "Leibniz's Endgame and the Ladies of the
       Courts," Journal of the History of Ideas 65: 75-100.
     * Hall, A. R., 1980. Philosophers at War: The Quarrel between Newton
       and Leibniz. Cambridge Univ. Press.
     * Hostler, J., 1975. Leibniz's Moral Philosophy. UK: Duckworth.
     * Jolley, Nicholas, ed., 1995. The Cambridge Companion to Leibniz.
       Cambridge Univ. Press.
     * LeClerc, Ivor, ed., 1973. The Philosophy of Leibniz and the Modern
       World. Vanderbilt Univ. 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 Univ. Press.
     * Riley, Patrick, 1996. Leibniz's Universal Jurisprudence: Justice as
       the Charity of the Wise. Harvard Univ. Press.

   Advanced
     * Adams, Robert M., 1994. Leibniz: Determinist, Theist, Idealist.
       Oxford Uni. Press.
     * Louis Couturat, 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 Univ. 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 Univ. Press.
     * Mercer, Christia, 2001. Leibniz's metaphysics : Its Origins and
       Development. Cambridge Univ. Press.
     * Robinet, André, 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 Univ. Press.
     * Wilson, Catherine, 1989. Leibniz's Metaphysics. Princeton Univ.
       Press.
     * Woolhouse, R. S., ed., 1993. G. W. Leibniz: Critical Assessments, 4
       vols. Routledge. A remarkable one-stop collection of many valuable
       articles.

   Online bibliography by Gregory Brown.

Other works cited

     * John D. Barrow and Frank J. Tipler, 1986. The Anthropic
       Cosmological Principle. Oxford Univ. Press.
     * Martin Davis, 2000. The Universal Computer: The Road from Leibniz
       to Turing. W W Norton.
     * Du Bois-Reymond, Paul, 18nn, "Leibnizian Thoughts in Modern
       Science," ???.
     * Ivor Grattan-Guinness, 1997. The Norton History of the Mathematical
       Sciences. W W Norton.
     * Hirano, Hideaki, 1997, "Cultural Pluralism And Natural Law."
       Unpublished.
     * Reinhard Finster, Gerd van den Heuvel: Gottfried Wilhelm Leibniz.
       Mit Selbstzeugnissen und Bilddokumenten. 4. Auflage. Rowohlt,
       Reinbek bei Hamburg 2000 (Rowohlts Monographien, 50481), ISBN
       3-499-50481-2
     * Benoît Mandelbrot, 1977. The Fractal Geometry of Nature. Freeman.
     * Simon Conway Morris, 2003. Life's Solution: Inevitable Humans in a
       Lonely Universe. Cambridge Uni. Press.
     * Ward, P. D., and Brownlee, D., 2000. Rare Earth: Why Complex Life
       is Uncommon in the Universe. Springer Verlag.
     * Zalta, E. N., 2000, " A (Leibnizian) Theory of Concepts,"
       Philosophiegeschichte und logische Analyse / Logical Analysis and
       History of Philosophy 3: 137-183.

Quotations

   More quotations. Wiener (1951: 567-70) lists 44 quotable "proverbs"
   beginning with "Justice is the charity of the wise."
     * "In the realm of spirit, seek clarity; in the material world, seek
       utility." Mates's (1986: 15) translation of Leibniz's motto.
     * "With every lost hour, a part of life perishes." "Deeds make
       people." Loemker's (1969: 58) translation of other Leibniz mottoes.
     * "The monad... is nothing but a simple substance which enters into
       compounds. Simple means without parts... Monads have no windows
       through which anything could enter or leave." Monadology (LL
       §67.1,7)
     * "I maintain that men could be incomparably happier than they are,
       and that they could, in a short time, make great progress in
       increasing their happiness, if they were willing to set about it as
       they should. We have in hand excellent means to do in 10 years more
       than could be done in several centuries without them, if we apply
       ourselves to making the most of them, and do nothing else except
       what must be done." (Translated in Riley 1972: 104, and quoted in
       Mates 1986: 120)
     * "There is also a type of a middle-of-the-roader who, feeling
       embarrassed, tacks back and forth, shifts the target for himself
       and others, hides behind words and phrases, or turns and twists the
       question so long that one no longer knows what it amounted to. This
       is what Leibniz did, who was much more of a mathematician and a
       learned man than a philosopher." ( Schopenhauer, On the Freedom of
       the Will, Ch. III)
     * "It is unworthy of excellent men to lose hours like slaves in the
       labour of calculation which could safely be relegated to anyone
       else if machines were used."

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