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Gottfried Leibniz (1646–1716); "Leibniz was a polymath who made significant contributions in many areas of physics, logic, mathematics, history, librarianship, and of course philosophy and theology, while also working on ideal languages, mechanical clocks, mining machinery..."

"A universal genius if ever there was one, and an inexhaustible source of original and fertile ideas, Leibniz was all the more interested in logic because it ..."

"Gottfried Wilhelm Leibniz was maybe the last Universal Genius incessantly active in the fields of theology, philosophy, mathematics, physics, ..."

"Leibniz was perhaps the last great Renaissance man who in Bacon's words took all knowledge to be his province."

G. W. Leibniz, by Bernhard Christoph Francke ca. 1700.

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Short biographies

Leibniz: Master of All Trades
By E.T. Bell

‘Jack of all trades, master of none’ has its spectacular exception like any other folk proverb, and Gottfried Wilhelm Leibniz (1646-1716) is one of them.
Mathematics was but one of the many fields in which Leibniz showed conspicuous genius: law, religion, statecraft, history, literature, logic, metaphysics, and speculative philosophy all owe to him contributions, any one of which would have secured his fame and have preserved his memory. ‘Universal genius’ can be applied to Leibniz without hyperbole, as it cannot to Newton, his rival in mathematics and his infinite superior in natural philosophy.

“…”

Leibniz may be said to have lived not one life but several. As a diplomat, historian, philosopher, and mathematician he did enough in each field to fill one ordinary working life. Younger than Newton by about four years, he was born at Leipzig on 1 July 1646, and living only seventy years against Newton’s eighty-five, died in Hanover on 14 November 1716. His father was a professor of moral philosophy and came of a good family which had served the government of Saxony for three generations. Thus young Leibniz’ earliest years were passed in an atmosphere of scholarship heavily charged with politics.
At the age of six, he lost his father, but not before he had acquired from him a passion for history. Although he attended a school in Leipzig, Leibniz was largely self-taught by incessant reading in his father’s library. At eight he began the study of Latin and by twelve had mastered it sufficiently to compose creditable Latin verse. From Latin he passed on to Greek which he also learned largely by his own efforts.
At this stage his mental development parallels that of Descartes: classical studies no longer satisfied him and he turned to logic. From his attempts as a boy of less than fifteen to reform logic as presented by the classicists, the scholastics, and the Christian fathers, developed the first gems of his Characteristica Universalis or Universal Mathematics, which, as has been shown by Couturat, Russell, and others, is the clue to his metaphysics. The symbolic logic invented by Boole in 1847-54 is only that part of the Characteristica which Leibniz called calculus raticinator.
At the age of fifteen Leibniz entered the University of Leipzig as a student in law. The law, however, did not occupy all his time. In his first two years he read widely in philosophy and for the first time became aware of the new world which the modern, or ‘natural’ philosophers, Kepler, Galileo, and Descartes had discovered. Seeing that this newer philosophy could be understood only by one acquainted with mathematics, Leibniz passed the summer of 1663 at the University of Jena, where he attended the mathematical lectures of Erhard Weigel, a man of considerable local reputation but scarcely a mathematician.
On returning to Leipzig he concentrated on law. By 1666, at the age of twenty, he was throroughly prepared for his doctor’s degree in law. This is the year, we recall, in which Newton began the rustication at Woolsthorpe that gave him the calculus and his law of universal gravitation. The Leipzig faculty, bilious with jealousy, refused Leibniz his degree, officially on account of his youth, actually because he knew more about law than the whole dull lot of them.
Before this he had taken his bachelor’s degree in 1663 at the age of seventeen with a brilliant essay foreshadowing one of the cardinal doctrines of his mature philosophy. We shall not take space to go into this, but it may be mentioned that one possible interpretation of Leibniz’ essay is the doctrine of the ‘organism as a whole’, which one progressive school of biologists and another of psychologists has found attractive in our own time.
Disgusted at the pettiness of the Leipzig faculty Leibniz left his native town for good and proceeded to Nuremberg where, on 5 November 1666, at the affiliated University of Altdorf, he was not only granted his doctor’s degree at once for his essay on a new method (the historical) of teaching law, but was begged to accept the University professorship of law. But, like Descartes refusing the offer of a lieutenant-generalship because he knew what he wanted out of life, Leibniz declined, saying he had very different ambitions. What these may have been he did not divulge. It seems unlikely that they could have been the higher pettifogging for princelets into which fate presently kicked him. Leibniz’s strategy was that he met the lawyers before the scientists.

“…”

Up till 1672 Leibniz knew but little of what in his time was modern mathematics. He was then twenty-six when his real mathematical education began at the hands of Huygens, whom he met in Paris in the intervals between one diplomatic plot and another. Christian Huygens (1629-95), while primarily a physicist, some of whose best work went into horology and the undulatory theory of light, was an accomplished mathematician. Huygens presented Leibniz with a copy of his mathematical work on the pendulum. Fascinated by the power of the mathematical method in competent hands, Leibniz begged Huygens to give him lessons, which Huygens, seeing that Leibniz had a first-class mind, gladly did. Leibniz had already drawn up an impressive list of discoveries he had made by means of his own methods – phases of the universal characteristic. Among these was a calculating machine far superior to Pascal’s, which handled only addition and substraction; Leibniz’ machine did also multiplication, division, and the extraction of roots. Under Huygens’ expert guidance Leibniz quickly found himself. He was a born mathematician.

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Download E.T. Bell's complete Leibniz biography here.

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Gottfried Wilhelm Leibniz was a man of astounding ability whose significant contributions to virtually every discipline—from history, law, theology, politics, philosophy, philology, metaphysics, and diplomacy to science, mathematics, and logic—have led many to term him the Aristotle of his age. Like Aristotle, Leibniz was a paragon of thought and intellect who was apparently able to absorb all that was known of the universe in his time.

Leibniz firmly believed there was something to be learned from every book; he therefore read voraciously, without discrimination. He regarded each person he met, whatever his station, as a vitally important source of information.

Leibniz’s insatiable curiosity, coupled with his extraordinary intelligence (his I.Q. has been estimated to have been at least 180, and probably much higher), led him to explore and master every branch of learning he encountered. His achievements are all the more remarkable when one considers that Leibniz was largely self-taught.

Leibniz, the son of a professor of moral philosophy, was born on July, 1, 1646 in Leipzig. Leibniz’s father Friedrich died in 1652, when Leibniz was just six years old. From that point on, Leibniz seems to have been the primary director of his own education. He began by reading every book printed in German in his father’s excellent library. He then taught himself at eight years of age to read Latin, and at ten, Greek. By the time he was fourteen years old, Leibniz was thoroughly familiar with history and the classical literature his father so admired.

At fifteen, Leibniz entered the University of Leipzig as a student of law. He earned his bachelor’s degree two years later. By the age of twenty he had fulfilled the requirements for his doctorate; however, because of his youth or perhaps the jealousy of his professors, he was denied the degree. Leibniz left Leipzig in disgust, never to return. He enrolled at the University of Altdorf in Nuremburg, which not only awarded him the coveted degree, but offered him a professorship as well.

Leibniz refused the professorship and chose, as had three generations of his family before him, to enter the service of the dukes of Hanover. Leibniz was officially the administrator of the ducal library, a position he held for forty years under four successive masters, but was often asked by the family of Hanover to act as their diplomat and political strategist.

In 1673 Leibniz, in Paris on a diplomatic mission, encountered Christiaan Huygens, who would become his lifelong friend. The Dutch physicist introduced Leibniz to the study of mathematics, at which Leibniz proved remarkably adept. Before long, he had invented a calculating machine that improved on one earlier devised by the French mathematician Blaise Pascal. Leibniz’s machine, besides having the capacity to add and subtract, could multiply, divide, and extract roots. By 1674, Leibniz had also constructed the foundations of his crowning mathematical achievement: the invention of the calculus and a system of notation with which to express it. A report of his calculus differentialis was published in 1684 in the scientific periodical Acta Eruditorum, of which Leibniz was editor.

Isaac Newton, who some years before had arrived independently at the calculus but had elected not to publish his discovery, made no reply to Leibniz until 1705. The year before, Leibniz had published a review disputing the conclusions drawn by Newton in his article on optics. Newton, always very sensitive to criticism, used the second edition of his widely disseminated Principia to accuse Leibniz of plagiarizing the calculus.

In 1712, England’s Royal Society, of which Newton was president, appointed a committee to investigate both men’s claims of priority in discovering the calculus. The committee’s report, the Commercium epistolicum, unequivocably supported Newton, though this scarcely consti- tutes objective evidence since Newton himself was the document’s primary author.

Though the passage of time has obscured the facts of the matter, the consensus of most historians is as follows: the differential and integral calculus, in its present form, was invented by Leibniz between 1675 and 1685; Newton devised the infinitesimal calculus and his method of fluxions around 1665 but chose to wait until much later to publish his discoveries. Great intellects, drawing from similar sources, are likely to arrive at similar conclusions. It is diffi- cult to understand why these two learned men were unable to accept gracefully the concurrency of their discoveries. Unfortunately, they allowed themselves to become embroiled in a bitter quarrel that diverted their attention from more profitable pursuits.

It is interesting to note that the repercussions of the controversy, sometimes called “the Great Sulk,” proved disastrous for British mathematics and science. The British considered it their patriotic duty to spurn Leibniz’s analytical methods and system of notation in favor of Newton’s, though Leibniz’s approach proved far more effective. In preferring Newton to the exclusion of Leibniz and other Continental mathematicians like Euler, Lagrange, Laplace, Gauss and the Bernoullis, the British removed themselves from the mainstream of scientific
thought at one of the most fruitful periods in history, and doomed themselves to mathematical obscurity for several hundred years.

Leibniz himself fared no better. In 1714, Leibniz’s master, George Ludwig of Hanover, was crowned King George I of England. Leibniz longed to join him in London, but was ordered to remain in Hanover and complete the new king’s genealogy. Leibniz, who never married, spent the last years of his life in loneliness, and in pain from gout. When he died on November 14, 1716, at the age of seventy, only his secretary attended his funeral to mourn
his passing. Nevertheless, Leibniz is today revered as the founder of modern European mathematics.

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BBC - Radio 4 - Test tubes and Tantrums: Isaac Newton and Gottfried Wilhelm Leibniz

It is probably impossible to overestimate the importance to science of differential and integral calculus. It is now generally accepted that Newton and Leibniz discovered it independently of each other, Newton first formulating his methods around 1665.

But when Leibniz, a German civil servant, published his work in 1684 and didn’t even mention the name of the Lucasian Professor of Mathematics, who had helped him in letters on more than one occasion, blood boiled in the lounges of learned societies and on podiums of lecture halls across Europe, and a schism in science opened up that would hold back British science and thinking, and would not heal for some 140 years.

Newton was buried in Westminster Abbey, a national hero. Leibniz, who has since been described as the last universal genius, died a poor failure, with only his former secretary attending his funeral.

Listen to the programme: here.

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The calculus quarrel

By Kathiann Kowalski, 02/01/2002

If you think mathematics is all logic and no emotion, guess again. Three hundred years ago, a furious feud erupted over who created calculus. Facing off in the fight were England's Sir Isaac Newton (1642-1727) and Germany's Baron Gottfried Wilhelm Leibniz (1646-1716).

What Is Calculus?

Calculus is the mathematics of change. Differential calculus, or differentiation, determines varying rates of change. Differentiation helps solve problems involving acceleration of moving objects, from a flywheel to the space shuttle, as well as rates of growth and decay, optimal values, graphs of curves, and other issues. Integration is the "inverse" (or opposite) of differentiation. It measures accumulations over periods of change. Integration can find volumes and lengths of curves, measure forces and work, and solve other problems. It is used in the day-to-day work of space scientists, architectural engineers, and theoretical physicists.

Today, anyone can learn calculus in an advanced high school class or college course. With Newton and Leibniz, though, it was another story.

Facing Off

Because plague temporarily closed Cambridge University's Trinity College, student Isaac Newton spent from 1665 to 1666 at his mother's farm in Woolsthorpe, England. During that wonderful year (annus mirabilis, as ancient Romans would have said), Newton developed many ideas about physics and mathematics, including his theory of gravity.

During this time, Newton also invented calculus. Newton showed a 1666 paper he had written on calculus to a few colleagues, but otherwise did not publish his news. Some historians suggest that Newton didn't want anyone criticizing him. Others say that Newton was an intensely private -- and extremely absent-minded -- person. A third explanation is that Newton still wanted to refine his mathematical method. He became a mathematics professor at Cambridge in 1669 and continued studying optics, astronomy, physics, and other sciences.

Germany's Gottfried Leibniz grew from a child prodigy into an adult philosopher, diplomat, scientist, and mathematician. In 1673, Leibniz visited London and learned about Newton and other mathematicians. In 1676, Leibniz and Newton exchanged letters through Henry Oldenberg, who was the secretary of England's Royal Society (a prestigious scientific association). However, Newton didn't say whether he'd finished inventing calculus or how it worked. In fact, his only references to it were cryptic.

By 1677, Leibniz had independently invented calculus. In 1684, Leibniz outlined his calculus in the journal Acta Eruditorum ("actions by educated people" or "smart stuff"). Leibniz published a more detailed description in 1686. Neither paper ever mentioned Newton.

Swiss mathematicians Jakob and Johannes Bernoulli (1654-1705 and 1657-1748) read Leibniz's article. They began using calculus and teaching it to others, Within a few years, Leibniz's Calculus Differentialis became famous.

But Newton wanted people to know that he had invented calculus first. Between 1687 and 1699, materials published by Newton and others claimed that he had invented calculus. However, Newton didn't give full details until 1704.

War in the Math World

At first, Newton and Leibniz acknowledged each other's accomplishments politely. Then their friends got into the act.

In continental Europe, the Bernoulli brothers led Leibniz's followers. Siding with Newton in England were academics John Keill (1671-1721), John Wallis (1616-1703), and Nicholas Fatio de Duillier (1664-1753).

The Leibniz side issued mathematical "challenges" for Newton to solve. Then, egged on by their respective fans, Newton and Leibniz slung criticism at each other's work. The sides hurled nasty names at each other, too. Leibniz called Newton's fans enfants perdus, or "lost children."

At first, the fight was about who discovered calculus first. But differences in philosophy, religion, and other factors made matters worse. Then, in 1710, Fatio de Duillier, on Newton's side, accused Leibniz of plagiarism. Plagiarism is saying someone else's work is your own. Feeling deeply offended, Leibniz asked the Royal Society for help.

By then, however, Newton was president of the Royal Society. Newton packed the review committee with his fans. He even drafted parts of the committee's report. Not surprisingly, the committee's 1713 report favored Newton.

Leibniz's fans fought back. Indeed, they argued, Newton had plagiarized Leibniz's work.

In 1714, Leibniz's employer, the Duke of Hanover, became England's King George I. Disheartened and left to do boring genealogical work, Leibniz died in 1716. Newton stayed bitter.

Who Won?

Newton may have won the first round, but England lost the second one. For decades, English and German mathematicians wouldn't speak to each other. And English mathematicians wanted nothing to do with Leibniz's work.

But Leibniz's calculus notation was easier to use -- see opposite. Newton had used dots that could easily be confused with stray ink spots. Thus, continental mathematicians advanced calculus more quickly than their English counterparts.

For today's science, the calculus quarrel became a win-win situation. It got both sides to publish their work so that later mathematicians could expand and apply it. Today, calculus helps solve problems in physics, biology, chemistry, economics, business, and other disciplines.

Both Newton and Leibniz made other scientific contributions, too. Among other things, Newton developed a theory of gravity and described basic laws of physics and motion. Leibniz worked on binary notation, logic, and a forerunner of the modern calculator.

Finally, the calculus quarrel illustrates the importance of publishing scientific work. Important discoveries should be shared.

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In best of all worlds, Leibniz surpasses Newton

By Tom Siegfried, 07/21/2003

When Gottfried Wilhelm von Leibniz declared that humans inhabit the best of all possible worlds, he really meant that the universe is a cool place because it permits the pursuit of science.

In modern translation, says mathematician Gregory Chaitin, Leibniz meant that God is a computer programmer.

Whether you take "God" in a devout religious sense (as Leibniz did), or as metaphorical shorthand for the ultimate nature of the universe, is beside the point. Dr. Chaitin's message is that the practice of science today reflects a new "digital philosophy" that was articulated by Leibniz more than three centuries ago.

A mathematician, philosopher, physicist and lawyer, Leibniz devised calculus independently of Isaac Newton, invented a primitive calculating device, and rediscovered the binary number system (previously used by musicians in India more than a millennium earlier). Expressing information using the binary digits 0 and 1 (as modern computers do) stemmed from Leibniz's desire to apply logic to the cosmos.

It was through logical analysis that Leibniz concluded that the world God created was the most nearly perfect possible. After all, Leibniz reasoned, God could have made a universe in any of many possible ways – some complicated, some simple.

Suppose, for instance, that God made the world the way a child might make abstract art – splashing dots of color on a sheet of paper with a crayon. Even for an apparently random pattern of dots, Leibniz showed that it would be possible to devise a mathematical formula describing their positions. In other words, you could use the formula to plot a curving line that would pass through all the dots – in the order they were made.

For most patterns of dots, though, the formula would be extremely complicated. A "better" world might be built by arbitrarily changing certain aspects of nature. But events in such a world, though obeying some complicated formula, would appear to be utterly chaotic, beyond the power of human scientists to comprehend.

"When a rule is extremely complex, that which conforms to it passes for random," Leibniz observed.

To say that the world is ruled by "laws of nature," then, is not very meaningful unless the laws are relatively simple. You could in principle find a rule to describe the world no matter how random it looks. But unless the rule is short and sweet, you have not iscovered a very useful law.

Fortunately, the world that humans actually inhabit succumbs to rather simple formulas; scientists can describe all sorts of processes with only a few fundamental equations.

"God has chosen the most perfect world," Leibniz wrote in his Discourse on Metaphysics, "the one which is at the same time the simplest in hypothesis and the richest in phenomena."

In Leibniz's writings, Dr. Chaitin sees the precursor of his own seminal work in describing nature in terms of information. He was a pioneer in the development of algorithmic information theory, a method for gauging the complexity of a scientific theory.

A good theory, Dr. Chaitin explains, compresses lots of observations about nature into a concise mathematical statement – best expressed as an algorithm, or computer program. The algorithmic information content of a theory is the length of the shortest program that can reproduce all the observations.

"The smaller the program is, the better the theory," Dr. Chaitin writes in a recent paper (online at arXiv.org/math.HO/0306303). That is, a good theory, or law of nature, reduces complex data to a short (or simple) formula.

Leibniz's anticipation of this concept, plus his invention of binary digits, planted a 17th-century seed that is only now flowering in many scientific pursuits based on information processing. Dr.
Chaitin cites recent advances in quantum information theory and quantum computing, the use of holographic information descriptions of black holes, and models of computation studied by Edward Fredkin (originator of the "digital philosophy" terminology).

"The digital philosophy paradigm is a direct intellectual descendant of Leibniz," writes Dr. Chaitin, of IBM's research laboratory in Yorktown Heights, N.Y. "The human race has finally caught up with this part of Leibniz's thinking."

The digital view of nature also represents a subtle revision of a more ancient philosophy – practiced by the followers of Pythagoras – often summarized by the statement that "Everything is number; God is a mathematician." Today, says Dr. Chaitin, the proper credo should be "Everything is software; God is a computer programmer."

This "digital" philosophy has become a new paradigm for science, and it's just what science needs to cope with the complexity that eludes description with traditional Newtonian physics, based on analysis of mass and motion, or matter and energy.

"In our new interest in complex systems, the concepts of energy and matter take second place to the concepts of information and computation," Dr. Chaitin asserts. The godlike authority of Newton and his materialist philosophy must yield to the new digital philosophy in order for science to extend the human ability to comprehend creation.

Newton's vision is the history of science; Leibniz's is the future.

"Newtonian physics," Dr. Chaitin avers, "is now receding into the dark, distant intellectual past."

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A chance and fateful meeting

By Donna Martin, 07/14/2006

The two philosophers could hardly have been more different.

Baruch de Spinoza, born in Amsterdam in 1632, was a descendent of Jews who had fled the Spanish and Portuguese Inquisitions for the relative freedom of the Dutch Republic. A precocious student of the Jewish school at Amsterdam, fluent in Hebrew and thoroughly versed in the Bible, he was excommunicated from the Jewish community at age 24 for his heretical beliefs about the nature of God, the origins of the Bible and his rejection of personal immortality. Self-assured, even arrogant in his beliefs, he moved to The Hague, where, cloaked in anonymity, he published his Tractatus Theologico-Politicus. This work established him as one of the first great theorists of the modern secular state.

Gotffried Wilhelm Leibniz, born in Leipzig in 1646, was the son of a professor of moral philosophy at the University of Leipzig, a center of Lutheran studies since the time of the Reformation. A polymath from his earliest years, he taught himself Latin by the age of 12, studied Aristotle's logic at 13 and matriculated at the University of Leipzig the following year. Although his father died when he was only 6, Gottfried was guided by a series of powerful men to a career in law and politics. One of his earliest and most influential mentors was Baron von Boineburg, a recent Catholic convert who was first minister to the powerful elector of Mainz. At Baron von Boineburg's request, Leibniz drafted a set of essays, Catholic Demonstrations, which tried to supply a rational foundation for a united Christian church. At this point, before his 24th year, Leibniz embarked on his lifelong involvement in church politics with the idea that the state should be grounded not on the "divine right" of kings but on eternal truths.

The previously unheralded meeting between Leibniz and Spinoza, like the charged meeting of Niels Bohr and Werner Heisenberg in the play "Copenhagen," is the central event of Matthew Stewart's The Courtier and the Heretic. While few details are known of the meeting of the two philosophers in The Hague in November 1676, it is clear that Spinoza's philosophy had a profound effect on Leibniz, 14 years Spinoza's junior. The effect on Spinoza, who was to die only a few months later at age 44, went unrecorded.

At first blush it seems unlikely that the urbane insider, Leibniz, would seek out Spinoza, an apostate Jew. But Leibniz had a deep commitment to reason, which also formed the basis of Spinoza's philosophy. In correspondence with other religious and political figures of the day, Leibniz was careful to cover his tracks, alluding to Spinoza and his work as if he knew him only by his despised reputation. Yet Leibniz, on a mission to Paris that he made last for four years, from 1672-76, read widely and was especially intrigued by Spinoza's work. Ultimately he secured an appointment in the court of Hanover, where he would spend the remaining 40 years of his life, but in 1676, before he left Paris, he made contact with a friend of Spinoza, who would share with him the ideas of Spinoza's Ethics, his as yet unpublished masterwork.

According to Leibniz's notes on his conversation with Spinoza's friend, Spinoza believed that "God alone is substance"; "all creatures are nothing but modes"; and "mind is the very idea of the body." Leibniz, whose own philosophy was in its formative stages, then secured the fateful meeting in The Hague.

It is no accident that these two great philosophers of the 17th century, though from profoundly different backgrounds, were each seeking a new understanding of God.

Copernicus and Galileo had done away with the idea that the earth was the center of the cosmos. Even generations before Darwin, the advances of science had thrown into doubt the belief that the human being was the purpose of creation. Descartes' conclusion that mind was what distinguished humans from other creatures and from mechanical principles was a sort of truce between established religion and the emerging sciences. For his critics, however, Descartes had created a "mind-body" dualism in which it was difficult to explain how, as distinct substances, mind and body could interact at all.

Spinoza rejected Cartesian dualism, saying that "man is a part of Nature and must follow its laws, and this alone is true worship." In effect, according to Spinoza, God and Nature were one and the same.

After meeting Spinoza, Leibniz was convinced that Spinoza's God was incompatible with orthodox belief. Clearly there was no place for the immortality of the soul or for a personal God who would work miracles or show compassion. Leibniz saw his charge as showing that God is a person, an intelligent being.

After an aborted attempt to publish his Ethics, Spinoza rightly feared public reaction. The book was published only after his death in 1677 as his Opera Posthuma. Leibniz obtained a copy of the book then, and in notes intended only for himself, vehemently disagreed with everything Spinoza said. In his own Discourse on Metaphysics, Leibniz asserted that in order for God to be good, God must be able to make choices. In fact, in a statement later to be derided by Voltaire, Leibniz asserted that God chose the best of all possible worlds. As a refutation to Spinoza's claim that there was only one substance, God, Leibniz declared that the world was made up of an infinity of self-contained entities that he called monads, existing in a pre-established harmony. In effect, this was an "argument from design."

Leibniz sought the approval of the renowned French Catholic theologian Antoine Arnauld, but his views were rejected. Despite his efforts to distinguish his views from those of Spinoza, Leibniz was doomed to be grouped with his intellectual nemesis as a rationalist. The 17th century saw the beginning of the modern secular state. It may be said that this state looks more like Spinoza's free republic than Leibniz's version of theocracy, but the beliefs that continue to guide individuals, such as faith in a personal God and the immortality of the soul, seem to follow more directly from Leibniz.

The biographical note on the author of The Courtier and the Heretic is teasingly brief: Matthew Stewart received his doctorate in philosophy from Oxford, founded a management consulting firm, then retired to a life of contemplation. Dr. Stewart obviously enjoys sharing the results of his contemplation with others; his writing is clear, often witty and engagingly gossipy, especially about Leibniz, whose vanity and penchant for flattery were made transparent by his vast collection of papers. Dr. Stewart's subtitle, implying that the fate of God in the modern world rests on these two philosophers, seems overly ambitious, but he does make an impressive case that the unlikely meeting of Leibniz and Spinoza in the 17th century was an epochal event.

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Debating the origin of evil in a godly universe

By Michael Dirda, 11/30/2008

Many are likely to know just two facts about the great polymath Gottfried Wilhelm Leibniz (1646- 1716): first, that he and Newton independently discovered calculus at roughly the same time, then argued over who should get the credit (Newton won); and, second, that he maintained that ours was "the best of all possible worlds," a phrase much mocked in Voltaire's sparkling philosophical satire Candide. If people know anything further about this German thinker, it's likely to be that he spent his life trying to effect a reconciliation between Protestantism and Catholicism and that he postulated the existence of invisible, atom- like "monads" as the metaphysical building blocks of the universe.

Poor Leibniz! For all his genius, he seems destined to be overshadowed by others, whether Newton, Voltaire or Spinoza (whom he visited, admired and disputed with) or, as Steven Nadler shows in The Best of All Possible Worlds, even by half-forgotten French priests. Of course, Nicolas Malebranche (1638-1715) and Antoine Arnauld (1612-1694) weren't simple provincial curates; they were, at least for the generation following the death of Descartes, France's strongest theological thinkers (excepting perhaps Pascal, who strangely enough barely figures in Nadler's book). Both Frenchmen knew the young Leibniz during his long stay in Paris, and all three corresponded with one another for decades afterward. Their lifelong, and sometimes heated, arguments about the nature of God form the basis of this engrossing book. Nadler makes clear the importance of their debate:

"What was at stake was nothing less than the meaning of existence, the understanding of why things are as they are. The choice was clear: either the universe is ultimately an arbitrary product, the effect of an indifferent will guided by no objective values and subject to no independent canons of reason or goodness; or it is the result of wisdom, intelligible to its core and informed by a rationality and a sense of value that are, in essence, not very different from our own; or (to mention the most terrifying possibility of all) it simply is, necessary through its causes and transparent to the investigations of metaphysics and science but essentially devoid of any meaning or value whatsoever."

The attempt to justify the ways of God to men -- theodicy, a term coined by Leibniz -- lies at the heart of the matter: "Why is there any evil at all in God's creation?" Essentially, Leibniz's answer is: Consider the whole. Explains Nadler, "It is not that everything will turn out for the best for me or for anyone else in particular. Nor is it necessarily the case that any other possible world would have been worse for me or for anyone else. Rather, Leibniz claims that any other possible world is worse overall than this one, regardless of any single person's fortunes in it." What is good for the whole isn't necessarily good for every one of its individual parts or components. As Nadler emphasizes, summarizing Leibniz, "all things are connected and every single aspect of the world makes a contribution to its being the best world."

That includes what we call evil. However, Leibniz offers no explanation of just how evil assists the overall goodness of things. (Sometimes he even seems to suggest that it serves to bring the good into greater relief.) We cannot penetrate so far into the Creator's mind or plan. Still "it is inconceivable . . . that an infinitely good and perfect God could choose anything less than the best." This conclusion may satisfy a devout Christian philosopher, but it offers scant consolation when we are in pain, or see the wicked succeed and the worthy fail, or when we face death.

Malebranche refined Leibniz's view by imagining that God needed to establish a world that wouldn't require constant adjustment or interference, one that ran on its own, following what He had determined were the simplest, most efficient general principles. Thus, "the actual world is not the most perfect world absolutely speaking; rather, it is only the most perfect world possible relative to those maximally simple laws." In other words, even God compromises. Our world could be better "but only at the cost of the simplicity of the means." Instead, Malebranche's Creator "wills to accomplish as much justice and goodness as He possibly can, not absolutely but consistent with the simplest laws." As Nadler emphasizes, to Malebranche "God . . . is more committed to acting in a general way and to a nature governed by the simplest laws than He is to the well-being of individuals." His "general volitions," as Malebranche dubs these cosmic rules, take precedence over "particular volitions," which are essentially those infrequent violations of the natural order that we call miracles. So it is in the established nature of things for it to rain, and sometimes the parched land receives needed water and sometimes rivers overflow. God isn't going to spend all his time constantly adjusting the weather and a zillion other phenomena just because the results aren't what the locals want or like.

What Arnauld objects to in Malebranche (and also in Leibniz) is the supposition that God's nature is like humankind's and that our human intellects can have access to the divine wisdom. God, Arnauld believes, is utterly alien to us -- "a hidden God," to use a Jansenist catchphrase -- and to imagine him making logical decisions, or weighing the pluses and minuses of contrasting worlds, is absurd, nothing but anthropomorphism. (As Spinoza once observed, "a triangle, if it could speak would . . . say that God is eminently triangular, and a circle that God's nature is eminently circular.") In fact, men and women are by their lesser natures incapable of making sense of God or his mysterious ways, and all these presumptuous attempts at theodicy are doomed to failure. God wanted to make the world and so He did, and there's an end to it. In essence, Leibniz believes in God's goodness and wisdom, and Malebranche further emphasizes His rationality, but to Arnauld God is simply pure, omnipotent will.

Which God you believe in matters: "Do we inhabit a cosmos that is fundamentally intelligible because its creation is grounded in a rational decision informed by certain absolute values? Is the world's existence the result of a reasonable act of creation and the expression of an infinite wisdom? Or, on the other hand, is the universe ultimately a nonrational, even arbitrary piece of work? . . . Does the origin of things lie in an indifferent action -- an apparently capricious exercise of causal power -- by a Creator who cannot possibly be motivated by reasons because His will finds no reasons independent of itself? In short, does the universe exist by ratio or by voluntas, by wisdom or power?"

There's much more detail, and much greater subtlety, in Nadler's account of these differing theological views of God and His universe. (For instance, Spinoza contributes the further twist that "this is not the best of all possible worlds; it is the only possible world.") Of course, Leibniz, Malebranche and Arnauld all posit a Christian God of some sort, and their arguments may seem quaint to rationalists of a largely secular age. But to those who believe in, or simply wonder about, a God-governed universe, these three 17th-century thinkers raise serious and perennially fascinating questions: Is God moral and rational or completely arbitrary, even capricious? Is it wrong to kill only because God says so, or are there absolute moral values (as Kant would argue in establishing the categorical imperative, his variant on the Golden Rule)? And, to be almost bathetic, if God gives us grace to withstand temptation, why does he sometimes fail to give us enough?

Besides this new book, Steven Nadler is the author of a magisterial biography of Spinoza, which I have read and recommend, and of impressive-sounding academic books on Arnauld and Malebranche, which I've only heard of. I can't imagine a better guide to 17th-century philosophical thought. Aimed at the general public, The Best of All Possible Worlds is written simply and clearly, without condescension, flashiness or over-simplification. But it's a demanding book nonetheless, and you need to pay attention. You'll be amply rewarded if you do.

More information on Gottfried Leibniz

Leibniz quotes

"Music is the pleasure the human mind experiences from counting without being aware that it is counting."

"Men act like brutes in so far as the sequences of their perceptions arise through the principle of memory only, like those empirical physicians who have mere practice without theory."

"This is why the ultimate reason of things must lie in a necessary substance, in which the differentiation of the changes only exists eminently as in their source; and this is what we call God."

"To love is to place our happiness in the happiness of another."

“[Wisdom is] the science of happiness or of the means of attaining the lasting contentment which consists in the continual achievement of a greater perfection or at least in variations of the same degree of perfection.”

“Although the world is not perfect, it is yet the best that is possible.”

*****

Complete set of works

Freedom and possibility (1680)
Meditations on knowledge, truth, and ideas (1684)
Contingency (1686)
First truths (1686)
Discourse on metaphysics (1686)
Real-life dialogue on human freedom and the origin of evil (1695)
Essay on dynamics (1695)
New system (1695)
The ultimate origin of things (1697)
Nature itself (1698)
Making the case for God (1710)
Principles of nature and grace (1714)
Monadology (1714)

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Leibniz’s exchange of papers with Clarke

In 1715 Leibniz wrote to his friend the Princess of Wales to warn her of the dangers Newton's philosophy posed for natural religion. Seizing this chance of initiating an exchange between two of the greatest minds in Europe, the princess showed his letter to the eminent Newtonian scientist and natural theologian, Samuel Clarke. From his reply developed an exchange of papers which was published in 1717. The correspondence was immediately seen as a crucial discussion of the significance of the new science, and it became one of the most widely read philosophical works of its time. Kant developed his theory of space and time from the problems at issue, and the post-Newtonian physics of the twentieth century has brought a revival of interest in Leibniz's objections: some of the problems are still not finally resolved. In this edition an introduction outlines the historical background, and there is a valuable survey of the subsequent discussions of the problem of space and time in the philosophy of science. Significant references to the controversy in Leibniz's other correspondence have also been collected, and the relevant passages from Newton's "Principia" and "Opticks" are appended.

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New Essays on Human Understanding

Challenging Locke's views in Essays on Human Understanding chapter by chapter, Leibniz's references to his contemporaries and his discussion of the ideas and institutions of the age make this work a fascinating and valuable document in the history of ideas.

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Leibniz in the Media

"Making the best of the worst", by Stan Thompson - January 07, 2009 - Mooresville Tribune

Been dreading '09? Gottfried Leibniz, the 17th century German philosopher, drew the admiration of the faithful and the scorn of the skeptical when he famously observed that if God is omnipotent, omniscient and benevolent, then this must necessarily be the best of all possible worlds.

For this simple statement of faith, Leibniz achieved immortality (of the earthly variety) at the hands of Voltaire, who lampooned him as "Doctor Pangloss" in the classic French novel, Candide.

"Oct. 29, 1675: Leibniz ∫ums It All Up", by Randy Alfred - October 29, 2008 - Wired Magazine

Gottfried Leibniz writes the integral sign ∫ in an unpublished manuscript, introducing the calculus notation that's still in use today.

Leibniz was a German mathematician and philosopher who readily crossed the lines between academic disciplines. He had a doctorate in law, served as secretary of the Nuremberg alchemical society and fancied himself a poet.