Gottfried Wilhelm Leibniz
German philosopher and
mathematician
born July 1 [June 21, old style],
1646, Leipzig
died November 14, 1716,
Hannover, Hanover
Main
German philosopher,
mathematician, and political adviser,
important both as a metaphysician and as
a logician and distinguished also for
his independent invention of the
differential and integral calculus.
Early life and education
Leibniz
was born into a pious Lutheran family
near the end of the Thirty Years’ War,
which had laid Germany in ruins. As a
child, he was educated in the Nicolai
School but was largely self-taught in
the library of his father, who had died
in 1652. At Easter time in 1661, he
entered the University of Leipzig as a
law student; there he came into contact
with the thought of men who had
revolutionized science and
philosophy—men such as Galileo, Francis
Bacon, Thomas Hobbes, and René
Descartes. Leibniz dreamed of
reconciling—a verb that he did not
hesitate to use time and again
throughout his career—these modern
thinkers with the Aristotle of the
Scholastics. His baccalaureate thesis,
De Principio Individui (“On the
Principle of the Individual”), which
appeared in May 1663, was inspired
partly by Lutheran nominalism (the
theory that universals have no reality
but are mere names) and emphasized the
existential value of the individual, who
is not to be explained either by matter
alone or by form alone but rather by his
whole being (entitate tota). This notion
was the first germ of the future
“monad.” In 1666 he wrote De Arte
Combinatoria (“On the Art of
Combination”), in which he formulated a
model that is the theoretical ancestor
of some modern computers: all reasoning,
all discovery, verbal or not, is
reducible to an ordered combination of
elements, such as numbers, words,
sounds, or colours.
After completing his legal studies in
1666, Leibniz applied for the degree of
doctor of law. He was refused because of
his age and consequently left his native
city forever. At Altdorf—the university
town of the free city of Nürnberg—his
dissertation De Casibus Perplexis (“On
Perplexing Cases”) procured him the
doctor’s degree at once, as well as the
immediate offer of a professor’s chair,
which, however, he declined. During his
stay in Nürnberg, he met Johann
Christian, Freiherr von Boyneburg, one
of the most distinguished German
statesmen of the day. Boyneburg took him
into his service and introduced him to
the court of the prince elector, the
archbishop of Mainz, Johann Philipp von
Schönborn, where he was concerned with
questions of law and politics.
King Louis XIV of France was a
growing threat to the German Holy Roman
Empire. To ward off this danger and
divert the King’s interests elsewhere,
the Archbishop hoped to propose to Louis
a project for an expedition into Egypt;
because he was using religion as a
pretext, he expressed the hope that the
project would promote the reunion of the
church. Leibniz, with a view toward this
reunion, worked on the Demonstrationes
Catholicae. His research led him to
situate the soul in a point—this was new
progress toward the monad—and to develop
the principle of sufficient reason
(nothing occurs without a reason). His
meditations on the difficult theory of
the point were related to problems
encountered in optics, space, and
movement; they were published in 1671
under the general title Hypothesis
Physica Nova (“New Physical
Hypothesis”). He asserted that movement
depends, as in the theory of the German
astronomer Johannes Kepler, on the
action of a spirit (God).
In 1672 the Elector sent the young
jurist on a mission to Paris, where he
arrived at the end of March. In
September, Leibniz met with Antoine
Arnauld, a Jansenist theologian
(Jansenism was a nonorthodox Roman
Catholic movement that spawned a
rigoristic form of morality) known for
his writings against the Jesuits.
Leibniz sought Arnauld’s help for the
reunion of the church. He was soon left
without protectors by the deaths of
Freiherr von Boyneburg in December 1672
and of the Elector of Mainz in February
1673; he was now, however, free to
pursue his scientific studies. In search
of financial support, he constructed a
calculating machine and presented it to
the Royal Society during his first
journey to London, in 1673.
Late in 1675 Leibniz laid the
foundations of both integral and
differential calculus. With this
discovery, he ceased to consider time
and space as substances—another step
closer to monadology. He began to
develop the notion that the concepts of
extension and motion contained an
element of the imaginary, so that the
basic laws of motion could not be
discovered merely from a study of their
nature. Nevertheless, he continued to
hold that extension and motion could
provide a means for explaining and
predicting the course of phenomena.
Thus, contrary to Descartes, Leibniz
held that it would not be contradictory
to posit that this world is a
well-related dream. If visible movement
depends on the imaginary element found
in the concept of extension, it can no
longer be defined by simple local
movement; it must be the result of a
force. In criticizing the Cartesian
formulation of the laws of motion, known
as mechanics, Leibniz became, in 1676,
the founder of a new formulation, known
as dynamics, which substituted kinetic
energy for the conservation of movement.
At the same time, beginning with the
principle that light follows the path of
least resistance, he believed that he
could demonstrate the ordering of nature
toward a final goal or cause.
The Hanoverian period
Leibniz
continued his work but was still without
an income-producing position. By October
1676, however, he had accepted a
position in the employment of John
Frederick, the duke of
Braunschweig-Lüneburg. John Frederick, a
convert to Catholicism from Lutheranism
in 1651, had become duke of Hanover in
1665. He appointed Leibniz librarian,
but, beginning in February 1677, Leibniz
solicited the post of councillor, which
he was finally granted in 1678. It
should be noted that, among the great
philosophers of his time, he was the
only one who had to earn a living. As a
result, he was always a
jack-of-all-trades to royalty.
Trying to make himself useful in all
ways, Leibniz proposed that education be
made more practical, that academies be
founded; he worked on hydraulic presses,
windmills, lamps, submarines, clocks,
and a wide variety of mechanical
devices; he devised a means of
perfecting carriages and experimented
with phosphorus. He also developed a
water pump run by windmills, which
ameliorated the exploitation of the
mines of the Harz Mountains, and he
worked in these mines as an engineer
frequently from 1680 to 1685. Leibniz is
considered to be among the creators of
geology because of the observations he
compiled there, including the hypothesis
that the Earth was at first molten.
These many occupations did not stop his
work in mathematics: In March 1679 he
perfected the binary system of
numeration (i.e., using two as a base),
and at the end of the same year he
proposed the basis for analysis situs,
now known as general topology, a branch
of mathematics that deals with selected
properties of collections of related
physical or abstract elements. He was
also working on his dynamics and his
philosophy, which was becoming
increasingly anti-Cartesian. At this
point, Duke John Frederick died on Jan.
7, 1680, and his brother, Ernest
Augustus I, succeeded him.
France was growing more intolerant at
home—from 1680 to 1682 there were harsh
persecutions of the Protestants that
paved the way for the revocation of the
Edict of Nantes on Oct. 18, 1685—and
increasingly menacing on its frontiers,
for as early as 1681, despite the
reigning peace, Louis XIV took
Strasbourg and laid claim to 10 cities
in Alsace. France was thus becoming a
real danger to the empire, which had
already been shaken on the east by a
Hungarian revolt and by the advance of
the Turks, who had been stopped only by
the victory of John III Sobieski, king
of Poland, at the siege of Vienna in
1683. Leibniz served both his prince and
the empire as a patriot. He suggested to
his prince a means of increasing the
production of linen and proposed a
process for the desalinization of water;
he recommended classifying the archives
and wrote, in both French and Latin, a
violent pamphlet against Louis XIV.
During this same period Leibniz
continued to perfect his metaphysical
system through research into the notion
of a universal cause of all being,
attempting to arrive at a starting point
that would reduce reasoning to an
algebra of thought. He also continued
his developments in mathematics; in 1681
he was concerned with the proportion
between a circle and a circumscribed
square and, in 1684, with the resistance
of solids. In the latter year he
published Nova Methodus pro Maximis et
Minimis (“New Method for the Greatest
and the Least”), which was an exposition
of his differential calculus.
Leibniz’ noted Meditationes de
Cognitione, Veritate et Ideis
(Reflections on Knowledge, Truth, and
Ideas) appeared at this time and defined
his theory of knowledge: things are not
seen in God—as Nicolas Malebranche
suggested—but rather there is an
analogy, a strict relation, between
God’s ideas and man’s, an identity
between God’s logic and man’s. In
February 1686, Leibniz wrote his
Discours de métaphysique (Discourse on
Metaphysics). In the March publication
of Acta, he disclosed his dynamics in a
piece entitled Brevis Demonstratio
Erroris Memorabilis Cartesii et Aliorum
Circa Legem Naturae (“Brief
Demonstration of the Memorable Error of
Descartes and Others About the Law of
Nature”). A further development of
Leibniz’ views, revealed in a text
written in 1686 but long unpublished,
was his generalization concerning
propositions that in every true
affirmative proposition, whether
necessary or contingent, the predicate
is contained in the notion of the
subject. It can be said that, at this
time, with the exception of the word
monad (which did not appear until 1695),
his philosophy of monadology was
defined.
In 1685 Leibniz was named historian
for the House of Brunswick and, on this
occasion, Hofrat (“court adviser”). His
job was to prove, by means of genealogy,
that the princely house had its origins
in the House of Este, an Italian
princely family, which would allow
Hanover to lay claim to a ninth
electorate. In search of these
documents, Leibniz began travelling in
November 1687. Going by way of southern
Germany, he arrived in Austria, where he
learned that Louis XIV had once again
declared a state of war; in Vienna, he
was well received by the Emperor; he
then went to Italy. Everywhere he went,
he met scientists and continued his
scholarly work, publishing essays on the
movement of celestial bodies and on the
duration of things. He returned to
Hanover in mid-July 1690. His efforts
had not been in vain. In October 1692
Ernest Augustus obtained the electoral
investiture.
Until the end of his life, Leibniz
continued his duties as historian. He
did not, however, restrict himself to a
genealogy of the House of Brunswick; he
enlarged his goal to a history of the
Earth, which included such matters as
geological events and descriptions of
fossils. He searched by way of monuments
and linguistics for the origins and
migrations of peoples; then for the
birth and progress of the sciences,
ethics, and politics; and, finally, for
the elements of a historia sacra. In
this project of a universal history,
Leibniz never lost sight of the fact
that everything interlocks. Even though
he did not succeed in writing this
history, his effort was influential
because he devised new combinations of
old ideas and invented totally new ones.
In 1691 Leibniz was named librarian
at Wolfenbüttel and propagated his
discoveries by means of articles in
scientific journals. In 1695 he
explained a portion of his dynamic
theory of motion in the Système nouveau
(“New System”), which treated the
relationship of substances and the
preestablished harmony between the soul
and the body: God does not need to bring
about man’s action by means of his
thoughts, as Malebranche asserted, or to
wind some sort of watch in order to
reconcile the two; rather, the Supreme
Watchmaker has so exactly matched body
and soul that they correspond—they give
meaning to each other—from the
beginning. In 1697, De Rerum
Originatione (On the Ultimate Origin of
Things) tried to prove that the ultimate
origin of things can be none other than
God. In 1698, De Ipsa Natura (“On Nature
Itself”) explained the internal activity
of nature in terms of Leibniz’ theory of
dynamics.
All of these writings opposed
Cartesianism, which was judged to be
damaging to faith. Plans for the
creation of German academies followed in
rapid succession. With the help of the
electress Sophia Charlotte, daughter of
Ernest Augustus and soon to become the
first queen of Prussia (January 1701),
the German Academy of Sciences in Berlin
was founded on July 11, 1700.
On Jan. 23, 1698, Ernest Augustus
died, and his son, George Louis,
succeeded him. Leibniz found himself
confronted with an uneducated, boorish
prince, a reveller who kept him in the
background. Leibniz took advantage of
every pretext to leave Hanover; he was
constantly on the move; his only comfort
lay in his friendship with Sophia
Charlotte and her mother, Princess
Sophia. Once again, he set to work on
the reunion of the church: in Berlin, it
was a question of uniting the Lutherans
and the Calvinists; in Paris, he had to
subdue Bishop Bénigne Bossuet’s
opposition; in Vienna (to which Leibniz
returned in 1700) he enlisted the
support of the Emperor, which carried
great weight; in England, it was the
Anglicans who needed convincing.
The death in England of William, duke
of Gloucester, in 1700 made George
Louis, great-grandson of James I, a
possible heir to the throne. It fell to
Leibniz, jurist and historian, to
develop his arguments concerning the
rights of the House of
Braunschweig-Lüneburg with respect to
this succession.
The War of the Spanish Succession
began in March 1701 and did not come to
a close until September 1714, with the
Treaty of Baden. Leibniz followed its
episodes as a patriot hostile to Louis
XIV. His fame as a philosopher and
scientist had by this time spread all
over Europe; he was named a foreign
member by the Academy of Sciences of
Paris in 1700 and was in correspondence
with most of the important European
scholars of the day. If he was
publishing little at this point, it was
because he was writing Théodicée, which
was published in 1710. In this work he
set down his ideas on divine justice.
Leibniz was impressed with the
qualities of the Russian tsar Peter the
Great, and in October 1711 the ruler
received him for the first time.
Following this, he stayed in Vienna
until September 1714, and during this
time the Emperor promoted him to the
post of Reichhofrat (“adviser to the
empire”) and gave him the title of
Freiherr (“baron”). About this time he
wrote the Principes de la nature et de
la Grâce fondés en raison, which
inaugurated a kind of preestablished
harmony between these two orders.
Further, in 1714 he wrote the
Monadologia, which synthesized the
philosophy of the Théodicée. In August
1714, the death of Queen Anne brought
George Louis to the English throne under
the name of George I. Returning to
Hanover, where he was virtually placed
under house arrest, Leibniz set to work
once again on the Annales Imperii
Occidentis Brunsvicenses (1843–46;
“Braunschweig Annals of the Western
Empire”). At Bad-Pyrmont, he met with
Peter the Great for the last time in
June 1716. From that point on, he
suffered greatly from gout and was
confined to his bed until his death.
Leibniz was a man of medium height
with a stoop, broad-shouldered but
bandy-legged, as capable of thinking for
several days sitting in the same chair
as of travelling the roads of Europe
summer and winter. He was an
indefatigable worker, a universal letter
writer (he had more than 600
correspondents), a patriot and
cosmopolitan, a great scientist, and one
of the most powerful spirits of Western
civilization.
Yvon Belaval
