GOTTFRIED WILHELM LEIBNIZ
(1646-1716)
CONTENTS
 Leibniz: An Overview
 His Life and Works
 His Major Ideas
 Leibniz's Writings
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Leibniz was a German mathematician and
rationalist philosopher--who, simultaneously with Newton, invented the
differential and integral calculus. He was a widely talented and
travelled individual in his early manhood--and kept up friendships and
correspondences with a wide range of scientists, philosophers and political
figures of the day.
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in Leipzig, Germany, son of Friedrich Leibnuetz, Professor of Moral Philosophy
at the University of Leipzig (who died in 1652 when Leibniz was only 6).
At an early age Leibniz taught himself Latin and studied extensively from
his father's library. At the age of 15 entered the university of Leipzing,
studying philosophy and mathematics. He graduated in 1663 with
a thesis on the principle of indivuation (Disputatio metaphysica de
principio individui)--a work which early pointed to the future directions
his thoughts would take him.
From 1663 to 1666 he took
up the study of law at the University of Leipzig. But in 1666 he
was refused admission to the doctoral program and moved his studies to
the University of Altdorf, where he received his doctorate in 1667.
During this period he published a paper on legal education--which drew
the attention of the Elector of Mainz.
Thus from 1667 to 1672
he found himself in the employ of the Elector of Mainz as a lawyer
and diplomat in the court of Mainz. During this time in Mainz,
he wrote his Hypothesis physica nova (1671).
These were still very troubled
times within Christendom and Leibniz thus put his thoughts to the possibilities
of a peace within the Holy Roman (German) Empire and with its neighbors,
especially the French king Louis XIV--a peace based on a new Christian
theology which would allow Catholics and Protestants to come together on
a higher theological plane.
In accordance with this hope
the Elector in 1672 sent him to Paris as part of a diplomatic mission to
Louis XIV. Leibniz would remain in Paris as a representative of the
Elector until the Elector's death in 1676.
Here in Paris he came into
contact with the "natural philosophers" (scientists) Huygens, Malbranche,
Arnauld and others. Huygens was to have a strong influence on Leibniz,
introducing him to his own conception of the nature of light--in contrast
to the Newtonian conception. Also, Leibniz subsequently engaged in
an extensive correspondence with Arnauld--laying out his metaphysical system
in counter to Newton's (Arnauld was Newtonian).
During these days he began
his work on a calculating machine which not only add and subtract, but
also multiply and divide--even find the roots of numbers.
From Paris he traveled to
England in1673, where he met Boyle and Oldenburg--showing them his new
machine. They in turn introduced him to the Royal Society, where
he demonstrated his new machine--and the Society as a result elected him
membership.
In 1675 he put together the
outlines of his new differential calculus (independently of Newton's development
of the calculus).
In 1676, upon the death of
the Archbishop of Mainz, the Duke of Brunswick at Hanover (Germany) called
Liebniz to work as a personal librarian. Leaving Paris for Hanover,
he undertook an extensive side-journey lasting out most of the rest of
1676. He returned to London--and then traveled to the Netherlands
where he met Leeuwenhoek in Delft and spent a month in Amsterdam with Spinoza.
Once having arrived in Hanover,
he would spend the rest of his days there--mostly involved in the preparation
of a history of the house of Brunswick. But he also took up work
on a number of mechanical devices that utilized his mathematical and technical
talents: hydraulic presses, windmills, lamps, submarines, clocks, carriages,
water pumps, etc. During this time he also developed a binary number
system . He also developed key components of the discipline of symbolic
logic. And he also turned his attention to philosophy, completing
works on metaphysics and systematic philosophy during the 1680s and 1690s.
The last part of his life
was lived in relative obscurity--and much of his work was unknown in his
own times (only discovered much later--some of it not until the 20th century--such
as his work on symbolic logic).
He also died in that same
obscurity. Though he himself in 1700 founded and served as the first
president to the Academy of Sciences in Berlin, his own passing in 1716
was not acknowledged there--nor in the Royal Society of London.
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His Metaphysical Vision
Leibniz truly believed in a
system of clear human reason or logic which could elevate human life beyond
the narrow, mean-spirited ways of his strife torn world (the Catholic-Protestant
wars and the monarchical ambitions of the German, French, Spanish and other
kings and princes made life in Europe very dangerous). He believed
that it was possible to create a mathematically pure system of theological
and political thought such as would bring the world to a fully reasoned
existence. His early work in the studies of law and his later work
in the field of mathematics where strongly motivated by this vision.
In accordance with this vision he set out to construct a metaphysics of
such clarity and precision that it might become the foundation for a new
world order.
The Monads--and God
Leibniz was highly opposed to
the Newtonian cosmology of absolute matter, space and time. In distinction
to Newton's theory of material substance, founded on the the atom and its
placement and movements, Leibniz proposed
monads as the foundation
of all reality. Leibniz' monads interestingly had no material existence--no
placement in time and space, no velocity or direction of movement.
His monads were more like what we would today call potential energy--each
monad being distinct in its potentiality, each monad being a part of a
larger "colony" of monads which, through the directives of God, combined
in distinct ways to form the observable parts of our universe.
God (alone) knows the potential
of every monad and knows how the world is to look as a result of how these
monads are brought together by him in various combinations to produce the
harmony of life or existence.
These single monads are not
mere Newtonian pieces of the larger cosmic puzzle, but are each tiny mirrorings
of the entire universe. Each monad has the capacity or potential
to express the fullness of the universe built through the relationship
of all the monads with each other--though the particular expression or
mirroring of each monad represents only a single view or perspective--the
view from where it sits in relationship to the whole picture. Only
God alone has the capacity to see the whole picture--from all perspectives
simultaneously. Only God alone has the capacity to choose which of
these views or visions will be the one that comes into actual being--through
an "unfolding" of the potential of the multiplicity of monads into the
harmonious actuality of their God-ordained behavior.
This is to say that only
God alone has the power to move this whole picture forward from potential
to fulfillment. The universe is entirely dependent upon God for its
actual existence--its movement from potential (from a virtually infinite
realm of possibilities) to the actual. It is not, as Newton's world
was, "auto-deterministic" or self-running in accordance to some absolute
plan like a well wound-up clock or some kind of perpetual motor moving
in accordance to the laws that describe, dictate or direct its actions.
Leibniz' world did not result
from a rule of physical cause-and-effect. One monad did not spur
another monad into being--like a billiard ball hitting other billiard balls
and setting off a round of cause-and-effect movements. Each monad
was independent, automonous. The linkage among the monads was entirely
through the design of God by which each monad moved from potential to actual
by God's separate and harmonious design of all the monads working
together.
Thus not only was Leibniz'
cosmos not self-running (as Newton saw things), it was not even truly existent
apart from the "intervention" from God. For Leibniz: "No God--no
universe." God was totally necessary to Leibniz' world--not just
as the original architect (as Newton acknowledged God) but as the actual
sustainer of all existence, all substance, all being, all "time," all events.
God
Who was/is this God? God
is the necessary being that stands outside the realm of monads--beyond
the realm of merely potential being. God alone is full being.
Further, God is the necessary cause of all that is--in the "contingent"
world of monads. God alone is not caused. God alone is
not dependent on anything else for his own "existence." God alone
causes "contingent" existence--and not just "in the beginning" (as with
Newton) but in all time and in all places and situations. Apart from
the actions of God, indeed, there would never be such things as time, places,
situations.
God is the "intellect" of
the universe, which everything else in the universe (all the monads) mirrors,
in full--but in relative form.
Necessary Truths and Contingent
Truths
Necessary Truths.
Necessary truths are those truths which are so by logical definition.
For instance the phrase, "a senior citizen is any elderly person."
How do we know this is true? It's true because we have said it was
true, by the very definition of our terms "senior citizen" and "elderly."
These are thus truths "by necessity."
Other forms of necessary
truths are: "a circle is a perfectly round line"; "a square is an
area enscribed by four straight lines of equal size meeting at right angles
to each other"; "8 + 3 = 11." These are true because we have ourselves
defined the word "eleven" to mean eleven and not ten--or because we have
given the name "circle" to the round object and the name "square" to the
boxy object. We could have reversed the words and taught ourselves
to see them accordingly--even teaching our children to use these words
in this new way and it would not change anything about reality. We
are only talking about things that are "true" by common definition.
If you change the definitions you only are changing our vocabulary, our
terminology--not the reality of the things in themselves.
Some people when asked what
color the sea is might say "green." Others might say "blue"
There is no point in arguing which of these statements is true, because
they are true by definition--that is by how a person defines the boundaries
of blue or green--especially where they meet each other on our personal
color charts!
This arbitrariness is the
very essence of all things that are true by definition, by necessity.
Contingent Truths.
Also--this necesary truth which is true by very definition or necessity
has no cause and effect to make it true, such as "if you go out in the
rain you will get wet." The latter kind of truth is a truth of fact,
a truth of science, a "contingent" truth. It is true because something
"causes" it to be true. A contingent truth is a very different
order of truth than a necessary truth.
In our modern thinking, every
event supposedly has its particular "cause," something that caused it to
be or to happen. We are not merely interested in the necessary truth
that "Johnny is wet." If we were Johnny's mother, we would certainly
want to know why Johnny is wet. We would be interested in
the contingency of his wetness--that is, the realm of cause-and-effect
about his wetness. (But Johnny himself in the face of such a question
might speak up: "Aw Mom, I'm not wet, I'm just a little damp."
He is offering up a necessary truth when his mother is looking for
a contingent truth: "how did you get this way?")
The thing that characterizes
modern culture is our preoccupation with contingent truths. We want
to know why things happen. We're like one of two people gazing
at a setting sun across a lake, blanketed by clouds of hues of pink and
orange and even red. One person might be thinking "how beautiful
this all is" (a truth by necessity). But we westerners would be too
busy to notice such beauty because our minds were working on the thought:
"why do these colors occur as they do; what causes the red, the orange
and the yellow?" We don't just want to receive the truths of the
events. We want to master those truths. And so we busy our
thoughts with the quest for contingent truths. We are of a scientific
bent or nature!
Anyway, it is this realm
of cause and effect truths that our modern, western, "empirical" science
is designed to explore. In the end, such science hopes to be able
to provide an explanation for everything that happens under the sun--in
terms of the causes of all things.
The ultimate contradictions
inherent in contingent truths. The difficulty, however, of trying
to describe life, the very universe, through such truths of fact or contingent
truths is that there is no end to their contingency. If everything
has a cause there can be nothing that has no cause. And yet something
has to start the series of cause-and-effect off. By this very logic
of cause-and-effect there can never be some kind of ultimate starting point,
a point at which things simply are, without a cause. And yet the
process of cause and effect necessarily requires some kind of a starting
point, one which would be the ultimate cause of all other causes.
Thus this logic cannot, because of its need to explain all events in terms
of their cause, provide any kind of explanation of this most important
of all causes: the first cause! At this most critical of points in
its line of logic, its very logic breaks down!
Thus without being able to
provide an explanation for first causes, there can be no true logic to
such a science. Indeed, all that factual or contingent science can
do is to study the appearances of events, and their apparent
causes. It cannot truly find the ultimate cause of anything.
Leibniz and the ultimate
source of all truth in God. Leibniz understood that all truths
ultimately point back in their contingency to the same ultimate cause:
God. It is God that sets off the course of all events. Everything
is contingent upon his being, his thoughts, his will. Unless you
can factor God into the picture you have offered no explanation whatsoever
about the cause of things!
Yet when you come back in
your logic to God, you are no longer talking about contingent truths--because
from the point of view of God all things have their truth "by necessity."
They are what they are and do what they do simply because God defines them
to be/to act that way.
Remember that Leibniz understood
that every monad had the potential to become everything. It is only
by the choices of God that they become what they actually become--they
become so by the arbitrary decisions or judgments of God. Through
the will of God they take the ultimate course that they do.
But you can never say why
God caused these things to take place as they do. Who could ever
claim to know the mind of God? To Leibniz, all we can do is describe
events--not explain them.
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Leibniz' major works or writings:
On the Art
of Combination (1666)
Hypothesis physica
nova (New Physical Hypothesis) (1671)
Discours de métaphysique
(Discourse on Metphysics) (1686)
The New System
(1695)
Nouveaux essais sur
l'entendement humaine (New Essays on Human Understanding) (1705)
Théodicée
(Theodicy) (1710)
The Dialogues of Hylas
and Philonous (1713)
Historia et origo
calculi differentialis (1713)
The
Monadology (1714)
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 Miles
H. Hodges
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