../03_The-West-to-1850/10_Dynasties/Leibniz.htm  

 GOTTFRIED WILHELM LEIBNIZ 

(1646-1716)



CONTENTS
GO TOLeibniz:  An Overview
GO TOHis Life and Works
GO TOHis Major Ideas
GO TOLeibniz's Writings

LEIBNIZ:  AN OVERVIEW

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.

HIS LIFE AND WORK

Leibniz was born and raised 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.

 

HIS MAJOR IDEAS


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.

LEIBNIZ'S WRITINGS

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