Gottfried Wilhelm Leibniz
(1646 - 1716)
(1646 - 1716)
Gottfried Wilhelm von Leibniz was a German mathematician and philosopher. He also worked as a political adviser. He was a very gifted man who made major contributions to several academic disciplines. In mathematics, he developed the method of differential and integral calculus independently from Newton. In philosophy, he was one of the most influential thinkers of the 17th and 18th centuries for establishing the principle of sufficient reason and the principle of pre-established harmony. He wrote multiple philosophical essays, including On the Art of Combination (1666) and Discourse on Metaphysics (1686).
He never produced a magnum opus similar to René Descartes’ Discours de la méthode or Isaac Newton’s Principia Mathematica, but he was nevertheless very well-known in educated circles. He develops his ideas in countless letters ad small essays. Today, he is considered a universal genius and one of the most original thinkers of the early modern period. He also made significant contributions to optics, mechanics (especially the theory of momentum), statistics, and probability theory and he was a pioneer in the use of binary systems and modern symbolic logic.
Gottfried Leibniz was born in Leipzig, Germany on July 1st, 1646. His family belonged to the educated elite: his mother was the daughter of a law professor and his father, who died before Leibniz was six, was a professor of law at the University of Leipzig as well as a jurist. Leibniz was sent to the Nicolai School but mostly taught himself from his father’s large library. At age twelve, he could read Latin and Greek, and by age twenty, he had worked through all the standard textbooks of mathematics, philosophy, theology, and law.
Leibniz was accepted into the University of Leipzig to study law in 1661. Here, he learned the philosophies of Galileo, Hobbes, and Descartes. After completing his baccalaureate thesis On the Principle of the Individual in 1663, he was refused his law doctorate on the grounds of being too young.
In 1666, Leibniz moved to Nuremberg to continue his studies at the University of Altdorf. That same year, he completed On the Art of Combination and was consequently offered a faculty position in 1667 when he completed his doctorate. He then began to focus on natural philosophy, composing New Physical Hypothesis (1671) and Discourse on Metaphysics (1686) as a two-part essay. During this time, Leibniz obtained a position with the Elector of Mainz.
In 1672, the Elector sent Leibniz to Paris on a diplomatic mission, which worked out very well for him because, at the time, Paris was a center of scientific research. He met Antoine Arnauld, Nicolas Malebranche, and Christiaan Huygens, who studied philosophy, physics, and mathematics with him. Leibniz developed a simple calculator and in 1673 took a trip to London to present it to the Royal Society.
Leibniz developed the idea that time and space are not substances but imaginary entities, and that extension and motion are the results of forces. In 1676, he discovered the formula for dynamics, which substitutes kinetic energy for the conservation of movement. Later that year, he was appointed as a librarian to Duke John Frederick. By 1678, Leibniz was serving as a councilor. During this period, he researched hydraulic presses, windmills, mechanical devices such as clocks, submarines, engineering for mining.
Leibniz was also perfecting his ideas about metaphysics and calculus, and in 1684, he published New Method for the Greatest and the Least, an exposition on differential calculus. Two years later, he completed Discourse on Metaphysics (1686). During this time, he was developing the philosophy of monadology, which he then defined in The Monadology (1714).
In 1700, Leibniz was inaugurated into the Academy of Sciences in Paris. In 1710, he published Theodicy and in 1714, The Monadology. When George I ascended the throne of England in 1714, he exiled Leibniz from the country, partly because of the war and partly because Leibniz was being accused of stealing ideas from Newton, though he had developed them independently. By 1716, he was suffering so badly from gout that he was confined to bed rest. He died on November 14th, 1716.
Leibniz writes about his development in a letter to Nicolas Remond in 1714: "…I have tried to uncover and unite the truth buried and scattered under the opinions of all the different philosophical sects, and I believe I have added something of my own which takes a few steps forward. The circumstances under which my studies proceeded from my earliest youth have given me some facility in this. I discovered Aristotle as a lad, and even the Scholastics did not repel me; even now I do not regret this. But then Plato too, and Plotinus, gave me some satisfaction, not to mention other ancient thinkers whom I consulted later. After finishing the trivial schools, I fell upon the moderns, and I recall walking in a grove on the outskirts of Leipzig called the Rosental, at the age of fifteen, and deliberating whether to preserve substantial forms or not. Mechanism finally prevailed and led me to apply myself to mathematics…. But when I looked for the ultimate reasons for mechanism, and even for the laws of motion, I was greatly surprised to see that they could not be found in mathematics but that I should have to return to metaphysics. This led me back to entelechies, and from the material to the formal, and at last brought me to understand, after many corrections and forward steps in my thinking, that monads or simple substances are the only true substances and that material things are only phenomena, though well founded and well connected. Of this, Plato, and even the later Academics and the skeptics too, had caught some glimpses… I flatter myself to have penetrated into the harmony of these different realms and to have seen that both sides are right provided that they do not clash with each other; that everything in nature happens mechanically and at the same time metaphysically but that the source of mechanics is metaphysics." (G III 606/L 654–55)
Monadology §§31–32: “Our reasonings are based on two great principles, that of contradiction… [and] that of sufficient reason.”
New Essays on Human Understanding: (1704) "Although time and place (i.e., the relations to what lies outside) do distinguish for us things which we could not easily tell apart by reference to themselves alone, things are nevertheless distinguishable in themselves. Thus, although diversity in things is accompanied by diversity of time or place, time and place do not constitute the core of identity and diversity, because they [sc. different times and places] impress different states upon the thing. To which it can be added that it is by means of things that we must distinguish one time or place from another, rather than vice versa." (A VI vi 230/RB 230)
I consider the notion of substance to be one of the keys to the true philosophy. (G III 245/AG 286)
Letter to Arnauld: “To put it briefly, I hold this identical proposition, differentiated only by the emphasis, to be an axiom, namely, that what is not truly one being is not truly one being either.” (G II 97/AG 86)
Letter to De Volder: “I think that it is obvious that primitive forces can be nothing but the internal strivings [tendentia] of simple substances, strivings by means of which they pass from perception to perception in accordance with a certain law of their nature, and at the same time harmonize with one another, representing the same phenomena of the universe in different ways, something that must necessarily arise from a common cause” (G II 275/AG 181).
The essay, A New System of Nature, 1695, presents a five-step argument for pre-established harmony:
(1) “[T]here is no real influence of one created substance on another.” (G IV 483/AG 143)
(2) “God originally created the soul (and any other real unity) in such a way that everything must arise for it from its own depths [fonds], through perfect spontaneity relative to itself, and yet with a perfect conformity relative to external things.” (G IV 484/AG 143)
(3) “This is what makes every substance represent the whole universe exactly and in its own way, from a certain point of view, and makes the perceptions or expressions of external things occur in the soul at a given time, in virtue of its own laws, as if in a world apart, and as if there existed only God and itself.” (G IV 484/AG 143)
(4) “[T]he organized mass, in which the point of view of the soul lies, being expressed more closely by the soul, is in turn ready to act by itself, following the laws of the corporeal machine, at the moment when the soul wills it to act, without disturbing the laws of the other – the spirits and blood then having exactly the motions that they need to respond to the passions and perceptions of the soul.” (G IV 484/AG 144)
(5) “It is this mutual relation, regulated in advance in each substance of the universe, which produces what we call their communication, and which alone brings about the union of soul and body.” (G IV 484–85/AG 144)
On final and efficient causes: (Monadology §§79 and 81): Souls act according to the laws of final causes, through appetitions, ends, and means. Bodies act according to the laws of efficient causes or of motions. And these two kingdoms, that of efficient causes and that of final causes, are in harmony with each other.
"In general, we must hold that everything in the world can be explained in two ways: through the kingdom of power, that is, through efficient causes, and through the kingdom of wisdom, that is, through final causes, through God, governing bodies for his glory, like an architect, governing them as machines that follow the laws of size or mathematics, governing them, indeed, for the use of souls, and through God governing for his glory souls capable of wisdom, governing them as his fellow citizens, members with him of a certain society, governing them like a prince, indeed like a father, through laws of goodness or moral laws." (GM VI 243/AG 126)
Monads are not spatial, they represent a unique point of view. Therefore, the universe is multi-perspectival. Monads are simple substances or mind-like entities that do not exist in space, but they represent the whole universe from a unique perspective: (Discourse on Metaphysics §14.) "Now, first of all, it is very evident that created substances depend upon God, who preserves them and who even produces them continually by a kind of emanation, just as we produce our thoughts. For God, so to speak, turns on all sides and in all ways the general system of phenomena which he finds it good to produce in order to manifest his glory, and he views all the faces of the world in all ways possible, since there is no relation that escapes his omniscience. The result of each view of the universe, as seen from a certain position, is a substance which expresses the universe in conformity with this view, should God see fit to render his thought actual and to produce this substance." (A VI iv 1549–50/AG 46–47)
On innate ideas: "Experience is necessary, I admit, if the soul is to be given such and such thoughts, and if it is to take heed of the ideas that are within us. But how could experience and the senses provide the ideas? Does the soul have windows? Is it similar to writing-tablets, or like wax? Clearly, those who take this view of the soul are treating it as fundamentally corporeal” (A VI vi 110/RB 110).
“God has chosen the most perfect world, that is, the one which is at the same time the simplest in hypotheses and the richest in phenomena” (A VI iv 1538/AG 39)