Gottfried Wilhelm Leibniz facts for kids
Quick facts for kids
Gottfried Wilhelm Leibniz
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Portrait by Christoph Bernhard Francke, 1695
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| Born | 1 July 1646 Leipzig, Saxony, Holy Roman Empire
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| Died | 14 November 1716 (aged 70) |
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| Era | 17th-/18th-century philosophy |
| Region | Western philosophy |
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| Doctoral advisor | Bartholomäus Leonhard von Schwendendörffer (Dr. jur. thesis advisor) |
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Main interests
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Mathematics, physics, geology, medicine, biology, embryology, epidemiology, veterinary medicine, paleontology, psychology, engineering, linguistics, philology, sociology, metaphysics, ethics, economics, diplomacy, history, politics, music theory, poetry, logic, theodicy, universal language, universal science |
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Notable ideas
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Algebraic logic
Binary code Calculus Differential equations Mathesis universalis Monads Best of all possible worlds Pre-established harmony Identity of indiscernibles Mathematical matrix Mathematical function Newton–Leibniz axiom Leibniz's notation Leibniz integral rule Integral symbol Leibniz harmonic triangle Leibniz's test Leibniz formula for π Leibniz formula for determinants Fractional derivative Chain rule Quotient rule Product rule Leibniz wheel Leibniz's gap Algebra of concepts Vis viva (principle of conservation of energy) Principle of least action Salva veritate Stepped reckoner Symbolic logic/Boolean algebra Semiotics Analysis situs Principle of sufficient reason Law of continuity Transcendental law of homogeneity Ars combinatoria (alphabet of human thought) Characteristica universalis Calculus ratiocinator Compossibility Partial fraction decomposition Protogaea Problem of why there is anything at all Pluralistic idealism Metaphysical dynamism Relationism Apperception A priori/a posteriori distinction Deontic logic Well-founded phenomenon |
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Influences
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Gottfried Wilhelm Leibniz (born July 1, 1646 – died November 14, 1716) was a brilliant German thinker. He was like a "polymath", meaning he was good at many different things. He was a mathematician, a philosopher, a scientist, and even a diplomat.
Leibniz is a very important person in the history of philosophy and the history of mathematics. He wrote about many subjects, including theology (the study of religion), ethics (what is right and wrong), politics, and law. He also made big contributions to physics and technology. He even thought about ideas that later became important in computer science and psychology.
One of his biggest achievements was developing calculus, a type of math used to study change. He did this at the same time as Isaac Newton, but they worked separately. Many mathematicians still prefer Leibniz's way of writing calculus. He also helped create the binary number system (using only 0s and 1s), which is the basic language of almost all modern computers. Because of this, some people call him the "founder of computer science."
In philosophy, Leibniz is known for his idea of "optimism." He believed that our world is the "best possible world" that God could have made. This idea was sometimes made fun of by other thinkers, like Voltaire. Leibniz was one of the main thinkers of the 17th century who believed in rationalism, which means using reason to understand the world. His ideas still influence modern logic and philosophy today.
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Biography of a Brilliant Mind
Early Life and Learning
Gottfried Leibniz was born in Leipzig, Germany, on July 1, 1646. This was near the end of a big war called the Thirty Years' War. His father was a professor at the University of Leipzig. When Leibniz was only six years old, his father passed away.
Leibniz was very lucky because he got to use his father's large personal library from a young age. This meant he could read many advanced books that most students wouldn't see until college. By the time he was 12, he was very good at Latin, the language most scholarly books were written in. He was so smart that at 13, he wrote 300 lines of Latin poetry in just one morning!
He started university at Leipzig when he was only 14. He quickly earned his bachelor's and master's degrees in philosophy. He then studied law and got his law degree in 1666. At 19, he wrote his first book, De Arte Combinatoria (On the Combinatorial Art). This book explored ways to combine ideas.
Even though he was very smart, the University of Leipzig didn't want to give him his law doctorate because he was so young. So, Leibniz went to another university, the University of Altdorf. There, he quickly earned his law doctorate in November 1666. He was offered a job there, but he turned it down because he wanted to explore other ideas.
Working for Important People
Leibniz's first job was as a secretary for a group interested in alchemy (an old form of chemistry). He soon met a powerful politician named Johann Christian von Boyneburg, who hired him as an assistant. This led Leibniz to work for the Elector (a ruler) of Mainz, helping to rewrite laws.
Leibniz also became involved in diplomacy. He suggested a plan to the French government: France should try to take Egypt to distract them from attacking German lands. He went to Paris in 1672 to discuss this. While there, he met Christiaan Huygens, a famous Dutch scientist. Huygens helped Leibniz realize he needed to learn more about math and physics. This pushed Leibniz to study on his own and eventually discover calculus.
In 1673, Leibniz visited London and showed off a calculating machine he had designed. This machine could add, subtract, multiply, and divide. The Royal Society, a famous scientific group, was so impressed that they made him a member.
After his patrons (the people who supported him) died, Leibniz needed a new job. He accepted a position with the Duke of Brunswick in Hanover in 1676. He stayed with the House of Brunswick for the rest of his life, working as a historian, political advisor, and librarian.
Life in Hanover and Later Years
In Hanover, Leibniz worked on many projects. He tried to improve mining operations using windmills, but this didn't work out. He became friends with important women in the royal family, like Electress Sophia of Hanover, who supported his intellectual work.
Leibniz published his most important math papers between 1682 and 1692 in a journal he helped start, the Acta Eruditorum. This journal helped him become famous in math and science.
He was asked to write a history of the House of Brunswick. He traveled a lot to find old documents for this project. He worked on it for many years but never finished it, partly because he was busy with so many other things. When his notes were finally published much later, they filled three large books!
In 1708, a dispute started with Isaac Newton over who invented calculus first. This argument, called the calculus priority dispute, lasted for the rest of Leibniz's life. Most historians today agree that both Newton and Leibniz discovered calculus independently.
Leibniz died in Hanover in 1716. He was not very popular at the time, and few people attended his funeral. His grave was unmarked for over 50 years. However, his ideas would later become much more appreciated.
Personal Life
Leibniz never married. He was known for being charming, polite, and having a good sense of humor. He had many friends across Europe. He was a Protestant Christian and believed deeply in God.
Leibniz as a Philosopher
Leibniz's philosophical ideas are found in many short writings, letters, and notes. He only published two philosophy books during his lifetime.
Key Philosophical Ideas
Leibniz had several main philosophical principles:
- Identity and Contradiction: If something is true, its opposite cannot also be true.
- Identity of Indiscernibles: Two different things cannot have all the exact same properties. If you can't tell them apart, they are actually the same thing. For example, two identical-looking leaves are still different because they are in different places.
- Sufficient Reason: Everything that exists, every event, and every truth must have a reason why it is that way and not otherwise.
- Pre-established Harmony: Things in the universe seem to interact, but Leibniz believed they actually follow their own "pre-programmed" paths that are perfectly coordinated by God. Like two clocks that always show the same time without being connected.
- Law of Continuity: Nature doesn't make sudden jumps. Everything changes smoothly.
- Optimism: Leibniz believed that God always chooses the best. So, this world, with all its flaws, is the "best of all possible worlds."
- Plenitude: The best possible world would include every real possibility.
Monads: The Building Blocks of Reality
Leibniz's most famous idea in philosophy is his theory of monads. He believed the universe is made of an infinite number of simple "substances" called monads.
- Monads are like tiny, unique, non-physical "mind-atoms." They have no parts and are the most basic units of existence.
- Each monad is unique and constantly changing its qualities.
- They are not affected by time and can only be created or destroyed by God.
- Monads don't interact directly with each other. Instead, because of "pre-established harmony," each monad follows its own internal "instructions" that perfectly match what's happening in all other monads. It's like each monad is a tiny mirror reflecting the entire universe.
- Leibniz believed that space, time, and motion are not absolute things, but rather ways we describe the relationships between monads. This idea was similar to Albert Einstein's later theory of relativity.
Why This World is the Best Possible
In his book Theodicy, Leibniz tried to explain why there is evil and imperfection in a world created by an all-good, all-wise, and all-powerful God.
- He argued that God, being perfect, would create the best possible world.
- Any flaws we see must be necessary parts of this "best possible world." If a better world could exist without those flaws, God would have created it.
- Leibniz believed that human beings, as creations, have limits in their wisdom and free will. This means they can make mistakes and bad choices, leading to "moral evil" (sin) and "physical evil" (suffering).
- God allows these evils as a necessary consequence of imperfection and as a way for humans to learn and grow.
Logic and Symbols
Leibniz was very interested in logic, the study of correct reasoning. He thought that symbols were very important for human understanding. He believed that if we had a perfect system of symbols, we could solve problems by simply calculating, like in math.
- He imagined a "calculus ratiocinator" (reasoning calculator) and a "universal characteristic" (universal language of symbols). These ideas were like early visions of symbolic logic and even modern computer programming languages.
- He thought that complex ideas could be made by combining symbols for simpler ideas, similar to how numbers are made from prime numbers.
- Leibniz's work in logic was so advanced that some people say he developed ideas that weren't fully understood until 200 years later.
Leibniz as a Mathematician
Leibniz made huge contributions to mathematics.
Calculus: A New Kind of Math
Leibniz is famous for inventing calculus (differential and integral calculus) at the same time as Isaac Newton.
- A key moment for Leibniz was in 1675 when he used integral calculus to find the area under a curve.
- He created many of the symbols we still use today, like the integral sign (∫), which looks like an elongated "S" from the Latin word summa (sum). He also used "d" for differentials, from the Latin word differentia (difference).
- He showed how integration and differentiation are opposite processes, an idea now called the fundamental theorem of calculus.
- The "product rule" in calculus is still known as "Leibniz's law."
Other Math Discoveries
- Functions: Leibniz was one of the first to use the term "function" in math to describe how one quantity depends on another.
- Linear Systems: He organized numbers from linear equations into arrays, which are now called matrices. This helped solve systems of equations. He also helped develop the idea of determinants, which are numbers calculated from matrices.
- Pi Formula: Leibniz discovered a formula for pi (π): 1 - 1/3 + 1/5 - 1/7 + ... = π/4. This series adds and subtracts fractions to get closer to the value of pi.
Leibniz as a Scientist and Engineer
Leibniz was not just a philosopher and mathematician; he was also a practical scientist and engineer. He believed that theory should always be combined with practical use.
Physics and the Nature of Reality
- Leibniz had different ideas about physics than Descartes and Newton. He believed that space, time, and motion were relative, meaning they depend on the observer, rather than being absolute. This idea was later supported by Albert Einstein.
- He developed a theory of motion based on "vis viva" (living force), which is similar to what we now call kinetic energy. He realized that total energy is conserved in some systems.
Other Sciences
- Geology: He suggested that the Earth has a molten core, which was a very advanced idea for his time.
- Biology: He studied fossils and comparative anatomy, showing an early understanding of how living things change over time.
- Medicine: He encouraged doctors to use careful observations and experiments in their work.
Psychology: Understanding the Mind
Leibniz was very interested in how the mind works. He is seen as an early pioneer in psychology.
- He wrote about attention, consciousness, memory, and learning.
- He introduced the idea of "petites perceptions" (small perceptions). These are tiny perceptions that we are not aware of, but they still influence us. He thought that there's a part of our mind we're not always conscious of, which was an early idea similar to the unconscious mind.
- He believed that the mind and body don't directly act on each other, but they work in perfect harmony, like two separate clocks that always keep the same time.
Technology and Computers
Leibniz was a true inventor. He designed many machines and tools.
- Calculating Machines: He invented the "stepped reckoner" in 1671, a machine that could perform all four basic math operations (add, subtract, multiply, divide). This was a big step towards modern calculators.
- Binary System: He deeply explored the binary numeral system (base 2), which uses only 0s and 1s. He saw how the ancient Chinese book I Ching used patterns that looked like binary code. This binary system is the foundation of all digital computers today.
- He even imagined a machine where binary numbers were shown by marbles, controlled by a basic form of punched cards. This idea was very similar to how modern computers work, using electrical signals instead of marbles.
Librarian and Organizer of Knowledge
Leibniz also worked as a librarian for the Duke of Brunswick. He was one of the first people to think about library science.
- He wanted to create a system to organize all books and information. He even suggested that publishers should provide summaries of all new books to make indexing easier.
- He believed in creating a huge empirical database to help all sciences grow. His ideas for a universal language and a "community of minds" can be seen as early visions of things like the World Wide Web.
Promoting Scientific Groups
Leibniz strongly believed that scientists should work together. He encouraged the creation of national scientific societies, like the Royal Society in Britain. He helped create the Berlin Academy of Sciences in 1700 and was its first president. This academy still exists today and publishes his works.
Leibniz's Influence and Legacy
When Leibniz died, his reputation wasn't very high. Many people remembered him mainly for his book Théodicée, which was made fun of by Voltaire in his famous story Candide. Also, the argument with Newton over calculus made some people doubt his math work.
However, over time, people began to rediscover and appreciate Leibniz's amazing ideas.
- In 1765, his book Nouveaux essais sur l'entendement humain was published, and thinkers like Immanuel Kant studied it closely.
- In the 20th century, philosophers like Bertrand Russell and Louis Couturat brought more attention to Leibniz's work, especially his ideas on logic.
- Today, Leibniz is considered one of the most important thinkers in history. His ideas on identity, individuation, and "possible worlds" are still discussed in philosophy.
- In 1985, the German government created the Gottfried Wilhelm Leibniz Prize, a very large award for scientific achievements, named in his honor.
- His collection of papers is so important that it was added to UNESCO's Memory of the World Programme in 2007.
Writings and Publications
Leibniz wrote in several languages, mainly Latin, French, and German. He published many articles and pamphlets during his life, but only a few books. After he died, people found an enormous collection of his writings: about 15,000 letters and over 40,000 other documents! Many of these letters were as long as essays.
A huge project is still ongoing to publish all of Leibniz's writings. This project started in 1901 and has faced many challenges, including world wars. So far, 57 volumes of his critical edition have been published.
Some of His Important Works
Here are a few of his well-known writings:
- 1666: De Arte Combinatoria (On the Art of Combination)
- 1684: "Nova methodus pro maximis et minimis" ("New method for maximums and minimums") – This is where he introduced his calculus notation.
- 1686: Discourse on Metaphysics
- 1704 (published 1765): Nouveaux essais sur l'entendement humain (New Essays on Human Understanding) – A response to John Locke's ideas.
- 1710: Théodicée (Theodicy) – His famous book about why this is the best possible world.
- 1714: Monadologie (Monadology) – Explaining his theory of monads.
Images for kids
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An old engraving of Gottfried Wilhelm Leibniz.
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Leibniz's "stepped reckoner" calculating machine.
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Leibniz's vast collection of letters and notes.
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A page from Leibniz's handwritten manuscript of the Monadology.
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A diagram of I Ching hexagrams that Leibniz studied, with his added numbers.
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A street sign in Berlin named after Leibniz.
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Commercium philosophicum et mathematicum (1745), a collection of letters between Leibniz and Johann Bernoulli.
