Gottfried Wilhelm Leibniz (1646-1716) was a German philosopher, mathematician, physicist, historian, diplomat, and inventor, one of the last great ‘universal geniuses’. His work spans nearly all fields of knowledge of his time, and his ideas have had a profound influence on Western philosophy, logic, mathematics, and science.
1. Independent Inventor of Differential and Integral Calculus
Leibniz developed, independently of Isaac Newton, the principles of differential and integral calculus. Although Newton developed his version earlier but published later, the notation we use today largely comes from Leibniz (such as the integral sign ∫ and dy/dx for the derivative).
The development of calculus was a monumental breakthrough that laid the foundation for much of modern mathematics and physical science. The bitter priority dispute that later arose between the supporters of Newton and Leibniz overshadowed the achievements of both men.
2. Pioneer of the Mechanical Calculator
Leibniz was fascinated by calculation and logic. Building on the work of Blaise Pascal, he designed and built one of the first mechanical calculators capable of addition, subtraction, multiplication, and division: the ‘Stepped Reckoner’.
Although the machine did not always work perfectly due to the technical limitations of the time, its principle of the ‘stepped drum’ (Leibniz wheel) was a major innovation used in mechanical calculators well into the 20th century.
3. The Binary System
Leibniz developed the modern binary number system, which uses only the digits 0 and 1. He saw this not only as an efficient way to perform calculations (which later proved crucial for computers) but also imbued it with deep philosophical and theological significance.
He viewed the binary system as a symbol of creation ‘ex nihilo’ (out of nothing), where 1 represented God and 0 represented nothingness. He was fascinated by the Chinese I Ching (Book of Changes), which he believed contained an early form of binary code.
4. Philosophy: Monads and ‘The Best of All Possible Worlds’
Leibniz’s metaphysics is complex and revolves around the concept of ‘monads’. These are the fundamental, indivisible substances that make up reality. Each monad is a unique ‘point of perception’ that reflects the entire universe from its own perspective.
Monads have no ‘windows’ and do not directly influence each other, but their development is predetermined by God in a ‘pre-established harmony’ (harmonia praestabilita). Within this system, Leibniz argued that God, as a perfect being, necessarily created the ‘best of all possible worlds’ – a world that combines the greatest possible perfection and variety with the simplest laws. This optimistic idea was later famously parodied by Voltaire in ‘Candide’.
5. The Principle of Sufficient Reason
A central principle in Leibniz’s philosophy is the ‘Principle of Sufficient Reason’ (principium rationis sufficientis). This states that nothing happens without a reason; for every truth or fact, there must be a reason or explanation why it is so and not otherwise.
This principle, along with the Principle of Non-Contradiction (something cannot be both true and false at the same time), formed the basis of his rationalist approach to knowledge and reality.
6. Diplomat and Political Advisor
In addition to his academic work, Leibniz was also active as a diplomat and advisor to various German noble houses, notably the House of Hanover. He traveled extensively throughout Europe, met important thinkers and politicians, and was involved in various political and diplomatic projects.
For example, he tried to unite the German states, achieve reconciliation between Catholics and Protestants, and form a European coalition against Louis XIV of France (including proposing a plan for a French invasion of Egypt to divert attention).
7. Enormous Correspondence
Leibniz maintained an extraordinarily extensive correspondence with over 1,100 scholars, philosophers, mathematicians, theologians, and politicians across Europe. These letters were an important medium for exchanging ideas in an era before scientific journals.
His correspondence contains a wealth of information about his thinking and the intellectual debates of his time. The complete publication and study of this vast correspondence are still ongoing.
8. Librarian and Historian
For much of his career, Leibniz worked as a librarian and court historian for the House of Hanover (and previously in Mainz). He was responsible for managing and expanding the ducal library.
He was also commissioned to write a history of the House of Welf (Hanover). This project led him to extensive archival research in Germany and Italy and resulted in significant contributions to the methods of historiography and source criticism, although he never completed the main work.
9. Interest in China
Leibniz had a great interest in Chinese culture, language, and philosophy, which was unusual for his time. He corresponded with Jesuit missionaries in China and studied Confucian texts.
He saw parallels between his own philosophy and certain Chinese concepts and believed in the possibility of a fruitful exchange between European and Chinese civilizations. His fascination with the binary system was partly inspired by his study of the I Ching.
10. Relatively Unknown at His Death
Despite his enormous intellectual contributions and his work for influential courts, Leibniz died in 1716 relatively isolated and undervalued. His last patron, George Louis of Hanover (who became King George I of Great Britain in 1714), had ordered him to remain in Hanover while the court moved to London.
The priority dispute with Newton had damaged his reputation in England, and his philosophical optimism was considered naive by some. Only later was the full breadth and depth of his work fully recognized.
