GOTTFRIED LEIBNIZ: BIOGRAPHY, CONTRIBUTIONS AND WORKS - PHILOSOPHY - 2024

Gottfried Wilhem Leibniz (1646-1716) was a German mathematician and philosopher. As a mathematician, his most famous contributions were the creation of the modern binary system and the differential and integral calculus. As a philosopher, he was one of the great rationalists of the seventeenth century along with Descartes and Spinoza, and is recognized for his metaphysical optimism.

Denis Diderot, who disagreed with Leibniz on several ideas, commented: «Perhaps no man has read, studied, meditated and written as much as Leibniz… What he has composed about the world, God, nature and the soul is of the most sublime eloquence. "

More than a century later, Gottlob Frege expressed a similar admiration, declaring that "in his writings Leibniz showed such a profusion of ideas that in this respect he is virtually of a class of his own."

Unlike many of his contemporaries, Leibniz does not have a single work to understand his philosophy. Instead, to understand his philosophy, it is necessary to take into account several of his books, correspondence, and essays.

Biography

Gottfried Wilhelm Leibniz was born on July 1, 1646 in Leipzig. Its birth occurred in the Thirty Years' War, just two years before this conflict ended.

Gottfried's father was named Federico Leibniz, who was serving as a professor of moral philosophy at the University of Leipzig, as well as a jurist. For his part, the mother was the daughter of a law professor and was named Catherina Schmuck.

Education

Gottfried's father died when he was still a child; he was barely six years old. From that moment on, both his mother and his uncle took care of his education.

His father had a large personal library, so Gottfried was able to access it from the young age of seven, and pursue his own training. The texts that interested him most at first were those related to the so-called Fathers of the Church, as well as those related to ancient history.

It is said that he had a great intellectual capacity, since at the young age of 12 he spoke Latin fluently and was in the process of learning Greek. When he was just 14 years old, in 1661, he enrolled at the University of Leipzig in the specialty of law.

At the age of 20, Gottfried completed his studies and was already a professional specialized in scholastic philosophy and logic, as well as in the classical field of law.

Motivation for teaching

In 1666 Leibniz prepared and presented his habilitation thesis, at the same time as his first publication. In this context, the University of Leipzig denied him the possibility of teaching at this study center.

Then, Leibniz delivered this thesis to another university, Altdorf University, from which he acquired a doctorate in just 5 months.

Later, this university offered him the possibility of teaching, but Leibniz rejected this proposal and, instead, dedicated his working life to serving two very important German families for the society of the time.

These families were the Schönborn, between 1666 and 1674, and the Hannovers, between 1676 and 1716.

First jobs

The first work experiences were obtained by Leibniz thanks to a job as an alchemist in the city of Nuremberg.

At that time he contacted Johann Christian von Boineburg, who had worked with Juan Felipe von Schönborn, who was serving as Archbishop-Elector of the city of Mainz, Germany.

Initially, Boineburg hired Leibniz as his assistant. Later he introduced him to Schönborn, with whom Leibniz wanted to work.

In order to get Schönborn's approval and for him to offer him a job, Leibniz prepared a letter dedicated to this character.

Eventually this action brought good results, since Schönborn contacted Leibniz with the intention of hiring him to rewrite the legal code corresponding to his electorate. In 1669 Leibniz was appointed adviser within the court of appeals.

The importance that Schönborn had in Leibniz's life was that thanks to him it was possible for him to become known in the social sphere in which he developed.

Diplomatic actions

One of the actions that Leibniz carried out while in the service of Schönborn was to write an essay in which he presented a series of arguments in favor of the German candidate for the Crown of Poland.

Leibniz had proposed to Schönborn a plan to revitalize and protect the German-speaking countries after the devastating and opportunistic situation left by the Thirty Years War. Although the elector listened to this plan with reservations, later Leibniz was summoned to Paris to explain the details of it.

Ultimately, this plan was not carried out, but that was the beginning of a Parisian stay for Leibniz that lasted for years.

Paris

This stay in Paris allowed Leibniz to be in contact with various renowned personalities in the field of science and philosophy. For example, he had several conversations with the philosopher Antoine Arnauld, who was considered the most relevant of the moment.

He also had several encounters with the mathematician Ehrenfried Walther von Tschirnhaus, with whom he even developed a friendship. In addition, she was able to meet the mathematician and physicist Christiaan Huygens, and had access to the publications of Blaise Pascal and René Descartes.

It was Huygens who acted as a mentor in the next path that Leibniz took, which was to strengthen his knowledge. Having been in contact with all these specialists, he realized that he needed to expand the areas of his knowledge.

Huygens' help was partial, since the idea was for Leibniz to follow a self-teaching program. This program had excellent results, discovering even elements of great importance and transcendence, such as his research related to infinite series and his own version of the differential calculus.

London

The reason why Leibniz was summoned to Paris did not take place (the implementation of the plan mentioned above), and Schönborn sent him and his nephew to London; the motive was a diplomatic action before the government of England.

In this context, Leibniz took the opportunity to interact with such illustrious figures as the English mathematician John Collins and the German-born philosopher and theologian Henry Oldenburg.

In these years, he took the opportunity to present to the Royal Society an invention that he had been developing since 1670. It was a tool through which it was possible to perform arithmetic calculations.

This tool was called stepped reckoner and it differed from other similar initiatives in that it could carry out the four basic mathematical operations.

After witnessing the operation of this machine, the members of the Royal Society appointed him an external member.

After this achievement, Leibniz was preparing to carry out the mission for which he had been sent to London, when he learned that the elector Juan Felipe von Schönborn had died. This caused him to go directly to Paris.

Hannover Family

The death of John Philip von Schönborn meant that Leibniz had to get another occupation and, fortunately, in 1669 the Duke of Brunswick invited him to visit the Hannover house.

At that time Leibniz declined this invitation, but his relationship with Brunkwick continued for several more years through an exchange of letters from 1671. Two years later, in 1673, the duke offered Leibniz a position as secretary.

Leibniz arrived at the Hannover house at the end of 1676. Previously he went to London again, where he received new knowledge, and there is even information that establishes that at that time he saw some documents of Isaac Newton.

However, most historians establish that this is not true, and that Leibniz reached his conclusions independently of Newton.

Long term service

Already being in the House of Brunswick, Leibniz began to work as a private counselor of Justice and was in the service of three rulers of this house. The work he carried out revolved around political advice, in the field of history and also as a librarian.

Likewise, he had the possibility to write about theological, historical and political issues related to this family.

While in the service of the House of Brunswick, this family grew in popularity, respect and influence. Although Leibniz was not very comfortable with the city as such, he did recognize that it was a great honor to be part of this duchy.

For example, in 1692 the Duke of Brunswick was appointed hereditary elector of the Germanic Roman Empire, which was a great opportunity for promotion.

Jobs

While Leibniz was dedicated to providing his services to the House of Brunswick, these allowed him to develop his studies and inventions, which were in no way linked to obligations directly related to the family.

So, in 1674 Leibniz began to develop the conception of calculus. Two years later, in 1676, he had already developed a system that had coherence and that saw the public light in 1684.

1682 and 1692 were very important years for Leibniz, since his documents in the field of mathematics were published.

Family history

The Duke of Brunswick at that time, named Ernesto Augusto, proposed to Leibniz one of the most important and challenging tasks he had; write the history of the House of Brunswick, beginning in the times associated with Charlemagne, and even before this time.

The duke's intention was to make said publication favorable to him within the framework of the dynastic motivations he possessed. As a consequence of this task, Leibniz dedicated himself to traveling throughout Germany, Italy and Austria between 1687 and 1690.

The writing of this book took several decades, which caused the annoyance of the members of the House of Brunswick. In fact, this work was never completed and two reasons are attributed for this:

In the first place, Leibniz was characterized as a meticulous man and very devoted to detailed investigation. Apparently, there were no really relevant and truthful data on the family, so it is estimated that the result would not have been to their liking.

Second, at that time Leibniz was dedicated to producing a lot of personal material, which could have prevented him from devoting all the time he had to the history of the House of Brunswick.

Many years later it became clear that, indeed, Leibniz had managed to compile and develop a good part of the task that had been assigned to him.

In the nineteenth century these writings of Leibniz were published, reaching three volumes in length, even though the heads of the House of Brunswick would have been comfortable with a much shorter and less rigorous book.

Dispute with Newton

During the first decade of 1700, the Scottish mathematician John Keill indicated that Leibniz had plagiarized Isaac Newton regarding the conception of the calculus. This accusation took place in an article written by Keill for the Royal Society.

Then, this institution carried out an extremely detailed investigation on both scientists, to determine who had been the author of this discovery. In the end it was determined that Newton was the first to discover the calculus, but Leibniz was the first to publish his dissertations.

Final years

In 1714 George Louis of Hannover became King George I of Great Britain. Leibniz had a lot to do with this appointment, but Jorge I was adverse and demanded that he show at least one volume of his family's history, otherwise he would not meet him.

In 1716 Gottfried Leibniz died in the city of Hannover. An important fact is that Jorge I did not attend his funeral, which highlights the separation between the two.

Main contributions

In mathematics

Calculation

Leibniz's contributions in mathematics were various; the best known and most controversial is the infinitesimal calculus. The infinitesimal calculus or simply calculus, is a part of modern mathematics that studies the limits, derivatives, integrals and infinite series.

Both Newton and Leibniz presented their respective theories of calculus in such a short period of time that there was even talk of plagiarism.

Today both are considered co-authors of the calculus, however, Leibniz's notation ended up being used due to its versatility.

It was Leibniz, in addition, who gave the name to this study and who contributed the symbolism used today: ∫ y dy = y² / 2.

Binary system

In 1679, Leibniz devised the modern binary system and presented it in his work Explication de l'Arithmétique Binaire in 1703. Leibniz's system uses the numbers 1 and 0 to represent all number combinations, unlike the decimal system.

Although it is often credited with its creation, Leibniz himself admits that this discovery is due to in-depth study and reinterpretation of an idea already known in other cultures, especially Chinese.

Leibniz's binary system would later become the basis of computation, since it is the one that governs almost all modern computers.

Adding machine

Leibniz was also enthusiastic about creating mechanical calculating machines, a project that was inspired by Pascal's calculator.

The Stepped Reckoner, as he called it, was ready in 1672 and was the first to allow addition, subtraction, multiplication and division operations. In 1673 he was already presenting it to some of his colleagues at the French Academy of Sciences.

The Stepped Reckoner incorporated a stepped drum gear device, or "Leibniz wheel." Although Leibniz's machine was impractical due to technical flaws, it laid the foundation for the first mechanical calculator marketed 150 years later.

Additional information about Leibniz's calculating machine is available from the Computer History Museum and the Encyclopædia Britannica.

In philosophy

It is difficult to encompass the philosophical work of Leibniz, since, although abundant, it is based mainly on diaries, letters and manuscripts.

Continuity and sufficient reason

Two of the most important philosophical principles proposed by Leibniz are the continuity of nature and sufficient reason.

On the one hand, the continuity of nature is related to the infinitesimal calculus: a numerical infinity, with infinitely large and infinitely small series, which follow a continuity and can be read from front to back and vice versa.

This reinforced in Leibniz the idea that nature follows the same principle and therefore "there are no jumps in nature."

On the other hand, sufficient reason refers to "nothing happens without a reason." In this principle, the subject-predicate relationship must be taken into account, that is, A is A.

Monads

This concept is closely related to that of plenitude or monads. In other words, 'monad' means that which is one, has no parts and is therefore indivisible.

They are about the fundamental things that exist (Douglas Burnham, 2017). Monads are related to the idea of ​​fullness, because a full subject is the necessary explanation of everything it contains.

Leibniz explains the extraordinary actions of God by establishing him as the complete concept, that is, as the original and infinite monad.

Metaphysical optimism

On the other hand, Leibniz is well known for his metaphysical optimism. "The best of all possible worlds" is the phrase that best reflects his task of responding to the existence of evil.

According to Leibniz, among all the complex possibilities within the mind of God, it is our world that reflects the best possible combinations and to achieve this, there is a harmonious relationship between God, the soul and the body.

In Topology

Leibniz was the first to use the term analysis situs, that is, analysis of position, which was later used in the 19th century to refer to what is known today as topology.

Informally, it can be said that the topology takes care of the properties of the figures that remain unchanged.

In medicine

For Leibniz, medicine and morals were closely related. He considered medicine and the development of medical thought as the most important human art, after philosophical theology.

It was part of scientific geniuses who, like Pascal and Newton, used the experimental method and reasoning as the basis of modern science, which was also reinforced by the invention of instruments such as the microscope.

Leibniz supported medical empiricism; He thought of medicine as an important basis for his theory of knowledge and the philosophy of science.

He believed in using bodily secretions to diagnose a patient's medical condition. His thoughts on animal experimentation and dissection for the study of medicine were clear.

He also made proposals for the organization of medical institutions, including ideas on public health.

In religion

His reference to God is clear and habitual in his writings. He conceived of God as an idea and as a real being, as the only necessary being, who creates the best of all worlds.

For Leibniz, since everything has a cause or reason, at the end of the investigation there is a single cause from which everything is derived. The origin, the point where everything begins, that "uncaused cause", is for Leibniz God himself.

Leibniz was very critical of Luther and accused him of rejecting philosophy as if it were the enemy of faith. In addition, he analyzed the role and importance of religion in society and its distortion by becoming only rites and formulas, which lead to a false conception of God as being unjust.

Plays

Leibniz wrote mainly in three languages: Scholastic Latin (ca. 40%), French (ca. 35%), and German (less than 25%).

Theodicy was the only book he published during his lifetime. It was published in 1710 and its full name is Theodicy Essay on the goodness of God, the freedom of man and the origin of evil.

Another work of his was published, albeit posthumously: New essays on human understanding.

Apart from these two works, Lebniz especially wrote academic articles and pamphlets.

Theodicy

The Theodicy contains the main theses and arguments of what began to be known as early as the 18th century as «optimism» (…): a rationalist theory on the goodness of God and his wisdom, on divine and human freedom, the nature of the created world and the origin and meaning of evil.

This theory is often summed up by the famous and frequently misinterpreted Leibnizian thesis that this world, despite the evil and suffering it contains, is "the best of all possible worlds." (Caro, 2012).

Theodicy is the Leibzinian rational study of God, with which he tries to justify divine goodness by applying mathematical principles to Creation.

Others

Leibniz acquired a great culture after reading the books in his father's library. He had a great interest in the word, he was aware of the importance of language in the advances of knowledge and the intellectual development of man.

He was a prolific writer, published numerous pamphlets, among which "De jure suprematum" stands out, an important reflection on the nature of sovereignty.

On many occasions, he signed with pseudonyms and wrote about 15,000 letters sent to more than a thousand recipients. Many of them have the length of an essay, rather than letters they were treated on different subjects of interest.

He wrote a lot during his life, but he left countless unpublished writings, so much so that his legacy is still being edited today. Leibniz's complete work already exceeds 25 volumes, averaging 870 pages per volume.

In addition to all his writings on philosophy and mathematics, he has medical, political, historical and linguistic writings.

References

1. Belaval, Y. (2017). Encyclopædia Britannica. Obtained from Gottfried Wilhelm Leibniz: britannica.com.
2. Caro, HD (2012). The Best of All Possible Worlds? Leibniz's Optimism and its Critics 1710 - 1755. Obtained from Open-Access-Repositorium der Humboldt-Universität zu Berlin: edoc.hu-berlin.de.
3. Douglas Burnham. (2017). Gottfried Leibniz: Metaphysics. Obtained from Internet Encyclopedia of Phylosophy: iep.utm.edu.
4. History of Computers and Computing. (2017). The Stepped Reckoner of Gottfried Leibniz. Retrieved from History of Computers and Computing: history-computer.com.
5. Lucas, DC (2012). David Casado de Lucas. Obtained from Notations in Differential Calculus: casado-d.org.