Gottfried Leibniz (1646 – 1716) was a philosopher, physicist and mathematician who had an important influence on the development of modern science. In addition, he is recognized as one of the representatives of the rationalist tradition of modernity, since he uses his knowledge in mathematics and physics in an important way to explain both natural and human phenomena.
We will see a biography of Gottfried Leibniz, as well as his main contributions in the mathematical, logical and philosophical area.
Gottfried Leibniz: biography of this philosopher and mathematician
Gottfried Leibniz was born on July 1, 1646 in Leipzig, Germany. Son of Friedrich Leibnütz and Catherina Schmuck, Leibniz grew up in a devout Lutheran family towards the end of the Thirty Years’ War, which had left the country in ruins.
During childhood he was educated at the Nicolai school, always accompanied by a self-taught apprenticeship in his father’s personal library, which in turn had been inherited from a professor of moral philosophy at the University of Leipzig. In fact, by the age of 12 Leibniz had learned Latin himself, and at the same time he was studying Greek.
In 1661, he began to train in rights at the University of Leipzig, where he was especially interested in the men who had starred in the first scientific and philosophical revolutions of modern Europe. The latter were Galileo, Thomas Hobbes, Francis Bacon and René Descartes, and even regained the thought of the scholastics and Aristotle.
After completing his law studies, Leibniz spent several years in Paris, where he trained in mathematics and physics. There he met the leading French philosophers of the time and studied more closely those who had previously interested him. Finally he trained with Christiaan Huygens, who turned out to be fundamental for the later development of theories on differential and integral calculus of Leibniz.
After making several trips to different parts of Europe, and having met the most representative philosophers of the time, Leibniz established an Academy of Sciences in Berlin, where he had a constant activity. He spent his last years trying to compile the greatest expressions of his philosophy. And without the latter being successful, he died in Hanover in November 1716.
Some contributions of Leibniz to philosophy and science
Like other philosophers and scientists of the time, Leibniz specialized in several areas. This allowed him to formulate different theories and lay the foundations for the modern development of science. To give some examples we will see below three of the main contributions of Leibniz, both in mathematics and logic as in philosophy.
1. Mathematics: the infinitesimal calculus
Together with Isaac Newton, Gottfried Leibniz is recognized as one of the creators of calculus. In Leibniz’s notebooks, the first use of integral calculus was reported in the year 1675. He had used it to find the area under the function y = x. It also introduced notations such as the integral sign (“S” elongated from the Latin “sum”), and the d (from the Latin word “differencia”) that is used for differential calculations. This gave rise to Leibniz’s Rule, which is precisely the rule of the product of differential calculus.
In the same way, it contributed to the definition of the mathematical entities that we call “infinitesimals” and to defining their algebraic properties, although with many paradoxes for the moment. The latter was revised and reformulated from the nineteenth century, with the development of modern calculus.
2. Logic: bases for the epistemological and modal logic
Gottfried Leibniz argued that the complexity of human reasoning could be translated into the language of calculations, and that, once understood, could be the solution to resolve differences of opinion and arguments.
For this reason he is recognized as the most significant logician of his time, at least from Aristotle. Among other things, he described the properties and method of linguistic resources such as conjunction, disjunction, negation, the whole, inclusion, identity and the empty set. All of them are useful to understand and perform valid reasoning and differentiate them from other invalid ones. This constitutes one of the main bases for the development of the epistemic type logic and also the modal logic.
3. Philosophy: the principle of individuation
In his thesis “On the principle of individuation”, which he made in the 1660s, Leibniz defends the existence of an individual value that constitutes a whole in itself. This was the first approximation to the German theory of monads.