Gottfried Leibniz (1646 – 1716) was a philosopher, physicist and mathematician who greatly influenced the development of modern science. He is also recognized as one of the representatives of the rationalist tradition of modernity, since he used his knowledge of mathematics and physics in an important way to explain both natural and human phenomena.

Next we will see a biography of Gottfried Leibniz , as well as his main contributions in the area of mathematics, logic and philosophy.

Gottfried Leibniz: biography of this philosopher and mathematician

Gottfried Leibniz was born on July 1, 1646 in Leipzig, Germany . The 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 his childhood he was educated at the Nicolai school, always accompanied by self-taught learning 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 on his own, and at the same time was studying Greek .

In 1661, he began his training in law at the University of Leipzig, where he was particularly interested in the men who had led the first scientific and philosophical revolutions in modern Europe. The latter were Galileo, Thomas Hobbes, Francis Bacon and René Descartes, and he even recovered the thought of the scholastics and Aristotle.

After completing his studies in law, Leibniz spent several years in Paris, where he trained in mathematics and physics . There he met the main French philosophers of the time and studied in greater detail those who had already interested him. Finally, he trained with Christiaan Huygens, who turned out to be fundamental for the subsequent development of Leibniz’s theories on differential and integral calculus.

After making several trips to different places in Europe, and having met the most representative philosophers of the time, Leibniz established an Academy of Sciences in Berlin , where he was constantly active. He spent his last years trying to compile the greatest expressions of his philosophy. Without success, he died in Hannover in November 1716.

Some contributions of Leibniz to philosophy and science

Like other philosophers and scientists of the time, Leibniz specialized in various areas. This allowed him to formulate different theories and lay the foundations for the modern development of science. To give a few examples, we will now look at three of Leibniz’s main contributions, both in mathematics and logic and in philosophy .

1. Mathematics: Infinitesimal Calculus

Together with Isaac Newton, Gottfried Leibniz is recognized as one of the creators of calculus. Leibniz’s notebooks report the first use of integral calculus in the year 1675. He had used it to find the area under the function y = x. He also introduced notations such as the integral sign (“S” from the Latin word “suma”), and the d (from the Latin word “differencia”) which is used for differential calculus. This gave rise to the Leibniz Rule , which is precisely the rule of the product of differential calculus.

Similarly, it contributed to the definition of the mathematical entities that we call “infinitesimal” and to define their algebraic properties, although with many paradoxes for the time being. The latter was revised and reformulated from the 19th century onwards, with the development of modern calculus.

2. Logic: bases for epistemological and modal logic

Faithful to his mathematical training, Gottfried Leibniz defended that the complexity of human reasoning could be translated into the language of calculations , and that, once understood, they could be the solution to resolve differences of opinion and arguments.

For the same reason it is recognized as the most significant logic of its time, at least since Aristotle. Among other things he described the properties and method of linguistic resources such as conjunction, disjunction, negation, ensemble, inclusion, identity and empty ensemble. All of them useful to understand and perform valid reasoning and differentiate them from non-valid ones. This constitutes one of the main bases for the development of epistemic-type logic and also modal logic .

3. Philosophy: the principle of individuation

In his thesis “On the principle of individuation”, which he wrote in the 1660s, Leibniz defends the existence of an individual value that constitutes a whole in itself, but which is possible to differentiate from the whole. This was the first approximation to the German theory of monads .

In analogy to physics, Leibniz held that monads are in the mental realm what atoms are in the physical realm. They are the ultimate elements of the universe and what gives substantial form to the being, through properties such as the following: they are eternal, they do not decompose into other simpler particles, they are divisive, active and subject to their own laws, as well as independent of each other and function as an individual representation of the universe itself.

Bibliographic references:

  • Belaval, Y. and Look, B. (2018). Gottfried Wilhelm Leibniz. Encyclopaedia Britannica. Retrieved October 22, 2018. Available at https://www.britannica.com/biography/Gottfried-Wilhelm-Leibniz.
  • Leibniz, G. (2017). New World Encyclopedia. Retrieved October 22, 2018. Available at http://www.newworldencyclopedia.org/entry/Gottfried_Leibniz.