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

Below we will see **a biography of Gottfried Leibniz**, As well as his main contributions in the mathematical, logical and philosophical fields.

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## Gottfried Leibniz: biography of this philosopher and mathematician

Gottfried Leibniz **was born July 1, 1646 in Leipzig, Germany**. Son of Friedrich Leibnütz and Catherina Schmuck, Leibniz grew up in a fervent 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 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, for the age of 12 Leibniz **he had learned Latin on his own, and at the same time was studying Greek**.

In 1661 he began 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 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 were already interested in him. He eventually trained with Christiaan Huygens, who was found to have played a decisive role in the further development of Leibniz’s theories of differential and integral calculus.

After having made several trips to different parts of Europe and meeting the most representative philosophers of the time, Leibniz **creates an Academy of Sciences in Berlin**, Where he had constant activity. He spent his last years trying to put together the greatest expressions of his philosophy. And without the latter succeeding, 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 various fields. 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 Leibniz’s major contributions, both in mathematics and in logic and in philosophy**.

### 1. Mathematics: infinitesimal calculus

With Isaac Newton, Gottfried Leibniz is recognized as one of the creators of calculus. In Leibniz’s notebooks, the first use of integral calculus is reported in 1675. He had used it to find the area under the function y = x. He also introduced notations such as the integral sign (“S” extended from the Latin “sum”), and the d (from the Latin word “difference”) which is used for differential calculations. **This gave birth to Leibniz’s rule**, Which is precisely the rule of the product of differential calculus.

He also contributed to the definition of mathematical entities that we call “infinitesimals” and to the definition of their algebraic properties, albeit with many paradoxes at the moment. The latter was revised and reformulated from the 19th century, with the development of modern calculus.

### 2. Logic: bases of epistemological and modal logic

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

At the same time, he is recognized as the most important logician of his time, at least since Aristotle. Among other things, he described the properties and method of linguistic resources such as conjunction, disjunction, negation, the whole, the inclusion, the identity and the empty whole. All of them are useful for understanding and executing valid reasoning and differentiating them from those which are not valid. It is one of the main bases for **the development of an epistemic type logic and also of 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 which constitutes a whole in itself, but which is possible differential from the whole. is to be **the first approach to German monad theory**.

By analogy with physics, Leibniz argued that monads are in the realm of mind what atoms are in the realm of physics. They are the ultimate elements of the universe and what gives a substantial form to the being, through properties such as the following: they are eternal, do not break down into other, simpler particles, are individual, active and subject to their own laws, in addition to being independent of each other and functioning as an individual representation of the universe itself.

#### Bibliographical references:

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