Gottfried Wilhem Leibniz was a German mathematician and philosopher. He was born on 1 July 1646 in Leipzig, Germany and died on November 14, 1716 in Hanover, Germany. His studies are in the areas of mathematics, metaphysics, logic, theology and linguistics.
However, his contributions go much further, having established notions for later sciences such as medicine, geology, biology, psychology and engineering.
As a mathematician, his most famous contributions were the creation of the modern binary system and the infinitesimal calculus. As a philosopher, he was one of the great rationalists of the seventeenth century with Descartes and Spinoza, and is recognized for his metaphysical optimism.
The Encyclopedia Britannica describes it as:" A man who could think for several days sitting in the same chair, as to travel the routes of Europe in summer and winter. An indefatigable worker, a frequent writer of letters, a patriot and cosmopolitan, a great scientist and one of the most powerful spirits of Western civilization ."(Belaval, 2017). Leibniz was, without doubt, a thinker of fertile ideas and an integral intellectual.
The most important contributions of Leibniz
Contributions in mathematics
There were several Leibniz contributions to mathematics; The most known and controversial is the infinitesimal calculus. The infinitesimal calculus, or simply calculus, is a part of modern mathematics that studies boundaries, derivatives, integrals, and infinite series.
Both Newton and Leibniz presented their respective theories of calculus in such a short period of time that they even talked about plagiarism.
Nowadays both are considered coauthor of the calculation, nevertheless, ended up being used the notation of Leibniz by its versatility.
It was also Leibniz who gave the name to this study and who gave him the symbology used today: ∫ and dy = y² / 2.
In 1679, Leibniz devised the modern binary system and introduced it in his work Explication de l'Arithmétique Binaire In 1703. The Leibniz system uses the numbers 1 and 0 to represent all the numerical combinations, as opposed to the decimal system.
Although it is often attributed to his creation, Leibniz himself admits that this discovery is due to the deep study and reinterpretation of an idea already known in other cultures, especially the China .
The binary system of Leibniz would later become the basis of computing, since it is the one that governs almost all modern computers.
Leibniz was also an enthusiast in the creation of 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 that allowed operations of addition, subtraction, multiplication and division. By 1673 he was introducing 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 the Leibniz machine was not practical due to its technical flaws, it laid the foundation for the first mechanical calculator marketed 150 years later.
Additional information about the Leibniz calculating machine is available from the Computer History Museum and the Encyclopædia Britannica.
Contributions in philosophy
It is complicated to include the philosophical work of Leibniz, since, although abundant, is based mainly on newspapers, letters and manuscripts.
Throughout his life, Leibniz only published one book, The"Theodicea"and the other,"New Essays on Human Understanding"was published posthumously in 1765.
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 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 leaps in Nature".
On the other hand, sufficient reason refers to"nothing happens without a reason". In this principle we must take into account the subject-predicate relationship, ie A is A.
"For every true predicate of a subject, there must be a set of other true predicates which constitute a sufficient reason for their truth."(Douglas Burnham, 2017).
That is, these predicates remain attached to the subject as a series of explanations of the sufficient reason of the same.
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.
These are 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 all that it contains.
Leibniz explains the extraordinary actions of God in establishing it as the complete concept, that is, as the original and infinite monad.
Leibniz is well known for his metaphysical optimism. "The best of all possible worlds"is the phrase that best reflects Leibniz's task of responding to the existence of evil.
According to Leibniz, of 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.
Through the Theodicy, Leibniz fully exposes this idea. The Theodicea was the only book published by Leibniz during his lifetime. The book was published in 1710 and its full name is"Theodicy Essay on God's Goodness, Man's Freedom and the Origin of Evil."
This book is the only extensive philosophical work that the German philosopher published during his lifetime. It contains the main theses and arguments of what began to be known in the eighteenth century as"optimism"(...): a rationalist theory about the goodness of God and his wisdom, about divine and human freedom, the nature of the created world And the origin and meaning of evil.
This theory is often summed up with the famous and often misunderstood 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.
References
- Belaval, Y. (2017). Encyclopædia Britannica . Retrieved from"Gottfried Wilhelm Leibniz": britannica.com.
- Caro, H. D. (2012). The Best of All Possible Worlds? Leibniz's Optimism and its Critics 1710-1755. Retrieved from the Open-Access-Repositorium der Humboldt-Universität zu Berlin: edoc.hu-berlin.de.
- Douglas Burnham. (2017). Gottfried Leibniz: Metaphysics . Retrieved from the Internet Encyclopedia of Philosophy: iep.utm.edu.
- History of Computers and Computing. (2017). The Stepped Reckoner of Gottfried Leibniz . Retrieved from"History of Computers and Computing: history-computer.com".
- Lucas, D.C. (2012). David Casado de Lucas. Obtained from Notations in Differential Calculus: casado-d.org.