Gottfried Leibniz


Gottfried Leibniz

Gottfried Wilhelm von Leibniz (July 1, 1646 in Leipzig - November 14, 1716 in Hanover) was a German philosopher, scientist, mathematician, diplomat, librarian, and lawyer of Sorb descent. Leibniz is credited with the term "function" (1694), which he used to describe a quantity related to a curve; such as a curve's slope or a specific point of said curve. Leibniz is generally, with Newton, jointly credited for the development of modern calculus; in particular, for his development of the integral and the Product rule.

He was born in Leipzig. He was a highly intelligent youth who entered Leipzig University at age 15. He graduated from there with a bachelor's degree in philosophy at 17 and with a doctorate in law at 20.

Leibniz constructed the first mechanical calculator capable of multiplication and division. He also developed the modern form of the binary numeral system, used in digital computers. Some have speculated that it may be interesting to consider what might have resulted from Leibniz combining his findings in binary arithmetic with those developments he made in mechanical calculation.

Although there is some question of original authorship, Leibniz is credited along with Isaac Newton with inventing the infinitesimal calculus in the 1670s. According to his notes, a critical breakthrough in his work here occurred on November 11, 1675, when he demonstrated integral calculus for the first time to find the area under the y=x function. He introduced several notations used in calculus to this day, for instance the integral sign ∫ representing an elongated S from the Latin word summa and the d used for differentials from the Latin word differentia.

Leibniz thought symbols to be very important for the understanding of things. He also tried to develop an alphabet of human thought, in which he tried to represent all fundamental concepts using symbols and combined these symbols to represent more complex thoughts. Leibniz never finished this.

His philosophical contribution to metaphysics is based on the Monadology, which introduces Monads as "substantial forms of being", which are akin to spiritual atoms, eternal, indecomposable, individual, following their own laws, not interacting ("windowless") but each reflecting the whole universe in pre-established harmony. In the way sketched above the notion of a monad solves the problem of the interaction of mind and matter that arises in Rene Descartes' system, as well as the individuation that seems problematic in Baruch Spinoza's system, which represents individual creatures as mere accidental modifications of the one and only substance. The Theodicee tries to justify the apparent imperfections of the world by claiming that it is optimal among all possible worlds. It must be the best possible and most balanced world, because it was created by a perfect God.

The statement that "we live in the best of all possible worlds" was regarded as amusing by Leibniz' contemporaries, notably François Marie Arouet de Voltaire who found it so absurd that he parodized him in his novel Candide, where Leibniz appear as a certain Dr. Pangloss. This parody is the root of the term panglossianism, which refer to people holding the view that we live in the best of all worlds.

Leibniz is believed to be the first person to suggest that the concept of feedback was useful for explaining many phenomena in many different fields of study.

Works

  • Monadologia (`The Monadology'), (1714)
  • Théodicée (`Theodicy'), (1710)
  • Nouveaux Essais sur L'entendement humaine (`New Essays on Human Understanding'), (1705)
  • Discours de métaphysique (`Discourse on Metphysics') (1686)
  • Hypothesis Physica Nova (`New Physical Hypothesis') (1671)
  • De Arte Combinatoria (`On the Art of Combination') (1666)

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