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Gottfried Wilhelm Leibniz



Gottfried Wilhelm Leibnitz (1646 - 1716)
Gottfried Wilhelm Leibniz


The Monadology

The German philosopher and mathematician Gottfried Wilhelm von Leibniz, b. July 1, 1646, d. Nov. 14, 1716, was a universal genius and a founder of modern science. Leibniz was born in Leipzig and educated at the universities of Leipzig, Jena, and Altdorf. Beginning in 1666, the year in which he was awarded a doctorate in law, he served Johann Philipp von Schönborn, archbishop elector of Mainz, in a variety of legal, political, and diplomatic capacities. In 1673, when the elector's reign ended, Leibniz went to Paris. He remained there for three years and also visited Amsterdam and London, devoting his time to the study of mathematics, science, and philosophy. In Amsterdam he met Benedict Spinoza and discussed with him some of his writings. From 1676 until his death, Leibniz served the Brunswick family in Hanover as librarian, judge, and minister. After 1686 he served primarily as historian, preparing a genealogy of the Hanovers based on the critical examination of primary source materials. In search of sources, he traveled to Austria and Italy from 1687 to 1690. In his later years, Leibniz attempted to build an institutional framework for the sciences in central Europe and Russia. At his urging, the Brandenburg Society (Berlin Academy of Science) was founded in 1700. He met several times with Peter the Great to recommend educational reforms in Russia and proposed what became the St. Petersburg Academy of Science.

Leibniz was a first-class mathematician and scientist. His contribution in mathematics was to discover, in 1675, the fundamental principles of infinitesimal calculus. This discovery was arrived at independently of the discoveries of the English scientist Sir Isaac Newton, whose system of calculus was invented in 1666. Leibniz's system was published in 1684, Newton's in 1687, and the method of notation devised by Leibniz was universally adopted. In 1672 he also invented a calculating machine capable of multiplying, dividing, and extracting square roots. Leibniz was also an excellent philosopher whose metaphysical system is peculiarly interesting in that it can be interpreted as a system of logical doctrines. His positions were drawn from science, logic, and metaphysics, and he believed that his "new principle, pre-established harmony," was proved in all these disciplines, as well as in religious and moral theory.

Leibniz was dissatisfied with the "new philosophy" since Descartes and with the concepts of absolute space, time and matter of Newtonian mechanics. He showed that Descartes' formulation of the laws of motion was scientifically unsound, and that his view of motion as miraculously imparted to essentially inert matter was metaphysically unsatisfactory. He described "atoms of matter" as contrary to reason, since the "smallest particle of matter," as atoms are described, is logically absurd. If it is extended, then it is further divisible; if not then it is not a particle of matter. The laws of motion he thought demanded that the elements involved should be bearers of energy. The only possible element must be a "simple substance, without parts." In his Monadology, this simple substance he called a "monad," a non-extended, indestructible and immaterial entity. Each monad represents an individual microcosm, mirroring the universe in varying degrees of perfection and developing independently of all other monads, with no causal connection between them. The only essential characteristic of a monad is that it is active, and therefore all monads are of the same kind. Though the observed world appears to be spatiotemporal, with bodies moving in it in causal relations which each other, and there appear various different entities of stones, plants, and humans, these appearances are systematically connected with real properties of the system of monads.

There is an infinite series of monads ranging from the completely active to the almost inert. Their proper activity is perception or "mirroring." Every monad perceives all other monads with some degree of clarity in that they are in pre-established harmony with each other. The less active monads present the appearance of materiality. Every "body" is a colony of monads with various degrees of activity, and the human being is therefore no longer a Cartesian miraclte of mind and body but part of the natural order of the universal mirroring. Each monad "unfolds" its states in accordance with its own principle and in harmony with other monads. Leibniz described the unfolding of the states as "appetition," applicable equally to purposive human activity and the movements of a sunflower to the sun.

In the Discourse on Metaphysics, which is an elaboration of a letter to his theologian friend Antoine Arnauld, Leibniz presents arguments for the doctrine of monads drawn from the nature of propositions. He states that in arguments for simple substances every proposition is of the subject-predicate form and that every true proposition has its predicate contained in its subject. Just as there is no interaction between monads, there are no relational propositions, and as a monad contains its states unfolded in it, so every true proposition contains its predicate in its subject. Arnauld was completely dissatisfied on metaphysical, religious, and moral grounds. If the state of every monad is contained in its concept, then human freedom is a myth and God is constrained. Leibniz's reply was that every actual state of affairs has hypothetical but not absolute necessity; free and spontaneous activity is allowed for in the pre-established harmony of all monads and their states. All monads choose the best and their capacity to discern the best varies with the degree of clearness with which they mirror the world. And as he famously says, God, with perfect knowledge and goodness, freely chose to create this, the best of all possible worlds.

Leibniz's works, particularly the Monadology, greatly influenced German philosophers of the 18th century, including Christian von Wolff and Immanuel Kant.

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The Concise Encyclopedia of Western Philosophy and Philosophers, J. O. Urmson and Jonathan Rée, editors. London: Unman Hyman, 1991.