Gottfried Wilhelm Leibniz was a German philosopher, mathematician, and scholar. He and Sir Isaac Newton independently developed the theory of the differential and integral calculus. Leibniz also developed the binary numeration system and invented a calculating machine. He believed the truths of arithmetic could be derived from purely logical principles.

Leibniz developed a complex philosophical system. He believed that the ultimate elements of reality are indivisible, mindlike substances called monads. He identified the changing states of monads as "perceptions." But Leibniz thought only those monads that are true minds--divine, angelic, human, or animal--could perceive consciously. Leibniz said monads are "windowless"--that is, their states are generated from within the monad itself rather than being caused from without.

Although monads do not interact causally with each other, Leibniz believed that God created the world in such a way that the perceptions of any monad are "harmonized" with all others. In this and other ways, the world that God has chosen to create is the "best of all possible worlds." God can conceive of other worlds that would be better than this world in some ways. However, such other worlds would necessarily be worse in other ways. Material objects are not ultimate realities. They are only "appearances" arising from the perceptions of monads.

Leibniz was born in Leipzig. He traveled extensively in Europe on various diplomatic missions for German rulers. He died in Hanover, where he spent much of his later life.

SOURCE: IBM 1999 WORLD BOOK