## Introduction

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Gottfried Wilhelm Leibniz 1646–1716
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German philosopher, scientist, and mathematician.

Leibniz was a major force in German intellectual life during the late seventeenth and early eighteenth centuries. His wide-ranging interests included linguistics, jurisprudence, and theology, but he is best remembered for his work in science, metaphysics, and mathematics. Leibniz developed calculus independently of Sir Isaac Newton and his work with binary arithmetic and logic contributed to the development of Boolean algebra and computers. He also contributed to the study of motion and developed a metaphysical system based on the existence of monads, which he described as the basic substance from which all things are composed. Though elements of Leibniz's philosophical teachings were ridiculed by later thinkers—for exapmple, Voltaire in *Candide* (1758)—Leibniz's ideas have influenced a number of seminal philosophers, including Georg Wilhelm Friedrich Hegel and Immanuel Kant.

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Biographical Information
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Leibniz was born in Leipzig in 1646, into a Protestant family. As a child, he read widely in his father's library and had mastered Latin and Greek by the time he was fourteen. In 1661 he entered the University of Leipzig, where he studied philosophy and law. Leibniz completed his legal studies in 1666 and applied for a doctorate of law, which the university refused to grant because of his age. He subsequently left Leipzig and obtained his degree at the University of Altdorf, which also offered him a professorship. Leibniz declined the offer, however, and took a position as secretary of the Rosicrucian Society in Nuremberg. There, through the influence of the retired statesman Johann Christian von Boyneburg, Leibniz met Johann Philipp von Schönborn, the elector of Mainz, who offered him a position in his court investigating issues of law and politics. From 1672 to 1676 Leibniz lived in Paris, where he furthered his studies in mathematics and science; improved on Blaise Pascal's calculator by adding the ability to perform multiplication and division; and made a number of important friends in the European intellectual community, including Antoine Arnauld, a theologian, and Christian Huygens, the famed Dutch mathematician and astronomer. In 1676 Leibniz left Paris for Hanover, Germany, to serve under Johann Friedrich, the Duke of Hanover. After the death of Johann Friedrich, Leibniz served under Ernst August and later under Georg Ludwig, who was eventually

crowned George I of England. In 1700 Leibniz persuaded Prince Frederick of Prussia to found the Berlin Society of Sciences, which later became the Prussian Royal Academy. Leibniz's fame as a philosopher and scientist reached its peak in the early 1700s; he was inducted into the Paris Academy of Sciences as a foreign member in 1700, was named president for life of the Berlin Society of Sciences, and was in correspondence with most of the major intellectuals of the period. Leibniz's popularity gradually deteriorated, however, and his death in 1716 passed virtually unnoticed.

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Major Works
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The philosopher's first work, *Disputatio metaphysica de principio individui* (1663), which he published while a student at the University of Leipzig, concerns the existential nature of the individual, which, Leibniz argued, cannot be explained by form or matter alone, but must be understood as a whole. As a corolary to his arguments, Leibniz suggested that ideas are similar to numbers, in that a complex statement can be derived from simpler statements through a process of combination similar to the multiplication of numbers. In his next major work, *Dissertatio de arte combinatoria* (1666; *On the Art of Combinations*), Leibniz elaborated on this concept and produced a model to explain how complex reasoning is reducible to ordered combinations of simpler elements. This model later became the theoretical ancestor for computers. In his *Meditationes de Cognitione, Veritate, et Ideis* (1684; *Thoughts on Knowledge, Truth, and Ideas*) Leibniz suggested a relationship between the knowledge of God and man. Leibniz published his work on the development of differential calculus in 1684 as *Nova methodus pro maximis et minimis, itemque tangentibus, quae nec fractas, nec irrationales quantitates moratum, et singulare pro illis calculi genus* (*New Method for the Greatest and the Least*). Although Newton had developed similar mathematical concepts as early as 1665, he had not published his findings. The debate over who should have priority as the inventor of calculus became a highly contested subject during the 18th century. *Discours de métaphysique* (1686; *Discourse on Metaphysics*) introduces his doctrine on the relationship between predicates and propositions. According to Leibniz, the predicate—attribute or concept—of any affirmative proposition that is true is contained within the idea of the subject. Leibniz contended that this theory held for both necessary and contingent propositions. (A contingent proposition states what is or is not possible.) In his *Système nouveau de la nature et de la communication des substances, aussi bien que de l'union qu'il ya entre l'âme et le corps* (1695; *New System*) Leibniz examined the relationships between substances and introduced the idea of a pre-established harmony, created by God, between the individual's body and soul, such that the two give meaning to each other. Leibniz published his *Essais de théodicée sur la bonté de Dieu, la liberté de l'homme et l'origine du mal (Theodicy: Essays on the Goodness of God, the Freedom of Man, and the Origin of Evil*) in 1710. In this work he expounded his ideas on divine justice and posited that all creatures act according to their nature and in accordance with the universal harmony. Leibniz argued that all creatures with reason are free and that evil is a lack that increases the beauty of the summation of all things. He also argued that God had created the best of all the possible worlds. In his last work, *Principia philosophiae, more geometrico demonstrata* (1714; *The Monadology*), Leibniz synthesized many of the concepts introduced in *Theodicy.*

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Critical Reception
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Although Leibniz was neglected toward the end of his life and for over a century afterwards, his work has been the object of increasing interest since the mid-nineteenth century to the present. In the 1840s, for instance, the English mathematician George Boole expanded on Leibniz's work on binary arithmetic to develop Boolean algebra. In the area of calculus, Leibniz's system of notation, rather than Newton's, has become the favored method. Much recent work on Leibniz's writings has focused on his metaphysics and his theology. Many of Leibniz's works were published posthumously, and though he never wrote a "grand synthesis" of his philosophy, a number of recent commentators have remarked on the completeness and coherence of Leibniz's philosophical system. Bertrand Russell stated that Leibniz's "greatness is more apparent now than it was at any earlier time. Apart from his eminence as a mathematician and as the inventor of the infinitesimal calculus, he was a pioneer in mathematical logic, of which he perceived the importance when no one else did so. And his philosophical hypotheses, though fantastic, are very clear, and capable of precise expression. Even his monads can still be useful as suggesting possible ways of viewing perception."