Leibniz, Gottfried Wilhelm
Gottfried Wilhelm Leibniz 1646–1716
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.
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.
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.
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."
Disputatio metaphysica de principio individui (philosophy) 1663
Dissertatio de arte combinatoria [On the Art of Combinations] (nonfiction) 1666
Nova methodus discendae docendaeque jurisprudentine [New Methods of Teaching and Learning Jurisprudence] (nonfiction) 1667
Hypothesis physica nova [New Physical Hypothesis] (nonfiction) 1671
Meditationes de Cognitione, Veritate, et Ideis [Thoughts on Knowledge, Truth, and Ideas] (philosophy) 1684
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] (mathematics) 1684
*Discours de métaphysique [Discourse on Metaphysics] (philosophy) 1686
†Systema theologicum [A System of Theology] (philosophy) 1686
‡Tentamen anagogicum: Essai anagogique dans la recherche des causes (nonfiction) 1690-95
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 [New System] (philosophy) 1695
§Nouveaux essais sur l'entendement humain [New Essays Concerning Human Understanding] (philosophy) 1700-05...
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SOURCE: "Leibniz's Premisses" and "Leibniz's Theory of Knowledge," in A Critical Exposition of the Philosophy of Leibniz, Cambridge at the University Press, 1900, pp. 1-7, 160-71.
[In the excerpts below, Russell comments on Leibniz's influences, the major tenets of his philosophy, and his ideas on knowledge. Russell contends that Leibniz's philosophy was an "unusually complete and coherent system."]
The philosophy of Leibniz, though never presented to the world as a systematic whole, was nevertheless, as a careful examination shows, an unusually complete and coherent system. As the method of studying his views must be largely dependent upon his method of presenting them, it seems essential to say something, however brief, as to his character and circumstances, and as to the ways of estimating how far any given work represents his true opinions.
The reasons why Leibniz did not embody his system in one great work are not to be found in the nature of that system. On the contrary, it would have lent itself far better than Spinoza's philosophy to geometrical deduction from definitions and axioms. It is in the character and circumstances of the man, not of his theories, that the explanation of his way of writing is to be found. For everything that he wrote he seems to have required some immediate stimulus, some near and pressing incentive. To please a prince, to refute a rival philosopher, or...
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SOURCE: "On Leibniz's Metaphysics," translated by R. Allison Ryan, in Leibniz: A Collection of Critical Essays, edited by Harry G. Frankfurt, Anchor Books, 1972, pp. 19-45.
[In the essay below, originally published in French in 1902, Couturat argues the importance of logic and reason in Leibniz's philosophy.]
In the preface to La Logique de Leibniz, we asserted that Leibniz's metaphysics rests entirely on his logic. This thesis is confirmed implicitly in our book and is evident from the texts we had occasion to cite there. Nevertheless, since it is contrary to the classical interpretations and to current opinion, it will be useful to establish it explicitly and in detail. Moreover, although it appears to us to be sufficiently proven by the texts which are already known, we are now able to confirm it by adducing some unpublished documents of unusual value and importance. The most interesting and most significant is a short work of four pages in which Leibniz himself has given a succinct account of his entire metaphysics in deducing it from the Principle of Reason. We cited its essential propositions in our preface and in the course of our book. We [now] want to make the new material available….1
This fragment is unfortunately not dated. But, by comparing it to short works and letters of known date, we can conjecture with high probability that it was written about 1686...
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SOURCE: "Leibniz," in A History of Western Philosophy, and Its Connection with Political and Social Circumstances from the Earliest Times to the Present Day, Simon and Schuster, 1945, pp. 581-96.
[In the excerpt below, Russell provides an overview of Leibniz's major philosophical tenets.]
Leibniz (1646-1716) was one of the supreme intellects of all time, but as a human being he was not admirable. He had, it is true, the virtues that one would wish to find mentioned in a testimonial to a prospective employee: he was industrious, frugal, temperate, and financially honest. But he was wholly destitute of those higher philosophic virtues that are so notable in Spinoza. His best thought was not such as would win him popularity, and he left his records of it unpublished in his desk. What he published was designed to win the approbation of princes and princesses. The consequence is that there are two systems of philosophy which may be regarded as representing Leibniz: one, which he proclaimed, was optimistic, orthodox, fantastic, and shallow; the other, which has been slowly unearthed from his manuscripts by fairly recent editors, was profound, coherent, largely Spinozistic, and amazingly logical. It was the popular Leibniz who invented the doctrine that this is the best of all possible worlds (to which F. H. Bradley added the sardonic comment "and everything in it is a necessary evil"); it was this Leibniz whom...
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SOURCE: "On Leibniz's Explication of 'Necessary Truth'," in Leibniz: A Collection of Critical Essays, edited by Harry G. Frankfurt, Anchor Books, 1972, pp. 19-45.
[In the following essay, originally published in German in 1966, Wilson examines Leibniz's concepts of necessary and contingent truths.]
Leibniz's remarks on necessity are dominated by two primary themes. The first, of course, is the thesis that a necessary truth may be defined as a proposition which possesses, "implicitly" if not "expressly," a specific logical form. (This is sometimes referred to, in recent works, as the thesis that necessary truths are "analytic") The second is Leibniz's frequently reiterated contention that while the word "necessary" has application both to voluntary action and in connection with explanations of why the world is as it is, "necessary" as used in these contexts is not equatable with "logically necessary." It is with respect to these contexts that Leibniz speaks of "moral necessity" and "physical necessity," claiming that a distinction must be recognized between different "degrees" or different "species" of necessity.1
These two theses can appear incompatible if it is assumed that when Leibniz defines a necessary truth as a proposition which possesses a specific logical form he is providing an analysis of his understanding of the meaning of the word "necessary." For if...
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SOURCE: "God and the Mind of God," in The Philosophy of Leibniz, Prentice-Hall, Inc., 1967, pp. 11-21.
[In the following excerpt, Rescher focuses on Leibniz's concept of substance and explains the centrality of God to Leibniz's philosophy.]
Leibniz, more than any other modern philosopher, took seriously the idea of a creation of the universe, giving it a centrally important place in his system. Like the theories of the medievals for whom he had such great respect, his system put God as the author of creation at the focal position in metaphysics. The concept of God provides the theoretical foundation upon which the structure of the Leibniz metaphysic is built.
God, for Leibniz, may be defined as "the perfect being."1 His existence is not a seriously problematic issue; it follows directly from the idea (or essence) of his perfection, by reasonings along the lines of the Ontological Argument of Anselm as refurbished by Descartes, and also by other, related arguments—a topic to which we will return at some length. Indeed, all characteristics of God must inhere in and derive from His attribute as "the perfect being." Three of these characteristics are of primary importance for Leibniz: omniscience, omnipotence, and (omni-) benevolence.2 These are the operative theological concepts in terms of which the drama of creation...
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SOURCE: An introduction to Leibniz: Philosophical Writings, revised edition, edited by G. H. R. Parkinson, translated by Mary Morris and G. H. R. Parkinson, Dent, 1973, pp. vii-xix.
[In the following excerpt from an essay written in 1972, Parkinson presents an overview of Leibniz's philosophical and scientific theories.]
Gottfried Wilhelm Leibniz was born in Leipzig on 1 July 1646. The son of a professor of moral philosophy, he studied at the Universities of Leipzig and Jena. Germany had been devastated by the Thirty Years' War, which ended in 1648, and the general cultural backwardness of the country was reflected in the German universities. It may have been this that decided Leibniz to reject the offer of a professorship in 1667, and to enter instead the service of the Baron of Boineburg, who had been a minister of the Elector of Mainz. This proved to be of great, perhaps of decisive importance in Leibniz's career. Whilst in Boineburg's service he was sent on a mission to Paris; this turned into a long stay, lasting from 1672 to 1676. Paris at this time was the intellectual capital of Europe, and Leibniz came into contact with such philosophers as Malebranche and Arnauld; he had access to Pascal's mathematical manuscripts; most important of all, he met the great Dutch physicist Christiaan Huygens, who in effect introduced him to higher mathematics. Leibniz could never equal Huygens as a physicist, but...
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SOURCE: "Miracles and Laws," in The Natural Philosophy of Leibniz, edited by Kathleen Okruhlik and James Robert Brown, D. Reidel Publishing Company, 1985, pp. 171-81.
[In the essay below, first delivered as a seminar paper in 1982, McRae discusses Leibniz's ideas on the laws governing the natural world and argues that Leibniz categorized miracles as occurrences outside the understanding of human explanation.]
Leibniz makes the charge, which he constantly renewed, that the laws of nature of the Cartesians and Newton's law of gravitation were really only formulations of perpetual miracles. To make his case he had to define miracle. Because the notion of miracle involves, at least for Leibniz, the notion of law as that to which a miraculous event is an exception, and because accordingly the criteria for miracles become inversely the criteria for laws, the entire polemic throws valuable light on Leibniz's conception of law.
We may, to begin with, observe that there are three types of law for Leibniz. First, there is the law of the whole universe, sometimes also referred to as the concept of the universe. Second, there are certain architectonic principles like the law of continuity and the law of determination by maxima and minima. These laws or principles govern not only the first kind of law, the law of the universe, but also the third kind of law, the laws of nature; for example, the...
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SOURCE: "Metaphysics and Its Method," in Leibniz and the Rational Order of Nature, Cambridge University Press, 1995, pp. 71-98.
[In the following excerpt, Rutherford examines Leibniz's concept of metaphysics. The critic suggests sources for Leibniz's ideas and focuses on such concepts as substance, cause, and the interpretation of sensory phenomena.]
Leibniz offers several definitions of the science of metaphysics. In one work he describes it simply as the "science of intelligibles" (C 556).1 In another he identifies it as the "science which has being, and consequently God, the source of being, for its object" (GP VI 227/H 243-4). In a third he characterizes "real metaphysics" as involving "important general truths based on reason and confirmed by experience, which hold for substances in general" (RB 431). In a fourth, finally, he says that metaphysics is "the science which discusses the causes of things using the principle that nothing happens without reason."2 Although there are significant variations among these definitions, they converge on a common conception. In the first place, metaphysics is the science of "intelligibles": concepts that owe nothing to sense but are derived solely from reason or intellect. What is distinctly conceivable by the intellect, however, is "being" or possibility, whose reality Leibniz grounds in the ideas of the divine understanding. Thus, insofar...
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Aiton, E. J. Leibniz: A Biography. Bristol, England: Adam Hilger, 1985, 370 p.
Places the evolution of Leibniz's philosophical and scientific thought within the intellectual and social context of his lifetime. Aiton draws mainly on printed editions of Leibniz's correspondence, works, and writings.
Broad, C. D. Leibniz: An Introduction, edited by C. Lewy. London: Cambridge University Press, 1975, 175 p.
Text of the late C. D. Broad's lectures given at Cambridge from 1948-50 on the philosophy of Leibniz.
Brown, Gregory. "Compossibility, Harmony, and Perfection in Leibniz." The Philosophical Review XCVI, No. 2 (April 1987): 173-203.
Examines Leibniz's doctrine of concepts and his ideas on perfection.
Chappell, Vere, ed. Gottfried Wilhelm Leibniz: Part II. New York: Garland Publishing, 1992, 459 p.
Reprints essays by prominent scholars in order to give an overview of contemporary thought on Leibniz.
Dascal, Marcelo. Leibniz: Language, Signs and Thought: A Collection of Essays. Philadelphia: John Benjamins Publishing Co., 1987, 203 p.
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