Gottfried Wilhelm Leibniz

German philosopher and mathematician

• Born: July 1, 1646
• Birthplace: Leipzig, Saxony (now in Germany)
• Died: November 14, 1716
• Place of death: Hanover (now in Germany)

Leibniz contributed to the development of rationalist metaphysics and a dynamic theory of motion. Contrary to Descartes, he believed that activity, and not extension, is essential to substance. He coined the term “monad” to refer to these fundamental units of existence, metaphysical entities that are not extended and are not of a material nature but are dynamic units of psychic activity.

Early Life

Gottfried Wilhelm Leibniz (GAWT-freet VIHL-hehlm LIP-nihts) was born into an academic family; his mother’s father was a professor, as was his own father (who died when Leibniz was six). Leibniz was intellectually gifted; he taught himself Latin and read profusely in the classics at an early age. When he was an adolescent, Leibniz began to entertain the notion of constructing an alphabet of human thought from which he could generate a universal, logically precise language. He regarded this language as consisting of primitive simple words expressing primitive simple concepts that are then combined into larger language complexes expressing complex thoughts. His obsession with this project played an important role throughout his life.

Leibniz was formally educated at the University of Leipzig, where he received his bachelor’s and master’s degrees for theses on jurisprudence, and at the University of Altdorf, where he received a doctorate in law in 1666. He declined a professorship at Altdorf and entered employment as secretary of the Rosicrucian Society. Eventually he was employed as a legal counsel by Johann Philipp von Schönborn, a governing official of Mainz.

Life’s Work

Leibniz’s philosophy was rationalist. According to this theory, human knowledge has its origins in the fundamental laws of thought instead of in human experience of the world as in the doctrine of empiricism. In fact, Leibniz argued that the laws of science could be deduced from fundamental metaphysical principles and that observation and empirical work were not necessary for arriving at knowledge of the world. What was needed instead was a proper method of calculating or demonstrating everything contained in certain fundamental tenets. For example, he believed that he could deduce the fundamental laws of motion from more basic metaphysical principles. In this general conception, he followed in the intellectual footsteps of René Descartes . The great problem with interpreting Leibniz’s contribution to this tradition of thought is that he published only one major book during his lifetime, and it does not contain a systematic account of his full philosophy. Accordingly, it is necessary to reconstruct his system from his short articles and his more than fifteen thousand letters.

Leibniz’s youthful dreams of constructing a perfect language quickly evolved into a theory of necessary and contingent propositions. He claimed that in every true affirmation the predicate is contained in the subject. This idea evolved from his conception of a perfect language that (in all of its true, complex statements) would perfectly reflect the universe. The true propositions of this language are necessarily true, and all necessary propositions are, according to Leibniz, ultimately reducible to identity statements. Such a conception was more plausible in the case of purely mathematical statements since, for example, 4 = 2 + 2 can be equated with 4 = 4.

Yet this conception seemed impossible in the case of contingent statements such as “the house is blue.” Leibniz avoided this problem by arguing that the necessity in what appears as contingent truths can be revealed (or resolved) only through an infinite analysis and therefore can be carried out in full only by God. It follows that, for humans, all contingent truths are only more or less probably true. Such truths are guaranteed by the principle of sufficient reason, which states that there must be some reason for whatever is the case. Necessary truths, or truths of reason, on the other hand, are guaranteed by the principle of contradiction, which states that the denial of such a truth is a contradiction (though this can be known only by God). A logical principle closely related to the principle of sufficient reason is the notion of the “identity of indiscernibles,” now known as Leibniz’s law. This principle states that it is impossible for two things to differ only numerically, that is, to be distinct yet have no properties that differ; if two things are distinct, there must be some reason for their distinctness.

Leibniz had elaborated the rudiments of his metaphysical system while at Mainz, but it was during his sojourn in Paris that his philosophy matured. In 1672, he was sent to Paris on a diplomatic mission for the German princes to persuade King Louis XIV to cease military activities in Europe and send forces to the Middle East. Leibniz remained in Paris for four years, and, though he failed to even gain an audience with the monarch, he met frequently with the greatest minds of the day, such as Christiaan Huygens , Nicolas de Malebranche, Antoine Arnauld, and Simon Foucher. He also carried out studies of the mathematics of Blaise Pascal and René Descartes, and built one of the first computers—a calculating machine able to multiply very large numbers. While residing in Paris, he also made a brief trip to England, where he met with Irish chemistRobert Boyle and visited the Royal Society , to which he was elected.

When he returned to Hanover, he accepted a post as director of the library to John Frederick, the duke of Brunswick, where he remained for the next ten years. It was only after working with Huygens in Paris on the nature of motion that Leibniz finally came to grips with the problem of the continuum. On his return trip from Paris, during which he visited philosopher Baruch Spinoza in Holland, he composed “Pacidius Philalethi” (1676), an extended analysis of this subject. This issue is traced back to the ancient Greeks and concerns the problem of resolving the motion of an object into its motions over discrete parts of space. If the body must pass through each successive parcel of space between two points, then it can never get from one point to another, since there are an infinity of such discrete parcels between any two points. It was in the context of this problem of motion and the continuum that Leibniz developed, in 1676, the differential calculus, publishing his results in 1684. Sir Isaac Newton had already discovered the calculus but did not publish his results until 1693, several years after Leibniz published his discoveries. Priority of discovery is accorded to Newton though the consensus now is that they arrived at the calculus independently.

Leibniz argued that Cartesian physics renders motion ultimately inexplicable on the basis of fundamental concepts, since it is grounded in the notion of matter as extension and does not accommodate dynamic properties. For Leibniz, the fundamental tenet is that activity is essential to substance. Substantial being is what is simple—what can be conceived by itself and what causes itself. The term “monad” was adopted by Leibniz to refer to this fundamental unit of existence. Monads are metaphysical entities that are not extended and are not of a material nature but are units of psychic activity. All entities are monadic, from God, the supreme monad who has created all the other grades of monads, to the lowest grade of being. The universe of monads is divided into two realms on the scale of perfection, that of nature and that of grace.

Because monadic substances are psychic rather than material, Leibniz’s philosophy has been labeled “panpsychistic idealism.” On the level of phenomena, Leibniz retained a mechanical model: Matter in the phenomenal realm is “secondary matter,” composed of monadic substances and having mass. Yet, according to Leibniz, substances and monads do not interact with each other. The universe consists of an infinity of such monadic substances, individuated by the principle of indiscernability and each of which undergoes changes. This change in the monad occurs entirely because of its own nature, according to a logically necessary law and not because of effects coming to it from outside. All these changes in the monads have been harmonized by God into what appears as a causal order. Leibniz referred to this as the “way of preestablished harmony” and likened it to the synchronized sounding of two clocks. Since each monad/substance is completely independent of all the others, Leibniz said (in his later writings) that they are “windowless”; that is, they do not look out on the world. Though this conception may appear to be rather unusual, it does account for the plurality of existents in the universe, since the substances are infinite and independent of one another.

The changes of a monad are changes in the degree to which it expresses the universe. This expression or “perception” occurs on all levels of being; all individuals express the rest of the universe through the changes that occur in it. Since each individual represents all individuals, metaphysical accommodation is made of the unity of the universe in the diversity of an infinity of monads. An exhaustive specification of the nature of one substance/monad would give an exhaustive specification of the natures of all other substances/monads (from a particular point of view). Since such a specification would be logically necessary (in any true assertion the predicate is contained in the subject), the complete description of the universe is a tautology, though this could only be fully known by God.

The characteristics of the monad, activity and perception, are analogous to the features of the mental lives of human beings. In connection with the notion of perception, Leibniz later introduced the notion of “apperception.” In Principes de la nature et de la grâce, fondés en raison (1714; The Principles of Nature and of Grace , 1890), he distinguished between perceiving the outer world and apperceiving the inner state of the monad (which is self-consciousness in a human being). In fact, differences between monads relate to their degree of clarity of perception and the presence of perception or apperception. At the bottom of the hierarchy of being are monads with confused perception and unselfconscious appetition. Leibniz’s theory of human understanding is developed in his Nouveaux essais sur l’entendement humain (1765; New Essays Concerning Human Understanding , 1896), written in response to English philosopher John Locke but not published in his lifetime. The perceptions of the human soul are expressions of the perceptions occurring in the body and are confused and unclear. Since all changes occur according to internal principles, all the ideas of the human mind are innate.

Leibniz was the first thinker to employ explicitly the notion of the unconscious, which he did in connection with the distinction between apperception and perception—not all perceptions are apperceived. These perceptions he refers to as “petites perceptions” and gives as his favored example the sound of a wave crashing on the beach; the sound is composed of tiny perceptions of droplets hitting the beach; although one is unaware of the droplets hitting the beach, one still perceives them (hears the sounds they make).

During his years in Hanover, Leibniz grew very close to Sophia, the wife of his patron Ernest Augustus, first elector of Hanover, and to Sophia’s daughter, Sophia Charlotte, who became the first queen of Prussia. Leibniz discussed many philosophical ideas with them, and from these conversations arose his only published book, Essais de théodicée sur la bonté de Dieu, la liberté de l’homme, et l’origine du mal (1710; Theodicy , 1951). In this text, Leibniz argued along Augustinian lines that evil exists in the world because the world could not be as good as it actually is without the evil that it contains. In fact, out of all the possible universes, Leibniz believed, this universe contains the greatest amount of good. This conception earned for Leibniz’s theories the appellation a “philosophy of optimism.”

Toward the end of his life, Leibniz became embroiled in an intellectual dispute with Samuel Clarke, a disciple of Newton. Leibniz claimed that Newtonian physics had contributed to a general decline of religion in England. Clarke defended Newtonian physics against this charge, while Leibniz attacked Newton’s conceptions on philosophical grounds in a series of letters. Leibniz asserted that the notions of absolute space and absolute time violated the principle of sufficient reason and that the concept of gravity introduced the incomprehensible notion of action at a distance. Leibniz had earlier argued that space and time have no substantive existence and are only the ordered relations between coexistent entities and the ordering of successively existent entities, respectively. The death of Leibniz ended the debate with Clarke, who immediately published the correspondence. In spite of his extensive contacts with savants throughout Europe, Leibniz’s death on November 14, 1716, was relatively unnoticed.

Significance

Leibniz remained in the humble employ of royal patrons his whole life, though at one point he was offered the position of head librarian at the Vatican, which he declined to accept. In 1700, the Berlin Society of Sciences was founded, and Leibniz was elected president for life. Throughout his life, Leibniz speculated about grandiose social-intellectual projects. He advocated the Christian conquest of the pagan lands, the compilation of a universal encyclopedia of human knowledge, the reuniting of the Protestant and Catholic churches, and the restoration of peace in Europe under the Holy Roman Empire. In a true Enlightenment spirit, Leibniz also advocated the establishment of scientific academies throughout the world and actually corresponded with Peter the Great concerning such an academy for Russia. In spite of such visionary plans, Leibniz was very conservative politically; he did not criticize existing institutions and was opposed to innovation in moral and religious matters. Yet he was friendly to all, avid of learning of the world from everyone he encountered.

Leibniz had a tremendous influence on his contemporaries. Virtually all philosophers in Germany were Leibnizian during the years after his death. One early Leibnizian who proved to be equally influential in Germany was Christian von Wolff. Wolff had corresponded with Leibniz from 1704 to 1716 on mathematical and philosophical topics. Wolff taught the Leibnizian system to Martin Knutzen, who in turn taught it to Immanuel Kant, who long remained a Leibnizian. One of Kant’s early essays in metaphysics was on the principle of sufficient reason and its relation to the logical principles of identity and contradiction.

Writing in the light of the Lisbon earthquake of 1756, Voltaire bitterly satirized the philosophical optimism of Leibniz (along with Alexander Pope) in his work Candide: Ou, L’Optimisme (1759; Candide: Or, All for the Best, 1759). Leibniz’s philosophical influence is still evident to this day. His law concerning the identity of indiscernibles is the starting point of much of the work done in the twenty-first century on semantics, and his notions of necessity and possibility are the ancestors of work by contemporary modal logicians on the nature of necessity.

Leibniz’s Major Works

1666

• Dissertatio de arte combinatoria

1686

• Discours de métaphysique (pb. 1846; Discourse on Metaphysics, 1902)

1704

• Nouveaux essais sur l’entendement humain (pb. 1765; New Essays Concerning Human Understanding, 1896)

1710

• 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, 1951)

1714

• La Mondologie (pb. 1840; also published as Lehrsütze über die Monadologie, 1720; Monadology, 1867)

1714

• Principes de la nature et de la grâce fondés en raison (pb. 1768?; The Principles of Nature and of Grace, 1890)

Bibliography

Broad, C. D. Leibniz: An Introduction. New York: Cambridge University Press, 1975. A compilation of the lecture notes used by Broad, published after his death. Reconstructs and analyzes the whole of Leibniz’s philosophy.

Hostler, John. Leibniz’s Moral Philosophy. New York: Barnes & Noble Books, 1975. A full study of the metaethical dimensions of Leibniz’s metaphysics. Argues that the metaphysics is worked out in the framework of his systematic moral ideas.

Jolley, Nicholas. Leibniz and Locke: A Study of the New Essays on Human Understanding. New York: Oxford University Press, 1984. A study of Leibniz’s response to Locke. Attempts to substantiate the notion that the guiding motive of Leibniz in writing his study was to refute Locke’s materialism.

‗‗‗‗‗‗‗, ed. The Cambridge Companion to Leibniz. New York: Cambridge University Press, 1995. Thirteen essays examine Leibniz’s life, his theories of metaphysics, knowledge, and morality, and his reception in the eighteenth century.

Leibniz, Gottfried Wilhelm. The Monadology and Other Philosophical Writings. Translated with an introduction and notes by Robert Latta. Oxford, England: Clarendon Press, 1898. Contains a two-hundred-page introduction to the whole of Leibniz’s philosophy. Extensive discussion of his influence on the development of psychology in late nineteenth century Germany.

McRae, Robert. Leibniz: Perception, Apperception, and Thought. Toronto, Canada: University of Toronto Press, 1976. Focuses on Leibniz’s theory of knowledge and attempts to explain how perception and apperception combine to provide for thought.

Mates, Benson. The Philosophy of Leibniz: Metaphysical Underpinnings. New York: Oxford University Press, 1986. This is an excellent introductory work on Leibniz, written by a logician. Covers all aspects of his general metaphysics.

Rescher, Nicholas. Leibniz: An Introduction to His Philosophy. Totowa, N.J.: Rowman and Littlefield, 1979. Argues that Leibniz’s unorthodox metaphysical system is ultimately aimed at providing a foundation for utterly orthodox views in ethics and religion.

‗‗‗‗‗‗‗. On Leibniz. Pittsburgh, Pa.: University of Pittsburgh Press, 2003. Eleven essays examine key aspects of Leibniz’s philosophy, personality, and personal and scholarly development. The final chapter explores how current issues in the philosophy of science can be addressed in terms of Leibniz’s principles.

Russell, Bertrand. A Critical Exposition of the Philosophy of Leibniz. Cambridge, England: Cambridge University Press, 1900. An important work, arguing that Leibniz’s philosophy can be understood in terms of five fundamental principles that are ultimately inconsistent.

Rutherford, Donald, and J. A. Cover, eds. Leibniz: Nature and Freedom. New York: Oxford University Press, 2005. A collection of essays exploring Leibniz’s ideas on free will, determinism, and the philosophy of nature.