Friday, February 17, 2012

G. W. Leibniz. Discourse on Metaphysics

G W. Leibniz's Discourse on Metaphysics is the olive branch of a mind at once seizing and being seized by the churning intellectualism of the seventeenth century. Gottfried Wilhelm Leibniz (1646-1617), forty at the time he penned his first mature outline of a universal metaphysic, was a man standing in between the ideological armies of Cartesian modernism and Aristotelian conservatism. His Discourse sounds above the crush of these two ideologies. It paves another way. And, in doing so, it has long outgrown its place as a piece of private correspondence to inform thinkers across the disciplines of the present day.

The roots of Leibniz’s intellectual modernism are traced to his youth. G. W. Leibniz was born July 1, 1646, at Leipzig, the son of a professor of moral philosophy. His mother also had university ties; her father was a Professor of Law. Culturally, the violence of the Thirty-Years war would subside in another two years time. Yet, Leibniz’s own intellectual violence grew with age. Upon his father’s death, the six-year old was allowed access to an expansive library. He taught himself enough Greek and Latin to, “immerse myself in the historians and poets.” He absorbed the ideas of Plato, Herodotus, Aristotle, Cicero, Augustine, Aquinas, and many others, all without intellectual prejudice. Leibniz’s gift to all was the unity of a curious mind. Authors were valued each for their own contribution. It was a habit of synthesis he would carry with him throughout life.

As a young man, Leibniz’s democratic intelligence had great effect upon his career. He studied law and philosophy at the universities of Leibzig and Altdorf, yet declined a university post in lieu of the broader opportunities of public service. (No doubt, the cultural stagnations attending a protracted war made a professorship repellent to the autodidact.) His employer was the Elector of Mainz. Leibniz’s flair for law, mining diplomatically from both scholastic canon and scientific analysis, brought him success and opportunities for travel. One diplomatic mission took him to Paris in the spring of 1672.

Paris in the seventeenth century was the intellectual center of the world. Aristotelian scholasticism, traditionally dominant in the schools, was failing in influence before the demonstrable results of the modern philosophers: Galileo, Torricelli, Cavaliere, Descartes, Pascal, and Hobbes. The substantial forms of the schoolmen were being poured into new wineskins of geometry, mechanics, and motion. New solutions reopened new problems to scrutiny: In a world of atomic flux, how can there be any continuity of matter? What is the relationship between contingency and necessity? Can we obtain a clear and distinct idea of things as they are (en res) by observing things as they appear to be?

In order to participate in the Parisian milieu, Leibniz needed to learn many new ideas. His education was Aristotelian. He was a humanist in the renaissance tradition. Therefore, the modernism of Paris was entirely new. He worked hard to understand and embrace the truths of its observational methodology. He negotiated meetings with the philosophers Antoine Arnauld and Nicolas Malebranche (he would also visit Baruch Spinoza in Holland). He read unpublished manuscripts by Pascal and Descartes. Yet, it was the teaching of Christiaan Huygens that equipped him to practice modern philosophy.

Huygens’s mathematical instruction found fertile soil; Leibniz’s progress was quick. He was elected to the Royal Society of London in 1673. His famous calculating machine was built that same year. He suggested ideas for improvements in barometry, time keeping and the calculation of distance, as well as for mechanical devices such as pumps, carriages, gears, and lenses. By the time Leibniz returned to Hanover in 1676, his mastery of mathematics was so thorough that, in 1675, at twenty-eight years of age, he had discovered the infinitesimal, or differential, calculus. Its dynamism formed the basis of all of Leibniz’s subsequent philosophical reasoning to his death on November 14, 1716.

Until 1675, a type of curve existed, called a mechanical or transcendent curve, which defied geometrical analysis. The mechanical curve resembles the shape made by a sail in the wind. Cartesians judged the curve to be forever inexplicable to mathematics because its explanation would require the knowledge of all possible numbers, a knowledge in extenso. Leibniz disagreed. The entire shape of the curve does not need to be explained, he reasoned, but only its geometrical movement. If the difference between each of its infinitesimally small points could be expressed geometrically, then all that would be needed to complete the analysis would be the movement of the equation. Expressing the generation of the curve geometrically–its “construction principle”–is tantamount to expressing the curve itself, and without the requirement of in extenso understanding. All that is needed to plot an infinitely complex shape is a foundational measurement and dynamic principle of continuity based on that measurement.

Leibniz’s mathematical insight was, in reality, an application of his rationalist understanding of knowledge. Throughout his educational life, he envisioned a universal characteristic language, an algebraic mathematics of logic (ars characteristica) by which all knowledge could not only be explained and compared, but ultimately constructed. Descartes had considered such a thing, but dismissed it since such a language would depend upon a true and absolute, if not omniscient, understanding. Leibniz, again, disagreed. Mathematics, he said, works by the dynamic manipulation of a handful of algebraic symbols. The sum of all equations is not needed to make mathematical advances. It was the same solution he proposed for the problem of the transcendental curve.

Yet, this application of thought traced far larger horizons. This was a worldview, a cosmology. The universal characteristic was a logos, a ratio of the universe. It was a logic so large that it could only be called a metaphysic. Leibniz’s universal characteristic required a metaphysical basis which would explain not only the change and extension of substances (if not a re-definition of substance itself), but also the contingency and necessity of God and of humanity. It would be a unique synthesis of truths from both Aristotelian scholasticism and Cartesian modernism. He appended descriptive abstracts of his metaphysic in his correspondence with Arnauld in 1686 (these are today incorporated as sectional summaries.) The whole was also prepared for publication, though its was not printed in his lifetime. It is known today as the Discourse on Metaphysics.

There are three principle aspects to the Discourse, all of which serve to make it a metaphysic in the style of his universal characteristic: first, there is existence; then, substance; and, lastly, there is proportion, or how these substances work together.

“God is an absolutely perfect being,” he writes, “whence it follows that God . . . acts in the most perfect manner.” Leibniz was not known for his religiosity, but was following his age by grounding his universal metaphysic in the nature of God. Descartes had done the same in the Meditations on First Philosophy (1641), as had the medieval scholastics. Substances must have reason for existing in the infinite variety he conceived. Therefore, God must exist and have a reason for making the world as it is. Leibniz found the answer in the perfection of God, which results in a world made as perfectly as possible. He expressed perfection through a variety/simplicity criterion in which the best solution finds geometric expression in the balance between the complexity of a figure and the simplicity of its informing equation: “God . . . has chosen the most perfect [method of creation], that is to say the one which is at the same time the simplest in hypothesis and the richest in phenomena.” Voltaire later ridiculed Leibniz through the character of Dr. Pangloss in Candide (1759) for his belief that this was the best of all possible worlds, yet Leibniz’s variety/simplicity criterion is understandable given the cosmological philosophy of the time.

The perfection of God makes simple substances a metaphysical, and not just philosophical, assertion. God, from an innumerable number of possible worlds, actualizes the substances that together express the most perfect world. There are no atoms, no vacuum, only an infinity of simple substances. Substances, also called “ideas” and “souls”, had not yet achieved the true idealism that would characterize their expression in Leibniz’s more mature Monadology (1714). Yet, the conceptual foundation was already there in the concept of expression and the identity of indiscernables.

To define these terms, it is helpful to reconsider the mechanical curve which Leibniz explained using the differential calculus. Each of the curve’s infinite number of points contains virtually the entire curve, though the curve itself stretches infinitely into space. This point-by-point containment corresponds to the concept of expression. Each substance in Leibniz’s metaphysic is entirely complete in itself. It contains in itself all that defines it, both past, present and future. Its relationships to other substances are also contained in its concept. Every substance uniquely reflects the universe from its own position in relation to the whole as a windowless world unto itself.

Such uniqueness is what is meant by the identity of indiscernibles. Leibniz’s epistemology defined a true expression as that which contains in its subject all which may be predicated of it. Therefore, a subject is absolutely complete in itself; it contains all of its possible predications. This means that no two substances are completely identical. The identity of indiscernibles was informed both by the pre-formationist biology of the day and the recent discovery of the microscope.

Having laid the foundation of his metaphysics, Leibniz now had only to put the machine in motion, a process he understood as a function of God’s harmonious interaction with the universe. Leibniz called the interaction of substances a pre-established harmony. The system that results is, as he had hoped, one of immense difference and organic dependency.

That is not to say there are no internal problems created by the system. His effort to defend his metaphysic against Arnauld’s charge of determinism attests to that. Indeed, Leibniz’s effort to make peace between necessity and contingency within the same metaphysic makes the Discourse a classic text on the subject. Scholars still debate whether freedom is possible in his system, constrained as it is by the completeness and resulting necessity of each substance.

On the other hand, scholars are finding much that is to be learned from Leibniz’s philosophy. Many of his ideas, never properly assembled and scattered through thousands of pages of correspondence (luckily, Leibniz, who served as chief librarian in the court of Hanover and who was offered a position at the Vatican, collected his correspondence), are today being published for the first time. Three volumes of the Prussian Academy’s forty-volume critical edition are available. Thus, Leibniz’s contribution to the history of ideas is being reassessed. The organic and dynamic relationship he saw in all things influences many disciplines, including modern metaphysics of modality, phenomenology, symbolic logic, the desire of physics for its own universal characteristic and even Chinese Studies (Leibniz made careful analysis of the I Ching and of Chinese political science). He has also been called the father of supercomputers, relay switches, and virtual reality. It is no wonder that Alfred North Whitehead included Leibniz in his century of ideas.

So then, G. W. Leibniz’s Discourse on Metaphysics is an olive branch arguing for the related dependency of all ideas upon each other, regardless of their source. To dismiss him as a system is to dismiss the consistency of the human mind and the possibility of intellectual progress. Therefore, reading the Discourse is both a tour and a possibility. It is a tour because the Discourse introduces its reader to the basic problems and ideas that informed the early Enlightenment. It is a possibility because those same ideas ultimately create and critique the philosophical story of today.



Leibniz, G. W. Samtliche Schriften und Briefe, ed. German Academy of Sciences. 40 vols. Darmstadt and Berlin: Akademie Verlag, 1923- .
---. Die Philosophischen Schriften von G. W. Leibniz. 7 vols. Ed. C. I. Gerhardt. Berlin: Weidmann, 1875-90.
---. Philosophical Papers and Letters, 2nd ed. Ed. and trans. L. E. Loemker. Dordrecht: Reidel, 1969.
---. Leibniz: Philosophical Writings. Ed. and trans. G. H. R. Parkinson. London: Dent, 1973.
---. New Essays on Human Understanding. Ed. and trans. P. Remnant and J. Bennett. Cambridge: Cambridge University Press, 1981.
---. Theodicy, trans. E. M. Huggard (LaSalle, IL: Open Court, 1985).
---. G. W. Leibniz: Philosophical Essays, ed. and trans. R. Ariew and D. Garber (Indianapolis: Hackett, 1989).
---. Leibniz: Monadology and other Philosophical Essays. Trans. Paul Schrecker and Anne Martin Schrecker. Bobbs-Merrill. Library of Liberal Arts. Indianapolis, 1965.
---. Leibniz: Selections. Ed. Philip P. Wiener. New York: Charles Scribners Sons, 1951.

Further Reading

Bobro, Marc and Kenneth Clatterbaugh “Unpacking the Monad: Leibniz’s Theory of Causality” Monist 7.3 (1996): 408.
Broad, C. D. Leibniz: an Introduction. Cambridge: Cambridge University Press, 1975.
Brown, Stuart. “Leibniz and the Classical Tradition” International Journal of the Classical Tradition 2.1 (1995): 68.
Hooker, M., ed. Leibniz: Critical and Interpretive Essays. Minneapolis: University of Minnesota Press, 1982.
Jolley, Nicholas, ed. The Cambridge Companion to Leibniz. Cambridge: Cambridge University Press, 1995.
Jolley, Nicholas. “Leibniz.” A Companion to the Philosophers. Ed. Robert L. Arrington. Malden, MA: Blackwell, 1999. 360-366.
Mates, B. The Philosophy of Leibniz: Metaphysics and Language. New York: Oxford University Press, 1986.
Riley, Patrick. Leibniz’ Universal Jurisprudence: Justice as the Charity of the Wise. Cambridge, MA: Harvard University Press, 1996.
Sesonske, Alexander. “Pre-Established Harmony and Other Comic Strategies” Journal of Aesthetics & Art Criticism 55.3 (1997): 253.
Steinhart, Eric. “Leibniz’s Palace of the Fates: A Seventeenth-Century Virtual Reality System” Presence: Teleoperators & Virtual Environments 6.1 (1997): 133.
The Monist 81.4 (1998) is entirely devoted to various aspects of Leibniz’s metaphysics.

Web Sites Gregory Brown’s Leibniz homepage. Brown’s website is an expansive portal to all things Leibniz. It includes links to the Leibniz Listserv, various societies and journals as well as information in the form of journal and encyclopedia articles. An article on Leibniz mathematical ideas which forms part of a collection of mathematical biographies made available online. This Stanford University website is Leibniz-at-a-glance, including dates of authorship for his principles works, events in his life, and a short bibliography for further reading which focuses specifically on his conceptual philosophy. An online publication of the article, “How to Make Our Ideas Clear” by Charles S. Pierce reprinted from Popular Science Monthly 12. Jan. 1878, 286-302. The article is concerned with logic in general and the contributions made by Descartes and Leibniz in particular. An online publication of George MacDonald Ross’s book, Leibniz (Oxford University Press (Past Masters) 1984) made available through the University of Leeds Electronic Text Centre. A comprehensive and understandable study of Leibniz’s thought, with special attention given to the mathematical basis of his insights in philosophy and logic. Leibniz Links: A selection of web pages devoted to the philosophy of G. W. Leibniz compiled by Paul Lodge. Philosophy Since the Enlightenment by Roger Jones. This website is very helpful for seeing Leibniz’s philosophy against the philosophical spectrum of present and past.
(c) 2002 Thom Chittom
Printed by permission, Barnes & Noble World Digital Library