The Idea of Monads from Gottfried Wilhelm Leibniz (1646-1716)

The Thirty Years War (1618-48) was ended by a set of treaties, collectively called The Peace of Westphalia, achieved when Leibniz was two years old. In the course of that war, Leibniz’ native Germany had been devastated and significantly reduced in population by the presence, passage, and battles of numerous marauding field armies. Leibniz, like Rene Descartes (1596-1650) in France a generation earlier, was spotted as gifted as a child. Both were educated to be lawyers, but left enduring legacies as geniuses in mathematics and philosophy. Like Descartes, Leibniz was (just as Spinoza, and Kant) a lifelong bachelor. Leibniz was employed as an administrator, researcher, diplomat, and advisor by aristocratic ruling families in Germany. Although Leibniz was brought up in a Lutheran culture, he experienced scholastic/ Aristotelian (Catholic) influences at university and also shows distinctly Calvinist tendencies of thought. Leibniz dreamed of reconciling science with Christian orthodoxy, and even of arranging the reunification of Protestant sects with the organization of Catholicism to heal the schisms fragmenting Christendom, schisms which had been used as justifications for the officially commanded mass murder, pillage, and sexual assault called the Thirty Years War.

Mathematics and Philosophy

Mathematics has been one of the most powerful inspirations for philosophy, and especially for idealism and rationalism. Mathematics suggests an ideal world of perfect and eternal objects: geometric figures, numbers, axiomatic principles, functions, and operators. Mathematics belongs in a category of apparently ideal objects, but is special in supporting a set of rules, axioms, and procedures by which reasoning, calculation, and deduction can generate conclusions which must be true when the initial premises are true. The discovery of mathematics, to the ancient Greeks a realm of eternal truths somehow structured just “behind” the visible world, provided an invitation to remove the rowdy personalities of gods and spirits from the invisible transcendent world at the same time as recreating the transcendent as the proper object of rigorous thought. Mathematics suggests control of the inwardness of mental processes that forms a firm foundation for special knowledge of the objective environment.

The contribution of mathematics as an inspiration for philosophy has included serving as a model of transcendence or of transcendent reality. Mathematical systems of ideas have a certain kind of transcendence with respect to the work-a-day world. The mathematical type of transcendence does not have much to do with freedom or creativity as long as the mathematical ideas are understood as existing independently of the person thinking them, although Stoics might see such ideas as a refuge in which the rationality of personal intelligence could find a grounding from which to assert itself against disruptive episodes of emotion. Mathematical systems have the transcendence of incorporeality, perfection, and eternity, rather than the transcendence of freedom and creativity. (The transcendence of incorporeality turns up also in the meaning of “sacrifice”. To sacrifice something is to make it sacred (transcendent) by translating it from its corporeal existence into incorporeality, by burning it, for example.) The transcendence of mathematical systems is inseparable from ideality but only the passive aspect of ideality, whereas the more important transcendence is in the active agency of ideality, namely subjective intelligence.

Mathematicians, such as Leibniz, seem to hold special mathematical patterns and systems in their minds so vividly and elaborately that, within their experience, those systems have the reality of alternate worlds or even as worlds with a reality superior to the one normally perceived. When people with those experiences turn to questions about the relationship between ordinary impressions of the world and the kind of knowledge that can be justified by the strictest rationality, they often envision startling discontinuities between apparent reality and ultimate reality, as exemplified just below. That peculiarity of experience, probably shared by computer programmers and computer game architects, should not be disregarded or explained away too confidently. Although the examples of philosophical mathematicians tend to be privileged and pampered adult males, there is a certain kind of childlike innocence to their distracted engagement with the world of ordinary impressions, an innocence that has some common ground with everyone’s experience.


Consider Leibniz’s idea of ‘monads’ as a way of conceiving individual subjectivities as separate universes, presented on this blog as the system of reality ‘transcendental humanism’. Leibniz’ idea of a ‘monad’ incorporates three previously familiar ideas: 1) Aristotle’s idea of particular substances, in which qualities inhere, 2) the grammatical (logical) subject, in which predicates inhere, and 3) everyone’s experience of personal subjectivity. The result is the monad, the ‘spiritual’ entity which is an individual person, a self-contained mind, an atomic theatre of experience. For Leibniz, monads are the entities created by God, the fundamental substances that make up the world. However, monads are not like the atoms of modern science that move about and transform, by electromagnetic bonding, into compounds with different characteristics. The Leibnizian monad cannot be said to move or to combine with others. It occupies a place without taking up space, in a way possibly similar to Platonic Ideas, whatever that may be. On the model of Aristotelian substances, each monad is unique, separate, and independent; but also, as “windowless”, completely closed to anything beyond itself. Each monad is a sort of absolute atom or separate universe, completely self-sufficient and independent of every other, and yet “mirroring” every other monad internally. For Leibniz, monads are reality, the metaphysical Being behind ordinary appearances of things in the world, and yet monads have no role in causing the appearances of our familiar world. All experiences of any monad (including your experiences and my experiences) are completely internal to the monad and completely pre-programmed by God, but programmed in such a way that the experiences are a “mirroring” of what is going on with the other monads.

For Leibniz, God, in his work of creation, calculated an exquisite balance between the principle of plenitude and the principle of simplicity to derive the best of all possible worlds, completely determined in every detail from the instant of creation. Inspired by the theory of ‘occasionalism’ proposed by Nicolas Malebranche (1638-1715), Leibniz accepted that physical cause-effect was a false impression from taking appearances too uncritically at face value. (David Hume (1711-76) was later to repeat that familiar denial of efficacy in cause-effect interactions, merely altering outright denial into skepticism.) On Leibniz’ view, every particle (Aristotelian substance) of the extended world was individually pre-programmed with all changes and movements it would ever have, and the whole set of those particles were coordinated in advance so as to appear as if chains of cause and effect were running their course. For Leibniz, “thought” in some sense is a fundamental feature of every particle or monad. Thought has no causal force, but rather is “reflective” of the ambient universe. That reflection of the world in the thought of every monad does not derive from contact or mutual sensitivity between particles. Leibniz’s monads must be entirely inward because they are windowless. The reflection of the world in thought is just pre-established in each mind by God the creator. The rest of the world cannot penetrate monads in any way. The only condition that prevents them from being truly separate universes or separate worlds is that they are each part of God’s work of creation, and in that sense all are coordinated in a higher-order universal Being.

Individuals are distinct, on Leibniz’s view, as isolated monads, but they have no power or freedom since their whole course of specific experiences is pre-ordained by God. The crucial dualism in the thought of Leibniz is between God and His distinctly lower creation. Leibniz’ vision did preserve the rationalist unity of language, thought, and (non-human) nature as co-ordinated features of God’s creation. Hume later presented, without appealing to the agency of God, another version of that same Calvinistic picture of the powerless isolation of every individual.

The discontinuity between Leibniz’ vision of metaphysical reality (the monads) and ordinary appearances was one of the most important inspirations for the philosophical work of Immanuel Kant (1724-1804). Kant was convinced by Leibniz and Hume on the point of individuals being very nearly “windowless monads”, but he could not accept the predetermined experience and the predetermined harmony imagined by Leibniz, nor could he accept Hume’s global skepticism. Kant’s transcendental idealism was an effort to transport individual freedom (transcendence) from the legacy of Stoicism (revived by Luther) into the mental scheme of modernity, to preserve the sense of transcendence and in doing so save modernity from descent into abject bourgeois philistinism. In that he was inspired by Jean-Jacques Rousseau (1712-78). Kant followed up Leibniz by concluding that the real world (noumena) was so different from the apparent world (phenomena) that 1) most of what we experience as “appearances” is contributed by our own nature as entities of intelligence, and 2) it is simply impossible to say anything meaningful about the noumenal Being behind appearances.

The metaphysical system of monads conceived by Leibniz relies on the foundation of the Christian God, exercising an absolute power of absolute rationality, and that has to be recognized as an untenable fantasy. Reasons for rejecting any idea of disembodied intelligence have been presented in previous postings, such as posting 32, May 17, 2012, Subjective Embodiment: Intelligence as a Particular, and posting 35, July 6, 2012, Transcendental Humanism. However, what Leibniz got right was the internal uniqueness of each subjectivity, along with a high degree of internal self-sufficiency to the entity of an individual intelligence. Leibniz’ monads illustrate the extreme discontinuity between the internality of experience and anything beyond itself, the discontinuity between a sensed placement or situation, as experienced internally (subjectively) by a person, and the actuality of nature. Recall that each intelligence is a self-constructed orientation (a bearing) within a grid of non-actuality consisting of accumulated and integrated memories, more or less desperate hopes and fears, mutually exclusive imagined possibilities, judgments of probabilities, and intentions, for example, none of which exists in the brute actuality of ambient nature. The internality of any particular intelligence has very little immediate congruity or continuity with any actuality beyond itself.

Major renovations are required to make Leibniz’ monads suitable for transcendental humanism. First, the idea of complete pre-determination by a personified and disembodied super-parent has to be removed. However, if God is not the source of an individual’s experiences, then some other account must be provided for those experiences. In other words, without God’s (or some other source’s) total pre-programming, the monads can’t be windowless and still have anything like ordinary experience. Kant removed a need for God’s agency in supplying experience by finding two replacement sources, an internal subjective source which he called “concepts” (a manifestation of personal intelligence), and an external source which he called “intuitions” (of phenomena). Departing from the particulars of Kant’s replacements, another way of describing that would be as an inward force of questioning intelligence encountering and making sense of the hard ground of nature. In spite of the discontinuity between their sense of the world and the brute actuality of the world, monads have, from their embodied activities, some accumulated familiarity with, or knowledge of, a world around them. In transcendental humanism the monads are not windowless, but rather have the elaborate windows of active and sensitive embodiment through which to accumulate experience of opening within a single world of nature and cultures, which multitudes of monads all share, a world within which each monad finds himself or herself, finds other monads, and constructs interactions and interconnections with them. Monads have both windows and effective force in creating their own experience.


The impressions of historical persons and ideas presented in this posting were informed at various stages of their development by the following works, which I salute and celebrate as inspirations, as well as sources of pleasure and excitement. Nobody could share my experience of reading these books and then agree with the proposition that all life is suffering. Faults in any of these postings are entirely my own.

The Best of All Possible Worlds: A Story of Philosophers, God, and Evil in the Age of Reason, written by: Steven Nadler, Published by: Princeton University Press (Mar 15 2010), Paperback: 320 pages, ISBN-10: 0691145318, ISBN-13: 978-0691145310.
(This is an engagingly written and wonderfully clear presentation of philosophical issues in Descartes, Leibniz, Malebranche, Arnauld, and Spinoza. It places these persons and issues very vividly in Paris during the 1670’s along with following developments.)

The Courtier And The Heretic: Leibniz, Spinoza, and the Fate of God in the Modern World, written by Matthew Stewart, Published by: WW Norton (Dec 27 2005), Hardcover: 320 pages, ISBN: 0393058980.
(The pleasure of reading this re-excited my interest in the history of philosophy after a lull. Stewart accomplishes the difficult feat of placing philosophical thinking within its cultural and historical setting in such a way as to recreate its drama and excitement for specific individuals and for the course of history, and making it a really good read. It inspired me to read the book listed next.)

Radical Enlightenment : Philosophy and the Making of Modernity 1650-1750, written by Jonathan I. Israel, Published by: Oxford University Press (July 2002), Paperback: 832 pages, ISBN: 0199254567.
(I read this during the spring of 2006, and found it deeply absorbing. It was packed with information I did not know and it remained readable through the whole 720 pages. Quite a writing accomplishment, among other things. It covers a fascinating period that has been a cultural blind spot for a long time.)

My impressions of Kant have benefited from my reading these:

Introduction to German Philosophy : From Kant to Habermas, written by Andrew Bowie, Published by: Polity Press (Oct 1, 2003), Paperback: 304 pages, ISBN: 0745625711.
(This is another one of those accessible presentations of vast research and insight. It shows modern philosophy as entirely bound up with the social transfiguration from Christendom/Old Regime to Modernity.)

The Roots of Romanticism, written by Isaiah Berlin, edited by Henry Hardy, Published by Princeton University Press (April 1, 2001); Paperback: 192 pages, ISBN-10: 0691086621, ( ISBN-13: 978-0691086620).

German Philosophy 1760-1860: The Legacy of Idealism, written by Terry Pinkard, Published by: Cambridge University Press (September 16, 2002), Paperback: 392 pages, ISBN-10: 0521663814, ISBN-13: 978-0521663816.

The following books informed my overview of the history of philosophy.

A History of Philosophy (Book One: Vol. I – Greece & Rome; Vol. II – Augustine to Scotus; Vol. III -Ockham to Suarez), written by Frederick Copleston, S.J., Published by: Image, Doubleday & Company, Inc. (March 19, 1985), Paperback: 479 pages, ISBN-10: 0385230311, (ISBN-13: 978-0385230315).

A History of Philosophy (Book Two: Volume IV – Descartes to Leibniz; Volume V – Hobbes to Hume; Volume VI – Wolff to Kant), written by Frederick Copleston, S.J., Published by: Image, Doubleday & Company, Inc. (March 19, 1985), Paperback: 509 pages, ISBN-10: 038523032X, (ISBN-13: 978-0385230322).

A History of Philosophy: Book Three (Volume VII, Fichte to Nietzsche, Volume VIII, Bentham to Russell, Volume IX, Maine De Biran to Sartre), written by Frederick Copleston, S.J., Published by: Image, Doubleday & Company, Inc. (March 19, 1985), Paperback: 480 pages, ISBN-10: 0385230338, (ISBN-13: 978-0385230339).

History of Philosophy (Historia de la Filosofia), written by Julian Marias, translated from Spanish to English by Stanley Appelbaum and Clarence C. Strowbridge, Published by: Dover Publications; 22nd edition (June 1, 1967), Paperback: 505 pages, ISBN-10: 0486217396, ISBN-13: 978-0486217390.

A History of Western Philosophy, written by Bertrand Russell, Published by Routledge; New edition (2000), Paperback: 848 pages, ISBN-10: 0415228549, ISBN-13: 978-0415228541. (Russell claims special expertise on Leibniz.)

A History of Western Political Thought, written by  J. S. McClelland, Published by Routledge (1996), Paperback: 824 pages, ISBN-10: 0415119626, ISBN-13: 978-0415119627.

As a thoughtful overview of the history of philosophy set within a beautifully atmospheric story of mystery and discovery, there is this gift from Norway:

Sophie’s World: A Novel About the History of Philosophy, written by Jostein Gaarder, translated from Norwegian to English by Paulette Moller (copyright 1994), Published by: Farrar, Straus and Giroux, (ISBN-10: 0374530718, ISBN-13: 978-0374530716).
(Gaarder credits the Roman author Cicero (106-43 B.C.) with forming the concept “humanism”, “a view of life that has the individual as its central focus.”)

Copyright © 2012 Sandy MacDonald. The moral right of the author is asserted.