The Monadology (French: La Monadologie, 1714) is one of Gottfried Leibniz's best known works representing his later philosophy. It is a short text which sketches in some 90 paragraphs a metaphysics of simple substances, or monads.


Leibniz Monadology 2
The first manuscript page of the Monadology

During his last stay in Vienna from 1712 to September 1714, Leibniz wrote two short texts in French which were meant as concise expositions of his philosophy. After his death Principes de la nature et de la grâce fondés en raison, which was intended for prince Eugene of Savoy, appeared in French in the Netherlands. Christian Wolff and collaborators published translations in German and Latin of the second text which came to be known as The Monadology. Without having seen the Dutch publication of the Principes they had assumed that it was the French original of the Monadology, which in fact remained unpublished until 1840.

The German translation appeared in 1720 as Lehrsätze über die Monadologie and the following year the Acta Eruditorum printed the Latin version as Principia philosophiae.[1] There are three original manuscripts of the text: the first written by Leibniz and overcharged with corrections and two further emended copies with some corrections appearing in one but not the other.[2] Leibniz himself inserted references to the paragraphs of his Théodicée ("Theodicy", i.e. a justification of God), sending the interested reader there for more details.



The monad, the word and the idea, belongs to the Western philosophical tradition and has been used by various authors.[3] Leibniz, who was exceptionally well read, could not have ignored this, but he did not use it himself until mid-1696 when he was sending for print his New System.[4] Apparently he found with it a convenient way to expose his own philosophy as it was elaborated in this period. What he proposed can be seen as a modification of occasionalism developed by latter-day Cartesians. Leibniz surmised that there are indefinitely many substances individually 'programmed' to act in a predetermined way, each substance being coordinated with all the others. This is the pre-established harmony which solved the mind-body problem, but at the cost of declaring any interaction between substances a mere appearance.


The rhetorical strategy adopted by Leibniz in The Monadology is fairly obvious as the text

  • begins with a description of monads (proceeding from simple to complicated instances),
  • then it turns to their principle or creator and
  • finishes by using both to explain the world.

(I) As far as Leibniz allows just one type of element in the building of the universe his system is monistic. The unique element has been 'given the general name monad or entelechy' and described as 'a simple substance' (§§1, 19). When Leibniz says that monads are 'simple,' he means that "which is one, has no parts and is therefore indivisible".[5] Relying on the Greek etymology of the word entelechie (§18),[6] Leibniz posits quantitative differences in perfection between monads which leads to a hierarchical ordering. The basic order is three-tiered: (1) entelechies or created monads (§48), (2) souls or entelechies with perception and memory (§19), and (3) spirits or rational souls (§82). Whatever is said about the lower ones (entelechies) is valid for the higher (souls and spirits) but not vice versa. As none of them is without a body (§72), there is a corresponding hierarchy of (1) living beings and animals (2), the latter being either (2) non-reasonable or (3) reasonable. The degree of perfection in each case corresponds to cognitive abilities and only spirits or reasonable animals are able to grasp the ideas of both the world and its creator. Some monads have power over others because they can perceive with greater clarity, but primarily, one monad is said to dominate another if it contains the reasons for the actions of other(s). Leibniz believed that any body, such as the body of an animal or man, has one dominant monad which controls the others within it. This dominant monad is often referred to as the soul.

(II) God is also said to be a simple substance (§47) but it is the only one necessary (§§38–9) and without a body attached (§72). Monads perceive others "with varying degrees of clarity, except for God, who perceives all monads with utter clarity".[7] God could take any and all perspectives, knowing of both potentiality and actuality. As well as that God in all his power would know the universe from each of the infinite perspectives at the same time, and so his perspectives—his thoughts—"simply are monads".[8] Creation is a permanent state, thus "[monads] are generated, so to speak, by continual fulgurations of the Divinity" (§47).[9] Any perfection comes from being created while imperfection is a limitation of nature (§42). The monads are unaffected by each other, but each have a unique way of expressing themselves in the universe, in accordance with God's infinite will.

(III) Composite substances or matter are "actually sub-divided without end" and have the properties of their infinitesimal parts (§65). A notorious passage (§67) explains that "each portion of matter can be conceived as like a garden full of plants, or like a pond full of fish. But each branch of a plant, each organ of an animal, each drop of its bodily fluids is also a similar garden or a similar pond". There are no interactions between different monads nor between entelechies and their bodies but everything is regulated by the pre-established harmony (§§78–9). Much like how one clock may be in synchronicity with another, but the first clock is not caused by the second (or vice versa), rather they are only keeping the same time because the last person to wind them set them to the same time. So it is with monads; they may seem to cause each other, but rather they are, in a sense, "wound" by God's pre-established harmony, and thus appear to be in synchronicity. Leibniz concludes that "if we could understand the order of the universe well enough, we would find that it surpasses all the wishes of the wisest people, and that it is impossible to make it better than it is—not merely in respect of the whole in general, but also in respect of ourselves in particular" (§90).[10]

In his day, atoms were proposed to be the smallest division of matter. Within Leibniz's theory, however, substances are not technically real, so monads are not the smallest part of matter, rather they are the only things which are, in fact, real. To Leibniz, space and time were an illusion, and likewise substance itself. The only things that could be called real were utterly simple beings of psychic activity "endowed with perception and appetite."[11] The other objects, which we call matter, are merely phenomena of these simple perceivers. "Leibniz says, 'I don't really eliminate body, but reduce [revoco] it to what it is. For I show that corporeal mass [massa], which is thought to have something over and above simple substances, is not a substance, but a phenomenon resulting from simple substances, which alone have unity and absolute reality.' (G II 275/AG 181)"[12] Leibniz's philosophy is sometimes called "'panpsychic idealism' because these substances are psychic rather than material".[13] That is to say, they are mind-like substances, not possessing spatial reality. "In other words, in the Leibnizian monadology, simple substances are mind-like entities that do not, strictly speaking, exist in space but that represent the universe from a unique perspective."[14] It is the harmony between the perceptions of the monads which creates what we call substances, but that does not mean the substances are real in and of themselves.[15]


Controversy in rationalism

The Monadology tried to answer two huge philosophical questions—both studied by Descartes—from a monist point of view. The first is about the nature of reality. The second, about the problem of communication of substances, is related to a common objection to mind-body dualism, namely, the body-soul interaction problem. Thus, Leibniz offered a new solution to the mind-matter interaction problem by positing a pre-established harmony between substances: the body is mere perceptions, which are all contained in a soul's complete concept. The soul and body interact and agree in virtue of the pre-established harmony, maintained by God. Leibniz also drew the relationship between "the kingdom of final causes", or teleological ones, and "the kingdom of efficient causes", or mechanical ones, which was not causal, but synchronous. So, monads and matter are only apparently linked, and there is not even any communication between different monads; there is only harmony, pre-established and maintained by God.

Leibniz fought against the Cartesian dualist system in his Monadology and instead opted for a monist idealism (since substances are all unextended). However, Leibniz was a pluralist in the sense that substances are disseminated in the world in an infinite number. For that reason the monad is an irreducible force, which makes it possible for the bodies to have the characteristics of inertia and impenetrability, and which contains in itself the source of all its actions. Monads are the first elements of every composed thing.

Philosophical conclusions

This theory leads to:

1. Idealism, since it denies things in themselves (besides monads) and multiplies them in different points of view. Monads are "perpetual living mirrors of the universe."

2. Metaphysical optimism, through the principle of sufficient reason, developed as follows:

a) Everything exists according to a reason (by the axiom "Nothing arises from nothing");

b) Everything which exists has a sufficient reason to exist;

c) Everything which exists is better than anything nonexistent (by the first point: since it is more rational, it also has more reality), and, consequently, it is the best possible being in the best of all possible worlds (by the axiom: "That which contains more reality is better than that which contains less reality").

See also


  1. ^ Lamarra A., Contexte Génétique et Première Réception de la Monadologie, Revue de Synthese 128 (2007) 311–323
  2. ^ Leibniz G.W., La Monadologie, edition établie par E. Boutroux, Paris LGF 1991
  3. ^ There is no indication that Leibniz has 'borrowed' it from a particular author, e.g. Giordano Bruno or John Dee, to mention just two popular sources
  4. ^ Woolhouse R. and Francks R., Leibniz's "New System" and associated contemporary texts, Cambridge Univ. Press 1997
  5. ^ Burnham, Douglas. "Gottfried Leibniz: Metaphysics." Internet Encyclopedia of Philosophy, [accessed May 2, 2016].
  6. ^ On pourrait donner le nom d'entéléchies à toutes les substances simples ou Monades créées, car elles ont en elles une certaine perfection (ἔχουσι τὸ ἐντελές)
  7. ^ Audi Robert, ed. "Leibniz, Gottfried Wilhelm." The Cambridge Dictionary of Philosophy. Cambridge; Cambridge University Press (1999): 193.
  8. ^ Look, Brandon C. "Gottfried Wilhelm Leibniz." Stanford University, [accessed February 27, 2016].
  9. ^ trans. Hedge. "Leibniz's vestige view of God's creative act is employed to support his view of substance as an inherently active being possessed of its own dynamic force" Scott D., Leibniz model of creation and his doctrine of substance, Animus 3 (1998) [1]
  10. ^ Burnham, Douglas. "Gottfried Leibniz: Metaphysics." Internet Encyclopedia of Philosophy, [accessed May 2, 2016].
  11. ^ Look, Brandon C. "Gottfried Wilhelm Leibniz." Stanford University, [accessed February 27, 2016].
  12. ^ Look, Brandon C. "Gottfried Wilhelm Leibniz." Stanford University, [accessed February 27, 2016].
  13. ^ Pestana, Mark. "Gottfried Wilhelm Leibniz." World Philosophers & Their Works (2000): 1–4.
  14. ^ Burnham, Douglas. "Gottfried Leibniz: Metaphysics." Internet Encyclopedia of Philosophy, [accessed May 2, 2016].
  15. ^ Burnham, Douglas. "Gottfried Leibniz: Metaphysics." Internet Encyclopedia of Philosophy, [accessed May 2, 2016].


  • Nicholas Rescher N., G. W. Leibniz's Monadology, University of Pittsburgh Press, 1991, ISBN 0-8229-5449-4, ISBN 978-0-8229-5449-1
  • Savile A., Routledge Philosophy Guidebook to Leibniz and the Monadology, Routledge (2000), ISBN 0-415-17113-X, ISBN 978-0-415-17113-7

External links

1745 in science

The year 1745 in science and technology involved some significant events.

A priori and a posteriori

The Latin phrases a priori (lit. "from the earlier") and a posteriori (lit. "from the later") are philosophical terms popularized by Immanuel Kant's Critique of Pure Reason (first published in 1781, second edition in 1787), one of the most influential works in the history of philosophy. However, in their Latin forms they appear in Latin translations of Euclid's Elements, of about 300 BC, a work widely considered during the early European modern period as the model for precise thinking.

These terms are used with respect to reasoning (epistemology) to distinguish "necessary conclusions from first premises" (i.e., what must come before sense observation) from "conclusions based on sense observation" which must follow it. Thus, the two kinds of knowledge, justification, or argument, may be glossed:

A priori knowledge or justification is independent of experience, as with mathematics (3 + 2 = 5), tautologies ("All bachelors are unmarried"), and deduction from pure reason (e.g., ontological proofs).

A posteriori knowledge or justification depends on experience or empirical evidence, as with most aspects of science and personal knowledge.There are many points of view on these two types of knowledge, and their relationship gives rise to one of the oldest problems in modern philosophy.

The terms a priori and a posteriori are primarily used as adjectives to modify the noun "knowledge" (for example, "a priori knowledge"). However, "a priori" is sometimes used to modify other nouns, such as "truth". Philosophers also may use "apriority" and "aprioricity" as nouns to refer (approximately) to the quality of being "a priori".Although definitions and use of the terms have varied in the history of philosophy, they have consistently labeled two separate epistemological notions. See also the related distinctions: deductive/inductive, analytic/synthetic, necessary/contingent.

Bernhard Lang

Bernhard Lang (* February 24, 1957 in Linz) is an Austrian composer, improvisationalist and programmer of musical patches and applications. His work can be described as modern contemporary music, with roots, however, in various genres such as 20th-century avant-garde, European classical music, jazz, free jazz, rock, punk, techno, EDM, electronica, electronic music and computer-generated music. His works are performed on all relevant festivals of modern music and range from solo pieces and chamber music to large ensemble pieces and works for orchestra and musical theater. Besides music for concert halls, Lang designs sound and music for theater, dance, film and sound installations.

Bernhard Lang came to prominence with his work cycle “Differenz / Wiederholung” (“difference / repetition”) in which he illuminated and examined the themes of reproductive and DJ cultures based on the philosophic work of Gilles Deleuze. Socio-cultural and societally critical questions, as in “Das Theater der Wiederholungen”, 2003 (“The Theatre of Repetitions”), are as closely examined as intrinsic musical and music-cultural problems (“I hate Mozart”, 2006). Another focus is the “recycling” of historic music, which Lang performs using self-programmed patches, applying filter and mutation processes (as in the “Monadologie” cycle).

Alongside classical European instruments, Lang also makes use of their amplified electrical counterparts (e.g. electric viola) as well as mutually microtonally de-tuned ensemble groups. Analogue and digital synthesizers, keyboards, rock music instruments (electric guitar and bass, drumset), turntables (the trailblazing instrument of the reproductive culture), rappers, Arabian singers, speech and live-electronics (mainly the self-programmed “Loop Generator”) are similarly used.

Discourse on Metaphysics

The Discourse on Metaphysics (French: Discours de métaphysique, 1686) is a short treatise by Gottfried Wilhelm Leibniz in which he develops a philosophy concerning physical substance, motion and resistance of bodies, and God's role within the universe. It is one of the few texts presenting in a consistent form the earlier philosophy of Leibniz.

The Discourse is closely connected to the epistolary discussion which he carried with Antoine Arnauld. However Leibniz refrained from sending the full text and it remained unpublished until the mid 19th century. Arnauld received only an abridged version in 37 points which resumed whole paragraphs and steered their discussion.

The metaphysical considerations proceed from God to the substantial world and back to the spiritual realm. The starting point for the work is the conception of God as an absolutely perfect being (I), that God is good but goodness exists independently of God (a rejection of divine command theory) (II), and that God has created the world in an ordered and perfect fashion (III–VII).

At the time of its writing Discourse made the controversial claim That the opinions of... scholastic philosophers are not to be wholly despised (XI). Early work in modern philosophy during the 17th century were based on a rejection of many of the precepts of medieval philosophy. Leibniz saw the failures of scholasticism merely as one of rigor. [If] some careful and meditative mind were to take the trouble to clarify and direct their thoughts in the manner of analytic geometers, he would find a great treasure of important truths, wholly demonstrable.

Leibniz claimed that God's omnipotence was in no way impugned by the thought of evil, but was rather solidified. He endorsed the view that God chose the best of all possible worlds. In other words, Leibniz believed this world (or reality) to be the best there possibly could be — taking all facts into account, no better world could be imagined, even if we believed that we could think of something more perfect.

Leibniz's conception of physical substance is expanded upon in The Monadology.

Edward Douglas Fawcett

Edward Douglas Fawcett (11 April 1866 – 14 April 1960) was an English mountaineer, philosopher and novelist.

Emergent organization

An emergent organization (alternatively emergent organisation) is an organization that spontaneously emerges from and exists in a complex dynamic environment or market place, rather than being a construct or copy of something that already exists. The term first appeared in the late 1990s and was the topic of the Seventh Annual Washington Evolutionary Systems Conference at University of Ghent, Belgium in May, 1999. Emergent organizations and their dynamics pose interesting questions; for example, how does such an organization achieve closure and stability?

Alternatively, James R. Taylor wrote in 2000 his seminal book, The Emergent Organization, where he suggests that all organizations emerge from communication, especially from the interplay of conversation and text. This idea concerns human organizations, but is consistent with Leibniz or Gabriel Tarde's monadology, or with Alfred North Whitehead's process philosophy, which explains the macro—both in human and non-human "societies"—from the processes taking place between its constituent parts.

Gottfried Wilhelm Leibniz

Gottfried Wilhelm (von) Leibniz (sometimes spelled Leibnitz) (; German: [ˈɡɔtfʁiːt ˈvɪlhɛlm fɔn ˈlaɪbnɪts] or [ˈlaɪpnɪts]; French: Godefroi Guillaume Leibnitz; 1 July 1646 [O.S. 21 June] – 14 November 1716) was a prominent German polymath and philosopher in the history of mathematics and the history of philosophy. His most notable accomplishment was conceiving the ideas of differential and integral calculus, independently of Isaac Newton's contemporaneous developments. Mathematical works have always favored Leibniz's notation as the conventional expression of calculus, while Newton's notation became unused. It was only in the 20th century that Leibniz's law of continuity and transcendental law of homogeneity found mathematical implementation (by means of non-standard analysis). He became one of the most prolific inventors in the field of mechanical calculators. While working on adding automatic multiplication and division to Pascal's calculator, he was the first to describe a pinwheel calculator in 1685 and invented the Leibniz wheel, used in the arithmometer, the first mass-produced mechanical calculator. He also refined the binary number system, which is the foundation of all digital computers.

In philosophy, Leibniz is most noted for his optimism, i.e. his conclusion that our universe is, in a restricted sense, the best possible one that God could have created, an idea that was often lampooned by others such as Voltaire. Leibniz, along with René Descartes and Baruch Spinoza, was one of the three great 17th-century advocates of rationalism. The work of Leibniz anticipated modern logic and analytic philosophy, but his philosophy also looks back to the scholastic tradition, in which conclusions are produced by applying reason to first principles or prior definitions rather than to empirical evidence.

Leibniz made major contributions to physics and technology, and anticipated notions that surfaced much later in philosophy, probability theory, biology, medicine, geology, psychology, linguistics, and computer science. He wrote works on philosophy, politics, law, ethics, theology, history, and philology. Leibniz also contributed to the field of library science. While serving as overseer of the Wolfenbüttel library in Germany, he devised a cataloging system that would serve as a guide for many of Europe's largest libraries. Leibniz's contributions to this vast array of subjects were scattered in various learned journals, in tens of thousands of letters, and in unpublished manuscripts. He wrote in several languages, but primarily in Latin, French, and German. There is no complete gathering of the writings of Leibniz translated into English.

Gottfried Wilhelm Leibniz bibliography

Gottfried Wilhelm Leibniz was a major contributor to mathematics, physics, philosophy, theology, logic, and early computer science; independent inventor of calculus in mathematics; inventor of energy and the action principle in physics; jurist, genealogist, diplomat, librarian; worked towards reunification of Catholic and Protestant faiths.

This in-progress article will list all his published and unpublished works primarily based on the Leibniz Library in Hannover , and its online catalog.

Hans Heinz Holz

Hans Heinz Holz (26 February 1927 – 11 December 2011) was a German Marxist philosopher.Born in Frankfurt am Main, he was professor of philosophy at the University of Marburg (from 1971 to 1979) and from 1979 to 1993 at the University of Groningen. He is known for his encyclopedic knowledge of the history of philosophy on one hand and for his openly expressed ideological viewpoints on the other. Influenced by Gottfried Wilhelm Leibniz's monadology, he regards Widerspiegelung (reflection) not only as an epistemological but also as an ontological category. Some critics spot here a hazard of deviating from materialism. Though Holz saw himself as in footsteps of Lenin, his vision is disputed among the leftist circles. He has contributed to far-left publications like Marxistische Blätter and Weißenseer Blätter. He joined the German Communist Party in 1994.

Leibniz's gap

Leibniz's gap is a philosophy of mind term that is used to refer to the problem that thoughts cannot be observed or perceived solely by examining brain properties, events, and processes. Here the word "gap" is a metaphor of a subquestion regarding the mind–body problem that allegedly must be answered in order to reach a more profound understanding of consciousness and emergence. A theory that could correlate brain phenomena with psychological phenomena would "bridge the gap".

The term Leibniz's gap was coined by Robert Cummins and was named after Gottfried Leibniz, who first presented the problem in his work The Monadology in 1714. Leibniz's passage describing the gap goes as follows:

The problem according to Leibniz is that there is a gap between concepts of modern neuroscience and those that we use to describe the brain such as "thought", "feeling", and "perception". This means that the physical observation of the brain yields data in the wrong vocabulary even if we are convinced that the mind is the brain. Leibniz himself sought to bridge the gap by introducing monads to explain the existence of immaterial, eternal souls. Leibniz's gap, however, applies to materialism and dualism alike. This brought late 19th century scientists to conclude that psychology must build on introspection; thus introspectionism was born. Computationalism seeks to answer the problem proposed by Leibniz's gap through functional analysis of the brain and its processes. There is the position that functionalism could address the gap since it allows something to be described in terms of what it does without explaining how it does it or identifying the physical form it takes. Today, however, Leibniz's gap is still in wide use in scientific debate as the mind body problem that remains unsolved.

List of works published posthumously

The following is a list of works that were published or distributed posthumously.

Mental substance

Mental substance is the idea held by dualists and idealists, that minds are made-up of non-physical substance. This substance is often referred to as consciousness.

This is opposed to the materialists, who hold that what we normally think of as mental substance is ultimately physical matter (i.e., brains).

Descartes, who was most famous for the assertion "I think therefore I am", has had a lot of influence on the mind–body problem. He describes his theory of mental substance (which he calls res cogitans distinguishing it from the res extensa) in the Second Meditation (II.8) and in Principia Philosophiae (2.002).

He used a more precise definition of the word "substance" than is currently popular: that a substance is something which can exist without the existence of any other substance. For many philosophers, this word or the phrase "mental substance" has a special meaning.

Gottfried Leibniz, belonging to the generation immediately after Descartes, held the position that the mental world was built up by monads, mental objects that are not part of the physical world (see Monadology).


Metamorphosis is a biological process by which an animal physically develops after birth or hatching, involving a conspicuous and relatively abrupt change in the animal's body structure through cell growth and differentiation. Metamorphosis is iodothyronine-induced and an ancestral feature of all chordates. Some insects, fishes, amphibians, mollusks, crustaceans, cnidarians, echinoderms, and tunicates undergo metamorphosis, which is often accompanied by a change of nutrition source or behavior. Animals that go through metamorphosis are called metamorphoses. Animals can be divided into species that undergo complete metamorphosis ("holometaboly"), incomplete metamorphosis ("hemimetaboly"), or no metamorphosis ("ametaboly").

Scientific usage of the term is technically precise, and it is not applied to general aspects of cell growth, including rapid growth spurts. References to "metamorphosis" in mammals are imprecise and only colloquial, but historically idealist ideas of transformation and monadology, as in Goethe's Metamorphosis of Plants, have influenced the development of ideas of evolution.

Monad (philosophy)

Monad (from Greek μονάς monas, "singularity" in turn from μόνος monos, "alone") refers, in cosmogony, to the Supreme Being, divinity or the totality of all things. The concept was reportedly conceived by the Pythagoreans and may refer variously to a single source acting alone, or to an indivisible origin, or to both. The concept was later adopted by other philosophers, such as Leibniz, who referred to the monad as an elementary particle. It had a geometric counterpart, which was debated and discussed contemporaneously by the same groups of people.


Monism attributes oneness or singleness (Greek: μόνος) to a concept e.g., existence. Various kinds of monism can be distinguished:

Priority monism states that all existing things go back to a source that is distinct from them; e.g., in Neoplatonism everything is derived from The One. In this view only one thing is ontologically basic or prior to everything else.

Existence monism posits that, strictly speaking, there exists only a single thing, the Universe, which can only be artificially and arbitrarily divided into many things.

Substance monism asserts that a variety of existing things can be explained in terms of a single reality or substance. Substance monism posits that only one kind of stuff exists, although many things may be made up of this stuff, e.g., matter or mind.

Neutral monism

In the philosophy of mind, neutral monism is the view that the mental and the physical are two ways of organizing or describing the same elements, which are themselves "neutral", that is, neither physical nor mental. This view denies that the mental and the physical are two fundamentally different things. Rather, neutral monism claims the universe consists of only one kind of stuff, in the form of neutral elements that are in themselves neither mental nor physical.

Pre-established harmony

Gottfried Leibniz's theory of pre-established harmony (French: harmonie préétablie) is a philosophical theory about causation under which every "substance" affects only itself, but all the substances (both bodies and minds) in the world nevertheless seem to causally interact with each other because they have been programmed by God in advance to "harmonize" with each other. Leibniz's term for these substances was "monads" which he described in a popular work (Monadology §7) as "windowless".

Well-founded phenomenon

Well-founded phenomena (Latin: phenomena bene fundata), in the philosophy of Gottfried Leibniz, are ways in which the world falsely appears to us, but which are grounded in the way the world is (as opposed to dreams or hallucinations, which are false appearances that are not thus grounded).

For Leibniz, the universe is made up of an infinite number of simple substances or monads, each of which contains a representation of the entire universe (past, present, and future), and which are all causally isolated from one another ("Monads have no windows through which anything could enter or depart.") For the most part the monads' perceptions are more or less confused and obscure, but some of them correspond either to the ways in which other monads are related or to the ways that the representation is genuinely ordered; these are the well-founded phenomena.

In the world of ordinary experience we might call a rainbow a well-ordered phenomenon; it appears to us to be a coloured arch in the sky, though there is in fact no arch there. We are not suffering from hallucinations, though, for the appearance is grounded in the way the world is ordered – in the behaviour of light, dust motes, water particles, etc.

For Leibniz, there are two main categories of well-founded phenomena: the ordinary world of individual objects and their interactions, and more abstract phenomena such as space, time, and causality. This is also found in his expression of pre-established harmony being the basis of causation.

Mathematics and

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