Monadology

The Monadology (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.

Text
During his last stay in Vienna from 1712 to September 1714, Leibniz wrote two short texts which were meant as concise expositions of his philosophy. After his death Principes de la Nature et de la Grace 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 Without having seen the Dutch publication they had assumed that it was the French original which in fact remained unpublished until 1840. The German translation appeared in 1720 as Lehrs&auml;tze &uuml;ber die Monadologie and the following year the Acta Eruditorum printed the Latin version as Principia philosophiae. 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. Leibniz himself inserted references to the paragraphs of his Theodicy, sending the interested reader there for more details.

Context
The "monad", the word and the idea, belongs to the western philosophical tradition and has been used by various authors. 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. 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 program being coordinated with all the others. This is the pre-established harmony which solved the mind body problem at the cost of declaring any interaction between substances a mere appearance, something which Leibniz accepted. Indeed it was space itself which became an appearance as in his system there was no need for distinguishing inside from outside. True substances were explained as metaphysical points which, Leibniz asserted, are both real and exact, mathematical points being exact but not real and physical ones being real but not exact. Clearly, besides metaphysics, the developing of calculus had also provided some grounds for seeking universal elementary constituents. At the empirical level, use of the microscope also corroborated Leibniz's view. "Scientists have had great difficulties over the origin of forms, entelechies or souls" notes §74 of The Monadology while displaying his synonyms for "monad".

Text
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 build 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). Relying on the etymology of the Greek word (§48), Leibniz posits quantitative differences in perfection between monads which leads to a hierarchical ordering. The basic order is three-tiered: (1) entelechies (2) souls and (3) spirits. Whatever is said about the lower ones (entelechies) is valid for the higher (souls and spirits) but not the obverse. 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 psychic abilities and only spirits or reasonable animals are able to grasp the ideas of both the world and its creator.

(II) God is also said to be a simple substance (§47) but it is the only one which is necessary (§§38-9) and without a body attached (§72). Creation is a permanent state so "[monads] are born from one moment to the next by continual flashes of lightening from the divinity". Any perfection comes from being created while imperfection is a limitation of nature (§42).

(III) Composite substances or matter are "actually sub-divided without end" and have the properties of their infinitesimal parts (§65). Some understanding how this is possible has been provided by the recent development of fractals. 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). 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).

Controversy in rationalism
When it was written, the Monadology tried to put an end from a monist point of view to the main question of what is reality, and particularly to the problem of communication of substances, both studied by Descartes called mind-body dualism. Thus, Leibniz offered a new solution to mind and matter interaction by means of a pre-established harmony expressed as the Best of all possible worlds form of optimism; in other words, he 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, as far as they act according to their degree of distinction only, as they were influenced by bodies, and vice versa.

Leibniz fought against the Cartesian dualist system in his Monadology and tried to surpass it through a metaphysical system considered at the same time monist (since only the unextended is substantial) and pluralist (as far as 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.

Paradoxes
Monads are manifest, since they are everywhere, and there is no extension without monads. They are, then, the plenum, that is to say, the condition of an infinitely dense universe, but nevertheless they are unextended. However, this doesn’t mean that they lack of any function (as far as they project and reflect force), matter (since they come with it) or that they are extended (considering that they don’t interact with anything in the world).

Extended matter would be the impenetrable quality of the unextended&mdash;the monad, without any doors or windows&mdash;as passively transmitted according to movements which, together with perception and apperception, compose action. In spite of that, a monad cannot remain placed in matter, which follows the monad itself, previously to the generation of matter in time. So, extension and monads coexist acausally by the means of a timeless creation, although they are reciprocally bound according to the appearances.

In brief, Leibniz states that matter is extended, but not only extended. It is, in addition, formed by unextended monads. Then, is matter both extended and unextended? No, accepting that, as far as monad constitutes matter, matter is nothing in itself[Why is this? Elaboration requested here. This is a rather weak attempt at creating a non-existent paradox(and can be analogized and reduced to the following sentence: matter has a form, and thought not (this is not to be confused with it being non-physical), exceedingly; thoughts exists in matter, thus matter is, but bound to be nothing but exactly: "thought", or at least not to be differentiable from matter, and must thus also be confined to the properties that be those of matter) created, presumably, merely for the sake of criticism, since there can be found at least one possible border in the virtual between the extended and the unextended, even though a border holds no functions, it marks a physical relation to at least two different locations, for since it is already given that there can be an extended part, object or substance in the physical, then is thus also given that at least one function exists for that object, namely; 1. Its creation, 2. It's destruction/reconstruction. Is it impossible for these skepticists to imagine an entity with principal parts that are lesser in functional potential, than that of its components in sum. Therefore, this criticism must have to be re-formulated, so that the meaning is changed in its predicative and linguistical functions, in order to work as a valid and proper argument, in short, two differentiable and principal functions, locations or entities can easily, and very aptly have at least one different property, despite possibly sharing theoretical infinite values]. Monad as an isolated being therefore represents the essence of German idealism.

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 non-existent (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").

The “best of possible worlds,” then, is that “containing the greatest variety of phenomena from the smallest amount of principles.” See fractal for a strong relationship.

References and notes

 * Nicholas Rescher N., G. W. Leibniz's Monadology, University of Pittsburgh Press, 1991, ISBN 0822954494, ISBN 978-0822954491
 * Savile A., Routledge Philosophy Guidebook to Leibniz and the Monadology,  Routledge (2000), ISBN 041517113X,  ISBN 978-0415171137