What is it that Leibniz calls a “Monad”?

Question

What is a “monad” as introduced by Gottfried Leibniz in his Monadology? What is the purpose of monads for Leibniz' philosophical arguments?

EDIT: I've found basic definitions like those found in the comments, too. However I also found rather confusing properties of monads, like they where "living mirrors of the universe" and can be sleeping or awake. So is the idea really that those monads (of which I think like "atoms") are like "minds" or living beings?

EDIT: Is there a notion of time / order of actions / cause associated with monads?

Answer 1

However I also found rather confusing properties of monads, like they where "living mirrors of the universe" [...] Is there a notion of time / order of actions / cause associated with monads?

Monads mirror – each one under its own aspect – the entire universe, and these mirrorings involve not only the present, but also past and virtual future states. But this must not be understood as causal influence or interaction, because this would contradict their being "fensterlos" (window-less) and their existence as substantial units. What is perceived as effect is really based on an ideal influence established by God, who by thinking through all possible states and courses of the world, accounts for every substance. This is the principle of "prästabilierte Harmonie".

[...] and can be sleeping or awake. So is the idea really that those monads (of which I think like "atoms") are like "minds" or living beings?

Leibniz uses the term Monad for individual substances, which have no parts. ("La Monade ... n'est autre chose, qu'une substance simple, qui entre dans les composés; simple, c'est à dire, sans parties") This is a continuation of, and includes, scholastic traditions ("ens et unum convertuntur").

This is in contrast to Descartes' dualism. Leibniz takes the modern concept of individuals, well-founded in Descartes' cogito argument, and lifts the soul-having "I" to being the substance. The infinite number of ideal, individual, and dynamic substances, which all mirror the entire universe, is Leibniz' answer to Descartes' dualism, Spinoza's monism, and Gassendi's atomism.

Only organic creatures (humans, animals, plants) are such units, not corpora which are mere aggregates and phaenomena. Decomposition of composites will, according to Leibniz, not lead to material units, because continuous division of corpora will not lead to something that could be called "unum per se". They are "metaphysische Punkte" (metaphysical points), can neither be made or destroyed physically, and are all different.

Monads are dynamic, and only differ by their inner states, their "Perzeptionen" (perceptions). Their dynamicism is due to an inner urge ("appetition"), which advances them from perception to perception. Leibniz calls monads, whose perception is accompanied by recollection souls. (So, in contrast to Descartes, according to Leibniz, animals have souls) Monads which represent "die äußeren Dinge" (the outer things) must be distinguished from "Apperzeptionen", which means self-awareness or reflexive cognition. Monads capable of this are called "vernünftige Seelen" or "Geister" (intelligent souls or spirits, "animae"). Now, there is a hierarchy of monads with regard to their apperceptions: From "schlummernden" (slumbering) up to the omniscient monad, the "monas monadum" (monad of monads) – God. Somewhere in between are animal and spirit monads. Also, every monad has a dedicated corpus, a body which is itself assembled from parts, which themselves have their dedicated monads, lower in the hierarchy. Only the monas monadum exists without one.

All in all, this is a very difficult topic. I hope I was of any help, and did not add to your confusion. I would not claim that I understand Leibniz' system myself in its entirety.

Source: Historisches Wörterbuch der Philosophie, Bd. 6: Monade, J. Ritter et al., 1971

Answer 2

The essential characteristic of monads is that they are irreducible; in this way they resemble (philosophical) atoms, which are similarly irreducible to simpler components. Where atoms and monads differ is that atoms are viewed as purely physical, and are therefore tiny. Monads, on the other hand, are immaterial, and are units of "force"; physical attributes (such as matter or motion) are merely phenomenal.

It may be worth pointing out that Leibniz came to this theory after reading Chinese philosophy, and that there are similarities to be found between his thought and that of, for example, Fazang, the 7th century Buddhist philosopher. I think that this element of his project often receives less attention than his mathematical, scientific and logical work.

Answer 3

Others have already commented on the concept itself, and I am certainly not a Leibniz expert, so I'd just like to recommend a look at The Fold: Leibniz and the Baroque, which deals with the concept of the monad in some depth. Google says the words 'monad' and 'time' show up together on 19 different pages of the text; from the fourth result of that query:

If space-time is not an empty area, but the order of coexistence and the succession of monads themselves, the order has to be marked out, oriented, vectored; in the instance of each monad movement has to go from the more-clear monad to the less-clear monad, or from the perfected accord to the less-perfected accord, for the clearest or the most perfected is reason itself. In the expression 'preestablished harmony', 'preestablished' is no less important than 'harmony'. Harmony is twice-established: by virtue of each expression, of each expressant that owes only to its own spontaneity or interiority, and by virtue of the common expression that establishes the concert of all these expressive spontaneities. It is as if Leibniz were delivering us an important message about communication: don't complain about not having enough communication, for there is always plenty of it. Communication seems to be of a constant and preestablished quantity in the world, akin to a sufficient reason. (Gilles Deleuze, The Fold 154)

Answer 4

I would encourage those interested in monads and what they stand for in Leibniz's philosophy, to access Julia Jorati's "Leibniz's Ontology of Force" – it is a very interesting and compelling discussion on Leibniz and involves small discussion on time too.

Main feature is that she defends Leibniz as force-ontologist and shows that monads are identified with active forces. That is, basic constituent of matter is metaphysical force. God is perfect and possesses unlimited force, whereas everything constituting matter is limited.

As for time, since the paper was not devoted to this discussion, she can only afford a one page's dsicussion to this topic. Additionally, she discusses the law of series, which will be relevant to discussions of time and change.

For example, ten years ago you already had the disposition to represent the current state of the world. That is an aspect of your primitive force—it is always “pregnant with the future,” as Leibniz sometimes puts it (e.g. letter to des Bosses, August 19, 1715, LDB 349; letter to de Volder, January 21, 1704, LDV 287). Yet, your disposition to represent the current state of the world was masked until just now. It was masked, presumably, by all of the representations of the intervening states of the world, which are incompatible with it.

Since I am not referring the final published version of this paper, I apologise if my quote differs in any way from the final version.