This is an easy, short work but one that is quite difficult to comprehend. So much of it goes against the widely accepted atomic view of the universe. If one wants to appreciate the depth of Leibniz's system, a knowledge of some of Aristotle's and Descartes' ideas is necessary, as is a familiarity of the competing materialist/atomist system of the time via John Locke and others.
First off, the monad is originally a Pythagorean idea. It is a point, self contained and the first of anything. Everything is equidistant from this point and this point precedes all constructions we make. It is represented as a point surrounded by a circle. Whatever is is in the monad. This point has zero dimensions of space; it is not extended. A one dimensional object would be a line with two points, a dyad. It isn't something in relation to something else, as say a line exists between two points.
Leibniz used monad in a different way. A monad is a first of its kind, not first in terms of anything existing which is what the Pythagorean monad sounds like. There can be more than one monad because they are unique. In fact there are seemingly an infinite number of monads. A monad is a created thing in that it's nature is the same throughout its existence until it's non-existence. Its time begins and ends with its existence, and so is timeless one could say.
The monad is defined by what describes it, using subject predicate logic. A predicate is either contained in a subject, or the subject is predicated of another subject. The monad contains all of its predicates. What describes it does not change because of anything except for itself. Monads cannot destroy themselves and are not affected by anything else. What is destroyed are combinations of different monads, extended in the various dimensions of space and accordingly time.
Anything that exists is either a monad or a complex of monads. Complexes are what we call bodies, which are composed of smaller parts and differ from one another by size, shape, and arrangement of parts. These complexes do not change the nature of the monads, its simple parts. Something can change over time in its size, shape, and arrangement of parts and be the same thing.
This leads to a crucial distinction which is central to understanding the monadology and I think is original to Leibniz. The distinction between intrinsic and extrinsic difference. This is now called Leibniz's Law or the Identity of Indiscernibles: if everything about something can be said about something else, then they are the same thing. In other words, an external difference does not make things different. There has to be an internal difference, of kind and not number.
"There are never in nature two beings which are precisely alone, and in which it is not possible to find some difference which is internal, or based on some intrinsic denomination"
A monad is not a physical thing. A monad does not causally affect other monads and is not affected by others. This is the strangest part of the work which leads to an even stranger explanation.
There are gradations of monads solely on their power to perceive monads clearly and distinctly (language borrowed from Descartes). This is a very important concept to grasp in Leibniz's philosophy. Everything has a degree of perception. This is how things interact with one another. They don't actually change, but are affected by other monads by varying degrees of perception. All monads reflect each other, that is they contain in themselves knowledge of every other monad. When it seems like a monad is affected, it is merely acting in accordance with the perception of the monad. Monads have the power to represent everything else. Just like in dreams and hallucinations where the mind can simulate powerful experiences, though this is only the workings of the mind itself and nothing externally is causing everything in the dream or the hallucination.
Monads can't affect each other because they are the unique ground for every single thing that can be said of the universe. There is something for each self-contained subject which needs no further explanation.
All monads are entelechies, a term borrowed from Aristotle who used it to describe the potential for action. Leibniz uses it to describe "incorporeal automata" which have the power of appetition, of going from one perception to another. Entelechies have perception and appetite, of being affected and attaining new affections. Entelechy is the innate potential everything has, which today we might call energy.
From the entelechy and Aristotle's potential/actual distinction, Leibniz lays out what would later be called the unconscious. Leibniz describes consciousness as apperception, a seizing of perception. Consciousness is essentially an intensification of attention on an object, an act of will or appetite which makes things clear and distinct, whereas unconsciousness is not a state of non-existence, but of indistinct and unclear perception.
Mind begins with memory, which repeats perceptions and can associate them with similar perceptions. Our mind seizes upon the strongest perceptions, determined by the nature of the body of other monads the mind is surrounded by and perceives strongest. These associations produce habits of behavior and the nature of "brute" organisms.
Humans however by reflection can abstract from experience and discover the necessary truths behind such associations. Souls however are only monads "whose perception is more distinct and is accompanied by memory." Thus gradations of being are determined by power to represent from the basic nature of each created monad.
We are unique among living things, for everything is alive in an unconscious sort of way, because we can raise our perception to comprehend God, and in that way we are "made in his image." Leibniz's argument for God is an ontological one; God must exist if he is possible. Instead of a first cause, God is a necessary substance from which everything comes, whose non-existence is inconceivable. By the power of our own mind, we discover what is behind the power of anything that exists in the universe, which is of course God.
It is still odd that every monad doesn't interact with one another, and yet it sure seems that way. Leibniz introduces the ever more strange explanation that God creates the harmony between monad's perceptions of each in creating the universe. This is related to the famous "best of all possible world" principle of Leibniz, or "principle of the best" which responds to the problem of evil under God's existence. God being a perfect and all good being would never create a world where our thoughts didn't align with the actions of bodies. Knowledge would be impossible, and there could no rewards and punishments for good behavior, making justice impossible. "And it is this which causes the existence of the best, which God knows through his wisdom, chooses through his goodness, and produces through his power."
Mind and body are not detached because the distinction arises from representation. The soul is the dominant entelechy, which is in parallel harmony with the entelechies it perceives stongest. Nothing in the universe is lifeless and mechanical, bodies are composed of unconsciously perceiving simple monads. Because of this, there isn't a transmigration of souls, as the soul is always with entelechies which can change without changing the nature of the soul or mind.
The monadology, as bizarre as it sounds, was a proposed alternative to the corpuscular or atomic theory of the universe, where everything is made of the same fundamental particles and differ only in arrangements and forces between the particles. Leibniz just didn't like this mechanistic universe which is externally determined. His predicate logic seemed to necessitate the existence of unique things. Unfortunately his system relies on essentialism, though a relatively limited one, and the necessary existence of God particularly for his resolution of the mind-body problem. For those of us who have accepted Hume and Kant's skepticism in our lives, this is too much.
This book is still worth reading for three ideas. One is the unconscious which Leibniz is the first to really lay out. Second is the suggestion that it is possible for the mind to understand the entire universe if one thinks clearly and distinctly enough, and the distinction of intrinsic and extrinsic difference. I think these concepts made their way into German idealism and even continental philosophy, in thinkers like Henri Bergson (intuition versus analysis) and Martin Heidegger (ready versus present to hand) and of course the whole enterprise of Psychoanalysis.
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