Historical Introduction to Philosophy/Metaphysics

The word metaphysics comes from the Greek words meta (after/beyond) and phisiká (nature). Metaphysical topics go "beyond physics" to attempt to explain the nature of the universe. Metaphysicists ask questions like:

• "What is fundamentally real?"
• "Is there something that all real things have in common?"
• "Is there a god who set everything into motion?"
• "Do we have free will?"
• "Is there a difference between a thing and an idea?"

Aristotle is sometimes credited with being the first to make metaphysics a distinct field of thought, though he was not the first to think and write on metaphysical topics. Ideas about the fundamental nature of reality showed up in the writings of ancient Greeks before Aristotle, and can be seen in writings of ancient Egyptians dating much further back.
Pythagoras reasoned that the fundamental nature of reality was mathematics. Unfortunately, none of Pythagoras' metaphysical writings survived, but many of his followers, the Pythagoreans, revealed a significant portion of his metaphysics. The Pythagoreans thought that numerical ratios and relationships found in nature (like musical scales) were the key to understanding reality.
Gottfried Wilhelm Leibniz believed the most basic thing that all things are made of to be the monad. “Monad” comes from the Greek word monas , which means a unit, individual, atom… something that is indivisible. Monads combine to form compounds, which make up the matter we interact with in the world. Leibniz defines monads in his work titled Monadology as simple substances that are indivisible, unextended (which means they don’t occupy space), formless, windowless, and impossible to destroy. When Leibniz says monads are windowless, he means that monads can not interact with each other; they are completely independent of each other. If it appears that two monads share some property in common, they actually each possess that property individually. For example, I have the property of being my mom’s son, and she has the property of having me as a son, but these properties are not the same; they exist independently of each other.
In Leibniz’s view, all things that exist are capable of acting. If you take the action out of a substance, it loses its existence. Monads themselves are units of activity. Because there are so many kinds of actions, it follows that there are different kinds of monads. In fact, Leibniz held that no two monads were alike.

Leibniz's metaphysics in the Monadology is broad and detailed. Before continuing with this article, please watch these videos hosted on YouTube for a primer on the Monadology:
Leibniz Monadology Part 1
Leibniz Monadology Part 2

Note the following points made in the videos:
- Monads are “simple substances” that have no parts.
- Monads have qualities (As Leibniz explains, qualities are necessary for existence).
- Monads are different from one another. This is true because if all monads were the same, we would not be able to perceive one thing in contrast with another.
- Matter we see in the world is made of compounds of monads. We can see things in the world are constantly changing, so we can judge from the behavior of compounds that monads are constantly changing.
- The source of change comes from w/in the monad. (Monads do not cause each other to do anything; they do not interact!)
- Monads undergo a series of changes. This series of changes involves a “multiplicity” within the monad (not to be confused with multiple parts, which monads do not have), because something about the monad changes, while something about it remains the same. This can be seen in compounds; things change, but they still retain qualities that we can identify them by. For example, a tree changes a lot from a small plant to a large tree, but we still can identify it as a tree.
- Something within the monad leads it from one perception to another. This Leibniz called appetition/desire. A monad’s desire cannot completely get to the perception it aims for, but it gets some of it, which leads to new perceptions, which may go on to attain more.
- Every thought that a person is consciously aware of focuses on a variety of things. This is an experience of multiplicity in simple substance. Simple substance do not have parts, but they are capable of perceiving multiple things at once.
- You cannot explain perception in terms of mechanics. Think of a machine that produces perceptions, which is big enough for you to walk inside of. What would you find? Nothing but parts pushing each other; nothing in the machine would explain where perception comes from, so such a machine could not possibly exist. Perception must therefore be contained in simple substances, not in compound machines (which just obey physical laws).
- Leibniz calls created monads (all monads except for the God monad) entelechies, which comes from the Greek words for “certain perfection” and “certain self-sufficiency”. This means created monads are perfect and self-sufficient by various degrees.
- The internal activities of simple substances come from the simple substances themselves.

God is a monad with the unique qualities of being uncreated and completely immaterial. All other monads are partly material and partly immaterial. Their ratio of immaterial to material is measured by how clearly they reflect every other monad in the universe. If we looked at God, we would see the entire universe clearly. If we look at dirt, we see an unclear reflection of the rest of the universe. Influenced by the Great Chain of Being, Leibniz recognized a hierarchy in nature, in which God is at the top, humans are somewhere in the middle, and animals, plants, minerals, and other things are below humans. In this hierarchy, the more immaterial a monad is, the closer it is to God, and vice versa.(1)
A common theme in Leibniz’s philosophy is that all the philosophy that was done before him has some truth to it. This is reflected in this theory of Monads which brings together materialism and idealism by placing materiality and immateriality in everything (except for God).
Each monad has a unique set of properties. Leibniz reasoned this to be the case because the compounds of monads we see in the world are distinguishable. If all monads had the same properties, nothing would be distinguishable, because things are set part from each other by differences in the combinations of monads they are made up of. Also, if all monads were the same, then nothing would change, because things could only go from one state to the same state through motion. Finally, Leibniz believed that there was evidence in nature for the uniqueness of each monad; no two things in nature share all their properties in common, and since these things get their qualities from the monads that make them up, there must be differences in their monads.
Monads are continuously changing, as things in nature are. Since monads can not be affected by anything external to them, changes must be internal. Leibniz defines perception as the “passing condition” in which a lot of things are represented within a monad. Every monad is capable of perception. Notice perception is not limited to what we are consciously aware of. Leibniz argued that Descartes was wrong to think that perceptions only exist when they are identified by a conscious awareness. Descartes’ philosophy of mind did not acknowledge any monadic activity outside the mind; for Descartes, God and the human mind were the only monads (though he did not understand the world in terms of monads). In defense of his accusation that Descartes was wrong, Leibniz argued that in the same way that people in a coma are not dead, monadic perception outside conscious awareness is not dead.(4)
When we think, the thing we think about varies. To Leibniz, this was evidence that perceptions change over time. The force by which monads change from one perception to another comes from within the monads. Leibniz called this force appetition. This appetite, or desire, tends to change a monad’s perception towards a new perception. Though the appetite cannot always get the perception it tended towards, it always results in some change, which results in new perceptions.(4)
Mechanistic causation cannot be the source of perceptions because perceptions are not produced by things bouncing off each other. Leibniz invites us to consider what a machine that produces perceptions might look like on the inside. It would be a bunch of parts pushing each other. Nothing in the machine could produce perceptions. Therefore, such a machine is impossible, and simple substances must be the source of perceptions. In this way, monads are self-sufficient, being the sources of their own internal activities. However, most monads are only self-sufficient in particular ways; if they were self-sufficient in every way, they would be God, and Leibniz reasoned that there is only one God (because all contingent truths trace back to God, the necessary substance.)(4)
Leibniz makes a distinction between souls and bare monads. Monads are simple substances that only have perceptions. Souls are simple substances that have more distinct perceptions than monads, and they have memories. Leibniz provides some evidence that the soul is more than a bare monad: When we are in dreamless sleep, we do not remember anything, and we can not distinguish one perception from another. So, during this time, our souls become bare monads, but since we snap out of these stages of sleep, our souls are something more than bare monads. Leibniz notes that animals are able to focus on certain perceptions, fading others into the background, using their sense organs. For example, when we focus on a computer screen and tune out the wall and computer desk surrounding the screen, our soul is perceiving the monitor more distinctly than the background. Leibniz asserts that the soul has more distinct perceptions in a similar way.(5)
Humans and other animals have memories. When we perceive something painful, and experience a similar perception in the future, we have a representation of the previous perception in our memory, which leads us to expect pain associated with the perception. We act like other animals when we use memory to anticipate one thing following from another. The thing that distinguishes humans from other animals is reasoning, which comes from knowledge of necessary and eternal truths. Leibniz notes that empiricists rely only on memory like other animals, whereas rationalists use what makes them uniquely human. Knowledge of necessary and eternal truths enables us to better understand ourselves and God. We are able to think of ourselves through knowledge of necessary truths. When we determine that things are in us, what our limits are, and the unlimited nature of God, we are using reason.
There are truths of reasoning and truths of fact. Truths of reasoning are necessary, and their opposite is impossible. Truths of fact are contingent, and their opposite is possible. Truths of reasoning can be found by analysis, breaking them down into simpler ideas and truths, until primary truths are found. Truths of reasoning are simple ideas that cannot be defined, and propositions that cannot be proven. These are assertions of primary principles, self-evident truths whose opposites are contradictions. It was these which Leibniz wanted to base a universal language on. Truths of reasoning can be proven through a finite process of analysis, whereas the process of proving truths of fact requires an infinite analysis of contingencies.
Since the sequence of contingent things (the following of one thing from another) is infinite, it’s impossible to arrive at the sufficient reason for anything within this sequence. Thus, the sufficient reason for the whole sequence of contingent things must be a necessary substance (substance whose existence is not contingent upon anything else) existing outside the sequence. This is called God. God is all-encompassing and one-of-a-kind because everything outside God depends on it. God contains all properties "eminently". Leibniz uses the term "eminently" in the context of a property to mean "with the resources to produce such a property, but not necessarily exhibiting the property oneself".(5)
Leibniz is credited with being the first to develop the Principle of the Identity of Indiscernibles. Thinkers before Leibniz have utilized the principle in one form or another (notably Rene Descartes), but Leibniz was the first to make the principle explicit. This principle holds that if and only if any two or more objects have all their intrinsic, non-relational properties in common, they are exactly the same. An “intrinsic, non-relational” property of a thing is something that is part of the essential nature of the thing, not something that relates the thing to another thing. Leibniz argued that two things can not possibly be distinct when they share all their non-relational properties.(2)
A monad x acts on another monad y inasmuch as the states of monad x explain the states of monad y. This does not mean monad x can directly influence monad y! Remember, monads do not interact; they are independent of each other. How can a monad "act" on another then? It is through an "ideal" influence rather than a real influence. Monad y is ideally influenced by monad x because God took into account monad y when designing monad x. God's idea of each monad can be found in every other monad, so that which can be clearly understood in one monad can explain what happens in another monad. Because of this, monad x can be both "passive" and "active" (ideally influenced and ideally influencing) with respect to monad y at the same time.

God’s ideas include an infinite number of possible universes. Only one universe can exist. Therefore, God had to have some sufficient reason for choosing this universe. That reason was that this universe is the best of all possible universes. God’s wisdom allows him to know this universe to be the best, his goodness leads him to choose this one, and his power allowed him to bring it into being. God adapted each monad to the others around it, giving them properties that relate them to properties of other monads. This is why monads are mirrors of the universe. When you look at a town from different angles, it looks quite different. There are an infinite number of perspectives from which you can look at the town and see a “different” town. In the same way, when you look at the universe from different perspectives, it is so diverse that it looks like different universes, but it is just one universe that looks different from the perspectives of the many monads.
All compound substances are connected. You can tell because the motion of a body of matter is felt by neighboring bodies. The further you are from a motion, the less you feel it, but you always feel some of it. If you could see every motion bouncing off a single body of matter, you would be able to know about the motions of everything in the universe. Not only that, but you would be able to know the past and future of every motion! Souls (monads with relatively distinct perceptions and memory) are similar to compound substances in that each contains a representation of all other monads in the universe, but we cannot see everything because we are incapable of perceiving infinitely complex things.(4)Remember, our souls can only distinctly see some things; if we saw all, we would be God.
Recall that monads stick together to form compounds, which forms the matter we interact with. The monads in a compound most distinctly represent the compound they are a part of. This is how monads are related to the bodies they are a part of. This relationship is reminiscent of the relationship between Aristotelian forms and matter; Aristotelian form/essence is as much a part of a thing as the matter that makes up the thing.(6) The metaphysical and physical are integrated. Leibniz’s monads are likewise metaphysical things that, when taken together with material compounds, make a thing what it is.
Leibniz was in favor of Heraclitus’ idea that everything is in constant flux. He notes that animals often change form (metamorphosis), which means that souls, the entities responsible for animal behavior, are also in constant flux, slowly transforming the bodies they are a part of. He rejected the Pythagorean idea that souls can somehow move from one body to another (transmigration), and he rejected the idea that human souls are separate from human bodies (an idea Descartes held to be clear and distinct).
Leibniz also rejected the idea that humans have purely immaterial souls. Despite rejecting these ideas, he still believed in immortality. For Leibniz, immortality is not a matter of the soul leaving the body and going somewhere else. It is simply a matter of souls slowly changing. What we call “death” he calls “infolding and shrinkage” of the soul. If you think about a living thing as a composite of indestructible monads which are capable of perceiving, it is easy to see why Leibniz thinks a soul continues to exist within a body after the body stops exhibiting behavior we associate with life. At the point of “death”, the soul loses its “organic coverings”(5), but is still active and perceptive.
Souls and bodies are connected through “pre-established harmony”. That is, the motion of animal bodies works as though it were influenced by their associated souls, even though there is no direct influence from one to the other. They were set up to operate in harmony from the beginning, when the God monad decided to bring them into existence.
The soul that every animal possesses lacks some of what the human mind possesses. Souls are reflections of the universe of things God created, but human minds are reflections of both the universe of created things and God himself. Minds are small divinities within themselves, capable of understanding the universe and imitating it to some extent. This allows a special relationship between minds and God, one that is more like a father/child relationship than an engineer/machine relationship. Living in this relationship with God, the author of the best universe, puts us in the City of God, the best monarchy that could possibly exist.
The City of God is a moral world inside of a natural world. Morality only exists in God’s relationship to minds, since only minds are capable of comprehending God’s goodness. The rest of the created universe perceives God’s wisdom and power, but not his goodness. Since this relationship exists, it is inevitable that all minds will receive just treatment for their sins against God, since God is the father to all his children (minds). If we were able to see everything God can see, we would realize the world is set up to be better than the wishes of the wisest men.
In correspondence with Samuel Clarke, Leibniz tried to show that the Principle of the Identity of Indiscernibles followed from his other big metaphysical principles, the Principle of Sufficient Reason and the Principle of the Best. Leibniz's argument followed this line of reasoning: God created this world for the reason that it is the best of all possible worlds. If in choosing a world to create, God chose between indiscernible worlds, he would have chosen between worlds that were equally as good as each other. Therefore, there are no two possible worlds that are indiscernible. Similarly, God had to choose between possible things to put in the world, and no two of them could have been indiscernible, for that would mean both possible things were equally as good, and God would have had no sufficient reason for choosing one over the other. So, on the assumptions that this is the best of all possible worlds, that God exists and follows the Principle of Sufficient Reason, no two things that differ in intrinsic, non-relational properties are the same; God had sufficient reason for making them different.(3)

References:

1) The System of Leibniz
2) The Principle of the Identity of Indiscernibles - Leibniz's Fourth Letter
3) Leibniz's Argument for the Identity of Indiscernables in his Correspondence with Clarke
4) Monadology
5) Monadology
6) Aristotle on Substance, Matter, and Form
7) Infinite Hierarchical Nesting of Matter