In his Monadology, Leibniz explores the idea that the world is composed of monads, or simple substances, and the consequences of their existence on reason, God, and evil.

Leibniz first explains monads and their properties as a basis for his philosophy. Monads are substances without parts which, when put together, make up a composite substance. Every monad is different, cannot be broken down, and cannot be changed by external forces, or else they would no longer be monads. They do, however, change based on their intrinsic nature; in other words, they are programmed to change a certain way at certain times. Monads consist only of perceptions, or states, and changes between perceptions, and a monad’s current state is a result of its previous state. Every mind is a monad, and each monad is a mind, and a monad with a memory constitutes a soul. Animals have souls according to Leibniz, but humans’ souls are more complex because they have a knowledge of eternal and necessary truths, giving us rationality.

In order to develop his theory further, Leibniz next examines human reason. We reason either through contradiction, or through sufficient reason. These allow humans to determine two types of truths: those of reasoning, which must be true at all times and whose opposite is impossible, and those of fact, which are true only at the time and whose opposite is possible. Necessary truths can be derived by resolving them into simpler and simpler truths until we arrive at primary truths or simple ideas. The ultimate necessary substance, the sufficient reason for the existence of all things, is God, who is perfect and incapable of limitation.

This God is infinite in power, knowledge, goodness, and will, and thus because he knows what will be best, has the power to make things happen for the best, and the desire to cause things to be the most perfect, he causes everything that happens to make this the best of all possible worlds. Because God has this ability, it is possible for monads to influence one another. When one monad desires another monad to change a certain way, God determines whether this change is in accordance with the best possible world, and if it is, the monad is affected, if not, the change does not occur. God does not make these decisions each time a monad has a desire, however, for God has decided on all such changes before their monads were created. In the beginning, when God was creating monads, he programmed each one to desire change in other monads according to the best possibility for this world. He also programmed each monad to change at the appropriate time in harmony with another monad’s desire for change. Although each monad has the free will to desire as it pleases, its choices have already been determined by God in a pre-established harmony.

Each monad is a constant mirror of the universe; the world seen through each monad is the same world, only it appears differently, as from a different angle. Because each monad reacts to everything that happens (through God as outlined above), in any monad one could see all that has happened, is happening, and will happen. From inside one’s own monad, however, one can only see that which is represented distinctly. Every being is a living automaton or machine which consists of smaller automatons, which contain smaller machines, and so on down to infinity. A living thing is a collection of these machines governed by the soul, which is the dominating monad. These living things cannot be immediately created or destroyed; they must change gradually, and thus never die but are simply transformed.

Leibniz also addresses the theodicy question of how evil can exist in the world if God is ultimately powerful, good, and knowledgeable. According to Leibniz, because God is all-powerful, he could have created the world differently, without evil. But, because God is all-knowing, he must know that this world would have evil in it when he created it, and because he is all-good, the world must be this way because it is the best way it can be. All evil that is in the world therefore serves some good purpose. God, because of his infinite justice, has also created the nature of this world and all things in it so that sins bring their own penalty and righteous acts their own reward. Although we may not understand the reasons for evil and why it sometimes seems to go unpunished, in order to be ultimately blessed and to gain happiness we ought to act in accordance with what seems to be God’s will. We also ought to be content with things as they are, because we are living in the best possible world.

Thus from the basis of monads Leibniz reasons out the existence and nature of God, the reason for evil in the universe, and even our role in it.