For Aristotle, movement was the reality of possibility, it is the future as presence.
Modern thinking uses mathematics to model movement. It is the points in space through which a body travels over time. You can model it mathematically.
Leibniz creates infinitesimal calculus with Newton.
Leibniz interprets this mathematization of reality by going back to the idea of "substantial form:" He calls it now the monads.
He defines the monad as a simple substance, without parts. The existence of compound bodies proves the existence of monads, since the existence of the compound proves the existence of the simple element. Thus, “they are the true atoms of nature”
Monads have neither extension, nor shape. They are infinitely small "power centers" of reality. There is an infinity of them, and each one is unique.
Extended bodies are not absolutely simple. Is the point on a line the same as the point on a circle? No.
There is an inner and an outer view of reality: What the monads (and their programs or logic) are, and what they manifest in our visible reality.
Nothing can get into a monad. This leads to the statement that “monads have no windows through which something can enter or leave it.”
The monads have no parts, but they have qualities. They are also distinguished from each other. “there has never been two beings in nature that are exactly like one another. ”
The Monad is Soul. The simple substance that makes up the mind/body unit is the soul. Indeed, the perception can not be explained only from the physical or mechanical body.
Two principles guide our reasoning: the non-contradiction principle (true/false, excluded middle) and that of sufficient reason: nothing happens without reason (or: there is a reason for everything.)
Leibniz also distinguishes two types of truths: truths of reasoning and truths of fact. The former are necessary (and their denial is impossible), while the truths of fact are contingent and their opposite is possible.
Monads can not act on each other (since they are without doors or windows), it is God who in the beginning of time has established the harmony of their relationship. ("pre-stabilized harmony.")
The goal for Leibniz is to explain the multitude of phenomena with as few "rules" or laws of nature, or philosophical principles, as possible. In this regard, we live in the best of all possible worlds.
This is the meaning of the famous passage: “By pretending there is a machine whose structure can think, feel, have perception, we can conceive it enlarged so that we can enter it as a mill. And this granted, we will find by visiting it on the inside that parts that push one another, and never enough to explain a perception. ”
Leibniz notes the importance of memory. It's purpose is to organize perceptions, and we share it with animals (such as the beaten dog who runs away when he sees the stick with which he was hit).
It is by knowledge of the eternal truths of reason and necessity that man differs from animals.
Truth of reasoning example: If A is B and B is C, then A is C. This is a necessary truth. Truth of fact: the cat is in the garden: contingent, because it might not be there.
Analysis is the process by which to uncover the ideas contained in the simple necessary truths, forming and melting them. Thus the theorems of mathematics can be reduced by analysis to definitions, axioms and propositions.
Some of these simple ideas can neither be defined nor demonstrated, because as first principles, they are not based on anything but everything else is based on them: it is the same utterances (of the type: A = A, a cat is a cat) “whose opposite contains an express contradiction”).
The truths of fact are contingent, but they also obey the principle of sufficient reason. But the immense variety of things in nature shows that the analysis could be boundless. This requires that “the last reason of things,” sufficient to explain it all, is separate from the infinite series of things.
This is a necessary substance, God.
So God is achieved by the principle of sufficient reason in the Monadology of Leibniz. The existence of God is based on this principle, “there is a sufficient reason for all the details, there is only one God and that God is enough.”
He is infinite, and the creatures derive their perfection of it, while they have their imperfections in their own nature.
God is the cause of all existence, but also species. Indeed, “God’s understanding is the region of eternal truths, or ideas on which they depend.” For example, if the sum of the angles of a triangle is always 180 degrees or 2 +2 = 4, it is because God willed it so.
God is a necessary and perfect essence, therefore, God possibility and actuality is one in God's existence.
The existence of God can be deduced a priori, that is to say, by simple reasoning, without having to rely on the experience, such as that of a hypothetical encounter with God. “... nothing can prevent the possibility which encloses no bounds, no negation and consequently no contradiction, this alone is enough to know that God exists a priori.” Leibniz endorses the ontological argument formulated by St. Anselm and taken up by Descartes in the Meditations.
Nevertheless, one can also infer God's existence a posteriori, from the experimental observation of the existence of contingent beings.
Act is the mark of perfection of the creatures, while suffering is the mark of their imperfection. But the monad acts as it has distinct perceptions, and suffers, as it has confused perceptions.
An infinity of universes are possible, but only one is in existence. There must be a reason that explains the choice of God for this world: he chose the best possible world, because of his wisdom and goodness.
Quotes:
"I know that I am advancing a great paradox by attempting to rehabilitate the old philosophy in some fashion and to restore the almost banished substantial forms to their former place. But perhaps I will not be condemned so easily when it is known that I have long meditated upon the modern philosophy, that I have given much time to experiments in physics and demonstrations in geometry, and that I had long been persuaded about the futility of these beings, which I finally was required to embrace in spite of myself and, as it were, by force, after having myself carried out certain studies. These studies made me recognize that our moderns do not give enough credit to Saint Thomas and to the other great men of his time and that there is much more solidity than one imagines in the opinions of the Scholastic philosophers and theologians, provided that they are used appropriately and in their proper place. I am even convinced that, if some exact and thoughtful mind took the trouble to clarify and summarize their thoughts after the manner of the analytic geometers, he would find there a great treasure of extremely important and wholly demonstrative truths." Leibniz: Discourse on Metaphysics (1686)
“The general principles of corporeal nature and of mechanics itself are more metaphysical than geometrical, and belong to some indivisible forms or natures as the causes of appearances, rather than to corporeal mass or extension.”