Summary : Leibniz defines the monad as a simple substance, without a party. The existence of compound bodies proves the existence of monads, since the existence of the compound proves the existence of simple. Thus, “what are the true atoms of nature” (see Leibniz quotes)
What may look like the parts absolutely simple, monads?
In fact, they have neither extension, nor figure. Indeed, the range being divisible, extended bodies are not absolutely simple: the same, the figures are divisible (can be cut, such as a triangle in half) and can characterize the complex bodies.
Similarly, monads can appear or disappear as suddenly (by creation or annihilation), for point of dissolution to fear for a single body (body only can see their complex parts to sever) or training ( one part being added to another to form a whole).
No external movement comes assign a monad (again, due to their simplicity, the movement consists mostly in a change in the arrangement of parts of them). Thus, nothing can get into a monad. This leads to the idea famous “monads have no windows through which something can enter or leave it.”
The monad is for the time being as something unknown, not even as a kind of empty, since it occupies a certain extent.
Leibniz will then try to give content to the monad, without contradicting its simplicity, it is perilous.
We must, first, that “monads have some qualities, otherwise it would not even beings.” It must also ensure that the compounds can be distinguished from each other.
Finally, it must also ensure that the monads can be distinguished from each other; Leibniz referring here to his principle of indiscernibles, stated in his New Essays following the principle of sufficient reason, according to which “there has never in nature two beings are exactly like one another. ”
The monads have no parts, but they have qualities.
On the other hand, if no external movement does affect the monad is, she knows, like all created internal movements, coming from an internal principle.
Finally, it is that it is found “a plurality of conditions and reports, although there may be no parties” are the perceptions.
The Monad is soul. The simple substance that makes up the different body is the soul. Indeed, the perception can not be explained only from the physical or mechanical body. This is the meaning of the famous passage: “By pretending there is a machine whose structure makes 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. ”
It may also appoint such entelechies monads or souls, because they have a certain perfection, as they are themselves sources of their internal (Aristotelian entelechy is a term that refers to a being that has reached its end, So who has attained a certain perfection).
Leibniz notes the importance of memory, which is organizing perceptions, but we share with animals (such as the beaten dog who runs away when he sees the stick with which we are used to hit him).
But it is by knowledge of the eternal truths of reason and necessary that man differs from animals.
Two principles guide our reasoning are: the contradiction (indeed contrary to true) 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 opposite is impossible), while the truths of fact are contingent and their opposite is possible.
An example: If A is B and B is C, A is C: is a truth of reasoning required. However, “there is a cat in the garden” is a contingent truth is, because the cat might not be there.
The 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 requests.
Some of these simple ideas can neither be defined nor demonstrated, because as first principles, they are not based on anything but it is on them that everything else is based: it is the same utterances (of the type: A = A, a cat is a cat) “whose opposite contains an express contradiction” 1).
The truths of fact, although contingent, also obey the principle of sufficient reason. But the immense variety of things in nature that the analysis could be boundless. This requires that “the last reason of things,” sufficient to explain all, is out of 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, “is 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 get 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, and would have otherwise.
God is a necessary and perfect essence, therefore, contains its existence. In other words, he “just be possible to be present,” “God alone has the privilege to be there, if possible.”
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. Its simple concept we can deduce its existence, “as nothing can prevent the possibility of which encloses no bounds, no negation and consequently no contradiction, this alone is enough to know that God exists a priori.” Here are reminiscent of the ontological argument formulated by St. Anselm and taken up by Descartes in the Meditations.
Nevertheless, one can also infer its existence a posteriori, from the experimental observation of the existence of contingent beings as are men or animals, “they can not have their reason being that in the necessary” .
Act is the mark of perfection of the creatures, while suffer is the mark of their imperfection. But the monad acts as it has distinct perceptions, and suffers, as it has confused perceptions.
Monads can not act on each other (as we have seen, they are without doors or windows), it is God who in the beginning of time has established the harmony of their relationship.
An infinity of universes are possible, but it can not exist one. There must be a reason that explains the choice of God to this world: he chose the best possible world, because of his wisdom and goodness.