Summary: Monadology (page 2)

Leibniz also distinguishes between two types of truths: truths of reason and truths of fact. The former are necessary — their opposites being impossible — while truths of fact are contingent, their opposites remaining possible.

For instance, if A is B and B is C, then A is C: this is a necessary truth of reason. By contrast, 'there is a cat in this garden' is a contingent truth of fact, because the cat might not have been there.

Analysis is the process of uncovering the simpler ideas contained within necessary truths — the ideas that constitute and underpin them. Thus, the theorems of mathematics can, through analysis, be reduced to definitions, axioms, and postulates.

Some of these simple ideas can neither be defined nor demonstrated, as they are primitive principles resting on nothing else — yet everything else rests upon them: these are identity statements (of the type: A = A; a cat is a cat) whose opposites involve an explicit contradiction ¹.

Although contingent, truths of fact also obey the principle of sufficient reason. The immense variety of things in nature means that such analysis could be endless. It is therefore necessary that the ultimate reason for things ² — sufficient to explain them all — be found beyond the infinite series of contingent beings.

This necessary substance is: God.

In Leibniz's Monadology, God is reached through the principle of sufficient reason, in which his existence is grounded:

As the sufficient reason for every detail of reality, there is only one God, and this God alone is sufficient ³.

He is infinite; creatures draw their perfection from him and their imperfections from their own nature.

God is not only the cause of all existence, but also of essences. Indeed, God's understanding is the domain of eternal truths, or the source of the ideas upon which they depend ⁴. Thus, the fact that the angles of a triangle always sum to 180°, or that 2 + 2 = 4, is so because God willed it — and could have willed otherwise.

God is a necessary and perfect being; his essence therefore entails his existence. In other words, it suffices to be possible for him to be actual ⁵; God alone has this privilege that he must exist, if he is possible ⁶.

The existence of God can therefore be deduced a priori — that is, through pure reasoning — without recourse to experience, such as a hypothetical encounter with God. From the mere concept of God, his existence can be inferred:

Since nothing can prevent the possibility of what contains no boundary, no negation, and thus no contradiction, this alone suffices to establish the existence of God a priori ⁷.

This recalls the ontological argument formulated by Saint Anselm and later taken up by Descartes in the Meditations on First Philosophy.

However, we can also deduce God's existence a posteriori, from the empirical observation of contingent beings such as humans or animals: These could only find their sufficient reason in a necessary being ⁸.

To act is the mark of perfection in creatures, while to suffer is the mark of their imperfection. The monad acts insofar as its perceptions are distinct, and suffers insofar as they are confused.

Monads cannot act upon one another — as we have seen, they have neither doors nor windows — and it is God who, at the beginning of time, established the harmony between them.

Infinitely many universes are possible, but only one can exist. There must therefore be a sufficient reason for God's choice of this universe: guided by his wisdom and goodness, he chose the best of all possible worlds.

¹ 35
² 38
³ 39
⁴ 43
⁵ 44
⁶ 45
⁷ ibid.
⁸ ibid.