Gottfried Leibniz

Indeed every monad must be different from every other. For there are never in nature two beings, which are precisely alike, and in which it is not possible to find some difference which is internal, or based on some intrinsic quality.

This is why the ultimate reason of things must lie in a necessary substance, in which the differentiation of the changes only exists eminently as in their source; and this is what we call God.

Men act like brutes in so far as the sequences of their perceptions arise through the principle of memory only, like those empirical physicians who have mere practice without theory.

It follows from what we have just said, that the natural changes of monads come from an internal principle, since an external cause would be unable to influence their inner being.

It can have its effect only through the intervention of God, inasmuch as in the ideas of God a monad rightly demands that God, in regulating the rest from the beginning of things, should have regard to itself.

I hold that the mark of a genuine idea is that its possibility can be proved, either a priori by conceiving its cause or reason, or a posteriori when experience teaches us that it is in fact in nature.

I also take it as granted that every created thing, and consequently the created monad also, is subject to change, and indeed that this change is continual in each one.

Finally there are simple ideas of which no definition can be given; there are also axioms or postulates, or in a word primary principles, which cannot be proved and have no need of proof.

The ultimate reason of things must lie in a necessary substance, in which the differentiation of the changes only exists eminently as in their source; and this is what we call God.

For since it is impossible for a created monad to have a physical influence on the inner nature of another, this is the only way in which one can be dependent on another.

I maintain also that substances, whether material or immaterial, cannot be conceived in their bare essence without any activity, activity being of the essence of substance in general.

Whence it follows that God is absolutely perfect, since perfection is nothing but magnitude of positive reality, in the strict sense, setting aside the limits or bounds in things which are limited.

I do not conceive of any reality at all as without genuine unity.

But in simple substances the influence of one monad over another is ideal only.

When a truth is necessary, the reason for it can be found by analysis, that is, by resolving it into simpler ideas and truths until the primary ones are reached.

There are also two kinds of truths: truth of reasoning and truths of fact. Truths of reasoning are necessary and their opposite is impossible; those of fact are contingent and their opposite is possible.

Music is the pleasure the human mind experiences from counting without being aware that it is counting.

Now where there are no parts, there neither extension, nor shape, nor divisibility is possible. And these monads are the true atoms of nature and, in a word, the elements of things.