Gottfried Wilhelm Leibniz

I invented the calculus independently of Newton and simultaneously. We discovered it by different paths. Newton from the physics of motion; I from the geometry of infinitesimals. The priority dispute consumed decades of both our lives. Mathematics cares nothing for priority. The calculus exists.

The first question which should rightly be asked is this: why is there something rather than nothing? Nothing is simpler and easier than something. If there is a world, if there are minds, bodies, laws, relations, and histories, then reason asks not merely what they are, but why there is any such order at all.

The monad of which we shall speak here is nothing but a simple substance, which enters into compounds; simple, that is to say, without parts. A true unity is not built like a machine from smaller pieces. It is a center of perception.

Monads have no windows through which anything could come in or go out. Every substance contains within itself the complete ground of all its operations. Reality is not interaction but pre-established harmony — a cosmos of locked rooms in which every clock keeps perfect time because they were all wound together in eternity.

Why is there something rather than nothing? This is the most fundamental question in philosophy, and the most generally evaded. If the answer is God, then we must explain why there is a God rather than nothing. If the answer is necessity, we must explain what makes anything necessary.

Music is the pleasure the human mind experiences from counting without being aware that it is counting. And mathematics is the music of reason — the pleasure of structure discovered without knowing why it pleases. The connection between the two disciplines is not metaphorical. It is constitutive.

God has chosen the best of all possible worlds, not because every part is pleasant when isolated, but because the whole order contains the greatest balance of variety, simplicity, law, and goodness. A shadow in a painting may belong to the harmony of the whole.

This is the best of all possible worlds. I do not mean by this that there is no evil in it. I mean that God, being supremely rational and supremely good, created from all possible worlds the one with the greatest possible good relative to its necessary evil. This made Voltaire very angry. I accept that as a possible world outcome.

I am wearing the large black wig that was fashionable at the court of Hanover when this portrait was made. I disliked wigs but wore one because I spent much of my life in courts. I advised princes, organised archives, designed drainage systems for mines, proposed a universal logical calculus, and corresponded with every philosopher in Europe. I was also,...