Metaphysics

If one word can describe Leibniz's cosmology, it is infinity. There are infinite objects in the universe (all of them minds, or monads), each with infinite properties. On the micro level the smallest particle of matter contains, on an even smaller scale, entire universes of ever smaller objects, which in turn contain micro particles that are entire universes themselves. Likewise this entire universe is a tiny particle, microscopic, within some larger world. And there are even infinities outside the infinities of existing things: there are infinite worlds of how things could have been, that are possible but, because they are inferior to ours, are not actual. This world is thus the best of an infinity of possible worlds, each possible world including the actual containing an infinity of objects, which in turn contain an infinity of objects getting ever smaller; while the entire universe is a small particle in some larger universe, on to infinity.

How God figures into all this is at first not clear. Just as there is no specific number that is the highest, one would think that God, being a specific being, could not be infinite. Any specific speed, size, or quantity, by virtue of being specific, cannot be infinite.

But God, being specific, after all, perhaps is the very thing that renders this infinity impossible. God may be seen as the one principle that makes Leibniz's infinity coherent. In a world infinitely divisible into smaller universes, infinite on the micro and macro level, God is the one thing that makes it all subsist. One would think that in such a schematic it is impossible that "the cosmos is one" is true. "Cosmos" means here the sum total of everything; nothing can be not part of the cosmos, and nor can there be other cosmoses outside of the one sum total of everything. Thus "the cosmos is one" must be true. But with Leibniz's cosmology it is hard to imagine any perspective from which such a cosmos could be said to subsist as a single thing; no matter how large our point of view, we are but the tiniest particles of some larger universe. With the concept of God, though, the absolute Real, this at least gives us some sense that there is a limit to the limitless, or at least an infinite perspective from which the infinity can be contemplated, no matter how small or large its point of view. Infinity can in fact be contemplated, but only from the perspective of a being infinite himself.

In Leibniz there are no two things exactly alike. Thus this requires an infinity of possible elements to the universe. Any finite number of elements can only create a finite number of possible combinations. 26 letters in the English language, if given the space of 100,000,000 characters in which to express something, can only be combined a fixed, finite number of ways, therefore to express a fixed number of concepts. Thus, with infinite objects, in a world infinitely divisible into completely distinct smaller universes, all composed of objects completely distinct from every other, there must be an infinity of elements. An infinity of possible combinations of elements would require an infinity of elements themselves. Gone is the Presocratic Greek desire to express diversity with a small, fixed number of concepts; for Leibniz there must be an infinity of elements. There are no atoms duplicated over and over, creating diversity through differing position and combination. There is no Earth, Air, Fire and Water that combine in various ways to create diversity. The diversity of the phenomenal world, if anything, is deceivingly uniform; really each object is made of much more complex and diverse "elements" than those that appear to us.

Without God such a world is anarchy; there is no fixed principle upon which it all hangs, nothing to make such an infinity subsist as one, or keep everything from disintegrating into more and more complexity and chaos. But with the principle of the best, God makes sure only the best possible cosmos comes to be out of all that is possible. He allows the infinite to progress in just the manner that maximizes good and minimizes pain. He is himself the principle of the One, which keeps such a cosmology from being the most incomprehensible mess that it would be, were it without the infinite intellect there to contemplate it. With God such a world does indeed live up to the Greek conception of "Kosmos"—order—so that there is a perspective from which it is all organized. With God it is akin to some vast organism, every particle of which works toward the organic function of the whole, all of them organized according to what is the best possible for everyone. Without God such a world is like an anarchy in which there is an infinity of elements combined in infinite ways, with no rule as to what happens, incomprehensible and unintelligible, given the variety of objects and concepts that would be required for one to explain even the smallest part of it.

According to the mental side of it, it is a rather Platonic cosmology. There are infinite truths, purely mental things and not constructed of matter; examples of these truths are the number of blades of grass on my building's lawn, the number of blades of grass per square foot on average, and on and on, the truths describing everything that is and will ever be. These truths would exist even if they were known and contemplated by no one at all: the mental stuff that could subsist without any minds. Some of these truths are necessary; that all grass is grass must be, and could not be otherwise. Contingent truths, whose contrary implies no contradiction, also express identities, in a sense. There is a sense in which the sum total of all contingent truths is a giant tautology. The number of blades of grass on a square foot of that lawn are as much properties of that square foot of lawn, as they are of the moon. Somewhere exists a truth that precisely such-and-such miles from the moon lies a square foot of grass with such-and-such number of blades. All the contingent truths express one another in a grand infinite system that is internally consistent and ultimately renders every truth tautological. The fact that I sit here typing now is repeated in every other truth, or is a property of every other object, no matter how far in time and space; say, for instance, that the first man to walk on Mars will do so precisely such and such time after Ratcliff typed these words. How then is there any truth that is not a necessary truth?

The answer is the infinite possible worlds that are not actual. Pluck a blade of grass from my building's lawn, and I've altered the properties of everything that is—the moon now has one less blade of grass exactly such-and-such miles from its surface. But were the entire cosmos, and every object in it altered, the world could have turned out a very different place. That some worlds that are not actual shows that the actual world could have turned out different, without logical contradiction, were every single object altered in its properties accordingly. Thus I could have gone out today, but didn't. Had I gone out today every single object in the infinite cosmos would have to be altered to allow for it, but it could in fact have been altered in such a way without a contradiction. This is what Leibniz means by the fact that I didn't go out today being inclined rather than necessitated. The fact that I didn't go out today is repeated infinite times by properties of infinite objects, but if those objects had certain properties in them altered accordingly, the entire infinite system changed, I could have gone out today without logical contradiction. To make a necessary truth false it would require the impossible—a true contradiction. But to make a contingent truth false it would take an alteration in every other of the infinite objects and the truths that belong to them.

Leibniz wrote mostly very short essays, and to read any one of them, you only get a very small aspect of his world. But read many on a variety of topics, and you will see that they all fit together into a grand system, each aspect fitting in logically with every other. Leibniz did not contradict much of what he'd said earlier, upon further reflection; for the most part he added to his cosmology to assimilate new considerations, rather than go back on what he'd already established. His very body of work is like an organism in itself, assimilating new ideas and organically fitting them into his grand vision for the All and Everything. Ultimately it is an incredible vision and intricately organized system. I have but touched its surface here, so go on and read the man for yourself. Genius is sometimes an understatement.

Angelhaunt.net: Because earth's madness is heaven's sense.