I've had this one sitting on the shelf for quite a while. As with so many things, my interest in Leibniz began with Deleuze. Since I've long planned to read his whole book on Leibniz, I wanted first to familiarize myself with the original material. This turns out to be a bit tricky in the case of Leibniz because he never prepared a single authoritative publication of his philosophical views. Instead, his ideas are scattered throughout various essays, letters, and notes, and there are several different collections of these available in English. In this volume, Ariew and Garber attempt to select and arrange pieces in roughly chronological order so as to provide an overall idea of Leibniz's thought and development. Reading through more of this material put my earlier encounter with The Monadology in a new context. Despite being written fairly late in Leibniz's life, The Monadology is not a deductive treatise comparable to Spinoza's Ethics, nor even a summary of the author's mature philosophical view. It's closer to a series of notes to himself by which Leibniz clarifies and orders one particular thread of his thinking (albeit a very important one, and certainly the one he became best known for). Since even Leibniz didn't manage to effectively summarize his own philosophy, I'm not expecting to do that here either. So I'll just write down a couple of things I found interesting.
His most interesting idea was clearly the monad, with the irreducible unity of its windowless interior eternally separated from an exterior matter that is continuously divisible to infinity. That is, for Leibniz, there are no material atoms, only spiritual ones. But it's also interesting to understand why Leibniz felt the need to invent the monad. The problem he faced was the passivity of pure matter, which in those days people saw as reducible to the combination of impenetrability and extension, neatly illustrated by the Cartesian model of a billiard ball world. In this world, the only consideration appeared to be the conservation of momentum, which is a simple linear product of the purely "geometric" concepts of mass (impenetrability) and velocity (change in extension). Leibniz could literally "prove" that this view was incomplete by constructing examples -- like a ball falling from a height to collide with another -- that showed there was something more than momentum involved in the dynamics of physical bodies, and that if you wanted to calculate what would happen, you would have to raise extension to a power. For him, this "more" or "power" indicated the activity of the monad. For us, it's just the conservation of energy -- the potential energy of a ball is proportional to the square of the height from which you drop it. Naturally, this argument isn't the only reason that Leibniz believes in the monad, but he does consider it one of his stronger arguments for its existence, judging by how often he returned to the example.
Another intriguing theme that runs through his philosophy is what he calls "the labyrinth of the continuum". The problem of the continuity of the real number line, along with the closely associated problem of the levels of infinity, really becomes urgent with the invention of the calculus. Leibniz is adamant that our customary way of envisioning the real number line is inadequate. It cannot be composed of an infinite set of points, which are just abstractions, but has to be thought of as the product of some sort of real process. This process is part of what Deleuze will take up in The Fold.
