Among quite a few other things, Leibniz was an important mathematician. He and Newton vied for credit for discovering the calculus of infinitesimals. He was also politically active as an advisor to assorted rulers and aristocrats. Like Descartes, Leibniz was, at least publicly, religious. His grandest political ambition was to see the Christian church re-unified (recall that Protestants had broken off from Catholics over the prior few centuries). Leibniz was arguably the first to have imagined anything like information technology. Among his grand ambitions was to formulate a universal symbolic language for science and philosophy that would be rigorously rule driven and free of all ambiguity. He even got as far as constructing a calculating machine, though not a very reliable one.
Leibniz’ metaphysical views seem pretty exotic at first glance. Leibniz took the world to consist of monads. Each monad is simple and indivisible. But monads are not merely physical, like atoms. Each monad would include both a physical aspect and a mental aspect. Physical objects are made up of monads that are also minds, just particularly dim-witted ones. Monads appear to interact with each other. We seem to influence each other and make things happen in the physical world. But according to Leibniz there is no actual interaction between monads. Instead, monads exist in a harmony that is pre-established by God. As a result, like an element in a spectral image or a droplet in a cloud, each monad carries in it a reflection all of creation.
If this seems to be a rather exotic picture of the world, let’s review the problems Leibniz is trying to negotiate in the wake of Descartes and Spinoza. The problem of mind/body interaction looms large after Descartes. If mind and body are distinct kinds of substances, then it is very hard to see how either can have any influence on the other. Leibniz metaphysics handles this problem neatly by making his substances, monads, have mind as an integral part. We needn’t worry about mind- body interaction if mind and body are already unified. Next, bear in mind the theologically challenging aspects of Spinoza’s monism. In taking there to be just one substance, Spinoza identifies God with all of nature and denies that people have any existence distinct from God/nature. God is not personal on this view. God/nature is really nothing like us at all. Spinoza’s God is so unlike the traditional God of Christianity that Spinoza is widely deemed to be an atheist. Worse, in taking humans to be mere parts of a self-caused and hence necessary God, we lack free will entirely on Spinoza’s view. Leibniz is eager to provide a philosophical route to avoiding Spinoza’s atheism and denial of free will. To avoid atheism, and in particular a variety of atheism where people are mere parts of an impersonal God/nature, Liebniz needs to posit a plurality of substances. Monads fit the bill. In order to preserve free will, which is also central to Christian theology, Leibniz needs for the substances that are mind not to be causally determined by other substances. The pre-established harmony of monads is his means of achieving this. But while Leibniz thereby avoids causal determinism, he seems to be saddled with a kind of theological determinism instead. Everything that happens, including every choice you make, will have been determined by God.
Leibniz was both intrigued and repelled by Spinoza’s thought. The two met for a few days while Leibniz was ostensibly on a diplomatic mission in Amsterdam. As much as Leibniz abhorred Spinoza’s views, he couldn’t dismiss Spinoza’s carefully reasoned and systematic response to Descartes’ thought. As a result, Leibniz devotes a considerable amount of creative intellectual energy to finding some way to avoid Spinoza’s heretical conclusions. Such was the influence of the outcast Jew of Amsterdam.