Leibniz was one of the greatest minds ever — deeply original, vastly prolific, encyclopedic like Aristotle, but working in the ferment of early modernity. He formulated many differently detailed systems, in an exploratory and tentative way. What he published during his lifetime was only a tiny fraction of his output, and not fully representative of his thought. The critical edition of his collected works will not be completed for many decades yet to come.
Leibniz favored an ethical and political ideal of what he called wise charity. An ethical being is one who does more for others than is required to satisfy rights and responsibilities or social contract, and demands less of others than would be justified, while taking care to act in ways that are sustainable and not self-destructive. I like this very much.
An avowed Lutheran who cultivated extensive dialogue with Catholic scholars and religious leaders, Leibniz was deeply disturbed by Europe’s terrible religious wars. He sought to promote tolerance, diplomacy, and understanding.
As a Platonist in theology who stressed the importance of Plato’s Euthyphro, Leibniz said that God is first and foremost supposed to be good and reasonable, not just obeyed. His God would never say “…because I said so!” Leibniz was highly sensitive to the dangers of subordinating Reason and the Good to any kind of arbitrary Will, be it divine or political. To those who objected that this limited God’s power, he replied that attributing an arbitrary will to God would degrade God to a mere tyrant and despot rather than a good and wise ruler (see Leibniz on Justice vs Power).
Leibniz partly anticipated Einstein in saying that space and time are relations.
He held that mathematical physics of the sort he helped develop was fundamentally compatible with — and complementary to — what I have referred to as Aristotle’s semantic physics.
He argued for what I take to be the Aristotelian position that identity is just discernibility.
Leibniz defended the principle of sufficient reason (cleverly phrased by the scholastics as “nothing comes from nothing”). At the same time, he held that all necessity is of the hypothetical (if-then) variety, which means that nothing is unconditionally necessary, either.
The famous monads apply his pioneering work on infinite series to an inspiration from his friend Leeuwenhoek’s discovery of microscopic organisms. On the one hand, each monad is supposed to be a self-contained microcosm of the entire universe; on the other hand, each monad contains many others that each contain many others that are also such microcosms (each with its own unique point of view on the whole), and so on to infinity. (See also Unity of Apperception.) Leibniz also had a fascinating theory of unconscious microperceptions.
Monads are said not to causally interact, but instead to mutually reflect one another in a purely synchronic way. For Leibniz, it is as though in reality everything has always already happened. It all comes down to one eternal act of God selecting the best of all possible already completely formed worlds. His thesis of the unreality of interaction seems bizarre and was never widely accepted, but the idea of synchronic mutual reflection is fascinating. (This is quite different from the pattern of determination in Hegelian mutual recognition, which has a substantial synchronic dimension but is based on interaction and has an irreducible diachronic component.) (See also Things In Themselves; Redding on Morals and Modality.)
I think Leibniz’s preformationism may be intended as a kind of edifying Platonic myth, but that is a side issue. Its practical consequence is a vision of determination and explanation by synchronic structure rather than sequential causality. Like most people, I think we also need a diachronic, interactive dimension. However, the possibilities of synchronic structural explanation are huge.
Leibniz controversially argued that we live in the best of all possible worlds. Whether or not we adopt such a view, it is important to understand that it was not nearly as naive as Voltaire’s famous satire made it out to be. For Leibniz, the criteria for a possible world are rather rigorous. A possible world is certainly not just any world we might idly imagine. All its details and all their realistic consequences must be able to coherently coexist.
Brandom has characterized Leibniz as an early inferentialist. In English, recent secondary literature is far better than most older accounts. In French, I was impressed by Yvon Belaval’s Leibniz, critique de Descartes (1960) and his student Michel Serres’ dissertation Le Système de Leibniz et ses modèles mathémathiques (1968).