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Gottfried Wilhelm Leibniz (1646–1716)

Leibniz gave the earliest clear articulation of the relational view — space is not a container but the ordering of things that coexist. No things, no space. He said this against Newton’s absolute space, and physics kept Newton’s space for the next two centuries. The relational intuition was there; the mathematics wasn’t. But Leibniz was a rationalist in the Descartes line — pre-established harmony, God as guarantor, monads that mirror the universe but never interact.

Gottfried Wilhelm Leibniz (1646–1716). Philosopher, mathematician, diplomat, librarian, polymath — one of the last people who could plausibly claim to know everything knowable. Born in Leipzig, he spent most of his career in Hanover as adviser to the House of Brunswick, pursuing philosophy and mathematics alongside political and diplomatic work. He co-invented calculus (independently of Newton, leading to one of the bitterest priority disputes in the history of science — Leibniz’s notation won). He designed calculating machines, proposed a universal logical language, corresponded with over a thousand people across Europe, and left behind a vast unpublished archive that scholars are still working through. His philosophy is a system of extraordinary ambition: monads, pre-established harmony, the best of all possible worlds (satirised by Voltaire in Candide). He died in Hanover largely forgotten; only his secretary attended the funeral.

Key concepts

The relational view of space. Space is not an absolute container — it is the ordering of things that coexist. No things, no space. Time, likewise, is the ordering of things that succeed one another. This was Leibniz’s position in the famous correspondence with Clarke (Newton’s proxy).

Monads. The basic units of reality — simple substances without parts, without extension, without windows. Each monad mirrors the entire universe from its own perspective. There is no interaction between monads — their apparent coordination is pre-established by God. A closed, determined, hierarchical system: each perspective irreducibly its own, and no perspective acting on another.

Pre-established harmony. Monads don’t interact — they only appear to. God arranged their internal programmes at creation so that they unfold in perfect coordination. This solves the mind-body problem by eliminating interaction altogether: everything that happens to a monad unfolds from its own nature.

The principle of sufficient reason. Nothing happens without a reason why it is so and not otherwise. Every truth has an explanation. This drives Leibniz’s metaphysics: the actual world is the best of all possible worlds because God had sufficient reason to choose it.

The universal characteristic. Leibniz dreamed of a universal formal language — a characteristica universalis — in which all truths could be expressed and disputes settled by calculation. “Let us calculate!” The project was never realised. Frege named it as a model in the preface to his Begriffsschrift, the start of the formal language tradition that Russell and the early Wittgenstein pursued — and that the later Wittgenstein abandoned.

Where Leibniz stops

Leibniz’s relational view of space stayed a philosophical position. In the Clarke correspondence it gave no relational account of rotation — the effects Newton’s bucket was meant to show — and without a mathematics of relational space and time it could not compete with Newton’s physics. In his metaphysics relations are not themselves real: space is an order among substances that do not act on one another, their coordination fixed by God at creation.

Key works

See also: Descartes · Spinoza · Rovelli