Gottfried Leibniz · Mathematics
Leibniz the metaphysician: the principle of sufficient reason, the monads as the true atoms of reality, and the famous and much-mocked claim that ours is the best of all possible worlds - the optimisation logic of a mathematician applied to existence itself.
At the foundation of Leibniz’s entire philosophy lie two great principles. The first is the principle of non-contradiction: nothing can both be and not be; a statement and its denial cannot both be true. This governs all necessary truths - the truths of logic and mathematics, which could not possibly be otherwise. The second, and the one that is distinctively Leibniz’s, is the principle of sufficient reason: nothing is so without a reason why it is so rather than otherwise. For every fact, every event, every truth, there must be a sufficient explanation - a reason that accounts for why this is the case and not something else. Nothing happens arbitrarily, by sheer brute chance; the universe is through and through intelligible.
This second principle is the demand of a profoundly mathematical mind turned upon the whole of reality. A mathematician cannot accept that a theorem is simply true for no reason; there must be a proof, a ground, a sufficient reason. Leibniz extended this demand to everything. Why does the world exist at all rather than nothing? Why is it arranged this way rather than another? There must, he insisted, be a sufficient reason - and pursuing that demand to its end led him to God, to the monads, and to the best of all possible worlds. The principle of sufficient reason is the engine of his metaphysics: it forbids any ‘that’s just how it is’, and forces every fact to surrender its explanation. To understand Leibniz is to see a mind that could not rest in any unexplained brute fact, and that built an entire cosmos to satisfy the demand that everything have its reason.
Leibniz asked what reality is ultimately made of, and his answer was as original as it is strange. The physical atoms of the materialists could not be the true ultimate units, he reasoned, because anything extended in space is divisible - it has a left half and a right half - and so cannot be truly simple and indivisible. The genuine atoms of nature must be unextended, point-like, and therefore not material at all. Leibniz called them monads: simple, indivisible, immaterial substances, the metaphysical points from which all reality is composed. Each monad is a kind of soul or mind-like unit, possessing perception (it represents or ‘mirrors’ the whole universe from its own point of view) and appetite (an internal principle of change). There are infinitely many, and they range from the bare, confused perceptions of the monads making up a stone to the clear, self-conscious perceptions of the rational mind.
This is the opening of the lesson. The rest — the dialogue, the primary source, and the recall — is in the app.
You learned Leibniz’s metaphysics: the principle of sufficient reason, the monads, and the claim that this is the best of all possible worlds. Explain how a mathematician’s habit of optimisation shaped his picture of reality.
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