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.
Most startling is Leibniz’s claim that the monads are causally isolated: they ‘have no windows’ through which anything could enter or leave. No monad acts on any other; each unfolds its own perceptions entirely from within, according to its own internal law. How, then, does the universe hold together - why do my perceptions match yours, why does mind seem to move body? Because God, in creating the monads, set them all in advance into a pre-established harmony, like a vast set of clocks each wound to keep perfect time with all the others without any causal connection between them. Each monad spontaneously runs through its own series of states, and God has arranged that these series correspond perfectly, so that the whole presents the seamless appearance of an interacting world. It is a breathtaking vision: reality as an infinity of windowless minds, each dreaming the same universe from its own perspective, synchronised by the foresight of God.
The doctrine that this is the best of all possible worlds is the most famous - and most ridiculed - of all Leibniz’s teachings. It is crucial to understand what it does and does not claim. It does not claim that the world is free of evil, suffering, or imperfection; Leibniz was no fool, and he saw the world’s miseries as clearly as anyone. It claims, rather, that this world contains the least evil compatible with the greatest overall perfection - that any other possible world God could have created would have been, on balance, worse. Evil exists, but it is the unavoidable shadow of greater goods: a world with free creatures will contain the misuse of freedom; a world governed by simple, regular laws will sometimes let those laws grind against us; the very richness and variety that make the world magnificent require limitation and contrast. God did not will the evils, but permitted them as the necessary cost of the best whole, as a wise architect accepts a flaw that the overall design requires. This is Leibniz’s answer to the ancient problem of evil - his theodicy, his attempt to justify the ways of God to a suffering world.
The doctrine met with derision, never more devastatingly than from Voltaire, whose 1759 novel Candide follows an innocent disciple of the Leibnizian philosopher ‘Dr Pangloss’ through a catalogue of horrors - earthquake, war, disease, rape, torture - while Pangloss insanely insists, through every catastrophe, that all is for the best in the best of all possible worlds. The satire was prompted in part by the real Lisbon earthquake of 1755, which killed tens of thousands and made glib optimism obscene. Voltaire’s caricature was unfair to the subtle Leibniz - Pangloss is a buffoon, not a faithful representation - but it was unanswerable as rhetoric, and it fixed forever in the popular mind the image of Leibnizian optimism as a fatuous denial of obvious suffering. To this day, ‘the best of all possible worlds’ and ‘Panglossian’ are terms of mockery. It is the fate of Leibniz’s boldest application of mathematical reason to existence: a rigorous deduction from the nature of a perfect God, transformed by a novelist’s genius into the very symbol of philosophy divorced from life.
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.
Leads to Voltaire.
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