Gottfried Wilhelm Leibniz

Key ideas

1. Monads. The ultimate constituents of reality are simple, mind-like substances, each with its own perceptions and appetitions, which Leibniz called monads. Bodies are phenomena resulting from monads, and monads have no windows: nothing passes into or out of them.
2. The two great principles. Reasoning rests on the principle of contradiction and the principle of sufficient reason. No fact can be real, and no statement true, without a sufficient reason why it is so and not otherwise, though we usually cannot know that reason.
3. Identity of indiscernibles. No two substances can resemble each other completely and differ only in number. Place and time alone cannot make two things different, so any such difference must rest on an intrinsic one.
4. Pre-established harmony. Created substances do not act causally on one another, yet mind and body agree, because God made each to unfold by its own law in accord with all the others. Leibniz compares them to two pendulums that keep time because each was well made, not because one pushes the other.
5. The best possible world. God is omnipotent, omniscient and good, and chose among infinitely many possible worlds the one that is simplest in its laws and richest in phenomena. Evil is permitted as part of the best whole; Voltaire mocked the view in Candide.
6. Against Locke on innate ideas. Necessary truths cannot come from the senses, which give only particular instances. They are in the mind as dispositions, like veins in marble that suggest a statue, and there are also perceptions of which we are not aware.
7. Reasoning as calculation. From 1666 Leibniz sketched a universal characteristic and a logical calculus. The same ambition lies behind his calculus notation, his binary arithmetic and his calculating machine.

Gottfried Wilhelm Leibniz (1646–1716; also spelled Leibnitz) was a German polymath, mathematician, diplomat and philosopher who invented the calculus independently of Newton. As a philosopher he argued that reality consists of simple, mind-like substances called monads, that nothing happens without a sufficient reason, and that this is the best of all possible worlds. With Descartes and Spinoza he is one of the three great rationalists.

He was born in Leipzig on 1 July 1646 (21 June, Old Style), studied at Leipzig and Altdorf and took a doctorate of law in 1667. A diplomatic mission took him to Paris from 1672 to 1676, where he learned from Huygens, read the unpublished manuscripts of Descartes and Pascal, and designed a calculating machine. On his way to Hanover he met Spinoza in November 1676. He spent the rest of his life at the Hanoverian court as librarian, historian and Privy Councillor, corresponding with over a thousand people. In his last years he was embroiled in the quarrel with Newton’s followers over the calculus, and when he died on 14 November 1716, Wikipedia reports, no courtier apart from his secretary attended the funeral.

He left no single masterwork. The Theodicy (1710) is the only philosophical book he published; the Monadology (1714) appeared after his death and the Discourse on Metaphysics (1686) not until 1846.

What are monads?

Suppose, Leibniz says in the Monadology (§17), that there were a machine “so constructed as to think, feel, and have perception”, enlarged until one could walk into it “as into a mill”. Inside we should “find only parts which work one upon another, and never anything by which to explain a perception.” Perception must therefore be sought in a “simple substance”, a monad, which is “without parts”. This is Leibniz’s mill, and the argument is still discussed in the philosophy of mind.

“The Monads have no windows, through which anything could come in or go out” (§7). Each is a substance unfolding its own perceptions, and bodies are phenomena resulting from them.

What are the two great principles?

“There can be no fact real or existing, no statement true, unless there be a sufficient reason, why it should be so and not otherwise, although these reasons usually cannot be known by us” (§32). This is the principle of sufficient reason. Beside it stands the principle of contradiction, and truths of reasoning, whose opposite is impossible, are distinguished from truths of fact, which are contingent (§33). He presented the identity of indiscernibles as a consequence of these principles: “it is not true that two substances can resemble each other completely and differ only in number.” In his correspondence with Samuel Clarke, Newton’s supporter, he used such principles against absolute space and for a relational view.

What is pre-established harmony?

If monads do not interact, how do mind and body agree? “The soul follows its own laws, and the body likewise follows its own laws; and they agree with each other in virtue of the pre-established harmony between all substances” (§78). God made each to unfold in accord with the others, as two perfectly made pendulums swing in time without touching. The alternatives he rejected were influence of one on the other and God’s constant intervention, which is called occasionalism.

Is this the best of all possible worlds?

Leibniz’s argument in the Theodicy is that an omnipotent, omniscient and good God could choose among infinitely many possible worlds, so if this world could be better, God would lack power, knowledge or will. He writes of “my fundamental assumption that God has chosen the best of all possible worlds” (Huggard’s translation). This is his theodicy, a reply to the problem of evil. The Stanford Encyclopedia stresses that he never says everything is wonderful: we see a part of the whole, and the best world is “the simplest in hypotheses and the richest in phenomena”. Voltaire’s Candide mocked the view, and analytic philosophy still uses Leibniz’s term “possible world” to define modal notions, as Wikipedia notes.

What did he say against Locke?

The New Essays, written in reply to Locke, reject the tabula rasa and defend innate ideas: the senses give only particular instances, so the universality of necessary truths must come from the understanding. He also held that “at every moment there is in us an infinity of perceptions, unaccompanied by awareness.”

What did he do in mathematics and logic?

Leibniz published his differential calculus in 1684, and his notation is the one now conventional. Newton developed his methods first, and historians now judge the invention independent. Wikipedia credits Leibniz with devising the modern binary system in 1703, though Thomas Harriot had devised the same system decades before, and notes that he anticipated ideas that surfaced later in computer science. His 1666 plan for a universal characteristic and logical calculus belongs to the history of logic.

How should you start reading Leibniz?

Start with the Monadology, §§1–9, the mill in §17 and §§31–33. The UGC NET syllabus, which spells his name Leibnitz, lists the monadology, truths of reason and fact, innate ideas, proofs for God, the principles of non-contradiction, sufficient reason and indiscernibles, pre-established harmony and the problem of freedom; see the UGC NET guide and the UPSC guide. The prefaces of the Theodicy and the New Essays come next.