Discourse on Metaphysics

Overview

Sixty pages, thirty-seven numbered sections, each a paragraph or two with a summarising heading. Leibniz wrote it in French in the winter of 1686, sent the list of headings to Antoine Arnauld to see whether a serious theologian would find it acceptable, got back a letter saying the ninth section contained conclusions that appalled him, and never published the work at all. It first appeared in print in 1846, a hundred and thirty years after his death.

That history matters for how it reads. This is not a book built for an audience. It is a philosopher setting down a system he has been assembling for twenty years, in the most compressed form he can manage, for a reader he expects to object. Sections that would be a chapter anywhere else are four sentences here.

Leibniz is also the only major philosopher of the period who was simultaneously a working mathematician, a diplomat, a mining engineer and a court historian, and the Discourse has the fingerprints of all of it. The argument about force in the middle of the book is a piece of real physics. The theology at the end is written by someone who spent years trying to reunite the churches.

The argument

Sections 1 to 7: God and the best world. God is the absolutely perfect being, and to act perfectly is not to act arbitrarily. Leibniz rejects the view, which he attributes to Descartes, that things are good because God wills them; if that were so, praising God’s goodness would be empty. God surveys the infinitely many possible worlds and creates the one that is best, and best means the most perfect ratio of richness to simplicity: the greatest variety of phenomena produced by the fewest and most elegant laws. Miracles are not violations of that order but part of the same plan at a higher level.

Sections 8 to 16: individual substance. The famous move. What is it to be an individual thing rather than a property? Leibniz’s answer is that an individual substance has a complete concept, so full that everything ever true of it can be derived from it. Alexander’s concept contains his victories and his death. From this he immediately draws consequences that Arnauld found intolerable. No two substances can be exactly alike, since that would make two concepts one. Substances cannot begin or end except by creation and annihilation. Every substance expresses the entire universe from its own position, so that in principle a sufficiently powerful mind could read the whole of history off any one of them. And nothing ever acts on anything else: what looks like causation is the agreement of independent, self-unfolding histories, a doctrine later named pre-established harmony.

Section 13 confronts the obvious objection. If Caesar’s concept always contained the crossing of the Rubicon, how was he free not to cross it? Leibniz distinguishes two kinds of truth. A necessary truth is one whose denial implies a contradiction, and its analysis terminates. A contingent truth is certain, grounded in God’s choice of the best, but its analysis is infinite and no finite demonstration of it exists. Caesar was inclined without being compelled.

Sections 17 to 22: physics. A sharp technical argument against Descartes’ law that the quantity of motion, size times speed, is conserved. Leibniz shows with a simple thought experiment about raising weights that the conserved quantity involves the square of the velocity, not the velocity, which is a genuine discovery and the ancestor of kinetic energy. He then defends final causes: the mechanical account of nature is correct and incomplete, and looking for the purpose a structure serves is often the faster route to the truth, as it is in optics.

Sections 23 to 29: ideas and knowledge. What it is to have an idea, the grades of clear, distinct and adequate knowledge, a careful treatment of Malebranche’s claim that we see all things in God, and the observation that the ontological argument is incomplete until someone shows that a most perfect being is possible.

Sections 30 to 37: evil, grace and the city of God. Why God is not the author of sin, discussed through the case of Judas; how a substance’s own nature is the source of what it does; and finally minds, which mirror not only the universe but God himself, and therefore belong to a community with him that is worth more than the whole of the rest of creation.

How to read it

Read sections 8, 9 and 13 first, then go back to the beginning. Section 8 is the doctrine, section 9 is what it costs, and section 13 is the defence. Everything else in the book is oriented to those three.

Read the Arnauld correspondence afterwards if you possibly can. It is in the Ariew and Garber collection, and it is the best philosophical exchange of the century: a first-rate theologian pressing exactly the objections you are forming, and Leibniz explaining himself better than he does in the Discourse itself.

Do not skip the physics. Sections 17 and 18 are short, the argument is intelligible without mathematics, and they show why Leibniz thought the mechanical philosophy needed a metaphysics under it.

If a section makes no sense, read the next one. The headings are a map, the order is deliberate, and Leibniz often supplies in section n plus one the illustration that section n needed.

The famous misreading comes from Voltaire. The best of all possible worlds is not the claim that everything in your life is fine. It is the claim that no better total arrangement of laws and events is jointly possible, which is compatible with a great deal of misery and is much harder to refute by pointing at an earthquake. Whether it is refuted by a different argument is a good question.

Questions it raises

• If the complete concept of Caesar already contains the Rubicon, is the distinction between inclining and necessitating a real difference or a change of vocabulary?
• God chooses the best world. Is there a best, or could there be an endless series of better ones, as Leibniz’s critics asked?
• No two substances are exactly alike. Is the identity of indiscernibles a necessary truth, a fact about how God creates, or a stipulation?
• Substances never interact, yet they agree perfectly. Is pre-established harmony an explanation of apparent causation, or the denial that there is anything to explain?
• Leibniz keeps final causes alongside mechanism. Can a science do both at once, and does modern biology?
• Each substance expresses the whole universe. What does express mean here, and how would you check whether it is true?