Leibniz’s Third Letter to Clarke: A Discourse on Absolute Space and the Principle of Sufficient Reason

Gottfried Wilhelm Leibniz

He claims that it’s impossible for God to have a reason to place the universe in one place instead of the other when all the relations between the bodies are preserved.

For Leibniz, the principle of sufficient reason does not include God’s will; therefore if every relation in the universe is going to stay the same, God will have no reason to place it in one place or the other, and since his will can’t affect the principle of sufficient reason, he can’t will the universe to be placed in different positions. He concludes that because there is reason or will that can place the universe in another position than it already is, there is no reason why space should be an absolute being or substance.

If relationalism is true could space be absolute or a substance?

Relationalism is the idea that space is merely the order of relations between bodies and not a body by itself. If space depends on relations, it follows that God has no reason or will that can bend the principle of sufficient reason (according to Leibniz) to place bodies in a contrary manner to what they are now, “for instance, by changing east into west” (letter 3: §5). If space is not a body, it does not have reference points to label any side of it as east or west except the way the bodies are placed. Therefore it does not matter if the universe is set the way it is now or in the opposite way, since the order of relations will still stay exactly the same due to its arrangement according to the principles of sufficient reason, causing east and west to be what they already are. Leibniz asserts that if east and west or any other direction can’t be changed to something that it’s not then all the different states of the universe are in fact absolutely indiscernible from each other.

What does it mean that the two states of the universe “is only to be found in our chimerical supposition of the reality of space?

As a result of his previous claim, Leibniz also asserts that the difference between two states of the universe “is only to be found in our chimerical supposition of the reality of space (letter 3: §5)”. In our minds we can imagine that if the universe were turned around, the old east would become the new west since we would take ourselves as an unaffected reference point in space. In reality for all the relations in the universe to stay true to the principle of sufficient reason, our direction would need to change from east to west as well. Therefore we can only create a supposed difference between the two states of the universe: if it were possible to turn the universe around there would be no difference at all between the original and the changed.

This brings us back to Leibniz’s first claim that the different states of the universe are absolutely indiscernible. Since the identity of indiscernibles states that if two things can’t be distinguished from each other they are not two distinct things, Leibniz concludes that the first universe is in fact the same as the other, contrary to our possible supposition that turning the universe around would make a difference.


  1. Leibniz, Gottfried W., and Samuel Clarke. Correspondence. Ed. Roger Ariew. Boston: Hackett Company, Incorporated, 2000.