This post is devoted to an argument Leibniz made during his correspondence with Clarke, so I should say something about the correspondence itself, which is fascinating. It’s a debate between two worldviews:

(A) The worldview put forward by Newton, which would be dominant for hundreds of years, defended by Clarke. This worldview asserts that space is absolute and that God interferes with the universe once in a while to keep it running properly.

(B) The worldview put forward and defended by Leibniz, which asserts that space is relative and that God does not interfere with the universe but rather set everything up properly at the beginning. The claim that space is relative would later be proven by Einstein, but Leibniz didn’t really have any conclusive evidence for the claim beyond his philosophical arguments.

The reason the correspondence got started is that Leibniz sent a letter to Caroline, the princess of Wales, and over the course of this letter he made the criticism that Newton’s worldview was dangerous to religion, because it implies that God has to interfere in the universe to keep it running properly like an incompetent mechanic. Clarke responded to this, saying that God would not really be the ruler of the universe if he did not interfere with it, much as a king would not really be king of his kingdom if the whole kingdom always operated perfectly without him doing anything. The rest of the discussion takes off from there and covers topics like immortality and the nature of space.

Anyway, in Leibniz’s third letter during this exchange, he makes the following argument against Clarke’s claim that space is absolute:

I say, then, that if space was an absolute being, something would happen for which it would be impossible that there should be a sufficient reason Рwhich is against my axiom. And I prove it thus: Space is something absolutely uniform, and without the things placed in it, one point of space absolutely does not differ in any respect whatsoever from another point of space. Now from this it follows (supposing space to be something in itself, besides the order of bodies among themselves) that it is impossible there should be a reason why God, preserving the same situations of bodies among themselves, should have placed them in space after one certain particular manner and not otherwise Рwhy everything was not placed the quite contrary way, for instance, by changing east into west. But if space is nothing else but this order of relation, and is nothing at all without bodies but the possibility of placing them, then those two states, the one such as it is now, the other supposed to be the quite contrary way, would not at all differ from one another. Their difference therefore is only to be found in our chimerical supposition of the reality of space in itself. But in truth the one would be exactly the same thing as the other, they being absolutely indiscernable, and consequently there is no room to inquire after a reason  for the preference of the one to the other.

This is a fascinating argument. It’s interesting that Leibniz was able to anticipate Einstein hundreds of years in advance, even if he couldn’t really prove that space was relative.