Space and time: are they real absolute containers, or only systems of relations among things?

Gottfried Wilhelm Leibniz, answered from the texts and cited to the page.

The position in brief

Space and time are not real things subsisting in themselves, not absolute containers in which God set the world. Space is the order of things that coexist; time the order of things that succeed one another; both are ideal — systems of relations, well-founded but not substances. Two principles dissolve the absolute. By sufficient reason: were space an absolute container, there could be no reason why God placed the universe here rather than shifted over, or created it at one moment rather than another, since the points of empty space and the moments of empty time are perfectly alike.¹²³

By the identity of indiscernibles: the universe shifted entire would be indiscernible from the universe unshifted, hence not a distinct state of affairs at all.⁴

Sources

1. But I shall only use, at the present, one demonstration, which the author here gives me occasion to insist upon. I say, then, that if space was an absolute being, there would something happen for which it would be impossible there should be a sufficient reason. Which is against my axiom. And I can prove it thus.

   The Controversy between Leibniz and Clarke, 1715-16, p. 694

2. But I shall only use, at present, one demonstration, which the author here gives me occasion to insist upon. I say, then, that if space were an absolute being, something would happen for which it would be impossible that there should be a sufficient reason—which is against my axiom. And I can prove it thus.

   From the Letters to Clarke (1715–16), pp. 517–518

3. And the case is the same even though space were nothing real but only the mere order of bodies. For still it would be abso¬ lutely indifferent, and there could be no other reason but mere will why three equal particles should be placed or ranged in the order 1, 2, 3, rather than in the contrary order. 1 " And therefore no argument can be drawn from this indifferency of all places to prove that no space is real.

   The Controversy between Leibniz and Clarke, 1715-16, p. 697

4. For when in his mind, he decides to put pawns on KR4 and QBz, no choice is involved; the pawns, as it were, only come into existence in situ. Now clearly God, when he created the world, was in the position of the man who invented the problem, not the man who set it out on the board.

   The Leibniz-Clarke Correspondence, pp. 28–29

Where the argument is made

• The Leibniz-Clarke Correspondence (1715-16, ed. Alexander), especially the third, fourth, and fifth letters
• 'On the Ultimate Origination of Things' (1697)
• Monadology and the New Essays on the ideality of space and time

How the argument was received

The Leibniz-Clarke correspondence is the classic confrontation of relational and absolute conceptions of space and time, and remains a touchstone in philosophy of physics. Clarke pressed Newton's rotating-bucket argument for absolute motion; the disputed question is whether relationalism can accommodate the dynamical facts of rotation and acceleration that seemed to require absolute space.