PHIL2109 Contemporary Metaphysics
Week 10: Space


  1. Is there such a thing as space? If so, what kind of thing is it? What is it like, and how does it relate to other things?

Space and its parts

  1. Space seems to have parts. Some of these are 3-dimensional, like space itself; these are volumes or regions of space. Perhaps it also has 2-dimensional parts (e.g. surfaces), 1-dimensional parts (e.g. lines), and 0-dimensional parts (e.g. points).
  2. Assuming that space has parts, what is the relationship between space and its parts?
  3. Here are two views:

Space and the physical objects in it

  1. Assuming that there is such a thing as space, and that there are physical objects in it, how is space related to these physical objects?
  2. Here are three views:
  3. What does general relativity tell us?

    On one way of understanding it, it says that material objects are just deformations in the fabric of space. This suggests that absolutism is right. Einstein's field equations also allow that space is perfectly empty.

The rotating bucket

  1. We are familiar with velocity being relative to a frame of reference. But is there such a thing as absolute velocity, or real velocity - velocity that is not relative to anything? It does often seem natural to ask, of two things that are moving relative to each other: which one is really moving? If there is, then perhaps this is a reason to think that absolutism is true.
  2. Newton argues that there is such a thing as absolute velocity. He grants that absolute velocity cannot be measured, because space is imperceptible. But we can argue for its existence. We can measure (empirically detect) absolute acceleration, which is the rate of change of absolute velocity. Thus, we are entitled to believe in absolute velocity.
  3. He runs a thought experiment about a rotating bucket.

    In the experiment there is a bucket which is half full of water, hanging by a rope. In stage 1 it is stationary, and there is no relative motion between the water and the bucket. In stage 2 the bucket is spun, and there is relative motion between the water and the bucket. In stage 3 the water catches up to the bucket, and there is again no relative motion between the water and the bucket.

    Newton says that in stage 2 the water is rotation with respect to the bucket, but it is not really rotating, whereas in stage 3 it is really rotating, and that is why its surface becomes concave. We can detect this real rotation (by looking at the surface), and thus detect real acceleration, and from that infer the existence of real velocity.
  4. But why not say that this 'real' rotation is just rotation relative to some physical object, perhaps the Earth, perhaps the surrounding galaxies? After all, doesn't it make sense to ask which is really rotating, the water or the universe around it? Mach asks: Suppose we move the walls of the bucket to the edge of the universe; wouldn't the water surface become concave in stage 2?

The two globes

  1. To counter this Newton offers another thought experiment. Imagine a universe whose sole material occupants are two exactly similar globes, attached to one another by a straight length of string. By detecting whether or not there is tension in the string we can tell whether or not they are really rotating.
  2. But Mach objects: how do we know that there would still be tension in the string even if there were no surrounding matter?
  3. We might also object that Newton's view suggests that absolute space could causally interact with matter, but how could that be?

Incongruent counterparts

  1. Kant gives an argument for the substantivist view of space that appeals to incongruent counterparts, for example a left and right hand (they are mirror images, that cannot be brought into spatial coincidence).
  2. Consider two worlds, one of whose sole occupant is a left hand, the other of whose sole occupant is a right hand. There seems to be a spatial difference between the two worlds - a difference in spatial facts. Question: why is there such a difference? Thus we have an argument from incongruent counterparts against relationalism and for absolutism.
  3. But does the substantivist really have the upper hand here?
  4. One concern is that we can't really make sense of a hand having an orientation with respect to space.

    Perhaps we might try the following analogy: just as there are two ways of placing an 'R' on a sheet of paper, each giving rise to a different orientation of the 'R' on the paper, so too there are two ways of placing a hand in space, each giving rise to a different orientation of the hand in space.

  5. Another concern is that there might be no such things as incongruent counterparts.
  6. One final concern is that the argument from incongruent counterparts misunderstands the relativist's position: she does not claim that space is necessarily relative, just that it is actually relative, leaving open the possibility that there are worlds in which it is absolute. So merely possible cases are no problem for her.