Space Can Only Be Mapped By Reference To Occupants

The following is a short paper I wrote for my metaphysics class. 

Wiggins claims that space can be mapped only by reference to its occupants. This doesn’t seem to be obviously true. Consider some world that has an infinite density, not much unlike how some scientists say the first moment of our universe was like, that is, every point of space is occupied by some matter. When the available space expands and the matter remains the same, the density of the world changes. This seems coherent. To say that space expands is to say that there are two points of space opposite of each other where that distance grows. But this seems coherent even without reference to matter occupying some point. So take T1 to be time in a world with infinite density. Then T2 is that same world where the available space is then doubled so that the world is then half the density. Now suppose the same thing without any matter in it whatsoever. We know that T1 and T2 have different amounts of space, and this difference is measured by some two points where the distance grows without any reference to any occupying object. The points being measured would be the outer limit or boundary of space to another boundary. So space can be mapped without any reference to occupants, but to the boundaries of space itself. 

Wiggins may reply that since spatial facts are dependent on particulars, and I have spatial facts, then I must be referring to some particular, and that particular would be the existence of space itself. Some world with infinite density has its particular space and another world with the same amount of matter and less density, hence more space, has its own particular space. Particulars then need not refer to solely material objects within space. But this seems to assume a meta space that regular space is expanding into, and we could propose the same solution ad infinitum. 

Wiggins may also reply that this isn’t what he means by “map out”. He may grant that you could have conceptual points of space without any reference to an occupying object, but that every single point would be indeterminate. So for example, take a perfect sphere with several equidistant points on the surface. Then suppose you wanted to choose a point to stick a flag on. Any point chosen would be arbitrary and in some sense identical to one another, so in this way, you cannot map out any difference to them. Every mapped point would be in some sense referring or communicating the exact same thing as every other point. The only way these points convey some meaningful content is if there is an object on the map which no longer makes the points equidistant in every respect, so mapping out space in a meaningful way requires reference to an occupying object. This seems to be a more charitable way to understand Wiggins, as I have no answer to this.