Spatial
Relations
A spatial relation is a distance between two
substances to a certain degree. Space
is a complex of shapes, lines, and points, themselves
abstract geometric properties that substances may
exemplify.
So I do not view space as a substance, given that space has parts that can
be exemplified. Space falls under the category of ordered
whole. Given that space is a complex of abstract properties, and given that
these properties are essential parts of propositions, and given that
propositions are necessary entities, it looks as though space is a necessary
entity. Space exists necessarily.
However, spatial substances
do not appear to be necessary entities. It seems perfectly possible for there
to be empty space—no things standing in any spatial relations.
Axioms of spatial relations are presently treated
under axioms for shapes.
Is
Space Curved?
No. Things in space exemplify curves, but given my
account of space as a complex of geometric properties, it makes no sense for
space itself to exemplify curves. In other words, space contains curves, though it does not itself exemplify curves.
In reply to general relativity’s alleged need for
curved space, see General
Relativity @ TWOW.
Is
Time a Dimension of Space?
No. See temporal relations.
Are
Distances Relative?
No. However, I realize that it follows from
Einstein’s special theory of relativity that the distance between two objects
is relative to an inertial frame. So there is no such thing as non-relative
distance. This seems to me to be a mistake. A distance seems to be a two-term
relation, not a three term one.
That isn’t to say that I question the equations of
special relativity. It’s just that I am skeptical of Einstein’s metaphysical
account of them. I think a metaphysically simpler account (simpler in terms of
the quantity of kinds of entities and the quantity of members of each kind) is
this: As two simple substances move more quickly, the causal interactions
between them slow down. They slow down because a
causal interaction takes place by virtue of a transfer of some third thing
(like energy) travelling at the speed of light, say. As energy travels in the
direction of motion, it takes it longer
to travel from one substance to the other. Indeed, as the substances approach
the speed of light, the time it takes the energy to “catch up” to the other
substance approaches infinite. This is why clocks slow down to zero as their
velocities approach the speed of light. In fact, you can calculate just how
much they slow down at any particular velocity given this metaphysical account,
and the calculations are exactly as the special theory equations predict. The
advantage of this account is that it’s ontologically simpler than Einstein’s.
For more on this topic, see Special
Relativity @ TWOW.