objects is devoid of any connexion with time. It
is space at an instant without any determinate relations between the
spaces at successive instants. It cannot be one timeless space because
the relations between objects change.
A few minutes ago in speaking of the deduction of the orthodox formulae
for relative motion I said that they followed as an immediate deduction
from the assumption of absolute points in absolute space. This reference
to absolute space was not an oversight. I know that the doctrine of the
relativity of space at present holds the field both in science and
philosophy. But I do not think that its inevitable consequences are
understood. When we really face them the paradox of the presentation of
the character of space which I have elaborated is greatly mitigated. If
there is no absolute position, a point must cease to be a simple entity.
What is a point to one man in a balloon with his eyes fixed on an
instrument is a track of points to an observer on the earth who is
watching the balloon through a telescope, and is another track of points
to an observer in the sun who is watching the balloon through some
instrument suited to such a being. Accordingly if I am reproached with
the paradox of my theory of points as classes of event-particles, and of
my theory of event-particles as groups of abstractive sets, I ask my
critic to explain exactly what he means by a point. While you explain
your meaning about anything, however simple, it is always apt to look
subtle and fine spun. I have at least explained exactly what I do mean
by a point, what relations it involves and what entities are the relata.
If you admit the relativity of space, you also must admit that points
are complex entities, logical constructs involving other entities and
their relations. Produce your theory, not in a few vague phrases of
indefinite meaning, but explain it step by step in definite terms
referring to assigned relations and assigned relata. Also show that your
theory of points issues in a theory of space. Furthermore note that the
example of the man in the balloon, the observer on earth, and the
observer in the sun, shows that every assumption of relative rest
requires a timeless space with radically different points from those
which issue from every other such assumption. The theory of the
relativity of space is inconsistent with any doctrine of one unique set
of points of one timeless space.
The fact is that there is no par
|