moment. For a moment is all nature at an instant. It cannot be the
intrinsic character of the moment. For the intrinsic character tells us
the limiting character of nature in space at that instant. Instantaneous
space must be an assemblage of abstractive elements considered in their
mutual relations. Thus an instantaneous space is the assemblage of
abstractive elements covered by some one moment, and it is the
instantaneous space of that moment.

We have now to ask what character we have found in nature which is
capable of according to the elements of an instantaneous space different
qualities of position. This question at once brings us to the
intersection of moments, which is a topic not as yet considered in these
lectures.

The locus of intersection of two moments is the assemblage of
abstractive elements covered by both of them. Now two moments of the
same temporal series cannot intersect. Two moments respectively of
different families necessarily intersect. Accordingly in the
instantaneous space of a moment we should expect the fundamental
properties to be marked by the intersections with moments of other
families. If M be a given moment, the intersection of M with another
moment A is an instantaneous plane in the instantaneous space of M; and
if B be a third moment intersecting both M and A, the intersection of M
and B is another plane in the space M. Also the common intersection of
A, B, and M is the intersection of the two planes in the space M, namely
it is a straight line in the space M. An exceptional case arises if B
and M intersect in the same plane as A and M. Furthermore if C be a
fourth moment, then apart from special cases which we need not consider,
it intersects M in a plane which the straight line (A, B, M) meets. Thus
there is in general a common intersection of four moments of different
families. This common intersection is an assemblage of abstractive
elements which are each covered (or 'lie in') all four moments. The
three-dimensional property of instantaneous space comes to this, that
(apart from special relations between the four moments) any fifth moment
either contains the whole of their common intersection or none of it. No
further subdivision of the common intersection is possible by means of
moments. The 'all or none' principle holds. This is not an _a priori_
truth but an empirical fact of nature.

It will be convenient to reserve the ordinary spatial terms 'plane,'
'straight line,' '