s whose successive occupation
means rest in the given time-system forms a timeless point in the
timeless space of that time-system. In this way each time-system
possesses its own permanent timeless space peculiar to it alone, and
each such space is composed of timeless points which belong to that
time-system and to no other. The paradoxes of relativity arise from
neglecting the fact that different assumptions as to rest involve the
expression of the facts of physical science in terms of radically
different spaces and times, in which points and moments have different
meanings.

The source of order has already been indicated and that of congruence is
now found. It depends on motion. From cogredience, perpendicularity
arises; and from perpendicularity in conjunction with the reciprocal
symmetry between the relations of any two time-systems congruence both
in time and space is completely defined (cf. _loc. cit._).

The resulting formulae are those for the electromagnetic theory of
relativity, or, as it is now termed, the restricted theory. But there is
this vital difference: the critical velocity c which occurs in these
formulae has now no connexion whatever with light or with any other fact
of the physical field (in distinction from the extensional structure of
events). It simply marks the fact that our congruence determination
embraces both times and spaces in one universal system, and therefore if
two arbitrary units are chosen, one for all spaces and one for all
times, their ratio will be a velocity which is a fundamental property of
nature expressing the fact that times and spaces are really comparable.

The physical properties of nature are expressed in terms of material
objects (electrons, etc.). The physical character of an event arises
from the fact that it belongs to the field of the whole complex of such
objects. From another point of view we can say that these objects are
nothing else than our way of expressing the mutual correlation of the
physical characters of events.

The spatio-temporal measurableness of nature arises from (i) the
relation of extension between events, and (ii) the stratified character
of nature arising from each of the alternative time-systems, and (iii)
rest and motion, as exhibited in the relations of finite events to
time-systems. None of these sources of measurement depend on the
physical characters of finite events as exhibited by the situated
objects. They are completely signified