the
relative theory. Each instant is irrevocable. It can never recur by the
very character of time. But if on the relative theory an instant of time
is simply the state of nature at that time, and the time-ordering
relation is simply the relation between such states, then the
irrevocableness of time would seem to mean that an actual state of all
nature can never return. I admit it seems unlikely that there should
ever be such a recurrence down to the smallest particular. But extreme
unlikeliness is not the point. Our ignorance is so abysmal that our
judgments of likeliness and unlikeliness of future events hardly count.
The real point is that the exact recurrence of a state of nature seems
merely unlikely, while the recurrence of an instant of time violates our
whole concept of time-order. The instants of time which have passed, are
passed, and can never be again.

Any alternative theory of time must reckon with these two considerations
which are buttresses of the absolute theory. But I will not now continue
their discussion.

The absolute theory of space is analogous to the corresponding theory of
time, but the reasons for its maintenance are weaker. Space, on this
theory, is a system of extensionless points which are the relata in
space-ordering relations which can technically be combined into one
relation. This relation does not arrange the points in one linear series
analogously to the simple method of the time-ordering relation for
instants. The essential logical characteristics of this relation from
which all the properties of space spring are expressed by mathematicians
in the axioms of geometry. From these axioms[3] as framed by modern
mathematicians the whole science of geometry can be deduced by the
strictest logical reasoning. The details of these axioms do not now
concern us. The points and the relations are jointly known to us in our
apprehension of space, each implying the other. What happens in space,
occupies space. This relation of occupation is not usually stated for
events but for objects. For example, Pompey's statue would be said to
occupy space, but not the event which was the assassination of Julius
Caesar. In this I think that ordinary usage is unfortunate, and I hold
that the relations of events to space and to time are in all respects
analogous. But here I am intruding my own opinions which are to be
discussed in subsequent lectures. Thus the theory of absolute space
requires that we are awa