ontains as parts any two of its days. It is
evident that a containing duration satisfies the conditions for
belonging to the same family as the two contained durations.

We are now prepared to proceed to the definition of a moment of time.
Consider a set of durations all taken from the same family. Let it have
the following properties: (i) of any two members of the set one contains
the other as a part, and (ii) there is no duration which is a common
part of every member of the set.

Now the relation of whole and part is asymmetrical; and by this I mean
that if A is part of B, then B is not part of A. Also we have
already noted that the relation is transitive. Accordingly we can easily
see that the durations of any set with the properties just enumerated
must be arranged in a one-dimensional serial order in which as we
descend the series we progressively reach durations of smaller and
smaller temporal extension. The series may start with any arbitrarily
assumed duration of any temporal extension, but in descending the
series the temporal extension progressively contracts and the successive
durations are packed one within the other like the nest of boxes of a
Chinese toy. But the set differs from the toy in this particular: the
toy has a smallest box which forms the end box of its series; but the
set of durations can have no smallest duration nor can it converge
towards a duration as its limit. For the parts either of the end
duration or of the limit would be parts of all the durations of the set
and thus the second condition for the set would be violated.

I will call such a set of durations an 'abstractive set' of durations.
It is evident that an abstractive set as we pass along it converges to
the ideal of all nature with no temporal extension, namely, to the ideal
of all nature at an instant. But this ideal is in fact the ideal of a
nonentity. What the abstractive set is in fact doing is to guide thought
to the consideration of the progressive simplicity of natural relations
as we progressively diminish the temporal extension of the duration
considered. Now the whole point of the procedure is that the
quantitative expressions of these natural properties do converge to
limits though the abstractive set does not converge to any limiting
duration. The laws relating these quantitative limits are the laws of
nature 'at an instant,' although in truth there is no nature at an
instant and there is only the abstractive set.