8] called
the law of convergence to simplicity by diminution of extent.

[8] Cf. _Organisation of Thought_, pp. 146 et seq. Williams and Norgate,
1917.

If A and B are two events, and A' is part of A and B' is part
of B, then in many respects the relations between the parts A' and
B' will be simpler than the relations between A and B. This is the
principle which presides over all attempts at exact observation.

The first outcome of the systematic use of this law has been the
formulation of the abstract concepts of Time and Space. In the previous
lecture I sketched how the principle was applied to obtain the
time-series. I now proceed to consider how the spatial entities are
obtained by the same method. The systematic procedure is identical in
principle in both cases, and I have called the general type of procedure
the 'method of extensive abstraction.'

You will remember that in my last lecture I defined the concept of an
abstractive set of durations. This definition can be extended so as to
apply to any events, limited events as well as durations. The only
change that is required is the substitution of the word 'event' for the
word 'duration.' Accordingly an abstractive set of events is any set of
events which possesses the two properties, (i) of any two members of the
set one contains the other as a part, and (ii) there is no event which
is a common part of every member of the set. Such a set, as you will
remember, has the properties of the Chinese toy which is a nest of
boxes, one within the other, with the difference that the toy has a
smallest box, while the abstractive class has neither a smallest event
nor does it converge to a limiting event which is not a member of the
set.

Thus, so far as the abstractive sets of events are concerned, an
abstractive set converges to nothing. There is the set with its members
growing indefinitely smaller and smaller as we proceed in thought
towards the smaller end of the series; but there is no absolute minimum
of any sort which is finally reached. In fact the set is just itself and
indicates nothing else in the way of events, except itself. But each
event has an intrinsic character in the way of being a situation of
objects and of having parts which are situations of objects and--to
state the matter more generally--in the way of being a field of the life
of nature. This character can be defined by quantitative expressions
expressing relations between various quantities i