hese
points will not be the points of an external timeless space but of
instantaneous spaces. We ultimately want to arrive at the timeless space
of physical science, and also of common thought which is now tinged with
the concepts of science. It will be convenient to reserve the term
'point' for these spaces when we get to them. I will therefore use the
name 'event-particles' for the ideal minimum limits to events. Thus an
event-particle is an abstractive element and as such is a group of
abstractive sets; and a point--namely a point of timeless space--will be
a class of event-particles.

Furthermore there is a separate timeless space corresponding to each
separate temporal series, that is to each separate family of durations.
We will come back to points in timeless spaces later. I merely mention
them now that we may understand the stages of our investigation. The
totality of event-particles will form a four-dimensional manifold, the
extra dimension arising from time--in other words--arising from the
points of a timeless space being each a class of event-particles.

The required character of the abstractive sets which form
event-particles would be secured if we could define them as having the
property of being covered by any abstractive set which they cover. For
then any other abstractive set which an abstractive set of an
event-particle covered, would be equal to it, and would therefore be a
member of the same event-particle. Accordingly an event-particle could
cover no other abstractive element. This is the definition which I
originally proposed at a congress in Paris in 1914[9]. There is however
a difficulty involved in this definition if adopted without some further
addition, and I am now not satisfied with the way in which I attempted
to get over that difficulty in the paper referred to.

[9] Cf. 'La Theorie Relationniste de l'Espace,' _Rev. de Metaphysique et
de Morale_, vol. XXIII, 1916.

The difficulty is this: When event-particles have once been defined it
is easy to define the aggregate of event-particles forming the boundary
of an event; and thence to define the point-contact at their boundaries
possible for a pair of events of which one is part of the other. We can
then conceive all the intricacies of tangency. In particular we can
conceive an abstractive set of which all the members have point-contact
at the same event-particle. It is then easy to prove that there will be
no abstractive set with the pro