ve element belonging to the punct. Then the definition of the
event-particle associated with the punct is that it is the group of all
the {sigma}-primes, where {sigma} has this particular meaning.

It is evident that--with this meaning of {sigma}--every abstractive set
equal to a {sigma}-prime is itself a {sigma}-prime. Accordingly an
event-particle as thus defined is an abstractive element, namely it is
the group of those abstractive sets which are each equal to some given
abstractive set. If we write out the definition of the event-particle
associated with some given punct, which we will call {pi}, it is as
follows: The event-particle associated with {pi} is the group of
abstractive classes each of which has the two properties (i) that it
covers every abstractive set in {pi} and (ii) that all the abstractive
sets which also satisfy the former condition as to {pi} and which it
covers, also cover it.

An event-particle has position by reason of its association with a
punct, and conversely the punct gains its derived character as a route
of approximation from its association with the event-particle. These two
characters of a point are always recurring in any treatment of the
derivation of a point from the observed facts of nature, but in general
there is no clear recognition of their distinction.

The peculiar simplicity of an instantaneous point has a twofold origin,
one connected with position, that is to say with its character as a
punct, and the other connected with its character as an event-particle.
The simplicity of the punct arises from its indivisibility by a moment.

The simplicity of an event-particle arises from the indivisibility of
its intrinsic character. The intrinsic character of an event-particle is
indivisible in the sense that every abstractive set covered by it
exhibits the same intrinsic character. It follows that, though there are
diverse abstractive elements covered by event-particles, there is no
advantage to be gained by considering them since we gain no additional
simplicity in the expression of natural properties.

These two characters of simplicity enjoyed respectively by
event-particles and puncts define a meaning for Euclid's phrase,
'without parts and without magnitude.'

It is obviously convenient to sweep away out of our thoughts all these
stray abstractive sets which are covered by event-particles without
themselves being members of them. They give us nothing new in the way of
int