perty of being covered by every
abstractive set which it covers. I state this difficulty at some length
because its existence guides the development of our line of argument. We
have got to annex some condition to the root property of being covered
by any abstractive set which it covers. When we look into this question
of suitable conditions we find that in addition to event-particles all
the other relevant spatial and spatio-temporal abstractive elements can
be defined in the same way by suitably varying the conditions.
Accordingly we proceed in a general way suitable for employment beyond
event-particles.

Let {sigma} be the name of any condition which some abstractive sets
fulfil. I say that an abstractive set is '{sigma}-prime' when it has the
two properties, (i) that it satisfies the condition {sigma} and (ii)
that it is covered by every abstractive set which both is covered by it
and satisfies the condition {sigma}.

In other words you cannot get any abstractive set satisfying the
condition {sigma} which exhibits intrinsic character more simple than
that of a {sigma}-prime.

There are also the correlative abstractive sets which I call the sets of
{sigma}-antiprimes. An abstractive set is a {sigma}-antiprime when it
has the two properties, (i) that it satisfies the condition {sigma} and
(ii) that it covers every abstractive set which both covers it and
satisfies the condition {sigma}. In other words you cannot get any
abstractive set satisfying the condition {sigma} which exhibits an
intrinsic character more complex than that of a {sigma}-antiprime.

The intrinsic character of a {sigma}-prime has a certain minimum of
fullness among those abstractive sets which are subject to the condition
of satisfying {sigma}; whereas the intrinsic character of a
{sigma}-antiprime has a corresponding maximum of fullness, and includes
all it can in the circumstances.

Let us first consider what help the notion of antiprimes could give us
in the definition of moments which we gave in the last lecture. Let the
condition {sigma} be the property of being a class whose members are all
durations. An abstractive set which satisfies this condition is thus an
abstractive set composed wholly of durations. It is convenient then to
define a moment as the group of abstractive sets which are equal to some
{sigma}-antiprime, where the condition {sigma} has this special meaning.
It will be found on consideration (i) that each abstractive set f