point' for the elements of the timeless space of a
time-system. Accordingly an instantaneous plane in the instantaneous
space of a moment will be called a 'level,' an instantaneous straight
line will be called a 'rect,' and an instantaneous point will be called
a 'punct.' Thus a punct is the assemblage of abstractive elements which
lie in each of four moments whose families have no special relations to
each other. Also if P be any moment, either every abstractive element
belonging to a given punct lies in P, or no abstractive element of
that punct lies in P.

Position is the quality which an abstractive element possesses in virtue
of the moments in which it lies. The abstractive elements which lie in
the instantaneous space of a given moment M are differentiated from
each other by the various other moments which intersect M so as to
contain various selections of these abstractive elements. It is this
differentiation of the elements which constitutes their differentiation
of position. An abstractive element which belongs to a punct has the
simplest type of position in M, an abstractive element which belongs
to a rect but not to a punct has a more complex quality of position, an
abstractive element which belongs to a level and not to a rect has a
still more complex quality of position, and finally the most complex
quality of position belongs to an abstractive element which belongs to a
volume and not to a level. A volume however has not yet been defined.
This definition will be given in the next lecture.

Evidently levels, rects, and puncts in their capacity as infinite
aggregates cannot be the termini of sense-awareness, nor can they be
limits which are approximated to in sense-awareness. Any one member of a
level has a certain quality arising from its character as also belonging
to a certain set of moments, but the level as a whole is a mere logical
notion without any route of approximation along entities posited in
sense-awareness.

On the other hand an event-particle is defined so as to exhibit this
character of being a route of approximation marked out by entities
posited in sense-awareness. A definite event-particle is defined in
reference to a definite punct in the following manner: Let the condition
{sigma} mean the property of covering all the abstractive elements which
are members of that punct; so that an abstractive set which satisfies
the condition {sigma} is an abstractive set which covers every
abstracti