Part II, Chapter II, Section ii
(Macmillan 1929,  pp. 104-107)

Actual entities atomize the extensive continuum. This
continuum is in itself merely the potentiality for division;
an actual entity effects this division. The objectification
of the contemporary world merely expresses that world
in terms of its potentiality for subdivision and in terms
of the mutual perspectives which any such subdivision
will bring into real effectiveness. These are the primary
governing data for any actual entity; for they express
how all actual entities are in the solidarity of one world.
With the becoming of any actual entity what was
previously potential in the space-time continuum is now
the primary real phase in something actual. For each
process of concrescence a regional standpoint in the world,
defining a limited potentiality for objectifications, has
been adopted. In the mere extensive continuum there
is no principle to determine what regional quanta shall
be atomized, so as to form the real perspective standpoint
for the primary data constituting the basic phase in the
concrescence of an actual entity. The factors in the
actual world whereby this determination is effected will
be discussed at a later stage of this investigation. They
constitute the initial phase of the 'subjective aim.' This
initial phase is a direct derivate from God's primordial
nature. In this function, as in every other, God is the
organ of novelty, aiming at intensification.

In the mere continuum there are contrary poten-
tialities; in the actual world there are definite atomic
actualities determining one coherent system of real divi-
sions throughout the region of actuality. Every actual
entity in its relationship to other actual entities is in
this sense somewhere in the continuum, and arises out of
the data provided by this standpoint. But in another
sense it is everywhere throughout the continuum; for its
constitution includes the objectifications of the actual
world and thereby includes the continuum; also the

THE EXTENSIVE CONTINUUM       106

potential objectifications of itself contribute to the real
potentialities whose solidarity the continuum expresses.
Thus the continuum is present in each actual entity, and
each actual entity pervades the continuum.

This conclusion can be stated otherwise. Extension,
apart from its spatialization and temporalization, is that
general scheme of relationships providing the capacity
that many objects can be welded into the real unity of
one experience. Thus, an act of experience has an objec-
tive scheme of extensive order by reason of the double
fact that its own perspective standpoint has extensive
content, and that the other actual entities are objectified
with the retention of their extensive relationships. These
extensive relationships are more fundamental than their
more special spatial and temporal relationships. Exten-
sion is the most general scheme of real potentiality, pro-
viding the background for all other organic relations.
The potential scheme does not determine its own atomiza-
tion by actual entities. It is divisible; but its real divi-
sion by actual entities depends upon more particular
characteristics of the actual entities constituting the ante-
cedent environment. In respect to time, this atomization
takes the special form" of the 'epochal theory of time.'
In respect to space, it means that every actual entity in
the temporal world is to be credited with a spatial volume
for its perspective standpoint. These conclusions are
required by the consideration of Zeno's arguments, in
connection with the presumption that an actual entity is
an act of experience. The authority of William James
can be quoted in support of this conclusion. He writes:
"Either your experience is of no content, of no change, or
it is of a perceptible amount of content or change. Your
acquaintance with reality grows literally by buds or drops
of perception. Intellectually and on reflection you can
divide these into components, but as immediately given,

² Cf. my Science and the Modern World, Ch. VII.
⁸ Cf. loc. cit. and Part IV of the present work.

106              PROCESS AND REALITY

they come totally or not at all." * James also refers to
Zeno. In substance I agree with his argument from Zeno;
though I do not think that he allows sufficiently for those
elements in Zeno's paradoxes which are the product of
inadequate mathematical knowledge. But I agree that
a valid argument remains after the removal of the invalid
parts.

The argument, so far as it is valid, elicits a contradic-
tion from the two premises: (i) that in a becoming some-
thing (res vera) becomes, and (ii) that every act of
becoming is divisible into earlier and later sections which
are themselves acts of becoming. Consider, for example,
an act of becoming during one second. The act is divisible
into two acts, one during the earlier half of the second,
the other during the later half of the second. Thus that
which becomes during the whole second presupposes that
which becomes during the first half-second. Analogously,
that which becomes during the first half-second presup-
poses that which becomes during the first quarter-second,
and so on indefinitely. Thus if we consider the process
of becoming up to the beginning of the second in question,
and ask what then becomes, no answer can be given. For,
whatever creature we indicate presupposes an earlier
creature which became after the beginning of the second
and antecedently to the earlier creature. Therefore there
is nothing which becomes, so as to effect a transition into
the second in question.

The difficulty is not evaded by assuming that something
becomes at each non-extensive instant of time. For at
the beginning of the second of time there is no next
instant at which something can become.

Zeno in his 'Arrow in Its Flight' seems to have had an
obscure grasp of this argument. But the introduction of
motion brings in irrelevant details. The true difficulty is
to understand how the arrow survives the lapse of time.

* Cf. Some Problems in Philosophy, Cf. X; my attention was drawn
to _ this passage by its quotation in Religion in The Philosophy of
William James, by Professor J. S. Bixler.