A member of the subjective species is, in its primary character, an element in the definiteness of the subjective form of a feeling. It is a determinate way in which a feeling can feel. It is an emotion, or an intensity, or an adversion, or an aversion, or a pleasure, or a pain. It de- fines the subjective form of feeling of one actual entity. A, may be that component of A’s constitution through which A is objectified for B. Thus when B feels Aj, it feels ‘A with that feeling.’ In this way, the eternal ob- ject which contributes to the definiteness of A’s feeling becomes an eternal object contributing to the definite- ness of A as an objective datum in B’s prehension of A. The eternal object can then function both subjectively and relatively. It can be a private element in a subjec- tive form, and also an agent in the objectification. In this latter character it may come under the operation of the category of transmutation and become a character- istic of a nexus as objectified for a percipient.
In the first stage of B’s physical feeling, the subjective form of B’s feeling is conformed to the subjective form of A’s feeling. Thus this eternal object in B’s experience will have a two-way mode of functioning. It will be among the determinants of A for B, and it will be among
Coordinate Division 447
the determinants of B’s way of sympathy with A. The
intensity of physical energy belongs to the subjective
species of eternal objects, but the peculiar form of the
flux of energy belongs to the objective species.
For example, ‘redness’ may first be the definiteness of an emotion which is a subjective form in the experience of A; it then becomes an agent whereby A is objectified for B, so that A is objectified in respect to its prehension with this emotion. But A may be only one occasion of a nexus, such that each of its members is objectified for B by a prehension with an analogous subjective form. Then by the operation of the category of transmutation, the nexus is objectified for B as illustrated by the charac- teristic ‘redness.’ The nexus will also be illustrated by its mathematical forms which are eternal objects of the objective species.
The feelings—or, more accurately, the quasi-feelings— introduced by the coordinate division of actual entities eliminate the proper status of the subjects entertaining the feelings. For the subjective forms of feelings are only explicable by the categoreal demands arising from the unity of the subject. Thus the coordinate division of an actual entity produces feelings whose subjective forms are partially eliminated and partially inexplicable. But this mode of division preserves undistorted the elements of definiteness introduced by eternal objects of the objective species.
Thus in so far as the relationships of these feelings require an appeal to subjective forms for their explana- tion, the gap must be supplied by the introduction of arbitrary laws of nature regulating the relations of inten- sities. Alternatively, the subjective forms become arbi- trary epiphenomenal facts, inoperative in physical nature, though claiming operative importance.
The order of nature, prevalent in the cosmic epoch in question, exhibits itself as a morphological scheme in-
448 Process and Reality
volving eternal objects of the objective species. The most fundamental elements in this scheme are those eternal objects in terms of which the general principles of coordinate division itself are expressed. These eternal objects express the theory of extension in its most gen- eral aspect. In this theory the notion of the atomicity of actual entities, each with its concrescent privacy, has been entirely eliminated. We are left with the theory of extensive connection, of whole and part, of points, lines, and surfaces, and of straightness and flatness.
The substance of this chapter can be recapitulated in a summary: Genetic division is concerned with an actual occasion in its character of a concrescent immediacy. Coordinate division is concerned with an actual occasion in its character of a concrete object. Thus for genetic division the primary fact about an occasion is its initial ‘dative’ phase; for coordinate division the primary fact is the final ‘satisfaction.’ But with the attainment of the ‘satisfaction,’ the immediacy of final causation is lost, and the occasion passes into its objective immortality, in virtue of which efficient causation is constituted. Thus in coordinate division we are analysing the complexity of the occasion in its function of an efficient cause. It is in this connection that the morphological scheme of ex- tensiveness attains its importance. In this way we obtain an analysis of the dative phase in terms of the ‘satisfactions’ of the past world. These satisfactions are systematically disposed in their relative status, according as one is, or is not, in the actual world of another. Also they are divisible into prehensions which can be treated as quasi-actualities with the same morphological system of relative status. This morphological system gains special order from the defining characteristic of the pres- ent cosmic epoch. The extensive continuum is this spe- cialized ordering of the concrete occasions and of the prehensions into which they are divisible.
Extensive Connection
in this chapter we enumerate the chief characteristics of the physical relationship termed ‘extensive connection.’ We also enumerate the derivative notions which are of importance in our physical experience. This importance has its origin in the characteristics enumerated. The definitions of the derivative notions, as mere definitions, are equally applicable to any scheme of relationship whatever its characteristics. But they are only of im- portance when the relationship in question has the char- acteristics here enumerated for extensive connection.
No attempt will be made to reduce these enumerated
characteristics to a logical minimum from which the
remainder can be deduced by strict deduction. There is
not a unique set of logical minima from which the rest
can be deduced. There are many such sets. The investi-
gation of such sets has great logical interest, and has an
importance which extends beyond logic. But it is irrele-
vant for the purposes of this discussion.
For the sake of brevity the terms ‘connection’ and ‘connected’ will be used in the place of ‘extensive connec- tion’ and ‘extensively connected.’ The term ‘region’ will be used for the relata which are involved in the scheme of ‘extensive connection.’ Thus, in the shortened phrase- ology, regions are the things which are connected.
A set of diagrams will illustrate the type of relationship
meant by ‘connection.’ The two areas, A and B, in each
diagram exhibit an instance of connection with each
other.
450 Process and Reality
DIAGRAMS I
(i) (ii)
A (CQ)
(iii) (iv)
a Cag
(v) (vi)
Such diagrams are apt to be misleading: for one reason,
because they introduce features as obvious, which it is
our business to define in terms of our fundamental notion
of ‘connection’; for another reason, because they intro-
duce features which are special to the two-dimensional,
spatial extensiveness of a sheet of paper.
In the three diagrams of Set II, the areas, A and B,
are not connected; but they are ‘mediately’ connected by
the area C.
Definition 1. Two regions are ‘mediately’ connected when they are both connected with a third region.
Assumption 1. Connection and mediate connection are
both of them symmetrical relations; that is to say, if
region A is connected, or mediately connected, with region
B, then region B is connected, or mediately connected,
with region A.
Extensive Connection 451
Diagrams Ii
(i) (ii)
(iii)
It is obvious that the part of this assumption which
concerns mediate connection can be proved from the
terms of the definition. In the subsequent development
of definitions and assumptions we shall not draw atten-
tion to such instances of the possibility of proof.
Assumption 2. No region is connected with all the
other regions; and any two regions are mediately
connected.
Assumption 3. Connection is not transitive; that is to
say, if A be connected with B, and B with C, it does not
thereby follow that A is connected with C; though in cer-
tain cases it does happen that A is connected with C.
Assumption 4. No region is connected, or mediately connected, with itself.
452 Process and Reality
This assumption is merely a convenient arrangement of nomenclature.
Definition 2. Region A is said to ‘include’ region B
when every region connected with B is also connected
with A. As an alternative nomenclature, region B will
be said to be ‘part’ of region A.
This definition of ‘inclusion’ is due to Professor de
Laguna; it constitutes an important addition to the
theory of extension. In such investigations, as the pres-
ent one, the definitions are the really vital portion of
the subject.
Assumption 5. When one region includes another, the two regions are connected.
Assumption 6. The relation of inclusion is transitive.
Assumption 7. A region does not include itself.
Assumption 8. The relation of inclusion is asymmetri-
cal; that is to say, if A includes B, then B does not
include A.
Assumption 9. Every region includes other regions;
and a pair of regions thus included in one region are not
necessarily connected with each other. Such pairs can
always be found, included in any given region.
Definition 3. Two regions are said to ‘overlap,’ when there is a third region which they both include.
Assumption 10. The relation of overlapping is sym- metrical.
Assumption 11. If one region includes another region, the two regions overlap.
Assumption 12. Two regions which overlap are con- nected.
Definition 4. A ‘dissection’ of any given region A, is a
set of regions, which is such that (i) all its members are
included in A, (ii) no two of its members overlap, (iii)
any region included in A, but not a member of the set,
either is included in one member of the set, or overlaps
more than one member of the set.
Assumption 15. There are many dissections of any given region.
Extensive Connection 453
Assumption 16. A dissection of a region is not a dissec- tion of any other region.
Definition 5. A region is called an ‘intersect’ of two
overlapping regions, A and B, when (i) either it is in-
cluded in both A and B, or it is one of the two regions
and is included in the other, and (ii) no region, also in-
cluded in both A and B, can overlap it without being
included in it.
Definition 6. 1. If there be one, and only one, inter-
sect of two regions, A and B, those regions are said to
overlap with ‘unique intersection’; if there be more than
one intersect, they are said to overlap with ‘multiple
intersection.’
Assumption 17. Any region included in both of two
overlapping regions, and not itself an intersect, is included
in one, and only one, intersect.
Assumption 18. If A includes B, then B is the sole intersect of A and B.
Assumption 19. An intersect of two regions, which is not one of the two regions, is included in both regions.
Assumption 20. Each pair of overlapping regions has at least one intersect.
Definition 7. Two regions are ‘externally’ connected when (i) they are connected, and (ii) they do not over- lap. The possibility of this definition is another of the advantages gained from the adoption of Professor de Laguna’s starting point, ‘extensive connection,’ over my original starting point,’ ‘extensive whole and extensive part.’ External connection is illustrated by diagrams (v) and (vi) in Set I of the diagrams. So far, we have not discriminated between the two cases illustrated respec- tively by these two diagrams. The notion of external connection is a long step towards the elaboration of the notion of a ‘surface,’ which has not yet been touched upon.
Definition 8. A region B is ‘tangentially’ included in a region A, when (i) B is included in A, and (ii) there are
1Cf. my Principles of Natural Knowledge, and Concept of Nature.
454 Process and Reality
regions which are externally connected with both A and B.
Definition 9. A region B is ‘non-tangentially’ included in a region A when (i) B is included in A, and (11) there is no third region which is externally connected with both A and B.
The possibility, at this stage, of the three definitions 7, 8, and 9, constitutes the advantage to be gained by start- ing from Professor de Laguna’s notion of ‘extensive con- nection.’ Non-tangential inclusion is illustrated by dia- gram (i) of the first set; and the two cases—as yet undis- criminated—of tangential inclusion are illustrated by diagrams (11) and (iil),
Definition 10. A set of regions is called an ‘abstractive
set,’ when (i) any two members of the set are such that
one of them includes the other non-tangentially,
(ii) there is no region included in every member of
the set.