Strain-Locus Wholly Determined by Experient; Seat and Pro- jectors Determine Focal Region; Animal Body Sole Agent in the Determination; Vivid Display of Real Potentiality of Contemporary World; New Definition of Straight Lines Explains this Doctrine; Ways of Speech, Interpretation of Direct Observation; Descartes’ Inspectio, Realitas Objectiva, Judicium.
Modern Doctrine of Private Psychological Fields; Secondary Qualities, Sensa; Abandons Descartes’ Realitas Objectiva;
Coordinate Division 433
Difficulties for Scientific Theory, All Observation in Pri- vate Psychological Fields; Llustration, Hume; Conclusion, Mathematical Form, Presentational Immediacy in One Sense Barren, in Another Sense has Overwhelming Significance.
IV. Measurement Depends on Counting and on Permanence; What Counted, What Permanent; Yard-measure Permanent, Straight; Infinitesimals no Explanation; Approximation to Straightness, Thus Straightness Presupposed; Inches Counted, Non-coincident; Modern Doctrine is Possibility of Coincidence, Doctrine Criticized; Coincidence is Test of Con- gruence, not Meaning; Use of Instrument Presupposes its Self-congruence; Finally All Measurement Depends on Direct Intuition of Permanence of Untested Instrument; Theory of Private Psychological Fields Makes Scientific Measurement Nonsense.
V. Meaning of Congruence in Terms of Geometry of Straight Lines; Systems of Geometry; Sets of Axioms: Equivalent Sets, Incompatible Sets; Three Important Geometries, Ellip- tic Geometry, Euclidean Geometry, Hyperbolic Geometry; Two Definitions of a Plane; Characteristic Distinction between the Three Geometries; Congruence Depends on Systematic Geometry.
VI. Physical Measurement, Least Action, Presupposes Geometrical Measurement; Disturbed by Individual Peculiarities; Phys- ical Measurement Expressible in Terms of Differential Geometry; Summary of Whole Argument.
Coordinate Division
‘Section I
THERE are two distinct ways of ‘dividing’ the satisfac- tion of an actual entity into component feelings, geneti- cally and coordinately. Genetic division is division of the conerescence; coordinate division is division of the concrete. In the ‘genetic’ mode, the prehensions are exhibited in their genetic relationship to each other. The actual entity is seen as a process; there is a growth from phase to phase; there are processes of integration and of
434 Process and Reality
reintegration. At length a complex unity of objective datum is obtained, in the guise of a contrast of actual entities, eternal objects, and propositions, felt with cor- responding complex unity of subjective form. This genetic passage from phase to phase is not in physical time: the exactly converse point of view expresses the relationship of concrescence to physical time. It can be put shortly by saying, that physical time expresses some features of the growth, but not the growth of the features. The final complete feeling is the ‘satisfaction.’
Physical time makes its appearance in the ‘coordinate’
analysis of the ‘satisfaction.’ The actual entity is the
enjoyment of a certain quantum of physical time. But
the genetic process is not the temporal succession: such a
view is exactly what is denied by the epochal theory of
time. Each phase in the genetic process presupposes the
entire quantum, and so does each feeling in each phase.
The subjective unity dominating the process forbids the
division of that extensive quantum which originates with
the primary phase of the subjective aim. The problem
dominating the concrescence is the actualization of the
quantum 2n solido. The quantum is that standpoint in
the extensive continuum which is consonant with the
subjective aim in its original derivation from God. Here
‘God’ is that actuality in the world, in virtue of which
there is physical ‘law.’
There is a spatial element in the quantum as well as a temporal element. Thus the quantum is an extensive region. This region is the determinate basis which the concrescence presupposes. This basis governs the ob- jectifications of the actual world which are possible for the novel concrescence. The coordinate divisibility of the satisfaction is the ‘satisfaction’ considered in its rela- tionship to the divisibility of this region.
The concrescence presupposes its basic region, and not the region its concrescence. Thus the subjective unity of the concrescence is irrelevant to the divisibility of the
Coordinate Division 435
region. In dividing the region we are ignoring the sub-
jective unity which is inconsistent with such division.
But the region is, after all, divisible, although in the
genetic growth it is undivided.
So this divisible character of the undivided region is
reflected into the character of the satisfaction. When
we divide the satisfaction coordinately, we do not find
feelings which are separate, but feelings which might be
separate. In the same way, the divisions of the region
are not divisions which are; they are divisions which
might be. Each such mode of division of the extensive
region yields ‘extensive quanta’: also an ‘extensive quan-
tum’ has been termed a ‘standpoint.’ This notion of a
‘standpoint’ must now be briefly explained.
The notion has reference to three allied doctrines. First, there is the doctrine of ‘the actual world’ as receiv- ing its definition from the immediate concrescent actu- ality in question. Each actual entity arises out of its own peculiar actual world. Secondly, there is the doc- trine of each actual world as a ‘medium.’ According to this doctrine, if S be the concrescent subject in question, and A and B be two actual entities in its actual world, then either A is in the actual world of B, or B is in the actual world of A, or A and B are contemporaries. If, for example, A be in the actual world of B, then for the immediate subject S there are (1) the direct objectifica- tion of A in S, and (2) the indirect objectification by reason of the chain of objectification, A in B and B in S. Such chains can be extended to any length by the inclu- sion of many intermediate actualities between A and S.
Thirdly, it is to be noticed that ‘decided’ conditions
are never such as to banish freedom. They only qualify
it. There is always a contingency left open for immediate
decision. This consideration is exemplified by an inde-
termination respecting ‘the actual world’ which is to
decide the conditions for an immediately novel concres-
cence. There are alternatives as to its determination,
which are left over for immediate decision. Some actual
436 Process and Reality
entities may be either in the settled past, or in the con- temporary nexus, or even left to the undecided future, according to immediate decision. Also the indirect chains of successive objectifications will be modified according to such choice. These alternatives are represented by the indecision as to the particular quantum of extension to be chosen for the basis of the novel concrescence.
The sense in which the coordinate divisions of the
satisfaction are ‘feelings which might be separate,’ has
now to be discussed.
Each such coordinate division corresponds to a defi- nite sub-region of the basic region. It expresses that component of the satisfaction which has the character of a unified feeling of the actual world from the stand- point of that sub-region. In so far as the objectification of the actual world from this restricted standpoint is concerned, there is nothing to distinguish this coordinate division from an actual entity. But it is only the physi- cal pole of the actual entity which is thus divisible. The mental pole is incurably one. Thus the subjective form of this coordinate division is derived from the origination of conceptual feelings which have regard to the complete region, and are not restricted to the sub-region in ques- tion. In other words, the conceptual feelings have regard to the complete actual entity, and not to the coordinate division in question. Thus the whole course of the gene- tic derivation of the coordinate division is not explicable by reference to the categoreal conditions governing the concrescence of feeling arising from the mere physical feeling of the restricted objective datum. The origina- tive energy of the mental pole constitutes the urge whereby its conceptual prehensions adjust and readjust subjective forms and thereby determine the specific modes of integration terminating in the ‘satisfaction.’
It is obvious that in so far as the mental pole is trivial
Coordinate Division 437
as to originality, what is inexplicable in the co-
ordinate division (taken as actually separate) becomes
thereby trivial. Thus for many abstractions concerning
low-grade actual entities, the coordinate divisions
approach the character of being actual entities on the
same level as the actual entity from which they are
derived.
It is thus an empirical question to decide in relation to special topics, whether the distinction between a coordi- nate division and a true actual entity is, or is not, rele- vant. In so far as it is not relevant we are dealing with an indefinitely subdivisible extensive universe.
A coordinate division is thus to be classed as a generic contrast. The two components of the contrast are, (1) the parent actual entity, and (ii) the proposition which is the potentiality of that superject having arisen from the physical standpoint of the restricted sub-region. The proposition is thus the potentiality of eliminating from the physical pole of the parent entity all the objectified actual world, except those elements derivable from that standpoint; and yet retaining the relevant elements of the subjective form.
The unqualified proposition is false, because the mental pole, which is in fact operative, would not be the mental pole under the hypothesis of the proposition. But, for many purposes, the falsity of the proposition is irrelevant. The proposition is very complex; and with the relevant qualifications depending on the topic in question, it expresses the truth. In other words, the unqualified false proposition is a matrix from which an indefinite number of true qualified propositions can be derived. The requi- site qualification depends on the special topic in ques- tion, and expresses the limits of the application of the unqualified proposition relevantly to that topic.
The unqualified proposition expresses the indefinite
divisibility of the actual world; the qualifications express
the features of the world which are lost sight of by the
438 Process and Reality
unguarded use of this principle. The actual world is atomic; but in some senses it is indefinitely divisible.
The atomic actual entities individually express the genetic unity of the universe. The world expands through recurrent unifications of itself, each, by the addi- tion of itself, automatically recreating the multiplicity anew.
The other type of indefinite multiplicity, introduced by the indefinite coordinate divisibility of each atomic actu- ality, seems to show that, at least for certain purposes, the actual world is to be conceived as a mere indefinite multiplicity.
But this conclusion is to be limited by the principle of
‘extensive order’ which steps in. The atomic unity of
the world, expressed by a multiplicity of atoms, is now
replaced by the solidarity of the extensive continuum.
This solidarity embraces not only the coordinate divi-
sions within each atomic actuality, but also exhibits
the coordinate divisions of all atomic actualities from
each other in one scheme of relationship.
In an earlier chapter (Part II, Ch. VIII, Sects. IV to IX) the sense, in which the world can be conceived as a medium for the transmission of influences, has been dis- cussed. This orderly arrangement of a variety of routes of transmission, by which alternative objectifications of an antecedent actuality A can be indirectly received into the constitution of a subsequent actuality B, is the foundation of the extensive relationship among diverse actual entities. But this scheme of external extensive relationships links itself with the schemes of internal division which are internal to the several actual entities. There is, in this way, one basic scheme of extensive con- nection which expresses on one uniform plan, (i) the general conditions to which the bonds, uniting the atomic actualities into a nexus, conform, and (ii) the general conditions to which the bonds, uniting the infinite num-
Coordin Ale Devislon 439
ber of coordinate subdivisions of the satisfaction of any actual entity, conform.
As an example of (ii), suppose that P is a coordinate division of an actual occasion A. Then P can be con- ceived as an actual occasion with its own actual world forming its initial datum in its first phase of genetic origination. In fact, P is the hypothetical satisfaction of a hypothetical process of concrescence with this stand- point. The other coordinate divisions of A are either in the ‘actual world’ for P, or are contemporary with P, or are coordinate divisions of P, or have a complex relation to P expressed by the property that each one of them is coordinately divisible into prehensions Q, Q, .. ., such that each of them has one or either of the three above- mentioned relations to P.
Further, in addition to the merely potential subdivi- sions of a satisfaction into coordinate feelings, there is the merely potential aggregation of actual entities into a super-actuality in respect to which the true actualities play the part of coordinate subdivisions. In other words, just as for some purposes, one atomic actuality can be treated as though it were many coordinate actualities, in the same way, for other purpose, a nexus of many actualities can be treated as though it were one actuality. This is what we habitually do in the case of the span of life of a molecule, or of a piece of rock, or of a human body.