Process and Reality — the Gifford Lectures, 1929

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 Congruence, 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, Elliptic 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; Physical Measurement Expressible in Terms of Differential Geometry; Summary of Whole Argument.

CHAPTER I

COORDINATE DIVISION

‘SECTION I

THERE are two distinct ways of ‘dividing’ the satisfaction of an actual entity into component feelings, genetically 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 ofp. 434 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 corresponding 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 objectifications of the actual world which are possible for the novel concrescence. The coordinate divisibility of the satisfaction is the ‘satisfaction’ considered in its relationship 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 thep. 435 region. In dividing the region we are ignoring the subjective 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 quantum’ 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 receiving its definition from the immediate concrescent actuality in question. Each actual entity arises out of its own peculiar actual world. Secondly, there is the doctrine 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 objectification 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 inclusion 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 indetermination respecting ‘the actual world’ which is to decide the conditions for an immediately novel concrescence. There are alternatives as to its determination, which are left over for immediate decision. Some actualp. 436 entities may be either in the settled past, or in the contemporary 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.

SECTION II

The sense in which the coordinate divisions of the satisfaction are ‘feelings which might be separate,’ has now to be discussed.