144 Process and Reality
alike ready-made for the initial motions which the Deity
impresses throughout the universe. It is not possible to
extract from the Scholiwm—construed with misplaced
concreteness—either a theism, or an atheism, or an epis-
temology, which can survive a comparison with the facts.
This is the inescapable conclusion to be inferred from
Hume’s Dialogues Concerning Natural Religion. Biology
is also reduced to a mystery; and finally physics itself
has now reached a stage of experimental knowledge
inexplicable in terms of the categories of the Scholzwm.
In the Timaeus, there are many phrases and state- ments which find their final lucid expression in the Scholium. While noting this concurrence of the two great cosmological documents guiding Western thought, it can- not be too clearly understood that, within its limits of abstraction, what the Scholium says is true, and that it is expressed with the lucidity of genius. Thus any cos- mological document which cannot be read as an interpre- tation of the Scholium is worthless. But there is another side to the Timaeus which finds no analogy in the Scholium. In general terms, this side of the Timaeus may be termed its metaphysical character, that is to say, its endeavour to connect the behaviour of things with the formal nature of things. The behaviour apart from the things is abstract, and so are the things apart from their behaviour. Newton—wisely, for his purposes— made this abstraction which the Timaeus endeavours to avoid.
In the first place, the Timaeus connects behaviour with the ultimate molecular characters of the actual entities. Plato conceives the notion of definite societies of actual molecular entities, each society with its defining charac- teristics. He does not conceive this assemblage of soci- eties as causa sui. But he does conceive it as the work of subordinate deities, who are the animating principles of those departments of nature. In Greek thought, either poetic or philosophic, the separation between the qvotc and such deities had not that absolute character which it has for us who have inherited the Semitic Jehovah.
Rhe Order of Nature 145
Newton could have accepted a molecular theory as easily as Plato, but there is this difference between them: Newton would have been surprised at the modern quan- tum theory and at the dissolution of quanta into vibra- tions; Plato would have expected it. While we note the many things said by Plato in the Timaeus which are now foolishness, we must also give him credit for that aspect of his teaching in which he was two thousand years ahead of his time. Plato accounted for the sharp-cut differences between kinds of natural things, by assuming an approxi- mation of the molecules of the fundamental kinds respectively to the mathematical forms of the regular solids. He also assumed that certain qualitative con- trasts in occurrences, such as that between musical notes, depended on the participation of these occurrences in some of the simpler ratios between integral numbers. He thus obtained a reason why there should be an approxi- mation to sharp-cut differences between kinds of mole- cules, and why there should be sharp-cut relations of harmony standing out amid dissonance. Thus ‘contrast’ —as the opposite of incompatibility—depends on a cer- tain simplicity of circumstance; but the higher contrasts depend on the assemblage of a multiplicity of lower con- trasts, this assemblage again exhibiting higher types of simplicity.
It is well to remember that the modern quantum- theory, with its surprises in dealing with the atom, is only the latest instance of a well-marked character of nature, which in each particular instance is only explained by some ad hoc dogmatic assumption. The theory of biological evolution would not in itself lead us to expect the sharply distinguished genera and species which we find in nature. There might be an occasional bunching of individuals round certain typical forms; but there is no explanation of the almost complete absence of inter- mediate forms. Again Newton’s Scholiuwm gives no hint of the ninety-two possibilities for atoms, or of the limited number of ways in which atoms can be combined so as to form molecules. Physicists are now explaining these
146 Process and Reality
chemical facts by means of conceptions which Plato would have welcomed.
There is another point in which the organic philosophy only repeats Plato. In the Timaeus the origin of the present cosmic epoch is traced back to an aboriginal dis- order, chaotic according to our ideals. This is the evolu- tionary doctrine of the philosophy of organism. Plato’s notion has puzzled critics who are obsessed with the Semitic * theory of a wholly transcendent God creating out of nothing an accidental universe. Newton held the Semitic theory. The Scholium made no provision for the evolution of matter—very naturally, since the topic lay outside its scope. The result has been that the non- evolution of matter has been a tacit presupposition throughout modern thought. Until the last few years the sole alternatives were: either the material universe, with its present type of order, is eternal; or else it came into being, and will pass out of being, according to the fiat of Jehovah. Thus, on all sides, Plato’s allegory of the evolution of a new type of order based on new types of dominant societies became a daydream, puzzling to commentators.
Milton, curiously enough, in his Paradise Lost wavers between the Timaeus and the Semitic doctrine. This is only another instance of the intermixture of classical and Hebrew notions on which his charm of thought depends. In the description of Satan’s journey across Chaos, Satan discovers
The secrets of the hoary deep, a dark
Illimitable ocean, without bound,
Without dimension, where length, breadth and highth, And time and’ place are lost; where eldest night
And Chaos, ancestors of Nature, hold
Eternal anarchy amidst the noise
Of endless wars, and by confusion stand.°
Milton is here performing for Plato the same poetic service that Lucretius performed for Democritus—with
° The book of Genesis is too primitive to bear upon this point. °Cf Paradise Lost, Bk. II.
The Order of Nature 147
less justification, since Plato was quite capable of being his own poet. Also the fact of Satan’s journey helped to evolve order; for he left a permanent track, useful for the devils and the damned.
The appeal to Plato in this section has been an appeal to the facts against the modes of expression prevalent in the last few centuries. These recent modes of expression are partly the outcome of a mixture of theology and philosophy, and are partly due to the Newtonian physics, no longer accepted as a fundamental statement. But language and thought have been framed according to that mould; and it is necessary to remind ourselves that this is not the way in which the world has been described by some of the greatest intellects. Both for Plato and for Aristotle the process of the actual world has been conceived as a real incoming of forms into real poten- tiality, issuing into that real togetherness which is an actual thing. Also, for the Timaeus, the creation of the world is the incoming of a type of order establishing a cosmic epoch. It is not the beginning of matter of fact, but the incoming of a certain type of social order.
The remainder of this chapter will be devoted to a
discussion—largely conjectural—of the hierarchy of soci-
eties composing our present epoch. In this way, the
preceding discussion of ‘order’ may be elucidated. It is
to be carefully noted that we are now deserting meta-
physical generality. We shall be considering the more
special possibilities of explanation consistent with our
general cosmological doctrine, but not necessitated by it.
The physical world is bound together by a general type
of relatedness which constitutes it into an extensive con-
tinuum. When we analyse the properties of this con-
tinuum we discover that they fall into two classes, of
which one—the more special—presupposes the other—
the more general.*® The more general type of properties
1° Cf. Part IV for a detailed discussion.
148 Process and Reality
expresses the mere fact of ‘extensive connection,’ of
‘whole and part,’ of various types of ‘geometrical ele-
ments’ derivable by ‘extensive abstraction’; but exclud-
ing the introduction of more special properties by which
straight lines are definable ** and measurability thereby
introduced.
In these general properties of extensive connection, we discern the defining characteristic of a vast nexus extend- ing far beyond our immediate cosmic epoch. It contains in itself other epochs, with more particular character- istics incompatible with each other. Then from the standpoint of our present epoch, the fundamental society in so far as it transcends our own epoch seems a vast confusion mitigated by the few, faint elements of order contained in its own defining characteristic of ‘extensive connection.’ We cannot discriminate its other epochs of vigorous order, and we merely conceive it as harbouring the faint flush of the dawn of order in our own epoch. This ultimate, vast society constitutes the whole environ- ment within which our epoch is set, so far as systematic characteristics are discernible by us in our present stage of development. In the future the growth of theory may endow our successors with keener powers of discern- ment.
Our logical analysis, in company with immediate intui- tion (inspectio), enables us to discern a more special society within the society of pure extension. This is the ‘geometrical’ society. In this society ** those specialized relationships hold, in virtue of which straight lines are defined. Systematic geometry is illustrated in such a geometrical society; and metrical relationships can be defined in terms of the analogies of function within the scheme of any one systematic geometry. These ‘analo- gies of function’ are what is meant by the notion of ‘con- gruence.’ This notion is nonsense apart from a syste- matic geometry. The inclusion of extensive quantity
*? Cf. Part IV, Ch. III, IV, V. *? Cf. Part IV, especially Ch. IPE VEY.
The Order of Nature 149
among fundamental categoreal notions is a complete mis- take. This notion is definable in terms of each systematic geometry finding its application in a geometrical society. It is to be noticed that a systematic geometry is deter- mined by the definition of straight lines applicable to the society in question. Contrary to the general opinion, this definition is possible in independence of the notion of ‘measurement.’ It cannot however be proved that in the same geometrical society there may not be competing families of loci with equal claims to the status of being a complete family of straight lines.
Given a family of straight lines, expressing a system of relatedness in a ‘geometric’ society, the notion of ‘con- gruence’ and thence of ‘measurement’ is now deter- minable in a systematic way throughout the society. But again in this case there certainly are competing systems of measurement. Hence in connection with each family of straight lines—allowing there be more than one such family—there are alternative systems ** of metrical geom- etry, no one system being more fundamental than the other. Our present cosmic epoch is formed by an ‘elec- tromagnetic’ society, which is a more special society con- tained within the geometric society. In this society yet more special defining characteristics obtain. These char- acteristics presuppose those of the two wider societies within which the ‘electromagnetic’ society is contained. But in the ‘electromagnetic’ society the ambiguity as to the relative importance of competing families of straight lines (if there be such competing families), and the am- biguity as to the relative importance of competing defini- tions of congruence, are determined in favour of one family and one ** congruence-definition. This determi- nation is effected by an additional set of physical rela- tionships throughout the society. But this set has lost
18 The existence of alternative systems was demonstrated by Cayley in his Sizth Memoir on Quantities in R. S., Trans. 13859. ;
14The transformations into an indefinite variety of coordinates, to which the ‘tensor theory’ refers, all presuppose one congruence defi- nition. The invariance of the Einsteinian ‘ds’ expresses this fact.
150 Process and Reality
its merely systematic character because it constitutes
our neighbourhood. ‘These relationships involve com-
ponents expressive of certain individual diversities, and
identities between the occasions which are the members
of the nexus. But these diversities and identities are
correlated according to a systematic law expressible in
terms of the systematic measurements derived from the
geometric nexus. We here arrive at the notion of physi-
cal quantities which vary from individual to individual;
this is the notion of the systematization of individual
differences, the notion of ‘Law.’
It is the ideal of mathematical physicists to formulate
this systematic law in its complete generality for our
epoch. It is sufficient for our purposes to indicate the
presumed character of this law by naming the members
of the society ‘electromagnetic occasions.’ Thus our pres-
ent epoch is dominated by a society of electromagnetic
occasions. In so far as this dominance approaches
completeness, the systematic law which physics seeks is
absolutely dominant. In so far as the dominance is
incomplete, the obedience is a statistical fact with its
corresponding lapses.
The electromagnetic society exhibits the physical elec-
tromagnetic field which is the topic of physical science.
The members of this nexus are the electromagnetic
occasions.
But in its turn, this electromagnetic society would pro-
vide no adequate order for the production of individual
occasions realizing peculiar ‘intensities’ of experience
unless it were pervaded by more special societies,
vehicles of such order. The physical world exhibits a
bewildering complexity of such societies, favouring each
other, competing with each other.