Whitehead’S Philosophy of Time 9780231899529

Table of contents :
Preface
Contents
Introduction
CHAPTER I. A Preliminary Account of Time and Nature
CHAPTER II. Temporal Transition and Atomic Events
CHAPTER III. The Theory of Extensive Abstraction
CHAPTER IV. The Order of Durations
CHAPTER V. The Reality of Space-Time
Glossary
Selective Bibliography
Notes

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WHITEHEAD'S

Philosophy of Time

WHITEHEAD'S

Philosophy of Time

William W . Hammerschmidt St. John's College in Annapolis

King's Crown Press, New York, 1947

Copyright 1 9 4 7 by WILLIAM W .

Printed by the

in the

Vermont

HAMMERSCHMIDT

United Printing

States Co.,

of

America

Brattleboro,

Vt.

KING'S CROWN PRESS

is a division of Columbia University Press organized for the purpose of making certain scholarly material available at minimum cost. Toward that end, the publishers have adopted every reasonable economy except such as would interfere with a legible format. The work is presented substantially as submitted by the author, without the usual editorial attention of Columbia Unitenity Press.

Preface IN WRITING this bode I have become indebted to many friends who have helped me by their criticism. I especially want to thank Dean Cunningham and Professors Sabine, Burtt, Church, Robinson and Smart who are or formerly were at the Sage School of Philosophy of Cornell University, Dr. John Coleman, Mr. Thomas Brady, and Dr. Mason Gross. My wife has helped me greatly throughout the writing of this essay. The Macmillan Company, Cambridge University Press, The University of California Press and Methuen & Co., Ltd. have generously granted permission to quote from books published by them. WILLIAM W .

St. John's College Annapolis, Maryland

HAMMERSCHMIDT

Contents INTRODUCTION

1

Chapter I A PRELIMINARY A C C O U N T O F T I M E AND N A T U R E

1.1

The Basis for the Theory of Time

3

1.2

The General Nature of Time

4

1.3

The Stages of Whitehead's Thought

7

1.4

Passage, Conformation, and Process

8

1.5

The Analysis of Nature in the Early Period (1900-1924)

9

1.6

The Transitional Period (1926-1929)

13

1.7

Process and Reality and Subsequent Works (1929-1939)

15

Chapter II T E M P O R A L T R A N S I T I O N AND A T O M I C E V E N T S

2.1

Introduction to Whitehead's Polemic on Temporal Transition

2.2

The Polemic against Simple Real Points of Time

19

2.3

The Polemic against Simple Real Points of Space

22

2.4

The Polemic against Infinitely Divisible Events

23

2.5

The Solution of the Problem of Becoming: the Early Period

26

2.6

The Solution of the Problem of Becoming: Science and the Modern World

26

2.7

The Solution of the Problem of Becoming: Religion in the Making, Time

29

2.8

The Solution of the Problem of Becoming: Process Reality

29

2.9

Atomism and Continuity

18

and 32

2.10 Criticism of Whitehead

34

2.11 Summary

37

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Chapter III T H E T H E O R Y OF EXTENSIVE ABSTRACTION 3.1

Introduction

38

3.2

The Basis of Whitehead's Analysis of Nature

39

3.3

Whitehead's Treatment of Velocity

40

3.4

Whitehead's Approach to Uniform Geometrical Elements

42

3.5

Final Survey of the Polemic against Instants

42

3.6

"Extension" and "Extensive Connection"

43

3.7

An Abstractive Set

44

3.8

Consideration of a Possible Objection to Abstractive Sets

46

3.9

Deduction of the Geometrical Elements

47

3.10

Continuity

48

3.11

Summary

48

Chapter IV T H E ORDER OF DURATIONS 4.1

Introduction

50

4.2

Our Four-Dimensional Space-Time

50

4.3

A Preface to a Discussion of Durations

51

4.4

Durations in Whitehead's Early and Transitional Periods

52

4.5

The Relativity of Durations in Whitehead's Early and Transitional Periods

53

The Relativity of Durations in Whitehead's Early and Transitional Periods (continued)

54

4.7

Space-Time Regions in Process and Reality: Causal Efficacy

58

4.8

Space-Time Regions in Process and Reality: Immediacy

62

4.6

Presentational

4.9

Remarks on Whitehead's Attempt to Obtain a Causal Theory of Time

63

4.10

Empiricism and the Space-Time of Causal Efficacy

65

4.11

The Presented Duration and the Concept of Rest

66

4.12

Empiricism and the Space-Time of Presentational Immediacy

68

Contents

ix

4.13 A Summary of the Alternative Derivations in the Theory of Extensive Abstraction

69

4.14 Temporal Order and Spatial Order

71

4.15 Summary

71 Chapter V T H E REALITY OF S P A C E - T I M E

5.1

Introduction

74

5.2

The Early Period: Absolute Time

75

5.3

The Early Period: Time and Eternal Objects

76

5.4

The Early Period: Time as Extension

78

5.5

The Early Period: the Present

78

5.6

The Early Period: the Past and the Future

79

5.7

Science and the Modern World

81

5.8

Time (1926)

83

5.9

Introduction to Time in Process and Reality

85

5.10 Time in Causal Efficacy: the Transitive Aspect

85

5.11 Time in Causal Efficacy: the Extensive Aspect

87

5.12 Time in Causal Efficacy: the Present

87

5.13 Time in Causal Efficacy: the Past and the Future

88

5.14 Time in Causal Efficacy: the Past and the Future (continued)

90

5.15 Time in Presentational Immediacy

92

5.16 Presentational Immediacy in Symbolism

92

5.17 Presentational Immediacy in Process and Reality

94

5.18 Summary

96

5.19 Some Personal Remarks on Whitehead's Space-Times

97

GLOSSARY

101

SELECTIVE BIBLIOGRAPHY

103

NOTES

105

Introduction THIS TREATISE is not an attempt to discuss all of Whitehead's philosophy. In the last fifteen years Whitehead has written in many fields. Aesthetics and general value-theory, religion, history, and contemporary society are included in his purview. While a study of these fields is essential to a full appreciation of Whitehead as a philosopher, I shall confine my discussion to that side of his work which represents at once his greatest ability and his most finished achievement, namely, his theory of process taken in its spatio-temporal aspect. Between his fortieth and sixty-fourth years (1901-1925), Whitehead published but a f e w important works that were not essentially a discussion of the spatio-temporal structure of nature and related concepts. And in his greatest work, Process and Reality, his treatment of space-time is the core of the metaphysical position he adopts. T h e course of this monograph will show the intricacy which his analysis of space-time attains and will indicate the importance of spatio-temporal considerations to his whole philosophy. Whitehead arrives at certain basic concepts implied by space-time, and he works out different phases of the subject with rigor and in detail. But he never collates all of these scattered reflections, nor does he arrange them in a logical order. My aim will be to do this work, and, if I am successful, a reader will find in this book a manageable basis for the criticism of Whitehead's writings on space-time. I am aware of the danger to accurate exegesis of giving Whitehead's writings more organization than he himself has given them. But the order in which I have arranged them, even in the instances where it is rather arbitrary, should not affect a reader's interpretation of the passages. Often it is a necessary arrangement dictated by the content of the passages. Even when this is not so, my rearrangement of his ideas adds nothing to them—it represents the introduction into the subject of no new content. My main analysis will center on the temporal properties of space-

2

Whitehead's Philosophy of Time

time, insofar as one can make a valid separation of time from spacetime. As the reader follows the exposition in the following pages, he will see for himself to what extent a theory of time involves a theory of space.

C H A P T E R

I

Λ Preliminary Account of Time and Nature It is hardly more than a pardonable exaggeration to say that the determination of the meaning of nature reduces itself principally to a discussion of the character of time and the character of space. — T H E C O N C E P T OF N A T U R E , P . 3 3

WHITEHEAD'S PHILOSOPHY contains many novel concepts, which led him to devise a special terminology for their treatment. Thus an attempt to understand his ideas is a technical undertaking which should not be started until one has acquainted himself with the key words in Whitehead's dictionary. This is especially important because Whitehead does not have just one system of thought, but three different systems, which represent a progress and development of his ideas. The full connotation of Whitehead's terms will not become clear until he has been carefully studied. Nevertheless a preliminary account of these terms and the context in which they are used may enable the reader to read Whitehead with more understanding than if he were to start in de novo. Therefore in this chapter I shall present a brief account of Whitehead's three theories of nature, with special emphasis on the terminology that he uses and the framework of ideas in which the theories are embedded. I.I

The basis for the theory of

time.

The unique features of Whitehead's philosophy of time derive from his belief that the analysis of nature should start with its perceivable properties, and proceed from them, rather than starting with any purely mental abstractions or with intuited or a priori data. 1 Whitehead believes that the fundamental properties of space-time may be perceived in an immediate empirical experience, 2 although in different periods of his thought he has different conceptions of the exact nature of this experience.* He consistently maintains this empirical bias, be•cf. 1.5, 1.6, 1.7.

4

Whitehead's

Philosophy

of Time

Iieving that spatio-temporal characters which are not immediate data of perception must at least be logically implied by such data. ι .2 The general

nature of

time.

There are several general presuppositions upon which Whitehead's theory of time depends. First, in Whitehead's opinion time is only one side of space-time and is an abstraction insofar as it ignores the spatial side of what is really a single manifold. 3 But although "there can be no time apart from space, and no space apart from time," 4 still space and time are quite readily distinguishable by everyone3 and may be treated in partial independence of each other6 for expository and critical purposes. The distinction between them can be expressed by saying that space exhibits the order and relations of events within a present, while time exhibits the relation of other events to those in a given present.7 Second, for Whitehead time is a succession of extended presents which constitute real extended "strata" of nature.8 There is a sharp distinction between the reality of a present and the reality of a past or future. And no present can be instantaneous; its existence requires its temporal extension. Third, time is measurable.® The passage of something without spatial extension is not directly measurable. Therefore the passage of that which is not spatially extended is not in time in Whitehead's sense. 10 This restriction on the use of the word time, it should be noted, is purely an arbitrary usage which he imposes to facilitate a discussion of the subject. Fourth, the advance of time is irreversible. 11 Whitehead sometimes ascribes the irreversibility of time to the fact that events are unique, particular, unchangeable. " A n event is what it is, when it is, and where it i s . " 1 2 Again, he ascribes the irreversibility of time to "that ultimate becomingness which is the creative advance of nature." 13 He seems to derive time's irreversibility from each of these facts, 14 suggesting that he is undecided which is the true source of time's irreversibility. Perhaps a distinction will resolve this difficulty. It seems clear that the uniqueness of a past event is not sufficient to insure that it will never again be in a present of nature. Its uniqueness insures that it

A Preliminary

Account

of Time and

Nature

5

has only one temporal location, but does not insure that the course of time cannot return to that event, just as one can travel around the earth and arrive at his starting place. Uniqueness is a character of spatial events as well as of temporal events, and the order of space is in no sense irreversible. So the unique particularity of events is not a sufficient condition for the irrevocableness of the past. On the other hand, the particularity of events is a necessary condition for the irreversibility of time. It must be added to the advance of nature in order to guarantee that advance. For if an event were universal instead of particular and could recur without requiring to be counted as a different event, it then would retain its numerical identity amid temporal diversity; there would not be a necessary irrevocableness of the past; and consequently time would not be necessarily irreversible.* Fifth, among the relations which hold between the regions of spacetime are the empirically known relations of "inclusion" and its converse "inclusion by." If Whitehead is correct, we can empirically know that every region in space-time includes smaller regions of space-time and is included by larger regions of space-time.15 From the perceptible we are carried on the one hand to ever larger regions and on the other hand to ever smaller regions. Inclusion and its converse are ubiquitous relations.16 Thus the perceptible itself is indefinite in extent. Inclusion yields the continuity of space-time, f Since every region extends over other regions, there is no smallest spatio-temporal region.17 Thus space-time is infinitely divisible into regions that are homogeneous with a given region. This property is of great usefulness in spatiotemporal analysis. Because of it Whitehead calls nature a continuum.18 There are no extended holes in space-time because of its continuity. For every imaginable hole is occupied by a region which is included in the locus of the supposed hole. J The relation of "inclusion by" yields the infinite extent of spacetime. Every spatio-temporal region implies a region which includes it as a part, and so on ad infinitum. Not only does every such region imply * For a technical discussion, cf. 5.3. t cf. Chapter 3. t T h e analysis of the serial nature of time through its infinite divisibility will be a dominant theme of chapters two and three.

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Philosophy

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Time

all others, but also the geometrical structure of every such region implies that the geometrical structure of all others shall conform t o it. Uniformity is intrinsic to the geometrical character of space-time. 19 * "each volume of space, or each lapse of time, includes in its essence aspects of all volumes of space, or of all lapses of time." [Sc 8 9 ] Whitehead also describes a characteristic of the creative advance of nature which does not readily lend itself to brief exposition. It is indicated by his doctrine that it is possible that the passage of nature is not completely describable by a single time-order. More than one serial order of presents may be required to describe adequately the true advance of nature. 2 0 O n the assumption that there are many time-series each percipient would perceive only one time-series which is irreversible, particular, with a unique past, present, and future. However, the total creative advance would proceed by an infinity of time-series, each exactly like the single time-series. N o present of one time-system would consist of exactly the same set of events as the present of another time-system. Events which constituted a present in one time-system would be strung along a line into the past and future of other timesystems, and conversely. Every event would be included in an infinity of presents which intersected in that event. T h e .spatio-temporal relations between the different time-systems would be symmetrical. T h e crux of the distinction between all nature as constituting a single time-series and all nature as constituting an infinity of time-series lies in the relation of simultaneity.·)· If, says Whitehead, among the events simultaneous with a given event the relation of simultaneity is non-connected,% then an infinity of real distinct time-series is not impossible. For if simultaneity is non-connected, two events may be simultaneous with a given event (in one time-series) and still in each other's past or future (in another time-series). That is, that b is simultaneous with λ in one time-series and c is simultaneous with a in another timeseries, does not imply that b is simultaneous with c in either time-series. b may be either in c's past or future. W i t h i n a single time-series even on the assumption of the non-transitivity of simultaneity, simultaneity * five. f £ that

I shall reserve the explicit discussion of this subject for chapters f o u r and As Γ shall show in chapter f o u r . By a connected set ( w i t h respect to a given relation R ) , I mean a set such f o r any pair X Y of its members either X R Y or Y R X .

A Preliminary Account of Time and

Nature

7

is connected and symmetrical. Extending over many time-systems, simultaneity would be non-connected and symmetrical.* In order to completely understand time, we must go beyond time and consider the reality of change (which Whitehead takes to be axiomatic). For Whitehead time is the relational and logical aspect of change; it is a set of relations which is internal to fact. He repudiates with vigor the Newtonian theory of absolute time as a real flowing container of facts. 21 Such a view, he contends, regards time as a reality instead of an aspect of reality—it makes substance of a shadow. 22 Equally vigorously he rejects the theory which considers time to be a set of relations, but which takes its relata to be matter or mere sense qualities—passive endurances which are in fact timeless and could not possibly explain or yield temporal advance, f His position is that these relata must have flux and creative passage in their essence.23 J ι .3 The stages of Whitehead's

thought.

The preceding account of Whitehead's principles has been stated in a general enough fashion to be valid for any stage of his thought. But before further examining Whitehead's theory of process and creative advance, we must distinguish between the several stages in the development of his philosophy. His successive books show an advance in the range of subjects included in his system and a modification of some of his early statements about space-time and process. For our purpose, the history of Whitehead's writing falls into three periods. The first period extends from his earliest publication through 1924. From a philosophical point of view, it is satisfactory to treat all of the work of this period as a single system and to classify it as the "early period" of Whitehead's thought. The period starting with the publication of Science and the Modern World (1926) and continuing to the publication of Process and Reality (1929), may be called the "transitional period." The publication of Process and Reality introduces the last period of Whitehead's thought. * I shall make a detailed analysis of the relations of these different possible time-series in chapter four. For the present, statements about a single time-series should be interpreted in the context of a possible infinity of real time-series. t c f . 5.3. X I shall give the details of Whitehead's argument to this conclusion in chapter five. In chapter two, I shall present his arguments to prove that this passage must be an atomic passage.

8

Whitehead's Philosophy of Time

For some purposes we can legitimately treat the early period and the transitional period as a single stage of thought.* Sometimes, again, the transitional period can be combined with the last period. But generally, we should clearly distinguish all three. T h e way in which they are genetically related will appear in the course of the exposition.

1.4 Passage, conformation, and process. Whitehead's conception of the creative advance of nature differs progressively from period to period of his writing. T h e name which Whitehead uses for creative advance in the early period is passage; in the transitional period it is conformation; and in the final period he uses process. By the creative advance of nature Whitehead means temporal advance of which the essence is flux and transition. It arises from the past as objectified in the present, generates its own nature, molds itself. This concept is, in the last analysis, an ultimate for him, capable of being understood only by its repeated use in a large number of contexts. He believes that the doctrine that nature is a creative advance is by far the most important single aspect of his thought. He admits that the idea of process was not in his mind "with sufficient emphasis" in the early period o f his work. 2 4 Even then, however, it played an indispensable part, "passage in nature—or, in other words, its creative advance—is its fundamental characteristic."

[ Ε 1 4 2 5 ] T i m e merely exhibits some as-

pects of the more fundamental fact of the passage of nature. 2 6 In accordance with Whitehead's conception of the possible multiplicity of time-systems, in all periods of his work we should carefully distinguish universal passage from the passage found in any single timesystem. For example, in the early period he finds a clear difference between the creative passage of nature, "which is not properly serial at all," and passage in any one time-series. " T h e various time-series each measure some aspect of the creative advance, and the whole bundle of them express all the properties of this advance which are measurable." [ N 178] In the early period, passage is creative but not atomic in itself. In the transitional period, the early creativity is more minutely analyzed and is extended into religion, value-theory, and aesthetics. As a result of this * e.g., in chapter four.

A Preliminary Account of Time and Nature analysis, the early creativity is superseded by an atomic

9 self-creativity,

which is not only atomic but is interrelated with all other units of selfcreativity. 27 * In addition, in Symbolism

Whitehead introduces a new

principle of "conformation." 2 8 Passage implies the conformation of present to past. He says o f conformation that "it expresses the stubborn fact that whatever is settled and actual must in due measure be conformed to by the self-creative activity."

[Sy 4 3 ] Each new occasion of

self-creativity must modify its nature and characters in conformity with the nature and characters of the immediate past around its own immediate region. "Conformation" indicates the self-imposed adjustment o f creativity to its immediate progenitors in space and time. This notion becomes a fundamental concept in Process and

Reality.

The notion of process expands in content and importance until in the late period it dominates almost all of Whitehead's philosophic picture. He says in his last book Modes

of Thought:

" I t is true that nothing is

finally understood until its reference to process has been made evident." [ M T 64] T h e essence o f nature is to pass by itself from itself into the future. 2 9 And this process is atomic. "There is a rhythm of process whereby creation produces natural pulsation, each pulsation forming a natural unit of historic fact." [ M T 120]

I.J

The analysis of nature in the early period

(1900-1924)

In the early period of his work, Whitehead's main intention is to give a classificatory analysis of perceived experience, exhibiting just what he finds in it as a datum, excluding any consideration of a mind or knower. He treats nature, or experience, as a self-contained entity to which considerations about the nature of mind are irrelevant. 30 Only the object

of

perceptual knowledge concerns him, and not the relations of subject qua mental to its objects. 3 1 H e is purposely restricting his material, in this period of his work, to what he claims are the bare data of natural knowledge, excluding the consideration of more speculative subjects. However, he does not deny the importance of research into the nature of reality which extends beyond his own analysis. 32 Whitehead draws two important consequences from this position. T h e first is that there is no epistemological distinction of data of percep* cf. 2.7, 2.8.

10

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of

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tion into primary and secondary qualities. That is, there is no way of saying that some qualities belong to perceived objects and others are products of mental excitement.33 For he forbids the introduction of mind into the analysis. The second conclusion that he draws from his position is that apparent nature constitutes all of nature.34 Since the total object of perception is self-explanatory, his analysis forbids us to introduce any unknown, but causally efficacious, world to explain the system of our perceptions. The nature we know is all the nature he cares to consider or to admit exists. To be precise, one must distinguish at least four uses of the word "nature" in this period. The first use of the term takes nature to be the spatio-temporal system of data given in perception exclusive of imagination, ideation and emotion. It is the distilled residuum of a more inclusive state of experience, arrived at by excluding the imaginative, logical, aesthetic, and moral sides of experience.35 In its second use the word nature refers to the whole state of experience; 36 but Whitehead hardly ever uses the term in this way. The third meaning is an extension of the first to include the whole spatio-temporal system of fact which is connected with our own local space-time region.37 It covers both perceived and unperceived phenomena. W e remember that our own perceived space-time region implies an infinite space-time region uniform with our own. This whole objective space-time system is often meant when Whitehead refers to nature. The fourth use of nature extends the third use of the term to include a few scientific entities (e.g., "instantaneous mass"), to which Whitehead does not attribute actual existence, but which a percipient may read into nature in order to analyze it. 38 In doubtful cases I shall endeavor to state which use of nature is intended. If the term is used or assigned to Whitehead without further specification, the third use will be the one intended. The analysis of nature, says Whitehead, reduces to an analysis of the types of entities disclosed in perception and the types of relations of these entities.39 Among the types of entities, events and eternal objects are basic. An event is, for Whitehead, any actual occurrence with an extended spatio-temporal locus. It may be an episode in the private life of an electron, or it may be the Allied invasion of Normandy. Whitehead makes no fundamental logical distinction between events, in this period

A Preliminary Account

of Time and

Nature

11

of his work, regardless of their spatio-temporal size. 40 All alike are extended, transitory, unique and particular. Every event has its own "substantial unity of being which is not an abstract derivative from logical construction." 41 An event is what becomes in nature and can never happen again 4 2 While it is concrete and particular—essentially just itself, there and then—yet there are no isolated real events. N o event is wholly concrete taken in isolation from other events. 43 The relations of an event to other events are essential to it. 44 Nature is an interwoven spatio-temporal system of events which extend over each other and are significant of each other. In The Principle of Relativity Whitehead tends to say that the only true reality is nature as a total fact. 45 But usually he recognizes a measure of unique self-identity in an event which is independent of its relations to other events. In the last analysis, for Whitehead, "the concrete facts of nature are events exhibiting a certain structure in their mutual relations and certain characters of their own." [ N 167] Space-time relations are included in the mutual relations of events. 46 The intrinsic characters of events are eternal objects. 47 By "character," Whitehead does not necessarily mean "predicate," however. The former term has a wider extension than the latter. 48 An object is said to "be situated" in an event of which it is a character. Although objects are characters of events and must be conceived in reference to some event or other, 49 still they are distinguishable from events. An object has five interrelated characteristics which distinguish it from an event. An object is (a) without intrinsic passage in time, (b) without spatio-temporal parts, (c) capable of being compared with another object, (d) universal, not particular, and (e) abstract, not concrete. In each of these respects events have exactly the opposite property from objects. Whitehead recognizes many kinds of objects in this period. Although some kinds are not given the same names in different books, we can list some of the most important of them. Roughly, five important classes of objects are sense-objects, perceptual objects, physical objects, scientific objects, and figures. Examples of these objects are respectively, blue, a chair either in delusion or fact, a chair in fact, a molecule, a geometrical shape. W e can also group objects in another way into those that are uniform

12

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Philosophy

of Time

and those that are non-uniform. A uniform object is one which is completely exhibited in any part of an event of which it is the character, i.e., it is homogeneous, as, for example, "red." A non-uniform object is one which requires an extended locus to show its complete nature, i.e., it cannot be found in any part of its situation which is less than the whole situation. An example is a musical tune. Still another important way to group objects is to distinguish those whose situation in events can be described by the two-termed relation of predicate-subject from those whose situation in events is a many-termed relation. In the latter case, the terms in the relation include the event which has the object as a character, the object itself, the percipient event, and possibly other events causally relevant. An example of the latter kind of object is a sense-object. An example of the former is a scientific object. A scientific object is called an adjective of the event in which it is situated. This type of object is never found in simple senseawareness.50 In this period of his thought, Whitehead considers that one of his most important contributions to the analysis of nature is his recognition that the two-termed relation of subject-predicate is only a very special case of a much wider range of relations between events and eternal objects. 81 Thus the immediate and inferred data of perception are roughly (a) events per se as particular and temporal, 52 (b) eternal objects which are the characters of events, 53 and (c) the relations of events and their characters.54 * Our perception of nature is exhausted by our knowledge of a public space-time continuum of events, characterized by objects, and related among themselves. 55 An event which is a focus of awareness of nature is called a "percipient event." 56 As an event, it is involved in a discussion of space-time. But the percipient character of the event is not essential to a discussion of nature. Consonantly with this position, the details of the nature of the percipient qua percipient receive little treatment by Whitehead, and he admits that what treatment he gives this aspect of events is not clear. 57 In any case this subject, so far as he discusses it in the early period, is of no concern to the present exegesis because of his restricted conception of nature. In the following discussion, by a percipient event * The relations may or may not be eternal objects. T h e space-time relations, for example, are not exhaustively constituted by eternal objects.

A Preliminary Account of Time and Nature

13

we should take him to mean merely an event capable of perceiving nature. 1.6 The transitional period ( 1 9 2 6 - 1 9 2 9 ) Whitehead's three main works in this period are Science and the Modern World, Religion in the Making, and Symbolism. In these books Whitehead places a new emphasis on creativeness, i.e., the self-creation of an atomic event. In accordance with this emphasis, Whitehead shows a tendency to merge the act of experience with the act of self-creation. It is almost natural, then, that that side of experience which deals with events insofar as they are not eternal objects, i.e., insofar as they are creative and becoming, should gradually expand into a new realm of perception. This is what actually happens. It becomes apparent in Religion in the Making that a new region of experience—known by an unreflective non-mental act of perception—is gradually playing an increasing role in Whitehead's thought. 58 And in Symbolism he explicitly introduces a division of experience into two complementary regions or levels, defined by two distinct modes of perception, which he calls perception in the mode of causal efficacy and perception in the mode of presentational immediacy. Whitehead now considers the sense-objects and perceptual objects of the early period to be almost exclusively restricted to the region perceived in presentational immediacy. In fact, insofar as Whitehead's earlier thinking concerned any of the clear-cut features of experience, it was an analysis of presentational immediacy. But insofar as the preceding discussion concerned the vague and unanaIyzable elements of time-experience, it was an analysis of causal efficacy. Perceptions in the mode of presentational immediacy, says Whitehead, include all the bright definite contemporary data of experience which are commonly grouped under sense-experience and gay, light, emotional experience. These data exhaust the brightly-lit parts of experience. Perceptions in causal efficacy, on the other hand, are vague, haunting, insistent and unmanageable. They are found in a heavy, primitive, almost undifferentiated experience. There is a feeling of causal influence by the immediate past—"heavy with the contact of things gone by, which lay their grip on our immediate selves."Be The data of both causal efficacy and presentational immediacy are the result of a total act of perception which is part of the self-creative act of

14

Whitehead's

Philosophy

of

Time

the percipient event.80 Self-creation is directly influenced by its immediate environment. So the nature of the data in both modes of perception is directly dependent on the nature of the immediate environment of the event which perceives them. But although the data of presentational immediacy are what they are partly because the environment is what it is, they are not adjectives of the environment nor do they necessarily have any objective counterpart at all. 61 They are primarily products of the percipient event, not of the perceived events.62 They are perceived consciously as projected into the contemporary external world which they illuminate.03 So they cannot in any sense be predicates of the events in which they appear to be situated. They are private data publicly projected. The data of causal efficacy are not private in this way. When we perceive them at all, they disclose, from a perspective, the true nature of causal creative fact around us—a fact which is not of our own making. 64 These data are forced upon us, not fashioned by us, and they express the causal stringency of the environment in which we live. They are the actual occasions causally efficacious on us. The data of causal efficacy are extended in public space-time and are perceived as having concrete extension. Thus causal efficacy gives us public knowledge without mediation. The data of presentational immediacy only appear to be in public space-time. However, even in this case, while the data qua qualitative are projections of the percipient, the space-time regions perceived in presentational immediacy are not projections but are the true public space-time regions themselves. The regions are genuine and the colors are splashed onto them.* In the final period, Whitehead retains and develops the notions of perception in causal efficacy and perception in presentational immediacy. But in dealing with presentational immediacy, he completely abandons the position that the perceived space-time regions are the true public space-time regions of our contemporaries. They are conceived as projected along with the data; sense-data and space-time are treated on the same level. Throughout the transitional period it becomes apparent that Whitehead is extending his philosophical speculation far beyond his analysis of nature in the early period. He does not expressly repudiate his earlier * For a criticism of this point see 5.15.

Λ Preliminary Account of Time and Nature

15

analysis of nature, yet in principle he passes beyond two of the fundamental working principles of the natural philosophy of the early period. He now makes it clear that he thinks the introduction of a mind into our analysis of experience makes a difference in that analysis, i.e., that the nature of the object may be partially explained by reference to a subject which perceives the object. He also makes it clear that the content and behavior of sense-experience is not self-explanatory, for an account of the behavior of the world of sense-experience requires reference to the realm of causal efficacy. So he passes beyond the natureanalysis of the early period, not because it is incorrect, but because it is only a part of the facts as he sees them. He holds that the dictum of the early period that apparent nature is the only nature is untrue unless apparent nature includes causal efficacy as well as presentational immediacy and the percipient as well as the object. It seems clear that most of the analysis of nature in the early period of Whitehead's work falls within the region of presentational immediacy in the new classification of experience. However, that part of the early analysis that dealt with the transitive character of time and its nonformal features mostly falls within the region of causal efficacy. Process, causal influence, the passage into the future, the derivation from the past—these all fall within causal efficacy. They are felt in causal efficacy; they are but faintly mirrored in presentational immediacy. j . 7 Process and Reality and subsequent works

(1929-1939).

In Process and Reality most of Whitehead's constructive analysis lies within the realm of causal efficacy. The distinction of causal efficacy from presentational immediacy in that work marks an almost complete shift in interest from the data of the latter to the data of the former. This is in contrast to the dominating imporance of the data included in this field in the early period. He now describes the origination of perception in presentational immediacy almost entirely in terms of concepts based on perception in causal efficacy. Presentational immediacy is a show, or drama, based on the fundamental functioning of organisms in process as they are perceived in causal efficacy. In Process and Reality causal efficacy becomes the object of a very intricate analysis of process and the organisms in process. The importance of process to Whitehead's cosmology in the late period of his specula-

16

Whitehead's

Philosophy

of

Time

tion has already been indicated.* His chief new concepts are creativity, an actual occasion, and a nexus of actual occasions. Process has creativity as its essence and is the becoming of actual occasions, which are never isolated but are always found in some nexus. Creativity, as Whitehead conceives it, is an ultimate concept incapable of expository definition. It is the pure notion of activity, in abstraction from all the determinate formal characters of creative action. It is the general formless aspect of change, lying in the very heart of creative process. Creative transitivity generates the transition of time and the extensive relationships of time. It is the motive force of the universe, the most real aspect of fact. 65 But creativity is not in itself a concrete fact. Rather it is that abstraction from fact, which is most fundamental to Whitehead's cosmology. It is the creative fluent character of the facts which taken together constitute the spatio-temporal universe. These facts are actual occasions. The concept of an "actual occasion" is the analogue of Whitehead's earlier notion of an "event." It is the most concrete fact, unique and particular, connected with all other actual occasions, with becoming as its essence, incapable of recurrence, perpetually perishing, extended, atomic, and with a mental pole and physical pole. For a theory of time, its significant difference from an event lies in its last two properties—it is atomic, and it has a mental pole and a physical pole. The physical pole is the aspect of an actual occasion in which creativity is revealed in its extensive and material character. But, in Whitehead's view, the mental pole is also indispensable to the atomicity of an actual occasion, and this atomicity is in turn indispensable to a self-consistent theory of temporal transition. Whitehead conceives every actual occasion to have a mental side or pole. This pole includes an aim at an aesthetically and morally harmonious nature as the result of the self-creation of the actual occasion. It includes aim at value, desire, dislike, moral sentiments, moral rigor—and indeed all of the attitudes, emotions, and valuations of aesthetics and morality. The manner in which an actual occasion feels these sentiments of valuation Whitehead calls the "subjective form" of the actual occasion. The aim itself is called the "subjective aim" of the actual occasion. It is a single aim, a unified purpose, possessed only by the actual occa• 1.5.

A Preliminary

Account

of Time and

Nature

17

sion as a whole. As a unitary aim, it is the source of the atomicity of the actual occasion. The physical pole of an actual occasion is extended and thus, in Whitehead's eyes, is indefinitely divisible into parts which physically are as real as itself. But, he declares, the mental pole is "incurably one" e e since it implies subjective aim. It is not capable of division into real parts. An actual occasion presents a single unified aim. 67 W e ignore the subjective aim when we consider only the physical pole of an actual occasion. Since every actual occasion has a finite extent in space-time, every actual occasion, says Whitehead, is indefinitely divisible into parts of creativity which are like itself insofar as the purely physical pole is concerned. These parts of an actual occasion, which Whitehead calls "prehensions," are homogeneous, qua physical. To this extent they are as real as the actual occasion itself. 68 But this is true only insofar as the prehensions are considered in the physical pole. There is a deficiency in the subjective aim of a prehension; it is incomplete and can find completeness only in the completeness and unity of the entire actual occasion which includes it. 69 Every actual occasion is a member of some set of actual occasions. Whitehead calls such a set a nexus (plural: nexus). From a physical standpoint as causal and extended every such group exhibits a "mutual immanence" of the members in each other. 70 There is a physical adjustment of the actual occasions of a set to each other. Whitehead says of any such set: 71 "if the group be considered merely in 'respect to this basic property of mutual immanence, however otherwise lacking in common relevance, then—conceived as exemplifying this general connectedness—the group is termed a Nexus." [I 258] The term nexus does not presuppose any special kind of social order among its members, either physically (as some special kind of kinematical or electromagnetic order) or from the mental side (as some kind of harmoniously conceived and harmoniously executed order in the subjective aims of its members) , 7 2 A nexus is merely a group of actual occasions that in some way influence each other. This concludes the introductory remarks on the progressive development of Whitehead's thought, and the shifts in terminology which it involved.

CHAPTER

II

Temporal Transition and Atomic Events 2.1 Introduction to Whitehead's polemic on temporal transition. THE ANALYSIS of continuous change may be regarded as the basis of Whitehead's physical philosophy. It includes a polemic on the conceptions of instants and temporal advance which were favored and implicitly adopted by all of the technical experts in natural science at the turn of the century. Whitehead entered the general field of philosophical publication with a portion of this polemic. 78 He considered that the interpretation of space and time adopted by scientific theorists did not give a satisfactory picture of nature. Nor did it yield a satisfactory method for the formal analysis of nature. Abstractions such as mathematical points were treated as realities, and realities such as temporal advance were treated as abstract properties of classes of these hypostatized fictions. As an immediate consequence the whole traditional scheme of confused fancy and fact failed to account for temporal advance, or even to permit it. Nature could not advance at any time past the immobile instant on which it was impaled as "the present." Change and temporal process were impossible if this scheme of abstractions was to be believed. Even the spatio-temporal framework into which theoretical physics and biology were thrown was unduly dissociated from the natural facts it purported to describe. It is a chief merit of Whitehead's physical philosophy that he tried to break open this ice-jam of traditional conceptions and to offer science and philosophy a scheme of thought which would better account for the passage of nature. Whitehead believes that the assumption of points as ultimate or primitive elements is quite justifiable for the mathematicians and geometers who are engaged in the purely analytical study of numbers and point sets.* He has no quarrel with the pure mathematicians and does not question their analyses. * Their conception of a point is, in his opinion, essentially that of an entity "without parts and without magnitude." 14

Temporal

Transition

and Atomic

Events

19

The extremely valuable work on the foundations of geometry produced during the nineteenth century has proceeded from the assumption of points as ultimate given entities. This assumption, for the logical purpose of mathematicians, is entirely justified. Namely, the mathematicians ask, What is the logical description of relations between points from which all geometrical theorems respecting such relations can be deduced? The answer to this question is now practically complete. . . . [E 5] Whitehead says that criticism becomes necessary when the mathematical point-continuum just referred to is assigned a röle beyond its analytical one and asserted to be a facsimile of the spatio-temporal continuum. 7 5 The product of such an analysis is: "Time . . . as a simple linear series of durationless instants with certain mathematical properties of serial continuity. . . ." [TSM 44] Whitehead's arguments against points and instants fall into three general classes: arguments asserting that no points are perceived in nature, arguments showing that it is impossible that they should be ultimate real elements of nature, and arguments showing the undesirability of a formal analysis of nature which treats them as ultimate elements. This last argument is not against mathematics taken as a closed system. It is against the current way in which mathematics is applied to nature. It maintains that contemporary mathematical physics does not sufficiently distinguish between what is truly primitive and what is derivative in nature. 2.2 The polemic

against simple real points of time.

Whitehead holds that no fact, insofar as we conceive it to be temporal, has the properties of a mathematical point. There are, he says, no temporally unextended simple facts. An argument to this conclusion in the early period of his writings is that there is no perception of any unextended spatio-temporal locus. W e do not perceive an instant at all, either as a locus of instantaneous space or as any other temporal element. All knowledge is confined to observations which take time. 76 Immediate experience gives no reason to assert that nature is composed of instants.* Time as a succession of instants corresponds to nothing which falls within * W e remember that in this period of Whitehead's thought, he held a very limited conception of what constitutes nature, cf. 1.5.

20

Whitehead's

Philosophy

of

Time

my own direct knowledge. I can only think of it metaphorically either as a succession of dots on a line or as a set of values of an independent variable in certain differential equations . . . nor am I aware of any fact which is instaneous nature. . . . [TSM 45-46] Another of Whitehead's arguments in the early period is that an instant cannot be a locus expressive of the basic physical concepts of velocity and energy. He remarks that in physics all fact involves energy in its very nature, e.g., mass consists of energy. Yet, he points out, physics also asserts that all facts are instantaneous. For, to the physicist, each instant of time constitutes a present of nature that includes all the facts real at the time. Whitehead maintains that it is impossible to consistently hold that facts are both instantaneous and have energy or momentum.77 He says of this view of nature: The difficulty with this view* is that velocity cannot be defined by simple reference to one instant . . . in this account . . . the fundamental physical quantities such as velocity, energy, etc., are excluded from nature and become merely expressive of the spectators' comparisons. [TSM 44-46] We should notice that in this passage, Whitehead really asserts two somewhat different propositions. The first is that the formal definition of velocity requires reference to more than a single instant. It requires reference to a neighborhood of instants. The second is that no instantaneous fact can have energy, etc., intrinsic to it. In this quotation, he emphasizes the second proposition and uses the first to support it. We must notice this distinction because there are passages78 that closely resemble this one, but which are intended to emphasize the first proposition. The first proposition leads to a totally different conclusion, namely, that instants are not desirable as primitive elements in the formal analysis of nature. The passage quoted is intended to lead to the conclusion that present-day physics must abandon the view that nature consists of successive instantaneous presents. Instantaneous masses cannot be composed of energy. Whitehead advances another argument against the reality of simple instants that is closely allied to this one. He maintains that an instant cannot express the essence of temporal transition itself. In the early period, using the concept of nature as "what is ob* The classical view of time.

Temporal

Transition

and Atomic

Events

21

served," 7 9 * he asserts: "the flux of time is essential to the concrete reality of nature, so that a loss of time-flux means a transference to a higher abstraction." [PR 10] Here, temporal flux itself is the primitive fact in question. 8 0 In this case, h e holds that if an instant cannot express the nature of time, then it cannot be a primitive constituent of time. It cannot be the temporal locus of a real fact. As "the present" it cannot generate or express that passage into the future which is to him the essence of time. It is static, immobile, and not capable of independent existence as a "present." It must, then, be an abstraction, not a primary simple fact. Whitehead asserts that the old view that things can persist by a kind of static endurance led to the general acceptance of instants as ultimate facts. If fact is non-temporal in its essence, then it needs no duration to express its essence, but can completely exhibit itself in an instant. In all of his philosophical writings f r o m 1919 to 1938, 8 1 Whitehead rejects this static view of nature. 8 2 For example, he says in Modes of Thought: It is nonsense to conceive of nature as a static fact, even for an instant devoid of duration. There is no nature apart from transition, and there is no transition apart from temporal duration-t This is the reason why the notion of an instant of time, conceived as a primary simple fact, is nonsense. [ M T 207] The notion of a 'point' in process is fallacious. The concept of 'point' is here meant to imply that process can be analysed into compositions of final realities, themselves devoid of process. [ M T 131] Whitehead finds yet another sort of difficulty with the conception of unextended simple instants of time. T h e difficulty concerns the "discreteness" of the point-continuum. If the succession of "presents" were the classical succession of instants, he asks, then what would correlate the instantaneous spaces of these presents ? T h e theory demands that there should be an instantaneous space for each instant, but it provides for no correlation of these spaces. 83 There can, of course, be correlations in observers' minds, but can there be a real correlation of the spaces? H e finds none. * Using the first sense of the term "nature," No. 1.5. f The italics are my own.

22 2.3

The polemic

Whitehead's Philosophy of Time against simple real points of space.

Whitehead presents several arguments against real points of space which are so closely analogous to his analysis of instants of time that there is no need to reproduce them in detail. Most of them we can carry over, mutatis mutandis, from the polemic on instants. Since there is nothing in space analogous to temporal transition, however, the argument that a point could not express the essence of transition has no analogue when we deal with space. But since in his view extension is common to space and time, the arguments against instants of time which are based solely on the extensive character of time apply equally to points of space. Whitehead uses the physical concept of "surface stress" to show the difficulty of regarding space as a collection of simple ultimate points.84 He says that the transmission of stress from one surface to another is an example of physical causation. He asserts that for the transmission of stress to occur at all, it would have to proceed from one surface to the next surface (in contact with the first surface). But there is no surface next to a given surface. Not only are all surfaces discrete, but there is always another surface between any two given surfaces. Hence the transmission of stress from a point on a surface to a point on the next surface is a physical impossibility. The conclusion drawn by Whitehead is that: " A t some stage in our account of stress we are driven to the concept of any extended quantity of material as a single unity. . . ."

[E3] In other words, the concept of space as a set of diverse discrete points cannot explain some of the facts of causal transmission. We can explain the transmission of stress, Whitehead asserts, only if we conceive nature to be a collection of atomic extended entities. The early date of this quotation shows that at the outset of his polemic in its published form Whitehead adumbrates the atomistic solution of the problem of transmission. He completely formulates and solves this problem only in much later works. Turning again to the temporal aspect of Whitehead's analysis: so far, it has been argued that the primary temporal relata, the primary real facts, are not instantaneous. Therefore they must be enduring entities, expressive of transition. Reality is not a succession of instan-

Temporal

Transition and Atomic

Events

23

taneous static facts, discretely separate and continuously distributed, but a succession of intrinsically temporal and mobile facts. 2.4 The polemic against infinitely divisible events. Not until Science and the Modern World did Whitehead again recognize or refer to the problem caused by point to point transition, so briefly mentioned in the passage from the Enquiry which has just been presented. When he does return to this problem in the later book he is concerned mainly with its temporal applications, and couches his analysis in terms of durations and intervals of time, speaking of infinitely divisible intervals instead of instants. Logically, his new arguments are variations of the preceding argument that finds transition from point to point impossible because there can be no adjacent points. This fact will presently become clear if one keeps in mind that to say an interval is infinitely divisible is to say that between the two points which mark its boundaries lies another point which divides it into two intervals. Whitehead's general argument is to the effect that any attempt to locate all the possible states of fact that start with a given state and lead to another state generates an infinite regress which precludes the possibility of success. This argument holds both of states conceived as instantaneous and states conceived as infinitely divisible. Whitehead's particular arguments are as follows. i. He asserts that all becoming must begin in an extended locus. But any assigned extended locus must be abandoned as the locus of the beginning of the becoming, in favor of a part of the locus. This allows no extended locus to define the true beginning of the becoming. Unextended loci are impossible. Therefore the becoming can have no true beginning and cannot rationally be said to become.85 it. In a variant of this argument Whitehead arrives at the infinite regress involved in delimiting the true beginning of any period of becoming precisely as he does in the preceding argument, then illustrates his point by adding that the becoming would have to commence "at what should be the infinite end of the regress. But there is no infinite end." The conclusion must be that becoming cannot be regarded as the continuous unfolding of a continuum.8® Hi. In the Gifford lectures87 he returns to the first argument above, adding a rejection of instants as loci of real becoming.

24

Whitehead's

Philosophy

of

Time

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. [G 95] That is, the present must change from one instant to some other instant. Yet whatever instant is chosen as the "successor" must be abandoned in favor of the instant between it and the former present. So there is an infinite regress of untenable choices for the next instant, i.e., there is no next instant. There cannot be a locus for the successor of an instantaneous present. Whitehead believes that these arguments constitute adequate proof that there can be no continuous becoming by way of instants or of infinitely divisible intervals of time. One may regard these arguments as special cases of the denial that nature can, in any sense, complete a true infinity by the successive completion of the discrete elements constituting the infinity. It is a denial that nature can close a bounded infinite set by successive absorption of the discrete elements of the set. On the other hand Whitehead believes that we cannot deny that nature can complete as a unit what is infinitely divisible, in retrospect, into sub-regions and instants. Herein lies the only avenue of escape from the dilemma of tenporal flow which can lead to a rational account of time. An enlargement of one of Whitehead's examples88 may clarify this matter. No mathematician can count the fractions with numerator 1 and denominator a power of 2, between 0 and 1, by successively giving them ostensive definition, i.e., pointing to them. He can count them only by a rule of serial arrangement. Now time knows no "rules." The present can illustrate an instant only by "ostensive definition." Hence it cannot illustrate all of the instants ("fractions") between two points, or the sub-regions defined by the instants. Indeed, time would not only have to make an infinite ostensive reference, but it would have to make it in a serial order, picking first the number closest to 0, second the number closest to that, etc. This is clearly impossible since there is no number closest to 0. Therefore time cannot enumerate the elements of a continuum. To continue the analogy, the sum of all the fractions with numerator 1 and denominator a power of 2, between 0 and 1, is obtainable. It is 1. Thus although 1 is a unit, yet it can be analyzed into an in* O f temporal advance.

Temporal

Transition

and Atomic

Events

25

finite series of fractional parts. Similarly, a unitary advance in time can be infinitely divisible and yet mathematically possible. Whitehead claims that becoming which is capable of satisfying these conditions can have no parts expressive of its essence. That is to say, it must be "heterogeneous" becoming, of which the sub-regions do not contain facts of the same order as the becoming itself. Only by such a solution can an infinite regress be choked off at the start. T h e sole possible solution is, to use his phrase, that there is a becoming of continuity and not a continuity of becoming. The conclusion is that in every act of becoming there is the becoming of something with temporal extension; but that the act itself is not extensive, in the sense that it is divisible into earlier and later acts of becoming which correspond to the extensive divisibility of what has become. [ G 95] O n e might object here that if infinite regresses are to be considered destructive of the reality of time, then what of the infinite regress of time into the past of world-history ? Whitehead does not deal with this objection, but we may remark that there is a significant distinction of world-history f r o m private biography. In the former it is gratuitous to assume a beginning. In the latter beginnings are given as presents, and the problem is to get from one beginning to the next one. It should be noticed that Whitehead's arguments against ( a ) the reality of instantaneous facts, and ( b ) infinitely divisible facts which are extended in time do not presuppose any special theory of the ontological nature of time, aside from the assumption, basic to him, that time is real. All of his arguments depend entirely on the extensive property of time. T h e single exception is the argument from the fact that instants cannot contain flux—that instantaneous fact cannot be internally in flux. T h e conclusion from the preceding exposition is (a) that becoming cannot have an instant of time as a locus but must be extended; and ( b ) that this extended becoming cannot be realized by the successive continuous realization of its sub -regions. On the contrary, it must be a unitary, although extended, realization. Whitehead now must face the problem of constructing a concept of an event in nature which will combine temporal extension with atomic unity. This is the problem of becoming.

26 2.$

Whitehead's

Philosophy

of

Time

The solution of the problem of becoming: the early period.

Whitehead's early assertions that events are atomic cannot be considered an attempt to solve the problem of the infinite regress of becoming which results f r o m infinitely divisible events. For if he had wished to avoid this regress, he would have asserted that all events are atomic. H e does not do this. O n the contrary, he expressly denies that some events are atomic. In his early works* he definitely rejects simple "instants" of becoming, but he sees no reason to assert that there must be a smallest extended unit of becoming. His acceptance of uniform objects proves this. H e admits that an object can be " u n i f o r m " ; that is, capable of exhibition without regard to the extension of the event in which it is situated. 89 Such an event is capable of infinite subdivision into smaller events like itself through which it must become. Clearly, in these passages Whitehead does not recognize the difficulty of an infinite regress of becoming. Whitehead does, however, say that some objects require a certain finite interval of time in order to exhibit their nature. 9 0 A molecule is an example. And, perhaps significantly for his later work, he holds that in general these "non-uniform" objects are of a more fundamental scientific character than uniform objects. 2.6 The solution of the problem of becoming: Modern World.

Science a n d t h e

Whitehead derives his first solution of the problem of becoming by conceiving all events to be atomic. H e thus universalizes a concept very similar to the earlier concept of non-uniform objects. He does not mention " u n i f o r m " characters of events in his later work. T h e "non-uniform object" is now the "pattern" of an event, and it always requires an atomic duration for its exhibition. " T h e potential pattern requires a duration; and the duration must be exhibited as an epochal whole, by the realization of the pattern." [Sc 159] Whitehead asserts that nature has two aspects, creativity and the realized products of creativity, the events. 81 Every event has in its essence a pattern, intrinsic to it, which is the realized character of creativity. 82 Events are atomic and require a definite temporal interval for the dis* Ε; Sc.

Temporal

Transition and Atomic

Events

27

play of their pattern, an interval of which no sub-interval is the locus of a comprehensible part of the pattern. Events so far guarantee the possibility of temporal advance which does not admit of an infinite regress in any unit of the advance. But creativity in itself can have no pattern, for it is not determinate and realized. Creativity in itself is monistic; it is not atomic in any essential sense. 98 There is no relational independence among its various "prehensive" aspects.94 According to Whitehead, the whole advance of nature is analyzable into series of durations. Λ duration is the whole of nature simultaneous with an event, and the durations of a series are contiguous one to another. 95 So the events of a time-series are contiguous, and there is no unoccupied region of time. In this context of creativity, events, and patterns, the problem of becoming concerns the manner in which creativity fits into the temporal continuum without itself yielding an infinite regress, to vitiate the escape afforded by patterns in events. There appear to be only four alternatives. Either creativity is prior in time to its product, the event, or it is in the same duration with it—that is, simultaneous with it, or it is not in time but generates time in successive and contiguous epochal intervals, or it is unreal. These alternatives seem equally untenable. If creativity is prior to the finished event, then there is still an infinite regress of becoming in the interval of time generated by the creativity. If creativity and the events lie within the same duration, then since the event occupies the whole temporal stretch of the duration, the creativity and the event must be simultaneous. This is nonsense, for the event is the finished product of creativity, since its pattern is intrinsic to it. The event would have to be finished even while the creativity is finishing it. If creativity is unreal, there is nothing to generate temporal succession. 96 None of Whitehead's writing will allow us to assign this interpretation to him. This is a possibility he refuses to consider. The final alternative, that creativity generates time by a series of successive and contiguous epochal durations, finds some support in Whitehead. For example, in Science and the Modern World?1 he apparently asserts that realization is the becoming of epochal durations, successive and contiguous. This, and some statements in the Gifford lectures, 98

Whitehead's

28

Philosophy

of

Time

suggest the inference that creativity generates a series of facts which are exclusive of the creativity that begot them. But if we consider this alternative we see that it is internally inconsistent. For if time is created in lumps, then different sections of a lump are both ( a ) simultaneous and ( b ) before or after each other. They are simultaneous because they are produced all of a piece, as when a teacher exhibits a ruler to his class, but they are diverse, as are the units of the ruler, and therefore not simultaneous. Furthermore, if we attribute this alternative to Whitehead, we ignore his basic principle that time and creativity are correlatives. He claims that time is only an aspect of creativity, and that, therefore, wherever there is creativity there is the generation of time coeval with the creativity. W e can say that there is a promenade of the creativity and time—step by step. His position implies that time, as an intrinsic expression of creativity, cannot be created in lumps if the creativity is not itself lumpy. And time cannot exclude creativity, for wherever there is creativity, there is the basic time-series. According to his theory, if creativity is continuous and basic to and excluded from the time of realized events, then it constitutes another timesystem which also is continuous and basic to and exclusive of the order and succession of events, and nothing whatsoever is solved. The difficulty with Whitehead's position in Science World

and the

Modern

may be that he bases the atomicity of temporal facts on realized

fact instead of making it intrinsic to the process of creative transition itself. He puts atomicity in the event, and the event is not the creativity. The event is the creature, distinct from the creativity. Yet all of the arguments which require atomicity present problems found in creativity itself. An atomism that answers those arguments must inhere in creativity itself. If Whitehead assumes atomism to be in the creature, then he must more clearly merge the creature with the creativity. W h i l e there is no solution of the problem of becoming in Science the Modern

World,

and

there is, at least, the clue to the only road by which

a solution can be found. Whitehead has the nucleus of a new theory here. The Gifford lectures are based on the thought that: The duration is that which is required for the realization of a pattern in the given event. Thus the divisibility and extensiveness is within the given duration. The epochial duration is not realized via its successive divisible parts, but is given with its parts. . . . [Sc 158]

Temporal

Transition

and Atomic

2.γ The solution of the problem Making, "Time."

Events

29

of becoming:

Religion in t h e

In Religion in the Making, * Whitehead effects a closer union of creativity and the creature. The epochal occasion has two sides. On one side it is a mode of creativity bringing together the universe. This side is the occasion as the cause of itself, its own creative act . . . on the other side the occasion is the creature. This creature is that one emergent fact. . . . But there are not two actual entities, the creativity and the creature. There is only one entity which is the self-creating creature. [R 88-89] This reflection is amplified in the article "Time."t Through this period Whitehead not only develops the union of creativity and creature into one atomic "occasion," or event, but he shows that he still is conscious of the necessity of evading infinitely regressive acts of becoming. It is notable that he transfers the atomicity of the creature to that side of the creature farthest from its purely physical aspect of simple creativity. For he introduces unity into the actual occasion through value, or "realized" self-enjoyment, f If it were not for the aspect of value, he says, the occasion would not be a true unity but would be infinitely subdivisible into parts like itself. There is no atomism intrinsic to creativity. Although value renders simple creativity an abstraction, nothing renders simple creativity per se exclusive of an infinite regress. Only through non-physical considerations does Whitehead find an atomism of becoming. 09 The center of all his later attempts to solve the problem of becoming is the assumption that the unity of an occasion is in its self-valuation and in its development of a unified aim at value. 2.8 The solution of the problem

of becoming:

Process and Reality.

In Process and Reality Whitehead ascribes the atomic unity, necessary to process, to "actual occasions," also called "actual entities." They are the final real things of which the world is made up, yielding no sub-occasions or aspects which are entirely real and without abstraction. 100 ^ * 1926. t Published later in 1926. t "Time." ff 1.7.

30

Whitehead's

Philosophy

of

Time

T h e conception of an actual occasion represents Whitehead's final effort to merge the creativity and the creature. T o him an actual occasion is an act of self-creativity, the creativity creating the creature yet just an aspect of the creature. H e declares that atomic unity resides in the merger of the creativity and the creature. A n d as before, he asserts that this unity lies in the aspect of an act of creation that is farthest from the creation qua physical becoming. Let us consider this more closely. Whitehead says that the most real aspect of an actual occasion is a "prehension." 1 0 1 * H e holds that a prehension has every characteristic of an actual entity with one exception, fatal to its reality: its "subjective f o r m " is incomplete when it is considered apart from the actual occasion of which it is the prehension. Itf might have been a complete actuality; but by reason of a certain incomplete partiality, a prehension is only a subordinate element in an actual entity. A reference to the complete actuality is required to give the reason why such a prehension is what it is in respect to its subjective form. [ G 25]

T h e subjective form of a prehension is the way in which the actual occasion of which the prehension is an element feels the data of the external world, or its own prior prehensions. 1 0 2 T h e actual occasion feels these data in a fashion which cannot be understood unless we consider its total aim at value. Its aim at value is its aim at attainment of selfenjoyment and realized harmony, harmony more complete than that of any mere prehension. W e cannot understand its valuations, emotions, purposes, and other elements of its mental pole, j in abstraction from its total aim. T h e conclusion is that "final causation and atomism are interconnected philosophical principles." [ G 25-26] Thus a prehension can never free itself from the incurable atomicity of the actual occasion to which it belongs. 1 0 3 It is not an independent time-filling reality, but only an aspect of one. Only the mental pole of the actual occasion forbids definitely into sub-occasions with every claim to basic actual occasion itself has. However, for Whitehead, mental side of an actual occasion would be to make a • cf. 1.7. + A prehension. t c f . 1.7.

its division inreality that the to ignore the vicious abstrac-

Temporal

Transition and Atomic

Events

31

tion. He maintains that an actual occasion is essentially atomic, but only because an actual occasion essentially aims at value. If we consider the purely physical pole of an actual occasion, says Whitehead, we find that prehensions do not refer to any higher atomic entity. Also, the prehension qua physical is not itself atomic, but is indefinitely divisible into smaller prehensions, if they are taken solely as physical.* As a purely physical process, the entire actual occasion allows of indefinite divisibility, from which is derived the formal analysis of the extensive spatio-temporal continuum.f "The conceptual pole does not share in the coordinate divisibility of the physical pole, and the extensive continuum is derived from this coordinate divisibility." [G 435-436] In this connection we should notice that Whitehead does not deny that the mental pole is extended. He does maintain however that it cannot admit of division into real parts. 104 This presentation of Whitehead's position will perhaps become clearer if some aspects of it are given in his own words. The genetic processj is not the temporal succession: such a view is exactly what is denied by the epochal theory of time . . . the subjective unity dominating the process forbids the division of that extensive quantum. . . . [G 401] In every act of becoming there is the becoming of something with temporal extension; but the act itself is not extensive, in the sense that it is divisible into earlier and later acts of becoming which correspond to the extensive divisibiliy of what has become. [G 96] The advance of time is, then, the becoming of fact which makes a finite advance in time, which occupies a temporal interval, but which has no real parts to permit of an infinite regress in describing it. To continue: It is obvious that in so far as the mental pole is trivial as to originality, what is inexplicable in the coordinate division^ (taken as actually sepa* In fact, Whitehead says, the complete prehension is not atomic; it can be divided into other prehensions and combined into other prehensions, G 332. f c f . 1.2. J By "genetic process" he means the internal process of self-development of an actual entity. fl By a "coordinate division" Whitehead means the becoming, exclusive of the mental pole, which fills the regions of an actual occasion, cf. G 402-405 (433436).

Whitehead's

32

Philosophy

of

Time

rate) thereby becomes trivial. Thus for many abstractions concerning lowgrade 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. [G 404] To summarize Whitehead's position: becoming consists of acts of creation which are temporally (and spatially) extended. Such an act has both a physical pole, and a mental or evaluative pole. As extensive, the act is divisible in retrospect into phases of itself (prehensions) which are like it except for an incompleteness of their evaluative side. Taken physically, and therefore abstractly, the prehensions of an act of creation form an infinitely regressive set of parts of the act. Taking them in their physical-mental unity we cannot conceive them to be parts of the act. W e can analyze the actual entity into prehensions, but we cannot reconstruct it by the mere addition of prehensions.* An actual entity is not divided into parts nor generated from parts nor by way of parts. There is a becoming of continuity, but there is no continuity of becoming.

2.9 Atomism

and

continuity.

So far this treatise has been concerned with Whitehead's interpretation of the way in which classical analysis treats the relation of a present to its immediate future. Several aspects of the way in which Whitehead treats this relation in his theory of atomic occasions can now be presented, (a) Whitehead believes that the principle, "every act of becoming must have an immediate successor," 105 is a basic principle of all analysis of time. It seems clear that this principle underlies his polemic on the problem of becoming, (b) In addition, he says that there is an intimacy of the present and its immediate future. In search for the general tone of this intimacy he asserts: "the processes of the past, in their perishing, are themselves energizing as the complex origin of each novel occasion." [I 356] (c) He believes that a major feature of the intimacy of present to future is the physical transmission of characters from an actual occasion to its successor in the immediate future. This type of transmission * If we could, the prehensions would themselves be the real actual occasions, not further reducible.

Temporal

Transition and Atomic

Events

33

is an important problem of the analysis of becoming. It is insoluble on the classical theory of instants. But Whitehead believes he describes it consistently enough in the theory of atomic occasions. It proceeds by the immediate introduction of a physical character from one occasion to another across their common boundary.* The notion of continuous transmission in science must be replaced by the notion of immediate transmission through a route of successive quanta of extensiveness. These quanta of extensiveness are the basic regions of successive contiguoust occasions. [G 435] (d) Since he maintains that the advance of time is the advance of successive contiguous occasions, he advocates two complementary definitions of continuity. The infinite divisibility, in an abstract consideration, of the complete unit of becoming yields exactly the type of continuity which is described in the ordinary treatises on kinematics. It is the continuity which has been presupposed in Whitehead's arguments against points and homogeneous becoming. The atomic generation of time yields a different conception of continuity, one which also has its roots in ancient philosophical analysis. Aristotle discusses it. "A is continuous with Β when the limits whereby they touch each other are one." J In order to understand the latter kind of continuity we must understand contiguity. Two occasions are "contiguous" when their regions are externally connected, where external connection is defined as follows. "Connection" and "region" are primitive notions. A connection is a relation which relates only two or more regions. Two regions are connected when in ordinary usage they have one or more points in common, no region being connected with itself. A region A "includes" a region Β when every region connected with Β is also connected with A. Two regions are "externally connected" when they are connected and include no third region. So "contiguous" roughly means having a common boundary but no common extended locus. This notion is the * Whitehead gives a very complicated account of some of the details of this derivation of physical character. I shall not complicate the issue here by recounting these details. t The italics are mine. J W . D . Ross, Aristotle, p. 91. Ross remarks immediately after this passage that points cannot be thus continuous.

34

Whitehead's

Philosophy

of Time

main basis for the explanation both of creative advance and of causal derivation of the future from the past, i.e., the physical transmission of character. Whitehead's theory implies that there is no real separation of two contiguous regions. The boundary of two contiguous occasions has no extension and therefore can have no real fact within it and can directly express or illustrate no real character of fact. If A and Β are contiguous, and A is red and Β is green, nothing separates the" red from the green. There is no intermediate region of which it can be asked if this region is both red and green or neither red nor green or one but not the other, i.e., there is no real region between A and B. So on the theory of atomic contiguous regions a boundary generates none of the classical problems of change. 2.10

Criticism of

Whitehead.

In critically appraising Whitehead's analysis of time, one might question whether his method of infusing atomicity into actual occasions by appealing to the mental pole genuinely solves the problem of becoming. The criticism of Whitehead's atomistic solutions of the problem of becoming centers on an assumption common to them all. This assumption is that creativity or becomingness in itself is not atomic. Whitehead always assumes that the atomism necessary to temporal events is an atomism of the side of events farthest from becoming. W e can trace this line of thought in its variations in his work. In his early period, Whitehead holds to the view that continuity in nature is a special property of events qua extended and that atomism in nature arises solely from objects.* This is his opinion before he recognizes the necessity that all events should be atomic events. In Science and the Mod,em World he substitutes what he calls the "patterns" of events for his previous idea of objects. And he assigns to the new patterns the old privilege of the objects that they alone can give atomicity to events and becoming. Thus he separates atomicity and becoming. In Religion in the Making and in Time, Whitehead partly abandons the separation of the pattern of an event from its becoming. But he * cf. 1.5.

Temporal

Transition and Atomic

Events

35

now stresses the importance of the aim at patterned self-realization which he attributes to every actual occasion. And he assumes that the unity of an actual occasion lies in this aspect of it. He never assumes that atomism springs from the side of an actual occasion which creates temporal transition. In Process and Reality, Whitehead presents his completed doctrine of the atomism of an actual occasion, in which he maintains that its atomism is due solely to its mental pole. The objections to this position center around the consideration that the physical pole taken in itself is essential to the whole actual occasion and therefore any logical impossibility in its formation is an essential impossibility of the whole actual occasion. The problem of becoming is simply to express without logical imperfections the manner in which creativity can occur. W e must be able to explain becoming without an infinite regress or admit that the problem of becoming is insoluble. Whitehead's solution endeavors to combine two quite distinct factors. The first factor is a purely homogeneous and infinitely divisible physical aspect of creativity, where creativity is that which in its own nature generates the temporal extension of the actual occasion. The second factor is an aspect of valuation and purpose which, although it is atomic and temporal, does not generate time or function as a prerequisite to its generation. The second factor—the subjective aim—has a certain dissociation from time. The subjective aim is temporal, it is in time, but it cannot generate time. Only the physical aspect of the genetic process can do that. So the physical pole makes time and the subjective aim is only in time. As Whitehead originally conceives it, the problem of becoming is one of the generation of time, the making of the future, not of the content which helps to fill the intervals of time in their generation. Also, it follows from the above remarks that the physical aspect of creativity is capable of abstraction from its mental aspect to the extent that the physical pole must, in itself, resolve the difficulties of becoming an extension. Even if purely physical creativity is an abstraction, it is abstracted only from purpose, emotion, evaluation, etc., and is therefore the basic reality, the essential element, to be considered in any discussion of time. Therefore, the unity of non-physical elements is

36

Whitehead's

Philosophy

of

Time

powerless to stop an infinite regress in physical fact. A classically continuous physical pole can allow only infinitely regressive becoming. I f this criticism is justified, Whitehead's actual entity reduces to a nexus* of its coordinate divisions and its prehensions. Only the prehension is left to function as the unit o f creativity. But Whitehead says that the physical pole of a prehension is no more atomic than is the physical pole of an event. 1 0 6 Perhaps this dilemma could be avoided by positing that a prehension requires a quantum of time for its complete physical expression. W e could then say that the prehension is the unit o f extensive creation. And it would be a unit in its purely physical nature—a drop or bud of creativity. It would be that which is generative of time, yet not analyzable into parts which are like itself, having no abstractable parts, but only sub-regions derived from its basic region. It would be simply and ultimately an atomic growth, self-engendered, of process. Neither the pattern it expresses, nor the data it feels, nor the emotions and purposes it entertains, would be in the least relevant to its essential physical atomicity. This proposed emendation of Whitehead would put the solution of the problem of becoming on the same ontological level as is the polemic itself. The difficulties of points and o f continuity are all primarily concerned with simple becoming, and originate on that level, not on the level of objects. Hence this solution and the polemic would be complementary analyses on a single level of physical fact. There are statements in Whitehead's last book, Modes

of

Thought,

which could be construed to support this emendation of Whitehead's doctrine. For example, There is a rhythm of process whereby creation produces natural pulsation, each pulsation forming a natural unit of historic fact. . . . If process be fundamental to actuality, then each ultimate individual fact must be describable as process. [ M T 120] However the reading of this passage is debatable and there is no other evidence that Whitehead ever desired to change the theory of atomic occasions given in the Gifford lectures. W e have not yet considered the manner in which temporal relations are founded in creativity. Investigation of this question raises some perplexing difficulties. In general every set o f relations must be supported • cf. 1.7.

Temporal Transition and Atomic Events

'37

in fact, and in particular every set of temporal relations must be based in process. So sub-atomic intervals require sub-atomic physical aspects of fact as their relata. According to the suggested modification of Whitehead's theory, there can be no sub-atomic physical relata of the necessary sub-atomic intervals. A modified theory of temporal relations seems required in which sub-atomic stretches of time are based on the atomic present by implication only. They can directly express no creativity in their regions, yet are sufficiently allied to the present to be real implicants of it. The whole temporal stretch of the unit of creativity is contained directly in this unit, is an intrinsic expression of it, and is the basis of the reality of the remainder of the time-system. Taken with an eye to the whole pulsation, the sub-regions are not empty, but express aspects of the creativity. Yet taken by themselves, they are empty because they directly express no content. The creativity does not reflect itself into its sub-intervals. The essence of becoming and transition requires a minimum of time for its expression. 2.11

Summary.

Whitehead's doctrine, as it is presented in this chapter, can be summarized briefly. No percipient of nature has any experience of instaneous facts. Instantaneous facts are such that we can never validly say they are changing. Ever)' fact must be such that we can validly say it is changing. Instantaneous facts cannot be the elements of temporal succession, for instantaneous facts do not permit temporal succession. No instantaneous fact can have an immediate successor. No infinitely divisible event can be the immediate successor of anything. Therefore, the penetration of time into the future cannot be by instantaneous facts or by infinitely divisible events.* Becoming must proceed by atomic extended events. In Science and the Modern World the atomicity of an event inheres in its pattern. In Process and Reality the atomicity of an actual occasion inheres in the unity of its aim at harmonious self-realization. Every actual occasion has a unified aim at selfrealization. No part of an atomic event or of an actual occasion has as complete reality as the event itself possesses. * Notice that an unexpressed axiom here is that every element of a temporal succession must have an immediate successor, cf. p. 32.

CHAPTER

III

The Theory of Extensive Abstraction 3.1

Introduction.

HAVING CONSIDERED Whitehead's doctrine that all real entities ate extended in space and time, we can now examine his analysis of the extended aspect of events in terms of formal definitions and theorems. Since we shall concern ourselves only with the extended aspect of events, we can disregard their atomic character. It is possible to admit that there are no real instantaneous facts, and still to use points as ultimate concepts, in a purely formal analysis of nature. T h e mathematical physicists can treat all of kinematics in terms of points as ultimate concepts, assuming that the points are arranged in certain serial orders. However, just as W h i t e h e a d did not wish to regard instants as realities, so he does not wish to analyze nature in terms of points or instants as ultimate formal concepts. H e offers instead his theory of extensive abstraction. This theory is a formal and quite rigorous analysis of space-time in terms of regions of space-time as primitive concepts. It derives all of the ordinary definitions and theorems of kinematics f r o m the geometrical properties of regions. Instead of treating a region as a class of points, it defines a point as a class of regions. T h e theory of extensive abstraction proposes a considerable group of definitions and theorems before it arrives at the definition of a point. But once a point is defined, the remainder of the theorems and definitions f o r m a system equivalent to those of ordinary kinematics, which assumes that it deals with a real point-continuum. T h u s Whitehead's analysis will not differ f r o m the classical analysis so far as the properties of continuity are concerned. W h y then does he prefer to treat points as he does? H e has two reasons for doing so, both of which lie in the set of definitions and theorems prior to the definition of a point. T h e first is based on considerations of methodology, derived f r o m his empiricism. The second

The Theory of Extensive

Abstraction

39

derives from the formal accomplishments of his theory—its theorems and definitions—prior to the definition of a point. 3.2 The basis of Whitehead's

analysis of nature.

Whitehead's position in the early period of his writing is a realism in which the final basis for any complete and satisfactory analysis of time and space must be the actually observable data of sensation or more refined perception. These elementary data must yield in themselves all the basic conceptions of temporal analysis. H e says: Nature at an instant, since it is not itself a natural entity, must be defined in terms of genuine natural entities. Unless we do so, our science, which employs the concept of instantaneous nature, must abandon all claim to be founded on observation. [ N 57] In this passage, Whitehead means by "nature" that which is immediately posited in sense-awareness or directly known. Similarly, space is a set of relations between observable realities. The only basic relata of space are the "immediate objects of knowledge." 107 This position is more phenomenalistic than that professed in the Gifford lectures. In them Whitehead also holds that all explanations of fact must be couched solely in terms of facts as elements. But here the range of what are elemental facts includes entities which we cannot directly perceive. The basic facts are microscopic actual occasions. W e know spatio-temporal nature because we can rigorously infer it from the extensive character of nature in the gross. In Process and Reality the atomic occasions of creativity are the final facts. 108 Whitehead believes that either position leads to the same conclusion about primitive geometrical concepts: that instants of time should be derived from periods of time, since only periods of time can directly express an ultimate character of fact. Whitehead thus asserts that he gives temporal and spatial regions their proper status as basic conceptions in natural description. They directly represent the pure idea of extension given to us in our experience of events extending over each other. It follows that his formal analysis will, if conducted properly, flow from the discerned properties of nature itself.

Whitehead's

40 3.3 Whitehead's

treatment

of

Philosophy

of

Time

velocity.

Whitehead professes to construe velocity in a more satisfactory manner than does the classical theory of instants. Velocity, he says, is not only an important formal concept; it is also a natural fact. The formal concept should preserve the empirical primacy of its factual referent. Whitehead contends that in the classical kinematics analytical velocity cannot preserve this primacy, but that the theory of extensive abstraction can. The theory that uses points as ultimates must treat velocity in nature as a logical abstraction, not as a fact. In that theory velocity is "merely expressive of the spectators' comparisons." 109 Whitehead's argument can be explained in the following way. 110 Suppose that an instantaneous point is taken as the fundamental fact in nature. How real is the velocity of this instantaneous fact, in the classical theory? In the classical theory, a region or "neighborhood" which includes a point is itself composed only of other points. N o point in itself can express velocity. The measure of velocity is the ratio of a small interval I of a spatial neighborhood to a small duration D of a temporal neighborhood. The measure of velocity at a point p is not such a ratio, however, for such a ratio would be 0 / 0 and that is mathematical nonsense. Rather instantaneous velocity is regarded either as the limit defined solely by a series composed of ratios I/D where I and D include p and progressively narrow down toward p without limit by excluding the points farthest away from p in 1 (space) and D (time), or it is regarded as the series itself. Either way of taking it gives an acceptable definition of velocity at a point in the classical theory. In classical theory D and I are sets of points. Neither singly nor in any ratio or other combination can they exhibit velocity as a fact, for no point in them does so. The measure of velocity at a point is the limit of a series of ratios of measures of classes, or it is the series itself. Hence the concept of classical velocity is not the same as the concept of simple physical velocity. Classical velocity is a derivative concept in the theoretical system where it should be primitive, to correspond to its primitive status in nature. In the theory of extensive abstraction, on the other hand, the concept of velocity appears twice, once as a primitive idea and again as derivative from the formal definition of a point. The second concept is admittedly highly abstract and is defined in exactly the same way as

The Theory of Extensive

Abstraction

41

classical velocity. 111 While the primitive definition of velocity is constructed in the same way as it is in the classical theory, in Whitehead's account I and D are ultimate loci of fact, not classes of points. As ultimate regions, I and D directly include velocity as a real character. Regions are not defined in terms of points; points are defined in terms of regions. Each ratio in the series of elements 1/D directly expresses velocity. This primitive concept of "velocity near a point" taking it now as a series itself and not as the limit of a series, directly expresses what Whitehead regards as an essential fact of nature. 112 It seems clear that if the doctrine of real velocity is compatible with Process and Reality, then real velocity must be internal to an actual occasion. Furthermore, it must be a property of any part of the physical side of an actual occasion, or else the (infinite) series of 1/D cannot be made without limit. Whitehead's theory of atomic occasions with indefinitely subdivisible prehensions* may admit of such a real velocity. For every sub-region of space in an actual occasion there is a corresponding sub-region of time, and in each of these sub-regions there is a real, though incomplete, transmission of characters. In the emendation of Whitehead's atomism, suggested earlier, f there would be no real component part of an atomic occasion. There would be no real characters of any part of an atomic event because there would be no real parts. In this emendation of Whitehead the concept of sub-atomic velocity would become nonsense. Velocity again would become an abstraction "merely expressive of the spectators' comparison." For interatomic and sub-atomic regions would be merely classes of atomic occasions. There could be no real sub-atomic velocity or interatomic velocity. However, velocity as a purely kinematical concept, expressing only a kinematical property in different time-systems of indefinitely subdivisible spatio-temporal regions, would still be applicable to nature. But velocity as a real flux of fact would not be consistent with this kind of atomic becoming. In all discussions of Whitehead's doctrine based on his empiricism, we should remember that he progresses from a phenomenalistic realism to a metaphysical theory in which the unit building-stones of the world * p. 31. t 2.10.

Whitehead's Philosophy of Time

42

are unobservable.* In the early period of his work he bases the criticism of instants and the empirical argument for extensive abstraction on the dual necessity of founding natural philosophy on observables and of accounting for natural change in terms of immediately observable data. In the Gifford lectures he rejects instants not because they are unobservable but because he believes they are impossible metaphysical entities. Likewise, in the Gifford lectures, he founds extensive abstraction on the metaphysical primacy of atomic occasions.

3.4 Whitehead's

approach to uniform geometrical

elements.

Quite apart from the foregoing considerations, Whitehead has an additional reason for preferring spatio-temporal regions as primitive ideas, because, prior to the definition of a point, they have a certain formal advantage over the usual kinematics and geometry. He claims that the derivation of points from primitive relations of regions yields more satisfactory definitions of the "uniform" geometrical elements than those based on points as ultimate concepts. Preeminent among them are the concepts of a "straight line" and a "flat surface." The fourth definition of Euclid's Elements runs: " A straight line is a line which lies evenly with the points in itself." 1 1 3 Whitehead comments about this definition: T h e weak point of the Euclidean definition of a straight line is, that nothing has been deduced from it. T h e notion expressed by the phrases "evenly," or "evenly placed," requires definition. T h e definition should be such that the uniqueness of the straight segment between two points can be deduced from it. N e i t h e r of these demands has ever been satisfied. . . . [G 428]

Whitehead promises that: It will be shown that the gap in the old classical theory can be remedied. Straight lines will be defined in terms of extensive notions! · · · and the uniqueness of the straight line joining two points will be proved to follow from the terms of the definition. [G 428]

3.3 Final survey of the polemic against instants. Before leaving Whitehead's polemic against instants, let us recapitu* cf. 1.5, 1.7. + The extensive nature of primitive regions.

The Theory of Extensive

Abstraction

43

late the three principles on which it is based. They are (a) that no instants are perceived in nature;* (b) that instants are impossible loci of fact; (c) that instants are not satisfactory primitive concepts in an analysis of nature. The next logical step is to build a positive theory of space-time upon the principles established by the preceding critique of instants. Whitehead's theory is called the theory of extensive abstraction. Its purpose is to discard the classical idea of a continuum as a mere closely packed collection of discrete points and to substitute for it the conception of the continuum as an exhibition of the interconnectedness of regions, derived from their basic extensiveness. "In place of emphasizing space and time in their capacity of disconnecting, we shall build up an account of their complex essences as derivative from the ultimate ways in which those things, ultimate in science, are interconnected." [E 4] Unanalyzed regions become primitive concepts, and their extensive relations to each other yield the discrete classes based on regions which are the analogue of the classical points. Discreteness is based upon what Whitehead regards as the more important relation of interconnectedness. The extended region is the simple given, either of observation! or of metaphysics,} and the analysis proceeds from the fundamental characters that a region exhibits. 3.6 "Extension"

and "extensive

connection."

In the Enquiry and other works of the early period the primitive relations of the theory of extensive abstraction are the relations of "extension" and "cogredience." 114 Extension, says Whitehead, is one of the two sources of all abstract spatio-temporal concepts. The notion is used fundamentally not as "deployment" but rather as "extension over," a relation of total inclusion which is asymmetrical.115 It is the relation of whole to part, or of larger event to sub-event. 116 Its three most important implicants for our discussion are continuity, inclusion of, and inclusion in: "The continuity of nature arises from extension. Every event extends over other events, and every event is extended over by other events." [N 59] * H e urges this argument only in his earlier works, t In the theory that Whitehead develops in the early period. t In the theory that Whitehead develops in the late period.

Whitehead's

44

Philosophy of

Time

In the Gifford lectures Whitehead makes the relation of "extensive connection" more primitive than "extension," since he believes that extensive connection is a more useful analytical notion, 1 1 7 although it yields no ideas that are not yielded by extension. Defined ostensively, two regions A and Β are extensively connected if there is no region completely separating them. 1 1 8 The relation, deduced from extensive connection, which is the counterpart of the extension of the early period is called "inclusion." Inclusion and extension may therefore be regarded as equivalent terms.

3 . 7 An abstractive

set.

The most important definition following from the primitive relation of extension or extensive connection is that of an "abstractive set." An abstractive set is at the heart of ordinary geometrical entities, such as surfaces, lines, and points. It is to be noted that we have and that we propose to define must define the various types notions, point, line, area. [ G

not defined either points, or lines, or areas; them in terms of abstractive sets. Thus we of abstractive sets without reference to the 421]

In the early period Whitehead defines an abstractive set, or abstractive class, as follows: 1 1 9 " A set of events is called an 'abstractive class' when (i) of any two of its members one extends over the other and (ii) there is no event which is extended over by every event of the set." [E 104] In this period of his work Whitehead regards the conception of an abstractive set as secondary in importance only to the conceptions of an event and a duration and the notion of extension. If we choose "extensive connection" as the primitive conception, an abstractive set is farther down in the order of definitions: " A set of regions is called an 'abstractive set' when ( i ) any two members are such that one of them includes the other non-tangentially, (ii) there is no region included in every member of the set." [G 421] "Inclusion" is equivalent to "extension over," e.g., "Region A is said to include region Β when every region connected with Β is also connected with A . " [ G 4 ] The analytical element in the later definition of an abstractive set which is not found in the early period is indicated by the phrase 'non-tangentially." Its definition is several stages

The Theory of Extensive

Abstraction

45

removed from extensive connection. Its import is that it excludes any two members of the set from having a common boundary. This insures that the ever smaller regions of the set do not approach the boundary of any region of the set. 120 This restriction is necessary so that an abstractive set will converge to a unique position. The general nature of an abstractive set is immediately evident from its definition. Each of its regions includes other regions, and the relation of inclusion is transitive, therefore every region of the set extends over an infinite series of successively smaller regions. Each set thus is a series, which starts with a region of any size and converges toward smaller regions without ever arriving at a terminal region. 121 One should notice that the primitive notion of "region" in the Gifford lectures is not a physical reality of the same rank as an event in the earlier period, of which the counterpart in Process and Reality is an actual occasion. The analytical usefulness of the theory however, is not affected by this change. The properties associated with the relation of inclusion, by which an abstractive set is defined, together constitute the "extrinsic character" of the set. 122 Whitehead asserts that an abstractive set is, in effect, the entity meant when one considers an instant of time, 123 and adds: "It subserves all the necessary purposes of giving a definite meaning to the concept of the properties of nature at an instant." [ N 61] Every point, line, surface and instantaneous volume is either a class of extended regions or a class of a class of regions, or a class of even higher order founded on regions. 124 According to Whitehead 125 the larger regions of the set usually have little interest and seldom enter explicitly into the analysis by sets. Most physical relations will be simplified or excluded in the process of convergence. The result is the ideal simplicity of nature at an instant. Whitehead believes that a point, as it is used in applied mathematics, has no relations which are not the common residue of the relations of all of the regions inclusive of the point. If this is true, then we can derive all of the physical concepts and relations associated with points— point-masses, etc.—from the physical properties of regions. While this position of Whitehead's may be arguable, it seems sufficient for his purpose to say merely that the theory of extensive abstraction offers a ge-

46

Whitehead's

Philosophy

of Time

ometrical and kinematical continuum which is identical in mathematical structure with that of classical physics. This identity guarantees that any theoretical work in physics based on kinematics or geometry can be based equally well on this methodologically sounder theory. 3.8 Consideration

of a possible objection

to abstractive

sets.

The following objection might be made to the conception of an abstractive set: Whitehead proposes to set up a geometry of space-time without using any unextended locus such as an instant or point or line, or even a surface, as a primitive element. This proposition requires that the regions in an abstractive set cannot have precisely defined boundaries, for any boundary must lack extension in at least one dimension, and hence must be an instant or surface. However, the convergence of an abstractive set to ever smaller regions necessitates that the discrimination of inclusion, i.e., whether a includes b or b includes a, should approach the discrimination of a simple boundary, and thus requires that both a and b should have precise boundaries. It is apparently forced upon us that the notion of a "boundary" is being used as a primitive conception in the definition of an abstractive set. If this is true, then Whitehead's attempt to define a point (or an instant) in terms of a region becomes circular. Failure of the definition of an abstractive set would vitiate the entire theory of extensive abstraction. On the other hand, perhaps there is no real difficulty here. It can be argued that the converging end of an abstractive set is not intrinsically different from its observable end. When we examine what we mean by a sub-atomic duration, it is neither nonsense nor an unextended instant of time. Regardless of their size, all regions are intrinsically the same; and if no difficulties arise in the portion of an abstractive set containing large regions, then by the same token there should be no trouble when microscopically small regions are under consideration. By a kind of mental magnification, any region, no matter how small, can be blown up to the apparent size of an observable region, i.e., an abstractive set is a homogeneous entity. For the present, whatever the outcome of this question, let us assume that the definition of an abstractive set can be finally justified, and go on to the rest of Whitehead's theory of extensive abstraction.

The Theory of Extensive 3.9 Deduction

Abstraction

of the geometrical

47

elements.

In the Enquiry Whitehead's definitions of surfaces, lines, points and similar concepts presuppose a four-dimensional flat space-time. It has three spatial dimensions and one temporal dimension. The definitions of the geometrical concepts have the generality of a fourfold region with a system of parallel lines and planes characteristic of a manifold of zero Riemannian curvature. Instead of defining the number of dimensions and system of parallels as a special case of the analysis of regions, Whitehead makes the latter presuppose the former. Also, he implicitly introduces "straightness" as an essential feature of the fourfold region. Thus he introduces straightness at the outset of the derivation of the geometrical elements. This method of approach is not necessary, and it is revised in Process and Reality. All that is essential to his position is a homogeneity of space-time. This would obtain in any space-time of constant Riemannian curvature. In Process and Reality Whitehead gives straightness a new definition that has at least two advantages over the earlier concept, (a) He eliminates straightness as a primitive notion, thus reducing the number of primitive conceptions by one. He defines it in terms of extensively connected regions after a long series of previous derivations, (b) The definition proves without circularity that only one straight line can contain any pair of given points. 126 Also, in Process and Reality Whitehead completes the definition of all of the geometrical elements, including points, lines, volumes, and surfaces, before he specifies the number of dimensions and the system of parallelism in the regions under analysis. This achievement is by far the most important advantage of the later theory of extensive abstraction over the earlier version. Straight lines, flat surfaces, and parallel planes and lines are defined before we specify which particular kind of parallelism (Euclidean or non-Euclidean) obtains in nature. The general definitions derived from extensive connection do not presuppose any particular theory of parallelism. They are equally complete and consistent in Euclidean or non-Euclidean geometry. Whitehead's disclosure in Process and Reality of the true relation of parallelism to extensive connection determines the order in which we should present an analysis of spatio-temporal properties. First, we should exhaust the implications of extensive connection. Second, we

48

Whitehead's Philosophy of Time

should specify the number of dimensions of the extensive universe. Third, we should select the order of parallelism we think obtains in space-time. Neither the number o f dimensions nor the order of parallels is deducible from extensive connection. However, extensive connection does require that there be some one or other number of dimensions and some system of parallels or other.

3.70

Continuity.

Whitehead does not explicitly undertake to prove that the theory of extensive abstraction yields the real continuum of classical kinematics. T h e first step in such a proof would be to define temporal order, given the requisite geometrical entities. Whitehead does this by defining the relation of "lying between," where its relata are temporal moments. 1 2 7 O f temporal order he then merely asserts and does not prove that: 1 2 8 " T h e serial order among moments of the same time-system has the Cantor-Dedekind kind of continuity."

[E 1 1 5 ]

In other words, he asserts that the numerical and analytical aspects of the theory of extensive abstraction can be validly interpreted in terms of the conventional system of points in a real continuum. I f his assertion is justified, the continuum deduced from extensive abstraction permits the use of usual modern mathematical methods, and the metrical analysis is that o f usual metrical geometry. Once the elementary geometrical conceptions are defined by the abstractive sets, the new system and the conventional modern system will have equivalent analytical properties.

3.11

Summary.

This chapter has been concerned with the relation of Whitehead's theory o f extensive abstraction to classical kinematics. A fundamental difference between the two formal analyses of space-time is in their choice of primitive concepts. The theory of extensive abstraction takes the notion of "regions" as primitive while classical kinematics regards points as primitive. Whitehead's three main reasons for preferring the theory o f extensive abstraction are: ( a ) it is an analysis more closely derived from natural fact itself, which is always extended ( b ) it recognizes the primacy of velocity or movement in nature, and ( c ) it defines a straight line without deductive circularity.

The Theory

of Extensive

Abstraction

49

Whitehead finds that extension, or the more general relation of extensive connection, is the source of a considerable portion of the analytic properties of space-time. An abstractive set, defined solely by extension or extensive connection, is the central entity involved in most of formal spatio-temporal analysis. Whitehead shows that all of the basic geometrical concepts can be defined solely by reference to extensive connection. He asserts that the theory of extensive abstraction is equivalent to classical kinematics so far as metrical analysis is concerned. Thus he admits that it has no pragmatic advantage over the usual kinematics subsequent to the definition of a point. At least two of the basic properties of space-time do not follow from extensive connection. They are not implied by it; therefore their specification forms another set of primitive propositions. These two properties are the number of dimensions of space-time and the order of parallelism of space-time. They will be discussed in the next chapter.

CHAPTER

IV

The Order of Durations 4.ι

Introduction.

of spacc-time in Process and Reality, to which the development of this chapter will conform, may be taken to exhibit the true logical order of generality inherent in the nature of regions. In the early period of his work Whitehead does not follow this intrinsic order of definitions and theorems as we have already seen. Instead, he assumes at the outset that he is dealing with four-dimensional flat regions. Hence it is difficult to disentangle this assumption from the properties of extension per se. But in the later work, Process and Reality, he carries through the analysis of regions without presupposing a definite kind of space-time.* According to Process and Reality, the selection of a certain number of dimensions and a certain geometry of space-time assigns particular values to general functions previously derived from extensive connection alone. The particular cases represent a selection from among the variety of possible space-time structures that are consistent with the general extensive properties of regions. They are, therefore, a more concrete specification of actual space-time. They form a completely new topic, superposed on the previous work.

T H E ANALYSIS

4.2

Our jour-dimensional

space-time.

A basic principle of Whitehead's analysis of nature is that the actual world has four dimensions—three dimensions of space and one dimension of time. The basic facts of nature, and the basic regions of extensive abstraction are four-dimensional volumes. In the ensuing discussion we should consider abstractive sets to be defined in terms of four-dimensional regions, expressing both space and time in their extension. 129 * In the transitional period Whitehead recognizes explicitly the order of generality that he formally set up only in the later period. But he defines a duration as he did in the early period.

The Order of Durations 4-3 A preface to a discussion of

51

durations.

The aim of an examination of spatio-temporal parallelism is, in the long run, to demonstrate the order of parallelism of lines and planes that are derived from extensive connection. We graft the system of instants, lines, and planes onto the extensive order that is derived already in order to obtain a completely specified map of space-time. * However, no one can perceive instants, lines, and planes simpliciter. Only regions of space-time are preceptible. Insofar as we can specify the ordei of spatio-temporal parallelism by empirical perception alone, we can specify it only by perceiving the parallel properties of spatio-temporal regions. But we cannot derive the order of parallelism from extensive connection. Therefore we must specify it through empirical perception, and to do so we must derive it from the properties of parallelism that extended spatio-temporal regions exhibit. Once parallelism is empirically specified, we can extend the statement of its properties to include instants, lines, and planes. But not before. Whitehead claims that we perceive part of a natural order of parallelism in space-time. It is the order of durations. The order of spatio-temporal parallels is more general than the order of durations. For example, there may be many orders of durations in a Euclidean order of spatio-temporal parallels. He does not defend any particular order of durations to the complete exclusion of all others, but rather he defines the concepts in terms of which any order of spatio-temporal parallelism must be described. Whitehead's analysis of durations employs concepts in the early period of his work which are quite different from those in the later version of his theory. In the earlier analysis, he adopts the following general position. A duration is an infinite set of simultaneous events. Simultaneity is a positive ultimate relation of events. All events simultaneous to an event constitute an infinity of durations with respect to one of which the event is cogredient. For any two distinct events simultaneous in one time-system there exist time-systems, indeed an infinite number of them, in which * That is, it is completely specified insofar as space-time is non-metrical. T h e definitions for a metrical analysis of space-time f o l l o w readily enough from the completed non-metrical map.

52

Whitehead's

Philosophy

of

Time

the two events are not simultaneous. An event perceives the duration most cogredient with it. In Process and Reality, Whitehead defends the following modification of his earlier position. Two events are contemporary if neither can causally affect the other. A duration is the locus of an infinite set of contemporary actual occasions for which the relation of "contemporary to" is connected* and transitive. If "contemporary to" were non-connected, then every event would lie in more than one duration, in accordance with the theory of relativity. Durations are defined in terms of concepts given by perception in the mode of causal efficacy. However the presented duration of an actual occasion is the duration that includes the region it perceives in presentational immediacy. An actual occasion is cogredient to its presented duration. W e cannot clearly perceive the order of durations in causal efficacy. W e can only infer it from perception of space-time in presentational immediacy. All measurements by physical apparatus are performed in the latter space-time. Even measurements cannot guarantee assertions about the geometrical nature of space-time. Only direct perception can do that.

4.4 Durations in Whitehead's early and transitional periods. In the early and transitional periods of his work, Whitehead conceives of a duration as a group of events with unlimited spatial extent and finite temporal thickness. 130 It is a slab or stratum of nature, f The defining characteristic of a duration is the relation of simultaneity. A duration is "a certain whole of nature which is limited only by the property of being a simultaneity." [ N 53] Simultaneity is an ultimate relation in nature, says Whitehead, immediately given in perception. 131 It is a relation which primarily concerns only events 132 for events are the basic elements generative of space and time. It is the relation between events in virtue of which they form a duration. In his early period, Whitehead believes that there is no duration with the smallest possible temporal extent. In Science and the Modern * cf. footnote t , page 6. t Following Whitehead, we can refer to the order of duration as the "stratification" of nature.

The Order of

Durations

53

World, he qualifies this by stipulating that in any case of creative realization of a pattern there is a minimum temporal extension which a duration can have and still exhibit a complete pattern. 133 * It is pertinent to ask in what sense simultaneity can be validly assigned to events far beyond our own immediate region of perception— events in the distant reaches of a duration. Whitehead's answer can be inferred from elements of his doctrine already discussed. First, events are known to extend as far as can be imagined. Every event implies another which adjoins it and extends beyond it. W e do not know these events in all of their sensory content or their adjectival nature. W e do know them in their basic significance as spatio-temporal regions expressive of spatio-temporal relations. 134 The duration as a whole is signified by that quality of relatedness (in respect to extension) possessed by the part which is immediately under observation; namely, by the fact that there is essentially a beyond to whatever is observed. [N 186] Second, the range of time must necessarily extend as far as the range of space (and conversely): "There can be no time apart from space; and no space apart from time; and no space and no time apart from the passage of events in nature." [N 142]

4.5 The relativity of durations in Whitehead's early and transitional periods. It has been customary to hold that there is one definite present instant of time at which all matter is simultaneously real. That is, there is only one present, only one past and one future, for all of nature. The advance of nature in one time-series is the complete advance of nature. What is past here is past everywhere, and for anyone or anybody. This view is not inconsistent, in Whitehead's eyes, with the views on creative advance already expressed, if the obvious changes from classical instants of time to durations and abstractive sets of durations (converging to instants) are made. 135 Creative advance would generate a single time-series of parallel durations adjoining and overlapping, but never intersecting in events which are not durations.136 There would be a single system of natural stratification stretching indefinitely away from a * 2.6.

54

Whitehead's Philosophy of Time

uniquely defined present into a unique past and a unique future. The strata can be represented mentally in one spatial dimension and one temporal dimension as merely a progression of cross-sections of all nature, progressing like the books on a single shelf of a bookcase, if the pages of the books are thought of as infinite, i.e., as durations. While there is no internal inconsistency in this union of time and creative advance, Whitehead prefers the position that the complete expression of the passage of nature requires an infinitude of time-systems, each of which is the type used in Newtonian physics: 187 "This passage* is not adequately expressed by any one time-system. The whole set of time-systems . . . expresses the totality of those properties of the creative advance which are capable of being rendered explicit in thought." [E 81] According to this view, no one time-system is the creative advance. Any single time-system is a partial expression of the whole fact that is creative advance. 138 When Whitehead speaks of a duration as all of "the present," or as a totality of mutually simultaneous events, he means that a duration is all of "the present in some time-system," or is a totality "in that sense of simultaneity." 189 Since there is no absolute or unique meaning to simultaneity, it is called the relativity theory of time. There is a meaning for the notion of a duration, but it is a different meaning for each different time-series. 140 Whitehead defends the possibility of this view throughout his work. He inclines to believe it is true. On the other hand, he never asserts it to be intrinsically required by his doctrine of creative advance. 141 It is, he maintains, a metaphysical hypothesis based on that refined human observation which is physical experimentation. 142 The appeal to human experience is not stressed; the chief reliance is placed upon all of the experimental physical evidence for a multiplicity of time-systems. This evidence is considerable, but not necessarily conclusive.

4.6 The relativity of durations in Whitehead's early and transitional periods (continued). Let us consider in detail Whitehead's hypothesis that nature exhibits alternative systems of spatio-temporal stratification.f Consider two objects a and b, each in motion relative to the other. * Of nature. t In presenting this hypothesis I shall ignore its hypothetical character.

The Order of

Durations

55

This motion is a real relation of the two objects. 148 The object a is situated in an event e(a) and this event is at rest in a certain space. That is, there is a certain set of events which are at rest with respect to e(a), and the whole set of events constitute a genuine space, a space in which b is moving. Similarly, the event e(b) in which b is situated is at rest in another space constituted in the same way, and in which a is in motion. There are, therefore, two spaces each in motion with respect to the other; and the points of one generate tracks in the other. Now consider th.it even if there is no apparent object in an event, still the event is there, where it is. So even if there are rates of speed which are not illustrated by any two objects, still the events in which the objects might have been do express this rate of speed with respect to each other. There is a space for each of these events in which it is at rest. Therefore, according to Whitehead's position, nature does not completely exhibit itself in only one real space. There is an infinitude of spaces, each in motion with respect to all the rest. An infinite set of spaces is required to express the spatial extensiveness of nature. When this fact is realized, Whitehead asserts, the classical unique time loses its obviousness. 144 For there is an intimate interdependence of time and space. If simultaneity is relative, then to each space there corresponds a unique time-series which is different from the time-series of any other space. 145 Each space represents the temporal advance of process according to a different sense of simultaneity. Each space is associated with a precise present, past, and future. No two spaces have the same present, past, or future. Accordingly, two events which are simultaneous in one space-time series are not simultaneous in another space-time.146 Each space-time has its own family of durations, and no duration is a member of two families. This exposition of relative simultaneity has used an unexplained but fundamental relation which obtains between an event and a duration inclusive of the event. This relation is the notion of rest in a space-time. It is part of Whitehead's primitive relation of "cogredience." An event, he says, can be cogredient with only one duration, 147 and it is so when its temporal extension is just that of the duration and in addition it, and all its parts, are unequivocally at rest within the duration. 148 W e remember that the definition of a duration involves no reference to the motion

Whitehead's

56

Philosophy

of

Time

of the objects situated in its events. This relation is inherent in the nature of events per se149 but it does not follow purely from "extension." 1 5 0 It is a primitive notion, extrinsic to the relations of extension or extensive connection, but intrinsic to a complete analysis of extended nature. Thus, according to the hypothesis that simultaneity is relative, the whole creative advance of nature requires a multiplicity of spaces and time, or better, space-times, for its exhibition. Each space-time expresses only an aspect of the whole and is thus, to that extent, an abstraction.161 Every event which is not a duration is contained in some durations of every space-time.152 No event is fully revealed in any space-time. If we let the events efdj and e(b) mentioned before be percipient events, then: "From different standpoints in nature they both live through the same events, which are all that there is in nature. . . . The two sets of observers merely diverge in setting the same events in different frameworks of space and of time." [E 32] A diagram may clarify some of this exposition.153

D" / Λ

8

7

C FIGURE 1

The Newtonian Time

L

Τ

/

, -tv B'

/

c FIGURE

2

The Time of Whitehead

The points on the page represent events (there-then). A line is a particular set of events. Thus in Figure 1 OB is the set of events which

The Order

of

Durations

take place at the origin the motion of a particle space axis of which O D tabular interpretation of

57

of the coordinate system. O E could represent with a velocity ( = tangent / E O B ) along the is an instantaneous position. W e can set u p a this diagram systematically as follows.

Fig. 1

Fig. 2

Ο

O'

The origin of coordinates of e(a) and e(b) at some given time.

AB

A'B'

The time-advance of origin of coordinates of the event e(a) in its own space.

CD

C'D'

A duration simultaneous with e(a) space-time of e(a).

OE

O'E'

The track made by e(b) e(a).

CD

G'F'

A duration simultaneous with e(b) space-time of e(b).

in the

in the space-time of in the

These diagrams presuppose coordinates, which have not yet been defined, but for the purpose at hand they should not be misleading or confusing. T h e significant difference between them is that the durations of e(a)

and of e(b)

are identical in the N e w t o n i a n system ( C D ) while

they are diverse in W h i t e h e a d ' s view ( C ' D ' , G ' F ' ) . All of nature at any time is included in some duration such as C D in the o n e theory, while in the other there is an infinitude of durations such as C ' D ' and G ' F ' , represented by all of the lines in the angle D ' O ' F ' and more. Each of these durations is the present in some one space-time, and it includes events in the past or the f u t u r e of each of the other space-times. Since a duration is not only a set of events but a basic datum of perception, it is pertinent at this point to ask: W h i c h duration including a percipient event e will be perceived by e? W h i t e h e a d answers that it is "a duration giving the best average of cogredience for all the subordinate parts of the percipient event."

[ N 111]

This is a necessarily

vague answer. A percipient event may, of course, have many parts which are moving with respect to its most inclusive self. Such parts are not all cogredient to the same durations. It would be extremely difficult to find a duration which corresponds to the average cogredience of the parts. W h i t e h e a d himself gives no clue to the procedure to be followed. However, h e does indicate that the special relation of simultaneity most

58

Whitehead's

Philosophy

of

Time

importantly concerned with e's own experience is the one intrinsic to e's cogredient duration. However, Whitehead adds that if most of the events perceived are not cogredient to its own cogredient duration, the percipient event may experience the time-system in which most of the events are cogredient. 1 5 4 Since the percipient event is a member of many time-systems, it makes no difference logically which of the time-systems is chosen for illumination by perception.

4.7

Space-time

regions

in Process a n d Reality: causal

efficacy.

In Process and Reality, Whitehead does not give simultaneity the logical primacy that it is given in the earlier works. He conceives of simultaneity as a positive relation in presentational immediacy. But it is not a direct relation in causal efficacy. He defines six of the fundamental regions of time solely in terms of causal efficacy, but the seventh, the presented duration, involves presentational immediacy. Let us consider these regions as they appertain to a percipient occasion Λί. First, there are all the actual occasions which can have exerted a causal influence on Λ ί ; their region is Ai's "causal past." Second, there are all the actual occasions on which Λί can have a causal influence; their region is Ai's "causal future." Third, there are the actual occasions which lie neither in Al's causal past nor in Al's causal future; they are M's "contemporaries." 1 5 5 Their defining characteristic is that they happen in causal independence of each other. 1 5 6 T h e relation of contemporaneousness thus defined is symmetrical. 157 Fourth, there is the locus of actual occasions such that (a) any two members of the locus are contemporaries and ( b ) any actual occasion contemporary to all the members of the locus is itself a member of the locus; this locus is a "duration." 1 5 8 Thus a duration is a complete

region of actual occasions for

which the relation of contemporaneousness is symmetrical and connected.* W e see that a duration inclusive of Λί constitutes a sub-region of M's contemporaries. Connexity is not an intrinsic feature of the whole region of Ai's contemporaries. Taking two contemporaries Ρ and Q of Λί, it is not at all necessary that Ρ is a contemporary of Q, or conversely. "According to modern relativistic views, we must admit that * B y a connected set ( w i t h respect to a g i v e n relation R ) , I mean a set such that f o r any pair X Y of its members either X R Y or Y R X . T h e relationship inv o l v e d is called " c o n n e x i t y . "

The Order of

Durations

59

there are many durations including Μ—in fact an infinite number—so that no one of them includes all M's contemporaries." [G 454] It is also clear from this passage that Whitehead maintains that an event retains its numerical identity amid the diversity of its relations to the infinitude of durations. Fifth, there is the locus of actual occasions which lie in the past of some members of D; this locus is "the past of the duration D". 1 5 9 Sixth, there is "the future of the duration D," which is the locus of actual occasions which lie in the future of some members of D.ieo The verbal exposition of these regions and relations tends to obscurity. Since they are dissections of space-times, they can be conveniently suggested by a space-time map, as were the loci defined by simultaneity. The Newtonian map presented below is modeled solely on Whitehead's own description of Newtonian time. 161 The map of Whitehead's space-time is represented by the general outlines of the map used in Einstein's theory of special relativity to portray the Lorentz transformation between different space-times. The justification of this procedure is only partial. Whitehead never explicitly denounced the Lorentz transformations; neither did he consider them to be necessary to his system. 162 The definitions of Process and Reality are more general than the Lorentz transformations. Since this is so, he would claim that the truth or falsity of the Lorentz transformations in no way affects the general applicability of his definitions to spatio-temporal analysis. The following diagrams should thus be taken as special illustrations of definitions permitting an infinitely wider range of illustration.* As in the earlier diagrams, the points on the page represent events there-now or there-then, and a line represents a particular set of events. H H ' is an instantaneous space of the space in which Λί is at rest. Lines parallel to H H ' would be earlier and later instantaneous spaces in which the points on AB are at rest. A moving object is represented by MI. Its instantaneous space is KK'. Each moving particle lies in a different instantaneous space. EF and CD are limiting lines. Between them must lie all events which can either causally affect Λί ( / EMC) or be causally affected by Λί, ( / D M F ) , i.e., they are Ai's causal world. Even if Y had * One could consistently represent Whitehead's definitions with a nonEuclidean map. Or one could draw some of the durations as curved lines, or as lines with angular departures from straightness, e.g.,