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THE CONCEPT OF NATURE 
 
CAMBRIDGE UNIVERSITY PRESS 
 
 C. F. CLAY, Manager 
 
 LONDON : FETTER LANE, E.C. 4 
 
 NEW YORK : THE MACMILLAN CO. 
 
 BOMBAY ") 
 
 CALCUTTA [-MACMILLAN AND CO., Ltd. 
 
 MADRAS J 
 
 TORONTO : THE MACMILLAN CO. OF 
 
 CANADA, Ltd. 
 TOKYO : MARUZEN-KABUSHIKI-KAISHA 
 
 ALL RIGHTS RESERVED 
 
THE CONCEPT OF NATURE 
 
 TARNER LECTURES DELIVERED IN TRINITY COLLEGE 
 NOVEMBER 1919 
 
 BY 
 
 A. N. WHITEHEAD, Sc.D., F.R.S. 
 
 FELLOW OF TRINITY COLLEGE, CAMBRIDGE, AND 
 
 PROFESSOR OF APPLIED MATHEMATICS IN 
 
 THE IMPERIAL COLLEGE OF SCIENCE 
 
 AND TECHNOLOGY 
 
 CAMBRIDGE 
 
 AT THE UNIVERSITY PRESS 
 
 1920 
 
PREFACE 
 
 
 The contents of this book were originally delivered at 
 Trinity College in the autumn of 19 19 as the inaugural 
 course of Tarner lectures. The Tarner lectureship is 
 an occasional office founded by the liberality of 
 Mr Edward Tarner. The duty of each of the successive 
 holders of the post will be to deliver a course on * the 
 Philosophy of the Sciences and the Relations or Want 
 of Relations between the different Departments of 
 Knowledge.' The present book embodies the endeavour 
 of the first lecturer of the series to fulfil his task. 
 
 The chapters retain their original lecture form and 
 remain as delivered with the exception of minor 
 changes designed to remove obscurities of expression. 
 The lecture form has the advantage of suggesting an 
 audience with a definite mental background which it is 
 the purpose of the lecture to modify in a specific way. 
 In the presentation of a novel outlook with wide rami- 
 fications a single line of communications from premises 
 to conclusions is not sufficient for intelligibility. Your 
 audience will construe whatever you say into conformity 
 with their pre-existing outlook. For this reason the first 
 two chapters and the last two chapters are essential 
 for intelligibility though they hardly add to the formal 
 completeness of the exposition. Their function is to 
 prevent the reader from bolting up side tracks in pursuit 
 of misunderstandings. The same reason dictates my 
 avoidance of the existing technical terminology of 
 
VI PREFACE 
 
 philosophy. The modern natural philosophy is shot 
 through and through with the fallacy of bifurcation 
 which is discussed in the second chapter of this work. 
 Accordingly all its technical terms in some subtle way 
 presuppose a misunderstanding of my thesis. It is 
 perhaps as well to state expHcitly that if the reader 
 indulges in the facile vice of bifurcation not a word of 
 what I have here written will be intelligible. 
 
 The last two chapters do not properly belong to the 
 special course. Chapter VIII is a lecture delivered in 
 the spring of 1920 before the Chemical Society of 
 the students of the Imperial College of Science and 
 Technology. It has been appended here as conveniently 
 summing up and applying the doctrine of the book 
 for an audience with one definite type of outlook. 
 
 This volume on *the Concept of Nature' forms a 
 companion book to my previous work An Enquiry con- 
 cerning the Principles of Natural Knowledge, Either 
 book can be read independently, but they supplement 
 each other. In part the present book supplies points 
 of view which were omitted from its predecessor; in 
 part it traverses the same ground with an alternative 
 exposition. For one thing, mathematical notation has 
 been carefully avoided, and the results of mathematical 
 deductions are assumed. Some of the explanations have 
 been improved and others have been set in a new light. 
 On the other hand important points of the previous 
 work have been omitted where I have had nothing fresh 
 to say about them. On the whole, whereas the former 
 work based itself chiefly on ideas directly drawn from 
 
PREFACE vii 
 
 mathematical physics, the present book keeps closer 
 to certain fields of philosophy and physics to the ex- 
 clusion of mathematics. The two works meet in their 
 discussions of some details of space and time. 
 
 I am not conscious that I have in any way altered my 
 views. Some developments have been made. Those 
 that are capable of a non-mathematical exposition have 
 been incorporated in the text. The mathematical de- 
 velopments are alluded to in the last two chapters. They 
 concern the adaptation of the principles of mathematical 
 physics to the form of the relativity principle which is 
 here maintained. Einstein's method of using the theory 
 of tensors is adopted, but the application is worked 
 out on different lines and from different assumptions. 
 Those of his results which have been verified by 
 experience are obtained also by my methods. The 
 divergence chiefly arises from the fact that I do not 
 accept his theory of non-uniform space or his assump- 
 tion as to the peculiar fundamental character of light- 
 signals. I would not however be misunderstood to be 
 lacking in appreciation of the value of his recent work 
 on general relativity which has the high merit of first 
 disclosing the way in which mathematical physics 
 should proceed in the light of the principle of relativity. 
 But in my judgment he has cramped the development 
 of his brilliant mathematical method in the narrow 
 bounds of a very doubtful philosophy. 
 
 The object of the present volume and of its pre- 
 decessor is to lay the basis of a natural philosophy which 
 is the necessary presupposition of a reorganised specu- 
 
viii PREFACE 
 
 lative physics. The general assimilation of space and 
 time which dominates the constructive thought can 
 claim the independent support of Minkowski from the 
 side of science and also of succeeding relativists, while on 
 the side of philosophers it was, I believe, one theme of 
 Prof. Alexander's GifFord lectures delivered some few 
 years ago but not yet published. He also summarised 
 his conclusions on this question in a lecture to the 
 AristoteUan Society in the July of 191 8. Since the 
 publication of An Enquiry concerning the Principles of 
 Natural Knowledge I have had the advantage of reading 
 Mr C. D. Broad's Perception ^ Physics ^ and Reality 
 [Camb. Univ. Press, 1914]. This valuable book has 
 assisted me in my discussion in Chapter II, though I 
 am unaware as to how far Mr Broad would assent to 
 any of my arguments as there stated. 
 
 It remains for me to thank the staff of the University 
 Press, its compositors, its proof-readers, its clerks, and 
 its managing officials, not only for the technical ex- 
 cellence of their work, but for the way they have 
 co-operated so as to secure my convenience. 
 
 A. N. W. 
 
 IMPERIAL COLLEGE OF SCIENCE 
 AND TECHNOLOGY. 
 
 Aprily 1920. 
 
CONTENTS 
 
 CHAP. PAGE 
 
 I NATURE AND THOUGHT . . . . . i 
 
 II THEORIES OF THE BIFURCATION OF NATURE . 26 
 
 III TIME 49 
 
 IV THE METHOD OF EXTENSIVE ABSTRACTION . 74 
 
 V SPACE AND MOTION 99 
 
 VI CONGRUENCE 120 
 
 VII OBJECTS 143 
 
 VIII SUMMARY -^ . 164 
 
 IX THE ULTIMATE PHYSICAL CONCEPTS . .185 
 
 NOTE : On the Greek Concept of a Point . . .197 
 NOTE: On Significance and Infinite Events . .197 
 INDEX 199 
 
^ 
 
THE CONCEPT OF NATURE 
 
 CHAPTER I 
 
 NATURE AND THOUGHT 
 
 The subject-matter of the Tarner lectures is defined by 
 the founder to be ' the Philosophy of the Sciences and 
 the Relations or Want of Relations between the different 
 Departments of Knowledge.' It is fitting at the first 
 lecture of this new foundation to dwell for a few moments 
 on the intentions of the donor as expressed in this 
 definition; and I do so the more willingly as I shall 
 thereby be enabled to introduce the topics to which the 
 present course is to be devoted. 
 
 We are justified, I think, in taking the second clause 
 of the definition as in part explanatory of the earlier 
 clause. What is the philosophy of the sciences? It is 
 not a bad answer to say that it is the study of the rela- 
 tions between the different departments of knowledge. 
 Then with admirable solicitude for the freedom of 
 learning there is inserted in the definition after the 
 word * relations' the phrase *or want of relations.' A 
 disproof of relations between sciences would in itself 
 constitute a philosophy of the sciences. But we could 
 not dispense either with the earlier or the later clause. 
 It is not every relation between sciences which enters 
 into their philosophy. For example biology and physics 
 are connected by the use of the microscope. Still, I may 
 safely assert that a technical description of the uses of 
 the microscope in biology is not part of the philosophy 
 of the sciences. Again, you cannot abandon the later 
 
2 THE CONCEPT OF NATURE [ch. 
 
 clause of the definition; namely that referring to the 
 relations between the sciences, without abandoning the 
 explicit reference to an ideal in the absence of which 
 philosophy must languish from lack of intrinsic interest. 
 That ideal is the attainment of some unifying concept 
 which will set in assigned relationships within itself all 
 that there is for knowledge, for feeling, and for emotion. 
 That far off ideal is the motive power of philosophic 
 research; and claims allegiance even as you expel it. 
 The philosophic pluralist is a strict logician; the 
 Hegelian thrives on contradictions by the help of his 
 absolute; the Mohammedan divine bows before the 
 creative will of Allah ; and the pragmatist will swallow 
 anything so long as it * works.' 
 
 The mention of these vast systems and of the age- 
 long controversies from which they spring, warns us 
 to concentrate. Our task is the simpler one of the 
 philosophy of the sciences. Now a science has already 
 a certain unity which is the very reason why that body 
 of knowledge has been instinctively recognised as 
 forming a science. The philosophy of a science is the 
 endeavour to express explicitly those unifying charac- 
 teristics which pervade that complex of thoughts and 
 make it to be a science. The philosophy of the sciences 
 — conceived as one subject — is the endeavour to exhibit 
 all sciences as one science, or — in case of defeat — ^the 
 disproof of such a possibility. 
 
 Again I will make a further simplification, and con- 
 fine attention to the natural sciences, that is, to the 
 sciences whose subject-matter is nature. By postulating 
 a common subject-matter for this group of sciences, a 
 unifying philosophy of natural science has been thereby 
 presupposed. 
 
I] 
 
 NATURE AND THOUGHT 
 
 What do we mean by nature? We have to discuss 
 the philosophy of natural science. Natural science is 
 the science of nature. But — ^What is nature.? 
 
 Nature is that which we observe in perception 1^ 
 through the senses. In this sense-perception we are/ 
 aware of something which is not thought and which is 
 self-contained for thought. This property of being self- 
 contained for thought lies at the base of natural science. 
 It means that nature can be thought of as a closed 
 
 system whose mutual relations do not require the jj 
 expres sion of the fact that tTiey^feTthoughtabout. [ 
 
 I'hus in a sense nature is independent of thought. By i 
 this statement no metaphysical pronouncement is in-| 
 tended. What I mean is that we can think about nature 
 without thinking about thought. I shall say that then 
 we are thinking * homogeneously ' about nature. 
 
 Of course it is possible to think of nature in conjunc- 
 tion with thought about the fact that nature is thought 
 about. In such a case I shall say that we are thinking 
 * heterogeneously ' about nature. In fact during the last 
 few minutes we have been thinking heterogeneously 
 about nature. Natural science is exclusively concerned 
 with homogeneous thoughts about nature. 
 
 But sense-perception has in it an element which is 
 not thought. It is a difficult psychological question 
 whether sense-perception involves thought; and if it 
 does involve thought, what is the kind of thought which 
 it necessarily involves. Note that it has been stated' 
 above that sense-perception is an awareness of some- \ 
 thing which is not thought. Namely, nature is not/ 
 thought. But this is a different question, namely that 
 the fact of sense-perce ption jias^ factor which is_ no t 
 thought. I catl^his factor * sense-awareness.' Accord- 
 
 
 I — 2 
 
4 THE CONCEPT OF NATURE [ch. 
 
 ingly the doctrine that natural science is exclusively 
 concerned with homogeneous thoughts about nature 
 does not immediately carry with it the conclusion that 
 natural science is not concerned with sense-awareness. 
 However, I do assert this further statement ; namely, 
 that though natural science is concerned with nature 
 which is the terminus of sense-perception, it is not con- 
 cerned with the sense-awareness itself. 
 
 I repeat the main line of this argument, and expand 
 it in certain directions. 
 
 Thought about nature is different from the sense- 
 perception of nature. Hence the fact of sense-perception 
 has an ingredient or factor which is not thought. I call 
 this ingredient sense-awareness. It is indifferent to my 
 argument whether sense-perception has or has not 
 thought as another ingredient. If sense-perception does 
 \ \ not involve thought, then sense-awareness and sense- 
 fT^ |, perception are identical. But the something perceived 
 f\Jrlf^^ perceived as an entity which is the terminus of the 
 'v^pT sense-awareness, something which for thought is 
 rjf I beyond the fact of that sense-awareness. Also the 
 ^ something perceived certainly does not contain other 
 
 sense-awarenesses which are different from the sense- 
 T awareness which is an ingredient in that perception. 
 p'^Af^l Accordingly nature as disclosed in sense-perception is 
 «r^^ self-contained as against sense-awareness, in addition 
 J^ to being self-contained as against thought. I will also 
 ' ' * express this self-containedness of nature by saying that 
 nature is closed to mind. 
 
 This closure of nature does not carry with it any 
 metaphysical doctrine of the disjunction of nature and 
 mind. It means that in sense-perception nature is 
 disclosed as a complex of entities whose mutual relations 
 
 // 
 
I] NATURE AND THOUGHT 5 
 
 are expressible in thought without reference to mind, I 
 that is, without reference either to sense-awareness or 
 to thought. Furthermore, I do not wish to be under- 
 stood as implying that sense-awareness and thought are 
 the only activities which are to be ascribed to mind. 
 Also I am not denying that there are relations of natural 
 entities to mind or minds other than being the termini 
 of the sense-awarenesses of minds. Accordingly I will 
 extend the meaning of the terms * homogeneous 
 thoughts' and * heterogeneous thoughts' which have 
 already been introduced. We are thinking * homogene- 
 ously' about nature when we are thinking about it 
 without thinking about thought or about sense-aware- 
 ness, and we are thinking * heterogeneously ' about 
 nature when we are thinking about it in conjunction 
 with thinking either about thought or about sense- 
 awareness or about both. 
 
 I also take the homogeneity of thought about nature 
 as excluding any reference to moral or aesthetic values 
 whose apprehension is vivid in proportion to self- 
 conscious activity. The values^of natur e are perhaps the 
 key to the metaphysical svntV>esis of pyistpnrp^ But such 
 a synthesis is exactly what I am not attempting. I am 
 concerned exclusively with the generalisations of widest 
 scope which can be effected respecting that which is 
 known to us as the direct deliverance of sense-awareness. 
 
 I have said that nature is disclosed in sense-percep- 
 tion as a complex of entities. It is worth considering 
 what we mean by an entity in this connexion. * Entity' 
 is simply the Latin equivalent for * thing ' unless some 
 arbitrary distinction is drawn between the words for 
 technical purposes. All thought has to be about things. 
 We can gain some idea of this necessity of things for 
 
6 THE CONCEPT OF NATURE [ch. 
 
 thought by examination of the structure of a proposi- 
 tion. 
 
 Let us suppose that a proposition is being communi- 
 cated by an expositor to a recipient. Such a proposition 
 is composed of phrases ; some of these phrases may be 
 demonstrative and others may be descriptive. 
 
 By a demonstrative phrase I mean a phrase which 
 makes the recipient aware of an entity in a way which 
 is independent of the particular demonstrative phrase. 
 You will understand that I am here using * demonstra- 
 tion' in the non-logical sense, namely in the sense in 
 which a lecturer demonstrates by the aid of a frog and 
 a microscope the circulation of the blood for an ele- 
 mentary class of medical students. I will call such 
 demonstration ' speculative ' demonstration, remember- 
 ing Hamlet's use of the word ' speculation' when he 
 
 says, 
 
 There is no speculation in those eyes. 
 
 Thus a demonstrative phrase demonstrates an entity 
 speculatively. It may happen that the expositor has 
 meant some other entity — ^namely, the phrase demon- 
 strates to him an entity which is diverse from the entity 
 which it demonstrates to the recipient. In that case 
 there is confusion ; for there are two diverse propositions, 
 namely the proposition for the expositor and the pro- 
 position for the recipient. I put this possibility aside 
 as irrelevant for our discussion, though in practice it 
 may be difficult for two persons to concur in the con- 
 sideration of exactly the same proposition, or even for 
 one person to have determined exactly the proposition 
 which he is considering. 
 
 Again the demonstrative phrase may fail to demon- 
 strate any entity. In that case there is no proposition 
 
I] NATURE AND THOUGHT 7 
 
 for the recipient. I think that we may assume (perhaps 
 rashly) that the expositor knows what he means. 
 
 A demonstrative phrase is a gesture. It is not itself 
 a constituent of the proposition, but the entity which it 
 demonstrates is such a constituent. You may quarrel 
 with a demonstrative phrase as in some way obnoxious 
 to you; but if it demonstrates the right entity, the 
 proposition is unaffected though your taste may be 
 offended. This suggestiveness of the phraseology is part 
 of the literary quality of the sentence which conveys 
 the proposition. This is because a sentence directly 
 conveys one proposition, while in its phraseology it 
 suggests a penumbra of other propositions charged with 
 emotional value. We are now talking of the one pro- 
 position directly conveyed in any phraseology. 
 
 This doctrine is obscured by the fact that in most 
 cases what is in form a mere part of the demonstrative 
 gesture is in fact a part of the proposition which it is 
 desired directly to convey. In such a case we will call 
 the phraseology of the proposition elliptical. In ordinary- 
 intercourse the phraseology of nearly all propositions 
 is elliptical. 
 
 Let us take some examples. Suppose that the ex- 
 positor is in London, say in Regent's Park and in 
 Bedford College, the great women's college which is 
 situated in that park. He is speaking in the college hall 
 and he says, 
 
 'This college building is commodious.' 
 
 The phrase ' this college building ' is a demonstrative 
 phrase. Now suppose the recipient answers, 
 
 * This is not a college building, it is the lion-house in 
 the Zoo.' 
 
 Then, provided that the expositor's original proposi- 
 
8 THE CONCEPT OF NATURE [ch. 
 
 tion has not been couched in elHptical phraseology, the 
 expositor sticks to his original proposition when he 
 replies, 
 
 'Anyhow, it is commodious.' 
 
 Note that the recipient's answer accepts the specula- 
 tive demonstration of the phrase ' This college building.' 
 He does not say, * What do you mean? ' He accepts the 
 phrase as demonstrating an entity, but declares that 
 same entity to be the lion-house in the Zoo. In his 
 reply, the expositor in his turn recognises the success 
 of his original gesture as a speculative demonstration, 
 and waives the question of the suitability of its mode of 
 suggestiveness with an * anyhow.' But he is now in a 
 position to repeat the original proposition with the aid 
 of a demonstrative gesture robbed of any suggestiveness, 
 suitable or unsuitable, by saying, 
 
 'It is commodious.' 
 
 The 'it^ of this final statement presupposes that 
 thought has seized on the entity as a bare objective for 
 consideration. 
 
 ^ We confine ourselves to entities disclosed in sense- 
 awareness. The entity is so disclosed as a relatum in the 
 complex which is nature. It dawns on an observer 
 because of its relations ; but it is an objective for thought 
 in its own bare individuality. Thought cannot proceed 
 otherwise ; namely, it cannot proceed without the ideal 
 bare *it' which is speculatively demonstrated. This 
 setting up of the entity as a bare objective does not 
 ascribe to it an existence apart from the complex in 
 which it has been found by sense-perception. The 'it' 
 \for thought is essentially a relatum for sense-awareness. 
 
 The chances are that the dialogue as to the college 
 building takes another form. Whatever the expositor 
 
I] NATURE AND THOUGHT 9 
 
 originally meant, he almost certainly now takes his 
 former statement as couched in elliptical phraseology, 
 and assumes that he was meaning, 
 
 * This is a college building and is commodious.' 
 Here the demonstrative phrase or the gesture, which 
 
 demonstrates the *it' which is commodious, has now 
 been reduced to * this ' ; and the attenuated phrase, under 
 the circumstances in which it is uttered, is sufficient for 
 the purpose of correct demonstration. This brings out 
 the point that the verbal form is never the whole phrase- 
 ology of the proposition ; this phraseology also includes 
 the general circumstances of its production. Thus the aim 
 of a demonstrative phrase is to exhibit a definite * it ' as a 
 bare objective for thought ; but the modus operandi of 
 a demonstrative phrase is to produce an awareness of 
 the entity as a particular relatum in an auxiliary complex, 
 chosen merely for the sake of the speculative demon- 
 stration and irrelevant to the proposition. For example, 
 in the above dialogue, colleges and buildings, as related 
 to the *it' speculatively demonstrated by the phrase 
 *this college building,' set that *it' in an auxiliary 
 complex which is irrelevant to the proposition 
 
 * It is commodious.' 
 
 Of course in language every phrase is invariably 
 highly elliptical. Accordingly the sentence 
 
 * This college building is commodious ' 
 means probably 
 
 'This college building is commodious as a college 
 building.' 
 
 But it will be found that in the above discussion 
 we can replace * commodious' by * commodious as a 
 college building' without altering our conclusion; 
 though we can guess that the recipient, who thought 
 
10 THE CONCEPT OF NATURE [ch. 
 
 he was in the Hon-house of the Zoo, would be less likely 
 to assent to 
 
 * Anyhow, it is commodious as a college building.' 
 A more obvious instance of elliptical phraseology 
 
 arises if the expositor should address the recipient with 
 the remark, 
 
 'That criminal is your friend.' 
 The recipient might answer, 
 *He is my friend and you are insulting.' 
 Here the recipient assumes that the phrase 'That 
 criminal' is elliptical and not merely demonstrative. Jn 
 fact, pure demo nstration is impossible thoudi it is the 
 ideal of ^thought . This practical impossibility of pure 
 demonstration is a difficulty which arises in the com- 
 munication of thought and in the retention of thought. 
 Namely, a proposition about a particular factor in nature 
 can neither be expressed to others nor retained for 
 repeated consideration without the aid of auxiliary com- 
 plexes which are irrelevant to it. 
 
 I now pass to descriptive phrases. The expositor says, 
 
 * A college in Regent's Park is commodious.' 
 
 The recipient knows Regent's Park well. The phrase 
 *A college in Regent's Park' is descriptive for him. If 
 its phraseology is not elliptical, which in ordinary life 
 it certainly will be in some way or other, this proposition 
 simply means, 
 
 'There is an entity which is a college building in 
 Regent's Park and is commodious.' 
 
 If the recipient rejoins, 
 
 ' The lion-house in the Zoo is the only commodious 
 building in Regent's Park,' 
 
 he now contradicts the expositor, on the assumption 
 that a lion-house in a Zoo is not a college building. 
 
I] NATURE AND THOUGHT ii 
 
 Thus whereas in the first dialogue the recipient 
 merely quarrelled with the expositor without con- 
 tradicting him, in this dialogue he contradicts him. Thus 
 a descriptive phrase is part of the proposition which it 
 helps to express, whereas a demonstrative phrase is not 
 part of 'the proposition which it helps to express. 
 
 Again the expositor might be standing in Green Park 
 — ^where there are no college buildings — and say, 
 
 *This college building is commodious.' 
 
 Probably no proposition will be received by the 
 recipient because the demonstrative phrase, 
 
 *This college building' 
 has failed to demonstrate owing to the absence of the 
 background of sense-awareness which it presupposes. 
 
 But if the expositor had said, 
 
 'A college building in Green Park is commodious,' 
 the recipient would have received a proposition, but a 
 false one. 
 
 Language is usually ambiguous and it is rash to make 
 general assertions as to its meanings. But phrases which 
 commence with ' this ' or * that ' are usually demonstrative, 
 whereas phrases which commence with *the' or *a' 
 are often descriptive. In studying the theory of pro- 
 positiond expression it is important to remember the 
 wide difference between the analogous modest words 
 *this' and 'that' on the one hand and *a' and *the' 
 on the other hand. The sentence 
 
 *The college building in Regent's Park is com- 
 modious ' 
 
 means, according to the analysis first made by Bertrand 
 Russell, the proposition, 
 
 * There is an entity which (i) is a college building in 
 Regent's Park and (ii) is commodious and (iii) is such 
 
12 THE CONCEPT OF NATURE [CH. 
 
 that any college building in Regent's Park is identical 
 with it.' 
 
 The descriptive character of the phrase * The college 
 building in Regent's Park' is thus evident. Also the 
 proposition is denied by the denial of any one of its 
 three component clauses or by the denial of any 
 combination of the component clauses. If we had 
 substituted * Green Park' for * Regent's Park' a false 
 proposition would have resulted. Also the erection of a 
 second college in Regent's Park would make the pro- 
 position false, though in ordinary life common sense 
 would politely treat it as merely ambiguous. 
 
 * The Iliad ' for a classical scholar is usually a demon- 
 strative phrase ; for it demonstrates to him a well-known 
 poem. But for the majority of mankind the phrase is 
 descriptive, namely, it is synonymous with ' The poem 
 named "the Iliad".' 
 
 Names may be either demonstrative or descriptive 
 phrases. For example 'Homer' is for us a descriptive 
 phrase, namely, the word with some slight difference 
 in suggestiveness means *The man who wrote the 
 Iliad.' 
 
 This discussion illustrates that thought places before 
 itself bare objectives, entities as we call them, which 
 the thinking clothes by expressing their mutual rela- 
 tions. Sense-awareness discloses fact with factors which 
 are the entities for thought. The s.eparate^d istinction of 
 an entity in thought is not a metaphys ical assertio a>_blit 
 
 ' a m ethodof procedure neces sar yfor the finite expression 
 
 of mdi vidual propositions. Apart from entities there 
 
 'could be no finite truths ; they are the means by which 
 
 the infinitude of irrelevance is kept out of thought. 
 
 \To sum up: the termini for thought are entities > 
 
I] NATURE AND THOUGHT 13 
 
 primarily with__bare individuality, se condarily with 
 pro perties and relations ascribed to them j n_th e pro- 
 cedure of thought ; the termin i for sense-awareness are 
 factors i n the fact of nature, .4:u:imarily re lata andjonly 
 seco ndarily discrimin a ted as distinct individualiti es. 
 
 No characteristic of nature which is immediately 
 posited for knowledge by sense-awareness can be 
 explained. It is impenetrable by thought, in the sense 
 that its peculiar essential character which enters into 
 experience by sense-awareness is for thought merely the 
 guardian of its individuality as a bare entity. Thus for 
 thought *red' is merely a definite entity, though for 
 awareness * red ' has the content of its individuality. The 
 transition from the *red' of awareness to the *red' of 
 thought is accompanied by a definite loss of content, 
 namely by the transition from the factor *red' to the/ 
 entity *red.' This loss in the transition to thought is] 
 compensated by the fact that thought is communicable/ 
 whereas sense-awareness is incommunicable. 
 
 Thus there are three components in our knowledge of 
 nature, namely, fact, factors, and entities. Fact is the 
 undifferentiated terminus of sense-awareness; factors 
 are termini of sense-awareness, differentiated as elements 
 of fact ; entities are factors in their function as the ter- 
 mini of tfiougEt. The entities thus spoken of are natural 
 entities. Thought is wider than nature, so that there are 
 entities for thought which are not natural entities. 
 
 When we speak of nature as a complex of related 
 entities, the * complex' is fact as an entity for thought, 
 to whose bare individuality is ascribed the property of 
 embracing in its complexity the natural entities. It is 
 our business to analyse this conception and in the course 
 of the analysis space and time should appear. Evidently 
 
14 THE CONCEPT OF NATURE [ch. 
 
 I the relation s holding between natural entities are 
 / themselves natural entities, namely they are also factors 
 of fact, there for sense-awareness. Accordingly the 
 structure of the natural complex can never be com- 
 pleted in thought, just as the factors of fact can never 
 be exhausted in sense-awareness. Unexhaustiveness is 
 an essential character of our knowledge of nature. Also 
 nature does not exhaust the matter for thought, namely 
 there are thoughts which would not occur in any homo- 
 geneous thinking about nature. 
 
 The question as to whether sense-perception involves 
 thought is largely verbal. If sense-perception involves 
 a cognition of individuality abstracted from the actual 
 position of the entity as a factor in fact, then it un- 
 doubtedly does involve thought. But if it is conceived 
 as sense-awareness of a factor in fact competent to 
 evoke emotion and purposeful action without further 
 cognition, then it does not involve thought. In such a 
 case the terminus of the sense-awareness is something 
 for mind, but nothing for thought. The sense-perception 
 of some lower forms of life may be conjectured to 
 approximate to this character habitually. Also occasion- 
 ally our own sense-perception in moments when thought- 
 activity has been lulled to quiescence is not far off the 
 attainment of this ideal limit. 
 
 The process of discrimination in sense-awareness has 
 two distinct sides. There is the discrimination of fact 
 into parts, and the discrimination of any part of fact as 
 exhibiting relations to entities which are not parts of 
 fact though they are ingredients in it. Namely the 
 immediate fact for awareness is the whole occurrence 
 of nature. It is nature as an event^^resent for sense- 
 awareness, and essentially passing. There is no holding 
 
I] NATURE AND THOUGHT 15 
 
 nature still and looking at it. We cannot redouble our 
 efforts to improve our knowledge of the terminus of our 
 present sense-awareness; it is our subsequent oppor- 
 tunity in subsequent sense-awareness which gains the 
 benefit of our good resolution. Thus the ultimate fact 
 for sense-awareness is an event. This whole' event is 
 discriminated by us into partial events. We are aware 
 of an event which is our bodily life, of an event which is 
 the course of nature within this room, and of a vaguely 
 perceived aggregate of other partial events. This is the 
 discrimination in sense-awareness of fact into parts. 
 
 I shall use the term *part' in the arbitrarily limited 
 sense of an event which is part of the whole fact dis- 
 closed in awareness. 
 
 Sense-awareness also yields to us other factors in 
 nature which are not events. For example, sky-blue is 
 seen as situated in a certain event. This relation of 
 situation requires further discussion which is postponed 
 to a later lecture. My present point is that sky-blue is 
 found in nature with a definite implication in events, 
 but is not an event itself. Accordingly in addition to 
 events, there are other factors in nature directly dis- 
 closed to us in sense-awareness. The conception in 
 thought of all the factors in nature as distinct entities 
 with definite natural relations is what I have in another 
 place^ called the * diversification of nature.' 
 
 There is one general conclusion to be drawn from the 
 foregoing discussion. It is that the first task of a philo- 
 sophy of science should be some general classification of 
 the entities disclosed to us in sense-perception. 
 
 Among the examples of entities in addition to * events ' 
 which we have used for the purpose of illustration are 
 ^ Cf. Enquiry. 
 
M 
 
 i6 THE CONCEPT OF NATURE [ch. 
 
 the buildings of Bedford College, Homer, and sky-blue. 
 Evidently these are very different sorts of things ; and it 
 is likely that statements which are made about one kind 
 of entity will not be true about other kinds. If human 
 thought proceeded with the orderly method which 
 abstract logic would suggest to it, we might go further 
 and say that a classification of natural entities should be 
 the first step in science itself. Perhaps you will be 
 inclined to reply that this classification has already been 
 effected, and that science is concerned with the ad- 
 ventures of material entities in space and time. 
 
 The history of the doctrine of matter has yet to be 
 written. It is the history of the influence of Greek 
 philosophy on science. That influence has issued in 
 one long misconception of the metaphysical status of 
 natural entities. The entity has been separated from the 
 factor which is the terminus of sense-awareness. It has 
 become the substratum for that factor, and the factor 
 
 J has been degraded into an attribute of the entity. In 
 phis way a distinction has been imported into nature 
 which is in truth no distinction at all. A natural entity 
 is merely a factor of fact, considered in itself. Its dis- 
 connexion from the complex of fact is a mere abstraction. 
 ^ |It is not the substratum of the factor, bixLllie-AcerjL 
 factor itself as bared in thou ght Thus what is a mere 
 (procedure of mind in the translation of sense-awareness 
 into discursive knowledge has been transmuted into a 
 fundamental character of nature. In this way matter 
 has emerged as being the metaphysical substratum of 
 its properties, and the course of nature is interpreted 
 as the history of matter. 
 
 Plato and Aristotle found Greek thought preoccupied 
 with the quest for the simple substances in terms of 
 
I] NATURE AND THOUGHT 17 
 
 which the course of events could be expressed. We 
 may formulate this state of mind in the question, What 
 is nature made of? The answers which their genius 
 gave to this question, and more particularly the con- 
 cepts which underlay the terms in which they framed 
 their answers, have determined the unquestioned pre- 
 suppositions as to time, space and matter which have 
 reigned in science. 
 
 In Plato the forms of thought are more fluid than in 
 Aristotle, and therefore, as I venture to think, the more 
 valuable. Their importance consists in the evidence 
 they yield of cultivated thought about nature before it 
 had been forced into a uniform mould by the long 
 tradition of scientific philosophy. For example in the 
 Timaeus there is a presupposition, somewhat vaguely 
 expressed, of a distinction between the general becoming 
 of nature and the measurable time of nature. In a later 
 lecture I have to distinguish between what I call the 
 passage of nature and particular time-systems which 
 exhibit certain characteristics of that passage. I will not 
 go so far as to claim Plato in direct support of this 
 doctrine, but I do think that the sections of the Timaeus 
 which deal with time become clearer if my distinction 
 is admitted. 
 
 This is however a digression. I am now concerned 
 with the origin of the scientific doctrine of matter in 
 Greek thought. In the Timaeus Plato asserts that nature 
 is made of fire and earth with air and water as inter- 
 mediate between them, so that * as fire is to air so is air 
 to water, and as air is to water so is water to earth.' He 
 also suggests a molecular hypothesis for these four 
 elements. In this hypothesis everything depends on the 
 shape of the atoms ; for earth it is cubical and for fire 
 
 W. N. 2 
 
i8 THE CONCEPT OF NATURE [ch. 
 
 it is pyramidal. To-day physicists are again discussing 
 
 the structure of the atom, and its shape is no sHght 
 
 factor in that structure. Plato's guesses read much more 
 
 [fantastically than does Aristotle's systematic analysis; 
 
 but in some ways they are more valuable. The main 
 
 outline of his ideas is comparable with that of modern 
 
 j science. It embodies concepts which any theory of 
 
 /natural philosophy must retain and in some sense must 
 
 / explain. Aristotle asked the fundamental question, 
 
 f What do we mean by * substance ' .^ Here the reaction 
 
 between his philosophy and his logic worked very 
 
 unfortunately. In his logic, the fundamental type of 
 
 affirmative proposition is the attribution of a predicate 
 
 Ito a subject. Accordingly, amid the many current uses 
 
 /of the term * substance ' which he analyses, he emphasises 
 
 / its meaning as * the ultimate substratum which is no 
 
 I longer predicated of anything else.' 
 
 The unquestioned acceptance of the Aristotelian logic 
 has led to an ingrained tendency to postulate a sub- 
 stratum for whatever is disclosed in sense-awareness, 
 namely, to look below what we are aware of for the 
 substance in the sense of the * concrete thing.' This 
 is the origin of the modern scientific concept of matter 
 and of ether, namely they are the outcome of this 
 insistent habit of postulation. 
 
 Accordingly ether has been invented by modern 
 science as the substratum of the events which are 
 spread through space and time beyond the reach of 
 ordinary ponderable matter. Personally, I think that 
 predication is a muddled notion confusing many different 
 relations under a convenient common form of speech. 
 For example, I hold that the relation of green to a blade 
 of grass is entirely different from the relation of green 
 
I] NATURE AND THOUGHT 19 
 
 to the event which is the Hfe history of that blade for 
 some short period, and is different from the relation 
 of the blade to that event. In a sense I call the 
 event the situation of the green, and in another sense 
 it is the situation of the blade. Thus in one sense the 
 blade is a character or property which can be predi- 
 cated of the situation, and in another sense the green 
 is a character or property of the same event which 
 is also its situation. In this way the predication of 
 properties veils radically different relations between 
 entities. 
 
 Accordingly * substance,' which is a correlative term 
 to ' predication,' shares in the ambiguity. If we are to 
 look for substance anywhere, I should find it in events 
 which are in some sense the ultimate substance of 
 nature. 
 
 Matter, in its modern scientific sense, is a return to 
 the Ionian effort to find in space and time some stuff 
 which composes nature. It has a more refined signi- 
 fication than the early guesses at earth and water by 
 reason of a certain vague association with the Aristotelian 
 idea of substance. 
 
 Earth, water, air, fire, and matter, and finally ether 
 are related in direct succession so far as concerns their 
 postulated characters of ultimate substrata of nature. 
 They bear witness *to the undying vitality of Greek 
 philosophy in its search for the ultimate entities which 
 are the factors of the fact disclosed in sense-awareness. 
 This search is the origin of science. 
 
 The succession of ideas starting from the crude 
 guesses of the early Ionian thinkers and ending in the 
 nineteenth century ether reminds us that the scientific 
 doctrine of matter is really a hybrid through which 
 
 Af.'S 
 
V 
 
 ^r 
 
 20 THE CONCEPT OF NATURE [ch. 
 
 philosophy passed on its way to the refined Aristotelian 
 concept of substance and to which science returned as 
 it reacted against philosophic abstractions. Earth, fire, 
 and water in the Ionic philosophy and the shaped 
 elements in the Timaeus are comparable to the matter 
 and ether of modern scientific doctrine. But substance 
 represents the final philosophic concept of the sub- 
 stratum which underlies any attribute. Matter (in the 
 scientific sense) is already in space and time. Thus 
 matter represents the refusal to think away spatial and 
 temporal characteristics and to arrive at the bare con- 
 cept of an individual entity. It is this refusal which has 
 caused the muddle of importing the mere procedure of 
 thought into the fact of nature. The entity, bared of 
 all characteristics except those of space and time, has ac- 
 quired a physical status as the ultimate texture of nature ; 
 so that the course of nature is conceived as being merely 
 the fortunes of matter in its adventure through space. 
 Thus the origin of the doctrine of matter is the out- 
 come of uncritical acceptance of space and time as 
 external conditions for natural existence. By this I do 
 not mean that any doubt should be thrown on facts of 
 space and time as ingredients in nature. What I do 
 mean is 'the unconscious presupposition of space and 
 time as being that within which nature is set.' This is 
 exactly the sort of presupposition which tinges thought 
 in any reaction against the subtlety of philosophical 
 I criticism. My theory of the formation of the scientific 
 I doctrine of matter is that first philosophy illegitimately 
 transformed the bare entity, which is simply an ab- 
 straction necessary for the method of thought, into 
 the metaphysical substratum of these factors in nature 
 which in various senses are assigned to entities as their 
 
I] NATURE AND THOUGHT 21 
 
 attributes ; and that, as a second step, scientists (includ- 
 ing philosophers who were scientists) in conscious or 
 unconscious ignoration of philosophy presupposed this 
 substratum, qua substratum for attributes, as never- 
 theless in time and space. 
 
 This is surely a muddle. The whole being of substance 
 is as a substratum for attributes. Thus time and space 
 should be attributes of the substance. This they 
 palpably are not, if the matter be the substance of 
 nature, since it is impossible to express spatio-temporal 
 truths without having recourse to relations involving 
 relata other than bits of matter. I waive this point 
 however, and come to another. It is not the substance f ^'^^ 
 whiclL is _in_ space ^ but the attributes. What we find in/ 
 space are the red of the rose and the smell of the jasmine/ 
 and the noise of cannon. We have all told our dentistsi 
 where our toothache is. Thus space is not a relatioiJ , 
 between substances, but between attributes. 
 
 Thus even if you admit that the adherents of sub- 
 stance can be allowed to conceive substance as matter, 
 it is a fraud to slip substance into space on the plea 
 that space expresses relations between substances. On 
 the face of it space has nothing to do with substances, 
 but only with their attributes. What I mean is, that 
 if you choose — as I think wrongly — ^to construe our ex- 
 perience of nature as an awareness of the attributes of 
 substances, we are by this theory precluded from finding 
 any analogous direct relations between substances as 
 disclosed in our experience. What we do find are I 
 relations between the attributes of substances. Thus if \ 
 matter is looked on as substance in space, the space in \ 
 which it finds itself has very little to do with the space j 
 of our experience. 
 
22 THE CONCEPT OF NATURE [ch. 
 
 The above argument has been expressed in terms of 
 the relational theory of space. But if space be absolute 
 — ^namely, if it have a being independent of things in it 
 — ^the course of the argument is hardly changed. For 
 things in space must have a certain fundamental relation 
 to space which we will call occupation. Thus the ob- 
 jection that it is the attributes which are observed as 
 related to space, still holds. 
 
 The scientific doctrine of matter is held in conjunc- 
 tion with an absolute theory of time. The same argu- 
 ments apply to the relations between matter and time 
 as apply to the relations between space and matter. 
 There is however (in the current philosophy) a difference 
 in the connexions of space with matter from those of 
 time with matter, which I will proceed to explain. 
 
 Space is not merely an ordering of material entities 
 so that any one entity bears certain relations to other 
 material entities. The occupation of space impresses a 
 certain character on each material entity in itself. By 
 reason of its occupation of space matter has extension. 
 By reason of its extension each bit of matter is divisible 
 into parts, and each part is a numerically distinct 
 entity from every other such part. Accordingly it 
 would seem that every material entity is not really one 
 entity. It is an essential multiplicity of entities. There 
 seems to be no stopping this dissociation of matter into 
 multiplicities short of finding each ultimate entity 
 occupying one individual point. This essential multi- 
 plicity of material entities is certainly not what is meant 
 by sciep^, nor does it correspond to anything disclosed 
 in sense-awareness. It is absolutely necessary that at 
 a certain stage in this dissociation of matter a halt should 
 be called, and that the material entities thus obtained 
 
I] NATURE AND THOUGHT 23 
 
 should be treated as units. The stage of arrest may be 
 arbitrary or may be set by the characteristics of nature ; 
 but all reasoning in science ultimately drops its space- 
 analysis and poses to itself the problem, ' Here is one 
 material entity, what is happening to it as a unit 
 entity?' Yet this material entity is still retaining its 
 extension, and as thus extended is a mere multiplicity. 
 Thus there is an essential atomic property in nature 
 which is independent of the dissociation of extension. 
 There is something which in itself is one, and which is 
 more than the logical aggregate of entities occupying 
 points within the volume which the unit occupies. 
 Indeed we may well be sceptical as to these ultimate 
 entities at points, and doubt whether there are any such 
 entities at all. They have the suspicious character thati 
 we are driven to accept them by abstract logic and not! 
 by observed fact. ' 
 
 Time (in the current philosophy) does not exert the 
 same disintegrating effect on matter which occupies it. 
 If matter occupies a duration of time, the whole matter 
 occupies every part of that duration. Thus the connexion 
 between matter and time differs from the connexion 
 between matter and space as expressed in current 
 scientific philosophy. There is obviously a greater 
 difficulty in conceiving time as the outcome of relations 
 between different bits of matter than there is in the 
 analogous conception of space. At an instant distinct 
 volumes of space are occupied by distinct bits of matter. 
 Accordingly there is so far no intrinsic difficulty in 
 conceiving that space is merely the resultant of relations 
 between the bits of matter. But in the one-dimensional 
 time the same bit of matter occupies different portions 
 of time. Accordingly time would have to be expressible 
 
24 THE CONCEPT OF NATURE [ch. 
 
 in terms of the relations of a bit of matter with itself. 
 My own view is a belief in the relational theory both of 
 space and of time, and of disbelief in the current form 
 of the relational theory of space which exhibits bits 
 
 I of matter as the relata for spatial relations. The true 
 relata are events. The distinction which I have just 
 pointed out between time and space in their connexion 
 with matter makes it evident that any assimilation of 
 time and space cannot proceed along the traditional line 
 of taking matter as a fundamental element in space- 
 formation. 
 
 The philosophy of nature took a wrong turn during 
 its development by Greek thought. This erroneous 
 presupposition is vague and fluid in Plato's Timaeus. 
 The general groundwork of the thought is still un- 
 committed and can be construed as merely lacking due 
 explanation and the guarding emphasis. But in 
 Aristotle's exposition the current conceptions were 
 hardened and made definite so as to produce a faulty 
 analysis of the relation between the matter and the form 
 of nature as disclosed in sense-awareness. In this phrase 
 the term 'matter' is not used in its scientific sense. 
 
 I will conclude by guarding myself against a mis- 
 apprehension. It is evident that the current doctrine of 
 matter enshrines some fundamental law of nature. Any 
 simple illustration will exemplify what I mean. For 
 example, in a museum some specimen is locked securely 
 in a glass case. It stays there for years : it loses its colour, 
 and perhaps falls to pieces. But it is the same specimen ; 
 and the same chemical elements and the same quantities 
 of those elements are present within the case at the end 
 as were present at the beginning. Again the engineer 
 and the astronomer deal with the motions of real per- 
 
I] NATURE AND THOUGHT 25 
 
 manences in nature. Any theory of nature which for 
 one moment loses sight of these great basic facts of 
 experience is simply silly. But it is permissible to point 
 out that the scientific expression of these facts has be- 
 come entangled in a maze of doubtful metaphysics; 
 and that, when we remove the metaphysics and start 
 afresh on an unprejudiced survey of nature, a new light 
 is thrown on many fundamental concepts which domi- 
 nate science and guide the progress of research. 
 
^ 
 
 CHAPTER II 
 
 THEORIES OF THE BIFURCATION 
 OF NATURE 
 
 j In my previous lecture I criticised the concept of matter 
 » as the substance whose attributes we perceive. This way 
 of thinking of matter is, I think, the historical reason 
 for its introduction into science, and is still the vague 
 view of it at the background of our thoughts which 
 makes the current scientific doctrine appear so obvious. 
 Namely we conceive ourselves as perceiving attributes 
 of things, and bits of matter are the things whose 
 attributes we perceive. 
 
 In the seventeenth century the sweet simplicity of 
 this aspect of matter received a rude shock. The trans- 
 mission doctrines of science were then in process of 
 elaboration and by the end of the century were un- 
 questioned, though their particular forms have since 
 been modified. The establishment of these transmission 
 theories marks a turning point in the relation between 
 science and philosophy. The doctrines to which I am 
 especially alluding are the theories of light and sound. 
 I have no doubt that the theories had been vaguely 
 floating about before as obvious suggestions of common 
 sense; for nothing in thought is ever completely new. 
 But at that epoch they were systematised and made 
 exact, and their complete consequences were ruthlessly 
 II deduced. It is the establishment of this procedure of 
 II taking the consequences seriously which marks the 
 ||real discovery of a theory. Systematic doctrines of 
 light and sound as being something proceeding from 
 
CH.ii] THEORIES OF BIFURCATION OF NATURE 27 
 
 the emitting bodies were definitely established, and in 
 particular the connexion of Hght with colour was laid 
 bare by Newton. 
 
 The result completely destroyed the simplicity of the 
 * substance and attribute' theory of perception. What 
 we see depends on the light entering the eye. Further- 
 more we do not even perceive what enters the eye. The 
 things transmitted are waves or — as Newton thought — 
 minute particles, and the things seen are colours. Locke 
 met this difficulty by a theory of primary and secondary 
 qualities. Namely, there are some attributes of the 
 matter which we do perceive. These are the primary 
 qualities, and there are other things which we perceive, 
 such as colours, which are not attributes of matter, but 
 are perceived by us as if they were such attributes. 
 These are the secondary qualities of matter. 
 
 Why should we perceive secondary qualities.'^ It 
 seems an extremely unfortunate arrangement that we 
 should perceive a lot of things that are not there. Yet 
 this is what the theory of secondary qualities in fact 
 comes to. There is now reigning in philosophy and in 
 science an apathetic acquiescence in the conclusion that 
 no coherent account can be given of nature as it is 
 disclosed to us in sense-awareness, without dragging in 
 its relations to mind. The modern account of nature is 
 not, as it should be, merely an account of what the mind 
 knows of nature ; but it is also confused with an account 
 of what nature does to the mind. The result has been 
 disastrous both to science and to philosophy, but chiefly 
 to philosophy. It has transformed the grand question 
 of the relations between nature and mind into the petty 
 form of the interaction between the human body and 
 mind. 
 
• 
 
 28 THE CONCEPT OF NATURE [ch. 
 
 Berkeley's polemic against matter was based on this 
 confusion introduced by the transmission theory of 
 light. He advocated, rightly as I think, the abandon- 
 ment of the doctrine of matter in its present form. He 
 had however nothing to put in its place except a theory 
 of the relation of finite minds to the divine mind. 
 
 But we are endeavouring in these lectures to limit 
 ourselves to nature itself and not to travel beyond 
 entities which are disclosed in sense-awareness. 
 
 Percipience in itself is taken for granted. We consider 
 indeed conditions for percipience, but only so far as 
 those conditions are among the disclosures of percep- 
 tion. We leave to metaphysics the synthesis of the 
 knower and the known. Some further explanation and 
 defence of this position is necessary, if the line of argu- 
 ment of these lectures is to be comprehensible. 
 
 The immediate thesis for discussion is that any meta- 
 physical interpretation is an illegitimate importation into 
 the philosophy of natural science. By a metaphysical 
 interpretation I mean any discussion of the how (beyond 
 nature) and of the why (beyond nature) of thought and 
 sense-awareness. In the philosophy of science we seek 
 the general notions which apply to nature, namely, to 
 what we are aware of in perception. It is the philosophy 
 of the thing perceived, and it should not be confused 
 with the metaphysics of reality of which the scope 
 embraces both perceiver and perceived. No perplexity 
 concerning the object of knowledge can be solved by 
 saying that there is a mind knowing it^. 
 
 In other words, the ground taken is this: sense- 
 awareness is an awareness of something. What then is 
 the general character of that something of which we 
 1 Cf. Enquiry, preface. 
 
II] THEORIES OF BIFURCATION OF NATURE 29 
 
 are aware? We do not ask about the percipient or 
 about the process, but about the perceived. I emphasise 
 this point because discussions on the philosophy of 
 science are usually extremely metaphysical — in my 
 opinion, to the great detriment of the subject. 
 
 The recourse to metaphysics is like throwing a match 
 into the powder magazine. It blows up the whole arena. 
 This is exactly what scientific philosophers do when 
 they are driven into a corner and convicted of inco- 
 herence. They at once drag in the mind and talk of 
 entities in the mind or out of the mind as the case may 
 be. For natural philosophy everything perceived is in 
 nature. We n^ay not pick and choose. For us the red 
 glow of the sunset should be as much part of nature as 
 are the molecules and electric waves by which men of 
 /science would explain the phenomenon. It is for natural/^ f 
 philosophy to analyse how these various elements of j^. \W^ia 
 I nature are connected. A^'^t-^t^^/iw M 
 
 In making this demand I conceive myself as adopting V^^iJ^ 
 our immediate instinctive attitude towards perceptual 
 knowledge which is only abandoned under the influence 
 of theory. We are instinctively willing to believe that by 
 due attention, more can be found in nature than that 
 which is observed at first sight. But we will not be 
 content with less. What we ask from the philosopliy of 
 science is some account of the coherence of things 
 perceptively known . 
 
 This means a refusal to countenance any theory of 
 psychic additions to the object known in perception. 
 For example, what is given in perception is the green 
 grass. This is an object which we know as an ingredient 
 in nature. The theory of psychic additions would treat 
 the greenness as a psychic addition furnished by the 
 
 U*^ 
 
 ^ 
 
 ^ MiCinAl ^<dcVsii fKACiJUftJi I 
 
I 
 
 30 THE CONCEPT OF NATURE [ch. 
 
 perceiving mind, and would leave to nature merely the 
 molecules and the radiant energy which influence the 
 mind towards that perception. My argument is that this 
 dragging in of the mind as making additions of its own 
 to the thing posited for knowledge by sense-awareness 
 is merely a way of shirking the problem of natural 
 philosophy. That problem is to discuss the relations 
 inter se of things known, abstracted from the bare fact 
 that they are known. Natural philosophy should never 
 ask, what is in the mind and what is in nature. To do so 
 is a confession that it has failed to express relations 
 between things perceptively known, namely to express 
 those natural relations whose expression is natural 
 philosophy. It may be that the task is too hard for us, 
 that the relations are too complex and too various for 
 our apprehension, or are too trivial to be worth the 
 trouble of exposition. It is indeed true that we have 
 gone but a very small way in the adequate formulation 
 of such relations. But at least do not let us endeavour 
 to conceal failure under a theory of the byplay of the 
 perceiving mind. 
 
 What I am essentially protesting against is the bi- 
 furcation of nature into two systems of reality, which, 
 in so far as they are real, are real in different senses. 
 One reality would be the entities such as electrons which 
 are the study of speculative physics. This would be the 
 reality which is there for knowledge ; although on this 
 theory it is never known. For what is known is the 
 other sort of reality, which is the byplay of the mind. 
 Thus there would be two natures, one is the conjecture 
 and the other is the dream. 
 
 Another way of phrasing this theory which I am 
 arguing against is to bifurcate nature into two divisions, 
 
II] THEORIES OF BIFURCATION OF NATURE 31 
 
 namely into the nature apprehended in awareness and 
 the nature which is the cause of awareness. The nature 
 which is the fact apprehended in awareness holds within 
 it the greenness of the trees, the song of the birds, the 
 warmth of the sun, the hardness of the chairs, and the 
 feel of the velvet. The nature which is the cause of 
 awareness is the conjectured system of molecules and 
 electrons which so affects the mind as to produce the 
 awareness of apparent nature. The meeting point of 
 these two natures is the mind, the causal nature being 
 influent and the apparent nature being effluent. 
 
 There are four questions which at once suggest 
 themselves for discussion in connexion with this bi- 
 furcation theory of nature. They concern (i) causality, 
 (ii) time, (iii) space, and (iv) delusions. These questions 
 are not really separable. They merely constitute four 
 distinct starting points from which to enter upon the 
 discussion of the theory. 
 
 Causal nature is the influence on the mind which is 
 the cause of the effluence of apparent nature from the 
 mind. This conception of causal nature is not to be 
 confused with the distinct conception of one part of 
 nature as being the cause of another part. For example, 
 the burning of the fire and the passage of heat from it 
 through intervening space is the cause of the body, its 
 nerves and its brain, functioning in certain ways. But 
 this is not an action of nature on the mind. It is an 
 interaction within nature. The causation involved in this 
 interaction is causation in a different sense from the 
 influence of this system of bodily interactions within 
 nature on the alien mind which thereupon perceives 
 redness and warmth. 
 
 The bifurcation theory is an attempt to exhibit 
 
32 THE CONCEPT OF NATURE [ch. 
 
 natural science as an investigation of the cause of the 
 fact of knowledge. Namely, it is an attempt to exhibit 
 apparent nature as an effluent from the mind because of 
 causal nature. The whole notion is partly based on the 
 implicit assumption that the mind can only know that 
 which it has itself produced and retains in some sense 
 within itself, though it requires an exterior reason both 
 as originating and as determining the character of its 
 activity. But in considering knowledge we should wipe 
 out all these spatial metaphors, such as * within the 
 mind' and * without the mind.' Knowledge is ultimate. 
 There can be no explanation of the * why ' of knowledge ; 
 we can only describe the * what ' of knowledge. Namely 
 we can analyse the content and its internal relations, 
 but we cannot explain why there is knowledge. Thus 
 causal nature is a metaphysical chimera ; though there is 
 need of a metaphysics whose scope transcends the 
 limitation to nature. The object of such a metaphysical 
 science is not to explain knowledge, but exhibit in its 
 utmost completeness our concept of reality. 
 
 However, we must admit that the causality theory of 
 nature has its strong suit. The reason why the bifurca- 
 tion of nature is always creeping back into scientific 
 philosophy is the extreme difficulty of exhibiting the 
 perceived redness and warmth of the fire in one system 
 of relations with the agitated molecules of carbon and 
 oxygen, with the radiant energy from them, and with the 
 various functionings of the material body. Unless we 
 produce the all-embracing relations, we are faced with a 
 bifurcated nature ; namely, warmth and redness on one 
 side, and molecules, electrons and ether on the other 
 side. Then the two factors are explained as being re- 
 spectively the cause and the mind's reaction to the cause. 
 
ii] THEORIES OF BIFURCATION OF NATURE 33 
 
 Time and space would appear to provide these all- 
 embracing relations which the advocates of the philo- 
 sophy of the unity of nature require. The perceived 
 redness of the fire and the warmth are definitely related 
 in time and in space to the molecules of the fire and the 
 molecules of the body. 
 
 It is hardly more than a pardonable exaggeration to 
 say that the determination of the meaning of nature 
 reduces itself principally to the discussion of the charac- 
 ter of time and the character of space. In succeeding 
 lectures I shall explain my own view of time and space. 
 I shall endeavour to show that they are abstractions 
 from more concrete elements of nature, namely, from 
 events. The discussion of the details of the process of 
 abstraction will exhibit time and space as interconnected, 
 and will finally lead us to the sort of connexions between 
 their measurements which occur in the modern theory 
 of electromagnetic relativity. But this is anticipating 
 our subsequent line of development. At present I wish 
 to consider how the ordinary views of time and space 
 help, or fail to help, in unifying our conception of nature. 
 
 First, consider the absolute theories of time and 
 space. We are to consider each, namely both time and 
 space, to be a separate and independent system of 
 entities, each system known to us in itself and for itself 
 concurrently with our knowledge of the events of 
 nature. Time is the ordered succession of durationless 
 instants ; and these instants are known to us merely as 
 the relata in the serial relation which is the time- 
 ordering relation, and the time-ordering relation is 
 merely known to us as relating the instants. Namely, 
 the relation and the instants are jointly known to us in 
 our apprehension of time, each implying the other. 
 
 W. N. ^ 
 
34 THE CONCEPT OF NATURE [ch. 
 
 This is the absolute theory of time. Frankly, I con- 
 fess that it seems to me to be very unplausible. I cannot 
 in my own knowledge find anything corresponding to 
 the bare time of the absolute theory. Time is known to 
 me as an abstraction from the passage of events. The 
 fundamental fact which renders this abstraction possible 
 is the passing of nature, its development, its creative 
 advance, and combined with this fact is another charac- 
 teristic of nature, namely the extensive relation between 
 events. These two facts, namely the passage of events 
 and the extension of events over each other, are in my 
 opinion the qualities from which time and space originate 
 as abstractions. But this is anticipating my own later 
 speculations. 
 
 Meanwhile, returning to the absolute theory, we are 
 to suppose that time is known to us independently of 
 any events in time. What happens in time occupies time. 
 This relation of events to the time occupied, namely 
 this relation of occupation, is a fundamental relation of 
 nature to time. Thus the theory requires that we are 
 aware of two fundamental relations, the time-ordering 
 relation between instants, and the time-occupation 
 relation between instants of time and states of nature 
 which happen at those instants. 
 
 There are two considerations which lend powerful 
 support to the reigning theory of absolute time. In 
 the first place time extends beyond nature. Our thoughts 
 are in time. Accordingly it seems impossible to derive 
 time merely from relations between elements of nature. 
 For in that case temporal relations could not relate 
 thoughts. Thus, to use a metaphor, time would ap- 
 parently have deeper roots in reality than has nature. 
 For we can imagine thoughts related in time without 
 
II] THEORIES OF BIFURCATION OF NATURE 35 
 
 any perception of nature. For example we can imagine 
 one of Milton's angels with thoughts succeeding each 
 other in time, who does not happen to have noticed 
 that the Almighty has created space and set therein a 
 material universe. As a matter of fact I think that Milton 
 set space on the same absolute level as time. But that 
 need not disturb the illustration. In the second place 
 it is difficult to derive the true serial character of time 
 from the relative theory. Each instant is irrevocable. It 
 can never recur by the very character of time. But if 
 on the relative theory an instant of time is simply the 
 state of nature at that time, and the time-ordering 
 relation is simply the relation between such states, then 
 the irrevocableness of time would seem to mean that 
 an actual state of all nature can never return. I admit 
 it seems unlikely that there should ever be such a 
 recurrence down to the smallest particular. But 
 extreme unlikeliness is not the point. Our ignorance is 
 so abysmal that our judgments of likeliness and un- 
 likeliness of future events hardly count. The real point 
 is that the exact recurrence of a state of nature seems 
 merely unlikely, while the recurrence of an instant of 
 time violates our whole concept of time-order. The 
 instants of time which have passed, are passed, and can 
 never be again. 
 
 Any alternative theory of time must reckon with these 
 two considerations which are buttresses of the absolute 
 theory. But I will not now continue their discussion. 
 
 The absolute theory of space is analogous to the 
 corresponding theory of time, but the reasons for its 
 maintenance are weaker. Space, on this theory, is a 
 system of extensionless points which are the relata in 
 space-ordering relations which can technically be com- 
 
 3—2 
 
36 THE CONCEPT OF NATURE [ch. 
 
 bined into one relation. This relation does not arrange 
 the points in one linear series analogously to the simple 
 method of the time-ordering relation for instants. The 
 essential logical characteristics of this relation from 
 which all the properties of space spring are expressed 
 by mathematicians in the axioms of geometry. From 
 these axioms^ as framed by modern mathematicians 
 the whole science of geometry can be deduced by the 
 strictest logical reasoning. The details of these axioms 
 do not now concern us. The points and the relations 
 are jointly known to us in our apprehension of space, 
 each implying the other. What happens in space, 
 occupies space. This relation of occupation is not 
 usually stated for events but for objects. For example, 
 Pompey's statue would be said to occupy space, but not 
 the event which was the assassination of Julius Caesar. 
 In this I think that ordinary usage is unfortunate, and 
 I hold that the relations of events to space and to time 
 are in all respects analogous. But here I am intruding 
 my own opinions which are to be discussed in subse- 
 quent lectures. Thus the theory of absolute space 
 requires that we are aware of two fundamental relations, 
 the space-ordering relation, which holds between points, 
 and the space-occupation relation between points of 
 space and material objects. 
 
 This theory lacks the two main supports of the corre- 
 sponding theory of absolute time. In the first place space 
 does not extend beyond nature in the sense that time 
 seems to do. Our thoughts do not seem to occupy space 
 in quite the same intimate way in which they occupy 
 time. For example, I have been thinking in a room, and 
 
 1 Cf. (for example) Projective Geometry by Veblen and Young, 
 vol. i. 1 9 10, vol. ii. 19 17, Ginn and Company, Boston, U.S.A. 
 
II] THEORIES OF BIFURCATION OF NATURE 37 
 
 to that extent my thoughts are in space. But it seems 
 nonsense to ask how much volume of the room they 
 occupied, whether it was a cubic foot or a cubic inch; 
 whereas the same thoughts occupy a determinate dura- 
 tion of time, say, from eleven to twelve on a certain date. 
 
 Thus whereas the relations of a relative theory of 
 time are required to relate thoughts, it does not seem so 
 obvious that the relations of a relative theory of space 
 are required to relate them. The connexion of thought 
 with space seems to have a certain character of indirect- 
 ness which appears to be lacking in the connexion of 
 thought with time. 
 
 Again the irrevocableness of time does not seem to 
 have any parallel for space. Space, on the relative theory, 
 is the outcome of certain relations between objects 
 commonly said to be in space ; and whenever there are 
 the objects, so related, there is the space. No difficulty 
 seems to arise like that of the inconvenient instants of 
 time which might conceivably turn up again when we 
 thought that we had done with them. 
 
 The absolute theory of space is not now generally 
 popular. The knowledge of bare space, as a system of 
 entities known to us in itself and for itself independently 
 of our knowledge of the events in nature, does not seem 
 to correspond to anything in our experience. Space, 
 like time, would appear to be an abstraction from events. 
 According to my own theory it only differentiates 
 itself from time at a somewhat developed stage of the 
 abstractive process. The more usual way of expressing 
 the relational theory of space would be to consider space 
 as an abstraction from the relations between material 
 objects. 
 
 Suppose now we assume absolute time and absolute 
 
38 THE CONCEPT OF NATURE [ch. 
 
 space. What bearing has this assumption on the con- 
 cept of nature as bifurcated into causal nature and 
 apparent nature ? Undoubtedly the separation between 
 the two natures is now greatly mitigated. We can pro- 
 vide them with two systems of relations in common ; for 
 both natures can be presumed to occupy the same space 
 and the same time. The theory now is this : Causal events 
 occupy certain periods of the absolute time and occupy 
 certain positions of the absolute space. These events 
 influence a mind which thereupon perceives certain 
 apparent events which occupy certain periods in the 
 absolute time and occupy certain positions of the 
 absolute space ; and the periods and positions occupied 
 by the apparent events bear a determinate relation to 
 the periods and positions occupied by the causal events. 
 Furthermore definite causal events produce for the 
 mind definite apparent events. Delusions are apparent 
 events which appear in temporal periods and spatial 
 positions without the intervention of these causal 
 events which are proper for influencing of the mind to 
 their perception. 
 
 The whole theory is perfectly logical. In these dis- 
 cussions we cannot hope to drive an unsound theory to 
 a logical contradiction. A reasoner, apart from mere 
 slips, only involves himself in a contradiction when he 
 is shying at a reductio ad absurdum. The substantial 
 reason for rejecting a philosophical theory is the ' ab- 
 
 jsurdum* to which it reduces us. In the case of the 
 philosophy of natural science the ' absurdum ' can only; 
 be that our perceptual knowledge has not the character 
 
 ; assigned to it by the theory. If our opponent affirms 
 that his knowledge has that character, we can only — 
 after making doubly sure that we understand each 
 
II] THEORIES OF BIFURCATION OF NATURE 39 
 
 other — ^agree to differ. Accordingly the first duty of 
 an expositor in stating a theory in which he disbelieves 
 is to exhibit it as logical. It is not there where his 
 trouble lies. 
 
 Let me summarise the previously stated objections 
 to this theory of nature. In the first place it seeks for ^ 
 the cause of th e knowled ge "f the thing knowr) j ngtipaH 
 qf ^ seekin g__ for the character of the thing known : 
 secondly it assumes a knowledge of time in itself apart 
 from events related in time : thirdly it assumes a know- 
 ledge of space in itself apart from events related in 
 space. There are in addition to these objections other 
 flaws in the theory. 
 
 Some light is thrown on the artificial status of causal 
 nature in this theory by asking, why causal nature is 
 presumed to occupy time and space. This really raises 
 the fundamental question as to what characteristics 
 causal nature should have in common with apparent 
 nature. Why — on this theory — should the cause which 
 influences the mind to perception have any character- 
 istics in common with the eflSuent apparent nature.? 
 In particular, why should it be in space ? Why should 
 it be in time.^* And more generally. What do we 
 know about mind which would allow us to infer any 
 particular characteristics of a cause which should in- 
 fluence mind to particular effects } 
 
 The transcendence of time beyond nature gives some 
 slight reason for presuming that causal nature should 
 occupy time. For if the mind occupies periods of time, 
 there would seem to be some vague reason for assuming 
 that influencing causes occupy the same periods of 
 time, or at least, occupy periods which are strictly 
 related to the mental periods. But if the mind does not 
 
^i 
 
 40 THE CONCEPT OF NATURE [cH. 
 
 occupy volumes of space, there seems to be no reason 
 why causal nature should occupy any volumes of space. 
 Thus space would seem to be merely apparent in the 
 same sense as apparent nature is merely apparent. 
 Accordingly if science is really investigating causes 
 which operate on the mind, it would seem to be entirely 
 on the wrong tack in presuming that the causes which 
 it is seeking for have spatial relations. Furthermore 
 there is nothing else in our knowledge analogous to 
 these causes which influence the mind to perception. 
 Accordingly, beyond the rashly presumed fact that they 
 occupy time, there is really no ground by which we can 
 determine any point of their character. They must 
 remain for ever unknown. 
 
 Now I assume as an axiom that science is not a 
 fairy tale. It is not engaged in decking out unknowable 
 entities with arbitrary and fantastic properties. What 
 then is it that science is doing, granting that it is 
 effecting something of importance } My answer is that 
 it is determining the character of things known, namely 
 the character of apparent nature. But we may drop the 
 term * apparent'; for there is but one nature, namely 
 the nature which is before us in perceptual knowledge. 
 The characters which science discerns in nature are 
 subtle characters, not obvious at first sight. They are 
 relations of relations and characters of characters. But 
 for all their subtlety they are stamped with a certain 
 simplicity which makes their consideration essential in 
 unravelling the complex relations between characters 
 of more perceptive insistence. 
 
 The fact that the bifurcation of nature into causal and 
 apparent components does not express what we mean 
 by our knowledge is brought before us when we realise 
 
II] THEORIES OF BIFURCATION OF NATURE 41 
 
 our thoughts in any discussion of the causes of our 
 perceptions. For example, the fire is burning and we ' 
 see a red coal. This is explained in science by radiant^ 
 energy from the coal entering our eyes. But in seeking] 
 for such an explanation we are not asking what are the j 
 sort of occurrences which are fitted to cause a mind to j 
 see red. The chain of causation is entirely different. The 
 mind is cut out altogether. The real question is, When 
 red is found in nature, what else is found there also? 
 Namely we are asking for an analysis of the accom- 
 paniments in nature of the discovery of red in nature. 
 In a subsequent lecture I shall expand this line of 
 thought. I simply draw attention to it here in order to 
 point out that the wave-th eory of light has not been 
 adoBt£d,hecause^ave s are just the s^ rFoLthings which 
 ought t o make ajni nd perceive colours. This is no part 
 oTtKe evidence which has ever been adduced for the 
 wave-theory, yet on the causal theory of perception, it 
 is really the only relevant part. In other words, science 
 is not discussing the causes of knowledge, but the 
 
 coherence of knowledge. The understanding which isli 
 
 sought by science is an understanding of relations! i 
 within nature. •' 
 
 So far I have discussed the bifurcation of nature in 
 connexion with the theories of absolute time and of 
 absolute space. My reason has been that the intro- 
 duction of the relational theories only weakens the case 
 for bifurcation, and I wished to discuss this case on 
 its strongest grounds. 
 
 For instance, suppose we adopt the relational theory 
 of space. Then the space in which apparent nature is set 
 is the expression of certain relations between the appa- 
 rent objects. It is a set of apparent relations between 
 
 KjI- 
 
42 THE CONCEPT OF NATURE [ch. 
 
 apparent relata. Apparent nature is the dream, and the 
 apparent relations of space are dream relations, and the 
 space is the dream space. Similarly the space in which 
 causal nature is set is the expression of certain rela- 
 tions between the causal objects. It is the expression 
 of certain facts about the causal activity which is going 
 on behind the scenes. Accordingly causal space belongs 
 to a different order of reality to apparent space. Hence 
 there is no pointwise connexion between the two and 
 it is meaningless to say that the molecules of the grass 
 are in any place which has a determinate spatial relation 
 to the place occupied by the grass which we see. This 
 conclusion is very paradoxical and makes nonsense of 
 all scientific phraseology. The case is even worse if we 
 admit the relativity of time. For the same arguments 
 apply, and break up time into the dream time and causal 
 time which belong to difl^erent orders of reality. 
 
 I have however been discussing an extreme form of 
 the bifurcation theory. It is, as I think, the most 
 defensible form. But its very definiteness makes it the 
 more evidently obnoxious to criticism. The intermediate 
 form allows that the nature we are discussing is always 
 the nature directly known, and so far it rejects the 
 bifurcation theory. But it holds that there are psychic 
 additions to nature as thus known, and that these 
 additions are in no proper sense part of nature. For 
 example, we perceive the red billiard ball at its proper 
 time, in its proper place, with its proper motion, with 
 its proper hardness, and with its proper inertia. But 
 its redness and its warmth, and the sound of the click 
 as a cannon is made oflr it are psychic additions, namely, 
 secondary qualities which are only the mind's way 
 of perceiving nature. This is not only the vaguely 
 
II] THEORIES OF BIFURCATION OF NATURE 43 
 
 prevalent theory, but is, I believe, the historical form of 
 the bifurcation theory in so far as it is derived from 
 philosophy. I shall call it the theory of psychic additions. 
 
 This theory of psychic additions is a sound common- 
 sense theory which lays immense stress on the obvious 
 reality of time, space, solidity and inertia, but distrusts 
 the minor artistic additions of colour, warmth and sound. 
 
 The theory is the outcome of common-sense in 
 retreat. It arose in an epoch when the transmission 
 theories of science were being elaborated. For example, 
 colour is the result of a transmission from the material 
 object to the perceiver's eye; and what is thus trans- 
 mitted is not colour. Thus colour is not part of the 
 reality of the material object. Similarly for the same 
 reason sounds evaporate from nature. Also warmth is 
 due to the transfer of something which is not tempera- 
 ture. Thus we are left with spatio-temporal positions, 
 and what I may term the * pushiness ' of the body. This 
 latias us to eighteenth and nineteenth century material- 
 ism, namely, the belief that what is real in nature is 
 matter, in time and in space and with inertia. 
 
 Evidently a distinction in quality has been presup- 
 posed separating off some perceptions due to touch from 
 other perceptions. These touch-perceptions are per- 
 ceptions of the real inertia, whereas the other perceptions 
 are psychic additions which must be explained on the 
 causal theory. This distinction is the product of an 
 epoch in which physical science has got ahead of medical 
 pathology and of physiology. Perceptions of push are 
 just as much the outcome of transmission as are per- 
 ceptions of colour. When colour is perceived the nerves 
 of the body are excited in one way and transmit their 
 message towards the brain, and when push is perceived 
 
44 THE CONCEPT OF NATURE [cH. 
 
 other nerves of the body are excited in another way and 
 transmit their message towards the brain. The message 
 of the one set is not the conveyance of colour, and the 
 message of the other set is not the conveyance of push. 
 But in one case colour is perceived and in the other 
 case the push due to the object. If you snip certain 
 nerves, there is an end to the perception of colour; and 
 if you snip certain other nerves, there is an end to the 
 perception of push. It would appear therefore that any 
 reasons which should remove colour from the reality of 
 nature should also operate to remove inertia. 
 
 Thus the attempted bifurcation of apparent nature 
 into two parts of which one part is both causal for its 
 own appearance and for the appearance of the other 
 part, which is purely apparent, fails owing to the failure 
 to establish any fundamental distinction between our 
 ways of knowing about the two parts of nature as thus 
 partitioned. I am not denying that the feeling of 
 muscular effort historically led to the formulation of 
 the concept of force. But this historical fact does not 
 warrant us in assigning a superior reality in nature to 
 material inertia over colour or sound. So far as reality 
 is concerned all our sense-perceptions are in the same 
 boat, and must be treated on the same principle . The 
 evenness of treatment is exactly what this compromise 
 theory fails to achieve. 
 
 The bifurcation theory however dies hard. The 
 reason is that there really is a difficulty to be faced in 
 relating within the same system of entities the redness 
 of the fire with the agitation of the molecules. In another 
 lecture I will give my own explanation of the origin of 
 the difficulty and of its solution. 
 
 Another favourite solution, the most attenuated form 
 
II] THEORIES OF BIFURCATION OF NATURE 45 
 
 which the bifurcation theory assumes, is to maintain 
 that the molecules and ether of science are purely 
 conceptual. Thus there is but one nature, namely 
 apparent nature, and atoms and ether are merely names 
 for logical terms in conceptual formulae of calculation. 
 But what is a formula of calculation } It is presum- 
 ably a statement that something or other is true for 
 natural occurrences. Take the simplest of all formulae, 
 Two and two make four. This — so far as it applies to 
 nature — asserts that if you take two natural entities, 
 and then again two other natural entities, the combined 
 class contains four natural entities. Such formulae 
 which are true for any entities cannot result in the 
 production of the concepts of atoms. Then again there 
 are formulae which assert that there are entities in 
 nature with such and such special properties, say, for 
 example, with the properties of the atoms of hydrogen. 
 Now if there are no such entities, I fail to see how 
 any statements about them can apply to nature. For 
 example, the assertion that there is green cheese in the 
 moon cannot be a premiss in any deduction of scientific 
 importance, unless indeed the presence of green cheese 
 in the moon has been verified by experiment. The 
 current answer to these objections is that, though atoms 
 are merely conceptual, yet they are an interesting and 
 picturesque way of saying something else which is true 
 of nature. But surely if it is something else that you 
 mean, for heaven's sake say it. Do away with this 
 elaborate machinery of a conceptual nature which 
 consists of assertions about things which don't exist in 
 order to convey truths about things which do exist. 
 I am maintaining the obvious position that scientific 
 laws, if they are true, are statements about entities 
 
46 THE CONCEPT OF NATURE [ch. 
 
 which we obtain knowledge of as being in nature ; and 
 that, if the entities to which the statements refer are 
 not to be found in nature, the statements about them 
 ; have no relevance to any purely natural occurrence. 
 I Thus the molecules and electrons of scientific theory 
 i are, so far as science has correctly formulated its laws, 
 ; each of them factors to be found in nature. The elec- 
 trons are only hypothetical in so far as we are not quite 
 certain that the electron theory is true. But their hypo- 
 thetical character does not arise from the essential nature 
 of the theory in itself after its truth has been granted. 
 Thus at the end of this somewhat complex discussion, 
 we return to the position which was affirmed at its 
 beginning. The primary tasl f^ of a philosophy of natural 
 science is to elucidate the concept of nature, considered 
 as one complex fact for knowledge, to exhibit the funda- 
 mental entities and the fundamental relations between 
 entities in terms of which all laws of nature have to be 
 stated, and to secure that the entities and relations thus 
 exhibited are adequate for the expression of all the 
 relations between entities which occur in nature. 
 
 The third requisite, namely that of adequacy, is the 
 one over which all the difficulty occurs. The ultimate 
 data of science are commonly assumed to be time, space, 
 material, qualities of material, and relations between 
 material objects. But data as they occur in the scientific 
 laws do not relate all the entities which present them- 
 selves in our perception of nature. For example, the 
 wave-theory of light is an excellent well-established 
 theory; but unfortunately it leaves out colour as per- 
 ceived. Thus the perceived redness — or, other colour — 
 has to be cut out of nature and made into the reaction 
 of the mind under the impulse of the actual events of 
 
II] THEORIES OF BIFURCATION OF NATURE 47 
 
 nature. In other words this concept of the fundamental 
 relations within nature is inadequate. Thus we have 
 to bend our energies to the enunciation of adequate 
 concepts. 
 
 But in so doing, are we not in fact endeavouring to 
 solve a metaphysical problem? I do not think so. We 
 are merely endeavouring to exhibit the type of relations 
 which hold between the entities which we. in fact per- 
 ceive as in nature. We are not called on to make any 
 pronouncement as to the psychological relation of 
 subjects to objects or as to the status of either in the 
 realm of reality. It is true that the issue of our endeavour 
 may provide material which is relevant evidence for a 
 discussion on that question. It can hardly fail to do so. 
 But it is only evidence, and is not itself the metaphysical 
 discussion. In order to make clear the character of this 
 further discussion which is out of our ken, I will set 
 before you two quotations. One is from Schelling and 
 I extract the quotation from the work of the Russian 
 philosopher Lossky which has recently been so ex- 
 cellently translated into English ^ — * In the *' Philosophy 
 of Nature '' I considered the subject-object called nature 
 in its activity of self-constructing. In order to under- 
 stand it, we must rise to an intellectual intuition of nature. 
 The empiricist does not rise thereto, and for this reason 
 in all his explanations it is always he himself that proves 
 to be constructing nature. It is no wonder, then, that 
 his construction and that which was to be constructed 
 so seldom coincide. A Natur-philosoph raises nature to 
 independence, and makes it construct itself, and he 
 never feels, therefore, the necessity of opposing nature 
 
 1 The Intuitive Basis of Knowledge, by N. O. Lossky, transl. by 
 Mrs Duddington, Macmillan and Co., 19 19. 
 
48 THE CONCEPT OF NATURE [ch. ii 
 
 as constructed {i.e. as experience) to real nature, or of 
 correcting the one by means of the other.' 
 
 The other quotation is from a paper read by the Dean 
 of St Paul's before the Aristotelian Society in May of 
 19 19. Dr Inge's paper is entitled *Platonism and 
 Human Immortality,' and in it there occurs the following 
 statement: *To sum up. The Platonic doctrine of im- 
 mortality rests on the independence of the spiritual world. 
 The spiritual world is not a world of unrealised ideals, 
 over against a real world of unspiritual fact. It is, on 
 the contrary, the real world, of which we have a true 
 though very incomplete knowledge, over against a world 
 of common experience which, as a complete whole, is 
 not real, since it is compacted out of miscellaneous data, 
 not all on the same level, by the help of the imagination. 
 There is no world corresponding to the world of our 
 common experience. Nature makes abstractions for us, 
 deciding what range of vibrations we are to see and hear, 
 what things we are to notice and remember.' 
 
 I have cited these statements because both of them 
 deal with topics which, though they lie outside the range 
 of our discussion, are always being confused with it. 
 The reason is that they lie proximate to our field of 
 thought, and are topics which are of burning interest 
 to the metaphysically minded. It is difficult for a 
 philosopher to realise that anyone really is confining 
 his discussion within the limits that I have set before 
 you. The boundary is set up just where he is beginning 
 to get excited. But I submit to you that among the 
 necessary prolegomena for philosophy and for natural 
 science is a thorough understanding of the types of 
 entities, and types of relations among those entities, 
 which are disclosed to us in our perceptions of nature. 
 
CHAPTER III 
 
 TIME 
 
 The two previous lectures of this course have been 
 mainly critical. In the present lecture I propose to 
 enter upon a survey of the kinds of entities which are 
 posited for knowledge in sense-awareness. My purpose 
 is to investigate the sorts of relations which these entities 
 of various kinds can bear to each other. A classification 
 of natural entities is the beginning of natural philosophy. 
 To-day we commence with the consideration of Time. 
 
 In the first place there is posited for us a general 
 fact: namely, something is going on; there is an oc- 
 currence for definition. 
 
 This general fact at once yields for our apprehension 
 two factors, which I will name, the * discerned' and the 
 * discernible.' The discerned is comprised of those 
 elements of the general fact which are discriminated 
 with their own individual peculiarities. It is the field 
 directly perceived. But the entities of this field have 
 relations to other entities which are not particularly 
 discriminated in this individual way. These other 
 entities are known merely as the relata in relation to the 
 entities of the discerned field. Such an entity is merely 
 a * something' which has such-and-such definite rela- 
 tions to some definite entity or entities in the discerned 
 field. As being thus related, they are — owing to the 
 particular character of these relations — ^known as 
 elements of the general fact which is going on. But we 
 are not aware of them except as entities fulfilling the 
 functions of relata in these relations. 
 
 Thus the complete general fact, posited as occurring, 
 comprises both sets of entities, namely the entities 
 
50 THE CONCEPT OF NATURE [ch. 
 
 perceived in their own individuality and other entities 
 merely apprehended as relata without further definition. 
 This complete general fact is the discernible and it 
 comprises the discerned. The discernible is all nature as 
 disclosed in that sense-awareness, and extends beyond 
 and comprises all of nature as actually discriminated 
 or discerned in that sense-awareness. The discerning 
 or discrimination of nature is a peculiar awareness of 
 special factors in nature in respect to their peculiar cha- 
 racters. But the factors in nature of which we have this 
 peculiar sense-awareness are known as not comprising 
 all the factors which together form the whole complex 
 of related entities within the general fact there for 
 discernment. This peculiarity of knowledge is what I 
 call its unexhaustive character. This character may be 
 metaphorically described by the statement that nature 
 as perceived always has a ragged edge. For example, 
 there is a world beyond the room to which our sight is 
 confined known to us as completing the space-relations 
 of the entities discerned within the room. The junction 
 of the interior world of the room with the exterior world 
 beyond is never sharp. Sounds and subtler factors 
 disclosed in sense-awareness float in from the outside. 
 Every type of sense has its own set of discriminated 
 entities which are known to be relata in relation with 
 entities not discriminated by that sense. For example we 
 see something which we do not touch and we touch 
 something which we do not see, and we have a general 
 sense of the space-relations between the entity dis- 
 closed in sight and the entity disclosed in touch. Thus 
 in the first place each of these two entities is known as 
 a relatum in a general system of space-relations and 
 in the second place the particular mutual relation of 
 
Ill] TIME 51 
 
 these two entities as related to each other in this general 
 system is determined. But the general system of space- 
 relations relating the entity discriminated by sight 
 with that discriminated by sight is not dependent on 
 the peculiar character of the other entity as reported 
 by the alternative sense. For example, the space- 
 relations of the thing seen would have necessitated an 
 entity as a relatum in the place of the thing touched 
 even although certain elements of its character had not 
 been disclosed by touch. Thus apart from the touch 
 an entity with a certain specific relation to the thing seen 
 would have been disclosed by sense-awareness but not 
 otherwise discriminated in respect to its individual 
 character. An entity merely known as spatially related 
 to some discerned entity is what we mean by the bare 
 idea of * place.' The concept of place marks the dis- 
 closure in sense-awareness of entities in nature known 
 merely by their spatial relations to discerned entities. 
 It is the disclosure of the discernible by means of its 
 relations to the discerned. 
 
 This disclosure of an entity as a relatum without 
 further specific discrimination of quality is the basis of 
 our concept of significance. In the above example the 
 thing seen was significant, in that it disclosed its spatial 
 relations to other entities not necessarily otherwise 
 entering into consciousness. Thus significance is re- 
 latedness, but it is relatedness with the emphasis on one 
 end only of the relation. 
 
 For the sake of simplicity I have confined the argu- 
 ment to spatial relations; but the same considerations 
 apply to temporal relations. The concept of 'period of 
 time ' marks the disclosure in sense-awareness of entities 
 in nature known merely by their temporal relations to 
 
 4—2 
 
52 THE CONCEPT OF NATURE [ch. 
 
 discerned entities. Still further, this separation of the 
 ideas of space and time has merely been adopted for the 
 sake of gaining simplicity of exposition by conformity 
 to current language. What we discern is the specific 
 character of a place through a period of time. This is 
 what I mean by an * event.' We discern some specific 
 character of an event. But in discerning an event we 
 are also aware of its significance as a relatum in the struc- 
 ture of events. This structure of events is the complex 
 of events as related by the two relations of extension and 
 cogredience. The most simple expression of the proper- 
 ties of this structure are to be found in our spatial and 
 temporal relations. A discerned event is known as related 
 in this structure to other events whose specific characters 
 are otherwise not disclosed in that immediate awareness 
 except so far as that they are relata within the structure. 
 The disclosure in sense-awareness of the structure 
 of events classifies events into those which are discerned 
 in respect to some further individual character and those 
 which are not otherwise disclosed except as elements 
 of the structure. These signified events must include 
 events in the remote past as well as events in the 
 future. We are aware of these as the far off periods of 
 unbounded time. But there is another classification of 
 events which is also inherent in sense-awareness. These 
 are the events which share the immediacy of the im- 
 mediately present discerned events. These are the events 
 whose characters together with those of the discerned 
 events comprise all nature present for discernment. 
 They form the complete general fact which is all nature 
 now present as disclosed in that sense-awareness. It is 
 in this second classification of events that the differentia- 
 tion of space from time takes its origin. The germ of 
 
Ill] TIME 53 
 
 space is to be found in the mutual relations of events 
 within the immediate general fact which is all nature 
 now discernible, namely within the one event which is 
 the totality of present nature. The relations of other 
 events to this totality of nature form the texture of time. 
 
 The unity of this general present fact is expressed by 
 the concept of simultaneity. The general fact is the 
 whole simultaneous occurrence of nature which is now 
 for sense-awareness. This general fact is what I have 
 called the discernible. But in future I will call it a 
 * duration/ meaning thereby a certain whole of nature 
 which is limited only by the property of being a simul- 
 taneity. Further in obedience to the principle of com- 
 prising within nature the whole terminus of sense-aware- 
 ness, simultaneity must not be conceived as an irrelevant 
 mental concept imposed upon nature. Our sense- 
 awareness posits for immediate discernment a certain 
 whole, here called a * duration'; thus a duration is a 
 definite natural entity. A duration is discriminated as 
 a complex of partial events, and the natural entities 
 which are components of this complex are thereby said 
 to be * simultaneous with this duration? Also in a 
 derivative sense they are simultaneous with each other 
 in respect to this duration. Thus simultaneity is a 
 definite natural relation. The word * duration ' is perhaps 
 unfortunate in so far as it suggests a mere abstract 
 stretch of time. This is not what I mean. A duration is 
 a concrete slab of nature limited by simultaneity which 
 is an essential factor disclosed in sense-awareness. 
 
 Nature is a process. As in the case of everything 
 directly exhibited in sense-awareness, there can be no 
 explanation of this characteristic of nature. All that 
 can be done is to use language which may speculatively 
 
54 THE CONCEPT OF NATURE [ch. 
 
 demonstrate it, and also to express the relation of this 
 factor in nature to other factors. 
 
 It is an exhibition of the process of nature that each 
 duration happens and passes. The process of nature can 
 also be termed the passage of nature. I definitely refrain 
 at this stage from using the word 'time/ since the 
 measurable time of science and of civilised life generally 
 merely exhibits some aspects of the more fundamental 
 fact of the passage of nature. I believe that in this 
 doctrine I am in full accord with Bergson, though he 
 uses *time' for the fundamental fact which I call the 
 * passage of nature.' Also the passage of nature is ex- 
 hibited equally in spatial transition as well as in temporal 
 transition. It is in virtue of its passage that nature is 
 always moving on. It is involved in the meaning of this 
 property of * moving on ' that not only is any act of sense- 
 awareness just that act and no other, but the terminus 
 of each act is also unique and is the terminus of no other 
 act. Sense-awareness seizes its only chance and presents 
 for knowledge something which is for it alone. 
 
 There are two senses in which the terminus of sense- 
 awareness is unique. It is unique for the sense-aware- 
 ness of an individual mind and it is unique for the 
 sense-awareness of all minds which are operating under 
 natural conditions. There is an important distinction 
 between the two cases, (i) For one mind not only is the 
 discerned component of the general fact exhibited in 
 any act of sense-awareness distinct from the discerned 
 component of the general fact exhibited in any other 
 act of sense-awareness of that mind, but the two corre- 
 sponding durations which are respectively related by 
 simultaneity to the two discerned components are 
 necessarily distinct. This is an exhibition of the temporal 
 
Ill] TIME 55 
 
 passage of nature ; namely, one duration has passed into 
 the other. Thus not only is the passage of nature an 
 essential character of nature in its rdle of the terminus of 
 sense-awareness, but it is also essential for sense- 
 awareness in itself. It is this truth which makes time 
 appear to extend beyond nature. But what extends 
 beyond nature to mind is not the serial and measurable 
 time, which exhibits merely the character of passage in 
 nature, but the quality of passage itself which is in no 
 way measurable except so far as it obtains in nature. 
 That is to say, * passage' is not measurable except as 
 it occurs in nature in connexion with extension. In 
 passage we reach a connexion of nature with the ultimate 
 metaphysical reality. The quality of passage in dura- 
 tions is a particular exhibition in nature of a quality 
 which extends beyond nature. For example passage is 
 a quality not only of nature, which is the thing known, 
 but also of sense-awareness which is the procedure of 
 knowing. Durations have all the reality that nature has," 
 though what that may be we need not now determine. 
 The measurableness of time is derivative from the 
 properties of durations. So also is the serial character 
 of time. We shall find that there are in nature competing 
 serial time-systems derived from different families of 
 durations. These are a peculiarity of the character of 
 passage as it is found in nature. This character has the 
 reality of nature, but we must not necessarily transfer 
 natural timeto extra-natural entities, (ii) Fortwo minds, 
 the discerned components of the general facts exhibited 
 in their respective acts of sense-awareness must be 
 different. For each mind, in its awareness of nature is 
 aware of a certain complex of related natural entities 
 in their relations to the living body as a focus. But the 
 
56 THE CONCEPT OF NATURE [ch. 
 
 associated durations may be identical. Here we are 
 touching on that character of the passage nature which 
 issues in the spatial relations of simultaneous bodies. 
 This possible identity of the durations in the case of 
 the sense-awareness of distinct minds is what binds 
 into one nature the private experiences of sentient 
 beings. We are here considering the spatial side of the 
 passage of nature. Passage in this aspect of it also seems 
 to extend beyond nature to mind. 
 
 It is important to distinguish simultaneity from in- 
 stantaneousness. I lay no stress on the mere current 
 usage of the two terms. There are two concepts which 
 I want to distinguish, and one I call simultaneity and 
 the other instantaneousness. I hope that the words are 
 judiciously chosen; but it really does not matter so 
 Jong as I succeed in explaining my meaning. Simul- 
 Itaneity is the property of a group of natural elements 
 which in some sense are components of a duration. 
 A duration can be all nature present as the immediate 
 fact posited by sense-awareness. A duration retains 
 within itself the passage of nature. There are within it 
 antecedents and consequents which are also durations 
 which may be the complete specious presents of quicker 
 consciousnesses. In other words a duration retains 
 temporal thickness. Any concept of all nature as imme- 
 diately known is always a concept of some duration 
 though it may be enlarged in its temporal thickness 
 beyond the possible specious present of any being known 
 to us as existing within nature. Thus simultaneity is an 
 ultimate factor in nature, immediate for sense-awareness. 
 
 Instantaneousness is a complex logical concept of a 
 procedure in thought by which constructed logical 
 entities are produced for the sake of the simple ex- 
 
Ill] TIME 57 
 
 pression in thought of properties of nature. Instan-I 
 taneousness is the concept of all nature at an instant, 
 where an instant is conceived as deprived of all tem- 
 poral extension. For example we conceive of the dis- 
 tribution of matter in space at an instant. This is a very 
 useful concept in science especially in applied mathe- 
 matics ; but it is a very complex idea so far as concerns 
 its connexions with the immediate facts of sense- 
 awareness. There is no such thing as nature at an instant 
 posited by sense-awareness. What sense-awareness 
 delivers over for knowledge is nature through a period. 
 Accordingly 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 upon observation. 
 
 I will use the term * moment ' to mean ' all nature at an 
 instant.' A moment, in the sense in which the term is 
 here used, has no temporal extension, and is in this re- 
 spect to be contrasted with a duration which has such 
 extension. What is directly yielded to our knowledge by 
 sense-awareness is a duration. Accordingly we have now 
 to explain how moments are derived from durations, and 
 also to explain the purpose served by their introduction. 
 
 A moment is a limit to which we approach as we 
 confine attention to durations of minimum extension. 
 Natural relations among the ingredients of a duration 
 gain in complexity as we consider durations of increasing 
 temporal extension. Accordingly there is an approach 
 to ideal simplicity as we approach an ideal diminution 
 of extension. 
 
 The word Mimit' has a precise signification in the 
 logic of number and even in the logic of non-numerical 
 
58 THE CONCEPT OF NATURE [ch. 
 
 one-dimensional series. As used here it is so far a mere 
 metaphor, and it is necessary to explain directly the 
 concept which it is meant to indicate. 
 
 Durations can have the two-termed relational pro- 
 perty of extending one over the other. Thus the duration 
 which is all nature during a certain minute extends over 
 the duration which is all nature during the 30th second 
 of that minute. This relation of 'extending over' — 
 * extension ' as I shall call it — is a fundamental natural 
 relation whose field comprises more than durations. It 
 is a relation which two limited events can have to each 
 other. Furthermore as holding between durations the 
 relation appears to refer to the purely temporal ex- 
 tension. I shall however maintain that the same relation 
 of extension lies at the base both of temporal and spatial 
 extension. This discussion can be postponed; and for 
 the present we are simply concerned with the relation 
 of extension as it occurs in its temporal aspect for the 
 limited field of durations. 
 
 The concept of extension exhibits in thought one side 
 of the ultimate passage of nature. This relation holds 
 because of the special character which passage assumes 
 in nature ; it is the relation which in the case of durations 
 expresses the properties of 'passing over.' Thus the 
 duration which was one definite minute passed over the 
 duration which was its 30th second. The duration of the 
 30th second was part of the duration of the minute. I shall 
 use the terms * whole 'and ' part ' exclusively in this sense, 
 that the * part ' is an event which is extended over by the 
 other event which is the ' whole.' Thus in my nomencla- 
 ture ' whole ' and ' part ' refer exclusively to this funda- 
 mental relation of extension; and accordingly in this 
 technical usage only events can be either wholes or parts. 
 
Ill] TIME 59 
 
 The continuity of nature arises from extension. Every I 
 event extends over other events, and every event is I 
 extended over by other events. Thus in the special case of 
 durations which are now the only events directly under 
 consideration, every duration is part of other durations ; 
 and every duration has other durations which are 
 parts of it. Accordingly there are no maximum dura- ) 
 tions and no minimum durations. Thus there is no/ 
 atomic structure of durations, and the perfect definition \ 
 of a duration, so as to mark out its individuality and 
 distinguish it from highly analogous durations over 
 which it is passing, or which are passing over it, is an 
 arbitrary postulate of thought. Sense-awareness posits 
 durations as factors in nature but does not clearly enable 
 thought to use it as distinguishing the separate indi- 
 vidualities of the entities of an allied group of slightly 
 differing durations. This is one instance of the in- 
 determinateness of sense-awareness. Exactness is an 
 ideal of thought, and is only realised in experience by 
 the selection of a route of approximation. 
 
 The absence of maximum and minimum durations 
 does not exhaust the properties of nature which make 
 up its continuity. The passage of nature involves the 
 existence of a family of durations. When two durations 
 belong to the same family either one contains the other, 
 or they overlap each other in a subordinate duration 
 without either containing the other; or they are com- 
 pletely separate. The excluded case is that of durations 
 overlapping in finite events but not containing a third 
 duration as a common part. 
 
 It is evident that the relation of extension is transitive ; 
 namely as applied to durations, if duration A is part of 
 duration B, and duration B is part of duration C, then A 
 
6o THE CONCEPT OF NATURE [ch. 
 
 is part of C. Thus the first two cases may be combined 
 into one and we can say that two durations which 
 belong to the same family either are such that there are 
 durations which are parts of both or are completely 
 separate. 
 
 Furthermore the converse of this proposition holds ; 
 namely, if two durations have other durations which are 
 parts of both or if the two durations are completely 
 separate, then they belong to the same family. 
 
 The further characteristics of the continuity of 
 nature — so far as durations are concerned — which has 
 not yet been formulated arises in connexion with' a 
 family of durations. It can be stated in this way : There 
 are durations which contain as parts any two durations 
 of the same family. For example a week contains as 
 parts any two of its days. It is evident that a containing 
 duration satisfies the conditions for belonging to the 
 same family as the two contained durations. 
 
 We are now prepared to proceed to the definition of 
 a moment of time. Consider a set of durations all taken 
 from the same family. Let it have the following pro- 
 perties : (i) of any two members of the set one contains 
 the other as a part, and (ii) there is no duration which 
 is a common part of every member of the set. 
 
 Now the relation of whole and part is asymmetrical ; 
 and by this I mean that if A is part of B, then B is not 
 part of A, Also we have already noted that the relation 
 is transitive. Accordingly we can easily see that the 
 durations of any set with the properties just enumerated 
 must be arranged in a one-dimensional serial order in 
 which as we descend the series we progressively reach 
 durations of smaller and smaller temporal extension. 
 The series may start with any arbitrarily assumed 
 
Ill] TIME 6i 
 
 duration of any temporal extension, but in descending 
 the series the temporal extension progressively con- 
 tracts and the successive durations are packed one within 
 the other like the nest of boxes of a Chinese toy. But 
 the set differs from the toy in this particular: the toy 
 has a smallest box which forms the end box of its series ; 
 but the set of durations can have no smallest duration 
 nor can it converge towards a duration as its limit. For 
 the parts either of the end duration or of the limit would 
 be parts of all the durations of the set and thus the 
 second condition for the set would be violated. 
 
 I will call such a set of durations an * abstractive set ' 
 of durations. It is evident that an abstractive set as we 
 pass along it converges to the ideal of all nature with 
 no temporal extension, namely, to the ideal of all nature 
 at an instant. But this ideal is in fact the ideal of a 
 nonentity. What the abstractive set is in fact doing is 
 to guide thought to the consideration of the progressive 
 simplicity of natural relations as we progressively 
 diminish the temporal extension of the duration con- 
 sidered. Now the whole point of the procedure is that 
 the quantitative expressions of these natural properties 
 do converge to limits though the abstractive set does 
 not converge to any limiting duration. The laws relating 
 these quantitative limits are the laws of nature * at an 
 instant,' although in truth there is no nature at an 
 instant and there is only the abstractive set. Thus an 
 abstractive set is effectively the entity meant when we 
 consider an instant of time without temporal extension. 
 It subserves all the necessary purposes of giving a 
 definite meaning to the concept of the properties of 
 nature at an instant. I fully agree that this concept is 
 fundamental in the expression of physical science. The 
 
62 THE CONCEPT OF NATURE [ch. 
 
 difficulty is to express our meaning in terms of the imme- 
 diate deliverances of sense-awareness, and I offer the 
 above explanation as a complete solution of the problem. 
 
 In this explanation a moment is the set of natural 
 properties reached by a route of approximation. An 
 abstractive series is a route of approximation. There are 
 different routes of approximation to the same limiting 
 set of the properties of nature. In other words there 
 are different abstractive sets which are to be regarded 
 as routes of approximation to the same moment. 
 Accordingly there is a certain amount of technical detail 
 necessary in explaining the relations of such abstractive 
 sets with the same convergence and in guarding against 
 possible exceptional cases. Such details are not suitable 
 for exposition in these lectures, and I have dealt with 
 them fully elsewhere^. 
 
 It is more convenient for technical purposes to look 
 on a moment as being the class of all abstractive sets of 
 durations with the same convergence. With this defini- 
 tion (provided that we can successfully explain what 
 we mean by the *same convergence' apart from a 
 detailed knowledge of the set of natural properties 
 arrived at by approximation) a moment is merely a class 
 of sets of durations whose relations of extension in 
 respect to each other have certain definite peculiarities. 
 We may term these connexions of the component 
 durations the * extrinsic' properties of a moment; the 
 * intrinsic ' properties of the moment are the properties 
 of nature arrived at as a limit as we proceed along any 
 one of its abstractive sets. These are the properties of 
 nature *at that moment,' or *at that instant.' 
 
 ^ Cf . An Enquiry concerning the Principles of Natural Knowledge^ 
 Cambridge University Press, 19 19. 
 
Ill] • TIME 63 
 
 The durations which enter into the composition of 
 a moment all belong to one family. Thus there is one 
 family of moments corresponding to one family of 
 durations. Also if we take two moments of the same 
 family, among the durations which enter into the com- 
 position of one moment the smaller durations are 
 completely separated from the smaller durations which 
 enter into the composition of the other moment. Thus 
 the two moments in their intrinsic properties must 
 exhibit the limits of completely different states of nature. 
 In this sense the two moments are completely separated. 
 I will call two moments of the same family * parallel.' 
 
 Corresponding to each duration there are two 
 moments of the associated family of moments which 
 are the boundary moments of that duration. A 
 * boundary moment' of a duration can be defined in 
 this way. There are durations of the same family as the 
 given duration which overlap it but are not contained 
 in it. Consider an abstractive set of such durations. 
 Such a set defines a moment which is just as much 
 without the duration as within it. Such a moment is a 
 boundary moment of the duration. Also we call upon 
 our sense-awareness of the passage of nature to inform 
 us that there are two such boundary moments, namely 
 the earlier one and the later one. We will call them the 
 initial and the final boundaries. 
 
 There are also moments of the same family such that 
 the shorter durations in their composition are entirely 
 separated from the given duration. Such moments will 
 be said to lie * outside' the given duration. Again other 
 moments of the family are such that the shorter dura- 
 tions in their composition are parts of the given dura- 
 tion. Such moments are said to lie * within' the given 
 
64 THE CONCEPT OF NATURE [ch. 
 
 duration or to * inhere ' in it. The whole family of parallel 
 moments is accounted for in this way by reference to 
 any given duration of the associated family of durations. 
 Namely, there are moments of the family which lie 
 without the given duration, there are the two moments 
 which are the boundary moments of the given duration, 
 and the moments which lie within the given duration. 
 Furthermore any two moments of the same family are 
 the boundary moments of some one duration of the 
 associated family of durations. 
 
 It is now possible to define the serial relation of 
 temporal order among the moments of a family. For 
 let A and C be any two moments of the family, these 
 moments are the boundary moments of one duration d 
 of the associated family, and any moment B which lies 
 within the duration d will be said to lie between the 
 moments A and C. Thus the three-termed relation of 
 * lying-between ' as relating three moments A, B, and C 
 is completely defined . Also our knowledge of the passage 
 of nature assures us that this relation distributes the 
 moments of the family into a serial order. I abstain 
 from enumerating the definite properties which secure 
 this result, I have enumerated them in my recently 
 published book^ to which I have already referred. 
 Furthermore the passage of nature enables us to know 
 that one direction along the series corresponds to 
 passage into the future and the other direction corre- 
 sponds to retrogression towards the past. 
 
 Such an ordered series of moments is what we mean 
 by time defined as a series. Each element of the series 
 exhibits an instantaneous state of nature. Evidently this 
 serial time is the result of an intellectual process of 
 
 1 CL Enquiry, 
 
Ill] TIME 65 
 
 abstraction. What I have done is to give precise defini- 
 tions of the procedure by which the abstraction is 
 effected. This procedure is merely a particular case of 
 the general method which in my book I name the 
 * method of extensive abstraction.' This serial time is 
 evidently not the very passage of nature itself. It 
 exhibits some of the natural properties which flow from 
 it. The state of nature * at a moment ' has evidently lost 
 this ultimate quality of passage. Also the temporal 
 series of moments only retains it as an extrinsic relation 
 of entities and not as the outcome of the essential being 
 of the terms of the series. 
 
 Nothing has yet been said as to the measurement of 
 time. Such measurement does not follow from the 
 mere serial property of time; it requires a theory of 
 congruence which will be considered in a later lecture. 
 
 In estimating the adequacy of this definition of the 
 temporal series as a formulation of experience it is 
 necessary to discriminate between the crude deliverance 
 of sense-awareness and our intellectual theories. The 
 lapse of time is a measurable serial quantity. The whole 
 of scientific theory depends on this assumption and any 
 theory of time which fails to provide such a measurable 
 series stands self-condemned as unable to account for 
 the most salient fact in experience. Our difficulties only 
 begin when we ask what it is that is measured. It is 
 evidently something so fundamental in experience that 
 we can hardly stand back from it and hold it apart so 
 as to view it in its own proportions. 
 
 We have first to make up our minds whether time is 
 to be found in nature or nature is to be found in time. 
 The difficulty of the latter alternative — namely of 
 making time prior to nature — is that time then becomes 
 
66 THE CONCEPT OF NATURE [ch. 
 
 a metaphysical enigma. What sort of entities are its 
 instants or its periods ? The dissociation of time from 
 events discloses to our immediate inspection that the 
 attempt to set up time as an independent terminus for 
 knowledge is like the effort to find substance in a shadow. 
 a- [Fhere is time because there are happenings, and apart 
 r ^/ jfrom happenings there is nothing. 
 
 It is necessary however to make a distinction. In 
 some sense time extends beyond nature. It is not true 
 that a timeiess sense-awareness and a timeless thought 
 combine to contemplate a timeful nature. Sense-aware- 
 ness and thought are themselves processes as well as 
 their termini in nature. In other words there is a 
 passage of sense-awareness and a passage of thought. 
 Thus the reign of the quality of passage extends beyond 
 nature. But now the distinction arises between passage 
 which is fundamental and the temporal series which is 
 a logical abstraction representing some of the properties 
 of nature. A temporal series, as we have defined it, 
 represents merely certain properties of a family of 
 durations — properties indeed which durations only 
 possess because of their partaking of the character of 
 passage, but on the other hand properties which only 
 durations do possess. Accordingly time in the sense of a 
 measurable temporal series is a character of nature only, 
 and does not extend to the processes of thought and of 
 sense-awareness except by a correlation of these processes 
 with the temporal series implicated in their procedures. 
 
 So far the passage of nature has been considered in 
 connexion with the passage of durations; and in this 
 connexion it is peculiarly associated with temporal 
 series. We must remember however that the character 
 of passage is peculiarly associated with the extension of 
 
Ill] TIME 67 
 
 events, and that from this extension spatial transition 
 arises just as much as temporal transition. The dis- 
 cussion of this point is reserved for a later lecture but 
 it is necessary to remember it now that we are pro- 
 ceeding to discuss the application of the concept of 
 passage beyond nature, otherwise we shall have too 
 narrow an idea of the essence of passage. 
 
 It is necessary to dwell on the subject of sense-aware- 
 ness in this connexion as an example of the way in 
 which time concerns mind, although measurable time is 
 a mere abstract from nature and nature is closed to mind. 
 
 Consider sense-awareness — ^not its terminus which 
 is nature, but sense-awareness in itself as a procedure 
 of mind. Sense-awareness is a relation of mind to 
 nature. Accordingly we are now considering mind as 
 a relatum in sense-awareness. For mind there is the 
 immediate sense-awareness and there is memory. The 
 distinction between memory and the present immediacy 
 has a double bearing. On the one hand it discloses that 
 mind is not impartially aware of all those natural 
 durations to which it is related by awareness. Its 
 awareness shares in the passage of nature. We can 
 imagine a being whose awareness, conceived as his 
 private possession, suffers no transition, although the 
 terminus of his awareness is our own transient nature. 
 There is no essential reason why memory should not 
 be raised to the vividness of the present fact ; and then 
 from the side of mind. What is the difference between 
 the present and the past? Yet with this hypothesis we 
 can also suppose that the vivid remembrance and the 
 present fact are posited in awareness as in their temporal 
 serial order. Accordingly we must admit that though 
 we can imagine that mind in the operation of sense- 
 
 5—2 
 
68 THE CONCEPT OF NATURE [ch. 
 
 awareness might be free from any character of passage, 
 yet in point of fact our experience of sense-awareness 
 exhibits our minds as partaking in this character. 
 
 On the other hand the mere fact of memory is an 
 escape from transience. In memory the past is present. 
 It is not present as overleaping the temporal succession 
 of nature, but it is present as an immediate fact for 
 the mind. Accordingly memory is a disengagement of 
 the mind from the mere passage of nature ; for what has 
 passed for nature has not passed for mind. 
 
 Furthermore the distinction between memory and 
 the immediate present is not so clear as it is conventional 
 to suppose. There is an intellectual theory of time as a 
 moving knife-edge, exhibiting a present fact without 
 temporal extension. This theory arises from the concept 
 of an ideal exactitude of observation. Astronomical 
 observations are successively refined to be exact to 
 tenths, to hundredths, and to thousandths of seconds. 
 But the final refinements are arrived at by a system of 
 averaging, and even then present us with a stretch of 
 time as a margin of error. Here error is merely a con- 
 ventional term to express the fact that the character of 
 experience does not accord with the ideal of thought. 
 I have already explained how the concept of a moment 
 conciliates the observed fact with this ideal; namely, 
 there is a limiting simplicity in the quantitative ex- 
 pression of the properties of durations, which is 
 arrived at by considering any one of the abstractive 
 sets included in the moment. In other words the 
 extrinsic character of the moment as an aggregate of 
 durations has associated with it the intrinsic character 
 of the moment which is the limiting expression of 
 natural properties. 
 
Ill] TIME 69 
 
 Thus the character of a moment and the ideal of 
 exactness which it enshrines do not in any way weaken 
 the position that the ultimate terminus of awareness is 
 a duration with temporal thickness. This immediate 
 duration is not clearly marked out for our apprehension. 
 Its earlier boundary is blurred by a fading into memory, 
 and its later boundary is blurred by an emergence from 
 anticipation. There is no sharp distinction either between 
 memory and the present immediacy or between the 
 present immediacy and anticipation. The present is a 
 wavering breadth of boundary between the two ex- ; 
 tremes. Thus our own sense-awareness with its extended 
 present has some of the character of the sense-awareness 
 of the imaginary being whose mind was free from passage 
 and who contemplated all nature as an immediate fact. 
 Our own present has its antecedents and its consequents, 
 and for the imaginary being all nature has its ante- 
 cedent and its consequent durations. Thus the only 
 difference in this respect between us and the imaginary 
 being is that for him all nature shares in the immediacy 
 of our present duration. 
 
 The conclusion of this discussion is that so far as 
 sense-awareness is concerned there is a passage of 
 mind which is distinguishable from the passage of 
 nature though closely allied with it. We may speculate, 
 if we like, that this alliance of the passage of mind with 
 the passage of nature arises from their both sharing in 
 some ultimate character of passage which dominates 
 all being. But this is a speculation in which we have 
 no concern. The immediate deduction which is suffi- 
 cient for us is that — so far as sense-awareness is con- 
 cerned — mind is not in time or in space in the same 
 sense in which the events of nature are in time, but 
 
!i 
 
 y 
 
 70 THE CONCEPT OF NATURE [ch. 
 
 that it is derivatively in time and in space by reason of 
 the peculiar alliance of its passage with the passage 
 of nature. Thus mind is in time and in space in a sense 
 peculiar to itself. This has been a long discussion to 
 arrive at a very simple and obvious conclusion. We all 
 feel that in some sense our minds are here in this room 
 and at this time. But it is not quite in the same sense 
 as that in which the events of nature which are the 
 existences of our brains have their spatial and temporal 
 positions. The fundamental distinction to remember is 
 that immediacy for sense-awareness is not the same as 
 instantaneousness for nature. This last conclusion bears 
 on the next discussion with which I will terminate this 
 lecture. This question can be formulated thus, Can 
 alternative temporal series be found in nature .f^ 
 
 A few years ago such a suggestion would have been 
 put aside as being fantastically impossible . It would have 
 had no bearing on the science then current, and was 
 akin to no ideas which had ever entered into the dreams 
 of philosophy. The eighteenth and nineteenth centuries 
 accepted as their natural philosophy a certain circle of 
 concepts which were as rigid and definite as those of 
 the philosophy of the middle ages, and were accepted 
 with as little critical research. I will call this natural 
 philosophy * materialism.' Not only were men of science 
 materialists, but also adherents of all schools of philo- 
 sophy. The idealists only differed from the philosophic 
 materialists on question of the alignment of nature in 
 reference to mind. But no one had any doubt that the 
 philosophy of nature considered in itself was of the 
 type which I have called materialism. It is the philo- 
 sophy which I have already examined in my two 
 lectures of this course preceding the present one. It 
 
Ill] TIME 71 
 
 can be summarised as the belief that nature is an aggre- 
 gate of material and that this material exists in some 
 sense at each successive member of a one-dimensional 
 series of extensionless instants of time. Furthermore 
 the mutual relations of the material entities at each 
 instant formed these entities into a spatial configuration 
 in an unbounded space. It would seem that space — on 
 this theory — ^would be as instantaneous as the instants, 
 and that some explanation is required of the relations 
 between the successive instantaneous spaces. The 
 materialistic theory is however silent on this point; 
 and the succession of instantaneous spaces is tacitly 
 combined into one persistent space. This theory is a 
 purely intellectual rendering of experience which has 
 had the luck to get itself formulated at the dawn of 
 scientific thought. It has dominated the language and 
 the imagination of science since science flourished in 
 Alexandria, with the result that it is now hardly possible 
 to speak without appearing to assume its immediate 
 obviousness. 
 
 But when it is distinctly formulated in the abstract 
 terms in which I have just stated it, the theory is very 
 far from obvious. The passing complex of factors which 
 compose the fact which is the terminus of sense-aware- 
 ness places before us nothing^ corresponding to the 
 trinity of this natural materialism. This trinity is com- 
 posed (i) of the temporal series of extensionless instants, 
 (ii) of the aggregate of material entities, and (iii) of 
 space which is the outcome of relations of matter. 
 
 There is a wide gap between these presuppositions 
 of the intellectual theory of materialism and the im- 
 mediate deliverances of sense-awareness. I do not 
 question that this materialistic trinity embodies im- 
 
72 THE CONCEPT OF NATURE [ch. 
 
 portant characters of nature. But it is necessary to 
 express these characters in terms of the facts of 
 experience. This is exactly what in this lecture I have 
 been endeavouring to do so far as time is concerned; 
 and we have now come up against the question, Is 
 there only one temporal series ? The uniqueness of the 
 temporal series is presupposed in the materialist 
 philosophy of nature. But that philosophy is merely a 
 theory, like the Aristotelian scientific theories so firmly 
 believed in the middle ages. If in this lecture I have 
 in any way succeeded in getting behind the theory to 
 the immediate facts, the answer is not nearly so certain. 
 The question can be transformed into this alternative 
 form. Is there only one family of durations? In this 
 question the meaning of a * family of durations' has 
 been defined earlier in this lecture. The answer is now 
 not at all obvious. On the materialistic theory the 
 instantaneous present is the only field for the creative 
 activity of nature. The past is gone and the future is 
 not yet. Thus (on this theory) the immediacy of per- 
 ception is of an instantaneous present, and this unique 
 present is the outcome of the past and the promise of 
 the future. But we deny this immediately given in- 
 stantaneous present. There is no such thing to be found 
 iin nature. As an ultimate fact it is a nonentity. What 
 is immediate for sense-awareness is a duration. Now a 
 duration has within itself a past and a future ; and the 
 temporal breadths of the immediate durations of sense- 
 awareness are very indeterminate and dependent on the 
 individual percipient. Accordingly there is no unique 
 factor in nature which for every percipient is pre- 
 eminently and necessarily the present. The passage of 
 nature leaves nothing between the past and the future. 
 
Ill] TIME 73 
 
 What we perceive as present is the vivid fringe of 
 memory tinged with anticipation. This vividness Hghts 
 up the discriminated field within a duration. But no 
 assurance can thereby be given that the happenings of 
 nature cannot be assorted into other durations of aker- 
 native famiHes. We cannot even know that the series 
 of immediate durations posited by the sense-awareness 
 of one individual mind all necessarily belong to the 
 same family of durations. There is not the slightest 
 reason to believe that this is so. Indeed if my theory of 
 nature be correct, it will not be the case. 
 
 The materialistic theory has all the completeness of 
 the thought of the middle ages, which had a complete 
 answer to everything, be it in heaven or in hell or in 
 nature. There is a trimness about it, with its instan- 
 taneous present, its vanished past, its non-existent 
 future, and its inert matter. This trimness is very 
 medieval and ill accords with brute fact. 
 
 The theory which I am urging admits a greater 
 ultimate mystery and a deeper ignorance. The past and 
 the future meet and mingle in the ill-defined present. 
 The passage of nature which is only another name for 
 the creative force of existence has no narrow ledge of 
 definite instantaneous present within which to operate. 
 Its operative presence which is now urging nature 
 forward must be sought for throughout the whole, in 
 the remotest past as well as in the narrowest breadth of 
 any present duration. Perhaps also in the unrealised ' 
 future. Perhaps also in the future which might be as i 
 well as the actual future which will be. It is impossible 
 to meditate on time and the mystery of the creative 
 passage of nature without an overwhelming emotion 
 at the limitations of human intelligence. 
 
CHAPTER IV 
 
 THE METHOD OF EXTENSIVE 
 ABSTRACTION 
 
 To-day's lecture must commence with the consideration 
 of Hmited events. We shall then be in a position to 
 enter upon an investigation of the factors in nature 
 which are represented by our conception of space. 
 
 The duration which is the immediate disclosure of 
 our sense-awareness is discriminated into parts. There 
 is the part which is the life of all nature within a room, 
 and there is the part which is the life of all nature 
 within a table in the room. These parts are limited 
 events. They have the endurance of the present duration, 
 and they are parts of it. But whereas a duration is an 
 unlimited whole and in a certain limited sense is all 
 that there is, a limited event possesses a completely 
 defined limitation of extent which is expressed for us 
 in spatio-temporal terms. 
 
 We are accustomed to associate an event with a certain 
 melodramatic quality. If a man is run over, that is an 
 event comprised within certain spatio-temporal limits. 
 We are not accustomed to consider the endurance of 
 the Great Pyramid throughout any definite day as an 
 event. But the natural fact which is the Great Pyramid 
 throughout a day, meaning thereby all nature within it, 
 is an event of the same character as the man's accident, 
 meaning thereby all nature with spatio-temporal limita- 
 tions so as to include the man and the motor during the 
 period when they were in contact. 
 
CH.iv] METHOD OF EXTENSIVE ABSTRACTION 75 
 
 We are accustomed to analyse these events into three 
 factors, time, space, and material. In fact, we at once 
 apply to them the concepts of the materialistic theory 
 of nature. I do not deny the utility of this analysis for 
 the purpose of expressing important laws of nature. 
 What I am denying is that anyone of these factors is 
 posited for us in sense-awareness in concrete inde- 
 pendence. We perceive one unit factor in nature; and 
 this factor is that something is going on then — there. 
 For example, w^ perceive the going-on of the Great 
 Pyramid in its relations to the goings-on of the sur- 
 rounding Egyptian events. We are so trained, both by 
 language and by formal teaching and by the resulting 
 convenience, to express our thoughts in terms of this 
 materialistic analysis that intellectually we tend to 
 ignore the true unity of the factor really exhibited in 
 sense-awareness. It is this unit factor, retaining in 
 itself the passage of nature, which is the primary 
 concrete element discriminated in nature. These 
 primary factors are what I mean by events. 
 
 Events are the field of a two-termed relation, namely 
 the relation of extension which was considered in the 
 last lecture. Events are the things related by the 
 relation of extension. If an event A extends over an 
 event B, then B is *part of ' ^, and ^ is a * whole of 
 which 5 is a part. Whole and part are invariably used 
 in these lectures in this definite sense. It follows that 
 in reference to this relation any two events A and B 
 may have any one of four relations to each other, 
 namely (i) A may extend over J5, or (ii) B may extend 
 over A, or (iii) A and B may both extend over some 
 third event C, but neither over the other, or (iv) A 
 and B may be entirely separate. These alternatives can 
 
76 THE CONCEPT OF NATURE [ch. 
 
 obviously be illustrated by Euler's diagrams as they 
 appear in logical textbooks. 
 
 The continuity of nature is the continuity of events. 
 This continuity is merely the name for the aggregate 
 of a variety of properties of events in connexion with 
 the relation of extension. 
 
 In the first place, this relation is transitive; secondly, 
 every event contains other events as parts of itself; 
 thirdly every event is a part of other events; fourthly 
 given any two finite events there are events each of 
 which contains both of them as parts ; and fifthly there 
 is a special relation between events which I term 
 * junction.' 
 
 Two events have junction when there is a third event 
 of which both events are parts, and which is such that 
 no part of it is separated from both of the two given 
 events. Thus two events with junction make up exactly 
 one event which is in a sense their sum. 
 
 Only certain pairs of events have this property. In 
 general any event containing two events also contains 
 parts which are separated from both events. 
 
 There is an alternative definition of the junction of 
 two events which I have adopted in my recent book^. 
 Two events have junction when there is a third event 
 such that (i) it overlaps both events and (ii) it has no 
 part which is separated from both the given events. If 
 either of these alternative definitions is adopted as the 
 definition of junction, the other definition appears as 
 an axiom respecting the character of junction as we 
 know it in nature. But we are not thinking of logical 
 definition so much as the formulation of the results 
 of direct observation. There is a certain continuity 
 
 ^ Cf. Enquiry. 
 
IV] METHOD OF EXTENSIVE ABSTRACTION 77 
 
 inherent in the observed unity of an event, and these 
 tv^o definitions of junction are really axioms based 
 on observation respecting the character of this con- 
 tinuity. 
 
 The relations of vv^hole and part and of overlapping 
 are particular cases of the junction of events. But it 
 is possible for events to have junction vi^hen they are 
 separate from each other; for example, the upper and 
 the lovvrer part of the Great Pyramid are divided by some 
 imaginary horizontal plane. 
 
 The continuity v^hich nature derives from events 
 has been obscured by the illustrations w^hich I have 
 been obliged to give. For example I have taken the 
 existence of the Great Pyramid as a fairly v^ell-knov^n 
 fact to w^hich I could safely appeal as an illustration. 
 This is a type of event v^hich exhibits itself to us as the 
 situation of a recognisable object ; and in the example; 
 chosen the object is so vvridely recognised that it has 
 received a name. An object is an entity of a different 
 type from an event. For example, the event w^hich is 
 the life of nature w^ithin the Great Pyramid yesterday 
 and to-day is divisible into two parts, namely the Great 
 Pyramid yesterday and the Great Pyramid to-day. But 
 the recognisable object w^hich is also called the Great 
 Pyramid is the same object to-day as it v^as yesterday. 
 I shall have to consider the theory of objects in another 
 lecture. 
 
 The w^hole subject is invested w^ith an unmerited \ ? 
 air of subtlety by the fact that vv^hen the event is the f^^ 1 
 situation of a well-marked object, we have no language j -^^^ 
 to distinguish the event from the object. In the easel '(jJ^*'^ 
 of the Great Pyramid, the object is the perceived unit k ^^j^ 
 entity which as perceived remains self-identical through- I .j^j^ 
 
78 THE CONCEPT OF NATURE [ch. 
 
 out the ages ; while the whole dance of molecules and 
 the shifting play of the electromagnetic field are 
 ingredients of the event. An object is in a sense out 
 '' of time. It is only derivatively in time by reason of its 
 having the relation to events which I term * situation.' 
 This relation of situation will require discussion in a 
 subsequent lecture. 
 
 The point which I want to make now is that being the 
 situation of a well-marked object is not an inherent 
 necessity for an event. Wherever and whenever some- 
 thing is going on, there is an event. Furthermore 
 * wherever and whenever ' in themselves presuppose an 
 event, for space and time in themselves are abstractions 
 from events. It is therefore a consequence of this 
 doctrine that something is always going on everywhere, 
 even in so-called empty space. This conclusion is in 
 accord with modern physical science which presupposes 
 the play of an electromagnetic field throughout space 
 and time. This doctrine of science has been thrown into 
 the materialistic form of an all-pervading ether. But 
 the ether is evidently a mere idle concept — inthephraseo- 
 f^y^ logy which Bacon applied to the doctrine of final 
 I causes, it is a barren virgin. Nothing is deduced from 
 it; and the ether merely subserves the purpose of 
 ; satisfying the demands of the materialistic theory. The 
 I important concept is that of the shifting facts of the 
 j fields of force. This is the concept of an ether of events 
 which should be substituted for that of a material 
 ether. 
 
 It requires no illustration to assure you that an event 
 is a complex fact, and the relations between two events 
 form an almost impenetrable maze. The clue discovered 
 by the common sense of mankind and systematically 
 
IV] METHOD OF EXTENSIVE ABSTRACTION 79 
 
 utilised in science is what I have elsewhere ^ called the 
 law of convergence to simplicity by diminution of 
 extent. 
 
 If A and B are two events, and A' is part of A and 
 B' is part of By then in many respects the relations 
 between the parts A' and B' will be simpler than the 
 relations between A and B. This is the principle which 
 presides over all attempts at exact observation. 
 
 The first outcome of the systematic use of this law 
 has been the formulation of the abstract concepts of 
 Time and Space. In the previous lecture I sketched 
 how the principle was applied to obtain the time-series. 
 I now proceed to consider how the spatial entities are 
 obtained by the same method. The systematic pro- 
 cedure is identical in principle in both cases, and I 
 have called the general type of procedure the * method 
 of extensive abstraction.' 
 
 You will remember that in my last lecture I defined 
 the concept of an abstractive set of durations. This 
 definition can be extended so as to apply to any events, 
 limited events as well as durations. The only change 
 that is required is the substitution of the word * event ' 
 for the word ' duration.' Accordingly an abstractive set 
 of events is any set of events which possesses the two 
 properties, (i) of any two members of the set one con- 
 tains the other as a part, and (ii) there is no event which 
 is a common part of every member of the set. Such a 
 set, as you will remember, has the properties of the 
 Chinese toy which is a nest of boxes, one within the 
 other, with the difference that the toy has a smallest 
 box, while the abstractive class has neither a smallest 
 
 ^ Cf. Organisation of Thought y pp. 146 et seq. Williams and 
 Norgate, 19 17. 
 
8o THE CONCEPT OF NATURE [ch. 
 
 event nor does it converge to a limiting event which is 
 not a member of the set. 
 
 Thus, so far as the abstractive sets of events are con- 
 cerned, an abstractive set converges to nothing. There 
 is the set with its members growing indefinitely smaller 
 and smaller as we proceed in thought towards the 
 smaller end of the series; but there is no absolute 
 minimum of any sort which is finally reached. In fact 
 the set is just itself and indicates nothing else in the 
 way of events, except itself. But each event hasjan 
 intrinsi^^c characte^^ the way of being a situation of 
 objects and of having parts which are situations of 
 objects and — to state the matter more generally — in the 
 way of being a field of the life of nature. This character 
 can be defined by quantitative expressions expressing 
 relations between various quantities intrinsic to the 
 event or between such quantities and other quantities 
 intrinsic to other events. In the case of events of con- 
 siderable spatio-temporal extension this set of quanti- 
 tative expressions is of bewildering complexity. If 
 e be an event, let us denote by q (e) the set of quanti- 
 tative expressions defining its character including its 
 connexions with the rest of nature. Let ^i, ^2> ^3> ^tc. 
 be an abstractive set, the members being so arranged 
 that each member such as e^ extends over all the suc- 
 ceeding members such as ^^+1, ^n+2> and so on. Then 
 corresponding to the series 
 
 ^l> ^2» ^3> •••> ^w) ^w+l> •••> 
 
 there is the series 
 
 (I (^i)» ^ (^2)» 9. (^3)» •••, (I W, ^ K+i), .... 
 Call the series of events s and the series of quanti- 
 tative expressions q {$), The series s has no last term and 
 
IV] METHOD OF EXTENSIVE ABSTRACTION 8i 
 
 no events which are contained in every member of the 
 series. Accordingly the series of events converges to 
 nothing. It is just itself. Also the series q {s) has no 
 last term. But the sets of homologous quantities 
 running through the various terms of the series do 
 converge to definite limits. For example if Q^ be a 
 quantitative measurement found in q (^j), and Q^ the 
 homologue to Q^ to be found in q {e^, and Q^ the 
 homologue to Q^ and ^2 to be found in q (^3), and so on, 
 then the series 
 
 6l> Q^y Qz^ •••> Qny Qn+l^ •••> 
 
 though it has no last term, does in general converge to 
 a definite limit. Accordingly there is a class of limits 
 / {s) w^hich is the class of the limits of those members of 
 <Z(^w) which have homologues throughout the series q{s) 
 as n indefinitely increases. We can represent this state- 
 ment diagrammatically by using an arrovv^ {■*) to mean 
 * converges to.' Then 
 
 ^1, ^2, ^3» •••> ^ny ^n+i, ... -^ nothing, 
 and 
 
 q (^i)> 9 (^2)> q (^3), ..., ^ K), q K-m), ... - / (s). 
 
 The mutual relations between the limits in the set 
 l{s), and also between these limits and the limits in 
 other sets l{s'), l{s"), ..., which arise from other 
 abstractive sets s\ s", etc., have a peculiar simplicity. 
 
 Thus the set s does indicate an ideal simplicity of 
 natural relations, though this simplicity is not the 
 character of any actual event in s. We can make an 
 approximation to such a simpHcity which, as estimated 
 numerically, is as close as we like by considering an 
 event which is far enough down the series towards the 
 small end. It will be noted that it is the infinite series, 
 
 W.N. 6 
 
82 THE CONCEPT OF NATURE [ch. 
 
 as it stretches away in unending succession towards 
 the small end, which is of importance. The arbitrarily 
 large event with which the series starts has no importance 
 at all. We can arbitrarily exclude any set of events at 
 the big end of an abstractive set without the loss of 
 any important property to the set as thus modified. 
 
 I call the limiting character of natural relations which 
 is indicated by an abstractive set, the ' intrinsic character ' 
 of the set; also the properties, connected with the 
 relation of whole and part as concerning its members, 
 by which an abstractive set is defined together form what 
 I call its * extrinsic character.' The fact that the ex- 
 trinsic character of an abstractive set determines a 
 definite intrinsic character is the reason of the import- 
 ance of the precise concepts of space and time. This 
 emergence of a definite intrinsic character from an 
 abstractive set is the precise meaning of the law of 
 convergence. 
 
 For example, we see a train approaching during a 
 minute. The event which is the life of nature within 
 that train during the minute is of great complexity and 
 the expression of its relations and of the ingredients 
 of its character baffles us. If we take one second of 
 that minute, the more limited event which is thus 
 obtained is simpler in respect to its ingredients, and 
 shorter and shorter times such as a tenth of that second, 
 or a hundredth, or a thousandth — so long as we have a 
 definite rule giving a definite succession of diminishing 
 events — give events whose ingredient characters con- 
 verge to the ideal simplicity of the character of the train 
 at a definite instant. Furthermore there are different 
 types of such convergence to simplicity. For example, 
 we can converge as above to the limiting character 
 
IV] METHOD OF EXTENSIVE ABSTRACTION 83 
 
 expressing nature at an instant within the whole volume 
 of the train at that instant, or to nature at an instant 
 within some portion of that volume — for example 
 within the boiler of the engine — or to nature at an 
 instant on some area of surface, or to nature at an instant 
 on some line within the train, or to nature at an instant 
 at some point of the train. In the last case the simple 
 limiting characters arrived at will be expressed as 
 densities, specific gravities, and types of material. 
 Furthermore we need not necessarily converge to an 
 abstraction which involves nature at an instant. We 
 may converge to the physical ingredients of a certain 
 point track throughout the whole minute. Accordingly 
 there are different types of extrinsic character of con- 
 vergence which lead to the approximation to different 
 types of intrinsic characters as limits. 
 
 We now pass to the investigation of possible con- 
 nexions between abstractive sets. One set may * cover' 
 another. I define * covering' as follows: An abstractive 
 set p covers an abstractive set q when every member of 
 p contains as its parts some members of q. It is evident 
 that if any event e contains as a part any member of 
 the set q, then owing to the transitive property of ex- 
 tension every succeeding member of the small end of q 
 is part of ^. In such a case I will say that the abstractive 
 set q * inheres in ' the event e. Thus when an abstractive 
 set p covers an abstractive set q, the abstractive set q 
 inheres in every member of/). 
 
 Two abstractive sets may each cover the other. When 
 this is the case I shall call the two sets * equal in ab- 
 stractive force.' When there is no danger of misunder- 
 standing I shall shorten this phrase by simply saying 
 that the two abstractive sets are * equal.' The possibility 
 
 6—2 
 
84 THE CONCEPT OF NATURE [CH. 
 
 of this equality of abstractive sets arises from the fact 
 that both sets, p and ^, are infinite series towards their 
 small ends. Thus the equality means, that given any 
 event x belonging to p, we can always by proceeding 
 far enough towards the small end of q find an event y 
 which is part of x, and that then by proceeding far 
 enough towards the small end of ^ we can find an event z 
 which is part oiy, and so on indefinitely. 
 *. / The importance of the equality of abstractive sets 
 •^"^^ arises from the assumption that the intrinsic characters 
 of the two sets are identical. If this were not the case 
 exact observation would be at an end. 
 
 It is evident that any two abstractive sets which are 
 equal to a third abstractive set are equal to each other. 
 An * abstractive element' is the whole group of ab- 
 stractive sets which are equal to any one of themselves. 
 Thus all abstractive sets belonging to the same element 
 are equal and converge to the same intrinsic character. 
 Thus an abstractive element is the group of routes of 
 approximation to a definite intrinsic character of ideal 
 simplicity to be found as a limit among natural facts. 
 
 If an abstractive set p covers an abstractive set q, then 
 any abstractive set belonging to the abstractive element 
 of which /) is a member will cover any abstractive set 
 belonging to the element of which ^ is a member. 
 Accordingly it is useful to stretch the meaning of the 
 term * covering,' and to speak of one abstractive element 
 
 * covering ' another abstractive element. If we attempt in 
 like manner to stretch the term * equal ' in the sense of 
 
 * equal in abstractive force,' it is obvious that an ab- 
 stractive element can only be equal to itself. Thus an 
 abstractive element has a unique abstractive force and is 
 the construct from events which represents one definite 
 
IV] METHOD OF EXTENSIVE ABSTRACTION 85 
 
 intrinsic character which is arrived at as a Hmit by the 
 use of the principle of convergence to simpHcity by 
 diminution of extent. 
 
 When an abstractive element A covers an abstractive 
 element B, the intrinsic character of ^ in a sense 
 includes the intrinsic character of B, It results that 
 statements about the intrinsic character of B are in a 
 sense statements about the intrinsic character of A; 
 but the intrinsic character of A is more complex than 
 that of B. 
 
 The abstractive elements form the fundamental 
 elements of space and time, and we now turn to the 
 consideration of the properties involved in the formation 
 of special classes of such elements. In my last lecture 
 I have already investigated one class of abstractive 
 elements, namely moments. Each moment is a group 
 of abstractive sets, and the events which are members 
 of these sets are all members of one family of durations. 
 The moments of one family form a temporal series; 
 and, allowing the existence of different families of 
 moments, there will be alternative temporal series in 
 nature. Thus the method of extensive abstraction ex- 
 plains the origin of temporal series in terms of the 
 immediate facts of experience and at the same time 
 allows for the existence of the alternative temporal 
 series which are demanded by the modern theory of 
 electromagnetic relativity. 
 
 We now turn to space. The first thing to do is to 
 get hold of the class of abstractive elements which are 
 in some sense the points of space. Such an abstractive 
 element must in some sense exhibit a convergence to 
 an absolute minimum of intrinsic character. Euclid 
 has expressed for all time the general idea of a point, 
 
86 THE CONCEPT OF NATURE [ch. 
 
 as being without parts and without magnitude. It is 
 this character of being an absolute minimum which we 
 want to get at and to express in terms of the extrinsic 
 characters of the abstractive sets which make up a point. 
 Furthermore, points which are thus arrived at repre- 
 sent the ideal of events without any extension, though 
 there are in fact no such entities as these ideal events. 
 These points will not be the points of an external time- 
 less space but of instantaneous spaces. We ultimately 
 want to arrive at the timeless space of physical science, 
 and also of common thought which is now tinged with 
 the concepts of science. It will be convenient to reserve 
 the term * point' for these spaces when we get to 
 them. I will therefore use the name * event-particles ' 
 for the ideal minimum limits to events. Thus an 
 event-particle is an abstractive element and as such is 
 a group of abstractive sets ; and a point — namely a point 
 of timeless space — ^will be a class of event-particles. 
 
 Furthermore there is a separate timeless space corre- 
 sponding to each separate temporal series, that is to 
 each separate family of durations. We will come back 
 to points in timeless spaces later. I merely mention 
 them now that we may understand the stages of our 
 investigation. The totality of event-particles will form a 
 four-dimensional manifold, the extra dimension arising 
 from time — in other words — arising from the points of 
 a timeless space being each a class of event-particles. 
 
 The required character of the abstractive sets which 
 form event-particles would be secured if we could define 
 them as having the property of being covered by any 
 abstractive set which they cover. For then any other 
 abstractive set which an abstractive set of an event- 
 particle covered, would be equal to it, and would 
 
IV] METHOD OF EXTENSIVE ABSTRACTION 87 
 
 therefore be a member of the same event-particle. 
 Accordingly an event-particle could cover no other 
 abstractive element. This is the definition which I 
 originally proposed at a congress in Paris in 1914^. 
 There is however a difficulty involved in this definition 
 if adopted without some further addition, and I am now 
 not satisfied with the way in which I attempted to get 
 over that difficulty in the paper referred to. 
 
 The difficulty is this : When event-particles have once 
 been defined it is easy to define the aggregate of event- 
 particles forming the boundary of an event ; and thence 
 to define the point-contact at their boundaries possible 
 for ^ pair of events of which one is part of the other. 
 We can then conceive all the intricacies of tangency. 
 In particular we can conceive an abstractive set of 
 which all the members have point-contact at the same 
 event-particle. It is then easy to prove that there will 
 be no abstractive set with the property of being 
 covered by every abstractive set which it covers. I state 
 this difficulty at some length because its existence guides 
 the development of our line of argument. We have got 
 to annex some condition to the root property of being 
 covered by any abstractive set which it covers. When 
 we look into this question of suitable conditions we find 
 that in addition to event-particles all the other relevant 
 spatial and spatio-temporal abstractive elements can 
 be defined in the same way by suitably varying the 
 conditions. Accordingly we proceed in a general way 
 suitable for employment beyond event-particles. 
 
 Let (J be the name of any condition which some 
 abstractive sets fulfil. I say that an abstractive set is 
 
 1 Cf. • La Theorie Relationniste de TEspace,' Rev. de Mita- 
 physique et de Morale ^ vol. xxiii, 191 6. 
 
88 THE CONCEPT OF NATURE [ch. 
 
 * or -prime' when it has the two properties, (i) that it 
 satisfies the condition a and (ii) that it is covered by 
 every abstractive set which both is covered by it and 
 satisfies the condition a. 
 
 In other words you cannot get any abstractive set 
 satisfying the condition a which exhibits intrinsic 
 character more simple than that of a o- -prime. 
 
 There are also the correlative abstractive sets which 
 I call the sets of a-antiprimes. An abstractive set is a 
 a-antiprime when it has the two properties, (i) that it 
 satisfies the condition a and (ii) that it covers every 
 abstractive set which both covers it and satisfies the 
 condition a. In other words you cannot get any ab- 
 stractive set satisfying the condition o- which exhibits 
 an intrinsic character more complex than that of a 
 cr-antiprime. 
 
 The intrinsic character of a cr -prime has a certain 
 minimum of fullness among those abstractive sets which 
 are subject to the condition of satisfying a; whereas 
 the intrinsic character of a a-antiprime has a corre- 
 sponding maximum of fullness, and includes all it can 
 in the circumstances. 
 
 Let us first consider what help the notion of anti- 
 primes could give us in the definition of moments 
 which we gave in the last lecture. Let the condition 
 or be the property of being a class whose members are 
 all durations. An abstractive set which satisfies this 
 condition is thus an abstractive set composed wholly 
 of durations. It is convenient then to define a moment 
 as the group of abstractive sets which are equal to some 
 a-antiprime, where the condition a has this special 
 meaning. It will be found on consideration (i) that 
 each abstractive set forming a moment is a o--antiprime. 
 
IV] METHOD OF EXTENSIVE ABSTRACTION 89 
 
 where (j has this special meaning, and (ii) that we have 
 excluded from membership of moments abstractive 
 sets of durations which all have one common boundary, 
 either the initial boundary or the final boundary. We 
 thus exclude special cases which are apt to confuse 
 general reasoning. The new definition of a moment, 
 which supersedes our previous definition, is (by the aid 
 of the notion of antiprimes) the more precisely drawn 
 of the two, and the more useful. 
 
 The particular condition which *(j' stood for in the 
 definition of moments included something additional 
 to anything which can be derived from the bare notion 
 of extension. A duration exhibits for thought a totality. 
 The notion of totality is something beyond that of 
 extension, though the two are interwoven in the notion 
 of a duration. 
 
 In the same way the particular condition ' a ' required 
 for the definition of an event-particle must be looked for 
 beyond the mere notion of extension. The same remark 
 is also true of the particular conditions requisite for the 
 other spatial elements. This additional notion is ob- 
 tained by distinguishing between the notion of *posi-, 
 tion ' and the notion of convergence to an ideal zero of 
 extension as exhibited by an abstractive set of events. 
 
 In order to understand this distinction consider a 
 point of the instantaneous space which we conceive 
 as apparent to us in an almost instantaneous glance. 
 This point is an event-particle. It has two aspects. In 
 one aspect it is there, where it is. This is its position in 
 the space. In another aspect it is got at by ignoring the 
 circumambient space, and by concentrating attention on 
 the smaller and smaller set of events which approximate 
 to it. This is its extrinsic character. Thus a point has 
 
90 THE CONCEPT OF NATURE [ch. 
 
 three characters, namely, its position in the whole 
 instantaneous space, its extrinsic character, and its 
 intrinsic character. The same is true of any other spatial 
 .element. For example an instantaneous volume in 
 instantaneous space has three characters, namely, its 
 position, its extrinsic character as a group of abstractive 
 sets, and its intrinsic character which is the limit of 
 natural properties which is indicated by any one of 
 these abstractive sets. 
 
 . Before we can talk about position in instantaneous 
 space, we must evidently be quite clear as to what we 
 mean by instantaneous space in itself. Instantaneous 
 space must be looked for as a character of a moment. 
 For a moment is all nature at an instant. It cannot be 
 the intrinsic character of the moment. For the intrinsic 
 character tells us the limiting character of nature in 
 space at that instant. Instantaneous space must be 
 an assemblage of abstractive elements considered in 
 their mutual relations. Thus an instantaneous space is 
 the assemblage of abstractive elements covered by some 
 one moment, and it is the instantaneous space of that 
 moment. 
 
 We have now to ask what character we have found in 
 nature which is capable of according to the elements of 
 an instantaneous space different qualities of position. 
 This question at once brings us to the intersection of 
 moments, which is a topic not as yet considered in 
 these lectures. 
 
 The locus of intersection of two moments is the 
 assemblage of abstractive elements covered by both of 
 them. Now two moments of the same temporal series 
 cannot intersect. Two moments respectively of different 
 families necessarily intersect. Accordingly in the in- 
 
IV] METHOD OF EXTENSIVE ABSTRACTION 91 
 
 stantaneous space of a moment we should expect the 
 fundamental properties to be marked by the inter- 
 sections with moments of other families. If M be a 
 given moment, the intersection of M with another 
 moment A is an instantaneous plane in the instan- 
 taneous space of M] and if 5 be a third moment 
 intersecting both M and A, the intersection of M and B 
 is another plane in the space M. Also the common 
 intersection of ^, By and M is the intersection of the 
 two planes in the space M, namely it is a straight line 
 in the space M. An exceptional case arises if B and M 
 intersect in the same plane as A and M. Furthermore 
 if C be a fourth moment, then apart from special cases 
 which we need not consider, it intersects M in a plane 
 which the straight line {A, B, M) meets. Thus there 
 is in general a common intersection of four moments 
 of different families. This common intersection is an 
 assemblage of abstractive elements which are each 
 covered (or *lie in') all four moments. The three- 
 dimensional property of instantaneous space comes to 
 this, that (apart from special relations between the four 
 moments) any fifth moment either contains the whole 
 of their common intersection or none of it. No further 
 subdivision of the common intersection is possible by 
 means of moments. The 'all or none' principle holds. 
 This is not an a priori truth but an empirical fact of 
 nature. 
 
 It will be convenient to reserve the ordinary spatial 
 terms * plane,' * straight line,' * point' for the elements 
 of the timeless space of a time-system. Accordingly an 
 instantaneous plane in the instantaneous space of a 
 moment will be called a * level,' an instantaneous straight 
 line will be called a *rect,' and an instantaneous point 
 
92 THE CONCEPT OF NATURE [ch. 
 
 will be called a * punct/ Thus a punct is the assemblage 
 of abstractive elements which lie in each of four moments 
 whose families have no special relations to each other. 
 Also if P be any moment, either every abstractive 
 element belonging to a given punct lies in P, or no 
 abstractive element of that punct lies in P. 
 
 Position is the quality which an abstractive element 
 possesses in virtue of the moments in which it lies. The 
 abstractive elements which lie in the instantaneous 
 space of a given moment M are differentiated from each 
 other by the various other moments which intersect M 
 so as to contain various selections of these abstractive 
 elements. It is this differentiation of the elements which 
 constitutes their differentiation of position. An ab- 
 stractive element which belongs to a punct has the 
 simplest type of position in M, an abstractive element 
 which belongs to a rect but not to a punct has a more 
 complex quality of position, an abstractive element 
 which belongs to a level and not to a rect has a still 
 more complex quality of position, and finally the most 
 complex quality of position belongs to an abstractive 
 element which belongs to a volume and not to a level. 
 A volume however has not yet been defined. This 
 definition will be given in the next lecture. 
 
 Evidently levels, rects, and puncts in their capacity 
 as infinite aggregates cannot be the termini of sense- 
 awareness, nor can they be limits which are approxi- 
 mated to in sense-awareness. Any one member of a 
 level has a certain quality arising from its character as 
 also belonging to a certain set of moments, but the level 
 as a whole is a mere logical notion without any route of 
 approximation along entities posited in sense-awareness. 
 
 On the other hand an event-particle is defined so as 
 
IV] METHOD OF EXTENSIVE ABSTRACTION 93 
 
 to exhibit this character of being a route of approxi- 
 mation marked out by entities posited in sense-aware- 
 ness. A definite event-particle is defined in reference 
 to a definite punct in the foUov^ing manner: Let the 
 condition a mean the property of covering all the 
 abstractive elements which are members of that punct ; 
 so that an abstractive set which satisfies the condition a 
 is an abstractive set which covers every abstractive 
 element belonging to the punct. Then the definition 
 of the event-particle associated with the punct is that 
 it is the group of all the cr-primes, where a has this 
 particular meaning. 
 
 It is evident that — ^with this meaning of <j — every 
 abstractive set equal to a cr -prime is itself a o- -prime. 
 Accordingly an event-particle as thus defined is an 
 abstractive element, namely it is the group of those 
 abstractive sets which are each equal to some given 
 abstractive set. If we write out the definition of the 
 event-particle associated with some given punct, which 
 we will call tt, it is as follows: The event-particle as- 
 sociated with 77 is the group of abstractive classes each 
 of which has the two properties (i) that it covers every 
 abstractive set in tt and (ii) that all the abstractive sets 
 which also satisfy the former condition as to 77 and which 
 it covers, also cover it. 
 
 An event-particle has position by reason of its 
 association with a punct, and conversely the punct 
 gains its derived character as a route of approximation 
 from its association with the event-particle. These two 
 characters of a point are always recurring in any treat- 
 ment of the derivation of a point from the observed 
 facts of nature, but in general there is no clear recogni- 
 tion of their distinction. 
 
94 THE CONCEPT OF NATURE [cH. 
 
 The peculiar simplicity of an instantaneous point has 
 a twofold origin, one connected with position, that is 
 to say with its character as a punct, and the other con- 
 nected with its character as an event-particle. The 
 simplicity of the punct arises from its indivisibility by 
 a moment. 
 
 The simplicity of an event-particle arises from the 
 indivisibility of its intrinsic character. The intrinsic 
 character of an event-particle is indivisible in the sense 
 that every abstractive set covered by it exhibits the 
 same intrinsic character. It follows that, though there 
 are diverse abstractive elements covered by event- 
 particles, there is no advantage to be gained by con- 
 sidering them since we gain no additional simplicity 
 in the expression of natural properties. 
 
 These two characters of simplicity enjoyed respec- 
 tively by event-particles and puncts define a meaning for 
 Euclid's phrase, * without parts and without magnitude.' 
 
 It is obviously convenient to sweep away out of our 
 thoughts all these stray abstractive sets which are 
 covered by event-particles without themselves being 
 members of them. They give us nothing new in the 
 way of intrinsic character. Accordingly we can think 
 of rects and levels as merely loci of event-particles. 
 In so doing we are also cutting out those abstractive 
 elements which cover sets of event-particles, without 
 these elements being event-particles themselves. There 
 are classes of these abstractive elements which are of 
 great importance. I will consider them later on in this 
 and in other lectures. Meanwhile we will ignore them. 
 Also I will always speak of * event-particles ' in pre- 
 ference to * puncts,' the latter being an artificial word 
 for which I have no great affection. 
 
IV] METHOD OF EXTENSIVE ABSTRACTION 95 
 
 Parallelism among rects and levels is now^ explicable. 
 
 Consider the instantaneous space belonging to a 
 moment Ay and let A belong to the temporal series of 
 moments v^hich I v^ill call a. Consider any other 
 temporal series of moments w^hich I v^ill call j8. The 
 moments of j8 do not intersect each other and they 
 intersect the moment ^ in a family of levels. None of 
 these levels can intersect, and they form a family of 
 parallel instantaneous planes in the instantaneous space 
 of moment A. Thus the parallelism of moments in a 
 temporal series begets the parallelism of levels in an 
 instantaneous space, and thence — as it is easy to see — 
 the parallelism of rects. Accordingly the Euclidean 
 property of space arises from the parabolic property of 
 time. It may be that there is reason to adopt a hyper- 
 bolic theory of time and a corresponding hyperbolic 
 theory of space. Such a theory has not been vi^orked out, 
 so it is not possible to judge as to the character of the 
 evidence v^hich could be brought forw^ard in its favour. 
 
 The theory of order in an instantaneous space is 
 immediately derived from time-order. For consider the 
 space of a moment M. Let a be the name of a time- 
 system to w^hich M does not belong. Let A^, A2, A^y etc. 
 be moments of a in the order of their occurrences. Then 
 Ai, A^y A^y etc. intersect M in parallel levels Z^, 4, 4, etc. 
 Then the relative order of the parallel levels in the 
 space of M is the same as the relative order of the corre- 
 sponding moments in the time-system «. Any rect in 
 M which intersects all these levels in its set of puncts, 
 thereby receives for its puncts an order of position on it. 
 So spatial order is derivative from temporal order. 
 Furthermore there are alternative time-systems, but 
 there is only one definite spatial order in each instan- 
 
96 THE CONCEPT OF NATURE [ch. 
 
 taneous space. Accordingly the various modes of 
 deriving spatial order from diverse time-systems must 
 harmonise with one spatial order in each instantaneous 
 space. In this way also diverse time-orders are com- 
 parable. 
 
 We have two great questions still on hand to be 
 settled before our theory of space is fully adjusted. 
 One of these is the question of the determination of the 
 methods of measurement within the space, in other 
 words, the congruence-theory of the space. The 
 measurement of space will be found to be closely 
 connected with the measurement of time, with respect 
 to which no principles have as yet been determined. 
 Thus our congruence-theory will be a theory both for 
 space and for time. Secondly there is the determination 
 of the timeless space which corresponds to any particular 
 time-system with its infinite set of instantaneous spaces 
 in its successive moments. This is the space — or rather, 
 these are the spaces — of physical science. It is very 
 usual to dismiss this space by saying that this is con- 
 ceptual. I do not understand the virtue of these phrases. 
 I suppose that it is meant that the space is the concep- 
 tion of something in nature. Accordingly if the space 
 of physical science is to be called conceptual, I ask, 
 What in nature is it the conception of? For example, 
 when we speak of a point in the timeless space of 
 physical science, I suppose that we are speaking of 
 something in nature. If we are not so speaking, our 
 scientists are exercising their w4ts in the realms of 
 pure fantasy, and this is palpably not the case. This 
 demand for a definite Habeas Corpus Act for the pro- 
 duction of the relevant entities in nature applies whether 
 space be relative or absolute. On the theory of relative 
 
IV] METHOD OF EXTENSIVE ABSTRACTION 97 
 
 space, it may perhaps be argued that there is no timeless 
 space for physical science, and that there is only the 
 momentary series of instantaneous spaces. 
 
 An explanation must then be asked for the meaning 
 of the very common statement that such and such a 
 man walked four miles in some definite hour. How can 
 you measure distance from one space into another 
 space? I understand walking out of the sheet of an 
 ordnance map. But the meaning of saying that Cam- 
 bridge at 10 o'clock this morning in the appropriate 
 instantaneous space for that instant is 52 miles from 
 London at 11 o'clock this morning in the appropriate 
 instantaneous space for that instant beats me entirely. 
 I think that, by the time a meaning has been produced 
 for this statement, you will find that you have constructed 
 what is in fact a timeless space. What I cannot under- 
 stand is how to produce an explanation of meaning 
 without in effect making some such construction. Also 
 I may add that I do not know how the instantaneous 
 spaces are thus correlated into one space by any method 
 which is available on the current theories of space. 
 
 You will have noticed that by the aid of the assump- 
 tion of alternative time-systems, we are arriving at an 
 explanation of the character of space. In natural science 
 * to explain ' means merely to discover * interconnexions.' 
 For example, in one sense there is no explanation of the 
 red which you see. It is red, and there is nothing else 
 to be said about it. Either it is posited before you in 
 sense-awareness or you are ignorant of the entity red. 
 But science has explained red. Namely it has dis- 
 covered interconnexions between red as a factor in 
 nature and other factors in nature, for example waves of 
 light which are waves of electromagnetic disturbances. 
 
 W.N. 7 
 
98 THE CONCEPT OF NATURE [ch. iv 
 
 There are also various pathological states of the body 
 which lead to the seeing of red without the occurrence 
 of light waves. Thus connexions have been discovered 
 between red as posited in sense-awareness and various 
 other factors in nature. The discovery of these con- 
 nexions constitutes the scientific explanation of our 
 vision of colour. In like manner the dependence of 
 the character of space on the character of time con- 
 stitutes an explanation in the sense in which science 
 seeks to explain. The systematising intellect abhors 
 bare facts. The character of space has hitherto been 
 presented as a collection of bare facts, ultimate and 
 disconnected. The theory which I am expounding 
 sweeps away this disconnexion of the facts of space. 
 
CHAPTER V 
 
 SPACE AND MOTION 
 
 The topic for this lecture is the continuation of the 
 task of explaining the construction of spaces as ab- 
 stracts from the facts of nature. It was noted at the 
 close of the previous lecture that the question of 
 congruence had not been considered, nor had the con- 
 struction of a timeless space which should correlate 
 the successive momentary spaces of a given time-system. 
 Furthermore it was also noted that there were many 
 spatial abstractive elements which we had not yet 
 defined. We will first consider the definition of some 
 of these abstractive elements, namely the definitions 
 of soHds, of areas, and of routes. By a * route' I mean 
 a linear segment, whether straight or curved. The ex- 
 position of these definitions and the preliminary ex- 
 planations necessary will, I hope, serve as a general 
 explanation of the function of event-particles in the 
 analysis of nature. 
 
 We note that event-particles have * position ' in respect 
 to each other. In the last lecture I explained that 
 * position' was quality gained by a spatial element in 
 virtue of the intersecting moments which covered it. 
 Thus each event-particle has position in this sense. 
 The simplest mode of expressing the position in nature 
 of an event-particle is by first fixing on any definite 
 time-system. Call it a. There will be one moment of 
 the temporal series of a which covers the given event- 
 particle. Thus the position of the event-particle in the 
 temporal series a is defined by this moment, which we 
 
 7—2 
 
100 THE CONCEPT OF NATURE [ch. 
 
 will call M, The position of the particle in the space 
 of M is then fixed in the ordinary way by three levels 
 which intersect in it and in it only. This procedure of 
 fixing the position of an event-particle shows that the 
 aggregate of event-particles forms a four-dimensional 
 manifold. A finite event occupies a limited chunk of 
 this manifold in a sense which I now proceed to explain. 
 Let e be any given event. The manifold of event- 
 particles falls into three sets in reference to e. Each 
 event-particle is a group of equal abstractive sets and 
 each abstractive set towards its small-end is composed 
 of smaller and smaller finite events. When we select 
 from these finite events which enter into the make-up 
 of a given event-particle those which are small enough, 
 one of three cases must occur. Either (i) all of these 
 small events are entirely separate from the given event e, 
 or (ii) all of these small events are parts of the event e^ 
 or (iii) all of these small events overlap the event e but 
 are not parts of it. In the first case the event-particle 
 will be said to *lie outside' the event e, in the second 
 case the event-particle will be said to *lie inside' the 
 event e, and in the third case the event-particle will be 
 said to be a *boundary-particle' of the event e. Thus there 
 are three sets of particles, namely the set of those which 
 lie outside the event e, the set of those which lie inside 
 the event e, and the boundary of the event e which is 
 the set of boundary-particles of e. Since an event is 
 four-dimensional, the boundary of an event is a three- 
 dimensional manifold. For a finite event there is a 
 continuity of boundary; for a duration the boundary 
 consists of those event-particles which are covered by 
 either of the two bounding moments. Thus the boundary 
 of a duration consists of two momentary three-dimen-^ 
 
V] SPACE AND MOTION loi 
 
 sional spaces. An event will be said to * occupy' the 
 aggregate of event-particles which lie within it. 
 
 Two events which have * junction' in the sense in 
 which junction was described in my last lecture, and 
 yet are separated so that neither event either overlaps 
 or is part of the other event, are said to be * adjoined.' 
 
 This relation of adjunction issues in a peculiar relation 
 between the boundaries of the two events. The two 
 boundaries must have a common portion which is in 
 fact a continuous three-dimensional locus of event- 
 particles in the four-dimensional manifold. 
 
 A three-dimensional locus of event-particles which 
 is the common portion of the boundary of two adjoined 
 events will be called a * solid.' A solid may or may not 
 lie completely in one moment. A solid which does not 
 lie in one moment will be called * vagrant.' A solid 
 which does lie in one moment will be called a volume. 
 A volume may be defined as the locus of the event- 
 particles in which a moment intersects an event, pro- 
 vided that the two do intersect. The intersection of a 
 moment and an event will evidently consist of those 
 event-particles which are covered by the moment and 
 lie in the event. The identity of the two definitions of a 
 volume is evident when we remember that an intersect- 
 ing moment divides the event into two adjoined events. 
 
 A solid as thus defined, whether it be vagrant or be 
 a volume, is a mere aggregate of event-particles illus- 
 trating a certain quality of position. We can also define 
 a solid as an abstractive element. In order to do so we 
 recur to the theory of primes explained in the preceding 
 lecture. Let the condition named a stand for the fact 
 that each of the events of any abstractive set satisfying it 
 has all the event-particles of some particular solid lying 
 
102 THE CONCEPT OF NATURE [ch. 
 
 in it. Then the group of all the or -primes is the abstractive 
 element which is associated with the given solid. I will 
 call this abstractive element the solid as an abstractive 
 element, and I will call the aggregate of event-particles 
 the solid as a locus. The instantaneous volumes in 
 instantaneous space which are the ideals of our sense- 
 perception are volumes as abstractive elements. What 
 we really perceive with all our efforts after exactness 
 are small events far enough down some abstractive 
 set belonging to the volume as an abstractive element. 
 
 It is difficult to know how far we approximate to any 
 perception of vagrant solids. We certainly do not think 
 that we make any such approximation. But then our 
 thoughts — in the case of people who do think about 
 such topics — are so much under the control of the 
 materialistic theory of nature that they hardly count 
 for evidence. If Einstein's theory of gravitation has any 
 truth in it, vagrant solids are of great importance in 
 science. The whole boundary of a finite event may be 
 looked on as a particular example of a vagrant solid 
 as a locus. Its particular property of being closed pre- 
 vents it from being definable as an abstractive element. 
 
 When a moment intersects an event, it also intersects 
 the boundary of that event. This locus, which is the 
 portion of the boundary contained in the moment, is 
 the bounding surface of the corresponding volume of 
 that event contained in the moment. It is a two- 
 dimensional locus. 
 
 The fact that every volume has a bounding surface is 
 the origin of the Dedekindian continuity of space. 
 
 Another event may be cut by the same moment in 
 another volume and this volume will also have its 
 boundary. These two volumes in the instantaneous 
 
V] SPACE AND MOTION 103 
 
 space of one moment may mutually overlap in the 
 familiar way which I need not describe in detail and thus 
 cut off portions from each other's surfaces. These por- 
 tions of surfaces are *momental areas/ 
 
 It is unnecessary at this stage to enter into the com- 
 plexity of a definition of vagrant areas. Their definition 
 is simple enough when the four-dimensional manifold 
 of event-particles has been more fully explored as to 
 its properties. 
 
 Momental areas can evidently be defined as abstrac- 
 tive elements by exactly the same method as applied 
 to solids. We have merely to substitute *area* for a 
 
 * solid' in the words of the definition already given. 
 Also, exactly as in the analogous case of a solid, what 
 we perceive as an approximation to our ideal of an area 
 is a small event far enough down towards the small end 
 of one of the equal abstractive sets which belongs to 
 the area as an abstractive element. 
 
 Two momental areas lying in the same moment can 
 cut each other in a momental segment which is not 
 necessarily rectilinear. Such a segment can also be 
 defined as an abstractive element. It is then called a 
 
 * momental route.' We will not delay over any general 
 consideration of these momental routes, nor is it 
 important for us to proceed to the still wider investiga- 
 tion of vagrant routes in general. There are however two 
 simple sets of routes which are of vital importance. One 
 is a set of momental routes and the other of vagrant 
 routes. Both sets can be classed together as straight 
 routes. We proceed to define them without any re- 
 ference to the definitions of volumes and surfaces. 
 
 The two types of straight routes will be called 
 rectilinear routes and stations. Rectilinear routes are 
 
104 THE CONCEPT OF NATURE [ch. 
 
 momental routes and stations are vagrant routes. 
 Rectilinear routes are routes which in a sense He in 
 rects. Any two event-particles on a rect define the set 
 of event-particles which lie between them on that rect. 
 Let the satisfaction of the condition a by an abstractive 
 set mean that the two given event-particles and the 
 event-particles lying between them on the rect all lie 
 in every event belonging to the abstractive set. The 
 group of or -primes, where g has this meaning, form an 
 abstractive element. Such abstractive elements are recti- 
 linear routes. They are the segments of instantaneous 
 straight lines which are the ideals of exact perception. 
 Our actual perception, however exact, will be the per- 
 ception of a small event sufficiently far down one of 
 the abstractive sets of the abstractive element. 
 
 A station is a vagrant route and no moment can inter- 
 sect any station in more than one event-particle. Thus 
 a station carries with it a comparison of the positions 
 in their respective moments of the event-particles 
 covered by it. Rects arise from the intersection of 
 moments. But as yet no properties of events have been 
 mentioned by which any analogous vagrant loci can 
 be found out. 
 
 The general problem for our investigation is to 
 determine a method of comparison of position in one 
 instantaneous space with positions in other instantaneous 
 spaces. We may limit ourselves to the spaces of the 
 parallel moments of one time-system. How are positions 
 in these various spaces to be compared ? In other words. 
 What do we mean by motion.^ It is the fundamental 
 question to be asked of any theory of relative space, 
 and like many other fundamental questions it is apt to 
 be left unanswered. It is not an answer to reply, that 
 
V] SPACE AND MOTION 105 
 
 we all know what we mean by motion. Of course we V 
 do, so far as sense-awareness is concerned. I am asking 
 that your theory of space should provide nature with 
 something to be observed. You have not settled the 
 question by bringing forward a theory according to 
 which there is nothing to be observed, and by then 
 reiterating that nevertheless we do observe this non- 
 existent fact. Unless motion is something as a fact in 
 nature, kinetic energy and momentum and all that 
 depends on these physical concepts evaporate from our 
 list of physical realities. Even in this revolutionary age 
 my conservatism resolutely opposes the identification 
 of momentum and moonshine. 
 
 Accordingly I assume it as an axiom, that motion 
 is a physical fact. It is something that we perceive as 
 in nature. Motion presupposes rest. Until theory arose 
 to vitiate immediate intuition, that is to say to vitiate 
 the uncriticised judgments which immediately arise 
 from sense-awareness, no one doubted that in motion 
 you leave behind that which is at rest. Abraham in his 
 wanderings left his birthplace where it had ever been. 
 A theory of motion and a theory of rest are the same 
 thing viewed from different aspects with altered em- 
 phasis. 
 
 Now you cannot have a theory of rest without in some 
 sense admitting a theory of absolute position. It is 
 usually assumed that relative space implies that there is 
 no absolute position. This is, according to my creed, a 
 mistake. The assumption arises from the failure to 
 make another distinction; namely, that there may be 
 alternative definitions of absolute position. This possi- 
 bility enters with the admission of alternative time- 
 systems. Thus the series of spaces in the parallel 
 
io6 THE CONCEPT OF NATURE [ch. 
 
 moments of one temporal series may have their own 
 definition of absolute position correlating sets of event- 
 particles in these successive spaces, so that each set 
 consists of event-particles, one from each space, all 
 with the property of possessing the same absolute 
 position in that series of spaces. Such a set of event- 
 particles will form a point in the timeless space of that 
 time-system. Thus a point is really an absolute position 
 in the timeless space of a given time-system. 
 
 But there are alternative time-systems, and each 
 time-system has its own peculiar group of points — that 
 is to say, its own peculiar definition of absolute position. 
 This is exactly the theory which I will elaborate. 
 
 In looking to nature for evidence of absolute position 
 it is of no use to recur to the four-dimensional manifold 
 of event-particles. • This manifold has been obtained by 
 the extension of thought beyond the immediacy of 
 observation. We shall find nothing in it except what we 
 have put there to represent the ideas in thought which 
 i arise from our direct sense-awareness of nature. To 
 ' find evidence of the properties which are to be found 
 in the manifold of event-particles we must always 
 recur to the observation of relations between events. 
 Our problem is to determine those relations between 
 events which issue in the property of absolute position 
 in a timeless space. This is in fact the problem of the 
 determination of the very meaning of the timeless 
 spaces of physical science. 
 
 In reviewing the factors of nature as immediately 
 disclosed in sense-awareness, we should note the 
 fundamental character of the percept of 'being here.' 
 We discern an event merely as a factor in a determinate 
 complex in which each factor has its own peculiar share. 
 
V] SPACE AND MOTION 107 
 
 There are two factors which are always ingredient in 
 this complex, one is the duration which is represented 
 in thought by the concept of all nature that is present 
 now, and the other is the peculiar locus standi for mind 
 involved in the sense-awareness. This locus standi in 
 nature is what is represented in thought by the concept 
 of ' here,' namely of an * event here/ 
 
 This is the concept of a definite factor in nature. This 
 factor is an event in nature which is the focus in nature 
 for that act of awareness, and the other events are 
 perceived as referred to it. This event is part of the 
 associated duration. I call it the * percipient event.' 
 This event is not the mind, that is to say, not the per- 
 cipient. It is that in nature from which the mind 
 perceives. The complete foothold of the mind in nature 
 is represented by the pair of events, namely, the present 
 duration which marks the * when ' of awareness and the 
 percipient event which marks the * where ' of awareness 
 and the *how' of awareness. This percipient event is 
 roughly speaking the bodily life of the incarnate mind. 
 But this identification is only a rough one. For the 
 functions of the body shade off into those of other events 
 in nature ; so that for some purposes the percipient event 
 is to be reckoned as merely part of the bodily life and 
 for other purposes it may even be reckoned as more than 
 the bodily life. In many respects the demarcation is 
 purely arbitrary, depending upon where in a sliding 
 scale you choose to draw the line. 
 
 I have already in my previous lecture on Time dis- 
 cussed the association of mind with nature. The difficulty 
 of the discussion lies in the liability of constant factors 
 to be overlooked. We never note them by contrast 
 with their absences. The purpose of a discussion of such 
 
io8 THE CONCEPT OF NATURE [ch. 
 
 factors may be described as being to make obvious 
 things look odd. We cannot envisage them unless we 
 manage to invest them with some of the freshness which 
 is due to strangeness. 
 
 It is because of this habit of letting constant factors 
 slip from consciousness that we constantly fall into the 
 error of thinking of the sense-awareness of a particular 
 factor in nature as being a two-termed relation between 
 the mind and the factor. For example, I perceive a 
 green leaf. Language in this statement suppresses all 
 reference to any factors other than the percipient mind 
 and the green leaf and the relation of sense-awareness. 
 It discards the obvious inevitable factors which are 
 essential elements in the perception. I am here, the 
 leaf is there ; and the event here and the event which is 
 the life of the leaf there are both embedded in a totality 
 of nature which is now, and within this totality there 
 are other discriminated factors which it is irrelevant to 
 mention. Thus language habitually sets before the mind 
 a misleading abstract of the indefinite complexity of 
 the fact of sense-awareness. 
 
 What I now want to discuss is the special relation of 
 the percipient event which is ^here' to the duration 
 which is ' now.' This relation is a fact in nature, namely 
 the mind is aware of nature as being with these two 
 factors in this relation. 
 
 Within the short present duration the ' here ' of the 
 percipient event has a definite meaning of some sort. 
 This meaning of 'here' is the content of the special 
 relation of the percipient event to its associated duration. 
 I will call this relation * cogredience.' Accordingly I ask 
 for a description of the character of the relation of 
 cogredience. The present snaps into a past and a present 
 
v] SPACE AND MOTION 109 
 
 when the * here ' of cogredience loses its single deter- 
 minate meaning. There has been a passage of nature 
 from the * here ' of perception within the past duration 
 to the different ' here ' of perception within the present 
 duration. But the two *heres' of sense-awareness 
 within neighbouring durations may be indistinguishable. 
 In this case there has been a passage from the past to 
 the present, but a more retentive perceptive force might 
 have retained the passing nature as one complete present 
 instead of letting the earlier duration slip into the past. 
 Namely, the sense of rest helps the integration of dura- 
 tions into a prolonged present, and the sense of motion 
 differentiates nature into a succession of shortened 
 durations. As we look out of a railway carriage in an 
 express train, the present is past before reflexion can 
 seize it. We live in snippits too quick for thought. On 
 the other hand the immediate present is prolonged 
 according as nature presents itself to us in an aspect of 
 unbroken rest. Any change in nature provides ground 
 for a differentiation among durations so as to shorten 
 the present. But there is a great distinction between 
 self -change in nature and change in external nature. 
 Self-change in nature is change in the quality of the 
 standpoint of the percipient event. It is the break up 
 of the *here' which necessitates the break up of the 
 present duration. Change in external nature is com- 
 patible with a prolongation of the present of contem- 
 plation rooted in a given standpoint. What I want to 
 bring out is that the preservation of a peculiar relation 
 to a duration is a necessary condition for the function 
 of that duration as a present duration for sense-aware- 
 ness. This peculiar relation is the relation of cogredi- 
 ence between the percipient event and the duration. 
 
no THE CONCEPT OF NATURE [cH. 
 
 Cogredience is the preservation of unbroken quality of 
 standpoint within the duration. It is the continuance 
 of identity of station within the whole of nature which 
 is the terminus of sense-awareness. The duration may 
 comprise change within itself, but cannot — so far as it 
 is one present duration — comprise change in the quality 
 of its peculiar relation to the contained percipient event. 
 
 In other words, perception is always 'here,* and a 
 duration can only be posited as present for sense-aware- 
 ness on condition that it affords one unbroken meaning 
 of *here' in its relation to the percipient event. It is 
 only in the past that you can have been * there ' with a 
 standpoint distinct from your present 'here.' 
 
 Events there and events here are facts of nature, and 
 the qualities of being * there ' and * here ' are not merely 
 qualities of awareness as a relation between nature and 
 mind. The quality of determinate station in the duration 
 which belongs to an event which is * here ' in one deter- 
 minate sense of 'here' is the same kind of quality of 
 station which belongs to an event which is 'there' in 
 one determinate sense of 'there.' Thus cogredience has 
 nothing to do with any biological character of the event 
 which is related by it to the associated duration. This 
 biological character is apparently a further condition 
 for the peculiar connexion of a percipient event with 
 the percipience of mind ; but it has nothing to do with 
 the relation of the percipient event to the duration 
 which is the present whole of nature posited as the 
 disclosure of the percipience. 
 
 Given the requisite biological character, the event in 
 its character of a percipient event selects that duration 
 with which the operative past of the event is practi- 
 cally cogredient within the limits of the exactitude of 
 
V] SPACE AND MOTION iii 
 
 observation. Namely, amid the alternative time-systems 
 which nature offers there will be one with a duration 
 giving the best average of cogredience for all the sub- 
 ordinate parts of the percipient event. This duration 
 will be the whole of nature which is the terminus posited 
 by sense-awareness. Thus the character of the percipient 
 event determines the time-system immediately evident 
 in nature. As the character of the percipient event 
 changes with the passage of nature — or, in other words, 
 as the percipient mind in its passage correlates itself 
 with the passage of the percipient event into another 
 percipient event — the time-system correlated with the 
 percipience of that mind may change. When the bulk 
 of the events perceived are cogredient in a duration 
 other than that of the percipient event, the percipience 
 may include a double consciousness of cogredience, 
 namely the consciousness of the whole within which the 
 observer in the train is *here,' and the consciousness of 
 the whole within which the trees and bridges and 
 telegraph posts are definitely * there/ Thus in per- 
 ceptions under certain circumstances the events dis- 
 criminated assert their own relations of cogredience. 
 This assertion of cogredience is peculiarly evident when 
 the duration to which the perceived event is cogredient 
 is the same as the duration which is the present whole 
 of nature — in other words, when the event and the per- 
 cipient event are both cogredient to the same duration. 
 
 We are now prepared to consider the meaning of 
 stations in a duration, where stations are a peculiar 
 kind of routes, which define absolute position in the 
 associated timeless space. 
 
 There are however some preliminary explanations. 
 A finite event will be said to extend throughout a 
 
112 THE CONCEPT OF NATURE [ch. 
 
 duration when it is part of the duration and is inter- 
 sected by any moment which lies in the duration. Such 
 an event begins with the duration and ends with it. 
 Furthermore every event which begins with the dura- 
 tion and ends with it, extends throughout the duration. 
 This is an axiom based on the continuity of events. By 
 beginning with a duration and ending with it, I mean 
 (i) that the event is part of the duration, and (ii) that 
 both the initial and final boundary moments of the 
 duration cover some event-particles on the boundary of 
 the event. 
 
 Every event which is cogredient with a duration 
 extends throughout that duration. 
 
 It is not true that all the parts of an event cogredient 
 with a duration are also cogredient with the duration. 
 The relation of cogredience may fail in either of two 
 ways. One reason for failure may be that the part does 
 not extend throughout the duration. In this case the 
 part may be cogredient with another duration which is 
 part of the given duration, though it is not cogredient 
 with the given duration itself. Such a part would be 
 cogredient if its existence were sufficiently prolonged 
 in that time-system. The other reason for failure arises 
 from the four-dimensional extension of events so that 
 there is no determinate route of transition of events in 
 linear series. For example, the tunnel of a tube railway 
 is an event at rest in a certain time-system, that is to say, 
 it is cogredient with a certain duration. A train travel- 
 ling in it is part of that tunnel, but is not itself at rest. 
 
 If an event e be cogredient with a duration d, and 
 d! be any duration which is part of d. Then d' belongs 
 to the same time-system as d. Also d' intersects e in 
 an event e' which is part of e and is cogredient with d' , 
 
v] SPACE AND MOTION 113 
 
 Let P be any event-particle lying in a given duration 
 rf. Consider the aggregate of events in which P lies 
 and which are also cogredient with d. Each of these 
 events occupies its own aggregate of event-particles. 
 These aggregates will have a common portion, namely 
 the class of event-particle lying in all of them. This class 
 of event-particles is what I call the * station' of the 
 event-particle P in the duration d. This is the station in 
 the character of a locus. A station can also be defined in 
 the character of an abstractive element. Let the pro- 
 perty o- be the name of the property which an abstractive 
 set possesses when (i) each of its events is cogredient 
 with the duration d and (ii) the event-particle P lies 
 in each of its events. Then the group of (t -primes, where 
 a has this meaning, is an abstractive element and is the 
 station of P in t/ as an abstractive element. The locus 
 of event-particles covered by the station oi P in d as 
 an abstractive element is the station of P in rf as a 
 locus. A station has accordingly the usual three 
 characters, namely, its character of position, its ex- 
 trinsic character as an abstractive element, and its 
 intrinsic character. 
 
 It follows from the peculiar properties of rest that 
 two stations belonging to the same duration cannot 
 intersect. Accordingly every event-particle on a station 
 of a duration has that station as its station in the duration. 
 Also every duration which is part of a given duration 
 intersects the stations of the given duration in loci which 
 are its own stations. By means of these properties we can 
 utilise the overlappings of the durations of one family — 
 that is, of one time-system — to prolong stations in- 
 definitely backwards and forwards. Such a prolonged 
 station will be called a point-track. A point-track is a 
 
 W.N. 8 
 
114 THE CONCEPT OF NATURE [ch. 
 
 locus of event-particles. It is defined by reference to 
 one particular time-system, a say. Corresponding to 
 any other time-system these will be a different group 
 of point- tracks. Every event-particle will lie on one 
 and only one point-track of the group belonging to any 
 one time-system. The group of point-tracks of the time- 
 system a is the group of points of the timeless space of a . 
 Each such point indicates a certain quality of absolute 
 position in reference to the durations of the family 
 associated with a, and thence in reference to the suc- 
 cessive instantaneous spaces lying in the successive 
 moments of a. Each moment of a will intersect a 
 point-track in one and only one event-particle. 
 
 This property of the unique intersection of a moment 
 and a point-track is not confined to the case when the 
 moment and the point-track belong to the same time- 
 system. Any two event-particles on a point-track are 
 sequential, so that they cannot lie in the same moment. 
 Accordingly no moment can intersect a point-track 
 more than once, and every moment intersects a point- 
 track in one event-particle. 
 
 Anyone who at the successive moments of a should 
 be at the event-particles where those moments intersect 
 a given point of a will be at rest in the timeless space 
 of time-system a. But in any other timeless space 
 belonging to another time-system he will be at a 
 different point at each succeeding moment of that time- 
 system. In other words he will be moving. He will be 
 moving in a straight line with uniform velocity. We 
 might take this as the definition of a straight line. 
 Namely, a straight line in the space of time-system /3 is 
 the locus of those points of jS which all intersect some 
 one point-track which is a point in the space of some 
 
V] SPACE AND MOTION 115 
 
 other time-system. Thus each point in the space of a 
 time-system a is associated with one and only one 
 straight Hne of the space of any other time-system ^. 
 Furthermore the set of straight Hnes in space ^ which 
 are thus associated with points in space a form a com- 
 plete family of parallel straight lines in space j8. Thus 
 there is a one-to-one correlation of points in space a 
 with the straight lines of a certain definite family of 
 parallel straight lines in space )3. Conversely there is 
 an analogous one-to-one correlation of the points in 
 space /3 with the straight lines of a certain family of 
 parallel straight lines in space « . These families will be 
 called respectively the family of parallels in /3 associated 
 with a, and the family of parallels in a associated with ^, 
 The direction in the space of ^ indicated by the family 
 of parallels in /S will be called the direction of a in space 
 jS, and the family of parallels in a is the direction of j8 
 in space a. Thus a being at rest at a point of space a 
 will be moving uniformly along a line in space j8 which 
 is in the direction of a in space j8, and a being at rest 
 at a point of space /S will be moving uniformly along a 
 line in space a which is in the direction of jS in space a . 
 I have been speaking of the timeless spaces which are 
 associated with time-systems. These are the spaces of 
 physical science and of any concept of space as eternal 
 and unchanging. But what we actually perceive is an 
 approximation to the instantaneous space indicated by 
 event-particles which lie within some moment of the 
 time-system associated with our awareness. The points 
 of such an instantaneous space are event-particles and 
 the straight lines are rects. Let the time-system be 
 named a, and let the moment of time-system a to 
 which our quick perception of nature approximates be 
 
 8—2 
 
ii6 THE CONCEPT OF NATURE [ch. 
 
 called M. Any straight line r in space a is a locus of 
 points and each point is a point-track which is a locus 
 of event-particles. Thus in the four-dimensional geo- 
 metry of all event-particles there is a two-dimensional 
 locus which is the locus of all event-particles on points 
 lying on the straight line r. I will call this locus of 
 event-particles the matrix of the straight line r. A 
 matrix intersects any moment in a rect. Thus the matrix 
 of r intersects the moment M in a rect p . Thus p is the 
 instantaneous rect in M which occupies at the moment 
 M the straight line r in the space of a. Accordingly 
 when one sees instantaneously a moving being and its 
 path ahead of it, what one really sees is the being at 
 some event-particle A lying in the rect p which is the 
 apparent path on the assumption of uniform motion. 
 But the actual rect p which is a locus of event-particles 
 is never traversed by the being. These event-parti- 
 cles are the instantaneous facts which pass with the 
 instantaneous moment. What is really traversed are 
 other event-particles which at succeeding instants 
 occupy the same points of space a as those occupied by 
 the event-particles of the rect p. For example, we see a 
 stretch of road and a lorry moving along it. The in- 
 stantaneously seen road is a portion of the rect p — of 
 course only an approximation to it. The lorry is the 
 moving object. But the road as seen is never traversed. 
 It is thought of as being traversed because the intrinsic 
 characters of the later events are in general so similar 
 to those of the instantaneous road that we do not 
 trouble to discriminate. But suppose a land mine under 
 the road has been exploded before the lorry gets there. 
 Then it is fairly obvious that the lorry does not traverse 
 what we saw at first. Suppose the lorry is at rest in 
 
V] SPACE AND MOTION 117 
 
 space p. Then the straight line r of space a is in the 
 direction of ^ in space a, and the rect p is the repre- 
 sentative in the moment M of the Hne r of space «. 
 The direction of p in the instantaneous space of the 
 moment M is the direction of jS in M, where M is a 
 moment of time-system a. Again the matrix of the 
 line r of space a will also be the matrix of some line s 
 of space /S which will be in the direction of a in space j8. 
 Thus if the lorry halts at some point P of space a which 
 lies on the line r, it is now moving along the line s of 
 space ^. This is the theory of relative motion; the 
 common matrix is the bond which connects the motion 
 of jS in space a with the motions of a in space p. 
 
 Motion is essentially a relation between some object 
 of nature and the one timeless space of a time-system. 
 An instantaneous space is static, being related to the 
 static nature at an instant. In perception when we see 
 things moving in an approximation to an instantaneous 
 space, the future lines of motion as immediately per- 
 ceived are rects which are never traversed. These 
 approximate rects are composed of small events, namely 
 approximate routes and event-particles, which are 
 passed away before the moving objects reach them. 
 Assuming that our forecasts of rectilinear motion are 
 correct, these rects occupy the straight lines in timeless 
 space which are traversed. Thus the rects are symbols 
 in immediate sense-awareness of a future which can 
 only be expressed in terms of timeless space. 
 
 We are now in a position to explore the fundamental 
 character of perpendicularity. Consider the two time- 
 systems a and p, each with its own timeless space and 
 its own family of instantaneous moments with their 
 instantaneous spaces. Let M and A^ be respectively a 
 
128 THE CONCEPT OF NATURE [ch. 
 
 moment of a and a moment of jS. In M there is the 
 direction of ^ and in A^ there is the direction of a. 
 But M and A^, being moments of different time-systems, 
 intersect in a level. Call this level A. Then A is an 
 instantaneous plane in the instantaneous space of M 
 and also in the instantaneous space of A^. It is the locus 
 of all the event-particles which lie both in M and in A^. 
 
 In the instantaneous space of M the level A is per- 
 pendicular to the direction of j8 in M, and in the 
 instantaneous space of N the level A is perpendicular 
 to the direction of a in N, This is the fundamental 
 property which forms the definition of perpendicularity. 
 The symmetry of perpendicularity is a particular in- 
 stance of the symmetry of the mutual relations between 
 two time-systems. We shall find in the next lecture 
 that it is from this symmetry that the theory of con- 
 gruence is deduced. 
 
 The theory of perpendicularity in the timeless space 
 of any time-system a follows immediately from this 
 theory of perpendicularity in each of its instantaneous 
 spaces. Let p be any rect in the moment M of a and 
 let A be a level in M which is perpendicular to p . The 
 locus of those points of the space of a which intersect 
 M in event-particles on p is the straight line r of space a , 
 and the locus of those points of the space of a which 
 intersect M in event-particles on A is the plane / of 
 space a. Then the plane / is perpendicular to the line r. 
 
 In this way we have pointed out unique and definite 
 properties in nature which correspond to perpen- 
 dicularity. We shall find that this discovery of definite 
 unique properties defining perpendicularity is of 
 critical importance in the theory of congruence which 
 is the topic for the next lecture. 
 
V] SPACE AND MOTION 119 
 
 I regret that it has been necessary for me in this 
 lecture to administer such a large dose of four-dimen- 
 sional geometry. I do not apologise, because I am really 
 not responsible for the fact that nature in its most 
 fundamental aspect is four-dimensional. Things are 
 what they are ; and it is useless to disguise the fact that 
 * what things are ' is often very difficult for our intellects 
 to follow. It is a mere evasion of the ultimate problems 
 to shirk such obstacles. 
 
CHAPTER VI 
 
 CONGRUENCE 
 
 The aim of this lecture is to establish a theory of con- 
 gruence. You must understand at once that congruence 
 is a controversial question. It is the theory of measure- 
 ment in space and in time. The question seems simple. 
 In fact it is simple enough for a standard procedure to 
 have been settled by act of parliament ; and devotion to 
 metaphysical subtleties is almost the only crime which 
 has never been imputed to any English parliament. 
 But the procedure is one thing and its meaning is 
 another. 
 
 First let us fix attention on the purely mathematical 
 question. When the segment between two points A 
 and B is congruent to that between the two points C 
 and Z), the quantitative measurements of the two seg- 
 ments are equal. The equality of the numerical measures 
 and the congruence of the two segments are not always 
 clearly discriminated, and are lumped together under 
 the term equality. But the procedure of measurement 
 presupposes congruence. For example, a yard measure 
 is applied successively to measure two distances between 
 two pairs of points on the floor of a room. It is of the 
 essence of the procedure of measurement that the 
 yard measure remains unaltered as it is transferred from 
 one position to another. Some objects can palpably 
 alter as they move — ^for example, an elastic thread; 
 but a yard measure does not alter if made of the proper 
 material. What is this but a judgment of congruence 
 applied to the train of successive positions of the yard 
 
CH.vi] CONGRUENCE 121 
 
 measure? We know that it does not alter because we 
 judge it to be congruent to itself in various positions. 
 In the case of the thread we can observe the loss of 
 self-congruence. Thus immediate judgments of con- 
 gruence are presupposed in measurement, and the 
 process of measurement is merely a procedure to extend 
 the recognition of congruence to cases where these 
 immediate judgments are not available. Thus we cannot 
 define congruence by measurement. 
 
 In modern expositions of the axioms of geometry 
 certain conditions are laid down which the relation of 
 congruence between segments is to satisfy. It is 
 supposed that we have a complete theory of points, 
 straight lines, planes, and the order of points on planes — 
 in fact, a complete theory of non-metrical geometry. 
 We then enquire about congruence and lay down the 
 set of conditions — or axioms as they are called — ^which 
 this relation satisfies. It has then been proved that 
 there are alternative relations which satisfy these con- 
 ditions equally well and that there is nothing intrinsic 
 in the theory of space to lead us to adopt any one of these 
 relations in preference to any other as the relation 
 of congruence which we adopt. In other words there 
 are alternative metrical geometries which all exist by 
 an equal right so far as the intrinsic theory of space is 
 concerned. 
 
 Poincare, the great French mathematician, held that 
 our actual choice among these geometries is guided 
 purely by convention, and that the effect of a change of 
 choice would be simply to alter our expression of the 
 physical laws of nature. By 'convention' I understand 
 Poincare to mean that there is nothing inherent in 
 nature itself giving any peculiar rdle to one of these 
 
122 THE CONCEPT OF NATURE [ch. 
 
 congruence relations, and that the choice of one par- 
 ticular relation is guided by the volitions of the mind at 
 the other end of the sense-awareness. The principle of 
 guidance is intellectual convenience and not natural 
 fact. 
 
 This position has been misunderstood by many of 
 Poincare's expositors. They have muddled it up with 
 another question, namely that owing to the inexactitude 
 of observation it is impossible to make an exact state- 
 ment in the comparison of measures. It follows that a 
 certain subset of closely allied congruence relations can 
 be assigned of which each member equally well agrees 
 with that statement of observed congruence when the 
 statement is properly qualified with its limits of 
 error. 
 
 This is an entirely different question and it pre- 
 supposes a rejection of Poincare's position. The absolute 
 indetermination of nature in respect of all the relations 
 of congruence is replaced by the indetermination of 
 observation with respect to a small subgroup of these 
 relations. 
 
 Poincare's position is a strong one. He in effect 
 challenges anyone to point out any factor in nature 
 which gives a preeminent status to the congruence 
 relation which mankind has actually adopted. But un- 
 deniably the position is very paradoxical. Bertrand 
 Russell had a controversy with him on this question, 
 and pointed out that on Poincare's principles there was 
 nothing in nature to determine whether the earth is 
 larger or smaller than some assigned billiard ball. 
 Poincare replied that the attempt to find reasons in 
 nature for the selection of a definite congruence relation 
 in space is like trying to determine the position of a 
 
VI] CONGRUENCE 123 
 
 ship in the ocean by counting the crew and observing 
 the colour of the captain's eyes. 
 
 In my opinion both disputants were right, assuming 
 the grounds on which the discussion was based. 
 Russell in effect pointed out that apart from minor 
 inexactitudes a determinate congruence relation is 
 among the factors in nature which our sense-awareness 
 posits for us. Poincare asks for information as to the 
 factor in nature which might lead any particular con- 
 gruence relation to play a preeminent r6le among the 
 factors posited in sense-awareness. I cannot see the 
 answer to either of these contentions provided that you 
 admit the materialistic theory of nature. With this 
 heory nature at an instant in space is an independent 
 fact. Thus we have to look for our preeminent con- 
 gruence relation amid nature in instantaneous space; 
 and Poincare is undoubtedly right in saying that nature 
 on this hypothesis gives us no help in finding it. 
 
 On the other hand Russell is in an equally strong 
 position when he asserts that, as a fact of observation, 
 we do find it, and what is more agree in finding the same 
 congruence relation. On this basis it is one of the most 
 extraordinary facts of human experience that all man- 
 kind without any assignable reason should agree in 
 fixing attention on just one congruence relation amid 
 the indefinite number of indistinguishable competitors 
 for notice. One would have expected disagreement on 
 this fundamental choice to have divided nations and to 
 have rent families. But the difficulty was not even dis- 
 covered till the close of the nineteenth century by a 
 few mathematical philosophers and philosophic mathe- 
 maticians. The case is not like that of our agreement 
 on some fundamental fact of nature such as the three 
 
124 THE CONCEPT OF NATURE [ch. 
 
 dimensions of space. If space has only three dimensions 
 we should expect all mankind to be aware of the fact, 
 as they are aware of it. But in the case of congruence, 
 mankind agree in an arbitrary interpretation of sense- 
 awareness when there is nothing in nature to guide it. 
 
 I look on it as no slight recommendation of the theory 
 of nature which I am expounding to you that it gives 
 a solution of this difficulty by pointing out the factor 
 in nature which issues in the preeminence of one 
 congruence relation over the indefinite herd of other 
 such relations. 
 
 The reason for this result is that nature is no longer 
 confined within space at an instant. Space and time 
 are now interconnected ; and this peculiar factor of time 
 which is so immediately distinguished among the 
 deliverances of our sense-awareness, relates itself to 
 one particular congruence relation in space. 
 
 Congruence is a particular example of the fundamental 
 fact of recognition. In perception we recognise. This 
 recognition does not merely concern the comparison of 
 a factor of nature posited by memory with a factor 
 posited by immediate sense-awareness. Recognition 
 takes place within the present without any intervention 
 of pure memory. For the present fact is a duration with 
 its antecedent and consequent durations which are 
 parts of itself. The discrimination in sense-awareness 
 of a finite event with its quality of passage is also 
 accompanied by the discrimination of other factors of 
 nature which do not share in the passage of events. 
 Whatever passes is an event. But we find entities in 
 nature which do not pass ; namely we recognise same- 
 nesses in nature. Recognition is not primarily an 
 intellectual act of comparison ; it is in its essence merely 
 
VI] CONGRUENCE 125 
 
 sense-awareness in its capacity of positing before us 
 factors in nature which do not pass. For example, 
 green is perceived as situated in a certain finite event 
 within the present duration. This green preserves its 
 self-identity throughout, whereas the event passes and 
 thereby obtains the property of breaking into parts. 
 The green patch has parts. But in talking of the green 
 patch we are speaking of the event in its sole capacity of 
 being for us the situation of green. The green itself is 
 numerically one self-identical entity, without parts 
 because it is without passage. 
 
 Factors in nature which are without passage will be 
 called objects. There are radically different kinds of ob- 
 jects which will be considered in the succeeding lecture. 
 
 Recognition is reflected into the intellect as comparison. 
 The recognised objects of one event are compared with 
 the recognised objects of another event. The com- 
 parison may be between two events in the present, or 
 it may be between two events of which one is posited 
 by memory-awareness and the other by immediate 
 sense-awareness. But it is not the events which are 
 compared. For each event is essentially unique and 
 incomparable. What are compared are the objects and 
 relations of objects situated in events. The event con- 
 sidered as a relation between objects has lost its passage 
 and in this aspect is itself an object. This object is not 
 the event but only an intellectual abstraction. The same 
 object can be situated in many events ; and in this sense 
 even the whole event, viewed as an object, can recur, 
 though not the very event itself with its passage and its 
 relations to other events. 
 
 Objects which are not posited by sense-awareness 
 may be known to the intellect. For example, relations 
 
 f' 
 
 ^- 
 
126 THE CONCEPT OF NATURE [ch. 
 
 between objects and relations between relations may 
 be factors in nature not disclosed in sense-awareness 
 but known by logical inference as necessarily in being. 
 Thus objects for our knowledge may be merely logical 
 abstractions. For example, a complete event is never 
 disclosed in sense-awareness, and thus the object which 
 is the sum total of objects situated in an event as thus 
 inter-related is a mere abstract concept. Again a right- 
 angle is a perceived object which can be situated in 
 many events; but, though rectangularity is posited by 
 sense-awareness, the majority of geometrical relations 
 are not so posited. Also rectangularity is in fact often 
 not perceived when it can be proved to have been there 
 for perception. Thus an object is often known merely 
 as an abstract relation not directly posited in sense- 
 awareness although it is there in nature. 
 
 The identity of quality between congruent segments 
 is generally of this character. In certain special cases 
 this identity of quality can be directly perceived. But 
 in general it is inferred by a process of measurement 
 depending on our direct sense-awareness of selected 
 cases and a logical inference from the transitive character 
 of congruence. 
 
 Congruence depends on motion, and thereby is 
 generated the connexion between spatial congruence 
 and temporal congruence. Motion along a straight line 
 has a symmetry round that line. This symmetry is ex- 
 pressed by the symmetrical geometrical relations of the 
 line to the family of planes normal to it. 
 
 Also another symmetry in the theory of motion arises 
 from the fact that rest in the points of p corresponds to 
 uniform motion along a definite family of parallel 
 straight lines in the space of a . We must note the three 
 
VI] CONGRUENCE 127 
 
 characteristics, (i) of the uniformity of the motion 
 corresponding to any point of p along its correlated 
 straight line in a , and (ii) of the equality in magnitude 
 of the velocities along the various lines of a correlated 
 to rest in the various points of jS, and (iii) of the 
 parallelism of the lines of this family. 
 
 We are nov^ in possession of a theory of parallels and 
 a theory of perpendiculars and a theory of motion, and 
 from these theories the theory of congruence can be 
 constructed. It vs^ill be remembered that a family of 
 parallel levels in any moment is the family of levels in 
 vs^hich that moment is intersected by the family of 
 moments of some other time-system. Also a family of 
 parallel moments is the family of moments of some one 
 time-system. Thus we can enlarge our concept of a 
 family of parallel levels so as to include levels in diffe- 
 rent moments of one time-system. With this enlarged 
 concept vv^e say that a complete family of parallel levels 
 in a time-system a is the complete family of levels in 
 v^hich the moments of a intersect the moments of j3. 
 This complete family of parallel levels is also evidently 
 a family lying in the moments of the time-system j8. 
 By introducing a third time-system y, parallel rects are 
 obtained. Also all the points of any one time-system 
 form a family of parallel point-tracks. Thus there are 
 three types of parallelograms in the four-dimensional 
 manifold of event-particles. 
 
 In parallelograms of the first type the two pairs of 
 parallel sides are both of them pairs of rects. In parallelo- 
 grams of the second type one pair of parallel sides 
 is a pair of rects and the other pair is a pair of point- 
 tracks. In parallelograms of the third type the two pairs 
 of parallel sides are both of them pairs of point-tracks. 
 
128 THE CONCEPT OF NATURE [ch. 
 
 The first axiom of congruence is that the opposite 
 sides of any parallelogram are congruent. This axiom 
 enables us to compare the lengths of any two segments 
 either respectively on parallel rects or on the same rect. 
 Also it enables us to compare the lengths of any two seg- 
 ments either respectively on parallel point-tracks or on the 
 same point-track. It follows from this axiom that two 
 objects at rest in any two points of a time-system j8 are 
 moving with equal velocities in any other time-system a 
 along parallel lines. Thus we can speak of the velocity 
 in a due to the time-system jS without specifying any 
 particular point in j3. The axiom also enables us to 
 measure time in any time-system ; but does not enable 
 us to compare times in different time-systems. 
 
 The second axiom of congruence concerns parallelo- 
 grams on congruent bases and between the same 
 parallels, which have also their other pairs of sides 
 parallel. The axiom asserts that the rect joining the 
 two event-particles of intersection of the diagonals is 
 parallel to the rect on which the bases lie. By the aid 
 of this axiom it easily follows that the diagonals of a 
 parallelogram bisect each other. 
 
 Congruence is extended in any space beyond parallel 
 rects to all rects by two axioms depending on perpen- 
 dicularity. The first of these axioms, which is the third 
 axiom of congruence, is that if ABC is a triangle of rects 
 in any moment and D is the middle event-particle of the 
 base BC^ then the level through 2) perpendicular to BC 
 contains A when and only when AB is congruent to 
 AC, This axiom evidently expresses the symmetry of 
 perpendicularity, and is the essence of the famous 
 pons asinorum expressed as an axiom. 
 
 The second axiom depending on perpendicularity. 
 
VI] CONGRUENCE 129 
 
 and the fourth axiom of congruence, is that if r and A 
 be a rect and an event-particle in the same moment and 
 AB and v^C be a pair of rectangular rects intersecting 
 r in 5 and C, and AD and AE be another pair of rect- 
 angular rects intersecting r in Z) and £", then either D 
 or E lies in the segment BC and the other one of the 
 two does not lie in this segment. Also as a particular 
 case of this axiom, if AB be perpendicular to r and in 
 consequence ^C be parallel to r, then Z> and E lie on 
 opposite sides of B respectively. By the aid of these 
 two axioms the theory of congruence can be extended 
 so as to compare lengths of segments on any two rects. 
 Accordingly Euclidean metrical geometry in space is 
 completely established and lengths in the spaces of 
 different time-systems are comparable as the result of 
 definite properties of nature which indicate just that 
 particular method of comparison. 
 
 The comparison of time-measurements in diverse 
 time-systems requires two other axioms. The first of 
 these axioms, forming the fifth axiom of congruence, 
 will be called the axiom of * kinetic symmetry.' It 
 expresses the symmetry of the quantitative relations 
 between two time-systems when the times and lengths 
 in the two systems are measured in congruent units. 
 
 The axiom can be explained as follows : Let a and ^ 
 be the names of two time-systems. The directions of 
 motion in the space of a due to rest in a point of ^ is 
 called the * j8-direction in a ' and the direction of motion 
 in the space of j8 due to rest in a point of a is called the 
 * a -direction in j8.' Consider a motion in the space of 
 a consisting of a certain velocity in the jS -direction of a 
 and a certain velocity at right-angles to it. This motion 
 represents rest in the space of another time-system — 
 
 W.N. 9 
 
130 THE CONCEPT OF NATURE [ch. 
 
 call it TT . Rest in tt will also be represented in the space 
 of )S by a certain velocity in the a -direction in /S and a 
 certain velocity at right-angles to this « -direction. Thus 
 a certain motion in the space of a is correlated to a 
 certain motion in the space of j8, as both representing 
 the same fact which can also be represented by rest in 
 TT. Now another time-system, which I will name or, 
 can be found which is such that rest in its space is 
 represented by the same magnitudes of velocities 
 along and perpendicular to the a -direction in j3 as those 
 velocities in a, along and perpendicular to the j8 -direc- 
 tion, which represent rest in tt. The required axiom of 
 kinetic symmetry is that rest in a will be represented in 
 a by the same velocities along and perpendicular to 
 the j3 -direction in a as those velocities in /3 along and 
 perpendicular to the a -direction which represent rest 
 in TT. 
 
 A particular case of this axiom is that relative velocities 
 are equal and opposite. Namely rest in a is represented 
 in j3 by a velocity along the a -direction which is equal 
 to the velocity along the ^S -direction in a which repre- 
 sents rest in j3. 
 
 Finally the sixth axiom of congruence is that the 
 relation of congruence is transitive. So far as this 
 axiom applies to space, it is superfluous. For the 
 property follows from our previous axioms. It is 
 however necessary for time as a supplement to the axiom 
 of kinetic symmetry. The meaning of the axiom is that 
 if the time-unit of system a is congruent to the time- 
 unit of system ^, and the time-unit of system ^ is 
 congruent to the time-unit of system y, then the time- 
 units of a and y are also congruent. 
 
 By means of these axioms formulae for the trans- 
 
VI] CONGRUENCE 131 
 
 formation of measurements made in one time-system 
 to measurements of the same facts of nature made in 
 another time-system can be deduced. These formulae 
 will be found to involve one arbitrary constant vy^hich 
 I v^ill call k. 
 
 It is of the dimensions of the square of a velocity. 
 Accordingly four cases arise. In the first case k is 
 zero. This case produces nonsensical results in opposi- 
 tion to the elementary deliverances of experience. We 
 put this case aside. 
 
 In the second case k is infinite. This case yields the 
 ordinary formulae for transformation in relative motion, 
 namely those formulae v^hich are to be found in every 
 elementary book on dynamics. 
 
 In the third case, k is negative. Let us call it — c^, 
 where c will be of the dimensions of a velocity. This 
 case yields the formulae of transformation which 
 Larmor discovered for the transformation of Maxwell's 
 equations of the electromagnetic field. These formulae 
 were extended by H. A. Lorentz, and used by Einstein 
 and Minkowski as the basis of their novel theory of 
 relativity. I am not now speaking of Einstein's more 
 recent theory of general relativity by which he deduces 
 his modification of the law of gravitation. If this be the 
 case which applies to nature, then c must be a close 
 approximation to the velocity of light in vacuo. Perhaps 
 it is this actual velocity. In this connexion ^in vacuo' 
 must not mean an absence of events, namely the absence 
 of the all-pervading ether of events. It must mean the 
 absence of certain types of objects. 
 
 In the fourth case, k is positive. Let us call it A^, 
 where A will be of the dimensions of a velocity. This gives 
 a perfectly possible type of transformation formulae, 
 
 9—2 
 
132 THE CONCEPT OF NATURE [ch. 
 
 but not one which explains any facts of experience. 
 It has also another disadvantage. With the assumption 
 of this fourth case the distinction between space and 
 time becomes unduly blurred. The whole object of 
 these lectures has been to enforce the doctrine that 
 space and time spring from a common root, and that 
 the ultimate fact of experience is a space-time fact. But 
 after all mankind does distinguish very sharply between 
 space and time, and it is owing to this sharpness of 
 distinction that the doctrine of these lectures is some- 
 what of a paradox. Now in the third assumption this 
 sharpness of distinction is adequately preserved. There 
 is a fundamental distinction between the metrical pro- 
 perties of point-tracks and rects. But in the fourth 
 assumption this fundamental distinction vanishes. 
 
 Neither the third nor the fourth assumption can 
 agree with experience unless we assume that the 
 velocity c of the third assumption, and the velocity h 
 of the fourth assumption, are extremely large compared 
 to the velocities of ordinary experience. If this be the 
 case the formulae of both assumptions will obviously 
 reduce to a close approximation to the formulae of the 
 second assumption which are the ordinary formulae of 
 dynamical textbooks. For the sake of a name, I will 
 call these textbook formulae the * orthodox' formulae. 
 
 There can be no question as to the general approxi- 
 mate correctness of the orthodox formulae. It would be 
 merely silly to raise doubts on this point. But the 
 determination of the status of these formulae is by no 
 means settled by this admission. The independence 
 of time and space is an unquestioned presupposition 
 of the orthodox thought which has produced the ortho- 
 dox formulae. With this presupposition and given the 
 
VI] CONGRUENCE 133 
 
 absolute points of one absolute space, the orthodox 
 formulae are immediate deductions. Accordingly, 
 these formulae are presented to our imaginations as 
 facts which cannot be otherwise, time and space being 
 what they are. The orthodox formulae have therefore 
 attained to the status of necessities which cannot be 
 questioned in science. Any attempt to replace these 
 formulae by others was to abandon the rdle of physical 
 explanation and to have recourse to mere mathematical 
 formulae. 
 
 But even in physical science difficulties have accumu- 
 lated round the orthodox formulae. In the first place 
 Maxwell's equations of the electromagnetic field are 
 not invariant for the transformations of the orthodox 
 formulae; whereas they are invariant for the trans- 
 formations of the formulae arising from the third of the 
 four cases mentioned above, provided that the velocity c 
 is identified with a famous electromagnetic constant 
 quantity. 
 
 Again the null results of the delicate experiments 
 to detect the earth's variations of motion through the 
 ether in its orbital path are explained immediately by 
 the formulae of the third case. But if we assume the 
 orthodox formulae we have to make a special and ar- 
 bitrary assumption as to the contraction of matter during 
 motion. I mean the Fitzgerald-Lorentz assumption. 
 
 Lastly Fresnel's coefficient of drag which represents 
 the variation of the velocity of light in a moving medium 
 is explained by the formulae of the third case, and 
 requires another arbitrary assumption if we use the 
 orthodox formulae. 
 
 It appears therefore that on the mere basis of 
 physical explanation there are advantages in the formulae 
 
134 THE CONCEPT OF NATURE [ch. 
 
 of the third case as compared with the orthodox for- 
 mulae. But the way is blocked by the ingrained belief 
 that these latter formulae possess a character of necessity. 
 It is therefore an urgent requisite for physical science 
 and for philosophy to examine critically the grounds 
 for this supposed necessity. The only satisfactory 
 method of scrutiny is to recur to the first principles of 
 our knowledge of nature. This is exactly what I am 
 endeavouring to do in these lectures. I ask what it is 
 that we are aware of in our sense-perception of nature. 
 I then proceed to examine those factors in nature which 
 lead us to conceive nature as occupying space and 
 persisting through time. This procedure has led us to 
 an investigation of the characters of space and time. It 
 results from these investigations that the formulae of 
 the third case and the orthodox formulae are on a level 
 as possible formulae resulting from the basic character 
 of our knowledge of nature. The orthodox formulae 
 have thus lost any advantage as to necessity which they 
 enjoyed over the serial group. The way is thus open to 
 adopt whichever of the two groups best accords with 
 observation. 
 
 I take this opportunity of pausing for a moment from 
 the course of my argument, and of reflecting on the 
 general character which my doctrine ascribes to some 
 familiar concepts of science. I have no doubt that some 
 of you have felt that in certain aspects this character 
 is very paradoxical. 
 
 This vein of paradox is partly due to the fact that 
 educated language has been made to conform to the 
 prevalent orthodox theory. We are thus, in expounding 
 an alternative doctrine, driven to the use of either strange 
 terms or of familiar words with unusual meanings. This 
 
VI] CONGRUENCE 135 
 
 victory of the orthodox theory over language is very /JjP 
 
 natural. Events are named after the prominent objects 
 situated in them, and thus both in language and in 
 thought the event sinks behind the object, and becomes 
 the mere play of its relations. The theory of space is 
 then converted into a theory of the relations of objects 
 instead of a theory of the relations of events. But objects 
 have not the passage of events. Accordingly space as a 
 relation between objects is devoid of any connexion 
 with time. It is space at an instant without any deter- 
 minate relations between the spaces at successive in- 
 stants. It cannot be one timeless space because the 
 relations between objects change. 
 
 A few minutes ago in speaking of the deduction of 
 the orthodox formulae for relative motion I said that 
 they followed as an immediate deduction from the 
 assumption of absolute points in absolute space. This 
 reference to absolute space was not an oversight. I know 
 that the doctrine of the relativity of space at present 
 holds the field both in science and philosophy. But 
 I do not think that its inevitable consequences are 
 understood. When we really face them the paradox of 
 the presentation of the character of space which I have 
 elaborated is greatly mitigated. If there is no absolute 
 position, a point must cease to be a simple entity. What 
 is a point to one man in a balloon with his eyes fixed on 
 an instrument is a track of points to an observer on the 
 earth who is watching the balloon through a telescope, 
 and is another track of points to an observer in the sun 
 who is watching the balloon through some instrument 
 suited to such a being. Accordingly if I am reproached 
 with the paradox of my theory of points as classes of 
 event-particles, and of my theory of event-particles as 
 
 u' 
 
 ■A 
 
 
136 THE CONCEPT OF NATURE [ch. 
 
 groups of abstractive sets, I ask my critic to explain 
 exactly what he means by a point. While you explain 
 your meaning about anything, however simple, it is 
 always apt to look subtle and fine spun. I have at least 
 explained exactly what I do mean by a point, what 
 relations it involves and what entities are the relata. 
 If you admit the relativity of space, you also must 
 admit that points are complex entities, logical constructs 
 involving other entities and their relations. Produce 
 your theory, not in a few vague phrases of indefinite 
 meaning, but explain it step by step in definite terms 
 referring to assigned relations and assigned relata. Also 
 show that your theory of points issues in a theory of 
 space. Furthermore note that the example of the man 
 in the balloon, the observer on earth, and the observer 
 in the sun, shows that every assumption of relative rest 
 requires a timeless space with radically different points 
 from those which issue from every other such assump- 
 tion. The theory of the relativity of space is incon- 
 sistent with any doctrine of one unique set of points of 
 one timeless space. 
 
 The fact is that there is no paradox in my doctrine 
 of the nature of space which is not in essence inherent 
 in the theory of the relativity of space. But this doctrine 
 has never really been accepted in science, whatever 
 people say. What appears in our dynamical treatises is 
 Newton's doctrine of relative motion based on the 
 doctrine of differential motion in absolute space. When 
 you once admit that the points are radically different 
 entities for differing assumptions of rest, then the 
 orthodox formulae lose all their obviousness. They 
 were only obvious because you were really thinking of 
 something else. When discussing this topic you can 
 
VI] CONGRUENCE 137 
 
 only avoid paradox by taking refuge from the flood of 
 criticism in the comfortable ark of no meaning. 
 
 The nev^ theory provides a definition of the con- 
 gruence of periods of time. The prevalent viev^ pro- 
 vides no such definition. Its position is that if we 
 take such time-measurements so that certain familiar 
 velocities which seem to us to be uniform are uniform, 
 then the laws of motion are true. Now in the first place 
 no change could appear either as uniform or non- 
 uniform without involving a definite determination of 
 the congruence for time-periods. So in appealing to 
 familiar phenomena it allows that there is some 
 factor in nature which we can intellectually construct 
 as a congruence theory. It does not however say any- 
 thing about it except that the laws of motion are then 
 true. Suppose that with some expositors we cut out 
 the reference to familiar velocities such as the rate of 
 rotation of the earth. We are then driven to admit that 
 there is no meaning in temporal congruence except 
 that certain assumptions make the laws of motion true. 
 Such a statement is historically false. King Alfred the 
 Great was ignorant of the laws of motion, but knew 
 very well what he meant by the measurement of time, 
 and achieved his purpose by means of burning candles. 
 Also no one in past ages justified the use of sand in 
 hour-glasses by saying that some centuries later in- 
 teresting laws of motion would be discovered which 
 would give a meaning to the statement that the sand 
 was emptied from the bulbs in equal times. Uniformity i 
 in change is directly perceived, and it follows that 
 mankind perceives in nature factors from which a theory 
 of temporal congruence can be formed. The prevalent 
 theory entirely fails to produce such factors. 
 
138 THE CONCEPT OF NATURE [ch. 
 
 The mention of the laws of motion raises another 
 point where the prevalent theory has nothing to say 
 and the new theory gives a complete explanation. It is 
 well known that the laws of motion are not valid for 
 any axes of reference which you may choose to take 
 fixed in any rigid body. You must choose a body which 
 is not rotating and has no acceleration. For example 
 they do not really apply to axes fixed in the earth 
 because of the diurnal rotation of that body. The law 
 which fails when you assume the wrong axes as at rest 
 is the third law, that action and reaction are equal and 
 opposite. With the wrong axes uncompensated centri- 
 fugal forces and uncompensated composite centrifugal 
 forces appear, due to rotation. The influence of these 
 forces can be demonstrated by many facts on the earth's 
 surface, Foucault's pendulum, the shape of the earth, 
 the fixed directions of the rotations of cyclones and 
 anticyclones. It is difficult to take seriously the sug- 
 gestion that these domestic phenomena on the earth 
 are due to the influence of the fixed stars. I cannot 
 persuade myself to believe that a little star in its 
 twinkling turned round Foucault's pendulum in the 
 Paris Exhibition of 186 1. Of course anything is believ- 
 able when a definite physical connexion has been 
 demonstrated, for example the influence of sunspots. 
 Here all demonstration is lacking in the form of any 
 coherent theory. According to the theory of these 
 lectures the axes to which motion is to be referred are 
 axes at rest in the space of some time-system. For 
 example, consider the space of a time-system a. There 
 are sets of axes at rest in the space of a . These are suitable 
 dynamical axes. Also a set of axes in this space which 
 is moving with uniform velocity without rotation is 
 
VI] CONGRUENCE 139 
 
 another suitable set. All the moving points fixed in 
 these moving axes are really tracing out parallel lines 
 with one uniform velocity. In other words they are 
 the reflections in the space of a of a set of fixed axes in 
 the space of some other time-system jS. Accordingly 
 the group of dynamical axes required for Newton's 
 Laws of Motion is the outcome of the necessity of 
 referring motion to a body at rest in the space of some 
 one time-system in order to obtain a coherent account 
 of physical properties. If we do not do so the meaning 
 of the motion of one portion of our physical configuration 
 is different from the meaning of the motion of another 
 portion of the same configuration. Thus the meaning 
 of motion being what it is, in order to describe the motion 
 of any system of objects without changing the meaning 
 of your terms as you proceed vdth your description, 
 you are bound to take one of these sets of axes as axes 
 of reference ; though you may choose their reflections 
 into the space of any time-system which you wish to 
 adopt. A definite physical reason is thereby assigned for 
 the peculiar property of the dynamical group of axes. 
 
 On the orthodox theory the position of the equations 
 of motion is most ambiguous. The space to which they 
 refer is completely undetermined and so is the measure- 
 ment of the lapse of time. Science is simply setting out 
 on a fishing expedition to see whether it cannot find 
 some procedure which it can call the measurement of 
 space and some procedure which it can call the measure- 
 ment of time, and something which it can call a system 
 of forces, and something which it can call masses, so 
 that these formulae may be satisfied. The only reason — 
 on this theory — ^why anyone should want to satisfy 
 these formulae is a sentimental regard for Galileo, 
 
140 THE CONCEPT OF NATURE [ch. 
 
 Newton, Euler and Lagrange. The theory, so far from 
 founding science on a sound observational basis, forces 
 everything to conform to a mere mathematical pre- 
 ference for certain simple formulae. 
 
 I do not for a moment believe that this is a true ac- 
 count of the real status of the Laws of Motion. These 
 equations want some slight adjustment for the new 
 formulae of relativity. But with these adjustments, 
 imperceptible in ordinary use, the laws deal with funda- 
 mental physical quantities which we know very well 
 and wish to correlate. 
 
 The measurement of time was known to all civilised 
 nations long before the laws were thought of. It is this 
 time as thus measured that the laws are concerned with. 
 Also they deal with the space of our daily life. When we 
 approach to an accuracy of measurement beyond that 
 of observation, adjustment is allowable. But within the 
 limits of observation we know what we mean when we 
 speak of measurements of space and measurements of 
 time and uniformity of change. It is for science to give an 
 intellectual account of what is so evident in sense-aware- 
 ness. It is to me thoroughly incredible that the ultimate 
 fact beyond which there is no deeper explanation is that 
 mankind has really been swayed by an unconscious 
 desire to satisfy the mathematical formulae which we 
 call the Laws of Motion, formulae completely unknown 
 till the seventeenth century of our epoch. 
 
 The correlation of the facts of sense-experience 
 effected by the alternative account of nature extends 
 beyond the physical properties of motion and the 
 properties of congruence. It gives an account of the 
 meaning of the geometrical entities such as points, 
 straight lines, and volumes, and connects the kindred 
 
VI] CONGRUENCE 141 
 
 ideas of extension in time and extension in space. The 
 theory satisfies the true purpose of an intellectual 
 explanation in the sphere of natural philosophy. This 
 purpose is to exhibit the interconnexions of nature, and 
 to show that one set of ingredients in nature requires 
 for the exhibition of its character the presence of the 
 other sets of ingredients. 
 
 The false idea which we have to get rid of is that of 
 nature as a mere aggregate of independent entities, each 
 capable of isolation. According to this conception these 
 entities, whose characters are capable of isolated defini- 
 tion, come together and by their accidental relations 
 form the system of nature. This system is thus thoroughly 
 accidental; and, even if it be subject to a mechanical 
 fate, it is only accidentally so subject. 
 
 With this theory space might be without time, and 
 time might be without space. The theory admittedly 
 breaks down when we come to the relations of matter 
 and space. The relational theory of space is an admission 
 that we cannot know space without matter or matter 
 without space. But the seclusion of both from time is 
 still jealously guarded. The relations between portions 
 of matter in space are accidental facts owing to the 
 absence of any coherent account of how space springs 
 from matter or how matter springs from space. Also 
 what we really observe in nature, its colours and its 
 sounds and its touches are secondary qualities; in 
 other words, they are not in nature at all but are acci- 
 dental products of the relations between nature and 
 mind. 
 
 The explanation of nature which I urge as an alter- 
 native ideal to this accidental view of nature, is that 
 nothing in nature could be what it is except as an 
 
142 THE CONCEPT OF NATURE [ch. vi 
 
 ingredient in nature as it is. The whole which is present 
 for discrimination is posited in sense-awareness as 
 necessary for the discriminated parts. An isolated event 
 is not an event, because every event is a factor in a 
 larger whole and is significant of that whole. 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 the events of nature. The isolation of an entity in 
 thought, when we think of it as a bare *it,' has no 
 counterpart in any corresponding isolation in nature. 
 Such isolation is merely part of the procedure of intel- 
 lectual knowledge. 
 
 The laws of nature are the outcome of the characters 
 of the entities which we find in nature. The entities 
 being what they are, the laws must be what they are; 
 and conversely the entities follow from the laws. We 
 are a long way from the attainment of such an ideal; 
 but it remains as the abiding goal of theoretical science. 
 
CHAPTER VII 
 
 OBJECTS 
 
 The ensuing lecture is concerned with the theory of 
 objects. Objects are e lements in nature which do not 
 p ass. The awareness of an object as some factor not 
 sharing in the passage of nature is what I call *recogni-| 
 tion.' Itis^i npossible J:o recognise an^event^ because 
 an event is essentially distinct from every o ther even t. 
 Recognition is an awareness of samenessj But to call 
 recognition an awareness of sameness implies an in- 
 tellectual act of comparison accompanied with judgment. 
 I use recognition for the non-intellectual relation of 
 sense-awareness which connects the mind with a factor 
 of nature without passage. On the intellectual side of 
 the mind's experience there are comparisons of things 
 recognised and consequent judgments of sameness or 
 diversity. Probably * sense-recognition ' would be a 
 better term for what I mean by * recognition.' I have 
 chosen the simpler term because I think that I shall be 
 able to avoid the use of * recognition ' in any other 
 meaning than that of * sense-recognition.' I am quite 
 willing to believe that recognition, in my sense of the 
 term, is merely an ideal limit, and that there is in fact 
 no recognition without intellectual accompaniments of 
 comparison and judgment. But recognition is that 
 relation of the mind to nature which provides the 
 material for the intellectual activity. 
 
 An object is an ingredient in the character of some 
 event. In fact the character of an event is nothing but 
 the objects which are ingredient in it and the ways in 
 
144 THE CONCEPT OF NATURE [ch. 
 
 (which those objects make their ingression into the 
 event. Thus the theory of objects is the theory of the 
 comparison of events. Events are only comparable 
 because they body forth permanences. We are com- 
 paring objects in events whenever we can say, * There 
 it is again.' Objects are the elements in nature which 
 can *be again.' 
 
 Sometimes permanences can be proved to exist 
 which evade recognition in the sense in which I am 
 using that term. The permanences which evade recogni- 
 tion appear to us as abstract properties either of events 
 or of objects. All the same they are there for recognition 
 although undiscriminated in our sense-awareness. The 
 demarcation of events, the splitting of nature up into 
 parts is effected by the objects which we recognise as 
 their ingredients. The discrimination of nature is the 
 recognition of objects amid passing events. It is a 
 compound of the awareness of the passage of nature, 
 of the consequent partition of nature, and of the defini- 
 tion of certain parts of nature by the modes of the 
 ingression of objects into them. 
 
 You may have noticed that I am using the term 
 * ingression' to denote the general relation of objects 
 to events. The ingression of an object into an event is 
 the way the character of the event shapes itself in virtue 
 of the being of the object. Namely the event is what it 
 is, because the object is what it is ; and when I am thinking 
 of this modification of the event by the object, I call 
 the relation between the two *the ingression of the 
 object into the event.' It is equally true to say that 
 objects are what they are because events are what they 
 
 iare. Nature is such that there can be no events and no 
 objects without the ingression of objects into events. 
 
VII] OBJECTS 145 
 
 Although there are events such that the ingredient! 
 objects evade our recognition. These are the events in( 
 empty space. Such events are only analysed for us by]| 
 the intellectual probing of science. 
 
 Ingression is a relation vv^hich has various modes. 
 There are obviously very various kinds of objects; 
 and no one kind of object can have the same sort of 
 relations to events as objects of another kind can have. 
 We shall have to analyse out some of the different 
 modes of ingression w^hich different kinds of objects 
 have into events. 
 
 But even if wt stick to one and the same kind of 
 objects, an object of that kind has different modes of 
 ingression into different events. Science and philo- 
 sophy have been apt to entangle themselves in a simple- 
 minded theory that an object is at one place at any definite 
 time, and is in no sense anyvs^here else. This is in fact 
 the attitude of common sense thought, thou gh it is no t 
 the attitud e of lang ua ge vv^hich is naively expressing the 
 facts oFexperience . Every other sentence in a w^ork of 
 literature which is endeavouring truly to interpret the 
 facts of experience expresses differences in surrounding 
 events due to the presence of some object. An object 
 is ingredient throughout its neighbourhood, and its 
 neighbourhood is indefinite. Also the modification of 
 events by ingression is susceptible of quantitative 
 differences. Finally therefore we are driven to admit / 
 that each object is in some sense ingredient throughout I 
 nature; though its ingression may be quantitatively ' 
 irrelevant in the expression of our individual experi- 
 ences. 
 
 This admission is not new either in philosophy or 
 science. It is obviously a necessary axiom for those 
 
 W.N. 10 
 
146 THE CONCEPT OF NATURE [ch. 
 
 philosophers who insist that reahty is a system. In 
 these lectures we are keeping off the profound and 
 vexed question as to what we mean by *reaUty.' I am 
 maintaining the humbler thesis that nature is a system. 
 But I suppose that in this case the less follows from 
 the greater, and that I may claim the support of these 
 philosophers. The same doctrine is essentially interwoven 
 in all modern physical speculation. As long ago as 1847 
 Faraday in a paper in the Philosophical Magazine 
 remarked that his theory of tubes of force im.plies that 
 in a sense an electric charge is everywhere. The modi- 
 fication of the electromagnetic field at every point of 
 space at each instant owing to the past history of each 
 electron is another way of stating the same fact. We 
 can however illustrate the doctrine by the more familiar 
 facts of life without recourse to the abstruse speculations 
 of theoretical physics. 
 
 The waves as they roll on to the Cornish coast tell 
 of a gale in mid-Atlantic ; and our dinner witnesses to 
 the-ingression of the cook into the dining room. It is 
 ' evident that the ingression of objects into events in- 
 cludes the theory of causation. I prefer to neglect this 
 aspect of ingression, because causation raises the 
 memory of discussions based upon theories of nature 
 which are alien to my own. Also I think that some new 
 light may be thrown on the subject by viewing it in 
 this fresh aspect. 
 
 The examples which I have given of the ingression 
 of objects into events remind us that ingression takes 
 a peculiar form in the case of some events; in a sense, 
 it is a more concentrated form. For example, the electron 
 has a certain position in space and a certain shape. 
 Perhaps it is an extremely small sphere in a certain 
 
VII] OBJECTS 147 
 
 test-tube. The storm is a gale situated in mid- Atlantic 
 with a certain latitude and longitude, and the cook is in 
 the kitchen. I will call this special form of ingression 
 the 'relation of situation'; also, by a double use of the 
 word * situation,' I will call the event in which an object 
 is situated * the situation of the object.' Thus a situation 
 is an event which is a relatum in the relation of situation. 
 Now our first impression is that at last we have come to 
 the simple plain fact of where the object really is ; and 
 that the vaguer relation which I call ingression should 
 not be muddled up with the relation of situation, as if 
 including it as a particular case. It seems so obvious 
 that any object is in such and such a position, and that 
 it is influencing other events in a totally different sense. 
 Namely, in a sense an object is the character of the 
 event which is its situation, but it onlv influences the 
 character of other events. Accordingly the relations of 
 situation and influencing are not generally the same sort 
 of relation, and should not be subsumed under the same 
 term ' ingression.' I believe that this notion is a mistake, 
 and that it is impossible to draw a clear distinction 
 between the two relations. 
 
 For example. Where was your toothache? You went 
 to a dentist and pointed out the tooth to him. He pro- 
 nounced it perfectly sound, and cured you by stopping 
 another tooth. Which tooth was the situation of the 
 toothache? Again, a man has an arm amputated, and 
 experiences sensations in the hand which he has lost. 
 The situation of the imaginary hand is in fact merely 
 thin air. You look into a mirror and see a fire. The flames 
 that you see are situated behind the mirror. Again at 
 night you watch the sky ; if some of the stars had vanished 
 from existence hours ago, you would not be any the 
 
 10 — 2 
 
148 THE CONCEPT OF NATURE [ch. 
 
 wiser. Even the situations of the planets differ from 
 those which science would assign to them. 
 
 Anyhow you are tempted to exclaim, the cook is in 
 the kitchen. If you mean her mind, I will not agree 
 with you on the point; for I am only talking of nature. 
 Let us think only of her bodily presence. What do you 
 mean by this notion? We confine ourselves to typical 
 manifestations of it. You can see her, touch her, and 
 hear her. But the examples which I have given you 
 show that the notions of the situations of what you see, 
 what you touch, and what you hear are not so sharply 
 separated out as to defy further questioning. You 
 cannot cling to the idea that we have two sets of ex- 
 periences of nature, one of primary qualities which 
 belong to the objects perceived, and one of secondary 
 qualities which are the products of our mental excite- 
 ments. All we know of nature is in the same boat, to 
 sink or swim together. The constructions of science 
 are merely expositions of the characters of things per- 
 ceived. Accordingly to affirm that the cook is a certain 
 dance of molecules and electrons is merely to affirm 
 that the things about her which are perceivable have 
 certain characters. The situations of the perceived 
 manifestations of her bodily presence have only a very 
 general relation to the situations of the molecules, to 
 be determined by discussion of the circumstances of 
 perception. 
 
 In discussing the relations of situation in particular 
 and of ingression in general, the first requisite is to note 
 that objects are of radically different types. For each 
 type ' situation ' and ' ingression ' have their own special 
 meanings which are different from their meanings for 
 other types, though connexions can be pointed out. 
 
VII] OBJECTS 149 
 
 It is necessary therefore in discussing them to deter- 
 mine what type of objects are under consideration. 
 There are, I think, an indefinite number of types of 
 objects. Happily we need not think of them all. The ) 
 idea of situation has its peculiar importance in reference 
 to three types of objects which I call sense-objects, 
 perceptual objects and scientific objects. The suitability 
 of these names for the three types is of minor import- 
 ance, so long as I can succeed in explaining what I mean 
 by them. 
 
 These three types form an ascending hierarchy, of 
 which each member presupposes the type below. Thel 
 base of the hierarchy is formed by the sense-objects. 
 These objects do not presuppose any other type of 
 objects. A sense-object is a factor of nature posited | 
 by sense-awareness which (i), in that it is an object, does I 
 not share in the passage of nature and (ii) is not a J 
 relation between other factors of nature. It will of 
 course be a relatum in relations which also implicate 
 other factors of nature. But it is always a relatum and 
 never the relation itself. Examples of sense-objects are 
 a particular sort of colour, say Cambridge blue, or a 
 particular sort of sound, or a particular sort of smell, 
 or a particular sort of feeling. I am not talking of a 
 particular patch of blue as seen during a particular 
 second of time at a definite date. Such a patch is an 
 event where Cambridge blue is situated. Similarly I am 
 not talking of any particular concert-room as filled with 
 the note. I mean the note itself and not the patch of 
 volume filled by the sound for a tenth of a second. It is 
 natural for us to think of the note in itself, but in the 
 case of colour we are apt to think of it merely as a 
 property of the patch. No one thinks of the note as a 
 
150 THE CONCEPT OF NATURE [ch. 
 
 property of the concert-room. We see the blue and we 
 hear the note. Both the blue and the note are im- 
 mediately posited by the discrimination of sense-aware- 
 ness which relates the mind to nature. The blue is 
 posited as in nature related to other factors in nature. 
 In particular it is posited as in the relation of being 
 situated in the event which is its situation. 
 
 The difficulties which cluster around the relation of 
 situation arise from the obstinate refusal of philosophers 
 to take seriously the ultimate fact of multiple relations. 
 By a multiple relation I mean a relation which in any 
 concrete instance of its occurrence necessarily involves 
 more than two relata. For example, when John likes 
 Thomas there are only two relata, John and Thomas. 
 But when John gives that book to Thomas there are 
 three relata, John, that book, and Thomas. 
 
 Some schools of philosophy, under the influence of 
 the Aristotelian logic and the Aristotelian philosophy, 
 endeavour to get on without admitting any relations at 
 all except that of substance and attribute. Namely all 
 apparent relations are to be resolvable into the con- 
 current existence of substances with contrasted at- 
 tributes. It is fairly obvious that the Leibnizian monad- 
 ology is the necessary outcome of any such philosophy. 
 If you dislike pluralism, there will be only one monad. 
 
 Other schools of philosophy admit relations but 
 obstinately refuse to contemplate relations with more 
 than two relata. I do not think that this limitation is 
 based on any set purpose or theory. It merely arises 
 from the fact that more complicated relations are a 
 bother to people without adequate mathematical training, 
 when they are admitted into the reasoning. 
 
 I must repeat that we have nothing to do in these 
 
VII] OBJECTS 151 
 
 lectures with the ultimate character of reality. It is 
 quite possible that in the true philosophy of reality 
 there are only individual substances with attributes, 
 or that there are only relations with pairs of relata. I do 
 not believe that such is the case ; but I am not concerned 
 to argue about it now. Our theme is Nature. So long 
 as we confine ourselves to the factors posited in the 
 sense-awareness of nature, it seems to me that there 
 certainly are instances of multiple relations between 
 these factors, and that the relation of situation for sense- 
 objects is one example of such multiple relations. 
 
 Consider a blue coat, a flannel coat of Cambridge 
 blue belonging to some athlete. The coat itself is a 
 perceptual object and its situation is not what I am 
 talking about. We are talking of someone's definite 
 sense-awareness of Cambridge blue as situated in some 
 event of nature. He may be looking at the coat directly. 
 He then sees Cambridge blue as situated practically in the 
 same event as the coat at that instant. It is true that the 
 blue which he sees is due to light which left the coat 
 some inconceivably small fraction of a second before. 
 This diflFerence would be important if he were looking at 
 a starwhosecolourwas Cambridge blue. The star might 
 have ceased to exist days ago, or even years ago. The 
 situation of the blue will not then be very intimately 
 connected with the situation (in another sense of 
 * situation ') of any perceptual object. This disconnexion 
 of the situation of the blue and the situation of some 
 associated perceptual object does not require a star for 
 its exemplification. Any looking glass will suffice. Look 
 at the coat through a looking glass. Then blue is seen 
 as situated behind the mirror. The event which is its 
 situation depends upon the position of the observer. 
 
152 THE CONCEPT OF NATURE [ch. 
 
 The sense-awareness of the blue as situated in a 
 certain event which I call the situation, is thus ex- 
 hibited as the sense-awareness of a relation between the 
 blue, the percipient event of the observer, the situation, 
 and intervening events. All nature is in fact required, 
 though only certain intervening events require their 
 characters to be of certain definite sorts. The ingression 
 of blue into the events of nature is thus exhibited as 
 systematically correlated. The awareness of the observer 
 depends on the position of the percipient event in this 
 systematic correlation. I will use the term 'ingression 
 into nature ' for this systematic correlation of the blue 
 with nature. Thus the ingression of blue into any definite 
 event is a part statement of the fact of the ingression 
 of blue into nature. 
 
 In respect to the ingression of blue into nature events 
 may be roughly put into four classes which overlap and 
 are not very clearly separated. These classes are (i) the 
 percipient events, (ii) the situations, (iii) the active 
 conditioning events, (iv) the passive conditioning events. 
 To understand this classification of events in the general 
 fact of the ingression of blue into nature, let us confine 
 attention to one situation for one percipient event and 
 to the consequent roles of the conditioning events for 
 the ingression as thus limited. The percipient event is 
 the relevant bodily state of the observer. The situation 
 is where he sees the blue, say, behind the mirror. The 
 active conditioning events are the events whose charac- 
 ters are particularly relevant for the event (which is the 
 situation) to be the situation for that percipient event, 
 namely the coat, the mirror, and the state of the room 
 as to light and atmosphere. The passive conditioning 
 events are the events of the rest of nature. 
 
VII] OBJECTS 153 
 
 In general the situation is an active conditioning 
 event; namely the coat itself, when there is no mirror 
 or other such contrivance to produce abnormal effects. 
 But the example of the mirror shows us that the situation 
 may be one of the passive conditioning events. We are 
 then apt to say that our senses have been cheated, 
 because we demand as a right that the situation should 
 be an active condition in the ingression. 
 
 This demand is not so baseless as it may seem when 
 presented as I have put it. All we know of the characters 
 of the events of nature is based on the analysis of the 
 relations of situations to percipient events. If situations 
 were not in general active conditions, this analysis 
 would tell us nothing. Nature would be an unfathom- 
 able enigma to us and there could be no science. Ac- 
 cordingly the incipient discontent when a situation is 
 found to be a passive condition is in a sense justifiable ; 
 because if that sort of thing went on too often, the rdle 
 of the intellect would be ended. 
 
 Furthermore the mirror is itself the situation of other 
 sense-objects either for the same observer with the 
 same percipient event, or for other observers with 
 other percipient events. Thus the fact that an event is a 
 situation in the ingression of one set of sense-objects 
 into nature is presumptive evidence that that event is 
 an active condition in the ingression of other sense- 
 objects into nature which may have other situations. 
 
 This is a fundamental principle of science which it has 
 derived from common sense. 
 
 I now turn to perceptual objects. When we look at 
 the coat, we do not in general say. There is a patch of 
 Cambridge blue ; what naturally occurs to us is, There 
 is a coat. Also the judgment that what we have seen is 
 
154 THE CONCEPT OF NATURE [ch 
 
 a garment of man's attire is a detail. What we perceive 
 is an object other than a mere sense-object. It is not a 
 mere patch of colour, but something more; and it is 
 that something more which we judge to be a coat. I 
 will use the word *coat' as the name for that crude 
 object which is more than a patch of colour, and without 
 any allusion to the judgments as to its usefulness as an 
 » article of attire either in the past or the future. The coat 
 which is perceived — in this sense of the word ' coat * — 
 is what I call a perceptual object. We have to investigate 
 the general character of these perceptual objects. 
 
 It is a law of nature that in general the situation of a 
 sense-object is not only the situation of that sense- 
 object for one definite percipient event, but is the 
 situation of a variety of sense-objects for a variety of 
 percipient events. For example, for any one percipient 
 event, the situation of a sense-object of sight is apt also 
 to be the situations of sense-objects of sight, of touch, 
 of smell, and of sound. Furthermore this concurrence 
 in the situations of sense-objects has led to the body — 
 i£, the percipient event — so adapting itself that the 
 perception of one sense-object in a certain situation 
 leads to a subconscious sense-awareness of other sense- 
 objects in the same situation. This interplay is especially 
 the case between touch and sight. There is a certain 
 correlation between the ingressions of sense-objects 
 of touch and sense-objects of sight into nature, and in a 
 slighter degree between the ingressions of other pairs 
 of sense-objects. I call this sort of correlation the * con- 
 veyance' of one sense-object by another. When you 
 see the blue flannel coat you subconsciously feel yourself 
 wearing it or otherwise touching it. If you are a 
 smoker, you may also subconsciously be aware of the 
 
VII] OBJECTS 155 
 
 faint aroma of tobacco. The peculiar fact, posited by 
 this sense-awareness of the concurrence of subconscious 
 sense-objects along with one or more dominating sense- 
 objects in the same situation, is the sense-awareness of 
 the perceptual object. The perceptual object is not 1 
 primarily the issue of a judgment. It is a factor of nature j u-fi 
 directly posited in sense-awareness. The element of L, -- — 
 judgment comes in when we proceed to classify thej;^ 
 particular perceptual object. For example, we say, - 
 That is flannel, and we think of the properties of flannel 
 and the uses of athletes' coats. But that all takes place 
 after we have got hold of the perceptual object. Anti- 
 cipatory judgments affect the perceptual object per- 
 ceived by focussing and diverting attention. 
 
 The perceptual object is the outcome of the habit of 
 experience. Anything which conflicts with this habit 
 hinders the sense-awareness of such an object. A sense- 
 object is not the product of the association of intellectual 
 ideas ; it is the product of the association of sense-objects 
 in the same situation. This outcome is not intellectual; 
 it is an object of peculiar type with its own particular 
 ingression into nature. 
 
 There are two kinds of perceptual objects, namely, 
 'delusive perceptual objects' and * physical objects.' 
 The situation of a delusive perceptual object is a 
 passive condition in the ingression of that object into 
 nature. Also the event which is the situation will have 
 the relation of situation to the object only for one 
 particular percipient event. For example, an observer 
 sees the image of the blue coat in a mirror. It is a blue 
 coat that he sees and not a mere patch of colour. This 
 shows that the active conditions for the conveyance 
 of a group of subconscious sense-objects by a dominating 
 
 ,^^^^ 
 
156 THE CONCEPT OF NATURE [CH. 
 
 sense-object are to be found in the percipient event. 
 Namely we are to look for them in the investigations 
 of medical psychologists. The ingression into nature of 
 the delusive sense-object is conditioned by the adapta- 
 tion of bodily events to the more normal occurrence, 
 which is the ingression of the physical object. 
 
 A perceptual object is a physical object when (i) its 
 situation is an active conditioning event for the in- 
 gression of any of its component sense-objects, and 
 (ii) the same event can be the situation of the perceptual 
 object for an indefinite number of possible percipient 
 events. Physical objects are the ordinary objects which 
 we perceive when our senses are not cheated, such as 
 chairs, tables and trees. In a way physical objects have 
 more insistent perceptive power than sense-objects. 
 Attention to the fact of their occurrence in nature is the 
 first condition for the survival of complex living or- 
 ganisms. The result of this high perceptive power of 
 physical objects is the scholastic philosophy of nature 
 which looks on the sense-objects as mere attributes of 
 the physical objects. This scholastic point of view is 
 directly contradicted by the wealth of sense-objects 
 which enter into our experience as situated in events 
 without any connexion with physical objects. For 
 example, stray smells, sounds, colours and more subtle 
 nameless sense-objects. There is no perception of 
 physical objects without perception of sense-objects. 
 But the converse does not hold: namely, there is 
 abundant perception of sense-objects unaccompanied 
 by any perception of physical objects. This lack of 
 reciprocity in the relations between sense-objects and 
 physical objects is fatal to the scholastic natural philo- 
 sophy. 
 
VII] OBJECTS 157 
 
 There is a great difference in the rSles of the situa- 
 tions of sense-objects and physical objects. The situa- 
 tions of a physical object are conditioned by uniqueness 
 and continuity. The uniqueness is an ideal limit to 
 which we approximate as we proceed in thought along 
 an abstractive set of durations, considering smaller 
 and smaller durations in the approach to the ideal limit 
 of the moment of time. In other words, when the 
 duration is small enough, the situation of the physical 
 object within that duration is practically unique. 
 
 The identification of the same physical object as 
 being situated in distinct events in distinct durations is 
 effected by the condition of continuity. This condition 
 of continuity is the condition that a continuity of passage 
 of events, each event being a situation of the object in 
 its corresponding duration, can be found from the earlier 
 to the later of the two given events. So far as the two 
 events are practically adjacent in one specious present, 
 this continuity of passage may be directly perceived. 
 Otherwise it is a matter of judgment and inference. 
 
 The situations of a sense-object are not conditioned 
 by any such conditions either of uniqueness or of con- 
 tinuity. In any durations however small a sense-object 
 may have any number of situations separated from each 
 other. Thus two situations of a sense-object, either in 
 the same duration or in different durations, are not 
 necessarily connected by any continuous passage of 
 events which are also situations of that sense-object. 
 
 The characters of the conditioning events involved in 
 the ingression of a sense-object into nature can be 
 largely expressed in terms of the physical objects which 
 are situated in those events. In one respect this is also 
 a tautology. For the physical object is nothing else than 
 
158 THE CONCEPT OF NATURE [ch. 
 
 the habitual concurrence of a certain set of sense-objects 
 in one situation. Accordingly when we know all about 
 the physical object, we thereby know its component 
 sense-objects. But a physical object is a condition for 
 the occurrence of sense-objects other than those which 
 are its components. For example, the atmosphere causes 
 the events which are its situations to be active con- 
 ditioning events in the transmission of sound. A mirror 
 which is itself a physical object is an active condition for 
 the situation of a patch of colour behind it, due to the 
 reflection of light in it. 
 
 "" Thus the origin of scientific knowledge is the en- 
 deavour to express in terms of physical objects the 
 various r6les of events as active conditions in the in- 
 gression of sense-objects into nature. It is in the progress 
 of this investigation that scientific objects emerge. They 
 embody those aspects of the character of the situations 
 of the physical objects which are most permanent and 
 are expressible without reference to a multiple relation 
 including a percipient event. Their relations to each 
 other are also characterised by a certain simplicity and 
 uniformity. Finally the characters of the observed 
 physical objects and sense-objects can be expressed in 
 terms of these scientific objects. In fact the whole 
 point of the search for scientific objects is the endeavour 
 to obtain this simple expression of the characters of 
 events. These scientific objects are not themselves 
 merely formulae for calculation ; because formulae must 
 refer to things in nature, and the scientific objects are 
 the things in nature to which the formulae refer. 
 
 A scientific object such as a definite electron is a 
 systematic correlation of the characters of all events 
 throughout all nature. It is an aspect of the systematic 
 
VII] OBJECTS 159 
 
 character of nature. The electron is not merely where 
 its charge is. The charge is the quantitative character 
 of certain events due to the ingression of the electron 
 into nature. The electron is its whole field of force. 
 Namely the electron is the systematic way in which all 
 events are modified as the expression of its ingression. 
 The situation of an electron in any small duration may 
 be defined as that event which has the quantitative 
 character which is the charge of the electron. We may 
 if we please term the mere charge the electron. But 
 then another name is required for the scientific object 
 which is the full entity which concerns science, and 
 which I have called the electron. 
 
 According to this conception of scientific objects, the 
 rival theories of action at a distance and action by 
 transmission through a medium are both incomplete 
 expressions of the true process of nature. The stream 
 of events which form the continuous series of situations 
 of the electron is entirely self-determined, both as 
 regards having the intrinsic character of being the series 
 of situations of that electron and as regards the time- 
 systems with which its various members are cogredient, 
 and the flux of their positions in their corresponding 
 durations. This is the foundation of the denial of action 
 at a distance ; namely the progress of the stream of the 
 situations of a scientific object can be determined by an 
 analysis of the stream itself. 
 
 On the other hand the ingression of every electron 
 into nature modifies to some extent the character of 
 every event. Thus the character of the stream of events 
 which we are considering bears marks of the existence 
 of every other electron throughout the universe. If we 
 like to think of the electrons as being merely what I call 
 
i6o THE CONCEPT OF NATURE [ch. 
 
 their charges, then the charges act at a distance. But 
 this action consists in the modification of the situation 
 of the other electron under consideration. This con- 
 ception of a charge acting at a distance is a wholly 
 artificial one. The conception which most fully expresses 
 the character of nature is that of each event as modified 
 by the ingression of each electron into nature. The ether 
 is the expression of this systematic modification of events 
 throughout space and throughout time. The best expres- 
 sion of the character of this modification is for physicists 
 to find out. My theory has nothing to do with that and 
 is ready to accept any outcome of physical research. 
 
 The connexion of objects with space requires eluci- 
 dation. Objects are situated in events. The relation of 
 situation is a different relation for each type of object, 
 and in the case of sense-objects it cannot be expressed 
 as a two-termed relation. It would perhaps be better 
 to use a different word for these different types of the 
 relation of situation. It has not however been necessary 
 to do so for our purposes in these lectures. It must be 
 understood however that, when situation is spoken of, 
 some one definite type is under discussion, and it may 
 happen that the argument may not apply to situation of 
 another type. In all cases however I use situation to 
 express a relation between objects and events and not 
 between objects and abstractive elements. There is a 
 derivative relation between objects and spatial elements 
 which I call the relation of location; and when this 
 relation holds, I say that the object is located in the 
 abstractive element. In this sense, an object may be 
 located in a moment of time, in a volume of space, an 
 area, a line, or a point. There will be a peculiar type of 
 location corresponding to each type of situation; and 
 
VII] OBJECTS i6i 
 
 location is in each case derivative from the corresponding 
 relation of situation in a v^ay w^hich I v^ill proceed to 
 explain. 
 
 Also location in the timeless space of some time-system 
 is a relation derivative from location in instantaneous 
 spaces of the same time-system. Accordingly location 
 in an instantaneous space is the primary idea w^hich w^e 
 have to explain. Great confusion has been occasioned 
 in natural philosophy by the neglect to distinguish be- 
 tw^een the different types of objects, the different types 
 of situation, the different types of location, and the 
 difference betw^een location and situation. It is im- 
 possible to reason accurately in the vague concerning 
 objects and their positions vs^ithout keeping these dis- 
 tinctions in viev^. An object is located in an abstractive 
 element, when an abstractive set belonging to that ele- 
 ment can be found such that each event belonging to 
 that set is a situation of the object. It v^ill be remem- 
 bered that an abstractive element is a certain group of 
 abstractive sets, and that each abstractive set is a set 
 of events. This definition defines the location of an 
 element in any type of abstractive element. In this 
 sense v^e can talk of the existence of an object at an 
 instant, meaning thereby its location in some definite 
 moment. It may also be located in some spatial element 
 of the instantaneous space of that moment. 
 
 A quantity can be said to be located in an abstractive 
 element vv^hen an abstractive set belonging to the element 
 can be found such that the quantitative expressions of 
 the corresponding characters of its events converge to 
 the measure of the given quantity as a limit v^hen we 
 pass along the abstractive set towards its converging 
 end. 
 
 W.N. II 
 
i62 THE CONCEPT OF NATURE [ch. 
 
 By these definitions location in elements of instanta- 
 neous spaces is defined. These elements occupy corre- 
 sponding elements of timeless spaces. An object located 
 in an element of an instantaneous space will also be said 
 to be located at that moment in the timeless element of 
 the timeless space which is occupied by that instantaneous 
 element. 
 
 It is not every object which can be located in a moment. 
 An object which can be located in every moment of some 
 duration will be called a * uniform' object throughout 
 that duration. Ordinary physical objects appear to us 
 to be uniform objects, and we habitually assume that 
 scientific objects such as electrons are uniform. But 
 some sense-objects certainly are not uniform. A tune 
 is an example of a non-uniform object. We have per- 
 ceived it as a whole in a certain duration ; but the tune 
 as a tune is not at any moment of that duration though 
 one of the individual notes may be located there. 
 
 It is possible therefore that for the existence of 
 certain sorts of objects, e,g, electrons, minimum quanta 
 of time are requisite. Some such postulate is apparently 
 indicated by the modern quantum theory and it is per- 
 fectly consistent with the doctrine of objects maintained 
 in these lectures. 
 
 Also the instance of the distinction between the 
 electron as the mere quantitative electric charge of its 
 situation and the electron as standing for the ingression 
 of an object throughout nature illustrates the indefinite 
 number of types of objects which exist in nature. We 
 can intellectually distinguish even subtler and subtler 
 types of objects. Here I reckon subtlety as meaning 
 seclusion from the immediate apprehension of sense- 
 awareness. Evolution in the complexity of life means an 
 
VII] OBJECTS 163 
 
 increase in the types of objects directly sensed. Deli- 
 cacy of sense-apprehension means perceptions of objects 
 as distinct entities which are mere subtle ideas to cruder 
 sensibilities. The phrasing of music is a mere abstract 
 subtlety to the unmusical; it is a direct sense-appre- 
 hension to the initiated. For example, if we could 
 imagine some lowly type of organic being thinking and 
 aware of our thoughts, it would wonder at the abstract 
 subtleties in which we indulge as we think of stones 
 and bricks and drops of water and plants. It only knows 
 of vague undifferentiated feelings in nature. It would 
 consider us as given over to the play of excessively 
 abstract intellects. But then if it could think, it would 
 anticipate; and if it anticipated, it would soon per- 
 ceive for itself. 
 
 In these lectures we have been scrutinising the 
 foundations of natural philosophy. We are stopping at 
 the very point where a boundless ocean of enquiries 
 opens out for our questioning. 
 
 I agree that the view of Nature which I have main- 
 tained in these lectures is not a simple one. Nature 
 appears as a complex system whose factors are dimly 
 discerned by us. But, as I ask you. Is not this the very 
 truth ? Should we not distrust the jaunty assurance with 
 which every age prides itself that it at last has hit upon 
 the ultimate concepts in which all that happens can be 
 formulated } The aim of science is to seek the simplest 
 explanations of complex facts. We are apt to fall into 
 the error of thinking that the facts are simple because 
 simplicity is the goal of our quest. The guiding motto 
 in the life of every natural philosopher should be, 
 
 Seek simplicity and distr ust it . 
 
 — — — ^ — "• — - -1^1 -^ »i ^"^^"^ 
 
CHAPTER VIII 
 SUMMARY 
 
 There is a general agreement that Einstein's investiga- 
 tions have one fundamental merit irrespective of any 
 criticisms which we may feel inclined to pass on them. 
 They have made us think. But when we have admitted 
 so far, we are most of us faced with a distressing per- 
 plexity. What is it that we ought to think about? The 
 purport of my lecture this afternoon will be to meet this 
 difficulty and, so far as I am able, to set in a clear Ught 
 the changes in the background of our scientific thought 
 which are necessitated by any acceptance, however 
 qualified, of Einstein's main positions. I remember that 
 I am lecturing to the members of a chemical society 
 who are not for the most part versed in advanced 
 mathematics. The first point that I would urge upon you 
 is that what immediately concerns you is not so much 
 the detailed deductions of the new theory as this general 
 change in the background of scientific conceptions 
 which will follow from its acceptance. Of course, the 
 detailed deductions are important, because unless our 
 colleagues the astronomers and the physicists find these 
 predictions to be verified we can neglect the theory 
 altogether. But we may now take it as granted that in 
 many striking particulars these deductions have been 
 found to be in agreement with observation. Accord- 
 ingly the theory has to be taken seriously and we are 
 anxious to know what will be the consequences of its 
 final acceptance. Furthermore during the last few weeks 
 
CH. VIII] SUMMARY 165 
 
 the scientific journals and the lay press have been filled 
 w^ith articles as to the nature of the crucial experiments 
 which have been made and as to some of the more 
 striking expressions of the outcome of the new theory. 
 
 * Space caught bending' appeared on the news-sheet 
 of a well-known evening paper. This rendering is a 
 terse but not inapt translation of Einstein's own way of 
 interpreting his results. I should say at once that I am 
 a heretic as to this explanation and that I shall expound 
 to you another explanation based upon some work of 
 my own, an explanation which seems to me to be more 
 in accordance with our scientific ideas and with the 
 whole body of facts which have to be explained. We 
 have to remember that a new theory must take account 
 of the old well-attested facts of science just as much as 
 of the very latest experimental results which have led 
 to its production. 
 
 To put ourselves in the position to assimilate and to 
 criticise any change in ultimate scientific conceptions we 
 must begin at the beginning. So you must bear with me 
 if I commence by making some simple and obvious 
 reflections. Let us consider three statements, (i) * Yes- 
 terday a man was run over on the Chelsea Embankment,' 
 (ii) * Cleopatra's Needle is on the Charing Cross Em- 
 bankment,' and (iii) * There are dark lines in the Solar 
 Spectrum.' The first statement about the accident to 
 the man is about what we may term an * occurrence,' 
 a * happening,' or an * event.' I will use the term 
 
 * event ' because it is the shortest. In order to specify an 
 observed event, the place, the time, and character of the 
 event are necessary. In specifying the place and the time 
 you are really stating the relation of the assigned event 
 to the general structure of other observed events. For 
 
i66 THE CONCEPT OF NATURE [ch. 
 
 example, the man was run over between your tea and 
 your dinner and adjacently to a passing barge in the 
 river and the traffic in the Strand. The point which I 
 want to make is this: Nature is known to us in our 
 experience as a complex of passing events. In this 
 complex we discern definite mutual relations between 
 component events, which we may call their relative 
 positions, and these positions we express partly in terms 
 of space and partly in terms of time. Also in addition 
 to its mere relative position to other events, each par- 
 ticular event has its own peculiar character. In other 
 words, nature is a structure of events and each event 
 has its position in this structure and its own peculiar 
 character or quality. 
 
 Let us now examine the other two statements in the 
 light of this general principle as to the meaning of 
 nature. Take the second statement, * Cleopatra's 
 Needle is on the Charing Cross Embankment.' At 
 first sight we should hardly call this an event. It seems 
 to lack the element of time or transitoriness. But does 
 it ? If an angel had made the remark some hundreds of 
 millions of years ago, the earth was not in existence, 
 twenty millions of years ago there was no Thames, 
 eighty years ago there was no Thames Embankment, 
 and when I was a small boy Cleopatra's Needle was 
 not there. And now that it is there, we none of us expect 
 it to be eternal. The static timeless element in the rela- 
 tion of Cleopatra's Needle to the Embankment is a 
 pure illusion generated by the fact that for purposes of 
 daily intercourse its emphasis is needless. What it 
 comes to is this : Amidst the structure of events which 
 form the medium within which the daily life of Lon- 
 doners is passed we know how to identify a certain 
 
VIII] SUMMARY 167 
 
 stream of events which maintain permanence of charac- 
 ter, namely the character of being the situations of 
 Cleopatra's Needle. Day by day and hour by hour we 
 can find a certain chunk in the transitory life of nature 
 and of that chunk we say, * There is Cleopatra's Needle/ 
 If we define the Needle in a sufficiently abstract manner 
 we can say that it never changes. But a physicist who 
 looks on that part of the life of nature as a dance of 
 electrons, will tell you that daily it has lost some mole- 
 cules and gained others, and even the plain man can 
 see that it gets dirtier and is occasionally washed. Thus 
 the question of change in the Needle is a mere matter of 
 definition. The more abstract your definition, the more 
 permanent the Needle. But whether your Needle change 
 or be permanent, all you mean by stating that it is 
 situated on the Charing Cross Embankment, is that 
 amid the structure of events you know of a certain con- 
 tinuous limited stream of events, such that any chunk 
 of that stream, during any hour, or any day, or any 
 second, has the character of being the situation of 
 Cleopatra's Needle. 
 
 Finally, we come to the third statement, * There are 
 dark lines in the Solar Spectrum.' This is a law of nature. 
 But what does that mean ? It means merely this. If any 
 event has the character of being an exhibition of the 
 solar spectrum under certain assigned circumstances, it 
 will also have the character of exhibiting dark lines in 
 that spectrum. 
 
 This long discussion brings us to the final conclusion 
 that the concrete facts of nature are events exhibiting 
 a certain structure in their mutual relations and certain 
 characters of their own. The aim of science is to express 
 the relations between their characters in terms of the 
 
i68 THE CONCEPT OF NATURE [ch. 
 
 mutual structural relations between the events thus 
 characterised. The mutual structural relations between 
 events are both spatial and temporal. If you think of 
 them as merely spatial you are omitting the temporal 
 element, and if you think of them as merely temporal 
 you are omitting the spatial element. Thus when you 
 think of space alone, or of time alone, you are dealing 
 in abstractions, namely, you are leaving out an essential 
 element in the life of nature as known to you in the 
 experience of your senses. Furthermore there are 
 different ways of making these abstractions which we 
 think of as space and as time ; and under some circum- 
 stances we adopt one way and under other circumstances 
 we adopt another way. Thus there is no paradox in 
 holding that what we mean by space under one set of 
 circumstances is not what we mean by space under 
 another set of circumstances. And equally what we 
 mean by time under one set of circumstances is not 
 what we mean by time under another set of circum- 
 stances. By saying that space and time are abstractions, 
 I do not mean that they do not express for us real facts 
 about nature. What I mean is that there are no spatial 
 facts or temporal facts apart from physical nature, 
 namely that space and time are merely ways of expressing 
 certain truths about the relations between events. Also 
 that under different circumstances there are different 
 sets of truths about the universe which are naturally 
 presented to us as statements about space. In such a 
 case what a being under the one set of circumstances 
 means by space will be different from that meant by a 
 being under the other set of circumstances. Accord- 
 ingly when we are comparing two observations made 
 under different circumstances we have to ask ' Do the 
 
VIII] SUMMARY 169^ 
 
 two observers mean the same thing by space and the 
 same thing by time ? ' The modern theory of relativity 
 has arisen because certain perplexities as to the con- 
 cordance of certain delicate observations such as the 
 motion of the earth through the ether, the perihelion 
 of mercury, and the positions of the stars in the neigh- 
 bourhood of the sun, have been solved by reference to 
 this purely relative significance of space and time. 
 
 I want now to recall your attention to Cleopatra^s 
 Needle, which I have not yet done with. As you are 
 walking along the Embankment you suddenly look up 
 and say, 'Hullo, there's the Needle.' In other words, 
 you recognise it. You cannot recognise an event; 
 because when it is gone, it is gone. You may observe 
 another event of analogous character, but the actual 
 chunk of the life of nature is inseparable from its unique 
 occurrence. But a character of an event can be recog- 
 nised. We all know that if we go to the Embankment 
 near Charing Cross we shall observe an event having the 
 character which we recognise as Cleopatra's Needle. 
 Things which we thus recognise I call objects. An 
 object is situated in those events or in that stream of 
 events of which it expresses the character. There are 
 many sorts of objects. For example, the colour green 
 is an object according to the above definition. It is the 
 purpose of science to trace the laws which govern the 
 appearance of objects in the various events in which they 
 are found to be situated. For this purpose we can 
 mainly concentrate on two types of objects, which I will 
 call material physical objects and scientific objects. 
 A material physical object is an ordinary bit of matter, 
 Cleopatra's Needle for example. This is a much more 
 complicated type of object than a mere colour, such as 
 
I70 THE CONCEPT OF NATURE [ch. 
 
 the colour of the Needle. I call these simple objects, 
 such as colours or sounds, sense-objects. An artist 
 will train himself to attend more particularly to sense- 
 objects where the ordinary person attends normally to 
 material objects. Thus if you were walking with an 
 artist, when you said * There's Cleopatra's Needle,' 
 perhaps he simultaneously exclaimed 'There's a nice 
 bit of colour.' Yet you were both expressing your 
 recognition of different component characters of the 
 same event. But in science we have found out that 
 when we know all about the adventures amid events of 
 material physical objects and of scientific objects we 
 have most of the relevant information which will enable 
 us to predict the conditions under which we shall 
 perceive sense-objects in specific situations. For ex- 
 ample, when we know that there is a blazing fire (i.e. 
 material and scientific objects undergoing various 
 exciting adventures amid events) and opposite to it a 
 mirror (which is another material object) and the 
 positions of a man's face and eyes gazing into the mirror, 
 we know that he can perceive the redness of the flame 
 situated in an event behind the mirror — thus, to a large 
 extent, the appearance of sense-objects is conditioned 
 by the adventures of material objects. The analysis of 
 these adventures makes us aware of another character 
 of events, namely their characters as fields of activity 
 which determine the subsequent events to which they 
 will pass on the objects situated in them. We express 
 these fields of activity in terms of gravitational, electro- 
 magnetic, or chemical forces and attractions. But the 
 exact expression of the nature of these fields of activity 
 forces us intellectually to acknowledge a less obvious 
 type of objects as situated in events. I mean molecules 
 
VIII] SUMMARY 17: 
 
 and electrons. These objects are not recognised in 
 isolation. We cannot well miss Cleopatra's Needle, if 
 we are in its neighbourhood ; but no one has seen a single 
 molecule or a single electron, yet the characters of 
 events are only explicable to us by expressing them in 
 terms of these scientific objects . Undoubtedly molecules 
 and electrons are abstractions. But then so is Cleo- 
 patra's Needle. The concrete facts are the events them- 
 selves — I have already explained to you that to be an 
 abstraction does not mean that an entity is nothing. It 
 merely means that its existence is only one factor of a 
 Inore concrete element of nature. So an electron is 
 abstra ct because you cannot wipe out the whole structure 
 of events and yet retain the electron in existence. In 
 the same way the grin on the cat is abstract; and the 
 molecule is really in the event in the same sense as the 
 grin is really on the cat's face. Now the more ultimate 
 sciences such as Chemistry or Physics cannot express 
 their ultimate laws in terms of such vague objects as 
 the sun, the earth, Cleopatra's Needle, or a human 
 body. Such objects more properly belong to Astro- 
 nomy, to Geology, to Engineering, to Archaeology, 
 or to Biology. Chemistry and Physics only deal with 
 them as exhibiting statistical complexes of the effects 
 of their more intimate laws. In a certain sense, they 
 only enter into Physics and Chemistry as technological 
 applications. The reason is that they are too vague. 
 Where does Cleopatra's Needle begin and where does 
 it end.? Is the soot part of it? Is it a different 
 object when it sheds a molecule or when its surface 
 enters into chemical combination with the acid of a 
 London fog? The definiteness and permanence of the 
 Needle is nothing to the possible permanent definiteness 
 
172 THE CONCEPT OF NATURE [ch. 
 
 of a molecule as conceived by science, and the per- 
 manent definiteness of a molecule in its turn yields to 
 that of an electron. Thus science in its most ultimate 
 formulation of law seeks objects with the most per- 
 manent definite simplicity of character and expresses 
 its final laws in terms of them. 
 
 Again when we seek definitely to express the relations 
 of events which arise from their spatio-temporal 
 structure, we approximate to simplicity by progressively 
 diminishing the extent (both temporal and spatial) of 
 the events considered. For example, the event which 
 is the life of the chunk of nature which is the Needle 
 during one minute has to the life of nature within a 
 passing barge during the same minute a very complex 
 spatio-temporal relation. But suppose we progressively 
 diminish the time considered to a second, to a hun- 
 dredth of a second, to a thousandth of a second, and 
 so on. As we pass along such a series we approximate 
 to an ideal simplicity of structural relations of the pairs 
 of events successively considered, which ideal we call 
 the spatial relations of the Needle to the barge at some 
 instant. Even these relations are too complicated for us, 
 and we consider smaller and smaller bits of the Needle 
 and of the barge. Thus we finally reach the ideal of an 
 event so restricted in its extension as to be without ex- 
 tension in space or extension in time. Such an event is 
 a mere spatial point-flash of instantaneous duration. 
 I call such an ideal event an * event-particle.' You must 
 not think of the world as ultimately built up of event- 
 particles. That is to put the cart before the horse. The 
 world we know is a continuous stream of occurrence 
 which we can discriminate into finite events forming by 
 their overlappings and containings of each other and 
 
VIII] SUMMARY 173 
 
 separations a spatio-temporal structure. We can express 
 the properties of this structure in terms of the ideal 
 limits to routes of approximation, which I have termed 
 event-particles. Accordingly event-particles are abstrac- 
 tions in their relations to the more concrete events. But 
 then by this time you will have comprehended that you 
 cannot analyse concrete nature without abstracting. 
 Also I repeat, the abstractions of science are entities 
 which are truly in nature, though they have no meaning 
 in isolation from nature. 
 
 The character of the spatio-temporal structure of 
 events can be fully expressed in terms of relations 
 between these more abstract event-particles. The ad- 
 vantage of dealing with event-particles is that though 
 they are abstract and complex in respect to the finite 
 events which we directly observe, they are simpler 
 than finite events in respect to their mutual relations. 
 Accordingly they express for us the demands of an ideal 
 accuracy, and of an ideal simplicity in the exposition of 
 relations. These event-particles are the ultimate elements 
 of the four-dimensional space-time manifold which the 
 theory of relativity presupposes. You will have observed 
 that each event-particle is as much an instant of time as 
 it is a point of space. I have called it an instantaneous 
 point-flash. Thus in the structure of this space-time 
 manifold space is not finally discriminated from time, 
 and the possibility remains open for diverse modes of 
 discrimination according to the diverse circumstances 
 of observers. It is this possibility which makes the 
 fundamental distinction between the new way of con- 
 ceiving the universe and the old way. The secret of 
 understanding relativity is to understand this. It is of 
 no use rushing in with picturesque paradoxes, such as 
 
174 THE CONCEPT OF NATURE [ch. 
 
 * Space caught bending,' if you have not mastered this 
 fundamental conception which underHes the whole 
 theory. When I say that it underHes the whole theory, 
 I mean that in my opinion it ought to underlie it, though 
 I may confess some doubts as to how far all expositions 
 of the theory have really understood its implications and 
 its premises. 
 
 Our measurements when they are expressed in terms 
 of an ideal accuracy are measurements which express 
 properties of the space-time manifold. Now there are 
 measurements of different sorts. You can measure 
 lengths, or angles, or areas, or volumes, or times. There 
 are also other sorts of measures such as measurements 
 of intensity of illumination, but I will disregard these 
 for the moment and will confine attention to those 
 measurements which particularly interest us as being 
 measurements of space or of time. It is easy to see that 
 four such measurements of the proper characters are 
 necessary to determine the position of an event-particle 
 in the space-time manifold in its relation to the rest of 
 the manifold. For example, in a rectangular field you 
 start from one corner at a given time, you measure a 
 definite distance along one side, you then strike out 
 into the field at right angles, and then measure a definite 
 distance parallel to the other pair of sides, you then rise 
 vertically a definite height and take the time. At the 
 point and at the time which you thus reach there is 
 occurring a definite instantaneous point-flash of nature. 
 In other words, your four measurements have deter- 
 mined a definite event-particle belonging to the four- 
 dimension space-time manifold. These measurements 
 have appeared to be very simple to the land-surveyor 
 and raise in his mind no philosophic difficulties. But 
 
VIII] SUMMARY 175 
 
 suppose there are beings on Mars sufficiently advanced 
 in scientific invention to be able to watch in detail the 
 operations of this survey on earth. Suppose that they 
 construe the operations of the English land-surveyors 
 in reference to the space natural to a being on Mars, 
 namely a Martio-centric space in which that planet is 
 fixed. The earth is moving relatively to Mars and is 
 rotating. To the beings on Mars the operations, con- 
 strued in this fashion, effect measurements of the greatest 
 complication. Furthermore, according to the relati- 
 vistic doctrine, the operation of time-measurement on 
 earth will not correspond quite exactly to any time- 
 measurement on Mars. 
 
 I have discussed this example in order to make you 
 realise that in thinking of the possibilities of measure- 
 ment in the space-time manifold, we must not confine 
 ourselves merely to those minor variations which might 
 seem natural to human beings on the earth. Let us 
 make therefore the general statement that four measure- 
 ments, respectively of independent types (such as mea- 
 surements of lengths in three directions and a time), 
 can be found such that a definite event-particle is 
 determined by them in its relations to other parts of 
 the manifold. 
 
 I^ (Ply p2^ p3y P^) ^^ ^ set of measurements of this 
 system, then the event-particle which is thus deter- 
 mined will be said to have />i, p^, p^y ^4 as its co-ordi- 
 nates in this system of measurement. Suppose that we 
 name it the/)-system of measurement. Then in the same 
 />-system by properly varying (/>!, p^, p^y p^ every 
 event-particle that has been, or will be, or instantane- 
 ously is now, can be indicated. Furthermore, according 
 to any system of measurement that is natural to us. 
 
176 THE CONCEPT OF NATURE [ch. 
 
 three of the co-ordinates will be measurements of space 
 and one will be a measurement of time. Let us always 
 take the last co-ordinate to represent the time-measure- 
 ment. Then we should naturally say that (/>i, />2, Pz) 
 determined a point in space and that the event-particle 
 happened at that point at the tivatp^. But we must not 
 make the mistake of thinking that there is a space in 
 addition to the space-time manifold. That manifold is 
 all that there is for the determination of the meaning of 
 space and time. We have got to determine the meaning 
 of a space-point in terms of the event-particles of the 
 four-dimensional manifold. There is only one way to 
 do this. Note that if we vary the time and take times 
 with the same three space co-ordinates, then the event- 
 particles, thus indicated, are all at the same point. But 
 seeing that there is nothing else except the event- 
 particles, this can only mean that the point (pi, />2> p^ 
 of the space in the /)-system is merely the collection of 
 event-particles (/>!, p^, p^, [pj)) where /)4 is varied and 
 (pi, p2y Pz) is kept fixed. It is rather disconcerting to 
 find that a point in space is not a simple entity ; but it 
 is a conclusion which follows immediately from the 
 relative theory of space. 
 
 Furthermore the inhabitant of Mars determines 
 event-particles by another system of measurements. 
 Call his system the ^-system. According to him 
 {qiy q2, ^3, g'4) determines an event-particle, and 
 (^1, ^2> ^3) determines a point and ^4 a time. But the 
 collection of event-particles which he thinks of as a 
 point is entirely different from any such collection 
 which the man on earth thinks of as a point. Thus the 
 ^-space for the man on Mars is quite different from the 
 ^-space for the land-surveyor on earth. 
 
VIII] SUMMARY 177 
 
 So far in speaking of space we have been talking of 
 the timeless space of physical science, namely, of our 
 concept of eternal space in v^hich the world adventures. 
 But the space which we see as we look about is instan- 
 taneous space. Thus if our natural perceptions are 
 adjustable to the ^-system of measurements we see 
 instantaneously all the event-particles at some definite 
 time ^4, and observe a succession of such spaces as time 
 moves on. The timeless space is achieved by stringing 
 together all these instantaneous spaces. The points of 
 an instantaneous space are event-particles, and the 
 points of an eternal space are strings of event-particles 
 occurring in succession. But the man on Mars will 
 never perceive the same instantaneous spaces as the 
 man on the earth. This system of instantaneous spaces 
 will cut across the earth-man's system. For the earth- 
 man there is one instantaneous space which is the 
 instantaneous present, there are the past spaces and the 
 future spaces. But the present space of the man on 
 Mars cuts across the present space of the man on the 
 earth. So that of the event-particles which the earth- 
 man thinks of as happening now in the present, the 
 man on Mars thinks that some are already past and are 
 ancient history, that others are in the future, and others 
 are in the immediate present. This break-down in the 
 neat conception of a past, a present, and a future is a 
 serious paradox. I call two event-particles which on 
 some or other system of measurement are in the same 
 instantaneous space * co-present' event-particles. Then 
 it is possible that A and B may be co-present, and that 
 A and C may be co-present, but that B and C may not 
 be co-present. For example, at some inconceivable 
 distance from us there are events co-present with us 
 
 W.N. 12 
 
178 THE CONCEPT OF NATURE [ch. 
 
 now and also co-present with the birth of Queen 
 Victoria. If A and B are co-present there will be some 
 systems in which A precedes B and some in which B 
 precedes A, Also there can be no velocity quick enough 
 to carry a material particle from ^ to j5 or from B to A. 
 These different measure-systems with their divergences 
 of time-reckoning are puzzling, and to some extent 
 affront our common sense. It is not the usual way in 
 which we think of the Universe. We think of one 
 necessary time-system and one necessary space. Ac- 
 cording to the new theory, there are an indefinite 
 number of discordant time-series and an indefinite 
 number of distinct spaces. Any correlated pair, a 
 time-system and a space-system, will do in which to fit 
 our description of the Universe. We find that under 
 given conditions our measurements are necessarily made 
 in some one pair which together form our natural 
 measure-system. The difficulty as to discordant time- 
 systems is partly solved by distinguishing between what 
 I call the creative advance of nature, which is not 
 properly serial at all, and any one time series. We 
 habitually muddle together this creative advance, which 
 we experience and know as the perpetual transition of 
 nature into novelty, with the single- time series which 
 we naturally employ for measurement. The 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. The 
 reason why we have not previously noted this difference 
 of time-series is the very small difference of properties 
 between any two such series. Any observable pheno- 
 mena due to this cause depend on the square of the 
 ratio of any velocity entering into the observation to 
 
VIII] SUMMARY 179 
 
 the velocity of light. Now^ Ught takes about fifty minutes 
 to get round the earth's orbit; and the earth takes 
 rather more than 17,531 half-hours to do the same. 
 Hence all the effects due to this motion are of the order 
 of the ratio of one to the square of 10,000. Accordingly 
 an earth-man and a sun-man have only neglected 
 effects whose quantitative magnitudes all contain the 
 factor i/io^. Evidently such effects can only be noted 
 by means of the most refined observations. They have 
 been observed how^ever. Suppose wc compare two 
 observations on the velocity of light made with the 
 same apparatus as we turn it through a right angle. 
 The velocity of the earth relatively to the sun is in one 
 direction, the velocity of light relatively to the ether 
 should be the same in all directions. Hence if space 
 when we take the ether as at rest means the same thing 
 as space when we take the earth as at rest, we ought to 
 find that the velocity of light relatively to the earth 
 varies according to the direction from which it comes. 
 
 These observations on earth constitute the basic 
 principle of the famous experiments designed to detect 
 the motion of the earth through the ether. You all 
 know that, quite unexpectedly, they gave a null result. 
 This is completely explained by the fact that, the space- 
 system and the time-system which we are using are 
 in certain minute ways different from the space and the 
 time relatively to the sun or relatively to any other body 
 with respect to which it is moving. 
 
 All this discussion as to the nature of time and space 
 has lifted above our horizon a great difficulty which 
 affects the formulation of all the ultimate laws of physics 
 — for example, the laws of the electromagnetic field, 
 and the law of gravitation. Let us take the law of 
 
i8o THE CONCEPT OF NATURE [CH. 
 
 gravitation as an example. Its formulation is as follows : 
 Two material bodies attract each other with a force 
 proportional to the product of their masses and umka 
 versely proportional to the square of their distances. In 
 this statement the bodies are supposed to be small 
 enough to be treated as material particles in relation to 
 their distances; and we need not bother further about 
 that minor point. The difficulty to which I want to 
 draw your attention is this : In the formulation of the 
 law one 'definite time and one definite space are pre- 
 supposed. The two masses are assumed to be in simul- 
 taneous positions. 
 
 But what is simultaneous in one time-system may not 
 be simultaneous in another time-system. So according 
 to our new views the law is in this respect not formulated 
 so as to have any exact meaning. Furthermore an 
 analogous difficulty arises over the question of distance. 
 The distance between two instantaneous positions, 
 i.e, between two event-particles, is different in different 
 space-systems. What space is to be chosen ? Thus again 
 the law lacks precise formulation, if relativity is accepted. 
 Our problem is to seek a fresh interpretation of the 
 law of gravity in which these difficulties are evaded. In 
 the first place we must avoid the abstractions of space 
 and time in the formulation of our fundamental ideas 
 and must recur to the ultimate facts of nature, namely 
 to events. Also in order to find the ideal simplicity of 
 expressions of the relations between events, we restrict 
 ourselves to event-particles. Thus the life of a material 
 particle is its adventure amid a track of event-particles 
 strung out as a continuous series or path in the four- 
 dimensional space-time manifold. These event-particles 
 are the various situations of the material particle. We 
 
viiij SUMMARY i8i 
 
 usually express this fact by adopting our natural space- 
 time system and by talking of the path in space of the 
 material particle as it exists at successive instants of time. 
 
 We have to ask ourselves what are the laws of nature 
 which lead the material particle to adopt just this path 
 among event-particles and no other. Think of the path 
 as a whole. What characteristic has that path got which 
 would not be shared by any other slightly varied path ? 
 We are asking for more than a law of gravity. We want 
 laws of motion and a general idea of the way to formulate 
 the effects of physical forces. 
 
 In order to answer our question we put the idea of the 
 attracting masses in the background and concentrate 
 attention on the field of activity of the events in the 
 neighbourhood of the path. In so doing we are acting 
 in conformity with the whole trend of scientific thought 
 during the last hundred years, which has more and more 
 concentrated attention on the field of force as the im- 
 mediate agent in directing motion, to the exclusion of 
 the consideration of the immediate mutual influence 
 between two distant bodies. We have got to find the 
 way of expressing the field of activity of events in the 
 neighbourhood of some definite event-particle E of the 
 four-dimensional manifold. I bring in a fundamental 
 physical idea which I call the * impetus ' to express this 
 physical field. The event-particle E is related to any 
 neighbouring event-particle P by an element of impetus. 
 The assemblage of all the elements of impetus relating 
 E to the assemblage of event-particles in the neighbour- 
 hood of E expresses the character of the field of activity 
 in the neighbourhood of E, Where I differ from Einstein 
 is that he conceives this quantity which I call the impetus 
 as merely expressing the characters of the space and 
 
i82 THE CONCEPT OF NATURE [ch. 
 
 time to be adopted and thus ends by talking of the 
 gravitational field expressing a curvature in the space- 
 time manifold. I cannot attach any clear conception to 
 his interpretation of space and time. My formulae 
 differ slightly from his, though they agree in those 
 instances where his results have been verified. I need 
 hardly say that in this particular of the formulation of the 
 law of gravitation I have drawn on the general method 
 of procedure which constitutes his great discovery. 
 
 Einstein showed how to express the characters of the 
 assemblage of elements of impetus of the field sur- 
 rounding an event-particle E in terms of ten quantities 
 
 which I will call J^* J12 (= .72i). J22. J23 (= ^32). etc. 
 It will be noted that there are four spatio-temporal 
 measurements relating E to its neighbour P, and that 
 there are ten pairs of such measurements if we are 
 allowed to take any one measurement twice over to 
 make one such pair. The ten J's depend merely on the 
 position of E in the four-dimensional manifold, and the 
 element of impetus between E and P can be expressed 
 in terms of the ten J's and the ten pairs of the four 
 spatio-temporal measurements relating E and P. The 
 numerical values of the J's will depend on the system 
 of measurement adopted, but are so adjusted to each 
 particular system that the same value is obtained for 
 the element of impetus between E and P, whatever be 
 the system of measurement adopted. This fact is ex- 
 pressed by saying that the ten J's form a ' tensor.' It is 
 not going too far to say that the announcement that 
 physicists would have in future to study the theor^^ 
 of tensors created a veritable panic among them when 
 the verification of Einstein's predictions was first 
 announced. 
 
VIII] SUMMARY 183 
 
 The ten J's at any event-particle E can be expressed in 
 terms of tw^o functions w^hich I call the potential and the 
 * associate-potential' at E. The potential is practically 
 what is meant by the ordinary gravitation potential, 
 when we express ourselves in terms of the Euclidean 
 space in reference to which the attracting mass is at 
 rest. The associate-potential is defined by the modifi- 
 cation of substituting the direct distance for the inverse 
 distance in the definition of the potential, and its calcu- 
 lation can easily be made to depend on that of the old- 
 fashioned potential. Thus the calculation of the J's — the 
 coefficients of impetus, as I will call them — does not 
 involve anything very revolutionary in the mathematical 
 knowledge of physicists. We now return to the path of 
 the attracted particle. We add up all the elements of 
 impetus in the whole path, and obtain thereby what I 
 call the 'integral impetus.' The characteristic of the 
 actual path as compared with neighbouring alternative 
 paths is that in the actual paths the integral impetus 
 would neither gain nor lose, if the particle wobbled out 
 of it into a small extremely near alternative path. Mathe- 
 maticians would express this by saying, that the integral 
 impetus is stationary for an infinitesimal displacement. 
 In this statement of the law of motion I have neglected 
 the existence of other forces. But that would lead me 
 too far afield. 
 
 The electromagnetic theory has to be modified to 
 allow for the presence of a gravitational field. Thus 
 Einstein's investigations lead to the first discovery of 
 any relation between gravity and other physical pheno- 
 mena. In the form in which I have put this modification, 
 we deduce Einstein's fundamental principle, as to the 
 motion of light along its rays, as a first approximation 
 
i84 THE CONCEPT OF NATURE [ch. viii 
 
 which IS absolutely true for infinitely short waves. 
 Einstein's principle, thus partially verified, stated in my 
 language is that a ray of light always follows a path such 
 that the integral impetus along it is zero. This involves 
 that every element of impetus along it is zero. 
 
 In conclusion, I must apologise. In the first place 
 I have considerably toned down the various exciting 
 peculiarities of the original theory and have reduced it 
 to a greater conformity with the older physics. I do not 
 allow that physical phenomena are due to oddities of 
 space. Also I have added to the dullness of the lecture 
 by my respect for the audience. You would have enjoyed 
 a more popular lecture with illustrations of delightful 
 paradoxes. But I know also that you are serious 
 students who are here because you really want to know 
 how the new theories may aflFect your scientific re- 
 searches. 
 
CHAPTER IX 
 THE ULTIMATE PHYSICAL CONCEPTS 
 
 The second chapter of this book lays down the first 
 principle to be guarded in framing our physical concept. 
 We must avoid vicious bifurcation Nature is nothing 
 else than the deliverance of sense-awareness. We have 
 no principles whatever to tell us what could stimulate 
 mind towards sense-awareness. Our sole task is to 
 exhibit in one system the characters and inter-relations 
 of all that is observed. Our attitude towards nature is 
 purely * behaviouristic,' so far as concerns the formulation 
 of physical concepts. 
 
 Our knowledge of nature is an experience of activity 
 (or passage). The things previously observed are active 
 entities, the * events.' They are chunks in the life of 
 nature. These events have to each other relations which 
 in our knowledge differentiate themselves into space- 
 relations and time-relations. But this differentiation 
 between space and time, though inherent in nature, is 
 comparatively superficial ; and space and time are each 
 partial expressions of one fundamental relation between 
 events which is neither spatial nor temporal. This 
 relation I call 'extension.' The relation of 'extending 
 over' is the relation of 'including,' either in a spatial or 
 in a temporal sense, or in both. But the mere 'inclu- 
 sion' is more fundamental than either alternative and 
 does not require any spatio-temporal differentiation. 
 In respect to extension two events are mutually related 
 so that either (i) one includes the other, or (ii) one over- 
 laps the other without complete inclusion, or (iii) they 
 
i86 THE CONCEPT OF NATURE [CH. 
 
 are entirely separate. But great care is required in the 
 definition of spatial and temporal elements from this 
 basis in order to avoid tacit limitations really depend- 
 ing on undefined relations and properties. 
 
 Such fallacies can be avoided by taking account of 
 two elements in our experience, namely, (i) our ob- 
 servational * present,' and (ii) our * percipient event.' 
 
 Our observational * present ' is what I call a * duration.' 
 It is the whole of nature apprehended in our immediate 
 observation. It has therefore the nature of an event, 
 but possesses a peculiar completeness which marks out 
 such durations as a special type of events inherent in 
 nature. A duration is not instantaneous. It is all that 
 there is of nature with certain temporal limitations. In 
 contradistinction to other events a duration will be 
 called infinite and the other events are finite^. In our 
 knowledge of a duration we distinguish (i) certain 
 included events which are particularly discriminated 
 as to their peculiar individualities, and (ii) the remaining 
 included events which are only known as necessarily in 
 being by reason of their relations to the discriminated 
 events and to the whole duration. 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. 
 \ I mean by this that every event is known as being related 
 \to other events which it does not include. This fact, 
 jthat every event is known as possessing the quality of 
 ^exclusion, shows that exclusion is as positive a relation 
 as inclusion. There are of course no merely negative 
 
 ^ Cf. note on ^significance,' pp. 197, 198. 
 2 Cf. Ch. Ill, pp. 51 et seq. 
 
IX] THE ULTIMATE PHYSICAL CONCEPTS 187 
 
 relations in nature, and exclusion is not the mere 
 negative of inclusion, though the two relations are 
 contraries. Both relations are concerned solely with^ 
 events, and exclusion is capable of logical definition in 
 terms of inclusion. 
 
 Perhaps the most obvious exhibition of significance 
 is to be found in our knowledge of the geometrical 
 character of events inside an opaque material object. 
 For example we know that an opaque sphere has a 
 centre. This knowledge has nothing to do with the 
 material; the sphere may be a solid uniform billiard 
 ball or a hollow lawn-tennis ball. Such knowledge is 
 essentially the product of significance, since the general 
 character of the external discriminated events has in- 
 formed us that there are events within the sphere and 
 has also informed us of their geometrical structure. 
 
 Some criticisms on *The Principles of Natural 
 Knowledge' show that difficulty has been found in 
 apprehending durations as real stratifications of nature. 
 I think that this hesitation arises from the unconscious 
 influence of the vicious principle of bifurcation, so 
 deeply embedded in modern philosophical thought. 
 We observe nature as extended in an immediate present 
 which is simultaneous but not instantaneous, and there- 
 fore the whole which is immediately discerned or 
 signified as an inter-related system forms a stratification 
 of nature which is a physical fact. This conclusion 
 immediately follows unless we admit bifurcation in the 
 form of the principle of psychic additions, here rejected. 
 
 Our * percipient event ' is that event included in our 
 observational present which we distinguish as being in 
 some peculiar way our standpoint for perception. It is 
 roughly speaking that event which is our bodily life 
 
i88 THE CONCEPT OF NATURE [CH. 
 
 within the present duration. The theory of perception 
 as evolved by medical psychology is based on signifi- 
 cance. The distant situation of a perceived object is 
 merely known to us as signified by our bodily state, 
 i,e, by our percipient event. In fact perception requires 
 sense-awareness of the significations of our percipient 
 event together with sense-awareness of a peculiar re- 
 lation (situation) between certain objects and the events 
 thus signified. Our percipient event is saved by being 
 the whole of nature by this fact of its significations. 
 This is the meaning of calling the percipient event 
 our standpoint for perception. The course of a ray of 
 light is only derivatively connected with perception. 
 What we do perceive are objects as related to events 
 signified by the bodily states excited by the ray. 
 These signified events (as is the case of images seen 
 behind a mirror) may have very little to do with the 
 actual course of the ray. In the course of evolution those 
 animals have survived whose sense-awareness is con- 
 centrated on those significations of their bodily states 
 which are on the average important for their welfare. 
 The whole world of events is signified, but there are 
 some which exact the death penalty for inattention. 
 
 The percipient event is always here and now in the 
 associated present duration. It has, what may be called, 
 an absolute position in that duration. Thus one definite 
 duration is associated with a definite percipient event, 
 and we are thus aware of a peculiar relation which 
 finite events can bear to durations. I call this relation 
 * cogredience.' The notion of rest is derivative from that 
 of cogredience, and the notion of motion is derivative 
 from that of inclusion within a duration without cogre- 
 dience with it. In fact motion is a relation (of varying 
 
IX] THE ULTIMATE PHYSICAL CONCEPTS 189 
 
 character) between an observed event and an observed 
 duration, and cogredience is the most simple character 
 or subspecies of motion. To sum up, a duration and a 
 percipient event are essentially involved in the general 
 character of each observation of nature, and the per- 
 cipient event is cogredient with the duration. 
 
 Our knowledge of the peculiar characters of different 
 events depends upon our power of comparison. I call 
 the exercise of this factor in our knowledge* recognition,' 
 and the requisite sense-awareness of the comparable 
 characters I call * sense-recognition.' Recognition and 
 abstraction essentially involve each other. Each of them 
 exhibits an entity for knowledge which is less than the 
 concrete fact, but is a real factor in that fact. The most 
 concrete fact capable of separate discrimination is the 
 event. We cannot abstract without recognition, and 
 we cannot recognise without abstraction. Perception 
 involves apprehension of the event and recognition of 
 the factors of its character. 
 
 The things recognised are what I call * objects.' In 
 this general sense of the term the relation of extension 
 is itself an object. In practice however I restrict the 
 term to those objects which can in some sense or other 
 be said to have a situation in an event; namely, in the 
 phrase ' There it is again ' I restrict the * there ' to be the 
 indication of a special event which is the situation of the 
 object. Even so, there are different types of objects, and 
 statements which are true of objects of one type are not 
 in general true of objects of other types. The objects 
 with which we are here concerned in the formulation 
 of physical laws are material objects, such as bits of 
 matter, molecules and electrons. An object of one of 
 these types has relations to events other than those 
 
190 THE CONCEPT OF NATURE [ch. 
 
 belonging to the stream of its situations. The fact of its 
 situations within this stream has impressed on all other 
 events certain modifications of their characters. In 
 truth the object in its completeness may be conceived 
 as a specific set of correlated modifications of the charac- 
 ters of all events, with the property that these modifica- 
 tions attain to a certain focal property for those events 
 which belong to the stream of its situations. The total 
 assemblage of the modifications of the characters of 
 events due to the existence of an object in a stream of 
 situations is what I call the 'physical field' due to the 
 object. . But the object cannot really be separated from 
 its field. The object is in fact nothing else than the 
 systematically adjusted set of modifications of the field. 
 The conventional limitation of the object to the focal 
 stream of events in which it is said to be ' situated ' is 
 convenient for some purposes, but it obscures the 
 ultimate fact of nature. From this point of view the 
 antithesis between action at a distance and action by 
 transmission is meaningless. The doctrine of this para- 
 graph is nothing else than another way of expressing the 
 unresolvable multiple relation of an object to events. 
 
 A complete time-system is formed by any one family 
 of parallel durations. Two durations are parallel if 
 either (i) one includes the other, or (ii) they overlap so 
 as to include a third duration common to both, or 
 (iii) are entirely separate. The excluded case is that of 
 two durations overlapping so as to include in common 
 an aggregate of finite events but including in common 
 no other complete duration. The recognition of the 
 fact of an indefinite number of families of parallel 
 durations is what differentiates the concept of nature 
 here put forward from the older orthodox concept of 
 
IX] THE ULTIMATE PHYSICAL CONCEPTS 191 
 
 the essentially unique time-systems. Its divergence from 
 Einstein's concept of nature will be briefly indicated later. 
 
 The instantaneous spaces of a given time-system are 
 the ideal (non-existent) durations of zero temporal 
 thickness indicated by routes of approximation along 
 series formed by durations of the associated family. 
 Each such instantaneous space represents the ideal of 
 nature at an instant and is also a moment of time. Each 
 time-system thus possesses an aggregate of moments 
 belonging to it alone. Each event-particle lies in one 
 and only one moment of a given time-system. An event- 
 particle has three characters^ : (i) its extrinsic character 
 which is its character as a definite route of convergence 
 among events, (ii) its intrinsic character which is the 
 peculiar quality of nature in its neighbourhood, namely, 
 the character of the physical field in the neighbourhood, 
 and (iii) its position. 
 
 The position of an event-particle arises from the 
 aggregate of moments (no two of the same family) in 
 which it lies. We fix our attention on one of these 
 moments which is approximated to by the short dura- 
 tion of our immediate experience, and we express 
 position as the position in this moment. But the event- 
 particle receives its position in moment M in virtue of 
 the whole aggregate of other moments M\ M" , etc., 
 in which it also lies. The differentiation of M into a 
 geometry of event-particles (instantaneous points) ex- 
 presses the diflferentiation of M by its intersections with 
 moments of alien time-systems. In this way planes and 
 straight lines and event-particles themselves find their 
 being. Also the parallelism of planes and straight lines 
 arises from the parallelism of the moments of one and 
 ^ Of. pp. 82 et seq. 
 
192 THE CONCEPT OF NATURE [ch. 
 
 the same time-system intersecting M, Similarly the 
 order of parallel planes and of event-particles on straight 
 lines arises from the time-order of these intersecting 
 moments. The explanation is not given here^. It is 
 sufficient now merely to mention the sources from which 
 the whole of geometry receives its physical explanation. 
 
 The correlation of the various momentary spaces of 
 one time-system is achieved by the relation of cogre- 
 dience. Evidently motion in an instantaneous space is 
 unmeaning. Motion expresses a comparison between 
 position in one instantaneous space with positions in 
 other instantaneous spaces of the same time-system. 
 Cogredience yields the simplest outcome of such com- 
 parison, namely, rest. 
 
 Motion and rest are immediately observed facts. 
 They are relative in the sense that they depend on the 
 time-system which is fundamental for the observation. 
 A string of event-particles whose successive occupation 
 means rest in the given time-system forms a timeless 
 point in the timeless space of that time-system. In this 
 way each time-system possesses its own permanent 
 timeless space peculiar to it alone, and each such space 
 is composed of timeless points which belong to that 
 time-system and to no other. The paradoxes of rela- 
 tivity arise from neglecting the fact that different as- 
 sumptions as to rest involve the expression of the facts 
 of physical science in terms of radically different spaces 
 and times, in which points and moments have different 
 meanings. 
 
 The source of order has already been indicated and 
 that of congruence is now found. It depends on motion. 
 
 1 Of. Principles of Natural Knowledge^ and previous chapters 
 of the present work. 
 
IX] THE ULTIMATE PHYSICAL CONCEPTS 193 
 
 From cogredience, perpendicularity arises; and from 
 perpendicularity in conjunction with the reciprocal 
 symmetry between the relations of any two time-systems 
 congruence both in time and space is completely defined 
 (cf. loc, cit.). 
 
 The resulting formulae are those for the electro- 
 magnetic theory of relativity, or, as it is now termed, the 
 restricted theory. But there is this vital difference: the 
 critical velocity c which occurs in these formulae has 
 now no connexion whatever with light or with any 
 other fact of the physical field (in distinction from the 
 extensional structure of events). It simply marks the 
 fact that our congruence determination embraces both 
 times and spaces in one universal system, and therefore 
 if two arbitrary units are chosen, one for all spaces and 
 one for all times, their ratio will be a velocity which is a 
 fundamental property of nature expressing the fact that 
 times and spaces are really comparable. 
 
 The physical properties of nature are expressed in 
 terms of material objects (electrons, etc.). The physical 
 character of an event arises from the fact that it belongs 
 to the field of the whole complex of such objects. From 
 another point of view we can say that these objects are 
 nothing else than our way of expressing the mutual 
 correlation of the physical characters of events. 
 
 The spatio-temporal measurableness of nature arises 
 from (i) the relation of extension between events, and 
 (ii) the stratified character of nature arising from each of 
 the alternative time-systems, and (iii) rest and motion, 
 as exhibited in the relations of finite events to time- 
 systems. None of these sources of measurement depend 
 on the physical characters of finite events as exhibited 
 by the situated objects. They are completely signified 
 
 W. N. 13 
 
194 THE CONCEPT OF NATURE [ch. 
 
 for events whose physical characters are unknown. Thus 
 the spatio-temporal measurements are independent of 
 the objectival physical characters. Furthermore the 
 character of our knowledge of a whole duration, which 
 is essentially derived from the significance of the part 
 within the immediate field of discrimination, constructs 
 it for us as a uniform whole independent, so far as its 
 extension is concerned, of the unobserved characters 
 of remote events. Namely, there is a definite whole of 
 nature, simultaneously now present, whatever may be 
 the character of its remote events. This consideration 
 reinforces the previous conclusion. This conclusion 
 leads to the assertion of the essential uniformity of the 
 momentary spaces of the various time-systems, and 
 thence to the uniformity of the timeless spaces of which 
 there is one to each time-system. 
 
 The analysis of the general character of observed 
 nature set forth above aflFords explanations of various 
 fundamental observational facts: (a) It explains the 
 differentiation of the one quality of extension into time 
 and space. (^S) It gives a meaning to the observed facts 
 of geometrical and temporal position, of geometrical 
 and temporal order, and of geometrical straightness and 
 planeness. (y) It selects one definite system of congruence 
 embracing both space and time, and thus explains the 
 concordance as to measurement which is in practice 
 attained. (S) It explains (consistently with the theory of 
 relativity) the observed phenomena of rotation, e.g. 
 Foucault's pendulum, the equatorial bulge of the earth, 
 the fixed senses of rotation of cyclones and anticyclones, 
 and the gyro-compass. It does this by its admission of 
 definite stratifications of nature which are disclosed by 
 the very character of our knowledge of it. (c) Its ex- 
 
IX] THE ULTIMATE PHYSICAL CONCEPTS 195 
 
 planations of motion are more fundamental than those 
 expressed in (8) ; for it explains what is meant by motion 
 itself. The observed motion of an extended object is 
 the relation of its various situations to the stratification 
 of nature expressed by the time-system fundamental to 
 the observation. This motion expresses a real relation 
 of the object to the rest of nature. The quantitative 
 expression of this relation will vary according to the 
 time-system selected for its expression. 
 
 This theory accords no peculiar character to light 
 beyond that accorded to other physical phenomena such 
 as sound. There is no ground for such a differentiation. 
 Some objects we know by sight only, and other objects 
 we know by sound only, and other objects we observe 
 neither by light nor by sound but by touch or smell or 
 otherwise. The velocity of light varies according to its 
 medium and so does that of sound. Light moves in 
 curved paths under certain conditions and so does 
 sound. Both light and sound are waves of disturbance 
 in the physical characters of events ; and (as has been 
 stated above, p. 188) the actual course of the light 
 is of no more importance for perception than is the 
 actual course of the sound. To base the whole philo- 
 sophy of nature upon light is a baseless assumption. 
 The Michelson-Morley and analogous experiments 
 show that within the limits of our inexactitude of 
 observation the velocity of light is an approximation to 
 the critical velocity ^ c^ which expresses the relation 
 between our space and time units. It is provable that 
 the assumption as to light by which these experiments 
 and the influence of the gravitational field on the light- 
 rays are explained is deducible as an approximation 
 from the equations of the electromagnetic field. This 
 
196 THE CONCEPT OF NATURE [ch. 
 
 completely disposes of any necessity for differentiating 
 light from other physical phenomena as possessing 
 any peculiar fundamental character. 
 
 It is to be observed that the measurement of extended 
 nature by means of extended objects is meaningless 
 apart from some observed fact of simultaneity inherent 
 in nature and not merely a play of thought. Otherwise 
 there is no meaning to the concept of one presentation 
 of your extended measuring rod AB. Why not AB' 
 where B' is the end B five minutes later ? Measurement 
 presupposes for its possibility nature as a simultaneity, 
 and an observed object present then and present now. 
 In other words, measurement of extended nature re- 
 quires some inherent character in nature affording a 
 rule of presentation of events. Furthermore congruence 
 cannot be defined by the permanence of the measuring 
 rod. The permanence is itself meaningless apart from 
 some immediate judgment of self-congruence. Other- 
 wise how is an elastic string differentiated from a rigid 
 measuring rod? Each remains the same self-identical 
 object. Why is one a possible measuring rod and the 
 other not so ? The meaning of congruence lies beyond 
 the self-identity of the object. In other words measure- 
 ment presupposes the measurable, and the theory of the 
 measurable is the theory of congruence. 
 
 Furthermore the admission of stratifications of nature 
 bears on the formulation of the laws of nature. It has 
 been laid down that these laws are to be expressed in 
 differential equations which, as expressed in any general 
 system of measurement, should bear no reference to 
 any other particular measure-system. This requirement 
 is purely arbitrary. For a measure-system measures 
 something inherent in nature; otherwise it has no 
 
IX] THE ULTIMATE PHYSICAL CONCEPTS 197 
 
 connexion with nature at all. And that something which 
 is measured by a particular measure-system may have a 
 special relation to the phenomenon whose law is being 
 formulated. For example the gravitational field due to 
 a material object at rest in a certain time-system may 
 be expected to exhibit in its formulation particular 
 reference to spatial and temporal quantities of that 
 time-system. The field can of course be expressed in 
 any measure-systems, but the particular reference will 
 remain as the simple physical explanation. 
 
 NOTE: ON THE GREEK CONCEPT OF A POINT 
 
 The preceding pages had been passed for press before I had 
 the pleasure of seeing Sir T. L. Heath's Euclid in Greek^. 
 In the original Euclid's first definition is 
 
 a-rjfjLelov iaTCVy ov fiipof; ovdev. 
 I have quoted it on p. 86 in the expanded form taught to me 
 in childhood, * without parts and without magnitude.' I should 
 have consulted Heath's English edition — a classic from the 
 moment of its issue — before committing myself to a statement 
 about Euclid. This is however a trivial correction not affecting 
 sense and not worth a note. I wish here to draw attention to 
 Heath's own note to this definition in his Euclid in Greek. He 
 summarises Greek thought on the nature of a point, from the 
 Pythagoreans, through Plato and Aristotle, to Euclid. My 
 analysis of the requisite character of a point on pp. 89 and 
 90 is in complete agreement with the outcome of the Greek 
 discussion. 
 
 NOTE: ON SIGNIFICANCE AND INFINITE EVENTS 
 
 The theory of significance has been expanded and made more 
 definite in the present volume. It had already been introduced 
 in the Principles of Natural Knowledge (cf. subarticles 3-3 to 
 3-8 and i6-i, 16-2, 19-4, and articles 20, 21). In reading over the 
 proofs of the present volume, I come to the conclusion that in the 
 
 1 Camb. Univ. Press, 1920. 
 
 13—3 
 
198 THE CONCEPT OF NATURE [ch.ix 
 
 light of this development my limitation of infinite events to dura- 
 tions is untenable. This limitation is stated in article 33 of the 
 Principles and at the beginning of Chapter IV (p. 74) of this book. 
 There is not only a significance of the discerned events embracing 
 the whole present duration, but there is a significance of a cogre- 
 dient event involving its extension through a whole time-system 
 backwards and forwards. In other words the essential ' beyond' 
 in nature is a definite beyond in time as well as in space [cf. 
 pp. 53, 194]. This follows from my whole thesis as to the assimila- 
 tion of time and space and their origin in extension. It also has 
 the same basis in the analysis of the character of our knowledge 
 of nature. It follows from this admission that it is possible to 
 define point-tracks [i.e. the points of timeless spaces] as abstrac- 
 tive elements. This is a great improvement as restoring the 
 balance between moments and points. I still hold however to the 
 statement in subarticle 35-4 of the Principles that the intersection 
 of a pair of non-parallel durations does not present itself to us as 
 one event. This correction does not affect any of the subsequent 
 reasoning in the two books. 
 
 I may take this opportunity of pointing out that the ' stationary 
 events' of article 57 of the Principles are merely cogredient 
 events got at from an abstract mathematical point of view. 
 
INDEX 
 
 In the case of terms of frequent occurrence, only those occurrences are 
 indexed which are of peculiar importance for the elucidation of meaning. 
 
 A [or an], ii 
 
 Abraham, 105 
 
 Absolute position, 105, 106, 114, 
 
 188 
 Abstraction, 33, 37, 168, 171, 173; 
 
 extensive, 65, 79, 85 
 Abstractive element, 84; set, 61, 
 
 79 
 Action at a distance, 159, 190 
 Action by transmission, 159, 190 
 Active conditions, 158 
 Activity, field of, 170, 181 
 Adjunction, loi 
 Aggregate, 23 
 Alexander, Prof., viii 
 Alexandria, 71 
 Alfred the Great, 137 
 Anticipation, 69 
 Anti-prime, 88 
 Apparent nature, 31, 39 
 Area, 99; momental, 103; vagrant, 
 
 103 
 Aristotelian logic, 150 
 Aristotle, 16, 17, 18, 24, 197 
 Associate-potential, 183 
 Atom, 17 
 
 Attribute, 21, 26, 150 
 Awareness, 3 
 Axiom, 36, 121 
 Axioms of congruence, 128 at seqq. 
 
 Bacon, Francis, 78 
 Behaviouristic, 185 
 Bergson, 54 
 Berkeley, 28 
 Between, 64 
 Beyond, 186, 198 
 Bifurcation, vi, 30, 185, 187 
 Boundary, 100; moment, 63; par- 
 ticle, 100 
 Broad, C. D., viii 
 
 Calculation, formula of, 45, 158 
 Cambridge, 97 
 Causal nature, 31, 39 
 Causation, 31, 146 
 Centrifugal force, 138 
 Change, uniformity of, 140 
 
 Character, extrinsic, 82, 89, 90, 113, 
 191; intrinsic, 80, 82, 90, 113, 191 
 
 Charge, 160 
 
 Closure of nature, 4 
 
 Coefficient of drag, 133 
 
 Coefficients of impetus, 183 
 
 Cogredience, no, 188 
 
 Coherence, 29 
 
 Comparison, 124, 125, 143, 189 
 
 Complex, 13 
 
 Conceptual nature, 45; space, 96 
 
 Concrete facts, 167, 171, 189 
 
 Conditioning events, 152 
 
 Conditions, active, 158 
 
 Congruence, 65, 96, 118, 120, 127, 196 
 
 Continuity, 157; Dedekindian, 102; 
 of events, 76; of nature, 59, 76 
 
 Convention, 121 
 
 Convergence, 62, 79; law of, 82 
 
 Conveyance, 154, 155 
 
 Co-present, 177 
 
 Covering, 83 
 
 Creative advance, 178 
 
 Critical velocity, 193, 195 
 
 Curvature of space- time, 182 
 
 Cyclone, 194 
 
 Dedekindian continuity, 102 
 Definite, 53, 194, 198 
 Delusions, 31, 38 
 Delusive perceptual object, 153 
 Demarcation of events, 144 
 Demonstrative phrase, 6 
 Descriptive phrase, 6, 10 
 Differential equations, 196 
 Discrimination, 14, 50, 144 
 Diversification of nature, 15 
 Duddington, Mrs, 47 
 Duration, 37. 53. 55. 186 
 Durations, families of, 59, 73, 190 
 Dynamical axes, 138 
 
 Einstein, vii, 102, 131, 164, 165, 
 
 181, 182, 183, 184, 191 
 Electromagnetic field, 179 
 Electron, 30, 146, 158, 171 
 Element, 17; abstractive, 84 
 Elliptical phraseology, 7 
 
200 
 
 INDEX 
 
 Empty space, 145 
 
 Entity, 5, 13 
 
 Equal in abstractive force, 83 
 
 Error, 68 
 
 Ether, 18, 78, 160; material, 78; 
 of events, 78 
 
 Euclid, 85, 94, 197 
 
 Euler, 140 
 
 Event, 15, 52, 75, 165; percipient, 
 107, 152, 186 
 
 Event-particle, 86, 93, 94, 172, 191 
 
 Events, conditioning, 152; con- 
 tinuity of, 76; demarcation of, 
 144; ether of, 78; infinite, 197, 
 198; limited, 74; passage of, 34; 
 signified, 52; stationary, 198; 
 stream of, 167; structure of, 52, 
 166 
 
 Exclusion, 186 
 
 Explanation, 97, 141 
 
 Extended nature, 196 
 
 Extension, 22, 58, 75, 185 
 
 Extensive abstraction, 65, 79, 85 
 
 Extrinsic character, 82, 89, 90, 113, 
 191; properties, 62 
 
 Fact, 12, 13 
 
 Factors, 12, 13, 15 
 
 Facts, concrete, 167, 171 
 
 Family of durations, 59, 63, 73; of 
 
 moments, 63 
 Faraday, 146 
 Field, gravitational, 197; of activity, 
 
 170, 181; physical, 190 
 Finite truths, 12 
 Fitzgerald, 133 
 
 Formula of calculation, 45, 158 
 Foucault, 138, 194 
 Four-dimensional manifold, 86 
 Fresnel, 133 
 Future, the, 72, 177 
 
 Galileo, 139 
 
 Geometrical order, 194 
 
 Geometry, 36; metrical, 129 
 
 Gravitation, 179 et seqq. 
 
 Gravitational field, 197 
 
 Greek philosophy, 16; thought, 197 
 
 Gyro-compass, 194 
 
 Heath, Sir T. L., 197 
 Here, 107 
 
 Idealists, 70 
 
 Immediacy, 52; of perception, 72 
 
 Impetus, 181, 182; coefficients of, 
 
 183; integral, 183 
 Inclusion, 186 
 Individuality, 13 
 
 Infinite events, 197, 198 
 
 Inge, Dr, 48 
 
 Ingredient, 14 
 
 Ingression, 144, 145, 148, 152 
 
 Inherence, 8^ 
 
 Inside, 106 
 
 Instant, 33, 35, 57 
 
 Instantaneous plane, 91 ; present, 72 ; 
 
 spaces, 86, 90, 177 
 Instantaneousness, 56, 57 
 Intersection, locus of, 90 
 Intrinsic character, 80, 82, 90, 113, 
 
 191; properties, 62 
 Ionian thinkers, 19 
 Irrelevance, infinitude of, 12 
 Irrevocableness, 35, 37 
 It, 8 
 
 Julius Caesar, 36 
 Junction, 76, loi 
 
 Kinetic energy, 105; symmetry, 129 
 Knowledge, 28, 32 
 
 Lagrange, 140 
 
 Larmor, 131 
 
 Law of convergence, 82 
 
 Laws of motion, 137, 139; of nature, 
 
 196 
 Leibnizian monadology, 150 
 Level, 91, 92 
 Light, 195; ray of, 188; velocity of, 
 
 131 
 Limit, 57 
 
 Limited events, 74 
 Location, 160, 161 
 Locke, 27 
 
 Locus, 102; of intersection, 90 
 London, 97 
 
 Lorentz, H. A., 131, 133 
 Lossky, 47 
 
 Manifold, four-dimensional, 86; 
 
 space-time, 173 
 Material ether, 78; object, 169 
 Materialism, 43, 70 
 Matrix, 116 
 
 Matter, 16, 17, 19, 20, 26 
 Maxwell, 131, 133 
 Measurableness, 196; of nature, 193 
 Measurement, 96, 120, 174, 196; of 
 
 time, 65, 140 
 Measure-system, 196 
 Memory, 68 
 Metaphysics, 28, 32 
 Metrical geometry, 129 
 Michelson-Morley, 195 
 Milton, 35 
 Mind, 27, 28 
 
INDEX 
 
 201 
 
 Minkowski, viii, 131 
 
 Molecule, 32, 171 
 
 Moment, 57, 60, 88 
 
 Momental area, 103; route, 103 
 
 Momentum, 105 
 
 Motion, 105, 114, 117, 127, 188, 192 
 
 Multiplicity, 22 
 
 Natural philosophy, 29, 30 
 Natural science, philosophy of, 46 
 Nature, 3; apparent, 31, 39; causal, 
 
 31, 39; conceptual, 45; continuity 
 
 of, 59, 76; discrimination of, 144; 
 
 extended, 196; laws of, 196; 
 
 passage of, 54; stratification of, 
 
 194, 196; system of, 146 
 Newton, 27, 136, 139, 140 
 
 Object, 77, 125, 143, 169, 189; 
 delusive perceptual, 155; material, 
 169; perceptual, 153; physical, 
 155. ''^57> scientific, 158, 169; uni- 
 form, 162 
 
 Occupation, 22, 34, 36, 100, loi 
 
 Order, source of, 192; spatial, 95, 
 194; temporal, 64, 95, 194 
 
 Organisation of thought, 79 
 
 Outside, 63, 100 
 
 Paradox, 192 
 
 Parallel, 63, 127; durations, 190 - 
 
 Parallelism, 95, 191 
 
 Parallelogram, 127 
 
 Paris, 87, 138 
 
 Parliament, 120 
 
 Part, 14, 15, 58 
 
 Passage of events, 34; of nature, 54 
 
 Past, the, 72, 177 
 
 Perception, 3 
 
 Perceptual objects, 149, 153 
 
 Percipience, 28 
 
 Percipient event, 107, 152, 186, 187 
 
 Period of time, 51 
 
 Permanence, 144 
 
 Perpendicularity, 117, 127, 193 
 
 Philosophy, i ; natural, 29, 30 ; of 
 
 natural science, 46 ; of the sciences, 
 
 2 
 Physical field, 190; object, 155, 156, 
 
 157 
 Physics, speculative, 30 
 Place, 51 
 
 Plane, 191; instantaneous, 91 
 Plato, 16, 17, 18, 24, 197 
 Poincare, 121, 122, 123 
 Point, 35, 89,^91, 114, 173, 176 
 Point-flash, 172, 173 
 Point of space, 85 
 Point, timeless, 192 
 
 Point- track, 113, 198 
 
 Pompey, 36 
 
 Position, 89, 90, 92, 93, 99, 113, 191 J 
 absolute, 105, 106, 114, 188 
 
 Potential, 183; associate-, 183 
 
 Predicate, 18 
 
 Predication, 18 
 
 Present, the, 69, 72, 177; instan- 
 taneous, 72; observational, 186 
 
 Primary qualities, 27 
 
 Prime, 88 
 
 Process, 53, 54; of nature, 54 
 
 Psychic additions, 29, 187 
 
 Punct, 92, 93, 94 
 
 Pythagoreans, 197 
 
 Quality, 27 
 Quantum of time, 162 
 Quantum theory, 162 
 
 Ray of light, 188 
 
 Reality, 30; of durations, 55, 187 
 
 Recognition, 124, 143, 189 
 
 Rect, 91, 92 
 
 Recurrence, 35 
 
 Relative motion, 117; velocity, 130 
 
 Relativity, 169; restricted theory 
 
 of, 193 
 Rest, 105, 114, 188, 192 
 Rotation, 138, 194 
 Route, 99; momental, 103; straight, 
 
 103 
 Russell, Bertrand, 11, 122, 123 
 
 Schelling, 47 
 
 Science, 2; metaphysical, 32 
 Scientific objects, 149, 158, 169 
 Secondary qualities, 27 
 Self-congruence, 196 
 Self-containedness of nature, 4 
 Sense-awareness, 3, 67 
 Sense-object, 149, 170 
 Sense-perception, 3, 14 
 Sense-recognition, 143, 189 
 Series, temporal, 66, 70, 85, 178 
 Set, abstractive, 61, 79 
 Significance, 51, 186, 187, 188, 194, 
 
 197, 198 
 Signified events, 52 
 Simplicity, 163, 173 
 Simultaneity, 53, 56, 196 
 Situation, 15, 78, 147, 148, 152, 160, 
 
 189 
 Solid, 99, loi, 102; vagrant, loi 
 Sound, 195 
 Space, 16, 17. 31.33, 79; empty, 145; 
 
 timeless, 86, 106, 114; uniformity 
 
 of, 194 
 Spaces, instantaneous, 86, 90 
 
202 
 
 INDEX 
 
 Space-system, 179 
 Space- time manifold, 173 
 Spatial-order, 95 
 Spatio-temporal structure, 173 
 Speculative demonstration, 6 
 Speculative physics, 30 
 Standpoint for perception, 107, 188 
 Station, 103, 104, 113 
 Stationary events, 198 
 Straight line, 91, 114, 191; route, 
 
 103 
 Stratification of nature, 187, 194, 
 
 196 
 Stream of events, 167 
 Structure of events, 52, 166 
 Structure, spatio-temporal, 173 
 Subject, 18 
 
 Substance, 16, 18, 19, 150 
 Substratum, 16, 18, 21 
 Symmetry, 118, 126; kinetic, 129 
 System of nature, 146 
 System, time-, 192 
 
 Tamer, Edward, v, i 
 
 Temporal order, 64, 95, 194 
 
 Temporal series, 66, 70, 85 
 
 Tensor, 182 
 
 Terminus, 4 
 
 The, II 
 
 Theory, quantum, 162 
 
 There, no, 189 
 
 This, II 
 
 Thought, 3, 14 
 
 Timaeus, the, 17, 20, 24 
 
 Time, 16, 17, 31, 33, 49. 79; 
 
 measurement of, 140; quantum of, 
 
 162; transcendence of, 39 
 Time-series, 178, also cf. Temporal 
 
 series 
 Time-system, see Time-series, also 
 
 91, 97, 104, 179, 192 
 Timeless point, 192; space, 86, 106, 
 
 114. 177 
 Totality, 89 
 
 Transcendence of time, 39 
 Transmission, 26, 28; action by, 159, 
 
 190 
 Tubes of force, 146 
 
 Unexhaustiveness, 50 
 Uniform object, 162 
 Uniformity of change, 140; of space, 
 194 
 
 Vagrant area, 103 ; solid, loi 
 
 Veblen and Young, 36 
 
 Velocity, critical, 193, 195; of liglit, 
 
 131, 195; relative, 130 
 Volume, 92, 10 1 
 
 When, 107 
 Where, 107 
 Whole, 58 
 Within, 63 
 
 Young, Veblen and, 36 
 
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