i^i^lil-^-'^ i-^£i f^i'z-- 'A\^i~. '^'■-Vy V CORNELL UNIVERSITY LIBRARY BOUGHT WITH THE INCX)ME OF THE SAGE ENDOWMENT FUND GIVEN IN 1891 BY HENRY WILLIAMS SAGE _ Corneri University Library Q 175.W59C7 The concept of nature. 3 1924 012 068 593 Cornell University Library The original of this book is in the Cornell University Library. There are no known copyright restrictions in the United States on the use of the text. http://www.archive.org/cletails/cu31924012068593 THE CONCEPT OF NATURE CAMBRIDGE UNIVERSITY PRESS C. F. CLAY, Manager LONDON : FETTER LANE, E.G. 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 EIGHTS 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 Tamer 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 diiferent 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 I'KJil'AUli 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 explicitly 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- vui 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 Aristotelian 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. April, 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 W.N. I 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. 1] NATURE AND THOUGHT 3 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 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 expression of the fact that they are thought about. Thus in a sense nature is independent of thought. By 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 thjB'fact that nature is thought about. In such a case I shall say that we are thinking * hieterogeneously ' 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-perception has a factor which is not thought. I call this factor 'sense-awareness.' Accord- 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- perception are identical. But the something perceived is perceived as an entity which is the terminus of the sense-awareness, something which for thought is beyond the fact of that sense-awareness. Also the something perceived certainly does not contain other sense-awarenesses which are different from the sense- awareness which is an ingredient in that perception. Accordingly nature as disclosed in sense-perception is self-contained as against sense-awareness, in addition to being self-contained as against thought. I will also express this self-containedness of nature by saying that nature is closed to m'nd. 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^ Js_ disclosed as a compjex o^entities whose mutual relations I] NATURE AND THOUGHT 5 are_exBressibl e in thou ght without reference to mind, that is, withouLl^erence either to ae nse-awarene ss ore to ihoughL- 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 nature are perhaps the key to the metaphysical synthesis of existence. 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 vnth 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 'W 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 lo THE CONCEPT OF NATURE L*^"- he was in the lion-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. In fact, pure demonstration is impossible though 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. t] 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 1 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- positional 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 separate distinction of an entity in thought is not a metaphysical assertion, but a method of procedure necessary for the finite expression of individual 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, secondarily with properties and relations ascribed to them in the pro- cedure of thought ; the termini for sense-awareness are factors in the fact of nature, primarily relata and only secondarily discriminated as distinct individualities. 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 undiff"erentiated terminus of sense-awareness; factors are termini of sense-awareness, diff"erentiated as elements of fact ; entities are factors in their function as the ter- mini of thought. 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. Ithe relations holding between natural entities are 4hemselves 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 ii 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 Df nature. It is nature as an event present for sense- , iwareness, and essentially passing. There is no holding I] NATURE AND THOUGHT 15 nature still and looking at it. We cannot redouble our eiforts 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 jwithin thisraom^ 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 1 Cf. Enquiry. 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 kmd 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 has been degraded into an attribute of the entity. In this 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, but the very factor itself as bared in thought. 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 NATURE AND THOUGHT 17 hich the course of events could be expressed. We ay formulate this state of mind in the question, What nature made of? The answers which their genius ive to this question, and more particularly the con- ;pts which underlay the terms in which they framed leir answers, have determined the unquestioned pre- ippositions as to time, space and matter which have ;igned in science. In Plato the forms of thought are more fluid than in ristotle, and therefore, as I venture to think, the more iluable. Their importance consists in the evidence ley yield of cultivated thought about nature before it ad been forced into a uniform mould by the long adition of scientific philosophy. For example in the imaeus there is a presupposition, somewhat vaguely ^pressed, of a distinction between the general becoming F nature and the measurable time of nature. In a later :cture I have to distinguish between what I call the assage of nature and particular time-systems which sihibit certain characteristics of that passage. I will not so far as to claim Plato in direct support of this octrine, but I do think that the sections of the Timaeus 'hich deal with time become clearer if my distinction i admitted. This is however a digression. I am now concerned ith the origin of the scientific doctrine of matter in Jreek thought. In the Timaeus Plato asserts that nature 1 made of fire and earth with air and water as inter- lediate between them, so that ' as fire is to air so is air ) water, and as air is to water so is water to earth.' He [so suggests a molecular hypothesis for these four iements. In this hypothesis everything depends on the bape 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 science. It embodies concepts which any theory of natural philosophy must retain and in some sense must explain. Aristotle asked the fundamental question, 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 to 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 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 1] 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 20 THE CONCEPT OF NATURE [CH. philosophy passed on its way to the refined AristoteHan 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 criticism. My theory of the formation of the scientific 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 which 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 dentists where our toothache is. Thus space is not a relation 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 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 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 science, 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 that 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 [" in terms of the relations of a bit of matter with itsel] My own view is a behef in the relational theory both c space and of time, and of disbelief in the current fori] of the relational theory of space which exhibits bit of matter as the relata for spatial relations. The tru relata are events. The distinction which I have jus pointed out between time and space in their cormexio) with matter makes it evident that any assimilation o time and space cannot proceed along the traditional lin of taking matter as a fundamental element in space formation. The philosophy of nature took a wrong turn durinj its development by Greek thought. This erroneou presupposition is vague and fluid in Plato's Timaem The general groundwork of the thought is still un committed and can be construed as merely lacking du explanation and the guarding emphasis. But ii Aristotle's exposition the current conceptions wer hardened and made definite so as to produce a fault analysis of the relation between the matter and the forr of nature as disclosed in sense-awareness. In this phras 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 c matter enshrines some fundamental law of nature. An simple illustration will exemplify what I mean. Fo example, in a museum some specimen is locked securel in a glass case. It stays there for years : it loses its coloui and perhaps falls to pieces. But it is the same specimen and the same chemical elements and the same quantitie of those elements are present within the case at the en as were present at the beginning. Again the engines and the astronomer deal with the motions of real pei 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 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 deduced. It is the establishment of this procedure of 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 light 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 colom-s, 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. Thcijmmediate 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 #ense-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 ^ 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 may 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 phenom,enon. It is for natural philosophy to analyse how these various elements of nature are connected. In making this demand I conceive myself as adopting 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 philosophy 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 3° 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 reahty 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. 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—^ 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. 1910, vol. ii. 1917, 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- surdum' 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 disbeheves 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 the knowledge of the thing known instead of seeking 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 effluent 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 aliow 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 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 eifecting 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 sort of occurrences which are fitted to cause a mind to 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-theory of light has not been adopted because waves are just the sort of things which ought to make a mind perceive colours. This is no part of the 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 is sought by science is an understanding of relations 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 42 THE CONCEPT OF NATURE [ce apparent relata. Apparent nature is the dream, and th apparent relations of space are dream relations, and th space is the dream space. Similarly the space in whic] causal nature is set is the expression of certain rela tions between the causal objects. It is the expressioi of certain facts about the causal activity which is goinj on behind the scenes. Accordingly causal space belong to a different order of reality to apparent space. Henc there is no pointwise connexion between the two an( it is meaningless to say that the molecules of the gras are in any place which has a determinate spatial relatioi to the place occupied by the grass which we see. Thi conclusion is very paradoxical and makes nonsense o all scientific phraseology. The case is even worse if w admit the relativity of time. For the same argument apply, and break up time into the dream time and causa time which belong to different orders of reality. I have however been discussing an extreme form o the bifurcation theory. It is, as I think, the mos defensible form. But its very definiteness makes it th more evidently obnoxious to criticism. The intermediat form allows that the nature we are discussing is alway the nature directly known, and so far it rejects th bifurcation theory. But it holds that there are psychi additions to nature as thus known, and that thes additions are in no proper sense part of nature. Fo example, we perceive the red biUiard ball at its prope time, in its proper place, with its proper motion, wit its proper hardness, and with its proper inertia. Bi] its redness and its warmth, and the sound of the clic as a cannon is made off it are psychic additions, namely secondary qualities which are only the mind's wa of perceiving nature. This is not only the vaguel 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 lands 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 Jih^t, 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. TThus the molecules and electrons of scientific theory 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 task 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^ail to do so. But it is only evidence, and is not itself the metaphysicd 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 ScheUing 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., 1919. 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 1919. 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 W.N. 4 50 THE CONCEPT OFl^ATURE [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 coniplex 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 oflF 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 in] 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 rSle 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 time to extra-natural entities, (ii) For two 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 long as I succeed in explaining my meaning. Simul- taneity 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- in] TIME 57 pression in thought of properties of nature. Instan- ,y 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 i employs the concept of instantaneous nature, must abandon all claim to be founded upon observation. y[_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, i A moment is a limit to which we approach as we i j 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 'limit' 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. in] TIME 59 I The continuity of nature arises from extension. Every event extends over other events, and every event is 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 itAis 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 III] TIME 6 1 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 NATUKt i^^n. 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.' 1 Cf . An Enquiry concerning the Principles of Natural Knowledge, Cambridge University Press, 1919. Ill] TIME 6; The durations which enter into the composition o a moment all belong to one family. Thus there is on* family of moments corresponding to one family o durations. Also if we take two moments of the samt family, among the durations which enter into the com position of one moment the smaller durations ar( completely separated from the smaller durations whicl enter into the composition of the other moment. Thui the two moments in their intrinsic properties mus 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 tw( moments of the associated family of moments whicl are the boundary moments of that duration, t 'boundary moment' of a duration can be defined ii this way. There are durations of the same family as th( given duration which overlap it but are not containe( in it. Consider an abstractive set of such durations Such a set defines a moment which is just as mucl without the duration as within it. Such a moment is ; boundary moment of the duration. Also we call upoi our sense-awareness of the passage of nature to inforn us that there are two such boundary moments, namel; the earlier one and the later one. We will call them th( initial and the final boundaries. There are also moments of the same family such tha the shorter durations in their composition are entirely separated from the given duration. Such moments wil be said to lie ' outside' the given duration. Again othe 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 givei 64 THE CONCEPT OF NATURE lch. 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 ^ Cf . 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 Ul- IN A lURr- l— 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. There is time because there are happenings, and apart from 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 timeless 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 exceptby 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 in] 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 pre'sent fact ; and then from the side of mind. What is the di fference b et ween ^e present an d the past ! Yet witlTtHis 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- 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. Xber£j.s_3JiJiit£ll£ctuaiJJieacy,.o£jinie_as.^ rrvnying Vnifp-prlgf^^ 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^gresent us with a stretch of tim£ -as a marffl Q_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 thougljtj 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 70 THE CONCEPT OF NATURE [ch. that it is derivatively in time and in space by reason of the peculiar alliance of its passage vi^ith 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 ? 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 7 can be summarised as the belief that nature is an aggre gate of material and that this material exists in som sense at each successive member of a one-dimensiona series of extensionless instants of time. Furthermor the mutual relations of the material entities at eacl instant formed these entities into a spatial configuratioi in an unbounded space. It would seem that space — oi this theory — ^would be as instantaneous as the instants and that some explanation is required of the relation between the successive instantaneous spaces. Thi materialistic theory is however silent on this point and the succession of instantaneous spaces is tacitb combined into one persistent space. This theory is ; purely intellectual rendering of experience which ha had the luck to get itself formulated at the dawn o scientific thought. It has dominated the language an< the imagination of science since science flourished ii Alexandria, with the result that it is now hardly possibli to speak without appearing to assume its immediate obviousness. But when it is distinctly formulated in the abstrac terms in which I have just stated it, the theory is ver^ far from obvious. The passing complex of factors whicl compose the fact which is the terminus of sense-aware ness places before us nothing corresponding to thi 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) o: space which is the outcome of relations of matter. There is a wide gap between these presupposition! of the intellectual theory of materialism and the im mediate deliverances of sense-awareness. I do no 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 I in 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 lights 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 alter- native families. 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 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 limited 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. JWe perceive one unit factor in nature; and this factor is that something is going on then — there. For example, we 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 B, 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 ^ Of. Enquiry. IV] METHOD OF EXTENSIVE ABSTRACTION 77 inherent in the observed unity of an event, and these two definitions of junction are really axioms based on observation respecting the character of this con- tinuity. The relations of whole and part and of overlapping are particular cases of the junction of events. But it is possible for events to have junction when they are separate from each other; for example, the upper and the lower part of the Great Pyramid are divided by some imaginary horizontal plane. The continuity which nature derives from events has been obscured by the illustrations which I have been obliged to give. For example I have taken the existence of the Great Pyramid as a fairly well-known fact to which I could safely appeal as an illustration. This is a type of event which exhibits itself to us as the situation of a recognisable object ; and in the example chosen the object is so widely recognised that it has received a name. An object is an entity of a different type from an event. For example, the event which is the life of nature within 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 which is also called the Great Pyramid is the same object to-day as it was yesterday. I shall have to consider the theory of objects in another lecture. The whole subject is invested with an unmerited air of subtlety by the fact that when the event is the situation of a well-marked object, we have no language to distinguish the event from the object. In the case of the Great Pyramid, the object is the perceived unit entity which as perceived remains self-identical through- 78 THE CUNUErr~u¥~rnrTTTRc. l^^n. 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 — in the phraseo- logy which Bacon applied to the doctrine of final 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 important concept is that of the shifting facts of the 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 elsew^here ^ 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 B, 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 t}'pe 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, pp. 146 et seq. Williams and Norgate, 1917. 8o THE CONCEPT Ut JNAi uku l^«. event nor does it converge to a limiting event which is ftot 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 grovidng 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 has an intrinsic character in 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 e^, €2, e^, etc. be an abstractive set, the members being so arranged that each member such as e^ extends over all the suc- ceeding members such as e^+i, e^+^y and so on. Then corresponding to the series ^l> ^2' ^3' •••■> ^ni ^n + lf •••> there is the series Q (^i)> Q («2)> q (^3). •••> ? (en), q (e^+i), .... Call the series of events 5 and the series of quanti- tative expressions q (s). The series 5 has no last term and IV] METHOD OF EXTENSIVE ABSTRACTION 8i no events w^hich are contained in every member of the series. Accordingly the series of events converges to nothing. It is just itself. Also the series q {$) 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 {e^, and Q^ the homologue to Q^ to be found in q {e^, and Q^ the homologue to Q^ and Q^ to be found in q {e^, and so on, then the series yi> ^2' >CZy '"■> icny >^n+li •••> though it has no last term, does in general converge to a definite limit. Accordingly there is a class of limits l{s) w^hich is the class of the limits of those members of g'(e„) v^hich have homologues throughout the series q{s) as n indefinitely increases. We can represent this state- ment diagrammatically by using an arrow (-*) to mean 'converges to.' Then ei, e^, ^3, ..., Bn, e^+i, ... ■* nothing, and ?(«i). 9(^2)'? (^3). •■■,q(en),qien+i), ...^lis). The mutual relations betv^^een the limits in the set l{s), and also betvsreen these limits and the limits in other sets l{s'), lis"), ..., v^hich arise from other abstractive sets s', s", etc., have a pecuHar simplicity. Thus the set 5 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 simplicity 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. 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 bafiles 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 oie. 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 L^h. of this equality of abstractive sets arises from the fact that both sets, p and q, are infinite series towards their small ends. Thus the equality means, that given any event x belonging to ^, 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 of jy, 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^ 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 limit by the use of the principle of convergence to simplicity by diminution of extent. When an abstractive element A covers an abstractive element B, the intrinsic character oi A in a. sense includes the intrinsic character of 5. 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. EucHd 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 hiving 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 vdth 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 a 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 a be the name of any condition which some abstractive sets fulfil. I say that an abstractive set is 1 Cf. 'La Thdorie Relationniste de I'Espace,' Rev. de MSta- physique et de Morale, vol. xxiii, 1916. 88 THE CONCEPT OF NATURE [ch. * a -prime' when it has the two properties, (i) that it satisfies the condition o 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 a -prime. There are also the correlative abstractive sets which I call the sets of a-antiprimes. An abstractive set is a cr -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 a which exhibits an intrinsic character more complex than that of a CT -antiprime. The intrinsic character of a o-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 «T 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 p2y p3' Pi) be a set of measurements of this system, then the event-particle which is thus deter- mined will be said to have pi, p2y Psy Pi ^s 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 (/>!, p2y pz, Pi) 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 (pi, p^, p^) determined a point in space and that the event-particle happened at that point at the time ^4. 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, p^, p^) of the space in the ^-system is merely the collection of event-particles {pi, p^, pz^ [pj)? where ^4 is varied and (Pi, p2, ps) 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 i9i> ?2> 93) 9i) determines an event-particle, and (?!> ?2J ^3) determines a point and q^ 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 p-space for the land-surveyor on earth. vni] SUMMARY 177 So far in speaking of space we liave been talking of the timeless space of physical science, namely, of our concept of eternal space in which 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 p^, 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 12 178 THE CONCEPT OF NAi UKii l^«. 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 A to B 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 vin] 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 however. Suppose we 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 12 — 2 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 uni- 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^, J^^ (- J21), J^^, J23 (= Jzz)^ 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 theory of tensors created a veritable panic among them when the verification of Einstein's predictions was first announced. vin] SUMMARY 183 The ten J's at any event-particle E can be expressed in terms of two functions which 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 tht motion of light along its rays, as a first approximation 1 84 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 affect 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 l86 THE CONCEPT OF NATURE L^h. 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 2 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, that 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, igS. ^ Cf. Ch. in, 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 pecuhar characters of different events depends upon our power of comparison. I call the exercise of this factorinour 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 I90 THE CONCEPT OF N ATI DTTE [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 diflFerentiation of M into a geometry of event-particles (instantaneous points) ex- presses the differentiation 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 ^ Cf. pp. 82 et seq. 192 THE CONCEPT Ol^ r^ A lUKu i^n. 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. ^ Cf. 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 (tf. 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. ^3 194 THE CONCEPT OF NATURE L^h. 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 affords explanations of various fundamental observational facts: (a) It explains the differentiation of the one quality of extension into time and space. (j8) 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. (e) Its ex- IX] THE ULTIMATE PHYSICAL CONCEPTS 195 planations of motion are more fundamental than those expressed in (S) ; 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^xpression. 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 CONCEFl Ut JNAlUKii l^«. 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 (TTjfjLelov icTTtv, ov fiepo<; ovOev. 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 JNAlUKJi L^n. .^ 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 \pr an], ii Abraham, 105 Absolute position, 105, 106, 114, 188 Abstraction, 33, 37, 168, ryi, 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 et 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, 8g, go, 113, 191; intrinsic, 80, 82,90, 113, 191 Charge, 160 Closure of nature, 4 Coefficient of drag, 133 Coefficients of impetus, 183 Cogredience, no, i88 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, i8i, 182, 183, 184, 191 Electromagnetic field, 179 Electron, 30, 146, 158, 171 Element, 17; abstractive, 84 Elliptical phraseology, 7 200 liMJJlA 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, 83 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 20 1 Minkowski, viii, 131 Molecule, 32, 171 Moment, 57, 60, 88 Momenta! 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. 157; 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 Parallslogram, 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; absolute, 105, 106, 114, 188 Potential, 183; associate-, 183 Predicate, 18 Predication, 18 Present, the, 69, 72, 177; instan- taneous, 72; observational, i85 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 ReaUty, 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 Schelhng, 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 SimpUcity, 163, 173 Simultaneity, 53, 56, 196 Situation, 15, 78, 147, 148, 152, 160, 189 Solid, 99, loi, 102; vagrant, 101 Sound, 195 Space, 16, 17, 31.33. 79; empty, 145; timeless, 86, 106, 114; uniformity of, 194 Spaces, instantaneous, 86, 90 202 liN L»r