{"collection":"philosophy-ethics","full_text_available":true,"graph_url":"https://unchartedknowledge.5gfusion.net/v2/api/page/gutenberg_18835/graph","html_url":"https://unchartedknowledge.5gfusion.net/v2/page/gutenberg_18835","id":"gutenberg_18835","license":"Public Domain (US)","rights_basis":"gutenberg_metadata_copyright_false","source":"gutenberg","source_url":"https://www.gutenberg.org/ebooks/18835","summary":null,"tags":["Category: Philosophy & Ethics","Category: Science - Physics","Knowledge, Theory of","Nature","Science -- Philosophy"],"text":"Produced by Janet Kegg, Laura Wisewell and the Online\nDistributed Proofreading Team at http://www.pgdp.net\n\n\n\n\n\n\n  +------------------------------------------------------------------+\n  |                                                                  |\n  | Transcriber's Note: In the parts containing mathematical         |\n  | notation, superscripts are denoted using a carat and subscripts  |\n  | using underscores, for example x^2, e_1, e_{n+1}. Greek          |\n  | letters used as symbols are written out, for example {sigma},    |\n  | but the one Greek phrase has been transliterated. All of these   |\n  | special characters are preserved in the UTF-8 and HTML versions  |\n  | of this ebook.                                                   |\n  |                                                                  |\n  | Italicised words are marked using underscores _like this_, but   |\n  | the letters used in the mathematics (which were all in italic    |\n  | font) have not been marked, to aid legibility and to avoid       |\n  | confusion with the subscripts.                                   |\n  |                                                                  |\n  | Two printer errors have been corrected. These are:               |\n  |                                                                  |\n  | \"...relating the entity discriminated by sight with that         |\n  | discriminated by [sight]...\" sight has been changed to touch as  |\n  | suggested by the sense.                                          |\n  |                                                                  |\n  | \"...[universely] proportional to...\" universely has been changed |\n  | to inversely.                                                    |\n  |                                                                  |\n  +------------------------------------------------------------------+\n\n\n\n\n                            The Concept of\n\n\n                                NATURE\n\n\n                         THE TARNER LECTURES\n                     DELIVERED IN TRINITY COLLEGE\n                            NOVEMBER 1919\n\n\n                        Alfred North Whitehead\n\n\n\n\nPREFACE\n\n\nThe contents of this book were originally delivered at Trinity College\nin the autumn of 1919 as the inaugural course of Tarner lectures. The\nTarner lectureship is an occasional office founded by the liberality of\nMr Edward Tarner. The duty of each of the successive holders of the post\nwill be to deliver a course on 'the Philosophy of the Sciences and the\nRelations or Want of Relations between the different Departments of\nKnowledge.' The present book embodies the endeavour of the first\nlecturer of the series to fulfil his task.\n\nThe chapters retain their original lecture form and remain as delivered\nwith the exception of minor changes designed to remove obscurities of\nexpression. The lecture form has the advantage of suggesting an audience\nwith a definite mental background which it is the purpose of the lecture\nto modify in a specific way. In the presentation of a novel outlook with\nwide ramifications a single line of communications from premises to\nconclusions is not sufficient for intelligibility. Your audience will\nconstrue whatever you say into conformity with their pre-existing\noutlook. For this reason the first two chapters and the last two\nchapters are essential for intelligibility though they hardly add to the\nformal completeness of the exposition. Their function is to prevent the\nreader from bolting up side tracks in pursuit of misunderstandings. The\nsame reason dictates my avoidance of the existing technical terminology\nof philosophy. The modern natural philosophy is shot through and\nthrough with the fallacy of bifurcation which is discussed in the second\nchapter of this work. Accordingly all its technical terms in some subtle\nway presuppose a misunderstanding of my thesis. It is perhaps as well to\nstate explicitly that if the reader indulges in the facile vice of\nbifurcation not a word of what I have here written will be intelligible.\n\nThe last two chapters do not properly belong to the special course.\nChapter\u00a0VIII is a lecture delivered in the spring of 1920 before the\nChemical Society of the students of the Imperial College of Science and\nTechnology. It has been appended here as conveniently summing up and\napplying the doctrine of the book for an audience with one definite type\nof outlook.\n\nThis volume on 'the Concept of Nature' forms a companion book to my\nprevious work _An Enquiry concerning the Principles of Natural\nKnowledge_. Either book can be read independently, but they supplement\neach other. In part the present book supplies points of view which were\nomitted from its predecessor; in part it traverses the same ground with\nan alternative exposition. For one thing, mathematical notation has been\ncarefully avoided, and the results of mathematical deductions are\nassumed. Some of the explanations have been improved and others have\nbeen set in a new light. On the other hand important points of the\nprevious work have been omitted where I have had nothing fresh to say\nabout them. On the whole, whereas the former work based itself chiefly\non ideas directly drawn from mathematical physics, the present book\nkeeps closer to certain fields of philosophy and physics to the\nexclusion of mathematics. The two works meet in their discussions of\nsome details of space and time.\n\nI am not conscious that I have in any way altered my views. Some\ndevelopments have been made. Those that are capable of a\nnon-mathematical exposition have been incorporated in the text. The\nmathematical developments are alluded to in the last two chapters. They\nconcern the adaptation of the principles of mathematical physics to the\nform of the relativity principle which is here maintained. Einstein's\nmethod of using the theory of tensors is adopted, but the application is\nworked out on different lines and from different assumptions. Those of\nhis results which have been verified by experience are obtained also by\nmy methods. The divergence chiefly arises from the fact that I do not\naccept his theory of non-uniform space or his assumption as to the\npeculiar fundamental character of light-signals. I would not however be\nmisunderstood to be lacking in appreciation of the value of his recent\nwork on general relativity which has the high merit of first disclosing\nthe way in which mathematical physics should proceed in the light of the\nprinciple of relativity. But in my judgment he has cramped the\ndevelopment of his brilliant mathematical method in the narrow bounds of\na very doubtful philosophy.\n\nThe object of the present volume and of its predecessor is to lay the\nbasis of a natural philosophy which is the necessary presupposition of a\nreorganised speculative physics. The general assimilation of space and\ntime which dominates the constructive thought can claim the independent\nsupport of Minkowski from the side of science and also of succeeding\nrelativists, while on the side of philosophers it was, I believe, one\ntheme of Prof. Alexander's Gifford lectures delivered some few years ago\nbut not yet published. He also summarised his conclusions on this\nquestion in a lecture to the Aristotelian Society in the July of 1918.\nSince the publication of _An Enquiry concerning the Principles of\nNatural Knowledge_ I have had the advantage of reading Mr C.\u00a0D. Broad's\n_Perception, Physics, and Reality_ [Camb. Univ. Press, 1914]. This\nvaluable book has assisted me in my discussion in Chapter\u00a0II, though I\nam unaware as to how far Mr Broad would assent to any of my arguments as\nthere stated.\n\nIt remains for me to thank the staff of the University Press, its\ncompositors, its proof-readers, its clerks, and its managing officials,\nnot only for the technical excellence of their work, but for the way\nthey have co-operated so as to secure my convenience.\n\nA.\u00a0N.\u00a0W.\n\n    IMPERIAL COLLEGE OF SCIENCE\n        AND TECHNOLOGY.\n            _April_, 1920.\n\n\n\n\nCONTENTS\n\n\n   CHAP.                                                  PAGE\n\n       I NATURE AND THOUGHT                                  1\n\n      II THEORIES OF THE BIFURCATION OF NATURE              26\n\n     III TIME                                               49\n\n      IV THE METHOD OF EXTENSIVE ABSTRACTION                74\n\n       V SPACE AND MOTION                                   99\n\n      VI CONGRUENCE                                        120\n\n     VII OBJECTS                                           143\n\n    VIII SUMMARY                                           164\n\n      IX THE ULTIMATE PHYSICAL CONCEPTS                    185\n\n         NOTE: ON THE GREEK CONCEPT OF A POINT             197\n\n         NOTE: ON SIGNIFICANCE AND INFINITE EVENTS         197\n\n         INDEX                                             199\n\n\n\n\nTHE CONCEPT OF NATURE\n\n\n\n\nCHAPTER I\n\nNATURE AND THOUGHT\n\n\nThe subject-matter of the Tarner lectures is defined by the founder to\nbe 'the Philosophy of the Sciences and the Relations or Want of\nRelations between the different Departments of Knowledge.' It is fitting\nat the first lecture of this new foundation to dwell for a few moments\non the intentions of the donor as expressed in this definition; and I do\nso the more willingly as I shall thereby be enabled to introduce the\ntopics to which the present course is to be devoted.\n\nWe are justified, I think, in taking the second clause of the definition\nas in part explanatory of the earlier clause. What is the philosophy of\nthe sciences? It is not a bad answer to say that it is the study of the\nrelations between the different departments of knowledge. Then with\nadmirable solicitude for the freedom of learning there is inserted in\nthe definition after the word 'relations' the phrase 'or want of\nrelations.' A disproof of relations between sciences would in itself\nconstitute a philosophy of the sciences. But we could not dispense\neither with the earlier or the later clause. It is not every relation\nbetween sciences which enters into their philosophy. For example biology\nand physics are connected by the use of the microscope. Still, I may\nsafely assert that a technical description of the uses of the microscope\nin biology is not part of the philosophy of the sciences. Again, you\ncannot abandon the later clause of the definition; namely that\nreferring to the relations between the sciences, without abandoning the\nexplicit reference to an ideal in the absence of which philosophy must\nlanguish from lack of intrinsic interest. That ideal is the attainment\nof some unifying concept which will set in assigned relationships within\nitself all that there is for knowledge, for feeling, and for emotion.\nThat far off ideal is the motive power of philosophic research; and\nclaims allegiance even as you expel it. The philosophic pluralist is a\nstrict logician; the Hegelian thrives on contradictions by the help of\nhis absolute; the Mohammedan divine bows before the creative will of\nAllah; and the pragmatist will swallow anything so long as it 'works.'\n\nThe mention of these vast systems and of the age-long controversies from\nwhich they spring, warns us to concentrate. Our task is the simpler one\nof the philosophy of the sciences. Now a science has already a certain\nunity which is the very reason why that body of knowledge has been\ninstinctively recognised as forming a science. The philosophy of a\nscience is the endeavour to express explicitly those unifying\ncharacteristics which pervade that complex of thoughts and make it to be\na science. The philosophy of the sciences--conceived as one subject--is\nthe endeavour to exhibit all sciences as one science, or--in case of\ndefeat--the disproof of such a possibility.\n\nAgain I will make a further simplification, and confine attention to the\nnatural sciences, that is, to the sciences whose subject-matter is\nnature. By postulating a common subject-matter for this group of\nsciences a unifying philosophy of natural science has been thereby\npresupposed.\n\nWhat do we mean by nature? We have to discuss the philosophy of natural\nscience. Natural science is the science of nature. But--What is nature?\n\nNature is that which we observe in perception through the senses. In\nthis sense-perception we are aware of something which is not thought and\nwhich is self-contained for thought. This property of being\nself-contained for thought lies at the base of natural science. It means\nthat nature can be thought of as a closed system whose mutual relations\ndo not require the expression of the fact that they are thought about.\n\nThus in a sense nature is independent of thought. By this statement no\nmetaphysical pronouncement is intended. What I mean is that we can think\nabout nature without thinking about thought. I shall say that then we\nare thinking 'homogeneously' about nature.\n\nOf course it is possible to think of nature in conjunction with thought\nabout the fact that nature is thought about. In such a case I shall say\nthat we are thinking 'heterogeneously' about nature. In fact during the\nlast few minutes we have been thinking heterogeneously about nature.\nNatural science is exclusively concerned with homogeneous thoughts about\nnature.\n\nBut sense-perception has in it an element which is not thought. It is a\ndifficult psychological question whether sense-perception involves\nthought; and if it does involve thought, what is the kind of thought\nwhich it necessarily involves. Note that it has been stated above that\nsense-perception is an awareness of something which is not thought.\nNamely, nature is not thought. But this is a different question, namely\nthat the fact of sense-perception has a factor which is not thought. I\ncall this factor 'sense-awareness.' Accordingly the doctrine that\nnatural science is exclusively concerned with homogeneous thoughts about\nnature does not immediately carry with it the conclusion that natural\nscience is not concerned with sense-awareness.\n\nHowever, I do assert this further statement; namely, that though natural\nscience is concerned with nature which is the terminus of\nsense-perception, it is not concerned with the sense-awareness itself.\n\nI repeat the main line of this argument, and expand it in certain\ndirections.\n\nThought about nature is different from the sense-perception of nature.\nHence the fact of sense-perception has an ingredient or factor which is\nnot thought. I call this ingredient sense-awareness. It is indifferent\nto my argument whether sense-perception has or has not thought as\nanother ingredient. If sense-perception does not involve thought, then\nsense-awareness and sense-perception are identical. But the something\nperceived is perceived as an entity which is the terminus of the\nsense-awareness, something which for thought is beyond the fact of that\nsense-awareness. Also the something perceived certainly does not contain\nother sense-awarenesses which are different from the sense-awareness\nwhich is an ingredient in that perception. Accordingly nature as\ndisclosed in sense-perception is self-contained as against\nsense-awareness, in addition to being self-contained as against thought.\nI will also express this self-containedness of nature by saying that\nnature is closed to mind.\n\nThis closure of nature does not carry with it any metaphysical doctrine\nof the disjunction of nature and mind. It means that in sense-perception\nnature is disclosed as a complex of entities whose mutual relations are\nexpressible in thought without reference to mind, that is, without\nreference either to sense-awareness or to thought. Furthermore, I do not\nwish to be understood as implying that sense-awareness and thought are\nthe only activities which are to be ascribed to mind. Also I am not\ndenying that there are relations of natural entities to mind or minds\nother than being the termini of the sense-awarenesses of minds.\nAccordingly I will extend the meaning of the terms 'homogeneous\nthoughts' and 'heterogeneous thoughts' which have already been\nintroduced. We are thinking 'homogeneously' about nature when we are\nthinking about it without thinking about thought or about\nsense-awareness, and we are thinking 'heterogeneously' about nature when\nwe are thinking about it in conjunction with thinking either about\nthought or about sense-awareness or about both.\n\nI also take the homogeneity of thought about nature as excluding any\nreference to moral or aesthetic values whose apprehension is vivid in\nproportion to self-conscious activity. The values of nature are perhaps\nthe key to the metaphysical synthesis of existence. But such a synthesis\nis exactly what I am not attempting. I am concerned exclusively with the\ngeneralisations of widest scope which can be effected respecting that\nwhich is known to us as the direct deliverance of sense-awareness.\n\nI have said that nature is disclosed in sense-perception as a complex of\nentities. It is worth considering what we mean by an entity in this\nconnexion. 'Entity' is simply the Latin equivalent for 'thing' unless\nsome arbitrary distinction is drawn between the words for technical\npurposes. All thought has to be about things. We can gain some idea of\nthis necessity of things for thought by examination of the structure of\na proposition.\n\nLet us suppose that a proposition is being communicated by an expositor\nto a recipient. Such a proposition is composed of phrases; some of these\nphrases may be demonstrative and others may be descriptive.\n\nBy a demonstrative phrase I mean a phrase which makes the recipient\naware of an entity in a way which is independent of the particular\ndemonstrative phrase. You will understand that I am here using\n'demonstration' in the non-logical sense, namely in the sense in which a\nlecturer demonstrates by the aid of a frog and a microscope the\ncirculation of the blood for an elementary class of medical students. I\nwill call such demonstration 'speculative' demonstration, remembering\nHamlet's use of the word 'speculation' when he says,\n\n    There is no speculation in those eyes.\n\nThus a demonstrative phrase demonstrates an entity speculatively. It may\nhappen that the expositor has meant some other entity--namely, the\nphrase demonstrates to him an entity which is diverse from the entity\nwhich it demonstrates to the recipient. In that case there is confusion;\nfor there are two diverse propositions, namely the proposition for the\nexpositor and the proposition for the recipient. I put this possibility\naside as irrelevant for our discussion, though in practice it may be\ndifficult for two persons to concur in the consideration of exactly the\nsame proposition, or even for one person to have determined exactly the\nproposition which he is considering.\n\nAgain the demonstrative phrase may fail to demonstrate any entity. In\nthat case there is no proposition for the recipient. I think that we\nmay assume (perhaps rashly) that the expositor knows what he means.\n\nA demonstrative phrase is a gesture. It is not itself a constituent of\nthe proposition, but the entity which it demonstrates is such a\nconstituent. You may quarrel with a demonstrative phrase as in some way\nobnoxious to you; but if it demonstrates the right entity, the\nproposition is unaffected though your taste may be offended. This\nsuggestiveness of the phraseology is part of the literary quality of the\nsentence which conveys the proposition. This is because a sentence\ndirectly conveys one proposition, while in its phraseology it suggests a\npenumbra of other propositions charged with emotional value. We are now\ntalking of the one proposition directly conveyed in any phraseology.\n\nThis doctrine is obscured by the fact that in most cases what is in form\na mere part of the demonstrative gesture is in fact a part of the\nproposition which it is desired directly to convey. In such a case we\nwill call the phraseology of the proposition elliptical. In ordinary\nintercourse the phraseology of nearly all propositions is elliptical.\n\nLet us take some examples. Suppose that the expositor is in London, say\nin Regent's Park and in Bedford College, the great women's college which\nis situated in that park. He is speaking in the college hall and he\nsays,\n\n    'This college building is commodious.'\n\nThe phrase 'this college building' is a demonstrative phrase. Now\nsuppose the recipient answers,\n\n    'This is not a college building, it is the lion-house in the Zoo.'\n\nThen, provided that the expositor's original proposition has not been\ncouched in elliptical phraseology, the expositor sticks to his original\nproposition when he replies,\n\n    'Anyhow, _it_ is commodious.'\n\nNote that the recipient's answer accepts the speculative demonstration\nof the phrase 'This college building.' He does not say, 'What do you\nmean?' He accepts the phrase as demonstrating an entity, but declares\nthat same entity to be the lion-house in the Zoo. In his reply, the\nexpositor in his turn recognises the success of his original gesture as\na speculative demonstration, and waives the question of the suitability\nof its mode of suggestiveness with an 'anyhow.' But he is now in a\nposition to repeat the original proposition with the aid of a\ndemonstrative gesture robbed of any suggestiveness, suitable or\nunsuitable, by saying,\n\n    '_It_ is commodious.'\n\nThe '_it_' of this final statement presupposes that thought has seized\non the entity as a bare objective for consideration.\n\nWe confine ourselves to entities disclosed in sense-awareness. The\nentity is so disclosed as a relatum in the complex which is nature. It\ndawns on an observer because of its relations; but it is an objective\nfor thought in its own bare individuality. Thought cannot proceed\notherwise; namely, it cannot proceed without the ideal bare 'it' which\nis speculatively demonstrated. This setting up of the entity as a bare\nobjective does not ascribe to it an existence apart from the complex in\nwhich it has been found by sense-perception. The 'it' for thought is\nessentially a relatum for sense-awareness.\n\nThe chances are that the dialogue as to the college building takes\nanother form. Whatever the expositor originally meant, he almost\ncertainly now takes his former statement as couched in elliptical\nphraseology, and assumes that he was meaning,\n\n    'This is a college building and is commodious.'\n\nHere the demonstrative phrase or the gesture, which demonstrates the\n'it' which is commodious, has now been reduced to 'this'; and the\nattenuated phrase, under the circumstances in which it is uttered, is\nsufficient for the purpose of correct demonstration. This brings out the\npoint that the verbal form is never the whole phraseology of the\nproposition; this phraseology also includes the general circumstances of\nits production. Thus the aim of a demonstrative phrase is to exhibit a\ndefinite 'it' as a bare objective for thought; but the _modus operandi_\nof a demonstrative phrase is to produce an awareness of the entity as a\nparticular relatum in an auxiliary complex, chosen merely for the sake\nof the speculative demonstration and irrelevant to the proposition. For\nexample, in the above dialogue, colleges and buildings, as related to\nthe 'it' speculatively demonstrated by the phrase 'this college\nbuilding,' set that 'it' in an auxiliary complex which is irrelevant to\nthe proposition\n\n    'It is commodious.'\n\nOf course in language every phrase is invariably highly elliptical.\nAccordingly the sentence\n\n    'This college building is commodious'\n\nmeans probably\n\n    'This college building is commodious as a college building.'\n\nBut it will be found that in the above discussion we can replace\n'commodious' by 'commodious as a college building' without altering our\nconclusion; though we can guess that the recipient, who thought he was\nin the lion-house of the Zoo, would be less likely to assent to.\n\n    'Anyhow, it is commodious as a college building.'\n\nA more obvious instance of elliptical phraseology arises if the\nexpositor should address the recipient with the remark,\n\n    'That criminal is your friend.'\n\nThe recipient might answer,\n\n    'He is my friend and you are insulting.'\n\nHere the recipient assumes that the phrase 'That criminal' is elliptical\nand not merely demonstrative. In fact, pure demonstration is impossible\nthough it is the ideal of thought. This practical impossibility of pure\ndemonstration is a difficulty which arises in the communication of\nthought and in the retention of thought. Namely, a proposition about a\nparticular factor in nature can neither be expressed to others nor\nretained for repeated consideration without the aid of auxiliary\ncomplexes which are irrelevant to it.\n\nI now pass to descriptive phrases. The expositor says,\n\n    'A college in Regent's Park is commodious.'\n\nThe recipient knows Regent's Park well. The phrase 'A college in\nRegent's Park' is descriptive for him. If its phraseology is not\nelliptical, which in ordinary life it certainly will be in some way or\nother, this proposition simply means,\n\n    'There is an entity which is a college building in Regent's Park\n    and is commodious.'\n\nIf the recipient rejoins,\n\n    'The lion-house in the Zoo is the only commodious building in\n    Regent's Park,'\n\nhe now contradicts the expositor, on the assumption that a lion-house in\na Zoo is not a college building.\n\nThus whereas in the first dialogue the recipient merely quarrelled with\nthe expositor without contradicting him, in this dialogue he contradicts\nhim. Thus a descriptive phrase is part of the proposition which it helps\nto express, whereas a demonstrative phrase is not part of the\nproposition which it helps to express.\n\nAgain the expositor might be standing in Green Park--where there are no\ncollege buildings--and say,\n\n    'This college building is commodious.'\n\nProbably no proposition will be received by the recipient because the\ndemonstrative phrase,\n\n    'This college building'\n\nhas failed to demonstrate owing to the absence of the background of\nsense-awareness which it presupposes.\n\nBut if the expositor had said,\n\n    'A college building in Green Park is commodious,'\n\nthe recipient would have received a proposition, but a false one.\n\nLanguage is usually ambiguous and it is rash to make general assertions\nas to its meanings. But phrases which commence with 'this' or 'that' are\nusually demonstrative, whereas phrases which commence with 'the' or 'a'\nare often descriptive. In studying the theory of propositional\nexpression it is important to remember the wide difference between the\nanalogous modest words 'this' and 'that' on the one hand and 'a' and\n'the' on the other hand. The sentence\n\n    'The college building in Regent's Park is commodious'\n\nmeans, according to the analysis first made by Bertrand Russell, the\nproposition,\n\n   'There is an entity which (i) is a college building in Regent's\n   Park and (ii) is commodious and (iii) is such that any college\n   building in Regent's Park is identical with it.'\n\nThe descriptive character of the phrase 'The college building in\nRegent's Park' is thus evident. Also the proposition is denied by the\ndenial of any one of its three component clauses or by the denial of any\ncombination of the component clauses. If we had substituted 'Green Park'\nfor 'Regent's Park' a false proposition would have resulted. Also the\nerection of a second college in Regent's Park would make the proposition\nfalse, though in ordinary life common sense would politely treat it as\nmerely ambiguous.\n\n'The Iliad' for a classical scholar is usually a demonstrative phrase;\nfor it demonstrates to him a well-known poem. But for the majority of\nmankind the phrase is descriptive, namely, it is synonymous with 'The\npoem named \"the Iliad\".'\n\nNames may be either demonstrative or descriptive phrases. For example\n'Homer' is for us a descriptive phrase, namely, the word with some\nslight difference in suggestiveness means 'The man who wrote the Iliad.'\n\nThis discussion illustrates that thought places before itself bare\nobjectives, entities as we call them, which the thinking clothes by\nexpressing their mutual relations. Sense-awareness discloses fact with\nfactors which are the entities for thought. The separate distinction of\nan entity in thought is not a metaphysical assertion, but a method of\nprocedure necessary for the finite expression of individual\npropositions. Apart from entities there could be no finite truths; they\nare the means by which the infinitude of irrelevance is kept out of\nthought.\n\nTo sum up: the termini for thought are entities, primarily with bare\nindividuality, secondarily with properties and relations ascribed to\nthem in the procedure of thought; the termini for sense-awareness are\nfactors in the fact of nature, primarily relata and only secondarily\ndiscriminated as distinct individualities.\n\nNo characteristic of nature which is immediately posited for knowledge\nby sense-awareness can be explained. It is impenetrable by thought, in\nthe sense that its peculiar essential character which enters into\nexperience by sense-awareness is for thought merely the guardian of its\nindividuality as a bare entity. Thus for thought 'red' is merely a\ndefinite entity, though for awareness 'red' has the content of its\nindividuality. The transition from the 'red' of awareness to the 'red'\nof thought is accompanied by a definite loss of content, namely by the\ntransition from the factor 'red' to the entity 'red.' This loss in the\ntransition to thought is compensated by the fact that thought is\ncommunicable whereas sense-awareness is incommunicable.\n\nThus there are three components in our knowledge of nature, namely,\nfact, factors, and entities. Fact is the undifferentiated terminus of\nsense-awareness; factors are termini of sense-awareness, differentiated\nas elements of fact; entities are factors in their function as the\ntermini of thought. The entities thus spoken of are natural entities.\nThought is wider than nature, so that there are entities for thought\nwhich are not natural entities.\n\nWhen we speak of nature as a complex of related entities, the 'complex'\nis fact as an entity for thought, to whose bare individuality is\nascribed the property of embracing in its complexity the natural\nentities. It is our business to analyse this conception and in the\ncourse of the analysis space and time should appear. Evidently the\nrelations holding between natural entities are themselves natural\nentities, namely they are also factors of fact, there for\nsense-awareness. Accordingly the structure of the natural complex can\nnever be completed in thought, just as the factors of fact can never be\nexhausted in sense-awareness. Unexhaustiveness is an essential character\nof our knowledge of nature. Also nature does not exhaust the matter for\nthought, namely there are thoughts which would not occur in any\nhomogeneous thinking about nature.\n\nThe question as to whether sense-perception involves thought is largely\nverbal. If sense-perception involves a cognition of individuality\nabstracted from the actual position of the entity as a factor in fact,\nthen it undoubtedly does involve thought. But if it is conceived as\nsense-awareness of a factor in fact competent to evoke emotion and\npurposeful action without further cognition, then it does not involve\nthought. In such a case the terminus of the sense-awareness is something\nfor mind, but nothing for thought. The sense-perception of some lower\nforms of life may be conjectured to approximate to this character\nhabitually. Also occasionally our own sense-perception in moments when\nthought-activity has been lulled to quiescence is not far off the\nattainment of this ideal limit.\n\nThe process of discrimination in sense-awareness has two distinct sides.\nThere is the discrimination of fact into parts, and the discrimination\nof any part of fact as exhibiting relations to entities which are not\nparts of fact though they are ingredients in it. Namely the immediate\nfact for awareness is the whole occurrence of nature. It is nature as an\nevent present for sense-awareness, and essentially passing. There is no\nholding nature still and looking at it. We cannot redouble our efforts\nto improve our knowledge of the terminus of our present sense-awareness;\nit is our subsequent opportunity in subsequent sense-awareness which\ngains the benefit of our good resolution. Thus the ultimate fact for\nsense-awareness is an event. This whole event is discriminated by us\ninto partial events. We are aware of an event which is our bodily life,\nof an event which is the course of nature within this room, and of a\nvaguely perceived aggregate of other partial events. This is the\ndiscrimination in sense-awareness of fact into parts.\n\nI shall use the term 'part' in the arbitrarily limited sense of an event\nwhich is part of the whole fact disclosed in awareness.\n\nSense-awareness also yields to us other factors in nature which are not\nevents. For example, sky-blue is seen as situated in a certain event.\nThis relation of situation requires further discussion which is\npostponed to a later lecture. My present point is that sky-blue is found\nin nature with a definite implication in events, but is not an event\nitself. Accordingly in addition to events, there are other factors in\nnature directly disclosed to us in sense-awareness. The conception in\nthought of all the factors in nature as distinct entities with definite\nnatural relations is what I have in another place[1] called the\n'diversification of nature.'\n\n[1] Cf. _Enquiry_.\n\nThere is one general conclusion to be drawn from the foregoing\ndiscussion. It is that the first task of a philosophy of science should\nbe some general classification of the entities disclosed to us in\nsense-perception.\n\nAmong the examples of entities in addition to 'events' which we have\nused for the purpose of illustration are the buildings of Bedford\nCollege, Homer, and sky-blue. Evidently these are very different sorts\nof things; and it is likely that statements which are made about one\nkind of entity will not be true about other kinds. If human thought\nproceeded with the orderly method which abstract logic would suggest to\nit, we might go further and say that a classification of natural\nentities should be the first step in science itself. Perhaps you will be\ninclined to reply that this classification has already been effected,\nand that science is concerned with the adventures of material entities\nin space and time.\n\nThe history of the doctrine of matter has yet to be written. It is the\nhistory of the influence of Greek philosophy on science. That influence\nhas issued in one long misconception of the metaphysical status of\nnatural entities. The entity has been separated from the factor which is\nthe terminus of sense-awareness. It has become the substratum for that\nfactor, and the factor has been degraded into an attribute of the\nentity. In this way a distinction has been imported into nature which is\nin truth no distinction at all. A natural entity is merely a factor of\nfact, considered in itself. Its disconnexion from the complex of fact is\na mere abstraction. It is not the substratum of the factor, but the very\nfactor itself as bared in thought. Thus what is a mere procedure of mind\nin the translation of sense-awareness into discursive knowledge has been\ntransmuted into a fundamental character of nature. In this way matter\nhas emerged as being the metaphysical substratum of its properties, and\nthe course of nature is interpreted as the history of matter.\n\nPlato and Aristotle found Greek thought preoccupied with the quest for\nthe simple substances in terms of which the course of events could be\nexpressed. We may formulate this state of mind in the question, What is\nnature made of? The answers which their genius gave to this question,\nand more particularly the concepts which underlay the terms in which\nthey framed their answers, have determined the unquestioned\npresuppositions as to time, space and matter which have reigned in\nscience.\n\nIn Plato the forms of thought are more fluid than in Aristotle, and\ntherefore, as I venture to think, the more valuable. Their importance\nconsists in the evidence they yield of cultivated thought about nature\nbefore it had been forced into a uniform mould by the long tradition of\nscientific philosophy. For example in the _Timaeus_ there is a\npresupposition, somewhat vaguely expressed, of a distinction between the\ngeneral becoming of nature and the measurable time of nature. In a later\nlecture I have to distinguish between what I call the passage of nature\nand particular time-systems which exhibit certain characteristics of\nthat passage. I will not go so far as to claim Plato in direct support\nof this doctrine, but I do think that the sections of the _Timaeus_\nwhich deal with time become clearer if my distinction is admitted.\n\nThis is however a digression. I am now concerned with the origin of the\nscientific doctrine of matter in Greek thought. In the _Timaeus_ Plato\nasserts that nature is made of fire and earth with air and water as\nintermediate between them, so that 'as fire is to air so is air to\nwater, and as air is to water so is water to earth.' He also suggests a\nmolecular hypothesis for these four elements. In this hypothesis\neverything depends on the shape of the atoms; for earth it is cubical\nand for fire it is pyramidal. To-day physicists are again discussing\nthe structure of the atom, and its shape is no slight factor in that\nstructure. Plato's guesses read much more fantastically than does\nAristotle's systematic analysis; but in some ways they are more\nvaluable. The main outline of his ideas is comparable with that of\nmodern science. It embodies concepts which any theory of natural\nphilosophy must retain and in some sense must explain. Aristotle asked\nthe fundamental question, What do we mean by 'substance'? Here the\nreaction between his philosophy and his logic worked very unfortunately.\nIn his logic, the fundamental type of affirmative proposition is the\nattribution of a predicate to a subject. Accordingly, amid the many\ncurrent uses of the term 'substance' which he analyses, he emphasises\nits meaning as 'the ultimate substratum which is no longer predicated of\nanything else.'\n\nThe unquestioned acceptance of the Aristotelian logic has led to an\ningrained tendency to postulate a substratum for whatever is disclosed\nin sense-awareness, namely, to look below what we are aware of for the\nsubstance in the sense of the 'concrete thing.' This is the origin of\nthe modern scientific concept of matter and of ether, namely they are\nthe outcome of this insistent habit of postulation.\n\nAccordingly ether has been invented by modern science as the substratum\nof the events which are spread through space and time beyond the reach\nof ordinary ponderable matter. Personally, I think that predication is a\nmuddled notion confusing many different relations under a convenient\ncommon form of speech. For example, I hold that the relation of green to\na blade of grass is entirely different from the relation of green to\nthe event which is the life history of that blade for some short period,\nand is different from the relation of the blade to that event. In a\nsense I call the event the situation of the green, and in another sense\nit is the situation of the blade. Thus in one sense the blade is a\ncharacter or property which can be predicated of the situation, and in\nanother sense the green is a character or property of the same event\nwhich is also its situation. In this way the predication of properties\nveils radically different relations between entities.\n\nAccordingly 'substance,' which is a correlative term to 'predication,'\nshares in the ambiguity. If we are to look for substance anywhere, I\nshould find it in events which are in some sense the ultimate substance\nof nature.\n\nMatter, in its modern scientific sense, is a return to the Ionian effort\nto find in space and time some stuff which composes nature. It has a\nmore refined signification than the early guesses at earth and water by\nreason of a certain vague association with the Aristotelian idea of\nsubstance.\n\nEarth, water, air, fire, and matter, and finally ether are related in\ndirect succession so far as concerns their postulated characters of\nultimate substrata of nature. They bear witness to the undying vitality\nof Greek philosophy in its search for the ultimate entities which are\nthe factors of the fact disclosed in sense-awareness. This search is the\norigin of science.\n\nThe succession of ideas starting from the crude guesses of the early\nIonian thinkers and ending in the nineteenth century ether reminds us\nthat the scientific doctrine of matter is really a hybrid through which\nphilosophy passed on its way to the refined Aristotelian concept of\nsubstance and to which science returned as it reacted against\nphilosophic abstractions. Earth, fire, and water in the Ionic philosophy\nand the shaped elements in the _Timaeus_ are comparable to the matter\nand ether of modern scientific doctrine. But substance represents the\nfinal philosophic concept of the substratum which underlies any\nattribute. Matter (in the scientific sense) is already in space and\ntime. Thus matter represents the refusal to think away spatial and\ntemporal characteristics and to arrive at the bare concept of an\nindividual entity. It is this refusal which has caused the muddle of\nimporting the mere procedure of thought into the fact of nature. The\nentity, bared of all characteristics except those of space and time, has\nacquired a physical status as the ultimate texture of nature; so that\nthe course of nature is conceived as being merely the fortunes of matter\nin its adventure through space.\n\nThus the origin of the doctrine of matter is the outcome of uncritical\nacceptance of space and time as external conditions for natural\nexistence. By this I do not mean that any doubt should be thrown on\nfacts of space and time as ingredients in nature. What I do mean is 'the\nunconscious presupposition of space and time as being that within which\nnature is set.' This is exactly the sort of presupposition which tinges\nthought in any reaction against the subtlety of philosophical criticism.\nMy theory of the formation of the scientific doctrine of matter is that\nfirst philosophy illegitimately transformed the bare entity, which is\nsimply an abstraction necessary for the method of thought, into the\nmetaphysical substratum of these factors in nature which in various\nsenses are assigned to entities as their attributes; and that, as a\nsecond step, scientists (including philosophers who were scientists) in\nconscious or unconscious ignoration of philosophy presupposed this\nsubstratum, _qua_ substratum for attributes, as nevertheless in time and\nspace.\n\nThis is surely a muddle. The whole being of substance is as a substratum\nfor attributes. Thus time and space should be attributes of the\nsubstance. This they palpably are not, if the matter be the substance of\nnature, since it is impossible to express spatio-temporal truths without\nhaving recourse to relations involving relata other than bits of matter.\nI waive this point however, and come to another. It is not the substance\nwhich is in space, but the attributes. What we find in space are the red\nof the rose and the smell of the jasmine and the noise of cannon. We\nhave all told our dentists where our toothache is. Thus space is not a\nrelation between substances, but between attributes.\n\nThus even if you admit that the adherents of substance can be allowed to\nconceive substance as matter, it is a fraud to slip substance into space\non the plea that space expresses relations between substances. On the\nface of it space has nothing to do with substances, but only with their\nattributes. What I mean is, that if you choose--as I think wrongly--to\nconstrue our experience of nature as an awareness of the attributes of\nsubstances, we are by this theory precluded from finding any analogous\ndirect relations between substances as disclosed in our experience. What\nwe do find are relations between the attributes of substances. Thus if\nmatter is looked on as substance in space, the space in which it finds\nitself has very little to do with the space of our experience.\n\nThe above argument has been expressed in terms of the relational theory\nof space. But if space be absolute--namely, if it have a being\nindependent of things in it--the course of the argument is hardly\nchanged. For things in space must have a certain fundamental relation to\nspace which we will call occupation. Thus the objection that it is the\nattributes which are observed as related to space, still holds.\n\nThe scientific doctrine of matter is held in conjunction with an\nabsolute theory of time. The same arguments apply to the relations\nbetween matter and time as apply to the relations between space and\nmatter. There is however (in the current philosophy) a difference in the\nconnexions of space with matter from those of time with matter, which I\nwill proceed to explain.\n\nSpace is not merely an ordering of material entities so that any one\nentity bears certain relations to other material entities. The\noccupation of space impresses a certain character on each material\nentity in itself. By reason of its occupation of space matter has\nextension. By reason of its extension each bit of matter is divisible\ninto parts, and each part is a numerically distinct entity from every\nother such part. Accordingly it would seem that every material entity is\nnot really one entity. It is an essential multiplicity of entities.\nThere seems to be no stopping this dissociation of matter into\nmultiplicities short of finding each ultimate entity occupying one\nindividual point. This essential multiplicity of material entities is\ncertainly not what is meant by science, nor does it correspond to\nanything disclosed in sense-awareness. It is absolutely necessary that\nat a certain stage in this dissociation of matter a halt should be\ncalled, and that the material entities thus obtained should be treated\nas units. The stage of arrest may be arbitrary or may be set by the\ncharacteristics of nature; but all reasoning in science ultimately drops\nits space-analysis and poses to itself the problem, 'Here is one\nmaterial entity, what is happening to it as a unit entity?' Yet this\nmaterial entity is still retaining its extension, and as thus extended\nis a mere multiplicity. Thus there is an essential atomic property in\nnature which is independent of the dissociation of extension. There is\nsomething which in itself is one, and which is more than the logical\naggregate of entities occupying points within the volume which the unit\noccupies. Indeed we may well be sceptical as to these ultimate entities\nat points, and doubt whether there are any such entities at all. They\nhave the suspicious character that we are driven to accept them by\nabstract logic and not by observed fact.\n\nTime (in the current philosophy) does not exert the same disintegrating\neffect on matter which occupies it. If matter occupies a duration of\ntime, the whole matter occupies every part of that duration. Thus the\nconnexion between matter and time differs from the connexion between\nmatter and space as expressed in current scientific philosophy. There is\nobviously a greater difficulty in conceiving time as the outcome of\nrelations between different bits of matter than there is in the\nanalogous conception of space. At an instant distinct volumes of space\nare occupied by distinct bits of matter. Accordingly there is so far no\nintrinsic difficulty in conceiving that space is merely the resultant of\nrelations between the bits of matter. But in the one-dimensional time\nthe same bit of matter occupies different portions of time. Accordingly\ntime would have to be expressible in terms of the relations of a bit of\nmatter with itself. My own view is a belief in the relational theory\nboth of space and of time, and of disbelief in the current form of the\nrelational theory of space which exhibits bits of matter as the relata\nfor spatial relations. The true relata are events. The distinction which\nI have just pointed out between time and space in their connexion with\nmatter makes it evident that any assimilation of time and space cannot\nproceed along the traditional line of taking matter as a fundamental\nelement in space-formation.\n\nThe philosophy of nature took a wrong turn during its development by\nGreek thought. This erroneous presupposition is vague and fluid in\nPlato's _Timaeus_. The general groundwork of the thought is still\nuncommitted and can be construed as merely lacking due explanation and\nthe guarding emphasis. But in Aristotle's exposition the current\nconceptions were hardened and made definite so as to produce a faulty\nanalysis of the relation between the matter and the form of nature as\ndisclosed in sense-awareness. In this phrase the term 'matter' is not\nused in its scientific sense.\n\nI will conclude by guarding myself against a misapprehension. It is\nevident that the current doctrine of matter enshrines some fundamental\nlaw of nature. Any simple illustration will exemplify what I mean. For\nexample, in a museum some specimen is locked securely in a glass case.\nIt stays there for years: it loses its colour, and perhaps falls to\npieces. But it is the same specimen; and the same chemical elements and\nthe same quantities of those elements are present within the case at the\nend as were present at the beginning. Again the engineer and the\nastronomer deal with the motions of real permanences in nature. Any\ntheory of nature which for one moment loses sight of these great basic\nfacts of experience is simply silly. But it is permissible to point out\nthat the scientific expression of these facts has become entangled in a\nmaze of doubtful metaphysics; and that, when we remove the metaphysics\nand start afresh on an unprejudiced survey of nature, a new light is\nthrown on many fundamental concepts which dominate science and guide the\nprogress of research.\n\n\n\n\nCHAPTER II\n\nTHEORIES OF THE BIFURCATION OF NATURE\n\n\nIn my previous lecture I criticised the concept of matter as the\nsubstance whose attributes we perceive. This way of thinking of matter\nis, I think, the historical reason for its introduction into science,\nand is still the vague view of it at the background of our thoughts\nwhich makes the current scientific doctrine appear so obvious. Namely we\nconceive ourselves as perceiving attributes of things, and bits of\nmatter are the things whose attributes we perceive.\n\nIn the seventeenth century the sweet simplicity of this aspect of matter\nreceived a rude shock. The transmission doctrines of science were then\nin process of elaboration and by the end of the century were\nunquestioned, though their particular forms have since been modified.\nThe establishment of these transmission theories marks a turning point\nin the relation between science and philosophy. The doctrines to which I\nam especially alluding are the theories of light and sound. I have no\ndoubt that the theories had been vaguely floating about before as\nobvious suggestions of common sense; for nothing in thought is ever\ncompletely new. But at that epoch they were systematised and made exact,\nand their complete consequences were ruthlessly deduced. It is the\nestablishment of this procedure of taking the consequences seriously\nwhich marks the real discovery of a theory. Systematic doctrines of\nlight and sound as being something proceeding from the emitting bodies\nwere definitely established, and in particular the connexion of light\nwith colour was laid bare by Newton.\n\nThe result completely destroyed the simplicity of the 'substance and\nattribute' theory of perception. What we see depends on the light\nentering the eye. Furthermore we do not even perceive what enters the\neye. The things transmitted are waves or--as Newton thought--minute\nparticles, and the things seen are colours. Locke met this difficulty by\na theory of primary and secondary qualities. Namely, there are some\nattributes of the matter which we do perceive. These are the primary\nqualities, and there are other things which we perceive, such as\ncolours, which are not attributes of matter, but are perceived by us as\nif they were such attributes. These are the secondary qualities of\nmatter.\n\nWhy should we perceive secondary qualities? It seems an extremely\nunfortunate arrangement that we should perceive a lot of things that are\nnot there. Yet this is what the theory of secondary qualities in fact\ncomes to. There is now reigning in philosophy and in science an\napathetic acquiescence in the conclusion that no coherent account can be\ngiven of nature as it is disclosed to us in sense-awareness, without\ndragging in its relations to mind. The modern account of nature is not,\nas it should be, merely an account of what the mind knows of nature; but\nit is also confused with an account of what nature does to the mind. The\nresult has been disastrous both to science and to philosophy, but\nchiefly to philosophy. It has transformed the grand question of the\nrelations between nature and mind into the petty form of the interaction\nbetween the human body and mind.\n\nBerkeley's polemic against matter was based on this confusion introduced\nby the transmission theory of light. He advocated, rightly as I think,\nthe abandonment of the doctrine of matter in its present form. He had\nhowever nothing to put in its place except a theory of the relation of\nfinite minds to the divine mind.\n\nBut we are endeavouring in these lectures to limit ourselves to nature\nitself and not to travel beyond entities which are disclosed in\nsense-awareness.\n\nPercipience in itself is taken for granted. We consider indeed\nconditions for percipience, but only so far as those conditions are\namong the disclosures of perception. We leave to metaphysics the\nsynthesis of the knower and the known. Some further explanation and\ndefence of this position is necessary, if the line of argument of these\nlectures is to be comprehensible.\n\nThe immediate thesis for discussion is that any metaphysical\ninterpretation is an illegitimate importation into the philosophy of\nnatural science. By a metaphysical interpretation I mean any discussion\nof the how (beyond nature) and of the why (beyond nature) of thought and\nsense-awareness. In the philosophy of science we seek the general\nnotions which apply to nature, namely, to what we are aware of in\nperception. It is the philosophy of the thing perceived, and it should\nnot be confused with the metaphysics of reality of which the scope\nembraces both perceiver and perceived. No perplexity concerning the\nobject of knowledge can be solved by saying that there is a mind knowing\nit[2].\n\n[2] Cf. _Enquiry_, preface.\n\nIn other words, the ground taken is this: sense-awareness is an\nawareness of something. What then is the general character of that\nsomething of which we are aware? We do not ask about the percipient or\nabout the process, but about the perceived. I emphasise this point\nbecause discussions on the philosophy of science are usually extremely\nmetaphysical--in my opinion, to the great detriment of the subject.\n\nThe recourse to metaphysics is like throwing a match into the powder\nmagazine. It blows up the whole arena. This is exactly what scientific\nphilosophers do when they are driven into a corner and convicted of\nincoherence. They at once drag in the mind and talk of entities in the\nmind or out of the mind as the case may be. For natural philosophy\neverything perceived is in nature. We may not pick and choose. For us\nthe red glow of the sunset should be as much part of nature as are the\nmolecules and electric waves by which men of science would explain the\nphenomenon. It is for natural philosophy to analyse how these various\nelements of nature are connected.\n\nIn making this demand I conceive myself as adopting our immediate\ninstinctive attitude towards perceptual knowledge which is only\nabandoned under the influence of theory. We are instinctively willing to\nbelieve that by due attention, more can be found in nature than that\nwhich is observed at first sight. But we will not be content with less.\nWhat we ask from the philosophy of science is some account of the\ncoherence of things perceptively known.\n\nThis means a refusal to countenance any theory of psychic additions to\nthe object known in perception. For example, what is given in perception\nis the green grass. This is an object which we know as an ingredient in\nnature. The theory of psychic additions would treat the greenness as a\npsychic addition furnished by the perceiving mind, and would leave to\nnature merely the molecules and the radiant energy which influence the\nmind towards that perception. My argument is that this dragging in of\nthe mind as making additions of its own to the thing posited for\nknowledge by sense-awareness is merely a way of shirking the problem of\nnatural philosophy. That problem is to discuss the relations _inter se_\nof things known, abstracted from the bare fact that they are known.\nNatural philosophy should never ask, what is in the mind and what is in\nnature. To do so is a confession that it has failed to express relations\nbetween things perceptively known, namely to express those natural\nrelations whose expression is natural philosophy. It may be that the\ntask is too hard for us, that the relations are too complex and too\nvarious for our apprehension, or are too trivial to be worth the trouble\nof exposition. It is indeed true that we have gone but a very small way\nin the adequate formulation of such relations. But at least do not let\nus endeavour to conceal failure under a theory of the byplay of the\nperceiving mind.\n\nWhat I am essentially protesting against is the bifurcation of nature\ninto two systems of reality, which, in so far as they are real, are real\nin different senses. One reality would be the entities such as electrons\nwhich are the study of speculative physics. This would be the reality\nwhich is there for knowledge; although on this theory it is never known.\nFor what is known is the other sort of reality, which is the byplay of\nthe mind. Thus there would be two natures, one is the conjecture and the\nother is the dream.\n\nAnother way of phrasing this theory which I am arguing against is to\nbifurcate nature into two divisions, namely into the nature apprehended\nin awareness and the nature which is the cause of awareness. The nature\nwhich is the fact apprehended in awareness holds within it the greenness\nof the trees, the song of the birds, the warmth of the sun, the hardness\nof the chairs, and the feel of the velvet. The nature which is the cause\nof awareness is the conjectured system of molecules and electrons which\nso affects the mind as to produce the awareness of apparent nature. The\nmeeting point of these two natures is the mind, the causal nature being\ninfluent and the apparent nature being effluent.\n\nThere are four questions which at once suggest themselves for discussion\nin connexion with this bifurcation theory of nature. They concern (i)\ncausality, (ii) time, (iii) space, and (iv) delusions. These questions\nare not really separable. They merely constitute four distinct starting\npoints from which to enter upon the discussion of the theory.\n\nCausal nature is the influence on the mind which is the cause of the\neffluence of apparent nature from the mind. This conception of causal\nnature is not to be confused with the distinct conception of one part of\nnature as being the cause of another part. For example, the burning of\nthe fire and the passage of heat from it through intervening space is\nthe cause of the body, its nerves and its brain, functioning in certain\nways. But this is not an action of nature on the mind. It is an\ninteraction within nature. The causation involved in this interaction is\ncausation in a different sense from the influence of this system of\nbodily interactions within nature on the alien mind which thereupon\nperceives redness and warmth.\n\nThe bifurcation theory is an attempt to exhibit natural science as an\ninvestigation of the cause of the fact of knowledge. Namely, it is an\nattempt to exhibit apparent nature as an effluent from the mind because\nof causal nature. The whole notion is partly based on the implicit\nassumption that the mind can only know that which it has itself produced\nand retains in some sense within itself, though it requires an exterior\nreason both as originating and as determining the character of its\nactivity. But in considering knowledge we should wipe out all these\nspatial metaphors, such as 'within the mind' and 'without the mind.'\nKnowledge is ultimate. There can be no explanation of the 'why' of\nknowledge; we can only describe the 'what' of knowledge. Namely we can\nanalyse the content and its internal relations, but we cannot explain\nwhy there is knowledge. Thus causal nature is a metaphysical chimera;\nthough there is need of a metaphysics whose scope transcends the\nlimitation to nature. The object of such a metaphysical science is not\nto explain knowledge, but exhibit in its utmost completeness our concept\nof reality.\n\nHowever, we must admit that the causality theory of nature has its\nstrong suit. The reason why the bifurcation of nature is always creeping\nback into scientific philosophy is the extreme difficulty of exhibiting\nthe perceived redness and warmth of the fire in one system of relations\nwith the agitated molecules of carbon and oxygen, with the radiant\nenergy from them, and with the various functionings of the material\nbody. Unless we produce the all-embracing relations, we are faced with a\nbifurcated nature; namely, warmth and redness on one side, and\nmolecules, electrons and ether on the other side. Then the two factors\nare explained as being respectively the cause and the mind's reaction to\nthe cause.\n\nTime and space would appear to provide these all-embracing relations\nwhich the advocates of the philosophy of the unity of nature require.\nThe perceived redness of the fire and the warmth are definitely related\nin time and in space to the molecules of the fire and the molecules of\nthe body.\n\nIt is hardly more than a pardonable exaggeration to say that the\ndetermination of the meaning of nature reduces itself principally to the\ndiscussion of the character of time and the character of space. In\nsucceeding lectures I shall explain my own view of time and space. I\nshall endeavour to show that they are abstractions from more concrete\nelements of nature, namely, from events. The discussion of the details\nof the process of abstraction will exhibit time and space as\ninterconnected, and will finally lead us to the sort of connexions\nbetween their measurements which occur in the modern theory of\nelectromagnetic relativity. But this is anticipating our subsequent line\nof development. At present I wish to consider how the ordinary views of\ntime and space help, or fail to help, in unifying our conception of\nnature.\n\nFirst, consider the absolute theories of time and space. We are to\nconsider each, namely both time and space, to be a separate and\nindependent system of entities, each system known to us in itself and\nfor itself concurrently with our knowledge of the events of nature. Time\nis the ordered succession of durationless instants; and these instants\nare known to us merely as the relata in the serial relation which is the\ntime-ordering relation, and the time-ordering relation is merely known\nto us as relating the instants. Namely, the relation and the instants\nare jointly known to us in our apprehension of time, each implying the\nother.\n\nThis is the absolute theory of time. Frankly, I confess that it seems to\nme to be very unplausible. I cannot in my own knowledge find anything\ncorresponding to the bare time of the absolute theory. Time is known to\nme as an abstraction from the passage of events. The fundamental fact\nwhich renders this abstraction possible is the passing of nature, its\ndevelopment, its creative advance, and combined with this fact is\nanother characteristic of nature, namely the extensive relation between\nevents. These two facts, namely the passage of events and the extension\nof events over each other, are in my opinion the qualities from which\ntime and space originate as abstractions. But this is anticipating my\nown later speculations.\n\nMeanwhile, returning to the absolute theory, we are to suppose that time\nis known to us independently of any events in time. What happens in time\noccupies time. This relation of events to the time occupied, namely this\nrelation of occupation, is a fundamental relation of nature to time.\nThus the theory requires that we are aware of two fundamental relations,\nthe time-ordering relation between instants, and the time-occupation\nrelation between instants of time and states of nature which happen at\nthose instants.\n\nThere are two considerations which lend powerful support to the reigning\ntheory of absolute time. In the first place time extends beyond nature.\nOur thoughts are in time. Accordingly it seems impossible to derive time\nmerely from relations between elements of nature. For in that case\ntemporal relations could not relate thoughts. Thus, to use a metaphor,\ntime would apparently have deeper roots in reality than has nature. For\nwe can imagine thoughts related in time without any perception of\nnature. For example we can imagine one of Milton's angels with thoughts\nsucceeding each other in time, who does not happen to have noticed that\nthe Almighty has created space and set therein a material universe. As a\nmatter of fact I think that Milton set space on the same absolute level\nas time. But that need not disturb the illustration. In the second place\nit is difficult to derive the true serial character of time from the\nrelative theory. Each instant is irrevocable. It can never recur by the\nvery character of time. But if on the relative theory an instant of time\nis simply the state of nature at that time, and the time-ordering\nrelation is simply the relation between such states, then the\nirrevocableness of time would seem to mean that an actual state of all\nnature can never return. I admit it seems unlikely that there should\never be such a recurrence down to the smallest particular. But extreme\nunlikeliness is not the point. Our ignorance is so abysmal that our\njudgments of likeliness and unlikeliness of future events hardly count.\nThe real point is that the exact recurrence of a state of nature seems\nmerely unlikely, while the recurrence of an instant of time violates our\nwhole concept of time-order. The instants of time which have passed, are\npassed, and can never be again.\n\nAny alternative theory of time must reckon with these two considerations\nwhich are buttresses of the absolute theory. But I will not now continue\ntheir discussion.\n\nThe absolute theory of space is analogous to the corresponding theory of\ntime, but the reasons for its maintenance are weaker. Space, on this\ntheory, is a system of extensionless points which are the relata in\nspace-ordering relations which can technically be combined into one\nrelation. This relation does not arrange the points in one linear series\nanalogously to the simple method of the time-ordering relation for\ninstants. The essential logical characteristics of this relation from\nwhich all the properties of space spring are expressed by mathematicians\nin the axioms of geometry. From these axioms[3] as framed by modern\nmathematicians the whole science of geometry can be deduced by the\nstrictest logical reasoning. The details of these axioms do not now\nconcern us. The points and the relations are jointly known to us in our\napprehension of space, each implying the other. What happens in space,\noccupies space. This relation of occupation is not usually stated for\nevents but for objects. For example, Pompey's statue would be said to\noccupy space, but not the event which was the assassination of Julius\nCaesar. In this I think that ordinary usage is unfortunate, and I hold\nthat the relations of events to space and to time are in all respects\nanalogous. But here I am intruding my own opinions which are to be\ndiscussed in subsequent lectures. Thus the theory of absolute space\nrequires that we are aware of two fundamental relations, the\nspace-ordering relation, which holds between points, and the\nspace-occupation relation between points of space and material objects.\n\n[3] Cf. (for example) _Projective Geometry_ by Veblen and Young, vol.\u00a0i.\n1910, vol.\u00a0ii. 1917, Ginn and Company, Boston, U.S.A.\n\nThis theory lacks the two main supports of the corresponding theory of\nabsolute time. In the first place space does not extend beyond nature in\nthe sense that time seems to do. Our thoughts do not seem to occupy\nspace in quite the same intimate way in which they occupy time. For\nexample, I have been thinking in a room, and to that extent my thoughts\nare in space. But it seems nonsense to ask how much volume of the room\nthey occupied, whether it was a cubic foot or a cubic inch; whereas the\nsame thoughts occupy a determinate duration of time, say, from eleven to\ntwelve on a certain date.\n\nThus whereas the relations of a relative theory of time are required to\nrelate thoughts, it does not seem so obvious that the relations of a\nrelative theory of space are required to relate them. The connexion of\nthought with space seems to have a certain character of indirectness\nwhich appears to be lacking in the connexion of thought with time.\n\nAgain the irrevocableness of time does not seem to have any parallel for\nspace. Space, on the relative theory, is the outcome of certain\nrelations between objects commonly said to be in space; and whenever\nthere are the objects, so related, there is the space. No difficulty\nseems to arise like that of the inconvenient instants of time which\nmight conceivably turn up again when we thought that we had done with\nthem.\n\nThe absolute theory of space is not now generally popular. The knowledge\nof bare space, as a system of entities known to us in itself and for\nitself independently of our knowledge of the events in nature, does not\nseem to correspond to anything in our experience. Space, like time,\nwould appear to be an abstraction from events. According to my own\ntheory it only differentiates itself from time at a somewhat developed\nstage of the abstractive process. The more usual way of expressing the\nrelational theory of space would be to consider space as an abstraction\nfrom the relations between material objects.\n\nSuppose now we assume absolute time and absolute space. What bearing\nhas this assumption on the concept of nature as bifurcated into causal\nnature and apparent nature? Undoubtedly the separation between the two\nnatures is now greatly mitigated. We can provide them with two systems\nof relations in common; for both natures can be presumed to occupy the\nsame space and the same time. The theory now is this: Causal events\noccupy certain periods of the absolute time and occupy certain positions\nof the absolute space. These events influence a mind which thereupon\nperceives certain apparent events which occupy certain periods in the\nabsolute time and occupy certain positions of the absolute space; and\nthe periods and positions occupied by the apparent events bear a\ndeterminate relation to the periods and positions occupied by the causal\nevents.\n\nFurthermore definite causal events produce for the mind definite\napparent events. Delusions are apparent events which appear in temporal\nperiods and spatial positions without the intervention of these causal\nevents which are proper for influencing of the mind to their perception.\n\nThe whole theory is perfectly logical. In these discussions we cannot\nhope to drive an unsound theory to a logical contradiction. A reasoner,\napart from mere slips, only involves himself in a contradiction when he\nis shying at a _reductio ad absurdum_. The substantial reason for\nrejecting a philosophical theory is the 'absurdum' to which it reduces\nus. In the case of the philosophy of natural science the 'absurdum' can\nonly be that our perceptual knowledge has not the character assigned to\nit by the theory. If our opponent affirms that his knowledge has that\ncharacter, we can only--after making doubly sure that we understand\neach other--agree to differ. Accordingly the first duty of an expositor\nin stating a theory in which he disbelieves is to exhibit it as logical.\nIt is not there where his trouble lies.\n\nLet me summarise the previously stated objections to this theory of\nnature. In the first place it seeks for the cause of the knowledge of\nthe thing known instead of seeking for the character of the thing known:\nsecondly it assumes a knowledge of time in itself apart from events\nrelated in time: thirdly it assumes a knowledge of space in itself apart\nfrom events related in space. There are in addition to these objections\nother flaws in the theory.\n\nSome light is thrown on the artificial status of causal nature in this\ntheory by asking, why causal nature is presumed to occupy time and\nspace. This really raises the fundamental question as to what\ncharacteristics causal nature should have in common with apparent\nnature. Why--on this theory--should the cause which influences the mind\nto perception have any characteristics in common with the effluent\napparent nature? In particular, why should it be in space? Why should it\nbe in time? And more generally, What do we know about mind which would\nallow us to infer any particular characteristics of a cause which should\ninfluence mind to particular effects?\n\nThe transcendence of time beyond nature gives some slight reason for\npresuming that causal nature should occupy time. For if the mind\noccupies periods of time, there would seem to be some vague reason for\nassuming that influencing causes occupy the same periods of time, or at\nleast, occupy periods which are strictly related to the mental periods.\nBut if the mind does not occupy volumes of space, there seems to be no\nreason why causal nature should occupy any volumes of space. Thus space\nwould seem to be merely apparent in the same sense as apparent nature is\nmerely apparent. Accordingly if science is really investigating causes\nwhich operate on the mind, it would seem to be entirely on the wrong\ntack in presuming that the causes which it is seeking for have spatial\nrelations. Furthermore there is nothing else in our knowledge analogous\nto these causes which influence the mind to perception. Accordingly,\nbeyond the rashly presumed fact that they occupy time, there is really\nno ground by which we can determine any point of their character. They\nmust remain for ever unknown.\n\nNow I assume as an axiom that science is not a fairy tale. It is not\nengaged in decking out unknowable entities with arbitrary and fantastic\nproperties. What then is it that science is doing, granting that it is\neffecting something of importance? My answer is that it is determining\nthe character of things known, namely the character of apparent nature.\nBut we may drop the term 'apparent'; for there is but one nature, namely\nthe nature which is before us in perceptual knowledge. The characters\nwhich science discerns in nature are subtle characters, not obvious at\nfirst sight. They are relations of relations and characters of\ncharacters. But for all their subtlety they are stamped with a certain\nsimplicity which makes their consideration essential in unravelling the\ncomplex relations between characters of more perceptive insistence.\n\nThe fact that the bifurcation of nature into causal and apparent\ncomponents does not express what we mean by our knowledge is brought\nbefore us when we realise our thoughts in any discussion of the causes\nof our perceptions. For example, the fire is burning and we see a red\ncoal. This is explained in science by radiant energy from the coal\nentering our eyes. But in seeking for such an explanation we are not\nasking what are the sort of occurrences which are fitted to cause a mind\nto see red. The chain of causation is entirely different. The mind is\ncut out altogether. The real question is, When red is found in nature,\nwhat else is found there also? Namely we are asking for an analysis of\nthe accompaniments in nature of the discovery of red in nature. In a\nsubsequent lecture I shall expand this line of thought. I simply draw\nattention to it here in order to point out that the wave-theory of light\nhas not been adopted because waves are just the sort of things which\nought to make a mind perceive colours. This is no part of the evidence\nwhich has ever been adduced for the wave-theory, yet on the causal\ntheory of perception, it is really the only relevant part. In other\nwords, science is not discussing the causes of knowledge, but the\ncoherence of knowledge. The understanding which is sought by science is\nan understanding of relations within nature.\n\nSo far I have discussed the bifurcation of nature in connexion with the\ntheories of absolute time and of absolute space. My reason has been that\nthe introduction of the relational theories only weakens the case for\nbifurcation, and I wished to discuss this case on its strongest grounds.\n\nFor instance, suppose we adopt the relational theory of space. Then the\nspace in which apparent nature is set is the expression of certain\nrelations between the apparent objects. It is a set of apparent\nrelations between apparent relata. Apparent nature is the dream, and\nthe apparent relations of space are dream relations, and the space is\nthe dream space. Similarly the space in which causal nature is set is\nthe expression of certain relations between the causal objects. It is\nthe expression of certain facts about the causal activity which is going\non behind the scenes. Accordingly causal space belongs to a different\norder of reality to apparent space. Hence there is no pointwise\nconnexion between the two and it is meaningless to say that the\nmolecules of the grass are in any place which has a determinate spatial\nrelation to the place occupied by the grass which we see. This\nconclusion is very paradoxical and makes nonsense of all scientific\nphraseology. The case is even worse if we admit the relativity of time.\nFor the same arguments apply, and break up time into the dream time and\ncausal time which belong to different orders of reality.\n\nI have however been discussing an extreme form of the bifurcation\ntheory. It is, as I think, the most defensible form. But its very\ndefiniteness makes it the more evidently obnoxious to criticism. The\nintermediate form allows that the nature we are discussing is always the\nnature directly known, and so far it rejects the bifurcation theory. But\nit holds that there are psychic additions to nature as thus known, and\nthat these additions are in no proper sense part of nature. For example,\nwe perceive the red billiard ball at its proper time, in its proper\nplace, with its proper motion, with its proper hardness, and with its\nproper inertia. But its redness and its warmth, and the sound of the\nclick as a cannon is made off it are psychic additions, namely,\nsecondary qualities which are only the mind's way of perceiving nature.\nThis is not only the vaguely prevalent theory, but is, I believe, the\nhistorical form of the bifurcation theory in so far as it is derived\nfrom philosophy. I shall call it the theory of psychic additions.\n\nThis theory of psychic additions is a sound common-sense theory which\nlays immense stress on the obvious reality of time, space, solidity and\ninertia, but distrusts the minor artistic additions of colour, warmth\nand sound.\n\nThe theory is the outcome of common-sense in retreat. It arose in an\nepoch when the transmission theories of science were being elaborated.\nFor example, colour is the result of a transmission from the material\nobject to the perceiver's eye; and what is thus transmitted is not\ncolour. Thus colour is not part of the reality of the material object.\nSimilarly for the same reason sounds evaporate from nature. Also warmth\nis due to the transfer of something which is not temperature. Thus we\nare left with spatio-temporal positions, and what I may term the\n'pushiness' of the body. This lands us to eighteenth and nineteenth\ncentury materialism, namely, the belief that what is real in nature is\nmatter, in time and in space and with inertia.\n\nEvidently a distinction in quality has been presupposed separating off\nsome perceptions due to touch from other perceptions. These\ntouch-perceptions are perceptions of the real inertia, whereas the other\nperceptions are psychic additions which must be explained on the causal\ntheory. This distinction is the product of an epoch in which physical\nscience has got ahead of medical pathology and of physiology.\nPerceptions of push are just as much the outcome of transmission as are\nperceptions of colour. When colour is perceived the nerves of the body\nare excited in one way and transmit their message towards the brain, and\nwhen push is perceived other nerves of the body are excited in another\nway and transmit their message towards the brain. The message of the one\nset is not the conveyance of colour, and the message of the other set is\nnot the conveyance of push. But in one case colour is perceived and in\nthe other case the push due to the object. If you snip certain nerves,\nthere is an end to the perception of colour; and if you snip certain\nother nerves, there is an end to the perception of push. It would appear\ntherefore that any reasons which should remove colour from the reality\nof nature should also operate to remove inertia.\n\nThus the attempted bifurcation of apparent nature into two parts of\nwhich one part is both causal for its own appearance and for the\nappearance of the other part, which is purely apparent, fails owing to\nthe failure to establish any fundamental distinction between our ways of\nknowing about the two parts of nature as thus partitioned. I am not\ndenying that the feeling of muscular effort historically led to the\nformulation of the concept of force. But this historical fact does not\nwarrant us in assigning a superior reality in nature to material inertia\nover colour or sound. So far as reality is concerned all our\nsense-perceptions are in the same boat, and must be treated on the same\nprinciple. The evenness of treatment is exactly what this compromise\ntheory fails to achieve.\n\nThe bifurcation theory however dies hard. The reason is that there\nreally is a difficulty to be faced in relating within the same system of\nentities the redness of the fire with the agitation of the molecules. In\nanother lecture I will give my own explanation of the origin of the\ndifficulty and of its solution.\n\nAnother favourite solution, the most attenuated form which the\nbifurcation theory assumes, is to maintain that the molecules and ether\nof science are purely conceptual. Thus there is but one nature, namely\napparent nature, and atoms and ether are merely names for logical terms\nin conceptual formulae of calculation.\n\nBut what is a formula of calculation? It is presumably a statement that\nsomething or other is true for natural occurrences. Take the simplest of\nall formulae, Two and two make four. This--so far as it applies to\nnature--asserts that if you take two natural entities, and then again\ntwo other natural entities, the combined class contains four natural\nentities. Such formulae which are true for any entities cannot result in\nthe production of the concepts of atoms. Then again there are formulae\nwhich assert that there are entities in nature with such and such\nspecial properties, say, for example, with the properties of the atoms\nof hydrogen. Now if there are no such entities, I fail to see how any\nstatements about them can apply to nature. For example, the assertion\nthat there is green cheese in the moon cannot be a premiss in any\ndeduction of scientific importance, unless indeed the presence of green\ncheese in the moon has been verified by experiment. The current answer\nto these objections is that, though atoms are merely conceptual, yet\nthey are an interesting and picturesque way of saying something else\nwhich is true of nature. But surely if it is something else that you\nmean, for heaven's sake say it. Do away with this elaborate machinery of\na conceptual nature which consists of assertions about things which\ndon't exist in order to convey truths about things which do exist. I am\nmaintaining the obvious position that scientific laws, if they are true,\nare statements about entities which we obtain knowledge of as being in\nnature; and that, if the entities to which the statements refer are not\nto be found in nature, the statements about them have no relevance to\nany purely natural occurrence. Thus the molecules and electrons of\nscientific theory are, so far as science has correctly formulated its\nlaws, each of them factors to be found in nature. The electrons are only\nhypothetical in so far as we are not quite certain that the electron\ntheory is true. But their hypothetical character does not arise from the\nessential nature of the theory in itself after its truth has been\ngranted.\n\nThus at the end of this somewhat complex discussion, we return to the\nposition which was affirmed at its beginning. The primary task of a\nphilosophy of natural science is to elucidate the concept of nature,\nconsidered as one complex fact for knowledge, to exhibit the fundamental\nentities and the fundamental relations between entities in terms of\nwhich all laws of nature have to be stated, and to secure that the\nentities and relations thus exhibited are adequate for the expression of\nall the relations between entities which occur in nature.\n\nThe third requisite, namely that of adequacy, is the one over which all\nthe difficulty occurs. The ultimate data of science are commonly assumed\nto be time, space, material, qualities of material, and relations\nbetween material objects. But data as they occur in the scientific laws\ndo not relate all the entities which present themselves in our\nperception of nature. For example, the wave-theory of light is an\nexcellent well-established theory; but unfortunately it leaves out\ncolour as perceived. Thus the perceived redness--or, other colour--has\nto be cut out of nature and made into the reaction of the mind under the\nimpulse of the actual events of nature. In other words this concept of\nthe fundamental relations within nature is inadequate. Thus we have to\nbend our energies to the enunciation of adequate concepts.\n\nBut in so doing, are we not in fact endeavouring to solve a metaphysical\nproblem? I do not think so. We are merely endeavouring to exhibit the\ntype of relations which hold between the entities which we in fact\nperceive as in nature. We are not called on to make any pronouncement as\nto the psychological relation of subjects to objects or as to the status\nof either in the realm of reality. It is true that the issue of our\nendeavour may provide material which is relevant evidence for a\ndiscussion on that question. It can hardly fail to do so. But it is only\nevidence, and is not itself the metaphysical discussion. In order to\nmake clear the character of this further discussion which is out of our\nken, I will set before you two quotations. One is from Schelling and I\nextract the quotation from the work of the Russian philosopher Lossky\nwhich has recently been so excellently translated into English[4]--'In\nthe \"Philosophy of Nature\" I considered the subject-object called nature\nin its activity of self-constructing. In order to understand it, we must\nrise to an intellectual intuition of nature. The empiricist does not\nrise thereto, and for this reason in all his explanations it is always\n_he himself_ that proves to be constructing nature. It is no wonder,\nthen, that his construction and that which was to be constructed so\nseldom coincide. A _Natur-philosoph_ raises nature to independence, and\nmakes it construct itself, and he never feels, therefore, the necessity\nof opposing nature as constructed (_i.e._ as experience) to real\nnature, or of correcting the one by means of the other.'\n\n[4] _The Intuitive Basis of Knowledge_, by N.\u00a0O. Lossky, transl. by Mrs\nDuddington, Macmillan and Co., 1919.\n\nThe other quotation is from a paper read by the Dean of St Paul's before\nthe Aristotelian Society in May of 1919. Dr Inge's paper is entitled\n'Platonism and Human Immortality,' and in it there occurs the following\nstatement: 'To sum up. The Platonic doctrine of immortality rests on the\n_independence_ of the spiritual world. The spiritual world is not a\nworld of unrealised ideals, over against a real world of unspiritual\nfact. It is, on the contrary, the real world, of which we have a true\nthough very incomplete knowledge, over against a world of common\nexperience which, as a complete whole, is not real, since it is\ncompacted out of miscellaneous data, not all on the same level, by the\nhelp of the imagination. There is no world corresponding to the world of\nour common experience. Nature makes abstractions for us, deciding what\nrange of vibrations we are to see and hear, what things we are to notice\nand remember.'\n\nI have cited these statements because both of them deal with topics\nwhich, though they lie outside the range of our discussion, are always\nbeing confused with it. The reason is that they lie proximate to our\nfield of thought, and are topics which are of burning interest to the\nmetaphysically minded. It is difficult for a philosopher to realise that\nanyone really is confining his discussion within the limits that I have\nset before you. The boundary is set up just where he is beginning to get\nexcited. But I submit to you that among the necessary prolegomena for\nphilosophy and for natural science is a thorough understanding of the\ntypes of entities, and types of relations among those entities, which\nare disclosed to us in our perceptions of nature.\n\n\n\n\nCHAPTER III\n\nTIME\n\n\nThe two previous lectures of this course have been mainly critical. In\nthe present lecture I propose to enter upon a survey of the kinds of\nentities which are posited for knowledge in sense-awareness. My purpose\nis to investigate the sorts of relations which these entities of various\nkinds can bear to each other. A classification of natural entities is\nthe beginning of natural philosophy. To-day we commence with the\nconsideration of Time.\n\nIn the first place there is posited for us a general fact: namely,\nsomething is going on; there is an occurrence for definition.\n\nThis general fact at once yields for our apprehension two factors, which\nI will name, the 'discerned' and the 'discernible.' The discerned is\ncomprised of those elements of the general fact which are discriminated\nwith their own individual peculiarities. It is the field directly\nperceived. But the entities of this field have relations to other\nentities which are not particularly discriminated in this individual\nway. These other entities are known merely as the relata in relation to\nthe entities of the discerned field. Such an entity is merely a\n'something' which has such-and-such definite relations to some definite\nentity or entities in the discerned field. As being thus related, they\nare--owing to the particular character of these relations--known as\nelements of the general fact which is going on. But we are not aware of\nthem except as entities fulfilling the functions of relata in these\nrelations.\n\nThus the complete general fact, posited as occurring, comprises both\nsets of entities, namely the entities perceived in their own\nindividuality and other entities merely apprehended as relata without\nfurther definition. This complete general fact is the discernible and it\ncomprises the discerned. The discernible is all nature as disclosed in\nthat sense-awareness, and extends beyond and comprises all of nature as\nactually discriminated or discerned in that sense-awareness. The\ndiscerning or discrimination of nature is a peculiar awareness of\nspecial factors in nature in respect to their peculiar characters. But\nthe factors in nature of which we have this peculiar sense-awareness are\nknown as not comprising all the factors which together form the whole\ncomplex of related entities within the general fact there for\ndiscernment. This peculiarity of knowledge is what I call its\nunexhaustive character. This character may be metaphorically described\nby the statement that nature as perceived always has a ragged edge. For\nexample, there is a world beyond the room to which our sight is confined\nknown to us as completing the space-relations of the entities discerned\nwithin the room. The junction of the interior world of the room with the\nexterior world beyond is never sharp. Sounds and subtler factors\ndisclosed in sense-awareness float in from the outside. Every type of\nsense has its own set of discriminated entities which are known to be\nrelata in relation with entities not discriminated by that sense. For\nexample we see something which we do not touch and we touch something\nwhich we do not see, and we have a general sense of the space-relations\nbetween the entity disclosed in sight and the entity disclosed in touch.\nThus in the first place each of these two entities is known as a relatum\nin a general system of space-relations and in the second place the\nparticular mutual relation of these two entities as related to each\nother in this general system is determined. But the general system of\nspace-relations relating the entity discriminated by sight with that\ndiscriminated by sight is not dependent on the peculiar character of the\nother entity as reported by the alternative sense. For example, the\nspace-relations of the thing seen would have necessitated an entity as a\nrelatum in the place of the thing touched even although certain elements\nof its character had not been disclosed by touch. Thus apart from the\ntouch an entity with a certain specific relation to the thing seen would\nhave been disclosed by sense-awareness but not otherwise discriminated\nin respect to its individual character. An entity merely known as\nspatially related to some discerned entity is what we mean by the bare\nidea of 'place.' The concept of place marks the disclosure in\nsense-awareness of entities in nature known merely by their spatial\nrelations to discerned entities. It is the disclosure of the discernible\nby means of its relations to the discerned.\n\nThis disclosure of an entity as a relatum without further specific\ndiscrimination of quality is the basis of our concept of significance.\nIn the above example the thing seen was significant, in that it\ndisclosed its spatial relations to other entities not necessarily\notherwise entering into consciousness. Thus significance is relatedness,\nbut it is relatedness with the emphasis on one end only of the relation.\n\nFor the sake of simplicity I have confined the argument to spatial\nrelations; but the same considerations apply to temporal relations. The\nconcept of 'period of time' marks the disclosure in sense-awareness of\nentities in nature known merely by their temporal relations to\ndiscerned entities. Still further, this separation of the ideas of space\nand time has merely been adopted for the sake of gaining simplicity of\nexposition by conformity to current language. What we discern is the\nspecific character of a place through a period of time. This is what I\nmean by an 'event.' We discern some specific character of an event. But\nin discerning an event we are also aware of its significance as a\nrelatum in the structure of events. This structure of events is the\ncomplex of events as related by the two relations of extension and\ncogredience. The most simple expression of the properties of this\nstructure are to be found in our spatial and temporal relations. A\ndiscerned event is known as related in this structure to other events\nwhose specific characters are otherwise not disclosed in that immediate\nawareness except so far as that they are relata within the structure.\n\nThe disclosure in sense-awareness of the structure of events classifies\nevents into those which are discerned in respect to some further\nindividual character and those which are not otherwise disclosed except\nas elements of the structure. These signified events must include events\nin the remote past as well as events in the future. We are aware of\nthese as the far off periods of unbounded time. But there is another\nclassification of events which is also inherent in sense-awareness.\nThese are the events which share the immediacy of the immediately\npresent discerned events. These are the events whose characters together\nwith those of the discerned events comprise all nature present for\ndiscernment. They form the complete general fact which is all nature now\npresent as disclosed in that sense-awareness. It is in this second\nclassification of events that the differentiation of space from time\ntakes its origin. The germ of space is to be found in the mutual\nrelations of events within the immediate general fact which is all\nnature now discernible, namely within the one event which is the\ntotality of present nature. The relations of other events to this\ntotality of nature form the texture of time.\n\nThe unity of this general present fact is expressed by the concept of\nsimultaneity. The general fact is the whole simultaneous occurrence of\nnature which is now for sense-awareness. This general fact is what I\nhave called the discernible. But in future I will call it a 'duration,'\nmeaning thereby a certain whole of nature which is limited only by the\nproperty of being a simultaneity. Further in obedience to the principle\nof comprising within nature the whole terminus of sense-awareness,\nsimultaneity must not be conceived as an irrelevant mental concept\nimposed upon nature. Our sense-awareness posits for immediate\ndiscernment a certain whole, here called a 'duration'; thus a duration\nis a definite natural entity. A duration is discriminated as a complex\nof partial events, and the natural entities which are components of this\ncomplex are thereby said to be 'simultaneous with this duration.' Also\nin a derivative sense they are simultaneous with each other in respect\nto this duration. Thus simultaneity is a definite natural relation. The\nword 'duration' is perhaps unfortunate in so far as it suggests a mere\nabstract stretch of time. This is not what I mean. A duration is a\nconcrete slab of nature limited by simultaneity which is an essential\nfactor disclosed in sense-awareness.\n\nNature is a process. As in the case of everything directly exhibited in\nsense-awareness, there can be no explanation of this characteristic of\nnature. All that can be done is to use language which may speculatively\ndemonstrate it, and also to express the relation of this factor in\nnature to other factors.\n\nIt is an exhibition of the process of nature that each duration happens\nand passes. The process of nature can also be termed the passage of\nnature. I definitely refrain at this stage from using the word 'time,'\nsince the measurable time of science and of civilised life generally\nmerely exhibits some aspects of the more fundamental fact of the passage\nof nature. I believe that in this doctrine I am in full accord with\nBergson, though he uses 'time' for the fundamental fact which I call the\n'passage of nature.' Also the passage of nature is exhibited equally in\nspatial transition as well as in temporal transition. It is in virtue of\nits passage that nature is always moving on. It is involved in the\nmeaning of this property of 'moving on' that not only is any act of\nsense-awareness just that act and no other, but the terminus of each act\nis also unique and is the terminus of no other act. Sense-awareness\nseizes its only chance and presents for knowledge something which is for\nit alone.\n\nThere are two senses in which the terminus of sense-awareness is unique.\nIt is unique for the sense-awareness of an individual mind and it is\nunique for the sense-awareness of all minds which are operating under\nnatural conditions. There is an important distinction between the two\ncases. (i) For one mind not only is the discerned component of the\ngeneral fact exhibited in any act of sense-awareness distinct from the\ndiscerned component of the general fact exhibited in any other act of\nsense-awareness of that mind, but the two corresponding durations which\nare respectively related by simultaneity to the two discerned components\nare necessarily distinct. This is an exhibition of the temporal passage\nof nature; namely, one duration has passed into the other. Thus not only\nis the passage of nature an essential character of nature in its _r\u00f4le_\nof the terminus of sense-awareness, but it is also essential for\nsense-awareness in itself. It is this truth which makes time appear to\nextend beyond nature. But what extends beyond nature to mind is not the\nserial and measurable time, which exhibits merely the character of\npassage in nature, but the quality of passage itself which is in no way\nmeasurable except so far as it obtains in nature. That is to say,\n'passage' is not measurable except as it occurs in nature in connexion\nwith extension. In passage we reach a connexion of nature with the\nultimate metaphysical reality. The quality of passage in durations is a\nparticular exhibition in nature of a quality which extends beyond\nnature. For example passage is a quality not only of nature, which is\nthe thing known, but also of sense-awareness which is the procedure of\nknowing. Durations have all the reality that nature has, though what\nthat may be we need not now determine. The measurableness of time is\nderivative from the properties of durations. So also is the serial\ncharacter of time. We shall find that there are in nature competing\nserial time-systems derived from different families of durations. These\nare a peculiarity of the character of passage as it is found in nature.\nThis character has the reality of nature, but we must not necessarily\ntransfer natural time to extra-natural entities. (ii) For two minds, the\ndiscerned components of the general facts exhibited in their respective\nacts of sense-awareness must be different. For each mind, in its\nawareness of nature is aware of a certain complex of related natural\nentities in their relations to the living body as a focus. But the\nassociated durations may be identical. Here we are touching on that\ncharacter of the passage nature which issues in the spatial relations of\nsimultaneous bodies. This possible identity of the durations in the case\nof the sense-awareness of distinct minds is what binds into one nature\nthe private experiences of sentient beings. We are here considering the\nspatial side of the passage of nature. Passage in this aspect of it also\nseems to extend beyond nature to mind.\n\nIt is important to distinguish simultaneity from instantaneousness. I\nlay no stress on the mere current usage of the two terms. There are two\nconcepts which I want to distinguish, and one I call simultaneity and\nthe other instantaneousness. I hope that the words are judiciously\nchosen; but it really does not matter so long as I succeed in explaining\nmy meaning. Simultaneity is the property of a group of natural elements\nwhich in some sense are components of a duration. A duration can be all\nnature present as the immediate fact posited by sense-awareness. A\nduration retains within itself the passage of nature. There are within\nit antecedents and consequents which are also durations which may be the\ncomplete specious presents of quicker consciousnesses. In other words a\nduration retains temporal thickness. Any concept of all nature as\nimmediately known is always a concept of some duration though it may be\nenlarged in its temporal thickness beyond the possible specious present\nof any being known to us as existing within nature. Thus simultaneity is\nan ultimate factor in nature, immediate for sense-awareness.\n\nInstantaneousness is a complex logical concept of a procedure in thought\nby which constructed logical entities are produced for the sake of the\nsimple expression in thought of properties of nature. Instantaneousness\nis the concept of all nature at an instant, where an instant is\nconceived as deprived of all temporal extension. For example we conceive\nof the distribution of matter in space at an instant. This is a very\nuseful concept in science especially in applied mathematics; but it is a\nvery complex idea so far as concerns its connexions with the immediate\nfacts of sense-awareness. There is no such thing as nature at an instant\nposited by sense-awareness. What sense-awareness delivers over for\nknowledge is nature through a period. Accordingly nature at an instant,\nsince it is not itself a natural entity, must be defined in terms of\ngenuine natural entities. Unless we do so, our science, which employs\nthe concept of instantaneous nature, must abandon all claim to be\nfounded upon observation.\n\nI will use the term 'moment' to mean 'all nature at an instant.' A\nmoment, in the sense in which the term is here used, has no temporal\nextension, and is in this respect to be contrasted with a duration which\nhas such extension. What is directly yielded to our knowledge by\nsense-awareness is a duration. Accordingly we have now to explain how\nmoments are derived from durations, and also to explain the purpose\nserved by their introduction.\n\nA moment is a limit to which we approach as we confine attention to\ndurations of minimum extension. Natural relations among the ingredients\nof a duration gain in complexity as we consider durations of increasing\ntemporal extension. Accordingly there is an approach to ideal simplicity\nas we approach an ideal diminution of extension.\n\nThe word 'limit' has a precise signification in the logic of number and\neven in the logic of non-numerical one-dimensional series. As used here\nit is so far a mere metaphor, and it is necessary to explain directly\nthe concept which it is meant to indicate.\n\nDurations can have the two-termed relational property of extending one\nover the other. Thus the duration which is all nature during a certain\nminute extends over the duration which is all nature during the\n30th\u00a0second of that minute. This relation of 'extending\nover'--'extension' as I shall call it--is a fundamental natural relation\nwhose field comprises more than durations. It is a relation which two\nlimited events can have to each other. Furthermore as holding between\ndurations the relation appears to refer to the purely temporal\nextension. I shall however maintain that the same relation of extension\nlies at the base both of temporal and spatial extension. This discussion\ncan be postponed; and for the present we are simply concerned with the\nrelation of extension as it occurs in its temporal aspect for the\nlimited field of durations.\n\nThe concept of extension exhibits in thought one side of the ultimate\npassage of nature. This relation holds because of the special character\nwhich passage assumes in nature; it is the relation which in the case of\ndurations expresses the properties of 'passing over.' Thus the duration\nwhich was one definite minute passed over the duration which was its\n30th\u00a0second. The duration of the 30th\u00a0second was part of the duration of\nthe minute. I shall use the terms 'whole' and 'part' exclusively in this\nsense, that the 'part' is an event which is extended over by the other\nevent which is the 'whole.' Thus in my nomenclature 'whole' and 'part'\nrefer exclusively to this fundamental relation of extension; and\naccordingly in this technical usage only events can be either wholes or\nparts.\n\nThe continuity of nature arises from extension. Every event extends over\nother events, and every event is extended over by other events. Thus in\nthe special case of durations which are now the only events directly\nunder consideration, every duration is part of other durations; and\nevery duration has other durations which are parts of it. Accordingly\nthere are no maximum durations and no minimum durations. Thus there is\nno atomic structure of durations, and the perfect definition of a\nduration, so as to mark out its individuality and distinguish it from\nhighly analogous durations over which it is passing, or which are\npassing over it, is an arbitrary postulate of thought. Sense-awareness\nposits durations as factors in nature but does not clearly enable\nthought to use it as distinguishing the separate individualities of the\nentities of an allied group of slightly differing durations. This is one\ninstance of the indeterminateness of sense-awareness. Exactness is an\nideal of thought, and is only realised in experience by the selection of\na route of approximation.\n\nThe absence of maximum and minimum durations does not exhaust the\nproperties of nature which make up its continuity. The passage of nature\ninvolves the existence of a family of durations. When two durations\nbelong to the same family either one contains the other, or they overlap\neach other in a subordinate duration without either containing the\nother; or they are completely separate. The excluded case is that of\ndurations overlapping in finite events but not containing a third\nduration as a common part.\n\nIt is evident that the relation of extension is transitive; namely as\napplied to durations, if duration A is part of duration B, and\nduration B is part of duration C, then A is part of C. Thus the\nfirst two cases may be combined into one and we can say that two\ndurations which belong to the same family _either_ are such that there\nare durations which are parts of both _or_ are completely separate.\n\nFurthermore the converse of this proposition holds; namely, if two\ndurations have other durations which are parts of both _or_ if the two\ndurations are completely separate, then they belong to the same family.\n\nThe further characteristics of the continuity of nature--so far as\ndurations are concerned--which has not yet been formulated arises in\nconnexion with a family of durations. It can be stated in this way:\nThere are durations which contain as parts any two durations of the same\nfamily. For example a week contains as parts any two of its days. It is\nevident that a containing duration satisfies the conditions for\nbelonging to the same family as the two contained durations.\n\nWe are now prepared to proceed to the definition of a moment of time.\nConsider a set of durations all taken from the same family. Let it have\nthe following properties: (i) of any two members of the set one contains\nthe other as a part, and (ii) there is no duration which is a common\npart of every member of the set.\n\nNow the relation of whole and part is asymmetrical; and by this I mean\nthat if A is part of B, then B is not part of A. Also we have\nalready noted that the relation is transitive. Accordingly we can easily\nsee that the durations of any set with the properties just enumerated\nmust be arranged in a one-dimensional serial order in which as we\ndescend the series we progressively reach durations of smaller and\nsmaller temporal extension. The series may start with any arbitrarily\nassumed duration of any temporal extension, but in descending the\nseries the temporal extension progressively contracts and the successive\ndurations are packed one within the other like the nest of boxes of a\nChinese toy. But the set differs from the toy in this particular: the\ntoy has a smallest box which forms the end box of its series; but the\nset of durations can have no smallest duration nor can it converge\ntowards a duration as its limit. For the parts either of the end\nduration or of the limit would be parts of all the durations of the set\nand thus the second condition for the set would be violated.\n\nI will call such a set of durations an 'abstractive set' of durations.\nIt is evident that an abstractive set as we pass along it converges to\nthe ideal of all nature with no temporal extension, namely, to the ideal\nof all nature at an instant. But this ideal is in fact the ideal of a\nnonentity. What the abstractive set is in fact doing is to guide thought\nto the consideration of the progressive simplicity of natural relations\nas we progressively diminish the temporal extension of the duration\nconsidered. Now the whole point of the procedure is that the\nquantitative expressions of these natural properties do converge to\nlimits though the abstractive set does not converge to any limiting\nduration. The laws relating these quantitative limits are the laws of\nnature 'at an instant,' although in truth there is no nature at an\ninstant and there is only the abstractive set. Thus an abstractive set\nis effectively the entity meant when we consider an instant of time\nwithout temporal extension. It subserves all the necessary purposes of\ngiving a definite meaning to the concept of the properties of nature at\nan instant. I fully agree that this concept is fundamental in the\nexpression of physical science. The difficulty is to express our\nmeaning in terms of the immediate deliverances of sense-awareness, and I\noffer the above explanation as a complete solution of the problem.\n\nIn this explanation a moment is the set of natural properties reached by\na route of approximation. An abstractive series is a route of\napproximation. There are different routes of approximation to the same\nlimiting set of the properties of nature. In other words there are\ndifferent abstractive sets which are to be regarded as routes of\napproximation to the same moment. Accordingly there is a certain amount\nof technical detail necessary in explaining the relations of such\nabstractive sets with the same convergence and in guarding against\npossible exceptional cases. Such details are not suitable for exposition\nin these lectures, and I have dealt with them fully elsewhere[5].\n\n[5] Cf. _An Enquiry concerning the Principles of Natural Knowledge_,\nCambridge University Press, 1919.\n\nIt is more convenient for technical purposes to look on a moment as\nbeing the class of all abstractive sets of durations with the same\nconvergence. With this definition (provided that we can successfully\nexplain what we mean by the 'same convergence' apart from a detailed\nknowledge of the set of natural properties arrived at by approximation)\na moment is merely a class of sets of durations whose relations of\nextension in respect to each other have certain definite peculiarities.\nWe may term these connexions of the component durations the 'extrinsic'\nproperties of a moment; the 'intrinsic' properties of the moment are the\nproperties of nature arrived at as a limit as we proceed along any one\nof its abstractive sets. These are the properties of nature 'at that\nmoment,' or 'at that instant.'\n\nThe durations which enter into the composition of a moment all belong to\none family. Thus there is one family of moments corresponding to one\nfamily of durations. Also if we take two moments of the same family,\namong the durations which enter into the composition of one moment the\nsmaller durations are completely separated from the smaller durations\nwhich enter into the composition of the other moment. Thus the two\nmoments in their intrinsic properties must exhibit the limits of\ncompletely different states of nature. In this sense the two moments are\ncompletely separated. I will call two moments of the same family\n'parallel.'\n\nCorresponding to each duration there are two moments of the associated\nfamily of moments which are the boundary moments of that duration. A\n'boundary moment' of a duration can be defined in this way. There are\ndurations of the same family as the given duration which overlap it but\nare not contained in it. Consider an abstractive set of such durations.\nSuch a set defines a moment which is just as much without the duration\nas within it. Such a moment is a boundary moment of the duration. Also\nwe call upon our sense-awareness of the passage of nature to inform us\nthat there are two such boundary moments, namely the earlier one and the\nlater one. We will call them the initial and the final boundaries.\n\nThere are also moments of the same family such that the shorter\ndurations in their composition are entirely separated from the given\nduration. Such moments will be said to lie 'outside' the given duration.\nAgain other moments of the family are such that the shorter durations in\ntheir composition are parts of the given duration. Such moments are said\nto lie 'within' the given duration or to 'inhere' in it. The whole\nfamily of parallel moments is accounted for in this way by reference to\nany given duration of the associated family of durations. Namely, there\nare moments of the family which lie without the given duration, there\nare the two moments which are the boundary moments of the given\nduration, and the moments which lie within the given duration.\nFurthermore any two moments of the same family are the boundary moments\nof some one duration of the associated family of durations.\n\nIt is now possible to define the serial relation of temporal order among\nthe moments of a family. For let A and C be any two moments of the\nfamily, these moments are the boundary moments of one duration d of\nthe associated family, and any moment B which lies within the duration\nd will be said to lie between the moments A and C. Thus the\nthree-termed relation of 'lying-between' as relating three moments A,\nB, and C is completely defined. Also our knowledge of the passage of\nnature assures us that this relation distributes the moments of the\nfamily into a serial order. I abstain from enumerating the definite\nproperties which secure this result, I have enumerated them in my\nrecently published book[6] to which I have already referred. Furthermore\nthe passage of nature enables us to know that one direction along the\nseries corresponds to passage into the future and the other direction\ncorresponds to retrogression towards the past.\n\n[6] Cf. _Enquiry_.\n\nSuch an ordered series of moments is what we mean by time defined as a\nseries. Each element of the series exhibits an instantaneous state of\nnature. Evidently this serial time is the result of an intellectual\nprocess of abstraction. What I have done is to give precise definitions\nof the procedure by which the abstraction is effected. This procedure is\nmerely a particular case of the general method which in my book I name\nthe 'method of extensive abstraction.' This serial time is evidently not\nthe very passage of nature itself. It exhibits some of the natural\nproperties which flow from it. The state of nature 'at a moment' has\nevidently lost this ultimate quality of passage. Also the temporal\nseries of moments only retains it as an extrinsic relation of entities\nand not as the outcome of the essential being of the terms of the\nseries.\n\nNothing has yet been said as to the measurement of time. Such\nmeasurement does not follow from the mere serial property of time; it\nrequires a theory of congruence which will be considered in a later\nlecture.\n\nIn estimating the adequacy of this definition of the temporal series as\na formulation of experience it is necessary to discriminate between the\ncrude deliverance of sense-awareness and our intellectual theories. The\nlapse of time is a measurable serial quantity. The whole of scientific\ntheory depends on this assumption and any theory of time which fails to\nprovide such a measurable series stands self-condemned as unable to\naccount for the most salient fact in experience. Our difficulties only\nbegin when we ask what it is that is measured. It is evidently something\nso fundamental in experience that we can hardly stand back from it and\nhold it apart so as to view it in its own proportions.\n\nWe have first to make up our minds whether time is to be found in nature\nor nature is to be found in time. The difficulty of the latter\nalternative--namely of making time prior to nature--is that time then\nbecomes a metaphysical enigma. What sort of entities are its instants\nor its periods? The dissociation of time from events discloses to our\nimmediate inspection that the attempt to set up time as an independent\nterminus for knowledge is like the effort to find substance in a shadow.\nThere is time because there are happenings, and apart from happenings\nthere is nothing.\n\nIt is necessary however to make a distinction. In some sense time\nextends beyond nature. It is not true that a timeless sense-awareness\nand a timeless thought combine to contemplate a timeful nature.\nSense-awareness and thought are themselves processes as well as their\ntermini in nature. In other words there is a passage of sense-awareness\nand a passage of thought. Thus the reign of the quality of passage\nextends beyond nature. But now the distinction arises between passage\nwhich is fundamental and the temporal series which is a logical\nabstraction representing some of the properties of nature. A temporal\nseries, as we have defined it, represents merely certain properties of a\nfamily of durations--properties indeed which durations only possess\nbecause of their partaking of the character of passage, but on the other\nhand properties which only durations do possess. Accordingly time in the\nsense of a measurable temporal series is a character of nature only, and\ndoes not extend to the processes of thought and of sense-awareness\nexcept by a correlation of these processes with the temporal series\nimplicated in their procedures.\n\nSo far the passage of nature has been considered in connexion with the\npassage of durations; and in this connexion it is peculiarly associated\nwith temporal series. We must remember however that the character of\npassage is peculiarly associated with the extension of events, and that\nfrom this extension spatial transition arises just as much as temporal\ntransition. The discussion of this point is reserved for a later lecture\nbut it is necessary to remember it now that we are proceeding to discuss\nthe application of the concept of passage beyond nature, otherwise we\nshall have too narrow an idea of the essence of passage.\n\nIt is necessary to dwell on the subject of sense-awareness in this\nconnexion as an example of the way in which time concerns mind, although\nmeasurable time is a mere abstract from nature and nature is closed to\nmind.\n\nConsider sense-awareness--not its terminus which is nature, but\nsense-awareness in itself as a procedure of mind. Sense-awareness is a\nrelation of mind to nature. Accordingly we are now considering mind as a\nrelatum in sense-awareness. For mind there is the immediate\nsense-awareness and there is memory. The distinction between memory and\nthe present immediacy has a double bearing. On the one hand it discloses\nthat mind is not impartially aware of all those natural durations to\nwhich it is related by awareness. Its awareness shares in the passage of\nnature. We can imagine a being whose awareness, conceived as his private\npossession, suffers no transition, although the terminus of his\nawareness is our own transient nature. There is no essential reason why\nmemory should not be raised to the vividness of the present fact; and\nthen from the side of mind, What is the difference between the present\nand the past? Yet with this hypothesis we can also suppose that the\nvivid remembrance and the present fact are posited in awareness as in\ntheir temporal serial order. Accordingly we must admit that though we\ncan imagine that mind in the operation of sense-awareness might be free\nfrom any character of passage, yet in point of fact our experience of\nsense-awareness exhibits our minds as partaking in this character.\n\nOn the other hand the mere fact of memory is an escape from transience.\nIn memory the past is present. It is not present as overleaping the\ntemporal succession of nature, but it is present as an immediate fact\nfor the mind. Accordingly memory is a disengagement of the mind from the\nmere passage of nature; for what has passed for nature has not passed\nfor mind.\n\nFurthermore the distinction between memory and the immediate present is\nnot so clear as it is conventional to suppose. There is an intellectual\ntheory of time as a moving knife-edge, exhibiting a present fact without\ntemporal extension. This theory arises from the concept of an ideal\nexactitude of observation. Astronomical observations are successively\nrefined to be exact to tenths, to hundredths, and to thousandths of\nseconds. But the final refinements are arrived at by a system of\naveraging, and even then present us with a stretch of time as a margin\nof error. Here error is merely a conventional term to express the fact\nthat the character of experience does not accord with the ideal of\nthought. I have already explained how the concept of a moment\nconciliates the observed fact with this ideal; namely, there is a\nlimiting simplicity in the quantitative expression of the properties of\ndurations, which is arrived at by considering any one of the abstractive\nsets included in the moment. In other words the extrinsic character of\nthe moment as an aggregate of durations has associated with it the\nintrinsic character of the moment which is the limiting expression of\nnatural properties.\n\nThus the character of a moment and the ideal of exactness which it\nenshrines do not in any way weaken the position that the ultimate\nterminus of awareness is a duration with temporal thickness. This\nimmediate duration is not clearly marked out for our apprehension. Its\nearlier boundary is blurred by a fading into memory, and its later\nboundary is blurred by an emergence from anticipation. There is no sharp\ndistinction either between memory and the present immediacy or between\nthe present immediacy and anticipation. The present is a wavering\nbreadth of boundary between the two extremes. Thus our own\nsense-awareness with its extended present has some of the character of\nthe sense-awareness of the imaginary being whose mind was free from\npassage and who contemplated all nature as an immediate fact. Our own\npresent has its antecedents and its consequents, and for the imaginary\nbeing all nature has its antecedent and its consequent durations. Thus\nthe only difference in this respect between us and the imaginary being\nis that for him all nature shares in the immediacy of our present\nduration.\n\nThe conclusion of this discussion is that so far as sense-awareness is\nconcerned there is a passage of mind which is distinguishable from the\npassage of nature though closely allied with it. We may speculate, if we\nlike, that this alliance of the passage of mind with the passage of\nnature arises from their both sharing in some ultimate character of\npassage which dominates all being. But this is a speculation in which we\nhave no concern. The immediate deduction which is sufficient for us is\nthat--so far as sense-awareness is concerned--mind is not in time or in\nspace in the same sense in which the events of nature are in time, but\nthat it is derivatively in time and in space by reason of the peculiar\nalliance of its passage with the passage of nature. Thus mind is in time\nand in space in a sense peculiar to itself. This has been a long\ndiscussion to arrive at a very simple and obvious conclusion. We all\nfeel that in some sense our minds are here in this room and at this\ntime. But it is not quite in the same sense as that in which the events\nof nature which are the existences of our brains have their spatial and\ntemporal positions. The fundamental distinction to remember is that\nimmediacy for sense-awareness is not the same as instantaneousness for\nnature. This last conclusion bears on the next discussion with which I\nwill terminate this lecture. This question can be formulated thus, Can\nalternative temporal series be found in nature?\n\nA few years ago such a suggestion would have been put aside as being\nfantastically impossible. It would have had no bearing on the science\nthen current, and was akin to no ideas which had ever entered into the\ndreams of philosophy. The eighteenth and nineteenth centuries accepted\nas their natural philosophy a certain circle of concepts which were as\nrigid and definite as those of the philosophy of the middle ages, and\nwere accepted with as little critical research. I will call this natural\nphilosophy 'materialism.' Not only were men of science materialists, but\nalso adherents of all schools of philosophy. The idealists only differed\nfrom the philosophic materialists on question of the alignment of nature\nin reference to mind. But no one had any doubt that the philosophy of\nnature considered in itself was of the type which I have called\nmaterialism. It is the philosophy which I have already examined in my\ntwo lectures of this course preceding the present one. It can be\nsummarised as the belief that nature is an aggregate of material and\nthat this material exists in some sense _at_ each successive member of a\none-dimensional series of extensionless instants of time. Furthermore\nthe mutual relations of the material entities at each instant formed\nthese entities into a spatial configuration in an unbounded space. It\nwould seem that space--on this theory--would be as instantaneous as the\ninstants, and that some explanation is required of the relations between\nthe successive instantaneous spaces. The materialistic theory is however\nsilent on this point; and the succession of instantaneous spaces is\ntacitly combined into one persistent space. This theory is a purely\nintellectual rendering of experience which has had the luck to get\nitself formulated at the dawn of scientific thought. It has dominated\nthe language and the imagination of science since science flourished in\nAlexandria, with the result that it is now hardly possible to speak\nwithout appearing to assume its immediate obviousness.\n\nBut when it is distinctly formulated in the abstract terms in which I\nhave just stated it, the theory is very far from obvious. The passing\ncomplex of factors which compose the fact which is the terminus of\nsense-awareness places before us nothing corresponding to the trinity of\nthis natural materialism. This trinity is composed (i) of the temporal\nseries of extensionless instants, (ii) of the aggregate of material\nentities, and (iii) of space which is the outcome of relations of\nmatter.\n\nThere is a wide gap between these presuppositions of the intellectual\ntheory of materialism and the immediate deliverances of sense-awareness.\nI do not question that this materialistic trinity embodies important\ncharacters of nature. But it is necessary to express these characters in\nterms of the facts of experience. This is exactly what in this lecture I\nhave been endeavouring to do so far as time is concerned; and we have\nnow come up against the question, Is there only one temporal series? The\nuniqueness of the temporal series is presupposed in the materialist\nphilosophy of nature. But that philosophy is merely a theory, like the\nAristotelian scientific theories so firmly believed in the middle ages.\nIf in this lecture I have in any way succeeded in getting behind the\ntheory to the immediate facts, the answer is not nearly so certain. The\nquestion can be transformed into this alternative form, Is there only\none family of durations? In this question the meaning of a 'family of\ndurations' has been defined earlier in this lecture. The answer is now\nnot at all obvious. On the materialistic theory the instantaneous\npresent is the only field for the creative activity of nature. The past\nis gone and the future is not yet. Thus (on this theory) the immediacy\nof perception is of an instantaneous present, and this unique present is\nthe outcome of the past and the promise of the future. But we deny this\nimmediately given instantaneous present. There is no such thing to be\nfound in nature. As an ultimate fact it is a nonentity. What is\nimmediate for sense-awareness is a duration. Now a duration has within\nitself a past and a future; and the temporal breadths of the immediate\ndurations of sense-awareness are very indeterminate and dependent on the\nindividual percipient. Accordingly there is no unique factor in nature\nwhich for every percipient is pre-eminently and necessarily the present.\nThe passage of nature leaves nothing between the past and the future.\nWhat we perceive as present is the vivid fringe of memory tinged with\nanticipation. This vividness lights up the discriminated field within a\nduration. But no assurance can thereby be given that the happenings of\nnature cannot be assorted into other durations of alternative families.\nWe cannot even know that the series of immediate durations posited by\nthe sense-awareness of one individual mind all necessarily belong to the\nsame family of durations. There is not the slightest reason to believe\nthat this is so. Indeed if my theory of nature be correct, it will not\nbe the case.\n\nThe materialistic theory has all the completeness of the thought of the\nmiddle ages, which had a complete answer to everything, be it in heaven\nor in hell or in nature. There is a trimness about it, with its\ninstantaneous present, its vanished past, its non-existent future, and\nits inert matter. This trimness is very medieval and ill accords with\nbrute fact.\n\nThe theory which I am urging admits a greater ultimate mystery and a\ndeeper ignorance. The past and the future meet and mingle in the\nill-defined present. The passage of nature which is only another name\nfor the creative force of existence has no narrow ledge of definite\ninstantaneous present within which to operate. Its operative presence\nwhich is now urging nature forward must be sought for throughout the\nwhole, in the remotest past as well as in the narrowest breadth of any\npresent duration. Perhaps also in the unrealised future. Perhaps also in\nthe future which might be as well as the actual future which will be. It\nis impossible to meditate on time and the mystery of the creative\npassage of nature without an overwhelming emotion at the limitations of\nhuman intelligence.\n\n\n\n\nCHAPTER IV\n\nTHE METHOD OF EXTENSIVE ABSTRACTION\n\n\nTo-day's lecture must commence with the consideration of limited events.\nWe shall then be in a position to enter upon an investigation of the\nfactors in nature which are represented by our conception of space.\n\nThe duration which is the immediate disclosure of our sense-awareness is\ndiscriminated into parts. There is the part which is the life of all\nnature within a room, and there is the part which is the life of all\nnature within a table in the room. These parts are limited events. They\nhave the endurance of the present duration, and they are parts of it.\nBut whereas a duration is an unlimited whole and in a certain limited\nsense is all that there is, a limited event possesses a completely\ndefined limitation of extent which is expressed for us in\nspatio-temporal terms.\n\nWe are accustomed to associate an event with a certain melodramatic\nquality. If a man is run over, that is an event comprised within certain\nspatio-temporal limits. We are not accustomed to consider the endurance\nof the Great Pyramid throughout any definite day as an event. But the\nnatural fact which is the Great Pyramid throughout a day, meaning\nthereby all nature within it, is an event of the same character as the\nman's accident, meaning thereby all nature with spatio-temporal\nlimitations so as to include the man and the motor during the period\nwhen they were in contact.\n\nWe are accustomed to analyse these events into three factors, time,\nspace, and material. In fact, we at once apply to them the concepts of\nthe materialistic theory of nature. I do not deny the utility of this\nanalysis for the purpose of expressing important laws of nature. What I\nam denying is that anyone of these factors is posited for us in\nsense-awareness in concrete independence. We perceive one unit factor in\nnature; and this factor is that something is going on then--there. For\nexample, we perceive the going-on of the Great Pyramid in its relations\nto the goings-on of the surrounding Egyptian events. We are so trained,\nboth by language and by formal teaching and by the resulting\nconvenience, to express our thoughts in terms of this materialistic\nanalysis that intellectually we tend to ignore the true unity of the\nfactor really exhibited in sense-awareness. It is this unit factor,\nretaining in itself the passage of nature, which is the primary concrete\nelement discriminated in nature. These primary factors are what I mean\nby events.\n\nEvents are the field of a two-termed relation, namely the relation of\nextension which was considered in the last lecture. Events are the\nthings related by the relation of extension. If an event A extends\nover an event B, then B is 'part of' A, and A is a 'whole' of\nwhich B is a part. Whole and part are invariably used in these\nlectures in this definite sense. It follows that in reference to this\nrelation any two events A and B may have any one of four relations\nto each other, namely (i) A may extend over B, or (ii) B may\nextend over A, or (iii) A and B may both extend over some third\nevent C, but neither over the other, or (iv) A and B may be\nentirely separate. These alternatives can obviously be illustrated by\nEuler's diagrams as they appear in logical textbooks.\n\nThe continuity of nature is the continuity of events. This continuity is\nmerely the name for the aggregate of a variety of properties of events\nin connexion with the relation of extension.\n\nIn the first place, this relation is transitive; secondly, every event\ncontains other events as parts of itself; thirdly every event is a part\nof other events; fourthly given any two finite events there are events\neach of which contains both of them as parts; and fifthly there is a\nspecial relation between events which I term 'junction.'\n\nTwo events have junction when there is a third event of which both\nevents are parts, and which is such that no part of it is separated from\nboth of the two given events. Thus two events with junction make up\nexactly one event which is in a sense their sum.\n\nOnly certain pairs of events have this property. In general any event\ncontaining two events also contains parts which are separated from both\nevents.\n\nThere is an alternative definition of the junction of two events which I\nhave adopted in my recent book[7]. Two events have junction when there\nis a third event such that (i) it overlaps both events and (ii) it has\nno part which is separated from both the given events. If either of\nthese alternative definitions is adopted as the definition of junction,\nthe other definition appears as an axiom respecting the character of\njunction as we know it in nature. But we are not thinking of logical\ndefinition so much as the formulation of the results of direct\nobservation. There is a certain continuity inherent in the observed\nunity of an event, and these two definitions of junction are really\naxioms based on observation respecting the character of this continuity.\n\n[7] Cf. _Enquiry_.\n\nThe relations of whole and part and of overlapping are particular cases\nof the junction of events. But it is possible for events to have\njunction when they are separate from each other; for example, the upper\nand the lower part of the Great Pyramid are divided by some imaginary\nhorizontal plane.\n\nThe continuity which nature derives from events has been obscured by the\nillustrations which I have been obliged to give. For example I have\ntaken the existence of the Great Pyramid as a fairly well-known fact to\nwhich I could safely appeal as an illustration. This is a type of event\nwhich exhibits itself to us as the situation of a recognisable object;\nand in the example chosen the object is so widely recognised that it has\nreceived a name. An object is an entity of a different type from an\nevent. For example, the event which is the life of nature within the\nGreat Pyramid yesterday and to-day is divisible into two parts, namely\nthe Great Pyramid yesterday and the Great Pyramid to-day. But the\nrecognisable object which is also called the Great Pyramid is the same\nobject to-day as it was yesterday. I shall have to consider the theory\nof objects in another lecture.\n\nThe whole subject is invested with an unmerited air of subtlety by the\nfact that when the event is the situation of a well-marked object, we\nhave no language to distinguish the event from the object. In the case\nof the Great Pyramid, the object is the perceived unit entity which as\nperceived remains self-identical throughout the ages; while the whole\ndance of molecules and the shifting play of the electromagnetic field\nare ingredients of the event. An object is in a sense out of time. It is\nonly derivatively in time by reason of its having the relation to events\nwhich I term 'situation.' This relation of situation will require\ndiscussion in a subsequent lecture.\n\nThe point which I want to make now is that being the situation of a\nwell-marked object is not an inherent necessity for an event. Wherever\nand whenever something is going on, there is an event. Furthermore\n'wherever and whenever' in themselves presuppose an event, for space and\ntime in themselves are abstractions from events. It is therefore a\nconsequence of this doctrine that something is always going on\neverywhere, even in so-called empty space. This conclusion is in accord\nwith modern physical science which presupposes the play of an\nelectromagnetic field throughout space and time. This doctrine of\nscience has been thrown into the materialistic form of an all-pervading\nether. But the ether is evidently a mere idle concept--in the\nphraseology which Bacon applied to the doctrine of final causes, it is a\nbarren virgin. Nothing is deduced from it; and the ether merely\nsubserves the purpose of satisfying the demands of the materialistic\ntheory. The important concept is that of the shifting facts of the\nfields of force. This is the concept of an ether of events which should\nbe substituted for that of a material ether.\n\nIt requires no illustration to assure you that an event is a complex\nfact, and the relations between two events form an almost impenetrable\nmaze. The clue discovered by the common sense of mankind and\nsystematically utilised in science is what I have elsewhere[8] called\nthe law of convergence to simplicity by diminution of extent.\n\n[8] Cf. _Organisation of Thought_, pp.\u00a0146 et\u00a0seq. Williams and Norgate,\n1917.\n\nIf A and B are two events, and A' is part of A and B' is part\nof B, then in many respects the relations between the parts A' and\nB' will be simpler than the relations between A and B. This is the\nprinciple which presides over all attempts at exact observation.\n\nThe first outcome of the systematic use of this law has been the\nformulation of the abstract concepts of Time and Space. In the previous\nlecture I sketched how the principle was applied to obtain the\ntime-series. I now proceed to consider how the spatial entities are\nobtained by the same method. The systematic procedure is identical in\nprinciple in both cases, and I have called the general type of procedure\nthe 'method of extensive abstraction.'\n\nYou will remember that in my last lecture I defined the concept of an\nabstractive set of durations. This definition can be extended so as to\napply to any events, limited events as well as durations. The only\nchange that is required is the substitution of the word 'event' for the\nword 'duration.' Accordingly an abstractive set of events is any set of\nevents which possesses the two properties, (i) of any two members of the\nset one contains the other as a part, and (ii) there is no event which\nis a common part of every member of the set. Such a set, as you will\nremember, has the properties of the Chinese toy which is a nest of\nboxes, one within the other, with the difference that the toy has a\nsmallest box, while the abstractive class has neither a smallest event\nnor does it converge to a limiting event which is not a member of the\nset.\n\nThus, so far as the abstractive sets of events are concerned, an\nabstractive set converges to nothing. There is the set with its members\ngrowing indefinitely smaller and smaller as we proceed in thought\ntowards the smaller end of the series; but there is no absolute minimum\nof any sort which is finally reached. In fact the set is just itself and\nindicates nothing else in the way of events, except itself. But each\nevent has an intrinsic character in the way of being a situation of\nobjects and of having parts which are situations of objects and--to\nstate the matter more generally--in the way of being a field of the life\nof nature. This character can be defined by quantitative expressions\nexpressing relations between various quantities intrinsic to the event\nor between such quantities and other quantities intrinsic to other\nevents. In the case of events of considerable spatio-temporal extension\nthis set of quantitative expressions is of bewildering complexity. If\ne be an event, let us denote by q(e) the set of quantitative expressions\ndefining its character including its connexions with the rest of nature.\nLet e_1, e_2, e_3, etc. be an abstractive set, the members being so\narranged that each member such as e_{n} extends over all the succeeding\nmembers such as e_{n+1}, e_{n+2} and so on. Then corresponding to the\nseries\n\n    e_1, e_2, e_3, ..., e_{n}, e_{n+1}, ...,\n\nthere is the series\n\n    q(e_1), q(e_2), q(e_3), ..., q(e_{n}), q(e_{n+1}), ....\n\nCall the series of events s and the series of quantitative expressions\nq(s). The series s has no last term and no events which are contained\nin every member of the series. Accordingly the series of events\nconverges to nothing. It is just itself. Also the series q(s) has no\nlast term. But the sets of homologous quantities running through the\nvarious terms of the series do converge to definite limits. For example\nif Q_1 be a quantitative measurement found in q(e_1), and Q_2 the homologue\nto Q_1 to be found in q(e_2), and Q_3 the homologue to Q_1 and Q_2 to be\nfound in q(e_3), and so on, then the series\n\n    Q_1, Q_2, Q_3, ..., Q_{n}, Q_{n+1}, ...,\n\nthough it has no last term, does in general converge to a definite\nlimit. Accordingly there is a class of limits l(s) which is the\nclass of the limits of those members of q(e_{n}) which have\nhomologues throughout the series q(s) as n indefinitely increases.\nWe can represent this statement diagrammatically by using an arrow (-->)\nto mean 'converges to.' Then\n\n    e_1, e_2, e_3, ..., e_{n}, e_{n+1}, ... --> nothing,\n\nand\n\n    q(e_1), q(e_2), q(e_3), ..., q(e_{n}), q(e_{n+1}), ... --> l(s).\n\nThe mutual relations between the limits in the set l(s), and also\nbetween these limits and the limits in other sets l(s'), l(s\"), ...,\nwhich arise from other abstractive sets s', s\", etc., have a peculiar\nsimplicity.\n\nThus the set s does indicate an ideal simplicity of natural relations,\nthough this simplicity is not the character of any actual event in s.\nWe can make an approximation to such a simplicity which, as estimated\nnumerically, is as close as we like by considering an event which is far\nenough down the series towards the small end. It will be noted that it\nis the infinite series, as it stretches away in unending succession\ntowards the small end, which is of importance. The arbitrarily large\nevent with which the series starts has no importance at all. We can\narbitrarily exclude any set of events at the big end of an abstractive\nset without the loss of any important property to the set as thus\nmodified.\n\nI call the limiting character of natural relations which is indicated by\nan abstractive set, the 'intrinsic character' of the set; also the\nproperties, connected with the relation of whole and part as concerning\nits members, by which an abstractive set is defined together form what I\ncall its 'extrinsic character.' The fact that the extrinsic character of\nan abstractive set determines a definite intrinsic character is the\nreason of the importance of the precise concepts of space and time. This\nemergence of a definite intrinsic character from an abstractive set is\nthe precise meaning of the law of convergence.\n\nFor example, we see a train approaching during a minute. The event which\nis the life of nature within that train during the minute is of great\ncomplexity and the expression of its relations and of the ingredients of\nits character baffles us. If we take one second of that minute, the more\nlimited event which is thus obtained is simpler in respect to its\ningredients, and shorter and shorter times such as a tenth of that\nsecond, or a hundredth, or a thousandth--so long as we have a definite\nrule giving a definite succession of diminishing events--give events\nwhose ingredient characters converge to the ideal simplicity of the\ncharacter of the train at a definite instant. Furthermore there are\ndifferent types of such convergence to simplicity. For example, we can\nconverge as above to the limiting character expressing nature at an\ninstant within the whole volume of the train at that instant, or to\nnature at an instant within some portion of that volume--for example\nwithin the boiler of the engine--or to nature at an instant on some area\nof surface, or to nature at an instant on some line within the train, or\nto nature at an instant at some point of the train. In the last case the\nsimple limiting characters arrived at will be expressed as densities,\nspecific gravities, and types of material. Furthermore we need not\nnecessarily converge to an abstraction which involves nature at an\ninstant. We may converge to the physical ingredients of a certain point\ntrack throughout the whole minute. Accordingly there are different types\nof extrinsic character of convergence which lead to the approximation to\ndifferent types of intrinsic characters as limits.\n\nWe now pass to the investigation of possible connexions between\nabstractive sets. One set may 'cover' another. I define 'covering' as\nfollows: An abstractive set p covers an abstractive set q when every\nmember of p contains as its parts some members of q. It is evident\nthat if any event e contains as a part any member of the set q, then\nowing to the transitive property of extension every succeeding member of\nthe small end of q is part of e. In such a case I will say that the\nabstractive set q 'inheres in' the event e. Thus when an abstractive\nset p covers an abstractive set q, the abstractive set q inheres\nin every member of p.\n\nTwo abstractive sets may each cover the other. When this is the case I\nshall call the two sets 'equal in abstractive force.' When there is no\ndanger of misunderstanding I shall shorten this phrase by simply saying\nthat the two abstractive sets are 'equal.' The possibility of this\nequality of abstractive sets arises from the fact that both sets, p\nand q, are infinite series towards their small ends. Thus the equality\nmeans, that given any event x belonging to p, we can always by\nproceeding far enough towards the small end of q find an event y\nwhich is part of x, and that then by proceeding far enough towards the\nsmall end of p we can find an event z which is part of y, and so\non indefinitely.\n\nThe importance of the equality of abstractive sets arises from the\nassumption that the intrinsic characters of the two sets are identical.\nIf this were not the case exact observation would be at an end.\n\nIt is evident that any two abstractive sets which are equal to a third\nabstractive set are equal to each other. An 'abstractive element' is the\nwhole group of abstractive sets which are equal to any one of\nthemselves. Thus all abstractive sets belonging to the same element are\nequal and converge to the same intrinsic character. Thus an abstractive\nelement is the group of routes of approximation to a definite intrinsic\ncharacter of ideal simplicity to be found as a limit among natural\nfacts.\n\nIf an abstractive set p covers an abstractive set q, then any\nabstractive set belonging to the abstractive element of which p is a\nmember will cover any abstractive set belonging to the element of which\nq is a member. Accordingly it is useful to stretch the meaning of the\nterm 'covering,' and to speak of one abstractive element 'covering'\nanother abstractive element. If we attempt in like manner to stretch the\nterm 'equal' in the sense of 'equal in abstractive force,' it is obvious\nthat an abstractive element can only be equal to itself. Thus an\nabstractive element has a unique abstractive force and is the construct\nfrom events which represents one definite intrinsic character which is\narrived at as a limit by the use of the principle of convergence to\nsimplicity by diminution of extent.\n\nWhen an abstractive element A covers an abstractive element B, the\nintrinsic character of A in a sense includes the intrinsic character\nof B. It results that statements about the intrinsic character of B\nare in a sense statements about the intrinsic character of A; but the\nintrinsic character of A is more complex than that of B.\n\nThe abstractive elements form the fundamental elements of space and\ntime, and we now turn to the consideration of the properties involved in\nthe formation of special classes of such elements. In my last lecture I\nhave already investigated one class of abstractive elements, namely\nmoments. Each moment is a group of abstractive sets, and the events\nwhich are members of these sets are all members of one family of\ndurations. The moments of one family form a temporal series; and,\nallowing the existence of different families of moments, there will be\nalternative temporal series in nature. Thus the method of extensive\nabstraction explains the origin of temporal series in terms of the\nimmediate facts of experience and at the same time allows for the\nexistence of the alternative temporal series which are demanded by the\nmodern theory of electromagnetic relativity.\n\nWe now turn to space. The first thing to do is to get hold of the class\nof abstractive elements which are in some sense the points of space.\nSuch an abstractive element must in some sense exhibit a convergence to\nan absolute minimum of intrinsic character. Euclid has expressed for all\ntime the general idea of a point, as being without parts and without\nmagnitude. It is this character of being an absolute minimum which we\nwant to get at and to express in terms of the extrinsic characters of\nthe abstractive sets which make up a point. Furthermore, points which\nare thus arrived at represent the ideal of events without any extension,\nthough there are in fact no such entities as these ideal events. These\npoints will not be the points of an external timeless space but of\ninstantaneous spaces. We ultimately want to arrive at the timeless space\nof physical science, and also of common thought which is now tinged with\nthe concepts of science. It will be convenient to reserve the term\n'point' for these spaces when we get to them. I will therefore use the\nname 'event-particles' for the ideal minimum limits to events. Thus an\nevent-particle is an abstractive element and as such is a group of\nabstractive sets; and a point--namely a point of timeless space--will be\na class of event-particles.\n\nFurthermore there is a separate timeless space corresponding to each\nseparate temporal series, that is to each separate family of durations.\nWe will come back to points in timeless spaces later. I merely mention\nthem now that we may understand the stages of our investigation. The\ntotality of event-particles will form a four-dimensional manifold, the\nextra dimension arising from time--in other words--arising from the\npoints of a timeless space being each a class of event-particles.\n\nThe required character of the abstractive sets which form\nevent-particles would be secured if we could define them as having the\nproperty of being covered by any abstractive set which they cover. For\nthen any other abstractive set which an abstractive set of an\nevent-particle covered, would be equal to it, and would therefore be a\nmember of the same event-particle. Accordingly an event-particle could\ncover no other abstractive element. This is the definition which I\noriginally proposed at a congress in Paris in 1914[9]. There is however\na difficulty involved in this definition if adopted without some further\naddition, and I am now not satisfied with the way in which I attempted\nto get over that difficulty in the paper referred to.\n\n[9] Cf. 'La Th\u00e9orie Relationniste de l'Espace,' _Rev. de M\u00e9taphysique et\nde Morale_, vol.\u00a0XXIII, 1916.\n\nThe difficulty is this: When event-particles have once been defined it\nis easy to define the aggregate of event-particles forming the boundary\nof an event; and thence to define the point-contact at their boundaries\npossible for a pair of events of which one is part of the other. We can\nthen conceive all the intricacies of tangency. In particular we can\nconceive an abstractive set of which all the members have point-contact\nat the same event-particle. It is then easy to prove that there will be\nno abstractive set with the property of being covered by every\nabstractive set which it covers. I state this difficulty at some length\nbecause its existence guides the development of our line of argument. We\nhave got to annex some condition to the root property of being covered\nby any abstractive set which it covers. When we look into this question\nof suitable conditions we find that in addition to event-particles all\nthe other relevant spatial and spatio-temporal abstractive elements can\nbe defined in the same way by suitably varying the conditions.\nAccordingly we proceed in a general way suitable for employment beyond\nevent-particles.\n\nLet {sigma} be the name of any condition which some abstractive sets\nfulfil. I say that an abstractive set is '{sigma}-prime' when it has the\ntwo properties, (i) that it satisfies the condition {sigma} and (ii)\nthat it is covered by every abstractive set which both is covered by it\nand satisfies the condition {sigma}.\n\nIn other words you cannot get any abstractive set satisfying the\ncondition {sigma} which exhibits intrinsic character more simple than\nthat of a {sigma}-prime.\n\nThere are also the correlative abstractive sets which I call the sets of\n{sigma}-antiprimes. An abstractive set is a {sigma}-antiprime when it\nhas the two properties, (i) that it satisfies the condition {sigma} and\n(ii) that it covers every abstractive set which both covers it and\nsatisfies the condition {sigma}. In other words you cannot get any\nabstractive set satisfying the condition {sigma} which exhibits an\nintrinsic character more complex than that of a {sigma}-antiprime.\n\nThe intrinsic character of a {sigma}-prime has a certain minimum of\nfullness among those abstractive sets which are subject to the condition\nof satisfying {sigma}; whereas the intrinsic character of a\n{sigma}-antiprime has a corresponding maximum of fullness, and includes\nall it can in the circumstances.\n\nLet us first consider what help the notion of antiprimes could give us\nin the definition of moments which we gave in the last lecture. Let the\ncondition {sigma} be the property of being a class whose members are all\ndurations. An abstractive set which satisfies this condition is thus an\nabstractive set composed wholly of durations. It is convenient then to\ndefine a moment as the group of abstractive sets which are equal to some\n{sigma}-antiprime, where the condition {sigma} has this special meaning.\nIt will be found on consideration (i) that each abstractive set forming\na moment is a {sigma}-antiprime, where {sigma} has this special meaning,\nand (ii) that we have excluded from membership of moments abstractive\nsets of durations which all have one common boundary, either the initial\nboundary or the final boundary. We thus exclude special cases which are\napt to confuse general reasoning. The new definition of a moment, which\nsupersedes our previous definition, is (by the aid of the notion of\nantiprimes) the more precisely drawn of the two, and the more useful.\n\nThe particular condition which '{sigma}' stood for in the definition of\nmoments included something additional to anything which can be derived\nfrom the bare notion of extension. A duration exhibits for thought a\ntotality. The notion of totality is something beyond that of extension,\nthough the two are interwoven in the notion of a duration.\n\nIn the same way the particular condition '{sigma}' required for the\ndefinition of an event-particle must be looked for beyond the mere\nnotion of extension. The same remark is also true of the particular\nconditions requisite for the other spatial elements. This additional\nnotion is obtained by distinguishing between the notion of 'position'\nand the notion of convergence to an ideal zero of extension as exhibited\nby an abstractive set of events.\n\nIn order to understand this distinction consider a point of the\ninstantaneous space which we conceive as apparent to us in an almost\ninstantaneous glance. This point is an event-particle. It has two\naspects. In one aspect it is there, where it is. This is its position in\nthe space. In another aspect it is got at by ignoring the circumambient\nspace, and by concentrating attention on the smaller and smaller set of\nevents which approximate to it. This is its extrinsic character. Thus a\npoint has three characters, namely, its position in the whole\ninstantaneous space, its extrinsic character, and its intrinsic\ncharacter. The same is true of any other spatial element. For example an\ninstantaneous volume in instantaneous space has three characters,\nnamely, its position, its extrinsic character as a group of abstractive\nsets, and its intrinsic character which is the limit of natural\nproperties which is indicated by any one of these abstractive sets.\n\nBefore we can talk about position in instantaneous space, we must\nevidently be quite clear as to what we mean by instantaneous space in\nitself. Instantaneous space must be looked for as a character of a\nmoment. For a moment is all nature at an instant. It cannot be the\nintrinsic character of the moment. For the intrinsic character tells us\nthe limiting character of nature in space at that instant. Instantaneous\nspace must be an assemblage of abstractive elements considered in their\nmutual relations. Thus an instantaneous space is the assemblage of\nabstractive elements covered by some one moment, and it is the\ninstantaneous space of that moment.\n\nWe have now to ask what character we have found in nature which is\ncapable of according to the elements of an instantaneous space different\nqualities of position. This question at once brings us to the\nintersection of moments, which is a topic not as yet considered in these\nlectures.\n\nThe locus of intersection of two moments is the assemblage of\nabstractive elements covered by both of them. Now two moments of the\nsame temporal series cannot intersect. Two moments respectively of\ndifferent families necessarily intersect. Accordingly in the\ninstantaneous space of a moment we should expect the fundamental\nproperties to be marked by the intersections with moments of other\nfamilies. If M be a given moment, the intersection of M with another\nmoment A is an instantaneous plane in the instantaneous space of M; and\nif B be a third moment intersecting both M and A, the intersection of M\nand B is another plane in the space M. Also the common intersection of\nA, B, and M is the intersection of the two planes in the space M, namely\nit is a straight line in the space M. An exceptional case arises if B\nand M intersect in the same plane as A and M. Furthermore if C be a\nfourth moment, then apart from special cases which we need not consider,\nit intersects M in a plane which the straight line (A, B, M) meets. Thus\nthere is in general a common intersection of four moments of different\nfamilies. This common intersection is an assemblage of abstractive\nelements which are each covered (or 'lie in') all four moments. The\nthree-dimensional property of instantaneous space comes to this, that\n(apart from special relations between the four moments) any fifth moment\neither contains the whole of their common intersection or none of it. No\nfurther subdivision of the common intersection is possible by means of\nmoments. The 'all or none' principle holds. This is not an _\u00e0\u00a0priori_\ntruth but an empirical fact of nature.\n\nIt will be convenient to reserve the ordinary spatial terms 'plane,'\n'straight line,' 'point' for the elements of the timeless space of a\ntime-system. Accordingly an instantaneous plane in the instantaneous\nspace of a moment will be called a 'level,' an instantaneous straight\nline will be called a 'rect,' and an instantaneous point will be called\na 'punct.' Thus a punct is the assemblage of abstractive elements which\nlie in each of four moments whose families have no special relations to\neach other. Also if P be any moment, either every abstractive element\nbelonging to a given punct lies in P, or no abstractive element of\nthat punct lies in P.\n\nPosition is the quality which an abstractive element possesses in virtue\nof the moments in which it lies. The abstractive elements which lie in\nthe instantaneous space of a given moment M are differentiated from\neach other by the various other moments which intersect M so as to\ncontain various selections of these abstractive elements. It is this\ndifferentiation of the elements which constitutes their differentiation\nof position. An abstractive element which belongs to a punct has the\nsimplest type of position in M, an abstractive element which belongs\nto a rect but not to a punct has a more complex quality of position, an\nabstractive element which belongs to a level and not to a rect has a\nstill more complex quality of position, and finally the most complex\nquality of position belongs to an abstractive element which belongs to a\nvolume and not to a level. A volume however has not yet been defined.\nThis definition will be given in the next lecture.\n\nEvidently levels, rects, and puncts in their capacity as infinite\naggregates cannot be the termini of sense-awareness, nor can they be\nlimits which are approximated to in sense-awareness. Any one member of a\nlevel has a certain quality arising from its character as also belonging\nto a certain set of moments, but the level as a whole is a mere logical\nnotion without any route of approximation along entities posited in\nsense-awareness.\n\nOn the other hand an event-particle is defined so as to exhibit this\ncharacter of being a route of approximation marked out by entities\nposited in sense-awareness. A definite event-particle is defined in\nreference to a definite punct in the following manner: Let the condition\n{sigma} mean the property of covering all the abstractive elements which\nare members of that punct; so that an abstractive set which satisfies\nthe condition {sigma} is an abstractive set which covers every\nabstractive element belonging to the punct. Then the definition of the\nevent-particle associated with the punct is that it is the group of all\nthe {sigma}-primes, where {sigma} has this particular meaning.\n\nIt is evident that--with this meaning of {sigma}--every abstractive set\nequal to a {sigma}-prime is itself a {sigma}-prime. Accordingly an\nevent-particle as thus defined is an abstractive element, namely it is\nthe group of those abstractive sets which are each equal to some given\nabstractive set. If we write out the definition of the event-particle\nassociated with some given punct, which we will call {pi}, it is as\nfollows: The event-particle associated with {pi} is the group of\nabstractive classes each of which has the two properties (i) that it\ncovers every abstractive set in {pi} and (ii) that all the abstractive\nsets which also satisfy the former condition as to {pi} and which it\ncovers, also cover it.\n\nAn event-particle has position by reason of its association with a\npunct, and conversely the punct gains its derived character as a route\nof approximation from its association with the event-particle. These two\ncharacters of a point are always recurring in any treatment of the\nderivation of a point from the observed facts of nature, but in general\nthere is no clear recognition of their distinction.\n\nThe peculiar simplicity of an instantaneous point has a twofold origin,\none connected with position, that is to say with its character as a\npunct, and the other connected with its character as an event-particle.\nThe simplicity of the punct arises from its indivisibility by a moment.\n\nThe simplicity of an event-particle arises from the indivisibility of\nits intrinsic character. The intrinsic character of an event-particle is\nindivisible in the sense that every abstractive set covered by it\nexhibits the same intrinsic character. It follows that, though there are\ndiverse abstractive elements covered by event-particles, there is no\nadvantage to be gained by considering them since we gain no additional\nsimplicity in the expression of natural properties.\n\nThese two characters of simplicity enjoyed respectively by\nevent-particles and puncts define a meaning for Euclid's phrase,\n'without parts and without magnitude.'\n\nIt is obviously convenient to sweep away out of our thoughts all these\nstray abstractive sets which are covered by event-particles without\nthemselves being members of them. They give us nothing new in the way of\nintrinsic character. Accordingly we can think of rects and levels as\nmerely loci of event-particles. In so doing we are also cutting out\nthose abstractive elements which cover sets of event-particles, without\nthese elements being event-particles themselves. There are classes of\nthese abstractive elements which are of great importance. I will\nconsider them later on in this and in other lectures. Meanwhile we will\nignore them. Also I will always speak of 'event-particles' in preference\nto 'puncts,' the latter being an artificial word for which I have no\ngreat affection.\n\nParallelism among rects and levels is now explicable.\n\nConsider the instantaneous space belonging to a moment A, and let A\nbelong to the temporal series of moments which I will call {alpha}.\nConsider any other temporal series of moments which I will call {beta}.\nThe moments of {beta} do not intersect each other and they intersect the\nmoment A in a family of levels. None of these levels can intersect, and\nthey form a family of parallel instantaneous planes in the instantaneous\nspace of moment A. Thus the parallelism of moments in a temporal series\nbegets the parallelism of levels in an instantaneous space, and\nthence--as it is easy to see--the parallelism of rects. Accordingly the\nEuclidean property of space arises from the parabolic property of time.\nIt may be that there is reason to adopt a hyperbolic theory of time and\na corresponding hyperbolic theory of space. Such a theory has not been\nworked out, so it is not possible to judge as to the character of the\nevidence which could be brought forward in its favour.\n\nThe theory of order in an instantaneous space is immediately derived\nfrom time-order. For consider the space of a moment M. Let {alpha} be\nthe name of a time-system to which M does not belong. Let A_1, A_2, A_3\netc. be moments of {alpha} in the order of their occurrences. Then A_1,\nA_2, A_3, etc. intersect M in parallel levels l_1, l_2, l_3, etc. Then\nthe relative order of the parallel levels in the space of M is the same\nas the relative order of the corresponding moments in the time-system\n{alpha}. Any rect in M which intersects all these levels in its set of\npuncts, thereby receives for its puncts an order of position on it. So\nspatial order is derivative from temporal order. Furthermore there are\nalternative time-systems, but there is only one definite spatial order\nin each instantaneous space. Accordingly the various modes of deriving\nspatial order from diverse time-systems must harmonise with one spatial\norder in each instantaneous space. In this way also diverse time-orders\nare comparable.\n\nWe have two great questions still on hand to be settled before our\ntheory of space is fully adjusted. One of these is the question of the\ndetermination of the methods of measurement within the space, in other\nwords, the congruence-theory of the space. The measurement of space will\nbe found to be closely connected with the measurement of time, with\nrespect to which no principles have as yet been determined. Thus our\ncongruence-theory will be a theory both for space and for time. Secondly\nthere is the determination of the timeless space which corresponds to\nany particular time-system with its infinite set of instantaneous spaces\nin its successive moments. This is the space--or rather, these are the\nspaces--of physical science. It is very usual to dismiss this space by\nsaying that this is conceptual. I do not understand the virtue of these\nphrases. I suppose that it is meant that the space is the conception of\nsomething in nature. Accordingly if the space of physical science is to\nbe called conceptual, I ask, What in nature is it the conception of? For\nexample, when we speak of a point in the timeless space of physical\nscience, I suppose that we are speaking of something in nature. If we\nare not so speaking, our scientists are exercising their wits in the\nrealms of pure fantasy, and this is palpably not the case. This demand\nfor a definite Habeas Corpus Act for the production of the relevant\nentities in nature applies whether space be relative or absolute. On the\ntheory of relative space, it may perhaps be argued that there is no\ntimeless space for physical science, and that there is only the\nmomentary series of instantaneous spaces.\n\nAn explanation must then be asked for the meaning of the very common\nstatement that such and such a man walked four miles in some definite\nhour. How can you measure distance from one space into another space? I\nunderstand walking out of the sheet of an ordnance map. But the meaning\nof saying that Cambridge at 10\u00a0o'clock this morning in the appropriate\ninstantaneous space for that instant is 52\u00a0miles from London at\n11\u00a0o'clock this morning in the appropriate instantaneous space for that\ninstant beats me entirely. I think that, by the time a meaning has been\nproduced for this statement, you will find that you have constructed\nwhat is in fact a timeless space. What I cannot understand is how to\nproduce an explanation of meaning without in effect making some such\nconstruction. Also I may add that I do not know how the instantaneous\nspaces are thus correlated into one space by any method which is\navailable on the current theories of space.\n\nYou will have noticed that by the aid of the assumption of alternative\ntime-systems, we are arriving at an explanation of the character of\nspace. In natural science 'to explain' means merely to discover\n'interconnexions.' For example, in one sense there is no explanation of\nthe red which you see. It is red, and there is nothing else to be said\nabout it. Either it is posited before you in sense-awareness or you are\nignorant of the entity red. But science has explained red. Namely it has\ndiscovered interconnexions between red as a factor in nature and other\nfactors in nature, for example waves of light which are waves of\nelectromagnetic disturbances. There are also various pathological\nstates of the body which lead to the seeing of red without the\noccurrence of light waves. Thus connexions have been discovered between\nred as posited in sense-awareness and various other factors in nature.\nThe discovery of these connexions constitutes the scientific explanation\nof our vision of colour. In like manner the dependence of the character\nof space on the character of time constitutes an explanation in the\nsense in which science seeks to explain. The systematising intellect\nabhors bare facts. The character of space has hitherto been presented as\na collection of bare facts, ultimate and disconnected. The theory which\nI am expounding sweeps away this disconnexion of the facts of space.\n\n\n\n\nCHAPTER V\n\nSPACE AND MOTION\n\n\nThe topic for this lecture is the continuation of the task of explaining\nthe construction of spaces as abstracts from the facts of nature. It was\nnoted at the close of the previous lecture that the question of\ncongruence had not been considered, nor had the construction of a\ntimeless space which should correlate the successive momentary spaces of\na given time-system. Furthermore it was also noted that there were many\nspatial abstractive elements which we had not yet defined. We will first\nconsider the definition of some of these abstractive elements, namely\nthe definitions of solids, of areas, and of routes. By a 'route' I mean\na linear segment, whether straight or curved. The exposition of these\ndefinitions and the preliminary explanations necessary will, I hope,\nserve as a general explanation of the function of event-particles in the\nanalysis of nature.\n\nWe note that event-particles have 'position' in respect to each other.\nIn the last lecture I explained that 'position' was quality gained by a\nspatial element in virtue of the intersecting moments which covered it.\nThus each event-particle has position in this sense. The simplest mode\nof expressing the position in nature of an event-particle is by first\nfixing on any definite time-system. Call it {alpha}. There will be one\nmoment of the temporal series of {alpha} which covers the given\nevent-particle. Thus the position of the event-particle in the temporal\nseries {alpha} is defined by this moment, which we will call M. The\nposition of the particle in the space of M is then fixed in the ordinary\nway by three levels which intersect in it and in it only. This procedure\nof fixing the position of an event-particle shows that the aggregate of\nevent-particles forms a four-dimensional manifold. A finite event\noccupies a limited chunk of this manifold in a sense which I now proceed\nto explain.\n\nLet e be any given event. The manifold of event-particles falls into\nthree sets in reference to e. Each event-particle is a group of equal\nabstractive sets and each abstractive set towards its small-end is\ncomposed of smaller and smaller finite events. When we select from these\nfinite events which enter into the make-up of a given event-particle\nthose which are small enough, one of three cases must occur. Either (i)\nall of these small events are entirely separate from the given event\ne, or (ii) all of these small events are parts of the event e, or\n(iii) all of these small events overlap the event e but are not parts\nof it. In the first case the event-particle will be said to 'lie\noutside' the event e, in the second case the event-particle will be\nsaid to 'lie inside' the event e, and in the third case the\nevent-particle will be said to be a 'boundary-particle' of the event\ne. Thus there are three sets of particles, namely the set of those\nwhich lie outside the event e, the set of those which lie inside the\nevent e, and the boundary of the event e which is the set of\nboundary-particles of e. Since an event is four-dimensional, the\nboundary of an event is a three-dimensional manifold. For a finite event\nthere is a continuity of boundary; for a duration the boundary consists\nof those event-particles which are covered by either of the two bounding\nmoments. Thus the boundary of a duration consists of two momentary\nthree-dimensional spaces. An event will be said to 'occupy' the\naggregate of event-particles which lie within it.\n\nTwo events which have 'junction' in the sense in which junction was\ndescribed in my last lecture, and yet are separated so that neither\nevent either overlaps or is part of the other event, are said to be\n'adjoined.'\n\nThis relation of adjunction issues in a peculiar relation between the\nboundaries of the two events. The two boundaries must have a common\nportion which is in fact a continuous three-dimensional locus of\nevent-particles in the four-dimensional manifold.\n\nA three-dimensional locus of event-particles which is the common portion\nof the boundary of two adjoined events will be called a 'solid.' A solid\nmay or may not lie completely in one moment. A solid which does not lie\nin one moment will be called 'vagrant.' A solid which does lie in one\nmoment will be called a volume. A volume may be defined as the locus of\nthe event-particles in which a moment intersects an event, provided that\nthe two do intersect. The intersection of a moment and an event will\nevidently consist of those event-particles which are covered by the\nmoment and lie in the event. The identity of the two definitions of a\nvolume is evident when we remember that an intersecting moment divides\nthe event into two adjoined events.\n\nA solid as thus defined, whether it be vagrant or be a volume, is a mere\naggregate of event-particles illustrating a certain quality of position.\nWe can also define a solid as an abstractive element. In order to do so\nwe recur to the theory of primes explained in the preceding lecture. Let\nthe condition named {sigma} stand for the fact that each of the events\nof any abstractive set satisfying it has all the event-particles of some\nparticular solid lying in it. Then the group of all the {sigma}-primes\nis the abstractive element which is associated with the given solid. I\nwill call this abstractive element the solid as an abstractive element,\nand I will call the aggregate of event-particles the solid as a locus.\nThe instantaneous volumes in instantaneous space which are the ideals of\nour sense-perception are volumes as abstractive elements. What we really\nperceive with all our efforts after exactness are small events far\nenough down some abstractive set belonging to the volume as an\nabstractive element.\n\nIt is difficult to know how far we approximate to any perception of\nvagrant solids. We certainly do not think that we make any such\napproximation. But then our thoughts--in the case of people who do think\nabout such topics--are so much under the control of the materialistic\ntheory of nature that they hardly count for evidence. If Einstein's\ntheory of gravitation has any truth in it, vagrant solids are of great\nimportance in science. The whole boundary of a finite event may be\nlooked on as a particular example of a vagrant solid as a locus. Its\nparticular property of being closed prevents it from being definable as\nan abstractive element.\n\nWhen a moment intersects an event, it also intersects the boundary of\nthat event. This locus, which is the portion of the boundary contained\nin the moment, is the bounding surface of the corresponding volume of\nthat event contained in the moment. It is a two-dimensional locus.\n\nThe fact that every volume has a bounding surface is the origin of the\nDedekindian continuity of space.\n\nAnother event may be cut by the same moment in another volume and this\nvolume will also have its boundary. These two volumes in the\ninstantaneous space of one moment may mutually overlap in the familiar\nway which I need not describe in detail and thus cut off portions from\neach other's surfaces. These portions of surfaces are 'momental areas.'\n\nIt is unnecessary at this stage to enter into the complexity of a\ndefinition of vagrant areas. Their definition is simple enough when the\nfour-dimensional manifold of event-particles has been more fully\nexplored as to its properties.\n\nMomental areas can evidently be defined as abstractive elements by\nexactly the same method as applied to solids. We have merely to\nsubstitute 'area' for a 'solid' in the words of the definition already\ngiven. Also, exactly as in the analogous case of a solid, what we\nperceive as an approximation to our ideal of an area is a small event\nfar enough down towards the small end of one of the equal abstractive\nsets which belongs to the area as an abstractive element.\n\nTwo momental areas lying in the same moment can cut each other in a\nmomental segment which is not necessarily rectilinear. Such a segment\ncan also be defined as an abstractive element. It is then called a\n'momental route.' We will not delay over any general consideration of\nthese momental routes, nor is it important for us to proceed to the\nstill wider investigation of vagrant routes in general. There are\nhowever two simple sets of routes which are of vital importance. One is\na set of momental routes and the other of vagrant routes. Both sets can\nbe classed together as straight routes. We proceed to define them\nwithout any reference to the definitions of volumes and surfaces.\n\nThe two types of straight routes will be called rectilinear routes and\nstations. Rectilinear routes are momental routes and stations are\nvagrant routes. Rectilinear routes are routes which in a sense lie in\nrects. Any two event-particles on a rect define the set of\nevent-particles which lie between them on that rect. Let the\nsatisfaction of the condition {sigma} by an abstractive set mean that\nthe two given event-particles and the event-particles lying between them\non the rect all lie in every event belonging to the abstractive set. The\ngroup of {sigma}-primes, where {sigma} has this meaning, form an\nabstractive element. Such abstractive elements are rectilinear routes.\nThey are the segments of instantaneous straight lines which are the\nideals of exact perception. Our actual perception, however exact, will\nbe the perception of a small event sufficiently far down one of the\nabstractive sets of the abstractive element.\n\nA station is a vagrant route and no moment can intersect any station in\nmore than one event-particle. Thus a station carries with it a\ncomparison of the positions in their respective moments of the\nevent-particles covered by it. Rects arise from the intersection of\nmoments. But as yet no properties of events have been mentioned by which\nany analogous vagrant loci can be found out.\n\nThe general problem for our investigation is to determine a method of\ncomparison of position in one instantaneous space with positions in\nother instantaneous spaces. We may limit ourselves to the spaces of the\nparallel moments of one time-system. How are positions in these various\nspaces to be compared? In other words, What do we mean by motion? It is\nthe fundamental question to be asked of any theory of relative space,\nand like many other fundamental questions it is apt to be left\nunanswered. It is not an answer to reply, that we all know what we mean\nby motion. Of course we do, so far as sense-awareness is concerned. I am\nasking that your theory of space should provide nature with something to\nbe observed. You have not settled the question by bringing forward a\ntheory according to which there is nothing to be observed, and by then\nreiterating that nevertheless we do observe this non-existent fact.\nUnless motion is something as a fact in nature, kinetic energy and\nmomentum and all that depends on these physical concepts evaporate from\nour list of physical realities. Even in this revolutionary age my\nconservatism resolutely opposes the identification of momentum and\nmoonshine.\n\nAccordingly I assume it as an axiom, that motion is a physical fact. It\nis something that we perceive as in nature. Motion presupposes rest.\nUntil theory arose to vitiate immediate intuition, that is to say to\nvitiate the uncriticised judgments which immediately arise from\nsense-awareness, no one doubted that in motion you leave behind that\nwhich is at rest. Abraham in his wanderings left his birthplace where it\nhad ever been. A theory of motion and a theory of rest are the same\nthing viewed from different aspects with altered emphasis.\n\nNow you cannot have a theory of rest without in some sense admitting a\ntheory of absolute position. It is usually assumed that relative space\nimplies that there is no absolute position. This is, according to my\ncreed, a mistake. The assumption arises from the failure to make another\ndistinction; namely, that there may be alternative definitions of\nabsolute position. This possibility enters with the admission of\nalternative time-systems. Thus the series of spaces in the parallel\nmoments of one temporal series may have their own definition of absolute\nposition correlating sets of event-particles in these successive spaces,\nso that each set consists of event-particles, one from each space, all\nwith the property of possessing the same absolute position in that\nseries of spaces. Such a set of event-particles will form a point in the\ntimeless space of that time-system. Thus a point is really an absolute\nposition in the timeless space of a given time-system.\n\nBut there are alternative time-systems, and each time-system has its own\npeculiar group of points--that is to say, its own peculiar definition of\nabsolute position. This is exactly the theory which I will elaborate.\n\nIn looking to nature for evidence of absolute position it is of no use\nto recur to the four-dimensional manifold of event-particles. This\nmanifold has been obtained by the extension of thought beyond the\nimmediacy of observation. We shall find nothing in it except what we\nhave put there to represent the ideas in thought which arise from our\ndirect sense-awareness of nature. To find evidence of the properties\nwhich are to be found in the manifold of event-particles we must always\nrecur to the observation of relations between events. Our problem is to\ndetermine those relations between events which issue in the property of\nabsolute position in a timeless space. This is in fact the problem of\nthe determination of the very meaning of the timeless spaces of physical\nscience.\n\nIn reviewing the factors of nature as immediately disclosed in\nsense-awareness, we should note the fundamental character of the percept\nof 'being here.' We discern an event merely as a factor in a determinate\ncomplex in which each factor has its own peculiar share.\n\nThere are two factors which are always ingredient in this complex, one\nis the duration which is represented in thought by the concept of all\nnature that is present now, and the other is the peculiar _locus standi_\nfor mind involved in the sense-awareness. This _locus standi_ in nature\nis what is represented in thought by the concept of 'here,' namely of an\n'event here.'\n\nThis is the concept of a definite factor in nature. This factor is an\nevent in nature which is the focus in nature for that act of awareness,\nand the other events are perceived as referred to it. This event is part\nof the associated duration. I call it the 'percipient event.' This event\nis not the mind, that is to say, not the percipient. It is that in\nnature from which the mind perceives. The complete foothold of the mind\nin nature is represented by the pair of events, namely, the present\nduration which marks the 'when' of awareness and the percipient event\nwhich marks the 'where' of awareness and the 'how' of awareness. This\npercipient event is roughly speaking the bodily life of the incarnate\nmind. But this identification is only a rough one. For the functions of\nthe body shade off into those of other events in nature; so that for\nsome purposes the percipient event is to be reckoned as merely part of\nthe bodily life and for other purposes it may even be reckoned as more\nthan the bodily life. In many respects the demarcation is purely\narbitrary, depending upon where in a sliding scale you choose to draw\nthe line.\n\nI have already in my previous lecture on Time discussed the association\nof mind with nature. The difficulty of the discussion lies in the\nliability of constant factors to be overlooked. We never note them by\ncontrast with their absences. The purpose of a discussion of such\nfactors may be described as being to make obvious things look odd. We\ncannot envisage them unless we manage to invest them with some of the\nfreshness which is due to strangeness.\n\nIt is because of this habit of letting constant factors slip from\nconsciousness that we constantly fall into the error of thinking of the\nsense-awareness of a particular factor in nature as being a two-termed\nrelation between the mind and the factor. For example, I perceive a\ngreen leaf. Language in this statement suppresses all reference to any\nfactors other than the percipient mind and the green leaf and the\nrelation of sense-awareness. It discards the obvious inevitable factors\nwhich are essential elements in the perception. I am here, the leaf is\nthere; and the event here and the event which is the life of the leaf\nthere are both embedded in a totality of nature which is now, and within\nthis totality there are other discriminated factors which it is\nirrelevant to mention. Thus language habitually sets before the mind a\nmisleading abstract of the indefinite complexity of the fact of\nsense-awareness.\n\nWhat I now want to discuss is the special relation of the percipient\nevent which is 'here' to the duration which is 'now.' This relation is a\nfact in nature, namely the mind is aware of nature as being with these\ntwo factors in this relation.\n\nWithin the short present duration the 'here' of the percipient event has\na definite meaning of some sort. This meaning of 'here' is the content\nof the special relation of the percipient event to its associated\nduration. I will call this relation 'cogredience.' Accordingly I ask for\na description of the character of the relation of cogredience. The\npresent snaps into a past and a present when the 'here' of cogredience\nloses its single determinate meaning. There has been a passage of nature\nfrom the 'here' of perception within the past duration to the different\n'here' of perception within the present duration. But the two 'heres' of\nsense-awareness within neighbouring durations may be indistinguishable.\nIn this case there has been a passage from the past to the present, but\na more retentive perceptive force might have retained the passing nature\nas one complete present instead of letting the earlier duration slip\ninto the past. Namely, the sense of rest helps the integration of\ndurations into a prolonged present, and the sense of motion\ndifferentiates nature into a succession of shortened durations. As we\nlook out of a railway carriage in an express train, the present is past\nbefore reflexion can seize it. We live in snippits too quick for\nthought. On the other hand the immediate present is prolonged according\nas nature presents itself to us in an aspect of unbroken rest. Any\nchange in nature provides ground for a differentiation among durations\nso as to shorten the present. But there is a great distinction between\nself-change in nature and change in external nature. Self-change in\nnature is change in the quality of the standpoint of the percipient\nevent. It is the break up of the 'here' which necessitates the break up\nof the present duration. Change in external nature is compatible with a\nprolongation of the present of contemplation rooted in a given\nstandpoint. What I want to bring out is that the preservation of a\npeculiar relation to a duration is a necessary condition for the\nfunction of that duration as a present duration for sense-awareness.\nThis peculiar relation is the relation of cogredience between the\npercipient event and the duration. Cogredience is the preservation of\nunbroken quality of standpoint within the duration. It is the\ncontinuance of identity of station within the whole of nature which is\nthe terminus of sense-awareness. The duration may comprise change within\nitself, but cannot--so far as it is one present duration--comprise\nchange in the quality of its peculiar relation to the contained\npercipient event.\n\nIn other words, perception is always 'here,' and a duration can only be\nposited as present for sense-awareness on condition that it affords one\nunbroken meaning of 'here' in its relation to the percipient event. It\nis only in the past that you can have been 'there' with a standpoint\ndistinct from your present 'here.'\n\nEvents there and events here are facts of nature, and the qualities of\nbeing 'there' and 'here' are not merely qualities of awareness as a\nrelation between nature and mind. The quality of determinate station in\nthe duration which belongs to an event which is 'here' in one\ndeterminate sense of 'here' is the same kind of quality of station which\nbelongs to an event which is 'there' in one determinate sense of\n'there.' Thus cogredience has nothing to do with any biological\ncharacter of the event which is related by it to the associated\nduration. This biological character is apparently a further condition\nfor the peculiar connexion of a percipient event with the percipience of\nmind; but it has nothing to do with the relation of the percipient event\nto the duration which is the present whole of nature posited as the\ndisclosure of the percipience.\n\nGiven the requisite biological character, the event in its character of\na percipient event selects that duration with which the operative past\nof the event is practically cogredient within the limits of the\nexactitude of observation. Namely, amid the alternative time-systems\nwhich nature offers there will be one with a duration giving the best\naverage of cogredience for all the subordinate parts of the percipient\nevent. This duration will be the whole of nature which is the terminus\nposited by sense-awareness. Thus the character of the percipient event\ndetermines the time-system immediately evident in nature. As the\ncharacter of the percipient event changes with the passage of\nnature--or, in other words, as the percipient mind in its passage\ncorrelates itself with the passage of the percipient event into another\npercipient event--the time-system correlated with the percipience of\nthat mind may change. When the bulk of the events perceived are\ncogredient in a duration other than that of the percipient event, the\npercipience may include a double consciousness of cogredience, namely\nthe consciousness of the whole within which the observer in the train is\n'here,' and the consciousness of the whole within which the trees and\nbridges and telegraph posts are definitely 'there.' Thus in perceptions\nunder certain circumstances the events discriminated assert their own\nrelations of cogredience. This assertion of cogredience is peculiarly\nevident when the duration to which the perceived event is cogredient is\nthe same as the duration which is the present whole of nature--in other\nwords, when the event and the percipient event are both cogredient to\nthe same duration.\n\nWe are now prepared to consider the meaning of stations in a duration,\nwhere stations are a peculiar kind of routes, which define absolute\nposition in the associated timeless space.\n\nThere are however some preliminary explanations. A finite event will be\nsaid to extend throughout a duration when it is part of the duration\nand is intersected by any moment which lies in the duration. Such an\nevent begins with the duration and ends with it. Furthermore every event\nwhich begins with the duration and ends with it, extends throughout the\nduration. This is an axiom based on the continuity of events. By\nbeginning with a duration and ending with it, I mean (i) that the event\nis part of the duration, and (ii) that both the initial and final\nboundary moments of the duration cover some event-particles on the\nboundary of the event.\n\nEvery event which is cogredient with a duration extends throughout that\nduration.\n\nIt is not true that all the parts of an event cogredient with a duration\nare also cogredient with the duration. The relation of cogredience may\nfail in either of two ways. One reason for failure may be that the part\ndoes not extend throughout the duration. In this case the part may be\ncogredient with another duration which is part of the given duration,\nthough it is not cogredient with the given duration itself. Such a part\nwould be cogredient if its existence were sufficiently prolonged in that\ntime-system. The other reason for failure arises from the\nfour-dimensional extension of events so that there is no determinate\nroute of transition of events in linear series. For example, the tunnel\nof a tube railway is an event at rest in a certain time-system, that is\nto say, it is cogredient with a certain duration. A train travelling in\nit is part of that tunnel, but is not itself at rest.\n\nIf an event e be cogredient with a duration d, and d' be any\nduration which is part of d. Then d' belongs to the same time-system\nas d. Also d' intersects e in an event e' which is part of e\nand is cogredient with d'.\n\nLet P be any event-particle lying in a given duration d. Consider\nthe aggregate of events in which P lies and which are also cogredient\nwith d. Each of these events occupies its own aggregate of\nevent-particles. These aggregates will have a common portion, namely the\nclass of event-particle lying in all of them. This class of\nevent-particles is what I call the 'station' of the event-particle P\nin the duration d. This is the station in the character of a locus. A\nstation can also be defined in the character of an abstractive element.\nLet the property {sigma} be the name of the property which an\nabstractive set possesses when (i) each of its events is cogredient with\nthe duration d and (ii) the event-particle P lies in each of its events.\nThen the group of {sigma}-primes, where {sigma} has this meaning, is an\nabstractive element and is the station of P in d as an abstractive\nelement. The locus of event-particles covered by the station of P in d\nas an abstractive element is the station of P in d as a locus. A station\nhas accordingly the usual three characters, namely, its character of\nposition, its extrinsic character as an abstractive element, and its\nintrinsic character.\n\nIt follows from the peculiar properties of rest that two stations\nbelonging to the same duration cannot intersect. Accordingly every\nevent-particle on a station of a duration has that station as its\nstation in the duration. Also every duration which is part of a given\nduration intersects the stations of the given duration in loci which are\nits own stations. By means of these properties we can utilise the\noverlappings of the durations of one family--that is, of one\ntime-system--to prolong stations indefinitely backwards and forwards.\nSuch a prolonged station will be called a point-track. A point-track is\na locus of event-particles. It is defined by reference to one particular\ntime-system, {alpha} say. Corresponding to any other time-system these\nwill be a different group of point-tracks. Every event-particle will lie\non one and only one point-track of the group belonging to any one\ntime-system. The group of point-tracks of the time-system {alpha} is the\ngroup of points of the timeless space of {alpha}. Each such point\nindicates a certain quality of absolute position in reference to the\ndurations of the family associated with {alpha}, and thence in reference\nto the successive instantaneous spaces lying in the successive moments\nof {alpha}. Each moment of {alpha} will intersect a point-track in one\nand only one event-particle.\n\nThis property of the unique intersection of a moment and a point-track\nis not confined to the case when the moment and the point-track belong\nto the same time-system. Any two event-particles on a point-track are\nsequential, so that they cannot lie in the same moment. Accordingly no\nmoment can intersect a point-track more than once, and every moment\nintersects a point-track in one event-particle.\n\nAnyone who at the successive moments of {alpha} should be at the\nevent-particles where those moments intersect a given point of {alpha}\nwill be at rest in the timeless space of time-system {alpha}. But in any\nother timeless space belonging to another time-system he will be at a\ndifferent point at each succeeding moment of that time-system. In other\nwords he will be moving. He will be moving in a straight line with\nuniform velocity. We might take this as the definition of a straight\nline. Namely, a straight line in the space of time-system {beta} is the\nlocus of those points of {beta} which all intersect some one point-track\nwhich is a point in the space of some other time-system. Thus each point\nin the space of a time-system {alpha} is associated with one and only\none straight line of the space of any other time-system {beta}.\nFurthermore the set of straight lines in space {beta} which are thus\nassociated with points in space {alpha} form a complete family of\nparallel straight lines in space {beta}. Thus there is a one-to-one\ncorrelation of points in space {alpha} with the straight lines of a\ncertain definite family of parallel straight lines in space {beta}.\nConversely there is an analogous one-to-one correlation of the points in\nspace {beta} with the straight lines of a certain family of parallel\nstraight lines in space {alpha}. These families will be called\nrespectively the family of parallels in {beta} associated with {alpha},\nand the family of parallels in {alpha} associated with {beta}. The\ndirection in the space of {beta} indicated by the family of parallels in\n{beta} will be called the direction of {alpha} in space {beta}, and the\nfamily of parallels in {alpha} is the direction of {beta} in space\n{alpha}. Thus a being at rest at a point of space {alpha} will be moving\nuniformly along a line in space {beta} which is in the direction of\n{alpha} in space {beta}, and a being at rest at a point of space {beta}\nwill be moving uniformly along a line in space {alpha} which is in the\ndirection of {beta} in space {alpha}.\n\nI have been speaking of the timeless spaces which are associated with\ntime-systems. These are the spaces of physical science and of any\nconcept of space as eternal and unchanging. But what we actually\nperceive is an approximation to the instantaneous space indicated by\nevent-particles which lie within some moment of the time-system\nassociated with our awareness. The points of such an instantaneous space\nare event-particles and the straight lines are rects. Let the\ntime-system be named {alpha}, and let the moment of time-system {alpha}\nto which our quick perception of nature approximates be called M. Any\nstraight line r in space {alpha} is a locus of points and each point is\na point-track which is a locus of event-particles. Thus in the\nfour-dimensional geometry of all event-particles there is a\ntwo-dimensional locus which is the locus of all event-particles on\npoints lying on the straight line r. I will call this locus of\nevent-particles the matrix of the straight line r. A matrix intersects\nany moment in a rect. Thus the matrix of r intersects the moment M in a\nrect {rho}. Thus {rho} is the instantaneous rect in M which occupies at\nthe moment M the straight line r in the space of {alpha}. Accordingly\nwhen one sees instantaneously a moving being and its path ahead of it,\nwhat one really sees is the being at some event-particle A lying in the\nrect {rho} which is the apparent path on the assumption of uniform\nmotion. But the actual rect {rho} which is a locus of event-particles is\nnever traversed by the being. These event-particles are the\ninstantaneous facts which pass with the instantaneous moment. What is\nreally traversed are other event-particles which at succeeding instants\noccupy the same points of space {alpha} as those occupied by the\nevent-particles of the rect {rho}. For example, we see a stretch of road\nand a lorry moving along it. The instantaneously seen road is a portion\nof the rect {rho}--of course only an approximation to it. The lorry is\nthe moving object. But the road as seen is never traversed. It is\nthought of as being traversed because the intrinsic characters of the\nlater events are in general so similar to those of the instantaneous\nroad that we do not trouble to discriminate. But suppose a land mine\nunder the road has been exploded before the lorry gets there. Then it is\nfairly obvious that the lorry does not traverse what we saw at first.\nSuppose the lorry is at rest in space {beta}. Then the straight line r\nof space {alpha} is in the direction of {beta} in space {alpha}, and the\nrect {rho} is the representative in the moment M of the line r of space\n{alpha}. The direction of {rho} in the instantaneous space of the moment\nM is the direction of {beta} in M, where M is a moment of time-system\n{alpha}. Again the matrix of the line r of space {alpha} will also be\nthe matrix of some line s of space {beta} which will be in the direction\nof {alpha} in space {beta}. Thus if the lorry halts at some point P of\nspace {alpha} which lies on the line r, it is now moving along the line\ns of space {beta}. This is the theory of relative motion; the common\nmatrix is the bond which connects the motion of {beta} in space {alpha}\nwith the motions of {alpha} in space {beta}.\n\nMotion is essentially a relation between some object of nature and the\none timeless space of a time-system. An instantaneous space is static,\nbeing related to the static nature at an instant. In perception when we\nsee things moving in an approximation to an instantaneous space, the\nfuture lines of motion as immediately perceived are rects which are\nnever traversed. These approximate rects are composed of small events,\nnamely approximate routes and event-particles, which are passed away\nbefore the moving objects reach them. Assuming that our forecasts of\nrectilinear motion are correct, these rects occupy the straight lines in\ntimeless space which are traversed. Thus the rects are symbols in\nimmediate sense-awareness of a future which can only be expressed in\nterms of timeless space.\n\nWe are now in a position to explore the fundamental character of\nperpendicularity. Consider the two time-systems {alpha} and {beta}, each\nwith its own timeless space and its own family of instantaneous moments\nwith their instantaneous spaces. Let M and N be respectively a moment of\n{alpha} and a moment of {beta}. In M there is the direction of {beta}\nand in N there is the direction of {alpha}. But M and N, being moments\nof different time-systems, intersect in a level. Call this level\n{lambda}. Then {lambda} is an instantaneous plane in the instantaneous\nspace of M and also in the instantaneous space of N. It is the locus of\nall the event-particles which lie both in M and in N.\n\nIn the instantaneous space of M the level {lambda} is perpendicular to\nthe direction of {beta} in M, and in the instantaneous space of N the\nlevel {lambda} is perpendicular to the direction of {alpha} in N. This\nis the fundamental property which forms the definition of\nperpendicularity. The symmetry of perpendicularity is a particular\ninstance of the symmetry of the mutual relations between two\ntime-systems. We shall find in the next lecture that it is from this\nsymmetry that the theory of congruence is deduced.\n\nThe theory of perpendicularity in the timeless space of any time-system\n{alpha} follows immediately from this theory of perpendicularity in each\nof its instantaneous spaces. Let {rho} be any rect in the moment M of\n{alpha} and let {lambda} be a level in M which is perpendicular to\n{rho}. The locus of those points of the space of {alpha} which intersect\nM in event-particles on {rho} is the straight line r of space {alpha},\nand the locus of those points of the space of {alpha} which intersect M\nin event-particles on {lambda} is the plane l of space {alpha}. Then the\nplane l is perpendicular to the line r.\n\nIn this way we have pointed out unique and definite properties in nature\nwhich correspond to perpendicularity. We shall find that this discovery\nof definite unique properties defining perpendicularity is of critical\nimportance in the theory of congruence which is the topic for the next\nlecture.\n\nI regret that it has been necessary for me in this lecture to administer\nsuch a large dose of four-dimensional geometry. I do not apologise,\nbecause I am really not responsible for the fact that nature in its most\nfundamental aspect is four-dimensional. Things are what they are; and it\nis useless to disguise the fact that 'what things are' is often very\ndifficult for our intellects to follow. It is a mere evasion of the\nultimate problems to shirk such obstacles.\n\n\n\n\nCHAPTER VI\n\nCONGRUENCE\n\n\nThe aim of this lecture is to establish a theory of congruence. You must\nunderstand at once that congruence is a controversial question. It is\nthe theory of measurement in space and in time. The question seems\nsimple. In fact it is simple enough for a standard procedure to have\nbeen settled by act of parliament; and devotion to metaphysical\nsubtleties is almost the only crime which has never been imputed to any\nEnglish parliament. But the procedure is one thing and its meaning is\nanother.\n\nFirst let us fix attention on the purely mathematical question. When the\nsegment between two points A and B is congruent to that between the\ntwo points C and D, the quantitative measurements of the two\nsegments are equal. The equality of the numerical measures and the\ncongruence of the two segments are not always clearly discriminated, and\nare lumped together under the term equality. But the procedure of\nmeasurement presupposes congruence. For example, a yard measure is\napplied successively to measure two distances between two pairs of\npoints on the floor of a room. It is of the essence of the procedure of\nmeasurement that the yard measure remains unaltered as it is transferred\nfrom one position to another. Some objects can palpably alter as they\nmove--for example, an elastic thread; but a yard measure does not alter\nif made of the proper material. What is this but a judgment of\ncongruence applied to the train of successive positions of the yard\nmeasure? We know that it does not alter because we judge it to be\ncongruent to itself in various positions. In the case of the thread we\ncan observe the loss of self-congruence. Thus immediate judgments of\ncongruence are presupposed in measurement, and the process of\nmeasurement is merely a procedure to extend the recognition of\ncongruence to cases where these immediate judgments are not available.\nThus we cannot define congruence by measurement.\n\nIn modern expositions of the axioms of geometry certain conditions are\nlaid down which the relation of congruence between segments is to\nsatisfy. It is supposed that we have a complete theory of points,\nstraight lines, planes, and the order of points on planes--in fact, a\ncomplete theory of non-metrical geometry. We then enquire about\ncongruence and lay down the set of conditions--or axioms as they are\ncalled--which this relation satisfies. It has then been proved that\nthere are alternative relations which satisfy these conditions equally\nwell and that there is nothing intrinsic in the theory of space to lead\nus to adopt any one of these relations in preference to any other as the\nrelation of congruence which we adopt. In other words there are\nalternative metrical geometries which all exist by an equal right so far\nas the intrinsic theory of space is concerned.\n\nPoincar\u00e9, the great French mathematician, held that our actual choice\namong these geometries is guided purely by convention, and that the\neffect of a change of choice would be simply to alter our expression of\nthe physical laws of nature. By 'convention' I understand Poincar\u00e9 to\nmean that there is nothing inherent in nature itself giving any peculiar\n_r\u00f4le_ to one of these congruence relations, and that the choice of one\nparticular relation is guided by the volitions of the mind at the other\nend of the sense-awareness. The principle of guidance is intellectual\nconvenience and not natural fact.\n\nThis position has been misunderstood by many of Poincar\u00e9's expositors.\nThey have muddled it up with another question, namely that owing to the\ninexactitude of observation it is impossible to make an exact statement\nin the comparison of measures. It follows that a certain subset of\nclosely allied congruence relations can be assigned of which each member\nequally well agrees with that statement of observed congruence when the\nstatement is properly qualified with its limits of error.\n\nThis is an entirely different question and it presupposes a rejection of\nPoincar\u00e9's position. The absolute indetermination of nature in respect\nof all the relations of congruence is replaced by the indetermination of\nobservation with respect to a small subgroup of these relations.\n\nPoincar\u00e9's position is a strong one. He in effect challenges anyone to\npoint out any factor in nature which gives a preeminent status to the\ncongruence relation which mankind has actually adopted. But undeniably\nthe position is very paradoxical. Bertrand Russell had a controversy\nwith him on this question, and pointed out that on Poincar\u00e9's principles\nthere was nothing in nature to determine whether the earth is larger or\nsmaller than some assigned billiard ball. Poincar\u00e9 replied that the\nattempt to find reasons in nature for the selection of a definite\ncongruence relation in space is like trying to determine the position of\na ship in the ocean by counting the crew and observing the colour of\nthe captain's eyes.\n\nIn my opinion both disputants were right, assuming the grounds on which\nthe discussion was based. Russell in effect pointed out that apart from\nminor inexactitudes a determinate congruence relation is among the\nfactors in nature which our sense-awareness posits for us. Poincar\u00e9 asks\nfor information as to the factor in nature which might lead any\nparticular congruence relation to play a preeminent _r\u00f4le_ among the\nfactors posited in sense-awareness. I cannot see the answer to either of\nthese contentions provided that you admit the materialistic theory of\nnature. With this theory nature at an instant in space is an independent\nfact. Thus we have to look for our preeminent congruence relation amid\nnature in instantaneous space; and Poincar\u00e9 is undoubtedly right in\nsaying that nature on this hypothesis gives us no help in finding it.\n\nOn the other hand Russell is in an equally strong position when he\nasserts that, as a fact of observation, we do find it, and what is more\nagree in finding the same congruence relation. On this basis it is one\nof the most extraordinary facts of human experience that all mankind\nwithout any assignable reason should agree in fixing attention on just\none congruence relation amid the indefinite number of indistinguishable\ncompetitors for notice. One would have expected disagreement on this\nfundamental choice to have divided nations and to have rent families.\nBut the difficulty was not even discovered till the close of the\nnineteenth century by a few mathematical philosophers and philosophic\nmathematicians. The case is not like that of our agreement on some\nfundamental fact of nature such as the three dimensions of space. If\nspace has only three dimensions we should expect all mankind to be aware\nof the fact, as they are aware of it. But in the case of congruence,\nmankind agree in an arbitrary interpretation of sense-awareness when\nthere is nothing in nature to guide it.\n\nI look on it as no slight recommendation of the theory of nature which I\nam expounding to you that it gives a solution of this difficulty by\npointing out the factor in nature which issues in the preeminence of one\ncongruence relation over the indefinite herd of other such relations.\n\nThe reason for this result is that nature is no longer confined within\nspace at an instant. Space and time are now interconnected; and this\npeculiar factor of time which is so immediately distinguished among the\ndeliverances of our sense-awareness, relates itself to one particular\ncongruence relation in space.\n\nCongruence is a particular example of the fundamental fact of\nrecognition. In perception we recognise. This recognition does not\nmerely concern the comparison of a factor of nature posited by memory\nwith a factor posited by immediate sense-awareness. Recognition takes\nplace within the present without any intervention of pure memory. For\nthe present fact is a duration with its antecedent and consequent\ndurations which are parts of itself. The discrimination in\nsense-awareness of a finite event with its quality of passage is also\naccompanied by the discrimination of other factors of nature which do\nnot share in the passage of events. Whatever passes is an event. But we\nfind entities in nature which do not pass; namely we recognise\nsamenesses in nature. Recognition is not primarily an intellectual act\nof comparison; it is in its essence merely sense-awareness in its\ncapacity of positing before us factors in nature which do not pass. For\nexample, green is perceived as situated in a certain finite event within\nthe present duration. This green preserves its self-identity throughout,\nwhereas the event passes and thereby obtains the property of breaking\ninto parts. The green patch has parts. But in talking of the green patch\nwe are speaking of the event in its sole capacity of being for us the\nsituation of green. The green itself is numerically one self-identical\nentity, without parts because it is without passage.\n\nFactors in nature which are without passage will be called objects.\nThere are radically different kinds of objects which will be considered\nin the succeeding lecture.\n\nRecognition is reflected into the intellect as comparison. The\nrecognised objects of one event are compared with the recognised objects\nof another event. The comparison may be between two events in the\npresent, or it may be between two events of which one is posited by\nmemory-awareness and the other by immediate sense-awareness. But it is\nnot the events which are compared. For each event is essentially unique\nand incomparable. What are compared are the objects and relations of\nobjects situated in events. The event considered as a relation between\nobjects has lost its passage and in this aspect is itself an object.\nThis object is not the event but only an intellectual abstraction. The\nsame object can be situated in many events; and in this sense even the\nwhole event, viewed as an object, can recur, though not the very event\nitself with its passage and its relations to other events.\n\nObjects which are not posited by sense-awareness may be known to the\nintellect. For example, relations between objects and relations between\nrelations may be factors in nature not disclosed in sense-awareness but\nknown by logical inference as necessarily in being. Thus objects for our\nknowledge may be merely logical abstractions. For example, a complete\nevent is never disclosed in sense-awareness, and thus the object which\nis the sum total of objects situated in an event as thus inter-related\nis a mere abstract concept. Again a right-angle is a perceived object\nwhich can be situated in many events; but, though rectangularity is\nposited by sense-awareness, the majority of geometrical relations are\nnot so posited. Also rectangularity is in fact often not perceived when\nit can be proved to have been there for perception. Thus an object is\noften known merely as an abstract relation not directly posited in\nsense-awareness although it is there in nature.\n\nThe identity of quality between congruent segments is generally of this\ncharacter. In certain special cases this identity of quality can be\ndirectly perceived. But in general it is inferred by a process of\nmeasurement depending on our direct sense-awareness of selected cases\nand a logical inference from the transitive character of congruence.\n\nCongruence depends on motion, and thereby is generated the connexion\nbetween spatial congruence and temporal congruence. Motion along a\nstraight line has a symmetry round that line. This symmetry is expressed\nby the symmetrical geometrical relations of the line to the family of\nplanes normal to it.\n\nAlso another symmetry in the theory of motion arises from the fact that\nrest in the points of {beta} corresponds to uniform motion along a\ndefinite family of parallel straight lines in the space of {alpha}. We\nmust note the three characteristics, (i) of the uniformity of the motion\ncorresponding to any point of {beta} along its correlated straight line\nin {alpha}, and (ii) of the equality in magnitude of the velocities\nalong the various lines of {alpha} correlated to rest in the various\npoints of {beta}, and (iii) of the parallelism of the lines of this\nfamily.\n\nWe are now in possession of a theory of parallels and a theory of\nperpendiculars and a theory of motion, and from these theories the\ntheory of congruence can be constructed. It will be remembered that a\nfamily of parallel levels in any moment is the family of levels in which\nthat moment is intersected by the family of moments of some other\ntime-system. Also a family of parallel moments is the family of moments\nof some one time-system. Thus we can enlarge our concept of a family of\nparallel levels so as to include levels in different moments of one\ntime-system. With this enlarged concept we say that a complete family of\nparallel levels in a time-system {alpha} is the complete family of\nlevels in which the moments of {alpha} intersect the moments of {beta}.\nThis complete family of parallel levels is also evidently a family lying\nin the moments of the time-system {beta}. By introducing a third\ntime-system {gamma}, parallel rects are obtained. Also all the points of\nany one time-system form a family of parallel point-tracks. Thus there\nare three types of parallelograms in the four-dimensional manifold of\nevent-particles.\n\nIn parallelograms of the first type the two pairs of parallel sides are\nboth of them pairs of rects. In parallelograms of the second type one\npair of parallel sides is a pair of rects and the other pair is a pair\nof point-tracks. In parallelograms of the third type the two pairs of\nparallel sides are both of them pairs of point-tracks.\n\nThe first axiom of congruence is that the opposite sides of any\nparallelogram are congruent. This axiom enables us to compare the\nlengths of any two segments either respectively on parallel rects or on\nthe same rect. Also it enables us to compare the lengths of any two\nsegments either respectively on parallel point-tracks or on the same\npoint-track. It follows from this axiom that two objects at rest in any\ntwo points of a time-system {beta} are moving with equal velocities in any\nother time-system {alpha} along parallel lines. Thus we can speak of the\nvelocity in {alpha} due to the time-system {beta} without specifying any\nparticular point in {beta}. The axiom also enables us to measure time in\nany time-system; but does not enable us to compare times in different\ntime-systems.\n\nThe second axiom of congruence concerns parallelograms on congruent\nbases and between the same parallels, which have also their other pairs\nof sides parallel. The axiom asserts that the rect joining the two\nevent-particles of intersection of the diagonals is parallel to the rect\non which the bases lie. By the aid of this axiom it easily follows that\nthe diagonals of a parallelogram bisect each other.\n\nCongruence is extended in any space beyond parallel rects to all rects\nby two axioms depending on perpendicularity. The first of these axioms,\nwhich is the third axiom of congruence, is that if ABC is a triangle\nof rects in any moment and D is the middle event-particle of the base\nBC, then the level through D perpendicular to BC contains A when\nand only when AB is congruent to AC. This axiom evidently expresses\nthe symmetry of perpendicularity, and is the essence of the famous pons\nasinorum expressed as an axiom.\n\nThe second axiom depending on perpendicularity, and the fourth axiom of\ncongruence, is that if r and A be a rect and an event-particle in the\nsame moment and AB and AC be a pair of rectangular rects intersecting r\nin B and C, and AD and AE be another pair of rectangular rects\nintersecting r in D and E, then either D or E lies in the segment BC and\nthe other one of the two does not lie in this segment. Also as a\nparticular case of this axiom, if AB be perpendicular to r and in\nconsequence AC be parallel to r, then D and E lie on opposite sides of B\nrespectively. By the aid of these two axioms the theory of congruence\ncan be extended so as to compare lengths of segments on any two rects.\nAccordingly Euclidean metrical geometry in space is completely\nestablished and lengths in the spaces of different time-systems are\ncomparable as the result of definite properties of nature which indicate\njust that particular method of comparison.\n\nThe comparison of time-measurements in diverse time-systems requires two\nother axioms. The first of these axioms, forming the fifth axiom of\ncongruence, will be called the axiom of 'kinetic symmetry.' It expresses\nthe symmetry of the quantitative relations between two time-systems when\nthe times and lengths in the two systems are measured in congruent\nunits.\n\nThe axiom can be explained as follows: Let {alpha} and {beta} be the names\nof two time-systems. The directions of motion in the space of {alpha} due\nto rest in a point of {beta} is called the '{beta}-direction in {alpha}'\nand the direction of motion in the space of {beta} due to rest in a\npoint of {alpha} is called the '{alpha}-direction in {beta}.' Consider a\nmotion in the space of {alpha} consisting of a certain velocity in the\n{beta}-direction of {alpha} and a certain velocity at right-angles to\nit. This motion represents rest in the space of another time-system--call\nit {pi}. Rest in {pi} will also be represented in the space of {beta} by\na certain velocity in the {alpha}-direction in {beta} and a certain\nvelocity at right-angles to this {alpha}-direction. Thus a certain\nmotion in the space of {alpha} is correlated to a certain motion in the\nspace of {beta}, as both representing the same fact which can also be\nrepresented by rest in {pi}. Now another time-system, which I will name\n{sigma}, can be found which is such that rest in its space is\nrepresented by the same magnitudes of velocities along and perpendicular\nto the {alpha}-direction in {beta} as those velocities in {alpha}, along\nand perpendicular to the {beta}-direction, which represent rest in {pi}.\nThe required axiom of kinetic symmetry is that rest in {sigma} will be\nrepresented in {alpha} by the same velocities along and perpendicular to\nthe {beta}-direction in {alpha} as those velocities in {beta} along and\nperpendicular to the {alpha}-direction which represent rest in {pi}.\n\nA particular case of this axiom is that relative velocities are equal\nand opposite. Namely rest in {alpha} is represented in {beta} by a\nvelocity along the {alpha}-direction which is equal to the velocity\nalong the {beta}-direction in {alpha} which represents rest in {beta}.\n\nFinally the sixth axiom of congruence is that the relation of congruence\nis transitive. So far as this axiom applies to space, it is superfluous.\nFor the property follows from our previous axioms. It is however\nnecessary for time as a supplement to the axiom of kinetic symmetry. The\nmeaning of the axiom is that if the time-unit of system {alpha} is\ncongruent to the time-unit of system {beta}, and the time-unit of system\n{beta} is congruent to the time-unit of system {gamma}, then the\ntime-units of {alpha} and {gamma} are also congruent.\n\nBy means of these axioms formulae for the transformation of\nmeasurements made in one time-system to measurements of the same facts\nof nature made in another time-system can be deduced. These formulae\nwill be found to involve one arbitrary constant which I will call k.\n\nIt is of the dimensions of the square of a velocity. Accordingly four\ncases arise. In the first case k is zero. This case produces\nnonsensical results in opposition to the elementary deliverances of\nexperience. We put this case aside.\n\nIn the second case k is infinite. This case yields the ordinary\nformulae for transformation in relative motion, namely those formulae\nwhich are to be found in every elementary book on dynamics.\n\nIn the third case, k is negative. Let us call it -c\u00b2, where c\nwill be of the dimensions of a velocity. This case yields the formulae\nof transformation which Larmor discovered for the transformation of\nMaxwell's equations of the electromagnetic field. These formulae were\nextended by H.\u00a0A. Lorentz, and used by Einstein and Minkowski as the\nbasis of their novel theory of relativity. I am not now speaking of\nEinstein's more recent theory of general relativity by which he deduces\nhis modification of the law of gravitation. If this be the case which\napplies to nature, then c must be a close approximation to the\nvelocity of light _in vacuo_. Perhaps it is this actual velocity. In\nthis connexion '_in vacuo_' must not mean an absence of events, namely\nthe absence of the all-pervading ether of events. It must mean the\nabsence of certain types of objects.\n\nIn the fourth case, k is positive. Let us call it h\u00b2, where h\nwill be of the dimensions of a velocity. This gives a perfectly possible\ntype of transformation formulae, but not one which explains any facts\nof experience. It has also another disadvantage. With the assumption of\nthis fourth case the distinction between space and time becomes unduly\nblurred. The whole object of these lectures has been to enforce the\ndoctrine that space and time spring from a common root, and that the\nultimate fact of experience is a space-time fact. But after all mankind\ndoes distinguish very sharply between space and time, and it is owing to\nthis sharpness of distinction that the doctrine of these lectures is\nsomewhat of a paradox. Now in the third assumption this sharpness of\ndistinction is adequately preserved. There is a fundamental distinction\nbetween the metrical properties of point-tracks and rects. But in the\nfourth assumption this fundamental distinction vanishes.\n\nNeither the third nor the fourth assumption can agree with experience\nunless we assume that the velocity c of the third assumption, and the\nvelocity h of the fourth assumption, are extremely large compared to\nthe velocities of ordinary experience. If this be the case the formulae\nof both assumptions will obviously reduce to a close approximation to\nthe formulae of the second assumption which are the ordinary formulae of\ndynamical textbooks. For the sake of a name, I will call these textbook\nformulae the 'orthodox' formulae.\n\nThere can be no question as to the general approximate correctness of\nthe orthodox formulae. It would be merely silly to raise doubts on this\npoint. But the determination of the status of these formulae is by no\nmeans settled by this admission. The independence of time and space is\nan unquestioned presupposition of the orthodox thought which has\nproduced the orthodox formulae. With this presupposition and given the\nabsolute points of one absolute space, the orthodox formulae are\nimmediate deductions. Accordingly, these formulae are presented to our\nimaginations as facts which cannot be otherwise, time and space being\nwhat they are. The orthodox formulae have therefore attained to the\nstatus of necessities which cannot be questioned in science. Any attempt\nto replace these formulae by others was to abandon the _r\u00f4le_ of\nphysical explanation and to have recourse to mere mathematical formulae.\n\nBut even in physical science difficulties have accumulated round the\northodox formulae. In the first place Maxwell's equations of the\nelectromagnetic field are not invariant for the transformations of the\northodox formulae; whereas they are invariant for the transformations of\nthe formulae arising from the third of the four cases mentioned above,\nprovided that the velocity c is identified with a famous\nelectromagnetic constant quantity.\n\nAgain the null results of the delicate experiments to detect the earth's\nvariations of motion through the ether in its orbital path are explained\nimmediately by the formulae of the third case. But if we assume the\northodox formulae we have to make a special and arbitrary assumption as\nto the contraction of matter during motion. I mean the Fitzgerald-Lorentz\nassumption.\n\nLastly Fresnel's coefficient of drag which represents the variation of\nthe velocity of light in a moving medium is explained by the formulae of\nthe third case, and requires another arbitrary assumption if we use the\northodox formulae.\n\nIt appears therefore that on the mere basis of physical explanation\nthere are advantages in the formulae of the third case as compared with\nthe orthodox formulae. But the way is blocked by the ingrained belief\nthat these latter formulae possess a character of necessity. It is\ntherefore an urgent requisite for physical science and for philosophy to\nexamine critically the grounds for this supposed necessity. The only\nsatisfactory method of scrutiny is to recur to the first principles of\nour knowledge of nature. This is exactly what I am endeavouring to do in\nthese lectures. I ask what it is that we are aware of in our\nsense-perception of nature. I then proceed to examine those factors in\nnature which lead us to conceive nature as occupying space and\npersisting through time. This procedure has led us to an investigation\nof the characters of space and time. It results from these\ninvestigations that the formulae of the third case and the orthodox\nformulae are on a level as possible formulae resulting from the basic\ncharacter of our knowledge of nature. The orthodox formulae have thus\nlost any advantage as to necessity which they enjoyed over the serial\ngroup. The way is thus open to adopt whichever of the two groups best\naccords with observation.\n\nI take this opportunity of pausing for a moment from the course of my\nargument, and of reflecting on the general character which my doctrine\nascribes to some familiar concepts of science. I have no doubt that some\nof you have felt that in certain aspects this character is very\nparadoxical.\n\nThis vein of paradox is partly due to the fact that educated language\nhas been made to conform to the prevalent orthodox theory. We are thus,\nin expounding an alternative doctrine, driven to the use of either\nstrange terms or of familiar words with unusual meanings. This victory\nof the orthodox theory over language is very natural. Events are named\nafter the prominent objects situated in them, and thus both in language\nand in thought the event sinks behind the object, and becomes the mere\nplay of its relations. The theory of space is then converted into a\ntheory of the relations of objects instead of a theory of the relations\nof events. But objects have not the passage of events. Accordingly space\nas a relation between objects is devoid of any connexion with time. It\nis space at an instant without any determinate relations between the\nspaces at successive instants. It cannot be one timeless space because\nthe relations between objects change.\n\nA few minutes ago in speaking of the deduction of the orthodox formulae\nfor relative motion I said that they followed as an immediate deduction\nfrom the assumption of absolute points in absolute space. This reference\nto absolute space was not an oversight. I know that the doctrine of the\nrelativity of space at present holds the field both in science and\nphilosophy. But I do not think that its inevitable consequences are\nunderstood. When we really face them the paradox of the presentation of\nthe character of space which I have elaborated is greatly mitigated. If\nthere is no absolute position, a point must cease to be a simple entity.\nWhat is a point to one man in a balloon with his eyes fixed on an\ninstrument is a track of points to an observer on the earth who is\nwatching the balloon through a telescope, and is another track of points\nto an observer in the sun who is watching the balloon through some\ninstrument suited to such a being. Accordingly if I am reproached with\nthe paradox of my theory of points as classes of event-particles, and of\nmy theory of event-particles as groups of abstractive sets, I ask my\ncritic to explain exactly what he means by a point. While you explain\nyour meaning about anything, however simple, it is always apt to look\nsubtle and fine spun. I have at least explained exactly what I do mean\nby a point, what relations it involves and what entities are the relata.\nIf you admit the relativity of space, you also must admit that points\nare complex entities, logical constructs involving other entities and\ntheir relations. Produce your theory, not in a few vague phrases of\nindefinite meaning, but explain it step by step in definite terms\nreferring to assigned relations and assigned relata. Also show that your\ntheory of points issues in a theory of space. Furthermore note that the\nexample of the man in the balloon, the observer on earth, and the\nobserver in the sun, shows that every assumption of relative rest\nrequires a timeless space with radically different points from those\nwhich issue from every other such assumption. The theory of the\nrelativity of space is inconsistent with any doctrine of one unique set\nof points of one timeless space.\n\nThe fact is that there is no paradox in my doctrine of the nature of\nspace which is not in essence inherent in the theory of the relativity\nof space. But this doctrine has never really been accepted in science,\nwhatever people say. What appears in our dynamical treatises is Newton's\ndoctrine of relative motion based on the doctrine of differential motion\nin absolute space. When you once admit that the points are radically\ndifferent entities for differing assumptions of rest, then the orthodox\nformulae lose all their obviousness. They were only obvious because you\nwere really thinking of something else. When discussing this topic you\ncan only avoid paradox by taking refuge from the flood of criticism in\nthe comfortable ark of no meaning.\n\nThe new theory provides a definition of the congruence of periods of\ntime. The prevalent view provides no such definition. Its position is\nthat if we take such time-measurements so that certain familiar\nvelocities which seem to us to be uniform are uniform, then the laws of\nmotion are true. Now in the first place no change could appear either as\nuniform or non-uniform without involving a definite determination of the\ncongruence for time-periods. So in appealing to familiar phenomena it\nallows that there is some factor in nature which we can intellectually\nconstruct as a congruence theory. It does not however say anything about\nit except that the laws of motion are then true. Suppose that with some\nexpositors we cut out the reference to familiar velocities such as the\nrate of rotation of the earth. We are then driven to admit that there is\nno meaning in temporal congruence except that certain assumptions make\nthe laws of motion true. Such a statement is historically false. King\nAlfred the Great was ignorant of the laws of motion, but knew very well\nwhat he meant by the measurement of time, and achieved his purpose by\nmeans of burning candles. Also no one in past ages justified the use of\nsand in hour-glasses by saying that some centuries later interesting\nlaws of motion would be discovered which would give a meaning to the\nstatement that the sand was emptied from the bulbs in equal times.\nUniformity in change is directly perceived, and it follows that mankind\nperceives in nature factors from which a theory of temporal congruence\ncan be formed. The prevalent theory entirely fails to produce such\nfactors.\n\nThe mention of the laws of motion raises another point where the\nprevalent theory has nothing to say and the new theory gives a complete\nexplanation. It is well known that the laws of motion are not valid for\nany axes of reference which you may choose to take fixed in any rigid\nbody. You must choose a body which is not rotating and has no\nacceleration. For example they do not really apply to axes fixed in the\nearth because of the diurnal rotation of that body. The law which fails\nwhen you assume the wrong axes as at rest is the third law, that action\nand reaction are equal and opposite. With the wrong axes uncompensated\ncentrifugal forces and uncompensated composite centrifugal forces\nappear, due to rotation. The influence of these forces can be\ndemonstrated by many facts on the earth's surface, Foucault's pendulum,\nthe shape of the earth, the fixed directions of the rotations of\ncyclones and anticyclones. It is difficult to take seriously the\nsuggestion that these domestic phenomena on the earth are due to the\ninfluence of the fixed stars. I cannot persuade myself to believe that a\nlittle star in its twinkling turned round Foucault's pendulum in the\nParis Exhibition of 1861. Of course anything is believable when a\ndefinite physical connexion has been demonstrated, for example the\ninfluence of sunspots. Here all demonstration is lacking in the form of\nany coherent theory. According to the theory of these lectures the axes\nto which motion is to be referred are axes at rest in the space of some\ntime-system. For example, consider the space of a time-system {alpha}.\nThere are sets of axes at rest in the space of {alpha}. These are\nsuitable dynamical axes. Also a set of axes in this space which is\nmoving with uniform velocity without rotation is another suitable set.\nAll the moving points fixed in these moving axes are really tracing out\nparallel lines with one uniform velocity. In other words they are the\nreflections in the space of {alpha} of a set of fixed axes in the space\nof some other time-system {beta}. Accordingly the group of dynamical\naxes required for Newton's Laws of Motion is the outcome of the\nnecessity of referring motion to a body at rest in the space of some one\ntime-system in order to obtain a coherent account of physical\nproperties. If we do not do so the meaning of the motion of one portion\nof our physical configuration is different from the meaning of the\nmotion of another portion of the same configuration. Thus the meaning of\nmotion being what it is, in order to describe the motion of any system\nof objects without changing the meaning of your terms as you proceed\nwith your description, you are bound to take one of these sets of axes\nas axes of reference; though you may choose their reflections into the\nspace of any time-system which you wish to adopt. A definite physical\nreason is thereby assigned for the peculiar property of the dynamical\ngroup of axes.\n\nOn the orthodox theory the position of the equations of motion is most\nambiguous. The space to which they refer is completely undetermined and\nso is the measurement of the lapse of time. Science is simply setting\nout on a fishing expedition to see whether it cannot find some procedure\nwhich it can call the measurement of space and some procedure which it\ncan call the measurement of time, and something which it can call a\nsystem of forces, and something which it can call masses, so that these\nformulae may be satisfied. The only reason--on this theory--why anyone\nshould want to satisfy these formulae is a sentimental regard for\nGalileo, Newton, Euler and Lagrange. The theory, so far from founding\nscience on a sound observational basis, forces everything to conform to\na mere mathematical preference for certain simple formulae.\n\nI do not for a moment believe that this is a true account of the real\nstatus of the Laws of Motion. These equations want some slight\nadjustment for the new formulae of relativity. But with these\nadjustments, imperceptible in ordinary use, the laws deal with\nfundamental physical quantities which we know very well and wish to\ncorrelate.\n\nThe measurement of time was known to all civilised nations long before\nthe laws were thought of. It is this time as thus measured that the laws\nare concerned with. Also they deal with the space of our daily life.\nWhen we approach to an accuracy of measurement beyond that of\nobservation, adjustment is allowable. But within the limits of\nobservation we know what we mean when we speak of measurements of space\nand measurements of time and uniformity of change. It is for science to\ngive an intellectual account of what is so evident in sense-awareness.\nIt is to me thoroughly incredible that the ultimate fact beyond which\nthere is no deeper explanation is that mankind has really been swayed by\nan unconscious desire to satisfy the mathematical formulae which we call\nthe Laws of Motion, formulae completely unknown till the seventeenth\ncentury of our epoch.\n\nThe correlation of the facts of sense-experience effected by the\nalternative account of nature extends beyond the physical properties of\nmotion and the properties of congruence. It gives an account of the\nmeaning of the geometrical entities such as points, straight lines, and\nvolumes, and connects the kindred ideas of extension in time and\nextension in space. The theory satisfies the true purpose of an\nintellectual explanation in the sphere of natural philosophy. This\npurpose is to exhibit the interconnexions of nature, and to show that\none set of ingredients in nature requires for the exhibition of its\ncharacter the presence of the other sets of ingredients.\n\nThe false idea which we have to get rid of is that of nature as a mere\naggregate of independent entities, each capable of isolation. According\nto this conception these entities, whose characters are capable of\nisolated definition, come together and by their accidental relations\nform the system of nature. This system is thus thoroughly accidental;\nand, even if it be subject to a mechanical fate, it is only accidentally\nso subject.\n\nWith this theory space might be without time, and time might be without\nspace. The theory admittedly breaks down when we come to the relations\nof matter and space. The relational theory of space is an admission that\nwe cannot know space without matter or matter without space. But the\nseclusion of both from time is still jealously guarded. The relations\nbetween portions of matter in space are accidental facts owing to the\nabsence of any coherent account of how space springs from matter or how\nmatter springs from space. Also what we really observe in nature, its\ncolours and its sounds and its touches are secondary qualities; in other\nwords, they are not in nature at all but are accidental products of the\nrelations between nature and mind.\n\nThe explanation of nature which I urge as an alternative ideal to this\naccidental view of nature, is that nothing in nature could be what it is\nexcept as an ingredient in nature as it is. The whole which is present\nfor discrimination is posited in sense-awareness as necessary for the\ndiscriminated parts. An isolated event is not an event, because every\nevent is a factor in a larger whole and is significant of that whole.\nThere can be no time apart from space; and no space apart from time; and\nno space and no time apart from the passage of the events of nature. The\nisolation of an entity in thought, when we think of it as a bare 'it,'\nhas no counterpart in any corresponding isolation in nature. Such\nisolation is merely part of the procedure of intellectual knowledge.\n\nThe laws of nature are the outcome of the characters of the entities\nwhich we find in nature. The entities being what they are, the laws must\nbe what they are; and conversely the entities follow from the laws. We\nare a long way from the attainment of such an ideal; but it remains as\nthe abiding goal of theoretical science.\n\n\n\n\nCHAPTER VII\n\nOBJECTS\n\n\nThe ensuing lecture is concerned with the theory of objects. Objects are\nelements in nature which do not pass. The awareness of an object as some\nfactor not sharing in the passage of nature is what I call\n'recognition.' It is impossible to recognise an event, because an event\nis essentially distinct from every other event. Recognition is an\nawareness of sameness. But to call recognition an awareness of sameness\nimplies an intellectual act of comparison accompanied with judgment. I\nuse recognition for the non-intellectual relation of sense-awareness\nwhich connects the mind with a factor of nature without passage. On the\nintellectual side of the mind's experience there are comparisons of\nthings recognised and consequent judgments of sameness or diversity.\nProbably 'sense-recognition' would be a better term for what I mean by\n'recognition.' I have chosen the simpler term because I think that I\nshall be able to avoid the use of 'recognition' in any other meaning\nthan that of 'sense-recognition.' I am quite willing to believe that\nrecognition, in my sense of the term, is merely an ideal limit, and that\nthere is in fact no recognition without intellectual accompaniments of\ncomparison and judgment. But recognition is that relation of the mind to\nnature which provides the material for the intellectual activity.\n\nAn object is an ingredient in the character of some event. In fact the\ncharacter of an event is nothing but the objects which are ingredient in\nit and the ways in which those objects make their ingression into the\nevent. Thus the theory of objects is the theory of the comparison of\nevents. Events are only comparable because they body forth permanences.\nWe are comparing objects in events whenever we can say, 'There it is\nagain.' Objects are the elements in nature which can 'be again.'\n\nSometimes permanences can be proved to exist which evade recognition in\nthe sense in which I am using that term. The permanences which evade\nrecognition appear to us as abstract properties either of events or of\nobjects. All the same they are there for recognition although\nundiscriminated in our sense-awareness. The demarcation of events, the\nsplitting of nature up into parts is effected by the objects which we\nrecognise as their ingredients. The discrimination of nature is the\nrecognition of objects amid passing events. It is a compound of the\nawareness of the passage of nature, of the consequent partition of\nnature, and of the definition of certain parts of nature by the modes of\nthe ingression of objects into them.\n\nYou may have noticed that I am using the term 'ingression' to denote the\ngeneral relation of objects to events. The ingression of an object into\nan event is the way the character of the event shapes itself in virtue\nof the being of the object. Namely the event is what it is, because the\nobject is what it is; and when I am thinking of this modification of the\nevent by the object, I call the relation between the two 'the ingression\nof the object into the event.' It is equally true to say that objects\nare what they are because events are what they are. Nature is such that\nthere can be no events and no objects without the ingression of objects\ninto events. Although there are events such that the ingredient objects\nevade our recognition. These are the events in empty space. Such events\nare only analysed for us by the intellectual probing of science.\n\nIngression is a relation which has various modes. There are obviously\nvery various kinds of objects; and no one kind of object can have the\nsame sort of relations to events as objects of another kind can have. We\nshall have to analyse out some of the different modes of ingression\nwhich different kinds of objects have into events.\n\nBut even if we stick to one and the same kind of objects, an object of\nthat kind has different modes of ingression into different events.\nScience and philosophy have been apt to entangle themselves in a\nsimple-minded theory that an object is at one place at any definite\ntime, and is in no sense anywhere else. This is in fact the attitude of\ncommon sense thought, though it is not the attitude of language which is\nna\u00efvely expressing the facts of experience. Every other sentence in a\nwork of literature which is endeavouring truly to interpret the facts of\nexperience expresses differences in surrounding events due to the\npresence of some object. An object is ingredient throughout its\nneighbourhood, and its neighbourhood is indefinite. Also the\nmodification of events by ingression is susceptible of quantitative\ndifferences. Finally therefore we are driven to admit that each object\nis in some sense ingredient throughout nature; though its ingression may\nbe quantitatively irrelevant in the expression of our individual\nexperiences.\n\nThis admission is not new either in philosophy or science. It is\nobviously a necessary axiom for those philosophers who insist that\nreality is a system. In these lectures we are keeping off the profound\nand vexed question as to what we mean by 'reality.' I am maintaining the\nhumbler thesis that nature is a system. But I suppose that in this case\nthe less follows from the greater, and that I may claim the support of\nthese philosophers. The same doctrine is essentially interwoven in all\nmodern physical speculation. As long ago as 1847 Faraday in a paper in\nthe _Philosophical Magazine_ remarked that his theory of tubes of force\nimplies that in a sense an electric charge is everywhere. The\nmodification of the electromagnetic field at every point of space at\neach instant owing to the past history of each electron is another way\nof stating the same fact. We can however illustrate the doctrine by the\nmore familiar facts of life without recourse to the abstruse\nspeculations of theoretical physics.\n\nThe waves as they roll on to the Cornish coast tell of a gale in\nmid-Atlantic; and our dinner witnesses to the ingression of the cook\ninto the dining room. It is evident that the ingression of objects into\nevents includes the theory of causation. I prefer to neglect this aspect\nof ingression, because causation raises the memory of discussions based\nupon theories of nature which are alien to my own. Also I think that\nsome new light may be thrown on the subject by viewing it in this fresh\naspect.\n\nThe examples which I have given of the ingression of objects into events\nremind us that ingression takes a peculiar form in the case of some\nevents; in a sense, it is a more concentrated form. For example, the\nelectron has a certain position in space and a certain shape. Perhaps it\nis an extremely small sphere in a certain test-tube. The storm is a\ngale situated in mid-Atlantic with a certain latitude and longitude, and\nthe cook is in the kitchen. I will call this special form of ingression\nthe 'relation of situation'; also, by a double use of the word\n'situation,' I will call the event in which an object is situated 'the\nsituation of the object.' Thus a situation is an event which is a\nrelatum in the relation of situation. Now our first impression is that\nat last we have come to the simple plain fact of where the object really\nis; and that the vaguer relation which I call ingression should not be\nmuddled up with the relation of situation, as if including it as a\nparticular case. It seems so obvious that any object is in such and such\na position, and that it is influencing other events in a totally\ndifferent sense. Namely, in a sense an object is the character of the\nevent which is its situation, but it only influences the character of\nother events. Accordingly the relations of situation and influencing are\nnot generally the same sort of relation, and should not be subsumed\nunder the same term 'ingression.' I believe that this notion is a\nmistake, and that it is impossible to draw a clear distinction between\nthe two relations.\n\nFor example, Where was your toothache? You went to a dentist and pointed\nout the tooth to him. He pronounced it perfectly sound, and cured you by\nstopping another tooth. Which tooth was the situation of the toothache?\nAgain, a man has an arm amputated, and experiences sensations in the\nhand which he has lost. The situation of the imaginary hand is in fact\nmerely thin air. You look into a mirror and see a fire. The flames that\nyou see are situated behind the mirror. Again at night you watch the\nsky; if some of the stars had vanished from existence hours ago, you\nwould not be any the wiser. Even the situations of the planets differ\nfrom those which science would assign to them.\n\nAnyhow you are tempted to exclaim, the cook is in the kitchen. If you\nmean her mind, I will not agree with you on the point; for I am only\ntalking of nature. Let us think only of her bodily presence. What do you\nmean by this notion? We confine ourselves to typical manifestations of\nit. You can see her, touch her, and hear her. But the examples which I\nhave given you show that the notions of the situations of what you see,\nwhat you touch, and what you hear are not so sharply separated out as to\ndefy further questioning. You cannot cling to the idea that we have two\nsets of experiences of nature, one of primary qualities which belong to\nthe objects perceived, and one of secondary qualities which are the\nproducts of our mental excitements. All we know of nature is in the same\nboat, to sink or swim together. The constructions of science are merely\nexpositions of the characters of things perceived. Accordingly to affirm\nthat the cook is a certain dance of molecules and electrons is merely to\naffirm that the things about her which are perceivable have certain\ncharacters. The situations of the perceived manifestations of her bodily\npresence have only a very general relation to the situations of the\nmolecules, to be determined by discussion of the circumstances of\nperception.\n\nIn discussing the relations of situation in particular and of ingression\nin general, the first requisite is to note that objects are of radically\ndifferent types. For each type 'situation' and 'ingression' have their\nown special meanings which are different from their meanings for other\ntypes, though connexions can be pointed out. It is necessary therefore\nin discussing them to determine what type of objects are under\nconsideration. There are, I think, an indefinite number of types of\nobjects. Happily we need not think of them all. The idea of situation\nhas its peculiar importance in reference to three types of objects which\nI call sense-objects, perceptual objects and scientific objects. The\nsuitability of these names for the three types is of minor importance,\nso long as I can succeed in explaining what I mean by them.\n\nThese three types form an ascending hierarchy, of which each member\npresupposes the type below. The base of the hierarchy is formed by the\nsense-objects. These objects do not presuppose any other type of\nobjects. A sense-object is a factor of nature posited by sense-awareness\nwhich (i), in that it is an object, does not share in the passage of\nnature and (ii) is not a relation between other factors of nature. It\nwill of course be a relatum in relations which also implicate other\nfactors of nature. But it is always a relatum and never the relation\nitself. Examples of sense-objects are a particular sort of colour, say\nCambridge blue, or a particular sort of sound, or a particular sort of\nsmell, or a particular sort of feeling. I am not talking of a particular\npatch of blue as seen during a particular second of time at a definite\ndate. Such a patch is an event where Cambridge blue is situated.\nSimilarly I am not talking of any particular concert-room as filled with\nthe note. I mean the note itself and not the patch of volume filled by\nthe sound for a tenth of a second. It is natural for us to think of the\nnote in itself, but in the case of colour we are apt to think of it\nmerely as a property of the patch. No one thinks of the note as a\nproperty of the concert-room. We see the blue and we hear the note. Both\nthe blue and the note are immediately posited by the discrimination of\nsense-awareness which relates the mind to nature. The blue is posited as\nin nature related to other factors in nature. In particular it is\nposited as in the relation of being situated in the event which is its\nsituation.\n\nThe difficulties which cluster around the relation of situation arise\nfrom the obstinate refusal of philosophers to take seriously the\nultimate fact of multiple relations. By a multiple relation I mean a\nrelation which in any concrete instance of its occurrence necessarily\ninvolves more than two relata. For example, when John likes Thomas there\nare only two relata, John and Thomas. But when John gives that book to\nThomas there are three relata, John, that book, and Thomas.\n\nSome schools of philosophy, under the influence of the Aristotelian\nlogic and the Aristotelian philosophy, endeavour to get on without\nadmitting any relations at all except that of substance and attribute.\nNamely all apparent relations are to be resolvable into the concurrent\nexistence of substances with contrasted attributes. It is fairly obvious\nthat the Leibnizian monadology is the necessary outcome of any such\nphilosophy. If you dislike pluralism, there will be only one monad.\n\nOther schools of philosophy admit relations but obstinately refuse to\ncontemplate relations with more than two relata. I do not think that\nthis limitation is based on any set purpose or theory. It merely arises\nfrom the fact that more complicated relations are a bother to people\nwithout adequate mathematical training, when they are admitted into the\nreasoning.\n\nI must repeat that we have nothing to do in these lectures with the\nultimate character of reality. It is quite possible that in the true\nphilosophy of reality there are only individual substances with\nattributes, or that there are only relations with pairs of relata. I do\nnot believe that such is the case; but I am not concerned to argue about\nit now. Our theme is Nature. So long as we confine ourselves to the\nfactors posited in the sense-awareness of nature, it seems to me that\nthere certainly are instances of multiple relations between these\nfactors, and that the relation of situation for sense-objects is one\nexample of such multiple relations.\n\nConsider a blue coat, a flannel coat of Cambridge blue belonging to some\nathlete. The coat itself is a perceptual object and its situation is not\nwhat I am talking about. We are talking of someone's definite\nsense-awareness of Cambridge blue as situated in some event of nature.\nHe may be looking at the coat directly. He then sees Cambridge blue as\nsituated practically in the same event as the coat at that instant. It\nis true that the blue which he sees is due to light which left the coat\nsome inconceivably small fraction of a second before. This difference\nwould be important if he were looking at a star whose colour was\nCambridge blue. The star might have ceased to exist days ago, or even\nyears ago. The situation of the blue will not then be very intimately\nconnected with the situation (in another sense of 'situation') of any\nperceptual object. This disconnexion of the situation of the blue and\nthe situation of some associated perceptual object does not require a\nstar for its exemplification. Any looking glass will suffice. Look at\nthe coat through a looking glass. Then blue is seen as situated behind\nthe mirror. The event which is its situation depends upon the position\nof the observer.\n\nThe sense-awareness of the blue as situated in a certain event which I\ncall the situation, is thus exhibited as the sense-awareness of a\nrelation between the blue, the percipient event of the observer, the\nsituation, and intervening events. All nature is in fact required,\nthough only certain intervening events require their characters to be of\ncertain definite sorts. The ingression of blue into the events of nature\nis thus exhibited as systematically correlated. The awareness of the\nobserver depends on the position of the percipient event in this\nsystematic correlation. I will use the term 'ingression into nature' for\nthis systematic correlation of the blue with nature. Thus the ingression\nof blue into any definite event is a part statement of the fact of the\ningression of blue into nature.\n\nIn respect to the ingression of blue into nature events may be roughly\nput into four classes which overlap and are not very clearly separated.\nThese classes are (i) the percipient events, (ii) the situations, (iii)\nthe active conditioning events, (iv) the passive conditioning events. To\nunderstand this classification of events in the general fact of the\ningression of blue into nature, let us confine attention to one\nsituation for one percipient event and to the consequent _r\u00f4les_ of the\nconditioning events for the ingression as thus limited. The percipient\nevent is the relevant bodily state of the observer. The situation is\nwhere he sees the blue, say, behind the mirror. The active conditioning\nevents are the events whose characters are particularly relevant for the\nevent (which is the situation) to be the situation for that percipient\nevent, namely the coat, the mirror, and the state of the room as to\nlight and atmosphere. The passive conditioning events are the events of\nthe rest of nature.\n\nIn general the situation is an active conditioning event; namely the\ncoat itself, when there is no mirror or other such contrivance to\nproduce abnormal effects. But the example of the mirror shows us that\nthe situation may be one of the passive conditioning events. We are then\napt to say that our senses have been cheated, because we demand as a\nright that the situation should be an active condition in the\ningression.\n\nThis demand is not so baseless as it may seem when presented as I have\nput it. All we know of the characters of the events of nature is based\non the analysis of the relations of situations to percipient events. If\nsituations were not in general active conditions, this analysis would\ntell us nothing. Nature would be an unfathomable enigma to us and there\ncould be no science. Accordingly the incipient discontent when a\nsituation is found to be a passive condition is in a sense justifiable;\nbecause if that sort of thing went on too often, the _r\u00f4le_ of the\nintellect would be ended.\n\nFurthermore the mirror is itself the situation of other sense-objects\neither for the same observer with the same percipient event, or for\nother observers with other percipient events. Thus the fact that an\nevent is a situation in the ingression of one set of sense-objects into\nnature is presumptive evidence that that event is an active condition in\nthe ingression of other sense-objects into nature which may have other\nsituations.\n\nThis is a fundamental principle of science which it has derived from\ncommon sense.\n\nI now turn to perceptual objects. When we look at the coat, we do not in\ngeneral say, There is a patch of Cambridge blue; what naturally occurs\nto us is, There is a coat. Also the judgment that what we have seen is\na garment of man's attire is a detail. What we perceive is an object\nother than a mere sense-object. It is not a mere patch of colour, but\nsomething more; and it is that something more which we judge to be a\ncoat. I will use the word 'coat' as the name for that crude object which\nis more than a patch of colour, and without any allusion to the\njudgments as to its usefulness as an article of attire either in the\npast or the future. The coat which is perceived--in this sense of the\nword 'coat'--is what I call a perceptual object. We have to investigate\nthe general character of these perceptual objects.\n\nIt is a law of nature that in general the situation of a sense-object is\nnot only the situation of that sense-object for one definite percipient\nevent, but is the situation of a variety of sense-objects for a variety\nof percipient events. For example, for any one percipient event, the\nsituation of a sense-object of sight is apt also to be the situations of\nsense-objects of sight, of touch, of smell, and of sound. Furthermore\nthis concurrence in the situations of sense-objects has led to the\nbody--_i.e._ the percipient event--so adapting itself that the\nperception of one sense-object in a certain situation leads to a\nsubconscious sense-awareness of other sense-objects in the same\nsituation. This interplay is especially the case between touch and\nsight. There is a certain correlation between the ingressions of\nsense-objects of touch and sense-objects of sight into nature, and in a\nslighter degree between the ingressions of other pairs of sense-objects.\nI call this sort of correlation the 'conveyance' of one sense-object by\nanother. When you see the blue flannel coat you subconsciously feel\nyourself wearing it or otherwise touching it. If you are a smoker, you\nmay also subconsciously be aware of the faint aroma of tobacco. The\npeculiar fact, posited by this sense-awareness of the concurrence of\nsubconscious sense-objects along with one or more dominating\nsense-objects in the same situation, is the sense-awareness of the\nperceptual object. The perceptual object is not primarily the issue of a\njudgment. It is a factor of nature directly posited in sense-awareness.\nThe element of judgment comes in when we proceed to classify the\nparticular perceptual object. For example, we say, That is flannel, and\nwe think of the properties of flannel and the uses of athletes' coats.\nBut that all takes place after we have got hold of the perceptual\nobject. Anticipatory judgments affect the perceptual object perceived by\nfocussing and diverting attention.\n\nThe perceptual object is the outcome of the habit of experience.\nAnything which conflicts with this habit hinders the sense-awareness of\nsuch an object. A sense-object is not the product of the association of\nintellectual ideas; it is the product of the association of\nsense-objects in the same situation. This outcome is not intellectual;\nit is an object of peculiar type with its own particular ingression into\nnature.\n\nThere are two kinds of perceptual objects, namely, 'delusive perceptual\nobjects' and 'physical objects.' The situation of a delusive perceptual\nobject is a passive condition in the ingression of that object into\nnature. Also the event which is the situation will have the relation of\nsituation to the object only for one particular percipient event. For\nexample, an observer sees the image of the blue coat in a mirror. It is\na blue coat that he sees and not a mere patch of colour. This shows that\nthe active conditions for the conveyance of a group of subconscious\nsense-objects by a dominating sense-object are to be found in the\npercipient event. Namely we are to look for them in the investigations\nof medical psychologists. The ingression into nature of the delusive\nsense-object is conditioned by the adaptation of bodily events to the\nmore normal occurrence, which is the ingression of the physical object.\n\nA perceptual object is a physical object when (i) its situation is an\nactive conditioning event for the ingression of any of its component\nsense-objects, and (ii) the same event can be the situation of the\nperceptual object for an indefinite number of possible percipient\nevents. Physical objects are the ordinary objects which we perceive when\nour senses are not cheated, such as chairs, tables and trees. In a way\nphysical objects have more insistent perceptive power than\nsense-objects. Attention to the fact of their occurrence in nature is\nthe first condition for the survival of complex living organisms. The\nresult of this high perceptive power of physical objects is the\nscholastic philosophy of nature which looks on the sense-objects as mere\nattributes of the physical objects. This scholastic point of view is\ndirectly contradicted by the wealth of sense-objects which enter into\nour experience as situated in events without any connexion with physical\nobjects. For example, stray smells, sounds, colours and more subtle\nnameless sense-objects. There is no perception of physical objects\nwithout perception of sense-objects. But the converse does not hold:\nnamely, there is abundant perception of sense-objects unaccompanied by\nany perception of physical objects. This lack of reciprocity in the\nrelations between sense-objects and physical objects is fatal to the\nscholastic natural philosophy.\n\nThere is a great difference in the _r\u00f4les_ of the situations of\nsense-objects and physical objects. The situations of a physical object\nare conditioned by uniqueness and continuity. The uniqueness is an ideal\nlimit to which we approximate as we proceed in thought along an\nabstractive set of durations, considering smaller and smaller durations\nin the approach to the ideal limit of the moment of time. In other\nwords, when the duration is small enough, the situation of the physical\nobject within that duration is practically unique.\n\nThe identification of the same physical object as being situated in\ndistinct events in distinct durations is effected by the condition of\ncontinuity. This condition of continuity is the condition that a\ncontinuity of passage of events, each event being a situation of the\nobject in its corresponding duration, can be found from the earlier to\nthe later of the two given events. So far as the two events are\npractically adjacent in one specious present, this continuity of passage\nmay be directly perceived. Otherwise it is a matter of judgment and\ninference.\n\nThe situations of a sense-object are not conditioned by any such\nconditions either of uniqueness or of continuity. In any durations\nhowever small a sense-object may have any number of situations separated\nfrom each other. Thus two situations of a sense-object, either in the\nsame duration or in different durations, are not necessarily connected\nby any continuous passage of events which are also situations of that\nsense-object.\n\nThe characters of the conditioning events involved in the ingression of\na sense-object into nature can be largely expressed in terms of the\nphysical objects which are situated in those events. In one respect this\nis also a tautology. For the physical object is nothing else than the\nhabitual concurrence of a certain set of sense-objects in one situation.\nAccordingly when we know all about the physical object, we thereby know\nits component sense-objects. But a physical object is a condition for\nthe occurrence of sense-objects other than those which are its\ncomponents. For example, the atmosphere causes the events which are its\nsituations to be active conditioning events in the transmission of\nsound. A mirror which is itself a physical object is an active condition\nfor the situation of a patch of colour behind it, due to the reflection\nof light in it.\n\nThus the origin of scientific knowledge is the endeavour to express in\nterms of physical objects the various _r\u00f4les_ of events as active\nconditions in the ingression of sense-objects into nature. It is in the\nprogress of this investigation that scientific objects emerge. They\nembody those aspects of the character of the situations of the physical\nobjects which are most permanent and are expressible without reference\nto a multiple relation including a percipient event. Their relations to\neach other are also characterised by a certain simplicity and\nuniformity. Finally the characters of the observed physical objects and\nsense-objects can be expressed in terms of these scientific objects. In\nfact the whole point of the search for scientific objects is the\nendeavour to obtain this simple expression of the characters of events.\nThese scientific objects are not themselves merely formulae for\ncalculation; because formulae must refer to things in nature, and the\nscientific objects are the things in nature to which the formulae refer.\n\nA scientific object such as a definite electron is a systematic\ncorrelation of the characters of all events throughout all nature. It is\nan aspect of the systematic character of nature. The electron is not\nmerely where its charge is. The charge is the quantitative character of\ncertain events due to the ingression of the electron into nature. The\nelectron is its whole field of force. Namely the electron is the\nsystematic way in which all events are modified as the expression of its\ningression. The situation of an electron in any small duration may be\ndefined as that event which has the quantitative character which is the\ncharge of the electron. We may if we please term the mere charge the\nelectron. But then another name is required for the scientific object\nwhich is the full entity which concerns science, and which I have called\nthe electron.\n\nAccording to this conception of scientific objects, the rival theories\nof action at a distance and action by transmission through a medium are\nboth incomplete expressions of the true process of nature. The stream of\nevents which form the continuous series of situations of the electron is\nentirely self-determined, both as regards having the intrinsic character\nof being the series of situations of that electron and as regards the\ntime-systems with which its various members are cogredient, and the flux\nof their positions in their corresponding durations. This is the\nfoundation of the denial of action at a distance; namely the progress of\nthe stream of the situations of a scientific object can be determined by\nan analysis of the stream itself.\n\nOn the other hand the ingression of every electron into nature modifies\nto some extent the character of every event. Thus the character of the\nstream of events which we are considering bears marks of the existence\nof every other electron throughout the universe. If we like to think of\nthe electrons as being merely what I call their charges, then the\ncharges act at a distance. But this action consists in the modification\nof the situation of the other electron under consideration. This\nconception of a charge acting at a distance is a wholly artificial one.\nThe conception which most fully expresses the character of nature is\nthat of each event as modified by the ingression of each electron into\nnature. The ether is the expression of this systematic modification of\nevents throughout space and throughout time. The best expression of the\ncharacter of this modification is for physicists to find out. My theory\nhas nothing to do with that and is ready to accept any outcome of\nphysical research.\n\nThe connexion of objects with space requires elucidation. Objects are\nsituated in events. The relation of situation is a different relation\nfor each type of object, and in the case of sense-objects it cannot be\nexpressed as a two-termed relation. It would perhaps be better to use a\ndifferent word for these different types of the relation of situation.\nIt has not however been necessary to do so for our purposes in these\nlectures. It must be understood however that, when situation is spoken\nof, some one definite type is under discussion, and it may happen that\nthe argument may not apply to situation of another type. In all cases\nhowever I use situation to express a relation between objects and events\nand not between objects and abstractive elements. There is a derivative\nrelation between objects and spatial elements which I call the relation\nof location; and when this relation holds, I say that the object is\nlocated in the abstractive element. In this sense, an object may be\nlocated in a moment of time, in a volume of space, an area, a line, or a\npoint. There will be a peculiar type of location corresponding to each\ntype of situation; and location is in each case derivative from the\ncorresponding relation of situation in a way which I will proceed to\nexplain.\n\nAlso location in the timeless space of some time-system is a relation\nderivative from location in instantaneous spaces of the same\ntime-system. Accordingly location in an instantaneous space is the\nprimary idea which we have to explain. Great confusion has been\noccasioned in natural philosophy by the neglect to distinguish between\nthe different types of objects, the different types of situation, the\ndifferent types of location, and the difference between location and\nsituation. It is impossible to reason accurately in the vague concerning\nobjects and their positions without keeping these distinctions in view.\nAn object is located in an abstractive element, when an abstractive set\nbelonging to that element can be found such that each event belonging to\nthat set is a situation of the object. It will be remembered that an\nabstractive element is a certain group of abstractive sets, and that\neach abstractive set is a set of events. This definition defines the\nlocation of an element in any type of abstractive element. In this sense\nwe can talk of the existence of an object at an instant, meaning thereby\nits location in some definite moment. It may also be located in some\nspatial element of the instantaneous space of that moment.\n\nA quantity can be said to be located in an abstractive element when an\nabstractive set belonging to the element can be found such that the\nquantitative expressions of the corresponding characters of its events\nconverge to the measure of the given quantity as a limit when we pass\nalong the abstractive set towards its converging end.\n\nBy these definitions location in elements of instantaneous spaces is\ndefined. These elements occupy corresponding elements of timeless\nspaces. An object located in an element of an instantaneous space will\nalso be said to be located at that moment in the timeless element of the\ntimeless space which is occupied by that instantaneous element.\n\nIt is not every object which can be located in a moment. An object which\ncan be located in every moment of some duration will be called a\n'uniform' object throughout that duration. Ordinary physical objects\nappear to us to be uniform objects, and we habitually assume that\nscientific objects such as electrons are uniform. But some sense-objects\ncertainly are not uniform. A tune is an example of a non-uniform object.\nWe have perceived it as a whole in a certain duration; but the tune as a\ntune is not at any moment of that duration though one of the individual\nnotes may be located there.\n\nIt is possible therefore that for the existence of certain sorts of\nobjects, _e.g._ electrons, minimum quanta of time are requisite. Some\nsuch postulate is apparently indicated by the modern quantum theory and\nit is perfectly consistent with the doctrine of objects maintained in\nthese lectures.\n\nAlso the instance of the distinction between the electron as the mere\nquantitative electric charge of its situation and the electron as\nstanding for the ingression of an object throughout nature illustrates\nthe indefinite number of types of objects which exist in nature. We can\nintellectually distinguish even subtler and subtler types of objects.\nHere I reckon subtlety as meaning seclusion from the immediate\napprehension of sense-awareness. Evolution in the complexity of life\nmeans an increase in the types of objects directly sensed. Delicacy of\nsense-apprehension means perceptions of objects as distinct entities\nwhich are mere subtle ideas to cruder sensibilities. The phrasing of\nmusic is a mere abstract subtlety to the unmusical; it is a direct\nsense-apprehension to the initiated. For example, if we could imagine\nsome lowly type of organic being thinking and aware of our thoughts, it\nwould wonder at the abstract subtleties in which we indulge as we think\nof stones and bricks and drops of water and plants. It only knows of\nvague undifferentiated feelings in nature. It would consider us as given\nover to the play of excessively abstract intellects. But then if it\ncould think, it would anticipate; and if it anticipated, it would soon\nperceive for itself.\n\nIn these lectures we have been scrutinising the foundations of natural\nphilosophy. We are stopping at the very point where a boundless ocean of\nenquiries opens out for our questioning.\n\nI agree that the view of Nature which I have maintained in these\nlectures is not a simple one. Nature appears as a complex system whose\nfactors are dimly discerned by us. But, as I ask you, Is not this the\nvery truth? Should we not distrust the jaunty assurance with which every\nage prides itself that it at last has hit upon the ultimate concepts in\nwhich all that happens can be formulated? The aim of science is to seek\nthe simplest explanations of complex facts. We are apt to fall into the\nerror of thinking that the facts are simple because simplicity is the\ngoal of our quest. The guiding motto in the life of every natural\nphilosopher should be, Seek simplicity and distrust it.\n\n\n\n\nCHAPTER VIII\n\nSUMMARY\n\n\nThere is a general agreement that Einstein's investigations have one\nfundamental merit irrespective of any criticisms which we may feel\ninclined to pass on them. They have made us think. But when we have\nadmitted so far, we are most of us faced with a distressing perplexity.\nWhat is it that we ought to think about? The purport of my lecture this\nafternoon will be to meet this difficulty and, so far as I am able, to\nset in a clear light the changes in the background of our scientific\nthought which are necessitated by any acceptance, however qualified, of\nEinstein's main positions. I remember that I am lecturing to the members\nof a chemical society who are not for the most part versed in advanced\nmathematics. The first point that I would urge upon you is that what\nimmediately concerns you is not so much the detailed deductions of the\nnew theory as this general change in the background of scientific\nconceptions which will follow from its acceptance. Of course, the\ndetailed deductions are important, because unless our colleagues the\nastronomers and the physicists find these predictions to be verified we\ncan neglect the theory altogether. But we may now take it as granted\nthat in many striking particulars these deductions have been found to be\nin agreement with observation. Accordingly the theory has to be taken\nseriously and we are anxious to know what will be the consequences of\nits final acceptance. Furthermore during the last few weeks the\nscientific journals and the lay press have been filled with articles as\nto the nature of the crucial experiments which have been made and as to\nsome of the more striking expressions of the outcome of the new theory.\n'Space caught bending' appeared on the news-sheet of a well-known\nevening paper. This rendering is a terse but not inapt translation of\nEinstein's own way of interpreting his results. I should say at once\nthat I am a heretic as to this explanation and that I shall expound to\nyou another explanation based upon some work of my own, an explanation\nwhich seems to me to be more in accordance with our scientific ideas and\nwith the whole body of facts which have to be explained. We have to\nremember that a new theory must take account of the old well-attested\nfacts of science just as much as of the very latest experimental results\nwhich have led to its production.\n\nTo put ourselves in the position to assimilate and to criticise any\nchange in ultimate scientific conceptions we must begin at the\nbeginning. So you must bear with me if I commence by making some simple\nand obvious reflections. Let us consider three statements, (i)\n'Yesterday a man was run over on the Chelsea Embankment,' (ii)\n'Cleopatra's Needle is on the Charing Cross Embankment,' and (iii)\n'There are dark lines in the Solar Spectrum.' The first statement about\nthe accident to the man is about what we may term an 'occurrence,' a\n'happening,' or an 'event.' I will use the term 'event' because it is\nthe shortest. In order to specify an observed event, the place, the\ntime, and character of the event are necessary. In specifying the place\nand the time you are really stating the relation of the assigned event\nto the general structure of other observed events. For example, the man\nwas run over between your tea and your dinner and adjacently to a\npassing barge in the river and the traffic in the Strand. The point\nwhich I want to make is this: Nature is known to us in our experience as\na complex of passing events. In this complex we discern definite mutual\nrelations between component events, which we may call their relative\npositions, and these positions we express partly in terms of space and\npartly in terms of time. Also in addition to its mere relative position\nto other events, each particular event has its own peculiar character.\nIn other words, nature is a structure of events and each event has its\nposition in this structure and its own peculiar character or quality.\n\nLet us now examine the other two statements in the light of this general\nprinciple as to the meaning of nature. Take the second statement,\n'Cleopatra's Needle is on the Charing Cross Embankment.' At first sight\nwe should hardly call this an event. It seems to lack the element of\ntime or transitoriness. But does it? If an angel had made the remark\nsome hundreds of millions of years ago, the earth was not in existence,\ntwenty millions of years ago there was no Thames, eighty years ago there\nwas no Thames Embankment, and when I was a small boy Cleopatra's Needle\nwas not there. And now that it is there, we none of us expect it to be\neternal. The static timeless element in the relation of Cleopatra's\nNeedle to the Embankment is a pure illusion generated by the fact that\nfor purposes of daily intercourse its emphasis is needless. What it\ncomes to is this: Amidst the structure of events which form the medium\nwithin which the daily life of Londoners is passed we know how to\nidentify a certain stream of events which maintain permanence of\ncharacter, namely the character of being the situations of Cleopatra's\nNeedle. Day by day and hour by hour we can find a certain chunk in the\ntransitory life of nature and of that chunk we say, 'There is\nCleopatra's Needle.' If we define the Needle in a sufficiently abstract\nmanner we can say that it never changes. But a physicist who looks on\nthat part of the life of nature as a dance of electrons, will tell you\nthat daily it has lost some molecules and gained others, and even the\nplain man can see that it gets dirtier and is occasionally washed. Thus\nthe question of change in the Needle is a mere matter of definition. The\nmore abstract your definition, the more permanent the Needle. But\nwhether your Needle change or be permanent, all you mean by stating that\nit is situated on the Charing Cross Embankment, is that amid the\nstructure of events you know of a certain continuous limited stream of\nevents, such that any chunk of that stream, during any hour, or any day,\nor any second, has the character of being the situation of Cleopatra's\nNeedle.\n\nFinally, we come to the third statement, 'There are dark lines in the\nSolar Spectrum.' This is a law of nature. But what does that mean? It\nmeans merely this. If any event has the character of being an exhibition\nof the solar spectrum under certain assigned circumstances, it will also\nhave the character of exhibiting dark lines in that spectrum.\n\nThis long discussion brings us to the final conclusion that the concrete\nfacts of nature are events exhibiting a certain structure in their\nmutual relations and certain characters of their own. The aim of science\nis to express the relations between their characters in terms of the\nmutual structural relations between the events thus characterised. The\nmutual structural relations between events are both spatial and\ntemporal. If you think of them as merely spatial you are omitting the\ntemporal element, and if you think of them as merely temporal you are\nomitting the spatial element. Thus when you think of space alone, or of\ntime alone, you are dealing in abstractions, namely, you are leaving out\nan essential element in the life of nature as known to you in the\nexperience of your senses. Furthermore there are different ways of\nmaking these abstractions which we think of as space and as time; and\nunder some circumstances we adopt one way and under other circumstances\nwe adopt another way. Thus there is no paradox in holding that what we\nmean by space under one set of circumstances is not what we mean by\nspace under another set of circumstances. And equally what we mean by\ntime under one set of circumstances is not what we mean by time under\nanother set of circumstances. By saying that space and time are\nabstractions, I do not mean that they do not express for us real facts\nabout nature. What I mean is that there are no spatial facts or temporal\nfacts apart from physical nature, namely that space and time are merely\nways of expressing certain truths about the relations between events.\nAlso that under different circumstances there are different sets of\ntruths about the universe which are naturally presented to us as\nstatements about space. In such a case what a being under the one set of\ncircumstances means by space will be different from that meant by a\nbeing under the other set of circumstances. Accordingly when we are\ncomparing two observations made under different circumstances we have to\nask 'Do the two observers mean the same thing by space and the same\nthing by time?' The modern theory of relativity has arisen because\ncertain perplexities as to the concordance of certain delicate\nobservations such as the motion of the earth through the ether, the\nperihelion of mercury, and the positions of the stars in the\nneighbourhood of the sun, have been solved by reference to this purely\nrelative significance of space and time.\n\nI want now to recall your attention to Cleopatra's Needle, which I have\nnot yet done with. As you are walking along the Embankment you suddenly\nlook up and say, 'Hullo, there's the Needle.' In other words, you\nrecognise it. You cannot recognise an event; because when it is gone, it\nis gone. You may observe another event of analogous character, but the\nactual chunk of the life of nature is inseparable from its unique\noccurrence. But a character of an event can be recognised. We all know\nthat if we go to the Embankment near Charing Cross we shall observe an\nevent having the character which we recognise as Cleopatra's Needle.\nThings which we thus recognise I call objects. An object is situated in\nthose events or in that stream of events of which it expresses the\ncharacter. There are many sorts of objects. For example, the colour\ngreen is an object according to the above definition. It is the purpose\nof science to trace the laws which govern the appearance of objects in\nthe various events in which they are found to be situated. For this\npurpose we can mainly concentrate on two types of objects, which I will\ncall material physical objects and scientific objects. A material\nphysical object is an ordinary bit of matter, Cleopatra's Needle for\nexample. This is a much more complicated type of object than a mere\ncolour, such as the colour of the Needle. I call these simple objects,\nsuch as colours or sounds, sense-objects. An artist will train himself\nto attend more particularly to sense-objects where the ordinary person\nattends normally to material objects. Thus if you were walking with an\nartist, when you said 'There's Cleopatra's Needle,' perhaps he\nsimultaneously exclaimed 'There's a nice bit of colour.' Yet you were\nboth expressing your recognition of different component characters of\nthe same event. But in science we have found out that when we know all\nabout the adventures amid events of material physical objects and of\nscientific objects we have most of the relevant information which will\nenable us to predict the conditions under which we shall perceive\nsense-objects in specific situations. For example, when we know that\nthere is a blazing fire (_i.e._ material and scientific objects\nundergoing various exciting adventures amid events) and opposite to it a\nmirror (which is another material object) and the positions of a man's\nface and eyes gazing into the mirror, we know that he can perceive the\nredness of the flame situated in an event behind the mirror--thus, to a\nlarge extent, the appearance of sense-objects is conditioned by the\nadventures of material objects. The analysis of these adventures makes\nus aware of another character of events, namely their characters as\nfields of activity which determine the subsequent events to which they\nwill pass on the objects situated in them. We express these fields of\nactivity in terms of gravitational, electromagnetic, or chemical forces\nand attractions. But the exact expression of the nature of these fields\nof activity forces us intellectually to acknowledge a less obvious type\nof objects as situated in events. I mean molecules and electrons. These\nobjects are not recognised in isolation. We cannot well miss Cleopatra's\nNeedle, if we are in its neighbourhood; but no one has seen a single\nmolecule or a single electron, yet the characters of events are only\nexplicable to us by expressing them in terms of these scientific\nobjects. Undoubtedly molecules and electrons are abstractions. But then\nso is Cleopatra's Needle. The concrete facts are the events\nthemselves--I have already explained to you that to be an abstraction\ndoes not mean that an entity is nothing. It merely means that its\nexistence is only one factor of a more concrete element of nature. So an\nelectron is abstract because you cannot wipe out the whole structure of\nevents and yet retain the electron in existence. In the same way the\ngrin on the cat is abstract; and the molecule is really in the event in\nthe same sense as the grin is really on the cat's face. Now the more\nultimate sciences such as Chemistry or Physics cannot express their\nultimate laws in terms of such vague objects as the sun, the earth,\nCleopatra's Needle, or a human body. Such objects more properly belong\nto Astronomy, to Geology, to Engineering, to Archaeology, or to Biology.\nChemistry and Physics only deal with them as exhibiting statistical\ncomplexes of the effects of their more intimate laws. In a certain\nsense, they only enter into Physics and Chemistry as technological\napplications. The reason is that they are too vague. Where does\nCleopatra's Needle begin and where does it end? Is the soot part of it?\nIs it a different object when it sheds a molecule or when its surface\nenters into chemical combination with the acid of a London fog? The\ndefiniteness and permanence of the Needle is nothing to the possible\npermanent definiteness of a molecule as conceived by science, and the\npermanent definiteness of a molecule in its turn yields to that of an\nelectron. Thus science in its most ultimate formulation of law seeks\nobjects with the most permanent definite simplicity of character and\nexpresses its final laws in terms of them.\n\nAgain when we seek definitely to express the relations of events which\narise from their spatio-temporal structure, we approximate to simplicity\nby progressively diminishing the extent (both temporal and spatial) of\nthe events considered. For example, the event which is the life of the\nchunk of nature which is the Needle during one minute has to the life of\nnature within a passing barge during the same minute a very complex\nspatio-temporal relation. But suppose we progressively diminish the time\nconsidered to a second, to a hundredth of a second, to a thousandth of a\nsecond, and so on. As we pass along such a series we approximate to an\nideal simplicity of structural relations of the pairs of events\nsuccessively considered, which ideal we call the spatial relations of\nthe Needle to the barge at some instant. Even these relations are too\ncomplicated for us, and we consider smaller and smaller bits of the\nNeedle and of the barge. Thus we finally reach the ideal of an event so\nrestricted in its extension as to be without extension in space or\nextension in time. Such an event is a mere spatial point-flash of\ninstantaneous duration. I call such an ideal event an 'event-particle.'\nYou must not think of the world as ultimately built up of\nevent-particles. That is to put the cart before the horse. The world we\nknow is a continuous stream of occurrence which we can discriminate into\nfinite events forming by their overlappings and containings of each\nother and separations a spatio-temporal structure. We can express the\nproperties of this structure in terms of the ideal limits to routes of\napproximation, which I have termed event-particles. Accordingly\nevent-particles are abstractions in their relations to the more concrete\nevents. But then by this time you will have comprehended that you cannot\nanalyse concrete nature without abstracting. Also I repeat, the\nabstractions of science are entities which are truly in nature, though\nthey have no meaning in isolation from nature.\n\nThe character of the spatio-temporal structure of events can be fully\nexpressed in terms of relations between these more abstract\nevent-particles. The advantage of dealing with event-particles is that\nthough they are abstract and complex in respect to the finite events\nwhich we directly observe, they are simpler than finite events in\nrespect to their mutual relations. Accordingly they express for us the\ndemands of an ideal accuracy, and of an ideal simplicity in the\nexposition of relations. These event-particles are the ultimate elements\nof the four-dimensional space-time manifold which the theory of\nrelativity presupposes. You will have observed that each event-particle\nis as much an instant of time as it is a point of space. I have called\nit an instantaneous point-flash. Thus in the structure of this\nspace-time manifold space is not finally discriminated from time, and\nthe possibility remains open for diverse modes of discrimination\naccording to the diverse circumstances of observers. It is this\npossibility which makes the fundamental distinction between the new way\nof conceiving the universe and the old way. The secret of understanding\nrelativity is to understand this. It is of no use rushing in with\npicturesque paradoxes, such as 'Space caught bending,' if you have not\nmastered this fundamental conception which underlies the whole theory.\nWhen I say that it underlies the whole theory, I mean that in my opinion\nit ought to underlie it, though I may confess some doubts as to how far\nall expositions of the theory have really understood its implications\nand its premises.\n\nOur measurements when they are expressed in terms of an ideal accuracy\nare measurements which express properties of the space-time manifold.\nNow there are measurements of different sorts. You can measure lengths,\nor angles, or areas, or volumes, or times. There are also other sorts of\nmeasures such as measurements of intensity of illumination, but I will\ndisregard these for the moment and will confine attention to those\nmeasurements which particularly interest us as being measurements of\nspace or of time. It is easy to see that four such measurements of the\nproper characters are necessary to determine the position of an\nevent-particle in the space-time manifold in its relation to the rest of\nthe manifold. For example, in a rectangular field you start from one\ncorner at a given time, you measure a definite distance along one side,\nyou then strike out into the field at right angles, and then measure a\ndefinite distance parallel to the other pair of sides, you then rise\nvertically a definite height and take the time. At the point and at the\ntime which you thus reach there is occurring a definite instantaneous\npoint-flash of nature. In other words, your four measurements have\ndetermined a definite event-particle belonging to the four-dimension\nspace-time manifold. These measurements have appeared to be very simple\nto the land-surveyor and raise in his mind no philosophic difficulties.\nBut suppose there are beings on Mars sufficiently advanced in\nscientific invention to be able to watch in detail the operations of\nthis survey on earth. Suppose that they construe the operations of the\nEnglish land-surveyors in reference to the space natural to a being on\nMars, namely a Martio-centric space in which that planet is fixed. The\nearth is moving relatively to Mars and is rotating. To the beings on\nMars the operations, construed in this fashion, effect measurements of\nthe greatest complication. Furthermore, according to the relativistic\ndoctrine, the operation of time-measurement on earth will not correspond\nquite exactly to any time-measurement on Mars.\n\nI have discussed this example in order to make you realise that in\nthinking of the possibilities of measurement in the space-time manifold,\nwe must not confine ourselves merely to those minor variations which\nmight seem natural to human beings on the earth. Let us make therefore\nthe general statement that four measurements, respectively of\nindependent types (such as measurements of lengths in three directions\nand a time), can be found such that a definite event-particle is\ndetermined by them in its relations to other parts of the manifold.\n\nIf (p_1, p_2, p_3, p_4) be a set of measurements of this system, then\nthe event-particle which is thus determined will be said to have p_1,\np_2, p_3, p_4 as its co-ordinates in this system of measurement. Suppose\nthat we name it the p-system of measurement. Then in the same p-system\nby properly varying (p_1, p_2, p_3, p_4) every event-particle that has\nbeen, or will be, or instantaneously is now, can be indicated.\nFurthermore, according to any system of measurement that is natural to\nus, three of the co-ordinates will be measurements of space and one will\nbe a measurement of time. Let us always take the last co-ordinate to\nrepresent the time-measurement. Then we should naturally say that (p_1,\np_2, p_3) determined a point in space and that the event-particle\nhappened at that point at the time p_4. But we must not make the mistake\nof thinking that there is a space in addition to the space-time\nmanifold. That manifold is all that there is for the determination of\nthe meaning of space and time. We have got to determine the meaning of a\nspace-point in terms of the event-particles of the four-dimensional\nmanifold. There is only one way to do this. Note that if we vary the\ntime and take times with the same three space co-ordinates, then the\nevent-particles, thus indicated, are all at the same point. But seeing\nthat there is nothing else except the event-particles, this can only\nmean that the point (p_1, p_2, p_3) of the space in the p-system is\nmerely the collection of event-particles (p_1, p_2, p_3, [p_4]), where\np_4 is varied and (p_1, p_2, p_3) is kept fixed. It is rather\ndisconcerting to find that a point in space is not a simple entity; but\nit is a conclusion which follows immediately from the relative theory of\nspace.\n\nFurthermore the inhabitant of Mars determines event-particles by another\nsystem of measurements. Call his system the q-system. According to him\n(q_1, q_2, q_3, q_4) determines an event-particle, and (q_1, q_2, q_3)\ndetermines a point and q_4 a time. But the collection of event-particles\nwhich he thinks of as a point is entirely different from any such\ncollection which the man on earth thinks of as a point. Thus the q-space\nfor the man on Mars is quite different from the p-space for the\nland-surveyor on earth.\n\nSo far in speaking of space we have been talking of the timeless space\nof physical science, namely, of our concept of eternal space in which\nthe world adventures. But the space which we see as we look about is\ninstantaneous space. Thus if our natural perceptions are adjustable to\nthe p-system of measurements we see instantaneously all the\nevent-particles at some definite time p_4, and observe a succession\nof such spaces as time moves on. The timeless space is achieved by\nstringing together all these instantaneous spaces. The points of an\ninstantaneous space are event-particles, and the points of an eternal\nspace are strings of event-particles occurring in succession. But the\nman on Mars will never perceive the same instantaneous spaces as the man\non the earth. This system of instantaneous spaces will cut across the\nearth-man's system. For the earth-man there is one instantaneous space\nwhich is the instantaneous present, there are the past spaces and the\nfuture spaces. But the present space of the man on Mars cuts across the\npresent space of the man on the earth. So that of the event-particles\nwhich the earth-man thinks of as happening now in the present, the man\non Mars thinks that some are already past and are ancient history, that\nothers are in the future, and others are in the immediate present. This\nbreak-down in the neat conception of a past, a present, and a future is\na serious paradox. I call two event-particles which on some or other\nsystem of measurement are in the same instantaneous space 'co-present'\nevent-particles. Then it is possible that A and B may be co-present,\nand that A and C may be co-present, but that B and C may not be\nco-present. For example, at some inconceivable distance from us there\nare events co-present with us now and also co-present with the birth of\nQueen Victoria. If A and B are co-present there will be some systems\nin which A precedes B and some in which B precedes A. Also there\ncan be no velocity quick enough to carry a material particle from A to\nB or from B to A. These different measure-systems with their\ndivergences of time-reckoning are puzzling, and to some extent affront\nour common sense. It is not the usual way in which we think of the\nUniverse. We think of one necessary time-system and one necessary space.\nAccording to the new theory, there are an indefinite number of\ndiscordant time-series and an indefinite number of distinct spaces. Any\ncorrelated pair, a time-system and a space-system, will do in which to\nfit our description of the Universe. We find that under given conditions\nour measurements are necessarily made in some one pair which together\nform our natural measure-system. The difficulty as to discordant\ntime-systems is partly solved by distinguishing between what I call the\ncreative advance of nature, which is not properly serial at all, and any\none time series. We habitually muddle together this creative advance,\nwhich we experience and know as the perpetual transition of nature into\nnovelty, with the single-time series which we naturally employ for\nmeasurement. The various time-series each measure some aspect of the\ncreative advance, and the whole bundle of them express all the\nproperties of this advance which are measurable. The reason why we have\nnot previously noted this difference of time-series is the very small\ndifference of properties between any two such series. Any observable\nphenomena due to this cause depend on the square of the ratio of any\nvelocity entering into the observation to the velocity of light. Now\nlight takes about fifty minutes to get round the earth's orbit; and the\nearth takes rather more than 17,531\u00a0half-hours to do the same. Hence all\nthe effects due to this motion are of the order of the ratio of one to\nthe square of 10,000. Accordingly an earth-man and a sun-man have only\nneglected effects whose quantitative magnitudes all contain the factor\n1/10^8. Evidently such effects can only be noted by means of the most\nrefined observations. They have been observed however. Suppose we\ncompare two observations on the velocity of light made with the same\napparatus as we turn it through a right angle. The velocity of the earth\nrelatively to the sun is in one direction, the velocity of light\nrelatively to the ether should be the same in all directions. Hence if\nspace when we take the ether as at rest means the same thing as space\nwhen we take the earth as at rest, we ought to find that the velocity of\nlight relatively to the earth varies according to the direction from\nwhich it comes.\n\nThese observations on earth constitute the basic principle of the famous\nexperiments designed to detect the motion of the earth through the\nether. You all know that, quite unexpectedly, they gave a null result.\nThis is completely explained by the fact that, the space-system and the\ntime-system which we are using are in certain minute ways different from\nthe space and the time relatively to the sun or relatively to any other\nbody with respect to which it is moving.\n\nAll this discussion as to the nature of time and space has lifted above\nour horizon a great difficulty which affects the formulation of all the\nultimate laws of physics--for example, the laws of the electromagnetic\nfield, and the law of gravitation. Let us take the law of gravitation\nas an example. Its formulation is as follows: Two material bodies\nattract each other with a force proportional to the product of their\nmasses and inversely proportional to the square of their distances.\nIn this statement the bodies are supposed to be small enough to be\ntreated as material particles in relation to their distances; and we\nneed not bother further about that minor point. The difficulty to which\nI want to draw your attention is this: In the formulation of the law one\ndefinite time and one definite space are presupposed. The two masses are\nassumed to be in simultaneous positions.\n\nBut what is simultaneous in one time-system may not be simultaneous in\nanother time-system. So according to our new views the law is in this\nrespect not formulated so as to have any exact meaning. Furthermore an\nanalogous difficulty arises over the question of distance. The distance\nbetween two instantaneous positions, _i.e._ between two event-particles,\nis different in different space-systems. What space is to be chosen?\nThus again the law lacks precise formulation, if relativity is accepted.\nOur problem is to seek a fresh interpretation of the law of gravity in\nwhich these difficulties are evaded. In the first place we must avoid\nthe abstractions of space and time in the formulation of our fundamental\nideas and must recur to the ultimate facts of nature, namely to events.\nAlso in order to find the ideal simplicity of expressions of the\nrelations between events, we restrict ourselves to event-particles. Thus\nthe life of a material particle is its adventure amid a track of\nevent-particles strung out as a continuous series or path in the\nfour-dimensional space-time manifold. These event-particles are the\nvarious situations of the material particle. We usually express this\nfact by adopting our natural space-time system and by talking of the\npath in space of the material particle as it exists at successive\ninstants of time.\n\nWe have to ask ourselves what are the laws of nature which lead the\nmaterial particle to adopt just this path among event-particles and no\nother. Think of the path as a whole. What characteristic has that path\ngot which would not be shared by any other slightly varied path? We are\nasking for more than a law of gravity. We want laws of motion and a\ngeneral idea of the way to formulate the effects of physical forces.\n\nIn order to answer our question we put the idea of the attracting masses\nin the background and concentrate attention on the field of activity of\nthe events in the neighbourhood of the path. In so doing we are acting\nin conformity with the whole trend of scientific thought during the last\nhundred years, which has more and more concentrated attention on the\nfield of force as the immediate agent in directing motion, to the\nexclusion of the consideration of the immediate mutual influence between\ntwo distant bodies. We have got to find the way of expressing the field\nof activity of events in the neighbourhood of some definite\nevent-particle E of the four-dimensional manifold. I bring in a\nfundamental physical idea which I call the 'impetus' to express this\nphysical field. The event-particle E is related to any neighbouring\nevent-particle P by an element of impetus. The assemblage of all the\nelements of impetus relating E to the assemblage of event-particles in\nthe neighbourhood of E expresses the character of the field of\nactivity in the neighbourhood of E. Where I differ from Einstein is\nthat he conceives this quantity which I call the impetus as merely\nexpressing the characters of the space and time to be adopted and thus\nends by talking of the gravitational field expressing a curvature in the\nspace-time manifold. I cannot attach any clear conception to his\ninterpretation of space and time. My formulae differ slightly from his,\nthough they agree in those instances where his results have been\nverified. I need hardly say that in this particular of the formulation\nof the law of gravitation I have drawn on the general method of\nprocedure which constitutes his great discovery.\n\nEinstein showed how to express the characters of the assemblage of\nelements of impetus of the field surrounding an event-particle E in\nterms of ten quantities which I will call J_{11}, J_{12}\n(=J_{21}), J_{22}, J_{23}(=J_{32}), etc. It will be noted that\nthere are four spatio-temporal measurements relating E to its\nneighbour P, and that there are ten pairs of such measurements if we\nare allowed to take any one measurement twice over to make one such\npair. The ten J's depend merely on the position of E in the\nfour-dimensional manifold, and the element of impetus between E and\nP can be expressed in terms of the ten J's and the ten pairs of the\nfour spatio-temporal measurements relating E and P. The numerical\nvalues of the J's will depend on the system of measurement adopted,\nbut are so adjusted to each particular system that the same value is\nobtained for the element of impetus between E and P, whatever be the\nsystem of measurement adopted. This fact is expressed by saying that the\nten J's form a 'tensor.' It is not going too far to say that the\nannouncement that physicists would have in future to study the theory of\ntensors created a veritable panic among them when the verification of\nEinstein's predictions was first announced.\n\nThe ten J's at any event-particle E can be expressed in terms of two\nfunctions which I call the potential and the 'associate-potential' at\nE. The potential is practically what is meant by the ordinary\ngravitation potential, when we express ourselves in terms of the\nEuclidean space in reference to which the attracting mass is at rest.\nThe associate-potential is defined by the modification of substituting\nthe direct distance for the inverse distance in the definition of the\npotential, and its calculation can easily be made to depend on that of\nthe old-fashioned potential. Thus the calculation of the J's--the\ncoefficients of impetus, as I will call them--does not involve anything\nvery revolutionary in the mathematical knowledge of physicists. We now\nreturn to the path of the attracted particle. We add up all the elements\nof impetus in the whole path, and obtain thereby what I call the\n'integral impetus.' The characteristic of the actual path as compared\nwith neighbouring alternative paths is that in the actual paths the\nintegral impetus would neither gain nor lose, if the particle wobbled\nout of it into a small extremely near alternative path. Mathematicians\nwould express this by saying, that the integral impetus is stationary\nfor an infinitesimal displacement. In this statement of the law of\nmotion I have neglected the existence of other forces. But that would\nlead me too far afield.\n\nThe electromagnetic theory has to be modified to allow for the presence\nof a gravitational field. Thus Einstein's investigations lead to the\nfirst discovery of any relation between gravity and other physical\nphenomena. In the form in which I have put this modification, we deduce\nEinstein's fundamental principle, as to the motion of light along its\nrays, as a first approximation which is absolutely true for infinitely\nshort waves. Einstein's principle, thus partially verified, stated in my\nlanguage is that a ray of light always follows a path such that the\nintegral impetus along it is zero. This involves that every element of\nimpetus along it is zero.\n\nIn conclusion, I must apologise. In the first place I have considerably\ntoned down the various exciting peculiarities of the original theory and\nhave reduced it to a greater conformity with the older physics. I do not\nallow that physical phenomena are due to oddities of space. Also I have\nadded to the dullness of the lecture by my respect for the audience. You\nwould have enjoyed a more popular lecture with illustrations of\ndelightful paradoxes. But I know also that you are serious students who\nare here because you really want to know how the new theories may affect\nyour scientific researches.\n\n\n\n\nCHAPTER IX\n\nTHE ULTIMATE PHYSICAL CONCEPTS\n\n\nThe second chapter of this book lays down the first principle to be\nguarded in framing our physical concept. We must avoid vicious\nbifurcation. Nature is nothing else than the deliverance of\nsense-awareness. We have no principles whatever to tell us what could\nstimulate mind towards sense-awareness. Our sole task is to exhibit in\none system the characters and inter-relations of all that is observed.\nOur attitude towards nature is purely 'behaviouristic,' so far as\nconcerns the formulation of physical concepts.\n\nOur knowledge of nature is an experience of activity (or passage). The\nthings previously observed are active entities, the 'events.' They are\nchunks in the life of nature. These events have to each other relations\nwhich in our knowledge differentiate themselves into space-relations and\ntime-relations. But this differentiation between space and time, though\ninherent in nature, is comparatively superficial; and space and time are\neach partial expressions of one fundamental relation between events\nwhich is neither spatial nor temporal. This relation I call 'extension.'\nThe relation of 'extending over' is the relation of 'including,' either\nin a spatial or in a temporal sense, or in both. But the mere\n'inclusion' is more fundamental than either alternative and does not\nrequire any spatio-temporal differentiation. In respect to extension two\nevents are mutually related so that either (i) one includes the other,\nor (ii) one overlaps the other without complete inclusion, or (iii)\nthey are entirely separate. But great care is required in the\ndefinition of spatial and temporal elements from this basis in order to\navoid tacit limitations really depending on undefined relations and\nproperties.\n\nSuch fallacies can be avoided by taking account of two elements in our\nexperience, namely, (i) our observational 'present,' and (ii) our\n'percipient event.'\n\nOur observational 'present' is what I call a 'duration.' It is the whole\nof nature apprehended in our immediate observation. It has therefore the\nnature of an event, but possesses a peculiar completeness which marks\nout such durations as a special type of events inherent in nature. A\nduration is not instantaneous. It is all that there is of nature with\ncertain temporal limitations. In contradistinction to other events a\nduration will be called infinite and the other events are finite[10]. In\nour knowledge of a duration we distinguish (i) certain included events\nwhich are particularly discriminated as to their peculiar\nindividualities, and (ii) the remaining included events which are only\nknown as necessarily in being by reason of their relations to the\ndiscriminated events and to the whole duration. The duration as a whole\nis signified[11] by that quality of relatedness (in respect to\nextension) possessed by the part which is immediately under observation;\nnamely, by the fact that there is essentially a beyond to whatever is\nobserved. I mean by this that every event is known as being related to\nother events which it does not include. This fact, that every event is\nknown as possessing the quality of exclusion, shows that exclusion is as\npositive a relation as inclusion. There are of course no merely\nnegative relations in nature, and exclusion is not the mere negative of\ninclusion, though the two relations are contraries. Both relations are\nconcerned solely with events, and exclusion is capable of logical\ndefinition in terms of inclusion.\n\n[10] Cf. note on 'significance,' pp.\u00a0197, 198.\n\n[11] Cf. Ch.\u00a0III, pp.\u00a051 et\u00a0seq.\n\nPerhaps the most obvious exhibition of significance is to be found in\nour knowledge of the geometrical character of events inside an opaque\nmaterial object. For example we know that an opaque sphere has a centre.\nThis knowledge has nothing to do with the material; the sphere may be a\nsolid uniform billiard ball or a hollow lawn-tennis ball. Such knowledge\nis essentially the product of significance, since the general character\nof the external discriminated events has informed us that there are\nevents within the sphere and has also informed us of their geometrical\nstructure.\n\nSome criticisms on 'The Principles of Natural Knowledge' show that\ndifficulty has been found in apprehending durations as real\nstratifications of nature. I think that this hesitation arises from the\nunconscious influence of the vicious principle of bifurcation, so deeply\nembedded in modern philosophical thought. We observe nature as extended\nin an immediate present which is simultaneous but not instantaneous, and\ntherefore the whole which is immediately discerned or signified as an\ninter-related system forms a stratification of nature which is a\nphysical fact. This conclusion immediately follows unless we admit\nbifurcation in the form of the principle of psychic additions, here\nrejected.\n\nOur 'percipient event' is that event included in our observational\npresent which we distinguish as being in some peculiar way our\nstandpoint for perception. It is roughly speaking that event which is\nour bodily life within the present duration. The theory of perception\nas evolved by medical psychology is based on significance. The distant\nsituation of a perceived object is merely known to us as signified by\nour bodily state, _i.e._ by our percipient event. In fact perception\nrequires sense-awareness of the significations of our percipient event\ntogether with sense-awareness of a peculiar relation (situation) between\ncertain objects and the events thus signified. Our percipient event is\nsaved by being the whole of nature by this fact of its significations.\nThis is the meaning of calling the percipient event our standpoint for\nperception. The course of a ray of light is only derivatively connected\nwith perception. What we do perceive are objects as related to events\nsignified by the bodily states excited by the ray. These signified\nevents (as is the case of images seen behind a mirror) may have very\nlittle to do with the actual course of the ray. In the course of\nevolution those animals have survived whose sense-awareness is\nconcentrated on those significations of their bodily states which are on\nthe average important for their welfare. The whole world of events is\nsignified, but there are some which exact the death penalty for\ninattention.\n\nThe percipient event is always here and now in the associated present\nduration. It has, what may be called, an absolute position in that\nduration. Thus one definite duration is associated with a definite\npercipient event, and we are thus aware of a peculiar relation which\nfinite events can bear to durations. I call this relation 'cogredience.'\nThe notion of rest is derivative from that of cogredience, and the\nnotion of motion is derivative from that of inclusion within a duration\nwithout cogredience with it. In fact motion is a relation (of varying\ncharacter) between an observed event and an observed duration, and\ncogredience is the most simple character or subspecies of motion. To sum\nup, a duration and a percipient event are essentially involved in the\ngeneral character of each observation of nature, and the percipient\nevent is cogredient with the duration.\n\nOur knowledge of the peculiar characters of different events depends\nupon our power of comparison. I call the exercise of this factor in our\nknowledge 'recognition,' and the requisite sense-awareness of the\ncomparable characters I call 'sense-recognition.' Recognition and\nabstraction essentially involve each other. Each of them exhibits an\nentity for knowledge which is less than the concrete fact, but is a real\nfactor in that fact. The most concrete fact capable of separate\ndiscrimination is the event. We cannot abstract without recognition, and\nwe cannot recognise without abstraction. Perception involves\napprehension of the event and recognition of the factors of its\ncharacter.\n\nThe things recognised are what I call 'objects.' In this general sense\nof the term the relation of extension is itself an object. In practice\nhowever I restrict the term to those objects which can in some sense or\nother be said to have a situation in an event; namely, in the phrase\n'There it is again' I restrict the 'there' to be the indication of a\nspecial event which is the situation of the object. Even so, there are\ndifferent types of objects, and statements which are true of objects of\none type are not in general true of objects of other types. The objects\nwith which we are here concerned in the formulation of physical laws are\nmaterial objects, such as bits of matter, molecules and electrons. An\nobject of one of these types has relations to events other than those\nbelonging to the stream of its situations. The fact of its situations\nwithin this stream has impressed on all other events certain\nmodifications of their characters. In truth the object in its\ncompleteness may be conceived as a specific set of correlated\nmodifications of the characters of all events, with the property that\nthese modifications attain to a certain focal property for those events\nwhich belong to the stream of its situations. The total assemblage of\nthe modifications of the characters of events due to the existence of an\nobject in a stream of situations is what I call the 'physical field' due\nto the object. But the object cannot really be separated from its field.\nThe object is in fact nothing else than the systematically adjusted set\nof modifications of the field. The conventional limitation of the object\nto the focal stream of events in which it is said to be 'situated' is\nconvenient for some purposes, but it obscures the ultimate fact of\nnature. From this point of view the antithesis between action at a\ndistance and action by transmission is meaningless. The doctrine of this\nparagraph is nothing else than another way of expressing the\nunresolvable multiple relation of an object to events.\n\nA complete time-system is formed by any one family of parallel\ndurations. Two durations are parallel if either (i) one includes the\nother, or (ii) they overlap so as to include a third duration common to\nboth, or (iii) are entirely separate. The excluded case is that of two\ndurations overlapping so as to include in common an aggregate of finite\nevents but including in common no other complete duration. The\nrecognition of the fact of an indefinite number of families of parallel\ndurations is what differentiates the concept of nature here put forward\nfrom the older orthodox concept of the essentially unique time-systems.\nIts divergence from Einstein's concept of nature will be briefly\nindicated later.\n\nThe instantaneous spaces of a given time-system are the ideal\n(non-existent) durations of zero temporal thickness indicated by routes\nof approximation along series formed by durations of the associated\nfamily. Each such instantaneous space represents the ideal of nature at\nan instant and is also a moment of time. Each time-system thus possesses\nan aggregate of moments belonging to it alone. Each event-particle lies\nin one and only one moment of a given time-system. An event-particle has\nthree characters[12]: (i) its extrinsic character which is its character\nas a definite route of convergence among events, (ii) its intrinsic\ncharacter which is the peculiar quality of nature in its neighbourhood,\nnamely, the character of the physical field in the neighbourhood, and\n(iii) its position.\n\n[12] Cf. pp.\u00a082 et\u00a0seq.\n\nThe position of an event-particle arises from the aggregate of moments\n(no two of the same family) in which it lies. We fix our attention on\none of these moments which is approximated to by the short duration of\nour immediate experience, and we express position as the position in\nthis moment. But the event-particle receives its position in moment M\nin virtue of the whole aggregate of other moments M{'}, M{''}, etc.,\nin which it also lies. The differentiation of M into a geometry of\nevent-particles (instantaneous points) expresses the differentiation of\nM by its intersections with moments of alien time-systems. In this way\nplanes and straight lines and event-particles themselves find their\nbeing. Also the parallelism of planes and straight lines arises from the\nparallelism of the moments of one and the same time-system intersecting\nM. Similarly the order of parallel planes and of event-particles on\nstraight lines arises from the time-order of these intersecting moments.\nThe explanation is not given here[13]. It is sufficient now merely to\nmention the sources from which the whole of geometry receives its\nphysical explanation.\n\n[13] Cf. _Principles of Natural Knowledge_, and previous chapters of the\npresent work.\n\nThe correlation of the various momentary spaces of one time-system is\nachieved by the relation of cogredience. Evidently motion in an\ninstantaneous space is unmeaning. Motion expresses a comparison between\nposition in one instantaneous space with positions in other\ninstantaneous spaces of the same time-system. Cogredience yields the\nsimplest outcome of such comparison, namely, rest.\n\nMotion and rest are immediately observed facts. They are relative in the\nsense that they depend on the time-system which is fundamental for the\nobservation. A string of event-particles whose successive occupation\nmeans rest in the given time-system forms a timeless point in the\ntimeless space of that time-system. In this way each time-system\npossesses its own permanent timeless space peculiar to it alone, and\neach such space is composed of timeless points which belong to that\ntime-system and to no other. The paradoxes of relativity arise from\nneglecting the fact that different assumptions as to rest involve the\nexpression of the facts of physical science in terms of radically\ndifferent spaces and times, in which points and moments have different\nmeanings.\n\nThe source of order has already been indicated and that of congruence is\nnow found. It depends on motion. From cogredience, perpendicularity\narises; and from perpendicularity in conjunction with the reciprocal\nsymmetry between the relations of any two time-systems congruence both\nin time and space is completely defined (cf. _loc. cit._).\n\nThe resulting formulae are those for the electromagnetic theory of\nrelativity, or, as it is now termed, the restricted theory. But there is\nthis vital difference: the critical velocity c which occurs in these\nformulae has now no connexion whatever with light or with any other fact\nof the physical field (in distinction from the extensional structure of\nevents). It simply marks the fact that our congruence determination\nembraces both times and spaces in one universal system, and therefore if\ntwo arbitrary units are chosen, one for all spaces and one for all\ntimes, their ratio will be a velocity which is a fundamental property of\nnature expressing the fact that times and spaces are really comparable.\n\nThe physical properties of nature are expressed in terms of material\nobjects (electrons, etc.). The physical character of an event arises\nfrom the fact that it belongs to the field of the whole complex of such\nobjects. From another point of view we can say that these objects are\nnothing else than our way of expressing the mutual correlation of the\nphysical characters of events.\n\nThe spatio-temporal measurableness of nature arises from (i) the\nrelation of extension between events, and (ii) the stratified character\nof nature arising from each of the alternative time-systems, and (iii)\nrest and motion, as exhibited in the relations of finite events to\ntime-systems. None of these sources of measurement depend on the\nphysical characters of finite events as exhibited by the situated\nobjects. They are completely signified for events whose physical\ncharacters are unknown. Thus the spatio-temporal measurements are\nindependent of the objectival physical characters. Furthermore the\ncharacter of our knowledge of a whole duration, which is essentially\nderived from the significance of the part within the immediate field of\ndiscrimination, constructs it for us as a uniform whole independent, so\nfar as its extension is concerned, of the unobserved characters of\nremote events. Namely, there is a definite whole of nature,\nsimultaneously now present, whatever may be the character of its remote\nevents. This consideration reinforces the previous conclusion. This\nconclusion leads to the assertion of the essential uniformity of the\nmomentary spaces of the various time-systems, and thence to the\nuniformity of the timeless spaces of which there is one to each\ntime-system.\n\nThe analysis of the general character of observed nature set forth above\naffords explanations of various fundamental observational facts:\n({alpha}) It explains the differentiation of the one quality of\nextension into time and space. ({beta}) It gives a meaning to the\nobserved facts of geometrical and temporal position, of geometrical and\ntemporal order, and of geometrical straightness and planeness. ({gamma})\nIt selects one definite system of congruence embracing both space and\ntime, and thus explains the concordance as to measurement which is in\npractice attained. ({delta}) It explains (consistently with the theory\nof relativity) the observed phenomena of rotation, _e.g._ Foucault's\npendulum, the equatorial bulge of the earth, the fixed senses of\nrotation of cyclones and anticyclones, and the gyro-compass. It does\nthis by its admission of definite stratifications of nature which are\ndisclosed by the very character of our knowledge of it. ({epsilon}) Its\nexplanations of motion are more fundamental than those expressed in\n({delta}); for it explains what is meant by motion itself. The observed\nmotion of an extended object is the relation of its various situations\nto the stratification of nature expressed by the time-system fundamental\nto the observation. This motion expresses a real relation of the object\nto the rest of nature. The quantitative expression of this relation will\nvary according to the time-system selected for its expression.\n\nThis theory accords no peculiar character to light beyond that accorded\nto other physical phenomena such as sound. There is no ground for such a\ndifferentiation. Some objects we know by sight only, and other objects\nwe know by sound only, and other objects we observe neither by light nor\nby sound but by touch or smell or otherwise. The velocity of light\nvaries according to its medium and so does that of sound. Light moves in\ncurved paths under certain conditions and so does sound. Both light and\nsound are waves of disturbance in the physical characters of events; and\n(as has been stated above, p.\u00a0188) the actual course of the light is of\nno more importance for perception than is the actual course of the\nsound. To base the whole philosophy of nature upon light is a baseless\nassumption. The Michelson-Morley and analogous experiments show that\nwithin the limits of our inexactitude of observation the velocity of\nlight is an approximation to the critical velocity 'c' which expresses\nthe relation between our space and time units. It is provable that the\nassumption as to light by which these experiments and the influence of\nthe gravitational field on the light-rays are explained is deducible _as\nan approximation_ from the equations of the electromagnetic field. This\ncompletely disposes of any necessity for differentiating light from\nother physical phenomena as possessing any peculiar fundamental\ncharacter.\n\nIt is to be observed that the measurement of extended nature by means of\nextended objects is meaningless apart from some observed fact of\nsimultaneity inherent in nature and not merely a play of thought.\nOtherwise there is no meaning to the concept of one presentation of your\nextended measuring rod AB. Why not AB' where B' is the end B\nfive minutes later? Measurement presupposes for its possibility nature\nas a simultaneity, and an observed object present then and present now.\nIn other words, measurement of extended nature requires some inherent\ncharacter in nature affording a rule of presentation of events.\nFurthermore congruence cannot be defined by the permanence of the\nmeasuring rod. The permanence is itself meaningless apart from some\nimmediate judgment of self-congruence. Otherwise how is an elastic\nstring differentiated from a rigid measuring rod? Each remains the same\nself-identical object. Why is one a possible measuring rod and the other\nnot so? The meaning of congruence lies beyond the self-identity of the\nobject. In other words measurement presupposes the measurable, and the\ntheory of the measurable is the theory of congruence.\n\nFurthermore the admission of stratifications of nature bears on the\nformulation of the laws of nature. It has been laid down that these laws\nare to be expressed in differential equations which, as expressed in any\ngeneral system of measurement, should bear no reference to any other\nparticular measure-system. This requirement is purely arbitrary. For a\nmeasure-system measures something inherent in nature; otherwise it has\nno connexion with nature at all. And that something which is measured\nby a particular measure-system may have a special relation to the\nphenomenon whose law is being formulated. For example the gravitational\nfield due to a material object at rest in a certain time-system may be\nexpected to exhibit in its formulation particular reference to spatial\nand temporal quantities of that time-system. The field can of course be\nexpressed in any measure-systems, but the particular reference will\nremain as the simple physical explanation.\n\n\nNOTE: ON THE GREEK CONCEPT OF A POINT\n\nThe preceding pages had been passed for press before I had the pleasure\nof seeing Sir T.\u00a0L. Heath's _Euclid in Greek_[14]. In the original\nEuclid's first definition is\n\n    s\u00eameion estin, ou meros outhen.\n\nI have quoted it on p.\u00a086 in the expanded form taught to me in\nchildhood, 'without parts and without magnitude.' I should have\nconsulted Heath's English edition--a classic from the moment of its\nissue--before committing myself to a statement about Euclid. This is\nhowever a trivial correction not affecting sense and not worth a note. I\nwish here to draw attention to Heath's own note to this definition in\nhis _Euclid in Greek_. He summarises Greek thought on the nature of a\npoint, from the Pythagoreans, through Plato and Aristotle, to Euclid. My\nanalysis of the requisite character of a point on pp.\u00a089 and 90 is in\ncomplete agreement with the outcome of the Greek discussion.\n\n[14] Camb. Univ. Press, 1920.\n\n\nNOTE: ON SIGNIFICANCE AND INFINITE EVENTS\n\nThe theory of significance has been expanded and made more definite in\nthe present volume. It had already been introduced in the _Principles of\nNatural Knowledge_ (cf. subarticles\u00a03.3 to 3.8 and 16.1, 16.2, 19.4, and\narticles\u00a020, 21). In reading over the proofs of the present volume, I\ncome to the conclusion that in the light of this development my\nlimitation of infinite events to durations is untenable. This limitation\nis stated in article\u00a033 of the _Principles_ and at the beginning of\nChapter\u00a0IV (p.\u00a074) of this book. There is not only a significance of the\ndiscerned events embracing the whole present duration, but there is a\nsignificance of a cogredient event involving its extension through a\nwhole time-system backwards and forwards. In other words the essential\n'beyond' in nature is a definite beyond in time as well as in space [cf.\npp.\u00a053, 194]. This follows from my whole thesis as to the assimilation\nof time and space and their origin in extension. It also has the same\nbasis in the analysis of the character of our knowledge of nature. It\nfollows from this admission that it is possible to define point-tracks\n[_i.e._ the points of timeless spaces] as abstractive elements. This is\na great improvement as restoring the balance between moments and points.\nI still hold however to the statement in subarticle\u00a035.4 of the\n_Principles_ that the intersection of a pair of non-parallel durations\ndoes not present itself to us as one event. This correction does not\naffect any of the subsequent reasoning in the two books.\n\nI may take this opportunity of pointing out that the 'stationary events'\nof article\u00a057 of the _Principles_ are merely cogredient events got at\nfrom an abstract mathematical point of view.\n\n\n\n\nINDEX\n\n_In the case of terms of frequent occurrence, only those occurrences are\nindexed which are of peculiar importance for the elucidation of\nmeaning._\n\n  A [_or_ an], 11\n\n  Abraham, 105\n\n  Absolute position, 105, 106, 114, 188\n\n  Abstraction, 33, 37, 168, 171, 173;\n    extensive, 65, 79, 85\n\n  Abstractive element, 84;\n    set, 61, 79\n\n  Action at a distance, 159, 190\n\n  Action by transmission, 159, 190\n\n  Active conditions, 158\n\n  Activity, field of, 170, 181\n\n  Adjunction, 101\n\n  Aggregate, 23\n\n  Alexander, Prof., viii\n\n  Alexandria, 71\n\n  Alfred the Great, 137\n\n  Anticipation, 69\n\n  Anti-prime, 88\n\n  Apparent nature, 31, 39\n\n  Area, 99;\n    momental, 103;\n    vagrant, 103\n\n  Aristotelian logic, 150\n\n  Aristotle, 16, 17, 18, 24, 197\n\n  Associate-potential, 183\n\n  Atom, 17\n\n  Attribute, 21, 26, 150\n\n  Awareness, 3\n\n  Axiom, 36, 121\n\n  Axioms of congruence, 128 et\u00a0seqq.\n\n\n  Bacon, Francis, 78\n\n  Behaviouristic, 185\n\n  Bergson, 54\n\n  Berkeley, 28\n\n  Between, 64\n\n  Beyond, 186, 198\n\n  Bifurcation, vi, 30, 185, 187\n\n  Boundary, 100;\n    moment, 63;\n    particle, 100\n\n  Broad, C.\u00a0D., viii\n\n\n  Calculation, formula of, 45, 158\n\n  Cambridge, 97\n\n  Causal nature, 31, 39\n\n  Causation, 31, 146\n\n  Centrifugal force, 138\n\n  Change, uniformity of, 140\n\n  Character, extrinsic, 82, 89, 90, 113, 191;\n    intrinsic, 80, 82, 90, 113, 191\n\n  Charge, 160\n\n  Closure of nature, 4\n\n  Coefficient of drag, 133\n\n  Coefficients of impetus, 183\n\n  Cogredience, 110, 188\n\n  Coherence, 29\n\n  Comparison, 124, 125, 143, 189\n\n  Complex, 13\n\n  Conceptual nature, 45;\n    space, 96\n\n  Concrete facts, 167, 171, 189\n\n  Conditioning events, 152\n\n  Conditions, active, 158\n\n  Congruence, 65, 96, 118, 120, 127, 196\n\n  Continuity, 157;\n    Dedekindian, 102;\n    of events, 76;\n    of nature, 59, 76\n\n  Convention, 121\n\n  Convergence, 62, 79;\n    law of, 82\n\n  Conveyance, 154, 155\n\n  Co-present, 177\n\n  Covering, 83\n\n  Creative advance, 178\n\n  Critical velocity, 193, 195\n\n  Curvature of space-time, 182\n\n  Cyclone, 194\n\n\n  Dedekindian continuity, 102\n\n  Definite, 53, 194, 198\n\n  Delusions, 31, 38\n\n  Delusive perceptual object, 153\n\n  Demarcation of events, 144\n\n  Demonstrative phrase, 6\n\n  Descriptive phrase, 6, 10\n\n  Differential equations, 196\n\n  Discrimination, 14, 50, 144\n\n  Diversification of nature, 15\n\n  Duddington, Mrs, 47\n\n  Duration, 37, 53, 55, 186\n\n  Durations, families of, 59, 73, 190\n\n  Dynamical axes, 138\n\n\n  Einstein, vii, 102, 131, 164, 165, 181, 182, 183, 184, 191\n\n  Electromagnetic field, 179\n\n  Electron, 30, 146, 158, 171\n\n  Element, 17;\n    abstractive, 84\n\n  Elliptical phraseology, 7\n\n  Empty space, 145\n\n  Entity, 5, 13\n\n  Equal in abstractive force, 83\n\n  Error, 68\n\n  Ether, 18, 78, 160;\n    material, 78;\n    of events, 78\n\n  Euclid, 85, 94, 197\n\n  Euler, 140\n\n  Event, 15, 52, 75, 165;\n    percipient, 107, 152, 186\n\n  Event-particle, 86, 93, 94, 172, 191\n\n  Events, conditioning, 152;\n    continuity of, 76;\n    demarcation of, 144;\n    ether of, 78;\n    infinite, 197, 198;\n    limited, 74;\n    passage of, 34;\n    signified, 52;\n    stationary, 198;\n    stream of, 167;\n    structure of, 52, 166\n\n  Exclusion, 186\n\n  Explanation, 97, 141\n\n  Extended nature, 196\n\n  Extension, 22, 58, 75, 185\n\n  Extensive abstraction, 65, 79, 85\n\n  Extrinsic character, 82, 89, 90, 113, 191;\n    properties, 62\n\n\n  Fact, 12, 13\n\n  Factors, 12, 13, 15\n\n  Facts, concrete, 167, 171\n\n  Family of durations, 59, 63, 73;\n    of moments, 63\n\n  Faraday, 146\n\n  Field, gravitational, 197;\n    of activity, 170, 181;\n    physical, 190\n\n  Finite truths, 12\n\n  Fitzgerald, 133\n\n  Formula of calculation, 45, 158\n\n  Foucault, 138, 194\n\n  Four-dimensional manifold, 86\n\n  Fresnel, 133\n\n  Future, the, 72, 177\n\n\n  Galileo, 139\n\n  Geometrical order, 194\n\n  Geometry, 36;\n    metrical, 129\n\n  Gravitation, 179 et\u00a0seqq.\n\n  Gravitational field, 197\n\n  Greek philosophy, 16;\n    thought, 197\n\n  Gyro-compass, 194\n\n\n  Heath, Sir T.\u00a0L., 197\n\n  Here, 107\n\n\n  Idealists, 70\n\n  Immediacy, 52;\n    of perception, 72\n\n  Impetus, 181, 182;\n    coefficients of, 183;\n    integral, 183\n\n  Inclusion, 186\n\n  Individuality, 13\n\n  Infinite events, 197, 198\n\n  Inge, Dr, 48\n\n  Ingredient, 14\n\n  Ingression, 144, 145, 148, 152\n\n  Inherence, 83\n\n  Inside, 106\n\n  Instant, 33, 35, 57\n\n  Instantaneous plane, 91;\n    present, 72;\n    spaces, 86, 90, 177\n\n  Instantaneousness, 56, 57\n\n  Intersection, locus of, 90\n\n  Intrinsic character, 80, 82, 90, 113, 191;\n    properties, 62\n\n  Ionian thinkers, 19\n\n  Irrelevance, infinitude of, 12\n\n  Irrevocableness, 35, 37\n\n  It, 8\n\n\n  Julius Caesar, 36\n\n  Junction, 76, 101\n\n\n  Kinetic energy, 105;\n    symmetry, 129\n\n  Knowledge, 28, 32\n\n\n  Lagrange, 140\n\n  Larmor, 131\n\n  Law of convergence, 82\n\n  Laws of motion, 137, 139;\n    of nature, 196\n\n  Leibnizian monadology, 150\n\n  Level, 91, 92\n\n  Light, 195;\n    ray of, 188;\n    velocity of, 131\n\n  Limit, 57\n\n  Limited events, 74\n\n  Location, 160, 161\n\n  Locke, 27\n\n  Locus, 102;\n    of intersection, 90\n\n  London, 97\n\n  Lorentz, H.\u00a0A., 131, 133\n\n  Lossky, 47\n\n\n  Manifold, four-dimensional, 86;\n    space-time, 173\n\n  Material ether, 78;\n    object, 169\n\n  Materialism, 43, 70\n\n  Matrix, 116\n\n  Matter, 16, 17, 19, 20, 26\n\n  Maxwell, 131, 133\n\n  Measurableness, 196;\n    of nature, 193\n\n  Measurement, 96, 120, 174, 196;\n    of time, 65, 140\n\n  Measure-system, 196\n\n  Memory, 68\n\n  Metaphysics, 28, 32\n\n  Metrical geometry, 129\n\n  Michelson-Morley, 195\n\n  Milton, 35\n\n  Mind, 27, 28\n\n  Minkowski, viii, 131\n\n  Molecule, 32, 171\n\n  Moment, 57, 60, 88\n\n  Momental area, 103;\n    route, 103\n\n  Momentum, 105\n\n  Motion, 105, 114, 117, 127, 188, 192\n\n  Multiplicity, 22\n\n\n  Natural philosophy, 29, 30\n\n  Natural science, philosophy of, 46\n\n  Nature, 3;\n    apparent, 31, 39;\n    causal, 31, 39;\n    conceptual, 45;\n    continuity of, 59, 76;\n    discrimination of, 144;\n    extended, 196;\n    laws of, 196;\n    passage of, 54;\n    stratification of, 194, 196;\n    system of, 146\n\n  Newton, 27, 136, 139, 140\n\n\n  Object, 77, 125, 143, 169, 189;\n    delusive perceptual, 155;\n    material, 169;\n    perceptual, 153;\n    physical, 155, 157;\n    scientific, 158, 169;\n    uniform, 162\n\n  Occupation, 22, 34, 36, 100, 101\n\n  Order, source of, 192;\n    spatial, 95, 194;\n    temporal, 64, 95, 194\n\n  Organisation of thought, 79\n\n  Outside, 63, 100\n\n\n  Paradox, 192\n\n  Parallel, 63, 127;\n    durations, 190\n\n  Parallelism, 95, 191\n\n  Parallelogram, 127\n\n  Paris, 87, 138\n\n  Parliament, 120\n\n  Part, 14, 15, 58\n\n  Passage of events, 34;\n    of nature, 54\n\n  Past, the, 72, 177\n\n  Perception, 3\n\n  Perceptual objects, 149, 153\n\n  Percipience, 28\n\n  Percipient event, 107, 152, 186, 187\n\n  Period of time, 51\n\n  Permanence, 144\n\n  Perpendicularity, 117, 127, 193\n\n  Philosophy, 1;\n    natural, 29, 30;\n    of natural science, 46;\n    of the sciences, 2\n\n  Physical field, 190;\n    object, 155, 156, 157\n\n  Physics, speculative, 30\n\n  Place, 51\n\n  Plane, 191;\n    instantaneous, 91\n\n  Plato, 16, 17, 18, 24, 197\n\n  Poincar\u00e9, 121, 122, 123\n\n  Point, 35, 89, 91, 114, 173, 176\n\n  Point-flash, 172, 173\n\n  Point of space, 85\n\n  Point, timeless, 192\n\n  Point-track, 113, 198\n\n  Pompey, 36\n\n  Position, 89, 90, 92, 93, 99, 113, 191;\n    absolute, 105, 106, 114, 188\n\n  Potential, 183;\n    associate-, 183\n\n  Predicate, 18\n\n  Predication, 18\n\n  Present, the, 69, 72, 177;\n    instantaneous, 72;\n    observational, 186\n\n  Primary qualities, 27\n\n  Prime, 88\n\n  Process, 53, 54;\n    of nature, 54\n\n  Psychic additions, 29, 187\n\n  Punct, 92, 93, 94\n\n  Pythagoreans, 197\n\n\n  Quality, 27\n\n  Quantum of time, 162\n\n  Quantum theory, 162\n\n\n  Ray of light, 188\n\n  Reality, 30;\n    of durations, 55, 187\n\n  Recognition, 124, 143, 189\n\n  Rect, 91, 92\n\n  Recurrence, 35\n\n  Relative motion, 117;\n    velocity, 130\n\n  Relativity, 169;\n    restricted theory of, 193\n\n  Rest, 105, 114, 188, 192\n\n  Rotation, 138, 194\n\n  Route, 99;\n    momental, 103;\n    straight, 103\n\n  Russell, Bertrand, 11, 122, 123\n\n\n  Schelling, 47\n\n  Science, 2;\n    metaphysical, 32\n\n  Scientific objects, 149, 158, 169\n\n  Secondary qualities, 27\n\n  Self-congruence, 196\n\n  Self-containedness of nature, 4\n\n  Sense-awareness, 3, 67\n\n  Sense-object, 149, 170\n\n  Sense-perception, 3, 14\n\n  Sense-recognition, 143, 189\n\n  Series, temporal, 66, 70, 85, 178\n\n  Set, abstractive, 61, 79\n\n  Significance, 51, 186, 187, 188, 194, 197, 198\n\n  Signified events, 52\n\n  Simplicity, 163, 173\n\n  Simultaneity, 53, 56, 196\n\n  Situation, 15, 78, 147, 148, 152, 160, 189\n\n  Solid, 99, 101, 102;\n    vagrant, 101\n\n  Sound, 195\n\n  Space, 16, 17, 31, 33, 79;\n    empty, 145;\n    timeless, 86, 106, 114;\n    uniformity of, 194\n\n  Spaces, instantaneous, 86, 90\n\n  Space-system, 179\n\n  Space-time manifold, 173\n\n  Spatial-order, 95\n\n  Spatio-temporal structure, 173\n\n  Speculative demonstration, 6\n\n  Speculative physics, 30\n\n  Standpoint for perception, 107, 188\n\n  Station, 103, 104, 113\n\n  Stationary events, 198\n\n  Straight line, 91, 114, 191;\n    route, 103\n\n  Stratification of nature, 187, 194, 196\n\n  Stream of events, 167\n\n  Structure of events, 52, 166\n\n  Structure, spatio-temporal, 173\n\n  Subject, 18\n\n  Substance, 16, 18, 19, 150\n\n  Substratum, 16, 18, 21\n\n  Symmetry, 118, 126;\n    kinetic, 129\n\n  System of nature, 146\n\n  System, time-, 192\n\n\n  Tarner, Edward, v, 1\n\n  Temporal order, 64, 95, 194\n\n  Temporal series, 66, 70, 85\n\n  Tensor, 182\n\n  Terminus, 4\n\n  The, 11\n\n  Theory, quantum, 162\n\n  There, 110, 189\n\n  This, 11\n\n  Thought, 3, 14\n\n  Timaeus, the, 17, 20, 24\n\n  Time, 16, 17, 31, 33, 49, 79;\n    measurement of, 140;\n    quantum of, 162;\n    transcendence of, 39\n\n  Time-series, 178, also cf. Temporal series\n\n  Time-system, see Time-series, also 91, 97, 104, 179, 192\n\n  Timeless point, 192;\n    space, 86, 106, 114, 177\n\n  Totality, 89\n\n  Transcendence of time, 39\n\n  Transmission, 26, 28;\n    action by, 159, 190\n\n  Tubes of force, 146\n\n\n  Unexhaustiveness, 50\n\n  Uniform object, 162\n\n  Uniformity of change, 140;\n    of space, 194\n\n\n  Vagrant area, 103;\n    solid, 101\n\n  Veblen and Young, 36\n\n  Velocity, critical, 193, 195;\n    of light, 131, 195;\n    relative, 130\n\n  Volume, 92, 101\n\n\n  When, 107\n\n  Where, 107\n\n  Whole, 58\n\n  Within, 63\n\n\n  Young, Veblen and, 36","title":"The Concept of Nature: The Tarner Lectures Delivered in Trinity College, November 1919","tradition":"philosophy-ethics","translated_text":null,"word_count":59431}